**4. Experimental steps**

**Experiment P1 P2 P3 P4 P5** 1 11111 2 12222 3 13333 4 21122 5 22233 6 23311 7 31213 8 32321 9 33132 10 11332 11 1 2 1 1 3 12 13221 13 2 1 2 3 1 14 2 2 3 1 2 15 2 3 1 2 3 16 3 1 3 2 3 17 3 2 1 3 1 18 3 3 2 1 2

*Assorted Dimensional Reconfigurable Materials*

**Table 3.**

**Table 4.**

**88**

*Complete plan of experiments as per L18 OA.*

*L18 orthogonal array.*

**SN Spray distance mm**

**Substrate rpm**

**Arc current A**

 75 150 300 20 25 75 250 400 30 35 75 350 500 40 50 125 150 300 30 35 125 250 400 40 50 125 350 500 20 25 175 150 400 20 50 175 250 500 30 25 175 350 300 40 35 10 75 150 500 40 35 75 250 300 20 50 75 350 400 30 25 13 125 150 400 40 25 14 125 250 500 20 35 15 125 350 300 30 50 16 175 150 500 30 50 17 175 250 300 40 25 18 175 350 400 20 35

**Carrier gas flow L/min**

**Powder flow rate g/min**

Al2O3-40%TiO2 powder from H C Starck, USA is utilized for coating for all the set of experiments. SS316 substrates are prepared with 27.5 mm diameter and 3 mm thickness plates and pieces of size 75 25 12 mm are prepared for coating so as to conduct the Abrasion test [7].

Each experiment is carried out with three substrate samples. The substrate samples are assembled in one specially fabricated cartridge [8]. To avoid nonuniformity in thickness, the substrate samples are ground to achieve relatively good finish. Later, sand blasting is carried out on the surface of all substrate samples to ensure proper removal of oxides and other impurities [9, 10]. For sand blasting, fused alumina of grit size 60 μm from Carborandum Universal is used [11, 12]. Al2O3-40% TiO2 powder is deposited on the substrates by using a controlled atmospheric plasma stray system of Metco USA through an SG 100 model Plasma Gun. To ensure the removal of moisture, the amalgamated powder is preheated before the plasma coating process up to 110°C [13].

As pre the L18 orthogonal array DoE, the experiments are conducted. The coating facility arrangement is shown in **Figure 1**. The parameters which are kept constant during the experiment are


The substrate samples are cleaned after the coating with ethanol and properly dried to eliminate accumulation of moisture [14]. As per ASTM B499-92014 [15], coating thickness is measured. An ultrasonic thickness gauge is used for this purpose. Using Mitutoyo surface roughness tester SV-C3100, surface roughness is measured as per ASTM D127 2013 [16]. The surface testing probe is applied on the coating surface for a length of 15 mm with a pitch of 0.001 mm. The scanning speed is kept constant at 2.0 mm/s. Microhardness is measured as per ASTM B 578-872,015 [17] by Metatech MVH-1. To measure porosity as well as microhardness, the samples are sectioned by wire cutting as well as slow speed grinding.

Later, molds are prepared using Bain mount-3 molding machine supplied by Chennai Matco. The substrate surfaces on the mold are polished with emery papers

**Figure 1.** *Coating facility arrangement.*

### *Assorted Dimensional Reconfigurable Materials*

ranging from 150 grit up to 2000 grit so as to get scale free and super finished surface. The porosity is measured using an Image Analysis Software as shown in **Figure 2**. The JPG images of the coatings are taken by using an electronic microscope OLIMBUS GX51 as per ASTM E2109-012014 [18]. A sample image of the sectioned coating surface is shown as **Figure 3**. Abrasion rate is measured on Abrasion test rig TR-50 as per ASTM G65 2000 [19] with 1000 g. as pre-load. **Figure 4** shows one of the abrasion test in progress. This test method covers laboratory procedures for determining the resistance of coating materials to scratching abrasion by means of the dry sand/rubber wheel test. Abrasion test results are reported as weight loss in grams for 20 revolutions of the wheel for a particular substrate. Materials of higher abrasion rate and high weight loss show a lower abrasion resistance.

**4.1 Details of coating output parameters**

*DOI: http://dx.doi.org/10.5772/intechopen.92175*

eters are shown below as Eqs. (1) and (2).

**No Mean coating thickness, μm**

**Table 5.**

**91**

*The values of measured output parameters–SS316.*

abrasion rate, and porosity % are given in **Table 5**.

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated…*

The measured values of coating thickness, surface roughness, microhardness,

To generate mathematical models for each of the output parameters, excel data analysis is used [18]. The mathematical models generated for all the output param-

R, Roughness ð Þ¼ μm 13*:*669392 þ 0*:*029373 � D � 0*:*007159 � N � 0*:*005758 � A

1 343.33 5.2 953 0.1602 14.2243 2 186.67 4.22 929 0.1322 11.5634 3 226.67 5.46 906 0.1998 13.2112 4 170 4.48 749 0.1023 18.0264 5 433.33 4.54 802 0.0601 11.4133 6 236.67 5.1 953 0.0855 9.5114 7 286.67 4.33 766 0.0973 14.7045 8 206.67 4.36 716 0.1022 18.9231 9 376.67 5.36 821 0.135 15.0654 10 366.67 4.72 766 0.0355 9.0012 11 516.67 4.35 841 0.0546 36.2234 12 600 4.74 841 0.0788 17.2133 13 416.67 4.36 821 0.0786 19.4231 14 476.67 4.39 802 0.0688 19.7324 15 323.33 4.42 821 0.1001 25.3381 16 346.67 3.95 802 0.1001 22.1099 17 203.33 5.43 766 0.1255 10.5224 18 283.33 5.03 784 0.0979 21.3422

þ 23*:*17571 � G þ 12*:*19609 � P þ 0*:*017778 � D � N

� 0*:*52605 � G � 0*:*093101 � P � 0*:*000006 � D � N � 0*:*000184 � D � A þ 0*:*001429 � D � G þ 0*:*00035 � D � P þ 0*:*000029 � N � A � 0*:*000099 � N � G þ 0*:*000056

� N � P þ 0*:*000789 � A � G � 0*:*000001 � A � P

**Mean microhardness HV**

**Mean abrasion rate, g**

þ 0*:*009069 � D � A þ 0*:*265778 � D � G þ 0*:*287119 � D � P þ 0*:*00872 � N � A � 0*:*02146 � N � G þ 0*:*015764 � N � P þ 0*:*019442 � A � G � 0*:*00704 � A � P � 1*:*40365 � G � P

(1)

(2)

**Mean porosity, %**

T, Thickness ð Þ¼ μm 1934*:*148 � 27*:*5317 � D � 4*:*39986 � N � 2*:*41271 � A

þ 0*:*000907 � G � P

**Mean surface roughness, μm**

**Figure 2.** *Measurement of porosity in progress.*

**Figure 3.** *Sample photograph of the sectioned coated surface.*

**Figure 4.** *Abrasion test in progress.*

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated… DOI: http://dx.doi.org/10.5772/intechopen.92175*

#### **4.1 Details of coating output parameters**

ranging from 150 grit up to 2000 grit so as to get scale free and super finished surface. The porosity is measured using an Image Analysis Software as shown in **Figure 2**. The JPG images of the coatings are taken by using an electronic microscope OLIMBUS GX51 as per ASTM E2109-012014 [18]. A sample image of the sectioned coating surface is shown as **Figure 3**. Abrasion rate is measured on Abrasion test rig TR-50 as per ASTM G65 2000 [19] with 1000 g. as pre-load. **Figure 4** shows one of the abrasion test in progress. This test method covers laboratory procedures for determining the resistance of coating materials to scratching abrasion by means of the dry sand/rubber wheel test. Abrasion test results are reported as weight loss in grams for 20 revolutions of the wheel for a particular substrate. Materials of higher abrasion rate and high weight loss show a

lower abrasion resistance.

*Assorted Dimensional Reconfigurable Materials*

*Measurement of porosity in progress.*

*Sample photograph of the sectioned coated surface.*

**Figure 2.**

**Figure 3.**

**Figure 4.**

**90**

*Abrasion test in progress.*

The measured values of coating thickness, surface roughness, microhardness, abrasion rate, and porosity % are given in **Table 5**.

To generate mathematical models for each of the output parameters, excel data analysis is used [18]. The mathematical models generated for all the output parameters are shown below as Eqs. (1) and (2).

$$\begin{array}{l} \text{T, thickness } (\mu\text{m}) = \textbf{1934.148} - \textbf{2.5317} \times \textbf{D} - \textbf{4.39986} \times \textbf{N} - \textbf{2.41271} \times \textbf{A} \\ \quad + \textbf{2.37571} \times \textbf{G} + \textbf{12.19609} \times \textbf{P} + \textbf{0.01778} \times \textbf{D} \times \textbf{N} \\ \quad + \textbf{0.009069} \times \textbf{D} \times \textbf{A} + \textbf{0.265778} \times \textbf{D} \times \textbf{G} + \textbf{0.287119} \times \textbf{P} \\ \quad + \textbf{0.00872} \times \textbf{N} \times \textbf{A} - \textbf{0.02146} \times \textbf{N} + \textbf{G} + \textbf{0.015764} \times \textbf{N} \times \textbf{P} \\ \quad + \textbf{0.019442} \times \textbf{A} \times \textbf{G} - \textbf{0.00704} \times \textbf{A} \times \textbf{P} - \textbf{1.40365} \times \textbf{G} \times \textbf{P} \\ \quad \text{(1)} \\ \textbf{R, Roughness } (\mu\text{m}) = \textbf{13.669392} + \textbf{0.029373} \times \textbf{D} - \textbf{0.007159} \times \textbf{N} - \textbf{0.005758} \times \textbf{A} \\ \quad - \textbf{0.52605} \times \textbf{G} - \textbf{0.093101} \times \textbf{P} - \textbf{0.000006} \times \textbf{D} \times \textbf{N} \\ \quad - \textbf{0.000184} \times \textbf{D} \times \textbf{A} + \textbf{0.001429} \times \textbf{D}$$

(2)


**Table 5.**

*The values of measured output parameters–SS316.*

H, Microhardness HV ð Þ¼ 2866*:*016 � 14*:*81975 � D � 5*:*535376 � N � 2*:*302965 � A � 6*:*870915 � G � 11*:*56905 � P þ 0*:*010359 � D � N � 0*:*002454 � D � A þ 0*:*207755 � D � G þ 0*:*180859 � D � P þ 0*:*010923 � N � A � 0*:*016017 � N � G þ 0*:*030724 � N � P þ 0*:*016899 � A � G þ 0*:*00575 � A � P � 0*:*54882 � G � P (3) A, Abrasion rate gð Þ¼ 0*:*84561453 þ 0*:*00023070 � D � 0*:*00160816 � N � 0*:*00127953 � A � 0*:*00654575 � G � 0*:*01238197 � P � 0*:*00000033 � D � N þ 0*:*00000114 � D � A � 0*:*00001169 � D � G � 0*:*00000214 � D � P þ 0*:*00000106 � N � A þ 0*:*00002805 � N � G þ 0*:*00001562 � N � P þ 0*:*00000362 � A � G þ 0*:*00002127 � A � P � 0*:*00001584 � G � P (4) P, Porosity %ð Þ¼ 43*:*36101115 � 0*:*55405377 � D þ 0*:*03082400 � N � 0*:*18845218 � A þ 1*:*40724984 � G þ 0*:*74786458 � P þ 0*:*00002005 � D � N þ 0*:*00120547 � D � A þ 0*:*00284447 � D � G � 0*:*00062184 � D � P � 0*:*00004973 � N � A � 0*:*00199498 � N � G þ 0*:*00226109 � N � P þ 0*:*00060184 � A � G þ 0*:*00091991 � A � P � 0*:*04473134 � G � P (5)

where, D = spray distance; N = substrate rpm; A = arc current; G = carrier gas flow rate; P = powder flow rate.

The values of roughness, abrasion rate and porosity are considered nonbeneficial and the values of thickness and hardness are considered as beneficial.

#### **4.2 Confirmation experiments**

For conducting confirmation tests, three trial samples of SS316 are used. The random values for all the input parameters, in between the maximum and


minimum levels are taken to conduct the confirmation tests. The predicted values using the proposed model along with the measured output parameters values for three samples are given in **Tables 6**–**10**. The percentage variation between the

80 170 315 25 30 21.33 18.52049 13.1802 95 190 425 35 40 20.01 18.41184 7.9868 140 200 480 35 45 9.56 10.53198 10.1532

To determine the effect each variable has on the output, the signal-to-noise ratio, or the SN number, needs to be calculated for each experiment conducted. In the equations below, yi is the mean value and si is the variance. yi is the value of the performance characteristic for a given experiment. More details about SN analysis is

SN ratio values for coating thickness on SS316 substrate are calculated for each

Spray distance has a significant effect on the coating thickness. Carrier gas flow is the next dominant parameter in the case of coating thickness. Similarly, SN ratio values are calculated for surface roughness for each parameter and level for all the output parameters as shown in **Table 12**. In the case of surface roughness, carrier

actual and predicted values are also shown in the tables.

given in https://google site sn analysis design of experiments.

parameter and level. The values are tabulated as shown in **Table 11**.

**5. SN analysis**

**93**

**Spray distance mm**

**Table 8.**

**Spray distance mm**

**Table 9.**

**Spray distance mm**

**Table 10.**

**Substrate rpm**

*DOI: http://dx.doi.org/10.5772/intechopen.92175*

**Arc current A**

*Measured and predicted values – Microhardness, SS316.*

*Measured and predicted values – Abrasion rate, SS316.*

*Measured and predicted values – Porosity %, SS316.*

**Arc current A**

**Arc current A**

**Substrate rpm**

**Substrate rpm**

**Carrier gas flow rate L/min**

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated…*

**Carrier gas flow L/min**

**Carrier gas flow rate L/min**

150 300 450 35 30 894 914.1079 2.2492 160 225 325 25 30 578 624.3352 8.0165 80 190 425 35 40 642 770.9902 20.0919

115 180 325 25 30 0.0911 0.088834 2.4868 120 215 425 35 40 0.0987 0.118253 19.8107 85 295 495 25 45 0.1265 0.125752 0.5911

**Powder flow rate g/min**

**Powder flow rate g/min**

> **Powder flow rate g/min**

**Hardness HV**

**Abrasion rate g**

> **Porosity %**

**Predicted values HV**

**Predicted values g**

**Predicted values %**

**% Variation**

**% Variation**

**% Variation**

**Table 6.**

*Measured and predicted values – Thickness, SS316.*


**Table 7.**

*Measured and predicted values – Roughness, SS316.*

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated… DOI: http://dx.doi.org/10.5772/intechopen.92175*


**Table 8.**

H, Microhardness HV ð Þ¼ 2866*:*016 � 14*:*81975 � D � 5*:*535376 � N � 2*:*302965

A, Abrasion rate gð Þ¼ 0*:*84561453 þ 0*:*00023070 � D � 0*:*00160816 � N

P, Porosity %ð Þ¼ 43*:*36101115 � 0*:*55405377 � D þ 0*:*03082400 � N � 0*:*18845218

þ 0*:*00091991 � A � P � 0*:*04473134 � G � P

where, D = spray distance; N = substrate rpm; A = arc current; G = carrier gas

For conducting confirmation tests, three trial samples of SS316 are used. The

150 300 450 35 30 278.33 306.8094 10.2322 160 225 325 25 30 206.33 218.2186 5.7619 80 190 425 35 40 322.67 296.4082 8.1388

**Powder flow rate g/min**

**Powder flow rate g/min**

100 200 350 25 40 4.23 4.476552 5.8286 150 300 450 35 30 4.38 5.264112 20.1852 160 225 325 25 30 5.02 5.577542 11.1064

**Coating thickness μm**

> **Coating roughness μm**

**Predicted values μm**

> **Predicted values μm**

random values for all the input parameters, in between the maximum and

**Carrier gas flow L/min**

**Carrier gas flow L/min**

The values of roughness, abrasion rate and porosity are considered nonbeneficial and the values of thickness and hardness are considered as beneficial.

flow rate; P = powder flow rate.

*Assorted Dimensional Reconfigurable Materials*

**4.2 Confirmation experiments**

**Substrate rpm**

*Measured and predicted values – Thickness, SS316.*

*Measured and predicted values – Roughness, SS316.*

**Arc current A**

**Substrate rpm**

**Arc current A**

**Spray distance mm**

**Table 6.**

**Table 7.**

**92**

**Spray distance mm**

� N þ 0*:*00120547 � D � A þ 0*:*00284447 � D � G

� A þ 1*:*40724984 � G þ 0*:*74786458 � P þ 0*:*00002005 � D

� 0*:*00062184 � D � P � 0*:*00004973 � N � A � 0*:*00199498 � N � G þ 0*:*00226109 � N � P þ 0*:*00060184 � A � G

þ 0*:*00575 � A � P � 0*:*54882 � G � P

� A � 6*:*870915 � G � 11*:*56905 � P þ 0*:*010359 � D � N � 0*:*002454 � D � A þ 0*:*207755 � D � G þ 0*:*180859 � D � P þ 0*:*010923 � N � A � 0*:*016017 � N � G þ 0*:*030724 � N � P þ 0*:*016899 � A � G

� 0*:*00127953 � A � 0*:*00654575 � G � 0*:*01238197 � P � 0*:*00000033 � D � N þ 0*:*00000114 � D � A � 0*:*00001169 � D � G � 0*:*00000214 � D � P þ 0*:*00000106 � N � A þ 0*:*00002805 � N � G þ 0*:*00001562 � N � P þ 0*:*00000362 � A � G þ 0*:*00002127 � A � P � 0*:*00001584 � G � P

(3)

(4)

(5)

**% variation**

**% Variation** *Measured and predicted values – Microhardness, SS316.*


**Table 9.**

*Measured and predicted values – Abrasion rate, SS316.*


**Table 10.**

*Measured and predicted values – Porosity %, SS316.*

minimum levels are taken to conduct the confirmation tests. The predicted values using the proposed model along with the measured output parameters values for three samples are given in **Tables 6**–**10**. The percentage variation between the actual and predicted values are also shown in the tables.

### **5. SN analysis**

To determine the effect each variable has on the output, the signal-to-noise ratio, or the SN number, needs to be calculated for each experiment conducted. In the equations below, yi is the mean value and si is the variance. yi is the value of the performance characteristic for a given experiment. More details about SN analysis is given in https://google site sn analysis design of experiments.

SN ratio values for coating thickness on SS316 substrate are calculated for each parameter and level. The values are tabulated as shown in **Table 11**.

Spray distance has a significant effect on the coating thickness. Carrier gas flow is the next dominant parameter in the case of coating thickness. Similarly, SN ratio values are calculated for surface roughness for each parameter and level for all the output parameters as shown in **Table 12**. In the case of surface roughness, carrier

gas flow has a significant effect. Substrate rpm is the next influencing parameter as per R value. The spray distance has a significant effect on the microhardness as shown in **Table 13**. The next dominant parameter in the case of microhardness is rpm. For coating abrasion rate, spray distance is the most dominating parameter and then comes the rpm as shown in **Table 14**. In the case of coating porosity % as


shown in **Table 15**, the most dominating parameter is carrier gas flow. The next

Level 1 23.62 23.88 25.24 24.94 23.18 Level 2 24.26 24.25 23.8 25.27 23.59 Level 3 24.39 24.15 23.23 22.07 25.51 Δ R 0.77 0.37 2.01 3.2 2.33 Rank 4 5 3 1 2

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated…*

**Spray distance Substrate rpm Arc current Carrier gas flow rate Powder flow rate**

An advanced optimization method, known as Teaching-Learning-Based Optimization (TLBO) is applied, to determine the best values of input parameters to obtain global optimum output parameters. TLBO is applied individually to each of the developed mathematical models given by Eqs. (1)–(5). Rao et al., proposed TLBO, which is based on the effect of influence of a teacher on the output of learners in a class. Teaching-learning ability of teacher and learners in a class room is mimicked in this algorithm [20, 21]. There are two modes of learning in this algorithm, interacting with other learners (known as learner phase) and through teacher (known as teacher phase).One of the attractive features of this algorithm is its algorithm-specific parameter-less concept. The algorithm is widely preferred among researchers due to its simplicity and its ability to provide the global optimum solutions in comparatively less number of function evaluations. Further details about the TLBO algorithm can be found at https://sites.google.com/site/tlborao. To execute TLBO algorithm for the optimisation of individual objective functions, a population size of 10 and 100 number of iterations with 30 independent runs is considered. The global optimum values for individual objective functions of T (Coating thickness), R (Surface roughness), H (Microhardness), Ab (Abrasion rate) and Po (Porosity %) obtained after applying TLBO are given in **Table 16**. Values obtained by applying the TLBO algorithm for the individual objective functions of T (Thickness), R (Roughness), H (Microhardness), Ab (Abrasion rate

**Optimum values of input parameters Value of the**

**Powder flow rate**

**function Spray**

**Carrier gas flow**

**Arc current**

Coating thickness 175 350 500 40 50 1068.8 μm Surface roughness 75 350 300 40 50 1.1503 μm Microhardness 175 350 500 40 50 1396 HV Abrasion rate 75.34 150 300 40 50 0.0073 g Porosity % 75 150 500 20 25 1.4935%

**objective**

**6. Application of teaching learning based optimization (TLBO)**

parameter which effects the most is powder flow rate.

*SN ratio matrix and ΔR values of porosity %, SS316.*

*DOI: http://dx.doi.org/10.5772/intechopen.92175*

**Table 15.**

**Objective function (Output parameter)**

**Table 16.**

**95**

**distance**

*Optimized output parameter values obtained by applying TLBO.*

**Substrate rpm**

#### **Table 11.**

*SN ratio matrix and ΔR values of coating thickness, SS316.*


#### **Table 12.**

*SN ratio matrix and ΔR values of coating roughness, SS316.*


#### **Table 13.**

*SN ratio matrix and ΔR values of microhardness, SS316.*


#### **Table 14.**

*SN ratio matrix and ΔR values of coating abrasion rate, SS316.*


*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated… DOI: http://dx.doi.org/10.5772/intechopen.92175*

**Table 15.**

gas flow has a significant effect. Substrate rpm is the next influencing parameter as per R value. The spray distance has a significant effect on the microhardness as shown in **Table 13**. The next dominant parameter in the case of microhardness is rpm. For coating abrasion rate, spray distance is the most dominating parameter and then comes the rpm as shown in **Table 14**. In the case of coating porosity % as

Level 1 50.73 49.83 49.58 50.7 49.77 Level 2 50.16 49.74 50.72 48.81 49.24 Lvel 3 48.83 50.15 49.42 50.2 50.71 Δ R 1.90 0.41 1.29 1.89 1.47 Rank 1 5 4 2 3

Level 1 13.56 13.05 13.72 13.47 13.71 Level 2 13.14 13.12 13.12 12.78 13.41 Level 3 13.46 13.99 13.32 13.9 13.03 Δ R 0.42 0.94 0.6 1.12 0.68 Rank 5 2 4 1 3

Level 1 58.79 58.14 58.3 58.55 58.45 Level 2 58.3 58.13 58.3 58.14 58.13 Level 3 57.79 58.61 58.28 58.19 58.3 Δ R 1.01 0.48 0.03 0.42 0.32 Rank 1 2 5 3 4

> **Arc Current**

Level 1 20.63 21.17 19.4 21.03 19.88 Level 2 21.82 21.39 21.1 19.87 21.2 Level 3 19.27 19.16 21.23 20.82 20.65 Δ R 2.55 2.23 1.84 1.16 1.32 Rank 1 2 3 5 4

**Carrier gas flow l/min**

**Powder flow rate g/min**

**Table 11.**

**Table 12.**

**Table 13.**

**Table 14.**

**94**

*SN ratio matrix and ΔR values of coating thickness, SS316.*

*Assorted Dimensional Reconfigurable Materials*

*SN ratio matrix and ΔR values of coating roughness, SS316.*

*SN ratio matrix and ΔR values of microhardness, SS316.*

*SN ratio matrix and ΔR values of coating abrasion rate, SS316.*

**Substrate rpm**

**Spray distance**

**Spray distance Substrate rpm Arc current Carrier gas flow rate Powder flow rate**

**Spray distance Substrate rpm Arc current Carrier gas flow rate Powder flow rate**

**Spray distance Substrate rpm Arc current Carrier gas flow rate Powder flow rate**

*SN ratio matrix and ΔR values of porosity %, SS316.*

shown in **Table 15**, the most dominating parameter is carrier gas flow. The next parameter which effects the most is powder flow rate.

### **6. Application of teaching learning based optimization (TLBO)**

An advanced optimization method, known as Teaching-Learning-Based Optimization (TLBO) is applied, to determine the best values of input parameters to obtain global optimum output parameters. TLBO is applied individually to each of the developed mathematical models given by Eqs. (1)–(5). Rao et al., proposed TLBO, which is based on the effect of influence of a teacher on the output of learners in a class. Teaching-learning ability of teacher and learners in a class room is mimicked in this algorithm [20, 21]. There are two modes of learning in this algorithm, interacting with other learners (known as learner phase) and through teacher (known as teacher phase).One of the attractive features of this algorithm is its algorithm-specific parameter-less concept. The algorithm is widely preferred among researchers due to its simplicity and its ability to provide the global optimum solutions in comparatively less number of function evaluations. Further details about the TLBO algorithm can be found at https://sites.google.com/site/tlborao.

To execute TLBO algorithm for the optimisation of individual objective functions, a population size of 10 and 100 number of iterations with 30 independent runs is considered. The global optimum values for individual objective functions of T (Coating thickness), R (Surface roughness), H (Microhardness), Ab (Abrasion rate) and Po (Porosity %) obtained after applying TLBO are given in **Table 16**.

Values obtained by applying the TLBO algorithm for the individual objective functions of T (Thickness), R (Roughness), H (Microhardness), Ab (Abrasion rate


#### **Table 16.**

*Optimized output parameter values obtained by applying TLBO.*

and Po (Porosity %) are 1068.8 μm, 1.1503 μm, 1396 HV, 0.0073 g, and 1.4935% respectively. For each of the output parameters, the corresponding values of process input parameters are also given in **Table 16**. It can be observed from **Table 16** that the optimum values of input parameters for getting optimum value of a particular objective (i.e., output parameter) are not the same for the other objectives. In real industrial situations, it is required to find the set of optimum values of input parameters that satisfies all the objectives simultaneously. Hence, the problem becomes a multi-objective problem with the ranges of the input parameters as constraints. In the current work, a combined objective function is formed considering all the five objectives simultaneously. This is called a priori approach of solving the multi-objective optimization problems.

�0*:*005758 � A � 0*:*52605 � G � 0*:*093101 � P � 0*:*000006 � D � N � 0*:*000184 � D � A þ 0*:*001429 � D � G þ 0*:*00035 � D � P þ 0*:*000029 � N � A � 0*:*000099 � N � G þ 0*:*000056 � N � P þ 0*:*000789 � A � G � 0*:*000001 � A � P þ 0*:*000907 � G

TLBO algorithm can be again applied on the combined objective function and after n number of iterations with independent runs to achieve the global optimum value of coefficient Zmax and the corresponding values of the optimum input

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated…*

In the field of atmospheric plasma coating with Al2O3-40%TiO2, mathematical modeling and its optimization is very rare. Mathematical models are generated in the present work using regression analysis for all the output parameters in terms of input parameters. The mathematical models developed will work as effective tools for manufactures to predict the effect of input parameters on output parameters within the considered ranges. Based on this model, they can take decisions and hence costly trials can be avoided to a very large extent. Confirmation tests are also carried out in the present work for each of the output parameters. The confirmation tests have given near about the same values compared to the predicted values and

The optimization is effectively carried out using teaching-learning-based optimization (TLBO) algorithm for each output parameter individually. A combined objective function is generated and this combined objective function can be again optimized using TLBO algorithm to get global optimum values of input parameters considering all the output parameters simultaneously. The TLBO algorithm has proved its effectiveness and simplicity in solving the multi-objective optimization problems. The AHP method is applied to decide the weights for the individual objective functions in the combined objective function in a systematic way and it takes into account the preferences of the decision maker. It is also concluded that a change in the weights of the individual objective functions in the combined objective function may give different sets of optimum values of input parameters.

(7)

� PÞ�

*DOI: http://dx.doi.org/10.5772/intechopen.92175*

parameters can be arrived.

the percentage of error is negligible.

**8. Conclusion**

**Author details**

**97**

Thankam Sreekumar Rajesh SVNIT, Surat, Gujarat, India

provided the original work is properly cited.

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

© 2020 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,

#### **7. Formation of combined objective function**

A pirori approach is used by forming a combined objective function, involving all the three objectives and this function is solved by applying TLBO algorithm for the given ranges of the input parameters.

$$\mathbf{Z\_{max}} = \boldsymbol{\alpha}\_{\Gamma} \ast \frac{\mathbf{T}}{\mathbf{T\_{max}}} + \boldsymbol{\alpha}\_{\mathbf{H}} \ast \frac{\mathbf{H}}{\mathbf{H\_{max}}} - \boldsymbol{\alpha}\_{\mathbf{Ab}} \ast \frac{\mathbf{Ab}}{\mathbf{Ab\_{min}}} - \boldsymbol{\alpha}\_{\mathbf{Po}} \ast \frac{\mathbf{Po}}{\mathbf{Po\_{min}}} - \boldsymbol{\alpha}\_{\mathbf{R}} \ast \frac{\mathbf{R}}{\mathbf{R\_{min}}} \tag{6}$$

The normalized weights of each output parameters are calculated using AHP (Arithmetic Hierarchy Method) [22] and these are ω<sup>T</sup> = 0.4027, ω<sup>R</sup> = 0.0694 ω<sup>H</sup> = 0.2595 ωAb = 0.1342 and ωPo = 0.1342. The weights are applied to combined objective function as given below in Eq. (7). For more details about AHP method pl. refer https://google site AHP Saaty.

Zmax ¼ ½ð0*:*4027*=*1068*:*8Þ � ð1934*:*148 � 27*:*5317 � D � 4*:*39986 � N �2*:*41271 � A þ 23*:*17571 � G þ 12*:*19609 � P þ 0*:*017778 � D � N þ 0*:*009069 � D � A þ 0*:*265778 � D � G þ 0*:*287119 � D � P þ 0*:*00872 � N � A � 0*:*02146 � N � G þ 0*:*015764 � N � P þ 0*:*019442 � A � G � 0*:*00704 � A � P � 1*:*40365 � G � PÞ� þ ½ð0*:*2595*=*1396Þ � ð2866*:*016 � 14*:*81975 � D � 5*:*535376 � N �2*:*302965 � A � 6*:*870915 � G � 11*:*56905 � P þ 0*:*010359 � D � N � 0*:*002454 � D � A þ 0*:*207755 � D � G þ 0*:*180859 � D � P þ 0*:*010923 � N � A � 0*:*016017 � N � G þ 0*:*030724 � N � P þ 0*:*016899 � A � G þ 0*:*00575 � A � P � 0*:*54882 � G � PÞ� � ð Þ 0*:*1342*=*0*:*0073 � ð0*:*84561453 þ 0*:*00023070 � D � 0*:*00160816 � N �0*:*00127953 � A � 0*:*00654575 � G � 0*:*01238197 � P � 0*:*00000033 � D � N þ 0*:*00000114 � D � A � 0*:*00001169 � D � G � 0*:*00000214 � D � P þ 0*:*00000106 � N � A þ 0*:*00002805 � N � G þ 0*:*00001562 � N � P þ 0*:*00000362 � A � G þ 0*:*00002127 � A � P � 0*:*00001584 � G � PÞ� � ½ð0*:*1342*=*1*:*4935Þ � ð43*:*36101115 � 0*:*55405377 � D þ0*:*03082400 � N � 0*:*18845218 � A þ 1*:*40724984 � G þ 0*:*74786458 � P þ 0*:*00002005 � D � N þ 0*:*00120547 � D � A þ 0*:*00284447 � D � G � 0*:*00062184 � D � P � 0*:*00004973 � N � A � 0*:*00199498 � N � G þ 0*:*00226109 � N � P þ 0*:*00060184 � A � G þ 0*:*00091991 � A � P � 0*:*04473134 � G � PÞ� � ½ð0*:*0694*=*1*:*1503Þ � ð13*:*669392 þ 0*:*029373 � D � 0*:*007159 � N

*An Experimental Investigation of Al2O3-40% TiO2 Powder Amalgamated… DOI: http://dx.doi.org/10.5772/intechopen.92175*

> �0*:*005758 � A � 0*:*52605 � G � 0*:*093101 � P � 0*:*000006 � D � N � 0*:*000184 � D � A þ 0*:*001429 � D � G þ 0*:*00035 � D � P þ 0*:*000029 � N � A � 0*:*000099 � N � G þ 0*:*000056 � N � P þ 0*:*000789 � A � G � 0*:*000001 � A � P þ 0*:*000907 � G � PÞ�

> > (7)

TLBO algorithm can be again applied on the combined objective function and after n number of iterations with independent runs to achieve the global optimum value of coefficient Zmax and the corresponding values of the optimum input parameters can be arrived.

#### **8. Conclusion**

and Po (Porosity %) are 1068.8 μm, 1.1503 μm, 1396 HV, 0.0073 g, and 1.4935% respectively. For each of the output parameters, the corresponding values of process input parameters are also given in **Table 16**. It can be observed from **Table 16** that the optimum values of input parameters for getting optimum value of a particular objective (i.e., output parameter) are not the same for the other objectives. In real industrial situations, it is required to find the set of optimum values of input parameters that satisfies all the objectives simultaneously. Hence, the problem becomes a multi-objective problem with the ranges of the input parameters as constraints. In the current work, a combined objective function is formed considering all the five objectives simultaneously. This is called a priori approach of

A pirori approach is used by forming a combined objective function, involving all the three objectives and this function is solved by applying TLBO algorithm for

� *<sup>ω</sup>*Ab <sup>∗</sup> Ab

The normalized weights of each output parameters are calculated using AHP (Arithmetic Hierarchy Method) [22] and these are ω<sup>T</sup> = 0.4027, ω<sup>R</sup> = 0.0694 ω<sup>H</sup> = 0.2595 ωAb = 0.1342 and ωPo = 0.1342. The weights are applied to combined objective function as given below in Eq. (7). For more details about AHP method pl.

Zmax ¼ ½ð0*:*4027*=*1068*:*8Þ � ð1934*:*148 � 27*:*5317 � D � 4*:*39986 � N

�2*:*41271 � A þ 23*:*17571 � G þ 12*:*19609 � P þ 0*:*017778 � D � N þ 0*:*009069 � D � A þ 0*:*265778 � D � G þ 0*:*287119 � D � P þ 0*:*00872 � N � A � 0*:*02146 � N � G þ 0*:*015764 � N � P þ 0*:*019442 � A � G � 0*:*00704 � A � P � 1*:*40365 � G � PÞ� þ ½ð0*:*2595*=*1396Þ � ð2866*:*016 � 14*:*81975 � D � 5*:*535376 � N �2*:*302965 � A � 6*:*870915 � G � 11*:*56905 � P þ 0*:*010359 � D � N � 0*:*002454 � D � A þ 0*:*207755 � D � G þ 0*:*180859 � D � P þ 0*:*010923 � N � A � 0*:*016017 � N � G þ 0*:*030724 � N � P þ 0*:*016899 � A � G þ 0*:*00575 � A � P � 0*:*54882 � G � PÞ�

� ð0*:*84561453 þ 0*:*00023070 � D � 0*:*00160816 � N �0*:*00127953 � A � 0*:*00654575 � G � 0*:*01238197 � P

� 0*:*00000033 � D � N þ 0*:*00000114 � D � A � 0*:*00001169 � D � G � 0*:*00000214 � D � P þ 0*:*00000106 � N � A þ 0*:*00002805 � N � G þ 0*:*00001562 � N � P þ 0*:*00000362 � A � G þ 0*:*00002127 � A � P � 0*:*00001584 � G � PÞ� � ½ð0*:*1342*=*1*:*4935Þ � ð43*:*36101115 � 0*:*55405377 � D þ0*:*03082400 � N � 0*:*18845218 � A þ 1*:*40724984 � G

þ 0*:*74786458 � P þ 0*:*00002005 � D � N þ 0*:*00120547 � D

� 0*:*00004973 � N � A � 0*:*00199498 � N � G þ 0*:*00226109 � N � P þ 0*:*00060184 � A � G þ 0*:*00091991 � A � P

� ½ð0*:*0694*=*1*:*1503Þ � ð13*:*669392 þ 0*:*029373 � D � 0*:*007159 � N

� A þ 0*:*00284447 � D � G � 0*:*00062184 � D � P

Ab min

� *<sup>ω</sup>*Po <sup>∗</sup> Po

Po min

� *<sup>ω</sup>*<sup>R</sup> <sup>∗</sup> <sup>R</sup>

Rmin

(6)

solving the multi-objective optimization problems.

**7. Formation of combined objective function**

<sup>þ</sup> *<sup>ω</sup>*<sup>H</sup> <sup>∗</sup> <sup>H</sup>

� ð Þ 0*:*1342*=*0*:*0073

� 0*:*04473134 � G � PÞ�

Hmax

the given ranges of the input parameters.

*Assorted Dimensional Reconfigurable Materials*

T max

refer https://google site AHP Saaty.

<sup>Z</sup> max <sup>¼</sup> *<sup>ω</sup>*<sup>T</sup> <sup>∗</sup> <sup>T</sup>

**96**

In the field of atmospheric plasma coating with Al2O3-40%TiO2, mathematical modeling and its optimization is very rare. Mathematical models are generated in the present work using regression analysis for all the output parameters in terms of input parameters. The mathematical models developed will work as effective tools for manufactures to predict the effect of input parameters on output parameters within the considered ranges. Based on this model, they can take decisions and hence costly trials can be avoided to a very large extent. Confirmation tests are also carried out in the present work for each of the output parameters. The confirmation tests have given near about the same values compared to the predicted values and the percentage of error is negligible.

The optimization is effectively carried out using teaching-learning-based optimization (TLBO) algorithm for each output parameter individually. A combined objective function is generated and this combined objective function can be again optimized using TLBO algorithm to get global optimum values of input parameters considering all the output parameters simultaneously. The TLBO algorithm has proved its effectiveness and simplicity in solving the multi-objective optimization problems. The AHP method is applied to decide the weights for the individual objective functions in the combined objective function in a systematic way and it takes into account the preferences of the decision maker. It is also concluded that a change in the weights of the individual objective functions in the combined objective function may give different sets of optimum values of input parameters.

#### **Author details**

Thankam Sreekumar Rajesh SVNIT, Surat, Gujarat, India

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

© 2020 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.
