Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based on RSM: A Case Study

*Aysun Sagbas*

## **Abstract**

In this book chapter a review and critical analysis on current research trends in wire electrical discharge machining (WEDM) and relation between different process parameters including pulse on time, pulse off time, servo voltage, peak current, dielectric flow rate, wire speed, wire tension on different process responses include material removal rate (MRR), surface roughness (Ra), sparking gap, wire lag and wire wear ration (WWR) and surface integrity factors was investigated. On the basis of critical evaluation of the available literature following conclusions are summarized. In addition, different modeling and optimization methods used in WEDM were discussed and a case study based on response surface method (RSM) including design of experiment (DoE) carried out to find optimal process parameters effect on surface roughness was conducted. In the final part of the present study was presented some recommendations about the trends for future WEDM researches.

**Keywords:** optimization, modeling, WEDM, RSM, DoE, surface quality

## **1. Introduction**

The aim of this book chapter is to present some knowledge about the contributions of various researchers on WEDM process and to conduct an optimization approach named response surface methodology to determine the optimal process parameters. In addition, this book chapter is concluded by highlighting the optimal ranges of parameters in WEDM process for various materials and indicating the future research directions which will provide a reference to machine tool operators and manufacturing industries depending upon their demands. Moreover, this paper reviews and examines the various notable works in the field of WEDM and emphasis is made on optimization and modeling of machining parameters. The chapter also explains various advantages and disadvantages of different modeling and optimization methods used, and presents with some recommendations about trends for future WEDM researchers.

WEDM has a key role in unconventional machining method since it facilitates production of certain materials such as zirconium, titanium and intricate shapes. Wire

EDM is a thermo- electrical process which material is eroded by a series of sparks between the work piece and the wire electrode. The part and wire are immersed in a dielectric fluid which also acts as a coolant [1]. In EDM process, wire movement is monitored quantitively to obtain three dimensional shape. EMD has been known for more than a half century and used to manufacture high accuracy of the workpiece in machining processes and metal, tool, die, etc. industries. The development of the WEDM process was the result of seeking a technique to machine the electrodes used in EDM. In the end of the 1970s, computer numerical control (CNC) system was integrated with WEDM process. This integration was brought about a major evolution of the machining process. Moreover, the broad capabilities of the WEDM process were extensively exploited for any through hole machining owing to the wire, which has to pass through the part to be machined. It is probably the most exciting and diversified machine tool adopted for this industry in the last 50 years, and has various beneficial to use. In this process, there is no contact between electrode and work piece. Hence, materials of any hardness can be cut as long as they can conduct electricity. In addition, the wire does not touch the workpiece. So, physical pressure imparted on the workpiece is not exist, and amount of clamping pressure required to hold the workpiece is very low [2, 3]. Schematic diagram of WEDM process is given in **Figure 1**.

Recently, WEDM process has been widely used in manufacturing industry such as metals, alloys, sintered materials, cemented carbides, ceramics and silicon because of making micro-parts. These different systems support WEDM process which has remained as a competitive and reduced cost machining option fulfilling the demanding machining part requirements imposed by the short product development cycles and the growing cost pressures [4]. One of the most widely and commonly used and popular non-traditional material removal procedure which is currently often applied to manufacture components with complex shapes having great accuracy and precision is WEDM. Although, Wire-EDM uses a wire which acts as an electrode which is continuously traveling and is generally made up of thin brass, tungsten or copper, and is having a small diameter of 0.05–0.3 mm. Wire motion is regulated numerically to accomplish converted 3-dimensional shape and high precision of workpiece [5, 6]. Basic uses of wire electrical discharge machining incorporate extrusion tools and die, fixtures and gauges, models, airship and medical parts, and fabrication of stamping,

**Figure 1.** *Schematic diagram of WEDM process.*

### *Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

grinding wheel form tools [7]. Moreover, WEDM has been replacing other traditional machining operations in many industries throughout the world namely drilling, milling, grinding, turning, taper turning, etc. The setting for the various process parameters required in WEDM process play crucial role in achieving optimal performance. The main goals of WEDM manufacturers and users are to achieve a better stability and higher productivity of the WEDM process. Wire electrical discharge machining manufacturers and users emphasize on achievement of higher machining productivity with a desired accuracy and surface finish.

Response Surface Methodology is an important technique to use in designing, formulating, developing, and analyzing for different scientific studies and various industrial products. It is well known optimization method involves mathematical and statistical techniques. In RSM approach the objective is to optimize the response that is influenced by several input variables. Moreover, it is effictive and useful in the improvement and development of existing studies and products. Also, it can be applied to solve the optimization problems in different industries and it is commonly used Biological and Clinical Science, Social Science, Food Science, and Physical and Engineering Sciences. In many different manufacturing industries, one of the important issues is whether the system includes a maximum or a minimum or a saddle point, which has a wide important in industry. Therefore, RSM has been increasingly used in different industries. In addition, in recent years more emphasis has been placed by the chemical and processing field for finding optimal regions where there is an improvement in response instead of finding the optimum response [8]. The first aim for response surface method is to find the optimum response effected various input variables. When there are constraints on the design data, then the experimental design has to meet requirements of the constraints. The second purpose is to evaluate how the response changes in a given direction by adjusting the input and output variables [9, 10]. In generally, conventional data processing methods are not appropriate for investigating the process and product parameters. Many researchers have investigated the suitability of different empirical models to predict the changes in the quality parameters during different drying processes. Based on the function fitting technique, a response surface model in high dimensional space was fitted to show the relation between experiment inputs and output with minimum process knowledge. So, it could be used as an different alternative for conventional models like numerical simulation during optimization with a reduced computational cost and time according to the other various optimization techniques. On the other hand, RSM-based models are only accurate for predicting the relationship between a limited number of input and output parameters. Box-Behnken and central composite design (CCD) commonly used in many research, both have its advantages [11–13].

In this study a predictive model (RS model) is developed and applied to optimize WEDM machining parameters using RSM approach. Experiments are carried out to test the the validity and accuracy of model and satisfactory results are obtained. The methodology described here is expected to be highly beneficial to manufacturing industries such as aerospace, chemistry, textile, automobile and tool making, etc. industries.

## **2. Literature review: process modeling and optimization**

Due to large number of process parameters and responses lots of researchers have attempted to improve the process capability. Some researchers have used different optimization techniques such as Taguchi technique, gray relational analysis (GRA), design of experiment, artificial neural network (ANN) modeling, desirability approach and evolutionary algorithm. Lots of authors tried to model this process using the Taguchi method and response surface methodology approach [5, 14–18] which utilized response surface methodology coupled with gray-Taguchi technique. Further, Lin [19] have combined Taguchi method with the GRA to optimize the micro milling EDM performance. Similarly, hybrid approach of Taguchi gray has been used by Rajyalakshmi and Ramaiah [20] for multiple performance optimization of WEDM machined Inconel 825. In contrast to WEDM performance evaluation, Sharma [2] have used one factor at a time approach to investigate the effect of various WEDM control parameters on performance characteristics. Except conventional techniques of optimization, some evolutionary algorithm has been in literature such as genetic algorithm (GA), artificial bee colony (ABC), particle swarm optimization (PSO), teaching learning-based optimization (TLBO) and differential evolution (DE). These algorithms provide a global optimum solution instead of local optimum solutions. The parametric settings named optimal solution is found out based on optimization techniques like VIKOR based Harmony search algorithm and desirability function approach to get perfect surface finish during electrical discharge coating and electrical discharge machining of AISI 1040 stainless steel and Nitinol respectively [5]. Further, statistical models have been developed by Kuppan et al. [21] to determine the relationship between EDM output responses and control parameters using response surface methodology. Similarly, Ramakrishnan and Karunamoorthy [22] have developed the mathematical model based on Box and Hunter central composite design to determine the effect of control parameters on EDM performance characteristics. Further, Ramakrishnan and Karunamoorthy [23] presented an Artificial Neural

#### **Figure 2.**

*Comparative study of published research work on WEDM [24].*

*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

Network model to predict the WEDM performance of Inconel 718 alloy. **Figure 2** shows a brief outline of past research works.

In cutting operation, WEDM primarily employed either for trim cut [25–27] or rough cut [28, 29]. To the best knowledge of authors, this technique can be successfully employed for machining of steel and steel alloys [30–33] aluminum and aluminum alloys, titanium and its alloys [27, 34] super alloys [35, 36] metal matrix composites [37, 38] green compact manufactured by powder metallurgy [39]. Investigations into the influences of machining input parameters on the performance of WEDM have been widely reported [25, 40–42]. Several attempts have been made to develop mathematical model of the WEDM process [39, 43–47]. In these works, productivity of the process and the surface roughness of the machined work piece are examined as measures of the process performance. Neural network models on material removal rate in EDM has been studied by Tsai and Wang [48] whereas Lee and Li [49] investigated on effects of process parameters in EDM using tungsten carbide as work material. Qu et al. [50] have, through examination of literature, concluded that research has not been directed towards EDM applications in the area of newly developed engineering materials and the boundaries that limit the material removal rate (MRR). Scott, Boyina et al. [43] used a factorial design method, to determine the optimal combination of control parameters in WEDM considering the measures of machining performance as metal removal rate and the surface finish. Tarng and Chung [51] carried out a neural network model to estimate cutting speed and surface finish using input parameters such as pulse duration, pulse interval, peak current, open, servo reference voltage, circuit voltage, electric capacitance and table speed. Trezise [52] presents that essential limits on machining accuracy are dimensional consistency of the wire and the positional accuracy of the work table. Sarkar et al. [25] studied the WEDM of titanium aluminide. They also attempted to develop an appropriate machining strategy for a maximum process yield criterion. A feed forward back propagation neural network was used to model the machining process. Ali [53] investigated on the effect and optimization of machining parameters on the surface roughness in the WEDM process of AlCu-TiC-Si P/M composite. The optimal machining parameters were obtained by using Taguchi experimental design method. The variation of MRR and surface roughness with machining parameters is mathematically modeled by using non-linear regression analysis method. Patil and Brahmankar [54] examined the effect of various input parameters such as pulse on time, pulse off time, ignition pulse current, wire speed, wire tension and flushing pressure on cutting speed and surface finish of Al/SiCp by using Taguchi methods. Shandilya et al. [38] concluded that to achieve higher value of the average cutting speed, lower value of voltage and higher value of pulse-off time should be used during WEDC of SiCp/6061 Al MMC. In the most recent work, They studied the effect of input process parameters on surface surface roughness during WEDM of SiCp/6061 Al MMC. There are some researches that used traditional approach for modeling WEDM like Tarng [51] which utilized feed forward neural network to model and simulated annealing (SA) algorithm is then applied to the neural network to solve the optimal cutting parameters problem. Other one of them is Lin et al. [19] which used Taguchi method with fuzzy logic for modeling and optimization. In addition, Huang [30] studied Wire-EDM based on Gray relational and statistical analyses. Furthermore Kuriakose et al. [55] applied data mining approach. Yuan et al. [56] used incorporating prior model into Gaussian processes regression for WEDM process modeling. Also Caydas, et al. [32] used neuro-fuzzy inference system (ANFIS) to model this process. Besides Cheng et al. [42] utilized a neural network integrated

simulated annealing approach for optimizing WEDM. Kapil K. at all [57] investigated the cutting rate and recast layer thickness while designing the servo feed, pulse ontime, servo voltage, and pulse off-time with the Box-Benkhen design of RSM. Kumar et all [45] the Box-Benkhen design of response surface methodology based and machine learning algorithm was applied for the WEDM process, to simultaneously optimize SR, MRR of CP-Ti G2 [58].

## **3. Case study**

In this study, desired surface roughness is obtained based on four input parameters by creating an experimental model of AISI 4030 steel and using response surface methodology. This study has shown that RSM model presented here has overcome WEDM complex that results in satisfactory surface quality characteristics. Each experimental test was conducted twice and averaged as Ra mean values to acquire database with high confidence. Furthermore, experiments were designed using the method that was introduced by Box and Hunter [59]. The experimental runs were performed as per the central composite design which is a type of response surface methodology designs. Response surface methodology has been used to plan and analyze the experiments. CCD was used in order to fit the second order response in surface as well as in optimization methods for finding relation between various individual input parameters and reactions. **Table 1** demonstrates coded value and actual values of individual parameters, and **Table 2** shows machining conditions in WEDM process.


#### **Table 1.**

*Experimental factors and factor levels.*


#### **Table 2.**

*Machining conditions in WEDM process.*

*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

**Figure 3.** *Cause and effect diagram for WEDM process parameter [24].*

#### **3.1 Process parameters used in study**

The most important performance measures in WEDM are metal removal rate, surface finish, and cutting width. They depend on machining parameters like discharge current, pulse duration, pulse frequency, wire speed, wire tension and dielectric flow rate. In WEDM process, it is seen that, input process parameters such as pulse-on time, pulse-off time, servo voltage, peak current, wire feed rate, wire tension, wire offset, water pressure, servo feed, wire material are having significant influence on process parameters named surface roughness, kerf width, material removal rate, wire wear rate, surface integrity aspects, etc. [3–9, 16–18]. The various input process parameters of WEDM and their inter-relationship is presented using Ishikawa's causeeffect diagram shown in **Figure 3**.

In this study, open circuit voltage, wire speed, and dielectric flushing pressure were selected as input parameters and surface roughness was selected as output parameter.

#### **3.2 Statistical analysis and modeling using RSM**

In Response surface methodology approach responses of interest is influence by several variables and in which the objective is to optimize these responses [59, 60]. In this method the effects of the noise factors have been considered. In addition, statistical optimization model can overcome the limitation of classical methods to obtain the optimum process conditions. Predictive model (RS model), which is an analytical function, in predicting response surface is formulated as following polynomial function:

$$\mathbf{Y} = \mathbf{a}\_0 + \sum\_{i=1}^{n} \mathbf{a}\_i \mathbf{X}\_i + \sum\_{i=1}^{n} \sum\_{j=1}^{n} \mathbf{a}\_{ij} \mathbf{X}\_i \mathbf{X}\_j + \dots + \mathcal{E} \tag{1}$$

where *Y* is the desired response, *a*0 is constant, *a*i and *aij* represent the coefficients linear, quadratic terms, respectively, *X*1 reveals the coded variables corresponding to the studied machining parameters, input variables, n is the number of the model parameters, *ε* is the random error.

In this study, a predictive model was developed to reach low surface roughness in terms of cutting parameters for milling operations. RSM design was tested with 30 data sets of central composite design of experiment. Surface roughness (Ra) measurements were made by using Phynix TR–100 portable surface roughness tester. Surface roughness measurements were made by using Phynix TR–100 portable surface roughness tester. To identify the significant factors for WEDM process, analysis of variance (**Table 3**) was employed by using Design Expert software.

This table demonstrates that the terms in the model have a significant effect on the responses. It is found that, the open circuit voltage has the most dominant effect on the surface roughness followed by the pulse duration and wire speed respectively. Goodness of fit for model generated by experimental data was evaluated and analyzed based on ANOVA. This includes the tests for significance of model, their coefficients and lack of fit model adequacy. ANOVA is used to create, access and analyze the experimental test data and goodness of fit model is generated afterwards. Through the backward elimination process, the final quadratic models of response equation in terms of coded factors are as follows:

$$\text{Y = 114+17.73X\_1 + 3.27X\_2 + 1.27X\_3 + 3.47X\_4 + 15.85X\_1X\_2 - 2.65X\_1X\_3 - 3.30X\_1X\_4}$$

$$\text{ + 0.91X\_2X\_3 + 8.019X\_2X\_4 \\ \text{ + 1.36X\_3X\_4 \\ -0.75X\_1}^2 - 0.111X\_2^2 + 0.15X\_3^2 - 0.44X\_4^2 \\ \quad \text{ + 2.0}$$

When the regression model above is examined, change in wire speed has significant impact on surface roughness. In this context, as wire speed increases, increase in surface roughness is observed. There is a strong linear relationship between the surface roughness and open circuit voltage, whereas there is a weak relationship between dielectric flushing pressure between surface roughness. It proves the complex influence of the adopted input variables on the analyzed value of the surface roughness. This model includes experimental test data that shows models importance, coefficients, and inadequacy in model fit.

In this study experimental surface roughness values were compared with surface roughness predicted values of the RS model. It was observed that the prediction of surface roughness closely agrees with that of the experimental values. Moreover, measured surface roughness has been correelated well with the predicted surface roughness values. It was also found that the RS model for the predicted values generates an average best fit percentage error of 6.83%. The involvement of process factors on surface roughness for WEDM process was analyzed with the help of surface graphs for the selected process factor combinations are presented in **Figures 4**–**15**. **Figures 4** and **5** represent interaction graphs wire speed between open circuit voltage and open circuit voltage between dielectric flushing pressure graphs respectively.

**Figure 4** shows that at lower wire speed the effect of open circuit voltage on surface roughness is statistically insignificant. However, at higher wire speed the effect of open circuit voltage on surface roughness is important and statistically significant. Similarly, with the rise in wire speed value, the lower value of open circuit results better surface roughness.

It is demonstrated that in **Figure 5**, at lower or higher open circuit value the effect of dielectric flushing pressure on surface roughness is very poor. **Figures 6** and **7** represent interaction graphs wire speed between pulse duration and dielectric flushing between pulse duration graphs respectively.

As seen in **Figure 6** at lower pulse duration the effect of wire speed on surface roughness is not statistically important, whereas, at higher pulse duration level this effect partly more significant. When the wire speed increases at low pulse duration


*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

#### **Table 3.**

*The analysis of variance (ANOVA) on the performance of surface roughness.*

#### **Figure 4.** *Interaction graph wire speed and open circuit voltage on surface roughness.*

#### **Figure 5.**

*Interaction graph open circuit voltage and dielectric flushing pressure on surface roughness.*

#### **Figure 6.**

*Interaction graph wire speed between pulse duration on surface roughness.*

value surface roughness increases. **Figures 7** and **8** show that the interaction graphs dielectric flushing pressure between pulse duration and dielectric flushing pressure between wire speed graphs respectively.

**Figure 7** exhibits that the increasing and decreasing dielectric flushing pressure and pulse duration values it has no statistically significant effect on surface roughness. In **Figures 8** and **9** they are represented the interaction graphs wire speed between dielectric flushing pressure and open circuit voltage between pulse duration graphs respectively.

*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

**Figure 7.** *Interaction graph dielectric flushing pressure between pulse duration on surface roughness.*

**Figure 8.**

*Interaction graph wire speed and dielectric flushing pressure on surface roughness.*

As seen in **Figure 8** in case of increasing or decreasing wire speed and dielectric values the magnitude of the surface roughness does not change significantly in level of significant 5%.

**Figure 9** demonstrates the variation of pulse duration and open circuit voltage concerning the surface roughness. It can be causes that increasing surface roughness with the increase in pulse duration when the open circuit increases. Similar trends were observed that lower pulse duration the effect of open circuit on surface roughness is poorer statistically. **Figures 10**–**15** represent 3D contour plot graphs input and

#### **Figure 9.**

*Interaction graph open circuit voltage and pulse duration on surface roughness.*

#### **Figure 10.**

*Contour plot graph wire speed and open circuit voltage on surface roughness.*

response variables. **Figures 10** and **11** represent 3D contour plot graphs wire speed between open circuit voltage and open circuit voltage between pulse duration graphs respectively.

As seen in **Figure 10** it was identified that the higher wire speed with the lower open circuit value results better surface roughness. Moreover, when wire speed is increased in case of lower open circuit voltage the value of surface roughness is very poor.

**Figure 11** exhibits the surface roughness decreases with an decrease in opencircuit voltage and increase pulse duration. Also, higher pulse duration with lower open circuit voltage the value of surface roughness is minimum. **Figures 12** and **13**

*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

#### **Figure 11.**

*Contour plot graph pulse duration and open circuit voltage on surface roughness.*

#### **Figure 12.**

*Contour plot graph pulse duration between dielectric flushing pressure on surface roughness.*

represent pulse duration between dielectric flushing pressure and wire speed between dielectric flushing pressure 3D contour plot graphs respectively.

It was noticed from **Figure 12** the lower magnitude of dielectric flushing pressure in case of lower wire speed value decreases surface roughness. **Figures 13** and **14** represent dielectric flushing pressure between wire speed and pulse duration between wire speed 3D contour plot graphs respectively.

As seen in **Figure 13** if dielectric flushing pressure is increased when wire speed is decreased, decreasing in surface roughness is observed. It was perceived that when the higher value of dielectric flushing pressure in case of lower wire speed the value of surface roughness is very poor.

#### *Response Surface Methodology - Research Advances and Applications*

#### **Figure 13.**

*Contour plot graph wire speed and dielectric flushing pressure on surface roughness.*

**Figure 14.** *Contour plot graph wire speed and pulse duration on surface roughness.*

**Figure 14** shows that at low wire speed with low pulse duration surface roughness value increases. The low values of dielectric when higher pulse duration may cause surface roughness also reduces. In addition, it is predictable from **Figure 14**, the combination of pulse duration and dielectric in lower range gives a good surface finish. **Figure 15** represents dielectric flushing pressure between open circuit voltage 3D contour plot graph.

From **Figure 15** with the increase in wire speed in case of lower open circuit voltage, it can be obtained lower surface roughness. Furthermore, increasing of high of dielectric flushing pressure in case of lower dielectric leads to decreasing surface roughness in WEDM process.

*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

**Figure 15.** *Contour plots graph dielectric flushing pressure and open circuit voltage on surface roughness.*

It is evident that, a predicted optimum surface roughness obtained from the response surface and contour plots by using RSM, a pulse duration of 346 (ns), open circuit voltage of 142 (V), wire speed of 8 (m/min) and dielectric flushing pressure of 12 (kg/cm2 ) is 2.63(μm). The objective of developed model is to establish the quantitative relationship between output and input control parameters. It is seen that, RSM model proposed here in has resolved the complex of WEDM process that results in satisfactory surface quality characteristics. Hence, the experimental results confirm that the developed model predicts effectively and the optimal process parameters significantly improve in the WEDM process. As a result, predicted optimum surface roughness was acquired. Results from the adopted design of the experiment, where the explanatory variables were determined independently of each other, is a desirable feature because it indicates the uniqueness of the prediction.

## **4. Conclusions and future scope**

This study mainly focuses on the development of empirical model of AISI 4340 steel in WEDM process to obtain the desired surface roughness in terms of four prominent input parameters using response surface methodology. In WEDM process, optimization of the response variable is very important and essential problem for various scientific studies and manufacturing industries. Because WEDM is an expensive production process and widely used in many manufacturing process such as aerospace, chemistry, textile, automobile and tool making industries. The essential purpose of the WEDM process is to achieve an accuracy and efficiency in production process. Several researchers have studied with different methods to improve the surface quality and increase the material removal rate of the WEDM process. However, the problem of selecting the cutting parameters in the WEDM process is not completely solved. Still there is lack of information about different WEDM wire types. Hence, more research should be done about comparing different inputs

on different responses. Finally, it seems that more researches can be strength the capabilities of WEDM process significantly to improve the machining productivity, accuracy and efficiency. From literature review it is obvious that most of the researchers examined lots of number of process parameters at a time to model and optimize various responses, which may not yield accurate optimal values for the process. Further, most of the researchers include both academics and applicants have given the importance to individual and multi -response modeling and its optimization. The proposed RSM approach can effectively assist engineers in determining the optimal process parameter settings for WEDM process for individual response variable. In the future, many studies should be made to investigate the process capability during WEDM of powdered products and multi response optimization on WEDM process by using integrated optimization methods.

## **Author details**

Aysun Sagbas Corlu Engineering Faculty, Namik Kemal University, Tekirdag, Turkey

\*Address all correspondence to: asagbas@nku.edu.tr

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Analysis and Optimization of Process Parameters in Wire Electrical Discharge Machining Based… DOI: http://dx.doi.org/10.5772/intechopen.107539*

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## **Chapter 7**

## Optimization of Baker**'**s Yeast Production on Grape Juice Using Response Surface Methodology

*Sawsan Mahmood, Ali Ali, Ayhem Darwesh and Wissam Zam*

## **Abstract**

The purpose of this study is to complete as an example the fermentation conditions allowing the production of *Saccharomyces cerevisiae* yeast biomass in large quantities using the juice as the same carbon source. Determination of the best of five factors affects the production of dry biomass by baker's yeast. The optimal value of the five factors affecting the process of biomass production by the baker's sourdough was determined. The experimental design was performed using CCD (Central Composite Experimental Design), and the response surface methodology method was used to determine the best possible amount of production of yeast and has reached (41.44 g/L) after 12 hours of fermentation, under the following optimal conditions (temperature (30.11°С), pH (4.75), sugar concentration (158.36 g/L), the ratio of carbon to nitrogen (an essential nutrient for yeast growth) that is (11.9), and initial concentration of yeasts (2.5 g/L). Three kinematic models (Monod, Verhulst, and Tessier) were also selected for the purpose of studying the kinetic performance of *S. cerevisiae* yeast, and the best results were obtained based on the Verhulst model. The Leudeking Piret model has also been successfully used to estimate substrate during fermentation.

**Keywords:** *Saccharomyces cerevisiae*, response surface methodology, kinetic models, assumption, statistics

## **1. Introduction**

Fermentation is one of the oldest methods used by humans since ancient times to preserve food and improve its organoleptic properties. More than 5000 fermented foods and beverages are produced worldwide, from alcohol, beer, and vinegar to cheese, yogurt, sourdough bread, olives, sausages, kimchi, and soybean paste [1].

Fermentation is simply the biochemical transformation of raw materials which is supported by the synthesis and stabilization of bacteria which convert sugars into simple acids, alcohols, and carbon dioxide to improve the flavor, texture, and aroma of processing and extend the shelf life of fermented products. Goods. During fermentation, many secondary metabolites including vitamins, antioxidants, and bioactive compounds are formed by the microbial community, contributing to the nutritional and nutraceutical value of the final product [2].

There has also been a rapid and significant development in fermentation technologies in recent years after understanding the bio-physiology of microorganisms and controlling it. Among this biology is the yeast, which has received more attention after recent developments in understanding its physiology [3].

Yeasts are micro-organisms, single-celled, unicellular eukaryotes. Their shapes and structure differ from one species to another. They are spherical or oval in shape and their dimensions range between 5 and 30 μm in length and 3–10 m in width. The yeast multiplies quickly and grows well in the contained environment. On sugars where they multiply by budding or by division [4, 5]. Yeasts play vital roles in food biotechnology, especially in fermented products [6].

*S. cerevisiae* yeast is the most important type of yeast due to its use in many industrial fields. It is used in the production of food, bread, pastries, ethyl alcohol, beer, wine, and as well as in the production of single-cell protein and a number of medicinal foods [7, 8].

*S. cerevisiae* yeast is considered to be the most important product of biotechnology due to its widespread use in the industrial field [9].

*S. cerevisiae* biomass is produced by using bioreactors that contribute to controlling growth conditions and the production is carried out according to batch or fed-batch fermentation system [10].

Baker's yeast industrially relies on a variety of disciplines, including variations of different generations, times and stages of aeration, differentiation of bioreactors, and control of the final stage of cultivation [11]. It is an aerobic process based on the expansion of cells from pure culture to larger bioreactors by increasing the volume at each stage of expression in the sugar medium [12].

Commercial bread yeast comes in three forms: Pressed yeast that is sold in the form of pressed briquettes or cubes wrapped with wax paper or cellophane, and its shelf life does not exceed one week from the date of its production due to the speed of its corruption. Active dry yeast is sold in airtight containers and needs to be reactivated before use, its cells are about 8–10% moisture and its shelf life ranges from six months to a year depending on the storage temperature. The instant dry yeast contains 4–5% moisture and its shelf life reaches more than a year and is added to the dough directly without the need for revitalization [13].

The global yeast market is estimated to be valued at USD 3.9 billion in 2020 and is projected to reach USD 6.1 billion by 2025 [14].

Molasses is the most used raw material in the production of Baker's yeast, it may be sourced from sugar beet or sugar cane, and contains about 50–55% of fermentable sugars, some vitamins and minerals that are important in cell proliferation, also any substance containing fermentable sugars can be used such as the date and grape juices [15].

In the last years, the price of molasses has increased because of their use in other industrial applications such as animal feeding or bioethanol production [16], thus rendering the evaluation of new substrates for yeast biomass propagation a trending topic for biomass producers' research. New assayed substrates include molasses mixtures with corn steep liquor (20:80), different agricultural waste products [17], and other possibilities such as date juice or agricultural waste sources, also called wood molasses that can be substrate only for yeast species capable of using xylose as a carbon source [18].

In this research, the possibility of using grape juice to produce a good yield from the yeast was studied in this study. Grape juice was chosen because it has a chemical composition similar to the chemical composition of molasses in terms of its good

#### *Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

content of hexane-sugars and its richness with many important nutrients for the growth of yeast cells, in addition to the fact that grape cultivation is spread in various parts of the world, including Syria, which is one of the grape-producing countries.

During the last war period, Syria was exposed to difficult economic conditions and the suspension of the work of the only sugar factory in the country, and this was accompanied by the suspension of the yeast factory and the tendency to import yeast. So, the researchers went to study the possibility of an alternative or additional option for molasses that supports yeast production, and this is in line with the researchers' interest. In different parts of the world studying the possibility of using available raw materials to support biotechnology industries and finding many options or alternatives that support any vital industry. The Syrian Arab Republic is the richest country in the Middle East in the cultivated varieties of grapes, and the number of varieties is about 100 varieties spread across the country where the most important varieties are spread, which are four varieties that represent 85 percent of the total grape production (Zaini 15%, Baladi 20%, Salti 20%, and Heloani 30%). The main objective of the present work is to study the optimization of *S. cerevisiae* biomass production, using grape juice as the only source of carbon, as grape juice is a good source of carbon and many important nutrients for the growth of yeast, and it has a chemical composition close to the chemical composition of molasses [19].

The efforts of many researchers are directed toward improving various biological manufacturing processes [20], including fermentation processes, with the aim to determine the best conditions for the production of the required product, as well as with the aim to solve the problems that may face the required manufacturing process, reaching the highest possible production of the final product and reducing the costs of the manufacturing process as possible [21, 22].

Several statistical experimental design methods have been used to optimize biological processes [23, 24].

These methods, including the central composite experimental design (CCD), are characterized by reducing the number of experiments required, reducing financial and energy costs, reducing the time required, as well as reducing the reagents and materials required during work [25, 26].

The central composite experimental design (CCD) is one of the methods that contributed to the improvement of a number of biological processes such as the production of antibiotics, enzymes, organic acids, and ethanol [27, 28].

The study was conducted by selecting the best for five measurements (temperature, initial pH, sugar content in the juice, carbon to nitrogen ratio, and primary yeast) in order to get high yields of yeast using optimization with the surface response methodology method, we use grape juice as carbon source for cell growth and produce *S. cerevisiae* at high performance, and finally predict the biomass production process with three kinetic models.

## **2. Material and methods**

#### **2.1 Origin and reactivation of the yeast** *S. cerevisiae*

The yeast used in this study is a commercial yeast from the sigma company, it is a dry powder form of *S. cerevisiae* (ATCC20408/S288c). This yeast needs to be reactivated before use with a suitable nutrient medium Yeast Peptone Glucose Agar

(YPGA) consisting of 20 g/L agar, 10 g/L yeast extract, 10 g/L glucose, 10 g/L peptones with a pH 6, with incubated at 30°С for 24 h.

### **2.2 Preparation of grape juice**

The Baladi grape (**Figure 1**) was chosen and it is one of the varieties available in Syria. Its production reaches 20% of the grape production. It is a local variety that is distinguished by the size of its large clusters and has a single conical shape, and the grains are spherical in shape, with a large size, a yellowish-white color, and a thin crust in a light pink color. The pulp is flaky, has a good taste, and has a distinctive flavor, one of the late-ripening varieties, and it is one of the famous and luxurious table varieties, suitable for remote transportation and long winter storage.

The grape is obtained from local markets. The grape berries were removed from their clusters and cleaned and washed with warm water. The juice was extracted by breaking and pressing in a doubly folded cloth, then the juice was pasteurized at 85°С for 3 minutes.

#### **2.3 Preparation of culture medium based on grape juice and inoculums**

The juice resulting from the above preparation was supplemented with mineral salts: 0.44 g of magnesium sulphate, 12.70 g of urea, and 5.30 g of ammonium sulphate. Finally, the medium was placed in 250 mL deltas at a volume of 100 mL per well and sterilized at 120° C for 20 min. The preculture was obtained by inoculating two colonies of *Saccharomyces cerevisiae* yeast in 250 mL flasks containing 100 mL of juice as mentioned above. Pre-cultures were incubated at 30°C for 3 h and then used as inoculum for potassium biomass production [29].

**Figure 1.** *The Baladi grape.*

*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

#### **2.4 Statistical design of experiments**

#### *2.4.1 Factor selection and organization of experiments*

Five independent variables were selected (temperature, initial pH, concentration of sugars in grape juice, the ratio of carbon to nitrogen, and initial concentration of yeasts).

In a previous study, carried out by Naser and Abdelrahman [30], with the aim of determining the optimal conditions for producing baker's yeast using sugar cane molasses and achieving the best yield and lowest production cost, the best results were obtained when using the concentration of sugars within the range (14–18) %, Yeast inoculum level 2 to 3 g/L, agitation speed between 150 r.p.m. and 200 r.p.m., adding (40–50) % urea and ammonium sulfate at pH = 5.

In another study by Muhammad et al. [31], the baker's yeast production process was improved and the effect of various physical and chemical factors on the production of yeast cells was evaluated. The optimal conditions were determined to obtain the maximum possible growth of yeast cells at a concentration of sugars equal to 100 g/L, the agitation speed at 150 r.p.m., at pH = 4.5, and T = 28°С.

Optimization of baker's yeast production using date juice as the sole carbon source using the response surface methodology method has been studied by Ali et al. [32] and the study showed the success of using date juice in obtaining a good yield of the yeast biomass at the initial conditions of the fermentation process (sugar concentration 70.93 g/L, temperature 32.9°С and pH 5.35).

A study carried out by Taleb et al. [33] showed that the use of ammonium sulfate and urea as a source of nitrogen during the production of break's yeast by (50–50) % contributed to improving production yield by more than 36%, and adding thiamine vitamin at a concentration of 0.6 had a positive role in improving production by more than 6%.

A study by Sokchea et al. [34] indicated that the best amount of biomass for yeast is obtained when the ratio between the concentration of glucose and nitrogen (C/N) used during the fermentation process is equal to 10.

After reviewing previous studies, the lower and upper levels of studied variables were selected, **Table 1** shows the lower and upper levels of studied variables.

A program Minitab 19 software was used to optimize the Baker's yeast production The CCD matrix is composed of a complete factorial design, 32 cube points, eight center points in a cube, 10 axial points, and four center points in axial design variable at a distance of α = 2.366 and two-level factorial. Each experiment was carried out twice and the average value is used.


#### **Table 1.**

*The lower and upper levels of studied variables.*

#### *2.4.2 Effect estimation*

The real values X have been calculated according to Eq. (1).

$$X = \begin{pmatrix} \mathfrak{x} - \mathfrak{x}\_\cdot \end{pmatrix} / \triangle \mathfrak{x} \tag{1}$$

Where, *X* is the coded value for the independent variable, *x*, is the natural value, *x0*, is the natural value at the center point, and *ΔX* is the step change value (the half of the interval (�1 + 1)).

Regression Equation in Uncoded Units:

$$\begin{aligned} \mathbf{Y}i &= \boldsymbol{\beta}\_{0} + \boldsymbol{\beta}\_{1}\mathbf{X}\_{1} + \boldsymbol{\beta}\_{2}\mathbf{X}\_{2} + \boldsymbol{\beta}\_{3}\mathbf{X}\_{3} + \boldsymbol{\beta}\_{4}\mathbf{X}\_{4} + \boldsymbol{\beta}\_{5}\mathbf{X}\_{5} + \boldsymbol{\beta}\_{11}\mathbf{X}\_{1}^{2} + \boldsymbol{\beta}\_{22}\mathbf{X}\_{2}^{2} + \boldsymbol{\beta}\_{33}\mathbf{X}\_{3}^{2} \\ &+ \boldsymbol{\beta}\_{44}\mathbf{X}\_{4}^{2} + \boldsymbol{\beta}\_{55}\mathbf{X}\_{5}^{2} + \boldsymbol{\beta}\_{12}\mathbf{X}\_{1}\mathbf{X}\_{2} + \boldsymbol{\beta}\_{13}\mathbf{X}\_{1}\mathbf{X}\_{3} + \boldsymbol{\beta}\_{14}\mathbf{X}\_{1}\mathbf{X}\_{4} + \boldsymbol{\beta}\_{15}\mathbf{X}\_{1}\mathbf{X}\_{5} \\ &+ \boldsymbol{\beta}\_{23}\mathbf{X}\_{2}\mathbf{X}\_{3} + \boldsymbol{\beta}\_{24}\mathbf{X}\_{2}\mathbf{X}\_{4} + \boldsymbol{\beta}\_{25}\mathbf{X}\_{2}\mathbf{X}\_{5} + \boldsymbol{\beta}\_{34}\mathbf{X}\_{3}\mathbf{X}\_{4} + \boldsymbol{\beta}\_{35}\mathbf{X}\_{3}\mathbf{X}\_{5} + \boldsymbol{\beta}\_{45}\mathbf{X}\_{4}\mathbf{X}\_{5} \end{aligned} \tag{2}$$

Yi is the predicted response (the Biomass production (g/L). The calculation of the effect of each variable and the establishment of a correlation between the response Yi and the variables X were performed using a Minitab 19 Statistical Software (Minitab, Inc., State College, PA, USA) [32].

#### **2.5 Statistical analysis**

The statistical analysis was performed using (ANOVA), in order to validate the square model regression. It included the following parameters: coefficient of determination R2 ; Fisher test (F); p-value and Student test (t); and the statistical significance test level was set at (probability <0.05) [32].

#### **2.6 Validation of biomass production in optimum medium**

After completing the optimization of the production of baker's yeast in grape juice, the optimum values obtained, and representative of the fermentation conditions were confirmed by conducting an experiment.

The experiment was carried out on 250 mL shake flasks and the agitation speed was 200 r.p.m. To do this, 100 mL of grape juice was seeded with 11 mL of the yeast pre-culture and the pH of the medium was adjusted to the obtained value of 4.75. Shake flasks were sterilized at 120°С for 20 min and incubated at 30°С (optimum Value) for 12 h.

#### **2.7 Analytical methods**

#### *2.7.1 Determination of total reducing sugars*

1 ml of the sample is taken after filtering it and placed in a glass tube, then 98% sulfuric acid and 0.6 mL of 5% (w/v) phenol were added and mixed well after which it is left at room temperature for 30 minutes, the absorbance is measured using a spectrophotometer (Analytik Jena- specord 200uv-vis spec.) at a wavelength of 490 nm, the concentration of the reducing sugar is calculated depending on the calibration curve, which was formed between different concentrations of standard

*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

solutions of glucose and between the absorbance values corresponding to each concentration [35].

#### *2.7.2 Determination of biomass concentration*

1 ml of the sample is taken and subjected to a centrifugation process for 5 minutes at 5000 r.p.m., after which the supernatant is collected on the surface and washed twice with water and then placed in a drying oven at 105°С, the drying continues until the weight is stable [36].

#### *2.7.3 Determine the fermentation power of the obtained yeast*

6.75 g of the sugar-phosphate mixture was mixed with 75 ml of calcium sulfate solution in the beaker. Then add 0.893 g of dry baker's yeast. Stir well to disperse the yeast. Then the fermentation power was measured using fermentometer (RHEO FERMENTOMETER F4) [37].

#### **2.8 Modeling**

In order to fit the experimental data, three kinetic models (Monod, Verhulst, and Tessier) were chosen.

Monod kinetic model is a substrate concentration-dependent, Verhulst kinetic model is an unstructured model that depends on biomass, and Tessier is an unstructured model for a substrate concentration-dependent [32].

The Kinetic parameters (μmax, Ks, and Xm), were determined after obtaining the curve fitting method of each model performed using Excel software (2016 Microsoft Corporation), and the results showed in **Table 2**, [38].

#### **2.9 Profile prediction of biomass and substrate concentration**

The integration of the Verhulst model was used (Eq. (3)), in order to predict the experimental profile of biomass of *S. cerevisiae* during time [32].


$$X = \left(\mathfrak{x}\_0 \stackrel{\*}{\\_exp}\, ^\mu\_m \stackrel{\*t}{)} / \left(\mathbb{1} - \left(\mathfrak{x}\_0/\mathfrak{x}\_m\right) ^\ast \left(\mathbb{1} - \,\_exp^\mu \stackrel{\*t}{)} \right) \right) \tag{3}$$

#### **Table 2.**

*Unstructured kinetic models to determine the kinetic parameters. [32].*

The substrate model (Leudeking Piret) as described below (Eq. (4)) was also applied to predict an experimental profile for total reducing sugars consumption by *S. cerevisiae* during the time fermentation.

$$-d\mathbf{s}/d\mathbf{t} = p^\* \left(d\mathbf{x}/dt\right) + q^\* \mathbf{x} \tag{4}$$

Where (p = 1/yx/s) and q is a maintenance coefficient (q = μmax/yx/x*0*.) Eq. (4) is rearranged as follows:

$$-\mathbf{ds} = \mathbf{p}^\* \, \mathbf{dx} + \mathbf{q} \int \mathbf{x}\_{(t)} \, ^\* \mathbf{dt} \tag{5}$$

Substituting Eq. (3) in Eq. (5) and integrating with initial conditions (S = S0; t = 0) give the following Equation:

$$\mathbf{S} = \mathbf{s}\_0 - \mathbf{p} \,\, \mathbf{x}\_0 \left\{ \,\_\exp \, \prescript{\mu}{}{\text{m}}^\* / \mathbf{1} - (\mathbf{x}\_0 / \mathbf{x}\_\mathbf{m}) \* (\mathbf{1} - \exp \, \prescript{\mu\_m \* t}{}{)} \right\} \tag{6}$$

$$- \mathbf{q} \* (\mathbf{x}\_\mathbf{m} / \mu\_\mathbf{m}) \* \ln \left( \mathbf{1} - \mathbf{x}\_0 / \mathbf{x}\_\mathbf{m} \right) \* (\mathbf{1} - \exp \, \prescript{\mu\_m \* t}{}{}$$

## **3. Results and discussion**

The improvement of dry yeast biomass production was studied by determining the optimum values of the following factors (temperature, initial pH, concentration of sugars in grape juice, the ratio of carbon to nitrogen, and initial concentration of yeasts) that have their influence on the production process using the central composite experimental design, and the central composite design for biomass production in **Table 3**.

Ammonium sulfate and urea were added as a source of nitrogen in a ratio of (50– 50) %, taking into account the achievement of the specified ratio between carbon and nitrogen for each experiment, and the agitation speed used during fermentation was 200 r.p.m.

Using the results obtained in diverse experiments, the correlation gives the influence of temperature (x1), initial pH (X2), total sugar concentration (X3), the ratio of carbon to nitrogen (x4), and initial concentration of yeasts (x5) on the response. This correlation is obtained by Minitab 19 software and expressed by the following secondorder polynomial (Eq. (7)).

$$\text{Y} = -261.1 + 8.96 \text{ T} + 16.10 \text{ pH} + 0.353 \text{ C} + 6.55 \text{ C}/\text{N} + 49.8 \text{ X}$$

$$-0.1527 \text{ T}^\* \text{T} - 1.769 \text{ pH}^\* \text{ pH} - 0.001414 \text{ C}^\* \text{C}$$

$$-0.3025 \text{ C}/\text{N}^\* \text{C}/\text{N} - 9.30 \text{ X}^\* \text{X} + 0.0316 \text{ T}^\* \text{ pH} + 0.00096 \text{ T}^\* \text{C} \qquad (7)$$

$$+ 0.0206 \text{ T}^\* \text{C}/\text{N} - 0.117 \text{ T}^\* \text{X} + 0.00414 \text{ pH}^\* \text{C} - 0.0390 \text{ pH}^\* \text{C}/\text{N}$$

$$- 0.165 \text{ pH}^\* \text{X} + 0.00163 \text{ C}^\* \text{C}/\text{N} + 0.0096 \text{ C}^\* \text{X} - 0.016 \text{ C}/\text{N}^\* \text{X}$$

**Table 4** shows the coefficient regression corresponding with t and p-values for all the linear and the analysis of variance (ANOVA), quadratic, and interaction effects of parameters tested. A positive sign in the t-value indicates a synergistic effect, while a negative sign represents an antagonistic effect of the parameters on the biomass concentration [39].


*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*


#### **Table 3.**

*The central composite design for biomass production.*

### **3.1 Model summary**

S: represents the standard deviation of the distance between the data values and the fitted values, the lower the value of S, the better the model describes the response. R-sq (R2 ): is the percentage of variation in the response that is explained by the model, the higher the R<sup>2</sup> value, the better the model fits your data. R2 is always between 0% and 100%. R-sq (adj): Adjusted R2 is the percentage of the variation in the response that is explained by the model. R-sq (pred): Predicted R2 is calculated with a formula that is equivalent to systematically removing each observation from the data set, estimating the regression equation, and determining how well the model predicts the removed observation. The value of the predicted R<sup>2</sup> ranges between 0% and 100%. By referring to the values obtained in the current study for these parameters, we find that the current study model is acceptable.

*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

The examination of **Table 4** shows that all coefficient regression of the quadratic terms are statistically significant p ≤ 0.05 and negatively affect the biomass production (**Figure 2**). In contrast, the interaction terms (T, C/N, X, T\* pH, T\*C, T\*C/N, T\*X, pH \*C, pH \*C/N, pH \*X, C\*C/N, C\*X, C/N\*X) are statistically not significant p > 0.05, and the interaction terms (pH, C, T\*T, pH \* pH, C\*C, C/N\*C/N, X\*X) are significant with p ˂0.05 and have a synergistic effect on the response.

It is known that the F-value with a low probability p-value indicates a high significance of the regression model [40].

Looking at the analysis of variance (ANOVA), the study shows that the model is important as the F-value had a low probability p-value (p = 0.000), and the resulting value of R<sup>2</sup> was equal to 92.9% and this indicates that only 7.1% of the variance is not explained by the model and therefore there is a good agreement between the model and the experimental data [41]. **Figure 3** shows the fit between the model and experimental data of cell growth.

By reviewing previous studies, Bennamoun et al. [42] used response surface methodology in order to improve and optimization of the medium components,


**Table 4.** *Estimated regression coefficients of t and p and analysis of variance (ANOVA).*

**Figure 2.** *Variable effect signification on biomass production.*

which enhance the polygalacturonase activity of the strain Aureobasidium pullulans, and they got good results (a very low p-value (0.001) and a high coefficient of determination (R2 = 0.9421), the results confirm the importance and success of using this method.

A previous study by Boudjema, Fazouane-Naimi, and HellaL [27] showed the success of using the experimental design method in the study of the production of *Saccharomyces cerevisiae* DIV13-Z087°СVS using sweet cheese serum, as it confirmed a high significance of the regression model, and the results showed a good agreement with experimental data (a low probability p-value ≤0.000 and a good correlation coefficient (R2 = 0.914%).

The optimization of the response Yi (Biomass production) and the prediction of the optimum levels of (temperature, initial pH, concentration of sugars in grape juice, the ratio of carbon to nitrogen, and initial concentration of yeasts) were obtained. This optimization resulted in surface plots (**Figure 4**), the figure shows that there is an optimum, located at the center of the field of study.

In addition, the use of the Minitab optimizer will give exact values of the optimum operating conditions of the process **Figure 5**.

**Figure 5** shows the maximum biomass production by *Saccharomyces cerevisiae* (41.444 g/L) corresponding to values of temperature (30.11°С), pH (4.75), sugar concentration (158.36 g/L), the ratio of carbon to nitrogen (11.9), initial yeast concentration (2.5 g/L). The amount of urea was 6.65 g/L and the amount of ammonium sulfate used was 6.65 g/L, so that the concentration of added urea and ammonium sulfate was (50–50)% and the required C/N ratio was achieved, and the stirring speed was equal to 200 r.p.m. during the fermentation process. Jiménez-Islas et al. [36] obtained the highest cell concentration of *S. cerevisiae* ATCC 9763 (7.9 g/L) after 26 h

*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

**Figure 3.** *The fit between the model and experimental data of cell growth.*

when the strain grew at 30°С and pH 5.5, so we note that our study gave a good result in achieving the greatest possible production of baker's yeast.

The validation of the baker's yeast biomass concentration and total reducing sugar consumption, over time fermentation, at optimized conditions, are presented in **Figure 6**.

At the beginning of the fermentation process, the concentration of the resulting biomass increases and is associated with the consumption of sugar. After 12 hours of the fermentation process, the sugar concentration has reached a very low level, and this is associated with a decrease in yeast production.

The same results were obtained by Ali et al. [32] where they study the optimization of Baker's Yeast production on Date extract using Response Surface Methodology (RSM), and the resulting yeast was equal to 40 g/L.

The measured fermentation power of the yeast obtained in this study from grape juice was 480 ml, so this is considered to have good fermentation capacity and is suitable for industrial use. The acceptable fermentation strength of yeast is not less than 350 ml according to the COFALEC (2012): General characteristics of dry baker's yeast.

Depending on the Monod model, the curve fitting of cell growth is formed (1/μ versus 1/S) and shown in **Figure 7**. **Figure 8** shows the resulting graph according to the Verhulst model (μ versus X), and in **Figure 9** the graphical curve is formed according to the growth of the Tessier model (μmax and Ks).

The kinetic parameters of growth of *Saccharomyces cerevisiae* using different kinetic models according to the curve fitting method are presented in **Table 5**.

The results obtained from the modeling process appear as follows: the Monod model gave a good value for the parameter R <sup>2</sup> equal to 0.94, which indicates that it is an acceptable model for studying the kinetic performance of a strain *S. cerevisiae,* and

#### **Figure 4.**

*Surface plot for the effect of different parameters on biomass production.*

**Figure 5.** *Values of optimal conditions on biomass production.*

*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

#### **Figure 6.**

*The biomass production, and total reducing sugar consumption over time at optimized conditions.*

**Figure 7.** *The line weaver Burk linear plot fitting the experimental data using the Monod kinetic model.*

#### **Figure 8.**

*A plot fitting the experimental data using the Verhulst kinetic model.*

the values of each of the maximum specific growth rate (μmax) and is the halfsaturation constant (Ks) were evaluated as 0.254 h�<sup>1</sup> and 291.99 g/L, respectively, which are good values indicating rapid growth of cells Yeast. Tessier's model gave the lowest value for R <sup>2</sup> compared to the Monod and Verhulst models, where it was 0.81. Whereas the Verhulst model gave the highest value for the parameter R <sup>2</sup> which

**Figure 9.** *A plot fitting the experimental data using the Tessier kinetic model.*

reached 0.99, also gave a high value for the maximum specified growth rate reached 1.0765 h�<sup>1</sup> , and the highest possible amount was obtained from the concentration of yeast according to the Tessier model reached 38.26 g/L. As a result, the Verhulst model is the best model for studying and controlling the kinetic behavior of a yeast strain *S. cerevisiae*.

A residual plot is a chart used to assess the quality of a regression fit. Examination of the remaining squares will help determine if the least-squares assumptions are ever met. When these assumptions are met, least squares regression typically yields an inaccurate estimation coefficient with minimal variance. The 4-in-1 residual plot displays four residual plots in a graph window. This configuration can be useful for comparing plans to determine if the Verhulst model meets the criteria for analysis. The remaining sections of the figure are:



**Table 5.**

*Kinetic parameters of* Saccharomyces cerevisiae *growth and substrate utilization using unstructured models.*

*Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

Minitab provides the following residual plots in **Figure 10**.

Examination of the remains indicates that there is nothing to complain about. The normal performance of the remaining sections does not seem to have much difference. There is nothing surprising here and it seems acceptable.

The kinematic models describe the growth rate of microorganisms based on biomass and substrate concentration and are useful because they help engineers design and control biological processes, including the Verhulst model which describes the experimental data obtained on the growth rate of yeast cells, where it describes the logarithmic growth of cells and shows that the first six hours of fermentation were during the initial cell growth phase, then the logarithmic growth phase began, which is characterized by a doubling of the number of yeast cells and an increase in the growth rate.

A profile of biomass and total reducing sugar concentration during fermentation time is compared to the values predicted by the equations model obtained in **Figures 11** and **12**.

During the fermentation, values of biomass between predicted and experimental data were approximately the same. And for total reducing sugar concentration, the values obtained by the Leudeking Piret model were identical to the predicted values, where the values (p = 1/y**x/s,** q = μ/yx/x0) were 3.81 g/g and 0.065 1/h, respectively.

On the basis of these results, good correlation coefficients showed that the proposed Verhulst model and the Luedeking Piret model were adequate to explain the development of the biomass production process in grape juice.

This study confirmed that the Logistic equation for the growth and the Leudeking Piret kinetic model for substrate utilization were able to fit the experimental data, and

**Figure 10.** *Residual plots for response.*

**Figure 11.** *The comparison between predicted and experimental data for biomass production of baker's yeast.*

**Figure 12.**

*The comparison between predicted and experimental data for total reducing sugar consumption.*

the same result was obtained by Kara Ali et al. [43] Where they used the logistic empirical kinetic model and Leudeking Piret model and they obtained good agreement with the experimental data.

Finally, what distinguishes this study from previous studies is the dependence on grape juice as a source of carbon with the aim of producing biomass from dry yeast, which researchers had not previously studied. The work has been done with a lot of numerical and experimental analysis.

This study will present an additional successful option for the production of yeast that commonly uses molasses. The improvement of the initial conditions of fermentation also contributed to the highest possible yield of yeast and good economic value. The fermentation power of the yeast was also good, so this study can be practically applied with the aim of producing a good mass of baker's yeast and using this yeast in various industrial and food fields.

## **4. Conclusion**

The central composite design (CCD) proposed in this study seems pertinent to describe the optimum biomass production of *Saccharomyces cerevisiae*. A second-order *Optimization of Baker's Yeast Production on Grape Juice Using Response Surface Methodology DOI: http://dx.doi.org/10.5772/intechopen.105899*

polynomial model was developed to evaluate the quantitative effects of temperature, initial pH, and concentration of sugars in grape juice, the ratio of carbon to nitrogen, initial concentration of yeasts in order to discover the optimum conditions for the biomass production from grape juice. According to the experimental results, a maximum biomass concentration of (41.444 g/L) corresponding to values of temperature (30.11°С), pH (4.75), sugar concentration (158.36 g/L), the ratio of carbon to nitrogen (11.9), initial concentration of yeasts (2.5 g/L), the amount of urea was 6.65 g/L and the amount of ammonium sulfate used was 6.65 g/L, so that the concentration of added urea and ammonium sulfate was (50–50)%, and the used agitation speed was equal to 200 r.p.m. during the fermentation process. The fermenter power of the obtained yeast was 470 ml. In addition, among three unstructured kinetic models, the Verhulst model was the most suitable model to signify the baker's yeast production on grape juice medium.

## **Acknowledgements**

The authors are thankful to everyone supported our work, and to every who collaboration and assistance to carry out this study.

## **Conflicts of interest**

The authors declare no conflict of interest.

## **Author details**

Sawsan Mahmood<sup>1</sup> \*, Ali Ali<sup>1</sup> , Ayhem Darwesh1 and Wissam Zam<sup>2</sup>

1 Tartous University, Faculty of Technical Engineering, Tartous, Syria

2 AL- Wadi University, Faculty of Pharmacy, Homs, Syria

\*Address all correspondence to: sawsanmahmood480@gmail.com

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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## **Chapter 8**

## Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings

*Julio Romero-Noguera, Nuria Pérez-Villares, Fernando Bolívar-Galiano and Rafael Bailón-Moreno*

## **Abstract**

Cleaning polychrome paintings and sculptures is an essential task in restoration treatment, since it irreversibly affects the appearance and material structure of such works of art. It is a completely "analogical" process consisting of removing surface dirt, aged varnishes or repainting (paints added to the original) based on the restorer's experience and knowledge, as well as on different internationally accepted criteria for such interventions. In this chapter we are presenting an example of the adaptation of the response surface model to this field, which is complex and difficult to adapt to quantitative parameters and has never before been studied with this approach. Using the MODDE Go® experiment optimization and statistical design software, the effectiveness of cleaning pictorial works of art has been studied using various formulas composed mainly of water and a low-toxicity monoterpene: limonene. The model's statistical validity is demonstrated, as well as its ability to determine the main factors that affect the cleaning by means of different responses (methods) to evaluate its effectiveness: an expert's opinion using visible light and ultraviolet light, the amount of varnish removed using gas chromatography coupled with mass spectrometry, and the effects on color, lightness and gloss. The main influential factors were the concentrations of the two main components of the proposed formulations, water and limonene, which regulate the cleaners' level of hydrophilia and lipophilicity, followed by the types of pigments and type of varnish used, and aging. Using an *in silico* simulation, the proposed model also enables specific compositions to be formulated for different scenarios and cleaning applications that are potentially effective and harmless to the pictorial materials and the restorers' health.

**Keywords:** cleaning, oil paintings, water, limonene, response surface

## **1. Introduction**

Since the second half of the 20th century, works of art have been restored based on a fundamentally scientific perspective, using a great variety of products and methods for analysis that have enabled the materials to be characterized in detail, and the results of the restoration treatment to be experimentally proven. However, the results

obtained have yet to be correlated with empirical models that adequately back them, which has not yet been studied enough [1–8].

The approach in this study uses an innovative model that compares the nature and conditions of the artwork to be cleaned, the composition of the cleaner and the results obtained after cleaning from multiple perspectives. This involves representing the complex phenomenon of cleaning and stripping varnishes over oil paint by using a model of surface responses. This model can be simulated *in silico* to highlight the synergistic and antagonistic relationships among the main factors involved in cleaning of oil paintings: the type of varnish, degree of aging, type of oil pigment and composition of the cleaner. To do so, different responses (methods) have been brought together to evaluate the cleaning's effectiveness: an expert's opinion using visible and ultraviolet light, the amount of varnish removed using gas chromatography coupled with mass spectrometry, and the effects on color, lightness and gloss. The simulation will also allow optimal cleaning products to be developed for specific cleaning treatments.

## **1.1 Cleaning works of art**

Cleaning is one of the fundamental treatments used in restoring paintings and other types of works of art, and also one of the most controversial ones, since it is the one that most affects their appearance. The term refers to three types of tasks [9]:


From classical antiquity to today, the criteria used in applying cleaning treatments to artworks have changed along with the development of concepts and theories as regards conservation and restoration.

The lack of control in using cleaning substances has led to the complete or partial loss of polychromy in many artworks. The substances used included highly aggressive products such as soap, diluted bleach and ash. Soda, urine, salt, alum, acids, ox gall, milk and egg yolk, for example, were also products commonly used in the 17th and 18th centuries. Gradually, an awareness of the potential aggressiveness of some of these substances for paints emerged [10].

In the 20th century, a great boost was given to the theory and practice of cleaning cultural assets, mainly due to what had been learned from the alterations caused by many of the products over time, and the risk involved in using solvents. The greatest stimulus came from the scientific advances made after the First World War, which provided a wide variety of products with physical and chemical properties that enabled problems to be solved and new techniques developed [11]. The research carried out in the second half of the century then laid the foundations for more scientifically based restoration work, concentrating on the main solvents' solubilization power as regards the materials to be removed [12–15]. There is now a growing awareness of the danger that cleaning can bring about for the artwork's integrity and the restorers' health.

## *Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

One alternative to solvents are water-based cleaning systems that include surfactants and other additives in complex detergent formulas [16–18]. It is essential to know the composition of the detergents and the surface to be cleaned in order to determine the effectiveness of the detergent, but even so it is difficult to choose the best cleaner in each case, even for highly trained and experienced restorers.

## **1.2 Strata involved in cleaning paintings: dirt, varnish and painting layer**

The main factors that can alter the appearance of an artwork's color over time are the accumulated dirt on the surface, the darkening and yellowing of the varnish and oil, pigment migration, and the effects of visible and ultraviolet light. When the cleaning is carried out for a polychromy, there are three layers that are affected (**Figure 1**): the dirt, the layer of varnish and the underlying pictorial layer (which in our case study is oil paint), which can alter the artwork's visual appearance [19]. We will briefly review their characteristics.

## *1.2.1 Dirt*

The dirt that we may find on the surface of a painting is a difficult concept to define and varies considerably depending on the circumstances. Surface dirt is understood to mean the sediments that are deposited on an artwork's surface in multiple layers and bound by different forces of attraction [20]. This generally includes particles of dust, carbon and other solid materials such as sand, soil, corrosive products and salts. It is responsible for the grayish veil over the pictorial surface and sometimes causes mechanical damage or reactions with the materials within it as its components

absorb some pollutants from the atmosphere. Non-polar surface dirt particles are bound together by weak intermolecular forces, and polar ones by stronger dipolar forces. It is usually sufficient to apply mechanical means and detersive substances in order to remove surface dirt [9].

Surface dirt on works of art is usually associated with fatty deposits made up of a complex mixture of components [21], predominantly natural lipids (triglycerides), which contain unsaturated fatty acids (susceptible to oxidation by air). This type of dirt remains attached to the surface after surface cleaning due to the greater strength of its molecular bonds and interactions [22]. To remove it, it is common to use organic solvents, which can damage the paint layer, both when it is applied and in the long term.

## *1.2.2 The varnish layer*

A varnish is a liquid which, when applied to a solid surface, dries forming a transparent film with varying degrees of gloss, hardness, flexibility, and protection depending on its composition [12]. It is a material of prime importance in the sphere of artistic techniques, which must have an even finish and be transparent, stable and reversible, while preventing efflorescence from developing. Its main purposes in a work of art are for protection and esthetics [23]. The natural varnishes traditionally used in painting are terpenoids, which undergo oxidation processes and other chemical changes that cause them to yellow and lose mechanical and optical properties [24–27]. One of the most frequent painting restoration tasks is to remove aged varnishes by using solvents and replace them with polymeric varnishes, generally acrylics, which are much more stable.

### *1.2.3 The pictorial layer: oil paint*

Oil painting has dominated the artistic sphere since the fifteenth century until today due to the variety of pictorial resources it offers as regards opacity, transparency and chiaroscuro [28]. A layer of oil is made up of finely ground particles of pigment evenly dispersed in a vegetable-based drying oil.

A drying oil is a liquid vehicle or binder composed mainly of triglycerides of fatty acids with 16 or 18 carbon atoms: palmitic, stearic (saturated) and mainly polyunsaturated ones. Among the unsaturated fatty acids, oleic acid (C18, one double bond), linoleic acid (C18, two double bonds) and linolenic acid (C18, three double bonds) are the most notable [29, 30]. The most widely used oils since ancient times have been walnut, poppy and especially flax, since they form transparent films after the drying process, with optimal mechanical and optical properties [31].

The oils dry by oxidation and subsequent polymerization of the triglycerides' unsaturated fatty acids, until they form a relatively hard yet elastic film. After a series of complex chemical reactions involving processes of crosslinking, oxidation of unsaturated acids and the hydrolysis of glyceride bonds, a new substance is formed that is usually called linoxin, with very different physical and chemical properties from the original liquid oil, and which will not return to its initial state by any means [32, 33]. Although the oil film dries out to the touch in weeks, it undergoes new chemical reactions throughout the life of the painting [19]. Natural aging makes the pictorial film less flexible and causes cracking and changes in opacity.

When one intends to clean or remove a varnish from a polychrome surface, it has to be taken into account that the pictorial layer may be altered [34], especially *Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

when glazing techniques are applied in the painting's finishing, in which the pictorial medium is a fine mixture of oil, pigments and varnish, and therefore has a composition and polarity that closely resemble the protective varnish that is going to be removed.

Solvents can also give rise to changes in the oil's properties and composition, fostering leaching of components with a low molecular weight such as ketones, alcohols and dicarboxylic acids, like azelaic acid. This process affects the physical properties of the pictorial layer, reducing its volume, increasing its density, and making it brittle and opaque [23].

The type of solvent used for cleaning is decisive. It is generally thought that the greater the polarity of the solvent, the greater the risk of leaching [15], since the oxidation and hydrolysis of the initial triglycerides over time causes changes in the oil paint's chemical structure, making it more polar [35]. The magnitude of the changes also depends on the length of exposure time. When solvents are applied repeatedly or in excessive amounts, they cause surface wear as pigments get washed away with the oily film protecting them. Finally, the nature of the pigment also influences the effect of the solvents on the oil. One well-known example of this is the effect of one of the most significant pigments in art history, lead white, which minimizes the action of solvents even on fairly young oil layers [19].

#### **1.3 Oil painting cleaning treatments**

#### *1.3.1 Cleaning methods*

Cleaning can be done mechanically or by means of solvents, or else by combining both approaches in mixed treatments. Mechanical cleaning is done with vacuum cleaners, dusters, soft paintbrushes, brushes, compressed air, rubber erasers, lasers or scalpels [36]. It is used for superficial cleaning and as a treatment prior to any intervention in the sphere of restoration, as well as in cases of varnishes, repainting or dirt that is impossible to remove by other means.

Physical and chemical methods involve cleaning with solvents to soften and disperse or solubilize the material to be removed, forming a homogeneous mixture with it. This is finished off with mechanical wiping using a cotton bud or inert media such as cellulose pads or gels that keep the product active for longer. In the sphere of conservation and restoration, these procedures are carried out following internationally accepted cleaning guidelines and standard solubility tests [31].

#### *1.3.2 Solvent properties*

There are two different, closely related processes in the action of solvents [37]:


According to the principles of thermodynamics, each type of substrate must be dissolved by a solvent of similar polarity. It is therefore essential for there to be chemical similarity between the molecules of the solvent and the solute, defined by the predominant intermolecular forces. What is commonly known as "like dissolves like"

therefore refers to the fact that a solvent will remove the layer of varnish and/or dirt when it interacts with it with the same type of intermolecular forces as those that hold its own molecules together. Hansen's solubility parameters and visual diagrams such as the Teas triangle are often used to characterize solvents and classify them for their use in restoration [38–40]. Other very important factors must also be considered, such as the penetration capacity, volatility and retention in the artwork, not forgetting the toxicity values for the restorer [12].

## **2. Response surface model**

All the above gives an idea of how enormously complicated it can be to approach the cleaning of artistic paintings from a scientific point of view. There are factors involved that are related to the material, which is chemically very complex and divided into three layers: dirt, varnish and the painting layer. These factors can in turn be subdivided into internal micro-layers with different compositions, as happens when a painting is repainted, in other words, when a new pictorial layer is added to an already finished work. Organic materials also appear, such as binders and varnishes, and also inorganic ones, such as many pigments. We could also distinguish between components that are natural or synthetic, original or added, and polar or non-polar. Metals can even appear if the work includes gilding or silver-plating techniques. Likewise, factors such as aging of the materials to be treated, deterioration agents, or previous restoration treatments are all very important. Lastly, when solvents are being applied, a single product is seldom used, since the habitual values of polarity required in cleaning and stripping varnishes are usually achieved by using solvent mixtures [37]. In restoration practices today, we should also add the frequent use of surfactants, chelating agents or enzymes [14, 21, 37].

Our research aims to analyze the most important factors affecting the effectiveness of cleaning a pictorial work of art so as to be able to put forward effective cleaning methods with few adverse effects. Due to the number of variables present, we used the MODDE Go® (Umetrics) software for statistical design of experiments and optimization, run on a PC with a 64-bit Windows 10 operating system. An effort has been made to include the utmost number of factors and reduce the number of experiments to a minimum, while being as representative as possible of the complex phenomenon that we are attempting to analyze.

As a way of explaining the rationale behind this procedure, think for example of carrying out four experimental points of four different concentrations of five components of a cleaner, plus one point for each of, let us say, five pigments present and two points for each of the factors of aging and the type of varnish. This would mean carrying out at least 20,480 different cleaning tests in the laboratory (45 × 5 × 22 = 20,480). Using statistically designed experiments, the representative sample has been reduced to only 72 cleaning trials. This has meant an enormous saving in time and material resources, which if an attempt had been made to carry out all of the theoretical tests would have made it impossible to actually do them.

The proposed response surface model uses analytical techniques (responses).

of a physical, chemical and visual nature to study the effectiveness of low-toxicity formulations, taking into account the main factors that influence cleaning: the composition of the cleaners, types of pigments and varnishes, and their aging. It also enables in silico simulations in order to develop optimal cleaning products for specific cleaning treatments depending on the characteristics of the pictorial work of art to be *Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

restored. Furthermore, in future research, three-dimensional vector models can be developed to analyze: 1) the material and physical–chemical aspects of cleaning, 2) the restoration technique used, and 3) the visual appearance, which can be evaluated using optical methods.

Below, we explain the fundamental points in the proposed design of experiments and some examples of the results obtained. The full technical details of the study can be consulted in Bailón-Moreno et al. [41].

#### **2.1 Preparation of samples**

The proposed cleaning methods were tested on reference samples containing the usual layers in an oil painting: support (linen canvas), preparation, paint layer and protective varnish.

The preparation applied over the canvas was composed of animal glue, calcium sulphate (CaSO4·2H2O) and zinc white (ZnO). The oil painting was handmade prepared with stand linseed oil and five different pigments, one for each type of sample: zinc white (ZnO), lead white (PbCO3)2Pb(OH)2, cadmium yellow (CdS), cadmium red (3CdS·2CdSe) and cobalt blue (CoO·nSnO2). All these products were purchased at Manuel Riesgo, Madrid, Spain) except lead white, wich was produced by ourselves [42].

After a drying period of 3 months, the samples were varnished following two possible procedures: using a traditional terpenoid varnish composed of mastic resin diluted in spirit of turpentine or using an acrylic synthetic varnish by Lefranc & Bourgeois®. In both cases, they were allowed to dry naturally for 12 months (**Figure 2**). Aged terpenoid varnishes such as mastic are affected by

chemical processes of crosslinking and oxidation that make them more polar than the original ones, and more difficult to remove using solvents in cleaning processes.

To imitate the deterioration of a layer of old paint varnish, some of the samples were subjected to artificial accelerated aging by exposure to ultraviolet light [31]. The rest of the samples were reserved to simulate a recent painting. The varnishes and oil color layers were applied with a micrometric adjustable paint applicator SH-1117/100 (Daesan CMC, South Korea).

## **2.2 Designing experiments. Software MODDE Go®**

The model consists of a set of polynomials (one for each response), which have a constant value, a0, representing the mean value of the response considered. These terms represent the linear effects of the factors on the responses, ∑ <sup>=</sup> 8 <sup>1</sup> *i i <sup>i</sup> a F* , quadratic terms, ∑ <sup>=</sup> 8 2 <sup>4</sup> *ii ii <sup>i</sup> a F* , and finally cross terms, ∑ ∑= = + 8 8 1 1 *ij i j i ji a FF* , which represent the synergistic and antagonistic effects between the different factors. S is the response and the values of ai, aj and aij are coefficients that multiply the factors Fi, Fj.

$$\text{Response} = \text{Coeff.} + \lfloor \text{Linear\\_eqs} \rfloor + \lfloor \text{Quadratic\\_eqs} \rfloor + \lfloor \text{Synergy.\\$ at\\_tag\_:} \text{egs} \rfloor$$

$$S = a\_0 + \sum\_{i=1}^{8} a\_i F\_i + \sum\_{i=4}^{8} a\_i F\_i^2 + \sum\_{i=1}^{8} \sum\_{j=i+1}^{8} a\_{ij} F\_i F\_j$$

The model was adjusted with the MODDE Go® software from the company Umetrics using the Partial Least Square (PLS) technique with pseudo-components with non-scaled, non-centred values. Bailón-Moreno et al. [41] show the coefficients associated with each response, S, depending on the model proposed, the coefficient of determination, R2, and the coefficient Q2.

The proposed model considers the cleaning of painted artworks to be a procedure affected by a set of values or variables that is evaluated via a set of responses. The factors can be quantitative or qualitative, depending on whether they can be represented by quantity or not, and they can also be of the process or composition type. The factors chosen are as follows (**Figure 3**).


The cleaning was evaluated via seven possible sets of responses: the physical state, the chemical analysis via gas chromatography/mass spectrometry (GC/MS), cleaning from the point of view of an expert's opinion (observed with visible light and ultraviolet light), and also how the cleaning affects the painting from an optical and colorimetric point of view (color, lightness and gloss) [43, 44]. MODDE Go® (Umetrics), was used to establish a statistical design for experiments in keeping with

*Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

**Figure 3.**

*Response surface model for cleaning oil paintings with composition factors, process factors and the responses studied.*

the response surface model put forward. It has 72 statistically representative tests, whose experimental conditions can be consulted in Bailón-Moreno et al. [41]. Every test was performed once.

## *2.2.1 Quantitative composition factors*

These are dependent on the composition of the proposed cleaning mixtures. Several criteria have been used in choosing the products [14, 21, 37].

	- One or two main solvents;
	- Optionally a co-solvent;
	- Optionally a surfactant with the possibility of a co-surfactant.

#### **Figure 4.**

*Masschelein–Kleiner diagram: Solubility of natural film-forming substances and position in the triangle of the two main components of the proposed cleaning formulas: water and limonene. Note how there is partial overlap between resins and oily layers.*

In keeping with these general requirements, five substances have been chosen. The proposed cleaning method is based on a mixture of two main components: one clearly polar, water; and the other strongly nonpolar, limonene (1-Methyl-4-(1 methylethenyl)-cyclohexene), a hydrocarbon (monoterpene) devoid of toxicity that is found as the main component in the essential oils of orange, lemon and other aromatic plants. The relative proportion of these components marks the polarity of the mixture and its greater or lesser effectiveness in dissolving each type of material (**Figure 4**).

The formulations have been stabilized by the presence of three products: Findet® 1214/N23 (KAO Chemicals Europe, Barcelona, Spain), comprised of a vegetablebased narrow-range ethoxylate with a C12-C14 fatty chain and 11 moles of ethylene oxide; and Glucopon® 600 (BASF, Barcelona, Spain), a non-ionic surfactant of the alkyl polyglycoside type, specifically a lauryl glucoside with 1.3 moles of glucose.

The cleaning compositions used contain, according to the response surface model, variable amounts of these substances that are statistically representative in all of their possible cleaning formulations. The concentration ranges for each component were Water and limonene: from 0 to 100%, Phenethyl alcohol: from 0 to 5%, Findet ® 1214/N23 and Glucopon® 600: from 0 to 10% [41].

*Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

**Figure 5.**

*Cleaning process of unaged mastic varnish on cadmium red oil with formulation N44.*

### *2.2.2 Cleaning trials*

The cleaning formulations were applied to the samples and allowed to act for 5 minutes. Afterwards, possible residues of the formulations were eliminated by washing with distilled water and subsequently White spirit (Talens). The process was repeated three times on each sample (**Figure 5**).

#### *2.2.3 Responses*

The cleaning was evaluated via seven possible sets of responses: the physical state, the chemical analysis via gas chromatography/mass spectrometry (GC/ MS), cleaning from the point of view of an expert's opinion (observed with visible light and ultraviolet light), and also how the cleaning affects the painting from an optical and colourimetric point of view (color, lightness and gloss). The complete description of the analytical study can be found in Bailón-Moreno et al. [41] (**Figures 6–8**).

## **3. Results and discussion**

#### **3.1 Validity of the model and most important factors**

In order to confirm the validity of the model, the predicted values for the model were compared with the values observed experimentally for each response, achieving very good concordance between the values observed empirically in the 72 experiments actually

#### **Figure 6.**

*Photographs with UV/(left) and oblique visible light (right) of the standard sample varnished with mastic on cadmium red oil after cleaning with formulation N44.*

#### **Figure 7.**

*Chromatogram of a standard sample composed of cadmium yellow oil and aged mastic varnish after cleaning with formulation N21. The peaks corresponding to the fatty acids are observed as main markers of the oil on the left (azelaic acid tR:7, palmitic acid tR:11.1, oleic acid tR:12.78 and stearic acid tR:13.02) and to the triterpenic resin acids as main resin markers on the right (ursonic acid tR:23.53, ursolic acid tR:23.97, moronic acid tR:25.99 and oleanonic acid tR:26.37).*

*Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

#### **Figure 8.**

*Gloss measurement of reference white (left) and zinc white varnished with mastic (right).*

carried out, and those predicted with the model. The absolute and relative errors were also calculated, correlating the latter with the experiments' order of implementation (run) so as to discard any bias related to the way and order in which they were implemented. Equally, they were correlated with the value of each response, either in their observed values or in their predicted values, so as to also discard any possible bias [41].

MODDE Go® provides an indicator based on the relative weight of each factor or a combination of factors over all of the responses as a whole, called VIP (Variable Importance in Projection). In the oil painting cleaning model and as the most important factors, the following stand out in order of importance:


The main factors that affect the cleaning process with the formulations proposed are water and limonene, as well as their synergies, antagonisms and quadratic terms. The concordance between the polarity of solvents and solutes is the fundamental matter in cleaning polychromies. Water acts as a modulator of polarity whereas limonene is a moderator of non-polarity, so their proportion in mixtures is decisive in the cleaning effect, as predicted by the model.

### **3.2** *In silico* **cleaning simulations**

After establishing the response surface model for cleaning varnishes on oil and having confirmed that the mathematical model is a good one, using the appropriate computer tools it is possible to carry out computer simulations, putting forward unlimited cleaning scenarios and analyzing them without having to carry them out physically. These types of techniques are often called "in silico", evoking the terms "in vivo" and "in vitro" common in the natural sciences and medicine.

The basis of these simulations has been created using the MODDE Go® 6.0 software, which allows triangular diagrams to be obtained that visually hold thousands of results in which all possible combinations of cleaner compositions have been simulated *in silico*, sweeping through all the ranges of concentrations of water, limonene, Findet® 1214/N23, Glucopon® 600 and phenethyl alcohol.

**Figure 9** shows an example of a triangle diagram. In this example, the main solvents (limonene and water) and the main surfactant (Findet 1214/N23) are located at the vertices of each triangle. Within a triangle, there are colored areas corresponding to the different responses given by each cleaner depending on the type of varnish and pigment. Each level corresponds to the scale of values for the response in question: expert opinion with ultraviolet lighting and visible light; O/V cleaning with GC-ME; affectation from color as a distance, dELab, in the CIELAB space; affectation from lightness, ∆L; and affectation from gloss, ∆G.

#### **Figure 9.**

*Example of a triangular diagram of the results from cleaning with acrylic varnish according to expert opinion with ultraviolet light. Aging (Yes), Varnish (Acrylic). Pigment: Cadmium Red. Glucopon® 600: 0.1%. Phenethyl alcohol 0.25%.*

## *Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

The example in **Figure 9** comes from cleaning an oil painting made using cadmium red as a pigment and varnished with acrylic varnish that has undergone an aging process. The cleaners that have been simulated contain all the possible compositions of water, limonene and Findet® 1214/N23 (up to 10%) within the established ranges, in this case maintaining a fixed concentration of 10% of Glucopon® 600 (the maximum concentration established in designing experiments) and 2.5% of phenethyl alcohol (intermediate concentration in designing experiments). The response shown on the color scale is the expert's opinion using ultraviolet light, UV. To help with the analysis, the bottom section of the triangle is shown, where the cleaner's area of action is to be found, given the proportions of its three main components.

The simulations that have been carried out using this system are as follows:


## **4. Conclusions**


## **Acknowledgements**

This research was funded by the following projects: *Desarrollo de Nuevas Sinergias Arte-Ciencia aplicadas a la Conservación y Restauración de los Palacios y Jardines de la Alhambra y el Generalife* (VIRARTE), MINECO, with reference HAR2016-79886-P; *Métodos sinérgicos Arte-Ciencia-Tecnología para la Conservación-Restauración de la Alhambra y otros Bienes Culturales* (VIRARTE II), MICINN, with referece PID2019- 109713RB-I00; *La aplicación de las algas procedentes de la Alhambra y el Generalife en técnicas artísticas y de conservación-restauración* (FICOARTE), Universidad de Granada, with reference A-HUM-279-UGR18. "Aplicación avanzada de las algas procedentes de la Alhambra y el Generalife en técnicas artísticas y de conservaciónrestauración", (FICOARTE 2) (PAIDI 2020) with reference P18-FR-4477.

## **Author details**

Julio Romero-Noguera1 \*, Nuria Pérez-Villares2 , Fernando Bolívar-Galiano2 and Rafael Bailón-Moreno3

1 Painting Department, Faculty of Fine Arts, University of Seville, Seville, Spain

2 Painting Department, Faculty of Fine Arts, University of Granada, Granada, Spain

3 Chemical Engineering Department, Faculty of Sciences, University of Granada, Granada, Spain

\*Address all correspondence to: juliorn@us.es

© 2022 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

*Response Surface Model Applied to Fine Arts: The Case of the Restoration of Paintings DOI: http://dx.doi.org/10.5772/intechopen.108514*

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## *Edited by Palanikumar Kayarogannam*

Response surface methodology (RSM) is the statistical and mathematical technique that lays its foundation of quality in any experiment and it aims to optimize the response. RSM is mainly used for modeling and optimization of process parameters. This book discusses advances in RSM and its applications. Chapters discuss topics such as cyclic generators for Box–Behnken Designs, the application of RSM for product design, and potential applications of RSM in manufacturing, food processing, the fine arts, and more.

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Response Surface Methodology - Research Advances and Applications

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