Section 5 Expert Systems

Chapter 5

Abstract

Methods

Mustafa B. Babanli

other problems are considered.

materials science is important to deal with big data.

1. Introduction

77

Fuzzy Logic and Fuzzy Expert

System-Based Material Synthesis

Analyzing a wide diversity of approaches to material selection and synthesis, one

Keywords: fuzzy logic, material synthesis, big data, fuzzy clustering, expert system

Development of new materials is one of important tasks of theoretical and practical interest. Traditionally, this task is implemented mainly on the basis of intensive (and sometimes "ad hoc") experiments which are time- and resource consuming or even not practically implementable. Nowadays, it is well understood that more systematic and effective approaches are needed which are based on computer-guided synthesis of materials. Such approaches rely on data-driven mathematical models and knowledge base obtained from big data previously collected during intensive experiments. Existing computational approaches include methods based on phase diagrams, simulation modeling, theory of associated solutions, methods of microstructure modeling, random fields, etc. In [1], authors analyze the way data-driven techniques are used in deciphering processingstructure-property-performance relationships in materials, with examples of forward (property prediction) and inverse (materials discovery) models. Such analysis can noticeably improve cost-effective materials discovery as the aim of Materials Genome Initiative (MGI). It is shown that adding data sciences to the paradigms of

Agrawal et al. [2] used the Japan National Institute for Materials Science (NIMS) MatNavi database [3] to develop models for prediction of fatigue strength of steel. Prediction accuracy is important for a number of applications due to the significant

can observe a tendency to shift research efforts from physical experiments to systematic analysis based on mathematical models and computational schemes. The latter, in turn, evolves from traditional analytical methods and computational schemes to modern approaches that are based on collaboration of fuzzy logic and soft computing, machine learning, big data and other new methods. In this study, emphasis is put on modeling of fuzzy relationship between performance of new materials and affecting factors. This chapter includes applications of fuzzy modelbased synthesis of different alloys. Fuzzy If-then rules based TiNiPt alloy synthesis problem, fuzzy expert system based synthesis of material for pressure vessel and

## Chapter 5

## Fuzzy Logic and Fuzzy Expert System-Based Material Synthesis Methods

Mustafa B. Babanli

## Abstract

Analyzing a wide diversity of approaches to material selection and synthesis, one can observe a tendency to shift research efforts from physical experiments to systematic analysis based on mathematical models and computational schemes. The latter, in turn, evolves from traditional analytical methods and computational schemes to modern approaches that are based on collaboration of fuzzy logic and soft computing, machine learning, big data and other new methods. In this study, emphasis is put on modeling of fuzzy relationship between performance of new materials and affecting factors. This chapter includes applications of fuzzy modelbased synthesis of different alloys. Fuzzy If-then rules based TiNiPt alloy synthesis problem, fuzzy expert system based synthesis of material for pressure vessel and other problems are considered.

Keywords: fuzzy logic, material synthesis, big data, fuzzy clustering, expert system

## 1. Introduction

Development of new materials is one of important tasks of theoretical and practical interest. Traditionally, this task is implemented mainly on the basis of intensive (and sometimes "ad hoc") experiments which are time- and resource consuming or even not practically implementable. Nowadays, it is well understood that more systematic and effective approaches are needed which are based on computer-guided synthesis of materials. Such approaches rely on data-driven mathematical models and knowledge base obtained from big data previously collected during intensive experiments. Existing computational approaches include methods based on phase diagrams, simulation modeling, theory of associated solutions, methods of microstructure modeling, random fields, etc. In [1], authors analyze the way data-driven techniques are used in deciphering processingstructure-property-performance relationships in materials, with examples of forward (property prediction) and inverse (materials discovery) models. Such analysis can noticeably improve cost-effective materials discovery as the aim of Materials Genome Initiative (MGI). It is shown that adding data sciences to the paradigms of materials science is important to deal with big data.

Agrawal et al. [2] used the Japan National Institute for Materials Science (NIMS) MatNavi database [3] to develop models for prediction of fatigue strength of steel. Prediction accuracy is important for a number of applications due to the significant complexity of fatigue testing and serious consequences of its failures. Actually, fatigue usually leads to more than 90% of all mechanical failures of structural components [4].

properties and synthesis of material for pressure vessel. Computer experiments of the proposed fuzzy models show better performance than the physical experiment-

The motivation to use fuzzy model is inspired by the necessity to construct an intuitively well-interpretable development strategy from imperfect and complex data. Analyzing a wide diversity of approaches to material selection and synthesis, one can observe a tendency to shift research efforts from physical experiments to systematic analysis based on mathematical models and computational schemes. The latter, in turn, evolutes from traditional analytical methods and computational schemes to modern approaches that are based on collaboration of fuzzy logic and soft computing, machine learning, big data, and other new methods. Uncertainty of materials properties requires to use fuzzy logic methods to more adequately model and predict possible material behavior. This will help to deal with imprecision of experimental data; partial reliability of experimental data, prediction results, and expert opinions; uncertainty of materials properties stemming from complex relationship between material components; and a necessity to analyze, summarize, and reason with a large amount of information of various types (numeric data, linguistic

Fuzzy logic methods have a good capability to effectively capture and process imprecise experimental data, that is, interpret, classify, learn, and compute with them. Fuzzy logic may help to improve abilities of big data principles to deal with a huge amount and variety of information. In this realm, fuzzy clustering and fuzzy logic-based knowledge bases and information search algorithms provide a bridge between complexity, imperfectness, qualitative nature of information, and research techniques. Particularly, this may help to get intuitive general interpretation of materials science results obtained by various techniques, and ways to get practical

Assume that big data on smart materials sourced from experiments is available. These big data describe relationship between alloy composition and its characteris-

The problem is to extract knowledge-based model from the considered data and to find an alloy composition which provides a predefined alloy characteristics. We will consider fuzzy knowledge-based synthesis model [17–20]. The problem is

First, fuzzy clustering of the big data is applied to determine fuzzy clusters

Second, fuzzy IF-THEN rule-based model is constructed from C1, C2,…, CK:

IF y<sup>1</sup> is Ak<sup>1</sup> and,…, and yn is Akn THEN z<sup>1</sup> is Bk<sup>1</sup> and,…,

Experiment Alloy composition (in %) Conditions Alloy characteristics # Metal 1, y<sup>1</sup> … Metal n, yn Cond.1 … Cond. l Char. 1, z<sup>1</sup> … Char. m, zm 1 y<sup>11</sup> … y1<sup>n</sup> T<sup>11</sup> … T1<sup>l</sup> z<sup>11</sup> … z1<sup>m</sup>

s ys<sup>1</sup> … ysn Ts<sup>1</sup> … Tsl zs<sup>1</sup> … zsm

⋮ ⋮

Big data of relationship between alloy composition and its characteristics.

2. Statement of material synthesis problem and solution methods

Fuzzy Logic and Fuzzy Expert System-Based Material Synthesis Methods

DOI: http://dx.doi.org/10.5772/intechopen.84493

information, graphical information, geometric information, etc.).

results would be then more evident.

tics (Table 1) [13, 15, 16].

solved as follows [21].

C1, C2,…, CK.

Table 1.

79

based analysis.

In [5], the authors processed the materials properties database for selecting and designing high-temperature alloys for solid oxide fuel cell (or SOFC) applications. Also, this work considers the selection of alloy compositions and properties, which are relevant to the SOFC application. The alloys of interest included such hightemperature alloys as Co, Ni, and Fe base superalloys, as well as stainless steels and Cr base alloys.

The fusion of clustering and regression methods with optimization approaches provides a new opportunity for materials discovery and design. In [6], they discuss the challenges and opportunities associated with materials research. The work [7] for the first time represents machine learning-based determination of viable new compound from true chemical white space, whereas no characterization was provided by promising chemistries. The authors consider an effective prediction model for materials properties that may be easily accessible and useful for researchers.

Existing works based on classical computational schemes used for material synthesis and selection provided good results. However, one important issue related to big data-based computerized material synthesis is that experimental data include measurement errors, partially reliable information, imprecise evaluations, etc. This mandates the use of fuzzy logic approaches for material synthesis. Let us consider some existing works in this regard.

Papers [8–10] show the necessity to account for nonlinearity and uncertainty factors that characterize modeling of material design problems. This requires searching for new ways in formalization of systematic approaches to material design. These papers are devoted to these factors.

Authors in [11] used a new combining tool with which it is possible to model and optimize new alloys that simultaneously satisfy up to 11 physical criteria. To develop a new polycrystalline nickel-base superalloy with the optimal combination of cost, density, gamma-primary phase and sol content, phase stability, durability, yield point, tensile strength, stress rupture, oxidation resistance, and elongation.

In [12], they have developed a rule-based fuzzy logic model for predicting shear strength of Ni-Ti alloy specimens which were produced using powder metallurgy method.

In [13], they applied the fuzzy set theory to knowledge mining from big data on material characteristics. The authors propose fuzzy clustering-generated If-Then rules as a basis for computer synthesis of new materials. These fuzzy If-Then rules describe relationship between material composition and material properties. Validity of the proposed approach is verified on an example of prediction properties of Ti-Ni alloy, and computer experiments of the proposed fuzzy model show its better performance than the physical experiment-based analysis.

In [14], ANFIS model is used to describe the high-temperature deformation behavior of Ni-based superalloy. The inputs of the ANFIS model are deformation temperature, strain rate, and true strain, and the output is true stress. The optimal numbers and types of membership function for the input variables are found. The results show that the constructed ANFIS model is effective in predicting the considered behavior of the Ni-based superalloy.

In this chapter, we propose fuzzy If-Then rule-based model to predict properties of new materials. The model is constructed on the basis of fuzzy clustering of big data on dependence between material composition and related properties. The motivation to use fuzzy model is inspired by the necessity to construct an intuitively well-interpretable development strategy from imperfect and complex data. The proposed approach is applied to synthesis of Ti-Ni-X alloys with required

properties and synthesis of material for pressure vessel. Computer experiments of the proposed fuzzy models show better performance than the physical experimentbased analysis.

## 2. Statement of material synthesis problem and solution methods

The motivation to use fuzzy model is inspired by the necessity to construct an intuitively well-interpretable development strategy from imperfect and complex data. Analyzing a wide diversity of approaches to material selection and synthesis, one can observe a tendency to shift research efforts from physical experiments to systematic analysis based on mathematical models and computational schemes. The latter, in turn, evolutes from traditional analytical methods and computational schemes to modern approaches that are based on collaboration of fuzzy logic and soft computing, machine learning, big data, and other new methods. Uncertainty of materials properties requires to use fuzzy logic methods to more adequately model and predict possible material behavior. This will help to deal with imprecision of experimental data; partial reliability of experimental data, prediction results, and expert opinions; uncertainty of materials properties stemming from complex relationship between material components; and a necessity to analyze, summarize, and reason with a large amount of information of various types (numeric data, linguistic information, graphical information, geometric information, etc.).

Fuzzy logic methods have a good capability to effectively capture and process imprecise experimental data, that is, interpret, classify, learn, and compute with them. Fuzzy logic may help to improve abilities of big data principles to deal with a huge amount and variety of information. In this realm, fuzzy clustering and fuzzy logic-based knowledge bases and information search algorithms provide a bridge between complexity, imperfectness, qualitative nature of information, and research techniques. Particularly, this may help to get intuitive general interpretation of materials science results obtained by various techniques, and ways to get practical results would be then more evident.

Assume that big data on smart materials sourced from experiments is available. These big data describe relationship between alloy composition and its characteristics (Table 1) [13, 15, 16].

The problem is to extract knowledge-based model from the considered data and to find an alloy composition which provides a predefined alloy characteristics. We will consider fuzzy knowledge-based synthesis model [17–20]. The problem is solved as follows [21].

First, fuzzy clustering of the big data is applied to determine fuzzy clusters C1, C2,…, CK.

Second, fuzzy IF-THEN rule-based model is constructed from C1, C2,…, CK:


IF y<sup>1</sup> is Ak<sup>1</sup> and,…, and yn is Akn THEN z<sup>1</sup> is Bk<sup>1</sup> and,…,

Table 1. Big data of relationship between alloy composition and its characteristics.

complexity of fatigue testing and serious consequences of its failures. Actually, fatigue usually leads to more than 90% of all mechanical failures of structural

In [5], the authors processed the materials properties database for selecting and designing high-temperature alloys for solid oxide fuel cell (or SOFC) applications. Also, this work considers the selection of alloy compositions and properties, which are relevant to the SOFC application. The alloys of interest included such hightemperature alloys as Co, Ni, and Fe base superalloys, as well as stainless steels and

The fusion of clustering and regression methods with optimization approaches provides a new opportunity for materials discovery and design. In [6], they discuss the challenges and opportunities associated with materials research. The work [7] for the first time represents machine learning-based determination of viable new compound from true chemical white space, whereas no characterization was provided by promising chemistries. The authors consider an effective prediction model for materials properties that may be easily accessible and useful for researchers. Existing works based on classical computational schemes used for material synthesis and selection provided good results. However, one important issue related to big data-based computerized material synthesis is that experimental data include measurement errors, partially reliable information, imprecise evaluations, etc. This mandates the use of fuzzy logic approaches for material synthesis. Let us consider

Papers [8–10] show the necessity to account for nonlinearity and uncertainty factors that characterize modeling of material design problems. This requires searching for new ways in formalization of systematic approaches to material

Authors in [11] used a new combining tool with which it is possible to model and

In [13], they applied the fuzzy set theory to knowledge mining from big data on material characteristics. The authors propose fuzzy clustering-generated If-Then rules as a basis for computer synthesis of new materials. These fuzzy If-Then rules describe relationship between material composition and material properties. Validity of the proposed approach is verified on an example of prediction properties of Ti-Ni alloy, and computer experiments of the proposed fuzzy model show its better

In [14], ANFIS model is used to describe the high-temperature deformation behavior of Ni-based superalloy. The inputs of the ANFIS model are deformation temperature, strain rate, and true strain, and the output is true stress. The optimal numbers and types of membership function for the input variables are found. The results show that the constructed ANFIS model is effective in predicting the con-

In this chapter, we propose fuzzy If-Then rule-based model to predict properties of new materials. The model is constructed on the basis of fuzzy clustering of big data on dependence between material composition and related properties. The motivation to use fuzzy model is inspired by the necessity to construct an intuitively well-interpretable development strategy from imperfect and complex data. The proposed approach is applied to synthesis of Ti-Ni-X alloys with required

optimize new alloys that simultaneously satisfy up to 11 physical criteria. To develop a new polycrystalline nickel-base superalloy with the optimal combination of cost, density, gamma-primary phase and sol content, phase stability, durability, yield point, tensile strength, stress rupture, oxidation resistance, and elongation. In [12], they have developed a rule-based fuzzy logic model for predicting shear strength of Ni-Ti alloy specimens which were produced using powder metallurgy

components [4].

Fuzzy Logic

Cr base alloys.

method.

78

some existing works in this regard.

design. These papers are devoted to these factors.

performance than the physical experiment-based analysis.

sidered behavior of the Ni-based superalloy.

$$\text{and}\,z\_m\,\text{is}\,B\_{km}, k=1,...,K\tag{1}$$

No. Linguistic value TFN 1. Very low (VL) (3, 3, 13.5) (1) 2. Low (L) (3, 13.5, 24) (2) 3. Average (A) (13.5, 24, 34.5) (3) 4. High (H) (24, 34.5, 45) (4) 5. Very high (VH) (34.5, 45, 45) (5)

41 50 9 322.3 329.4 341.3 331.2 39 50 11 318.2 335.7 347.6 334.7 29 50 21 406.4 424.5 440.3 426.6 20 50 30 515.3 533.8 546.8 534.9

Composition Transformation temperatures

y2 (martensitic start temperature, K)

y3 (austenitic finish temperature, K)

y4 (austenitic start temperature, K)

y1 (martensitic finish temperature, K)

Fuzzy Logic and Fuzzy Expert System-Based Material Synthesis Methods

No. Linguistic value TFN 1. Very low (VL) (3, 3, 13.75) (1) 2. Low (L) (3, 13.75, 24.5) (2) 3. Average (A) (13.75, 24.5, 35.25) (3) 4. High (H) (24.5, 35.25, 46) (4) 5. Very high (VH) (35.25, 46, 46) (5)

No. Linguistic value TFN 1. Very low (VL) (0, 3.977, 19.2) 2. Low (L) (6.709, 18.6, 30.48) 3. Average (A) (14.53, 24.7, 34.86) 4. High 1 (H1) (21.16, 39.33, 57.51) 5. High 2 (H2) (20.88, 30.73, 40.59)

Table 3.

Table 2.

x1 (Ni, %)

x2 (Ti, %)

x3 (Pd, %)

DOI: http://dx.doi.org/10.5772/intechopen.84493

A big data fragment on Ti-Ni-Pd alloy composition [22].

Table 4.

Table 5.

81

Codebook for input 1 (Ni).

Codebook for input 2 (Pd).

Linguistic terms for input 1 (Ni).

Third, fuzzy inference is implemented on the basis of the fuzzy IF-THEN rules to compute optimal values B<sup>0</sup> 1,…, B<sup>0</sup> <sup>m</sup> of alloy characteristics z1, …, zm. The fuzzy inference is mainly based on composition of a fuzzy input information on material constituents (and other conditions) and fuzzy relation which describes fuzzy IF-THEN rules. A different approach to fuzzy reasoning also exists and is applied in case of scarce rule base. This is based on fuzzy inference by using similarity of fuzzy input information and antecedents of existing fuzzy rules; a resulting output is then computed as linear interpolation of fuzzy rule consequents.

By using fuzzy inference, optimal values B<sup>0</sup> 1,…, B<sup>0</sup> <sup>m</sup> are found as those closed to the ideal vector of characteristics <sup>B</sup><sup>∗</sup> <sup>¼</sup> <sup>B</sup><sup>∗</sup> <sup>1</sup> ; …; B<sup>∗</sup> m . For material synthesis, also fuzzy expert system approach is used. In this case, fuzzy expert system ESPLAN implements IF-THEN rule base obtained from fuzzy clustering of data.

The use of fuzzy rules and fuzzy inference provides us important tools for transition from intensive experiments which deal with a physical model to a fuzzy logic-based mathematical model. Further experiments are conducted not by using physical model but by using fuzzy logic-based mathematical model.

## 3. Material synthesis of Ti-Ni-X alloys by using ideal vector of characteristics

#### 3.1 Synthesis of Ti-Ni-Pd alloys with given characteristics

A problem of computational synthesis of Ti-Ni-Pd alloy with predefined characteristics is considered. A big data fragment describing dependence alloy composition and the corresponding characteristics is shown in Table 2.

A problem of computational synthesis is related to determination of alloy composition with corresponding values of the characteristics close to the target values:

$$z\_1 = (\text{302.3}), z\_2 = (\text{323.3}), z\_3 = (\text{347.1}), z\_4 = (\text{331.3})\tag{2}$$

Thus, <sup>B</sup><sup>∗</sup> <sup>¼</sup> <sup>B</sup><sup>∗</sup> <sup>1</sup> ; B<sup>∗</sup> <sup>2</sup>; B<sup>∗</sup> 3 <sup>¼</sup> ð Þ ð Þ <sup>302</sup>:<sup>3</sup> ;ð Þ <sup>323</sup>:<sup>3</sup> ;ð Þ <sup>347</sup>:<sup>1</sup> ;ð Þ <sup>331</sup>:<sup>3</sup> can be considered as an ideal solution.

In order to describe relationship between alloy composition and the characteristics values, the fuzzy IF-THEN rules were obtained by using FCM clustering of the considered big data:

IF Ni is L and Pd is A2 THEN Mf is A and Ms is A and As is aand Af is A IF Ni is Aand Pd is A1 THEN Mf is L and Ms is L2 and Af is L2 and As is L IF Ni is H2 and Pd is L1 THEN Mf is VL and Ms is VL and As is Land Af isVL, IF Ni is H1 and Pd is L2 THEN Mf is L and Ms is L and Af is L and As is L IF Ni is VH and Pd is VH THEN Mf is H and Ms is H and Af is VH and As is VH The codebooks for inputs are shown in Tables 3 and 4. The linguistic approximation of the inputs is shown in Tables 5 and 6. The codebooks for the outputs are shown in Tables 7–10.

Fuzzy Logic and Fuzzy Expert System-Based Material Synthesis Methods DOI: http://dx.doi.org/10.5772/intechopen.84493


#### Table 2.

and zm isBkm, k ¼ 1,…, K (1)

<sup>m</sup> of alloy characteristics z1, …, zm. The fuzzy

. For material synthesis, also

<sup>m</sup> are found as those closed to

Third, fuzzy inference is implemented on the basis of the fuzzy IF-THEN rules

1,…, B<sup>0</sup>

<sup>1</sup> ; …; B<sup>∗</sup> m

fuzzy expert system approach is used. In this case, fuzzy expert system ESPLAN

The use of fuzzy rules and fuzzy inference provides us important tools for transition from intensive experiments which deal with a physical model to a fuzzy logic-based mathematical model. Further experiments are conducted not by using

A problem of computational synthesis of Ti-Ni-Pd alloy with predefined characteristics is considered. A big data fragment describing dependence alloy compo-

A problem of computational synthesis is related to determination of alloy composition with corresponding values of the characteristics close to the target values:

In order to describe relationship between alloy composition and the characteristics values, the fuzzy IF-THEN rules were obtained by using FCM clustering of the

z<sup>1</sup> ¼ ð Þ 302:3 , z<sup>2</sup> ¼ ð Þ 323:3 , z<sup>3</sup> ¼ ð Þ 347:1 , z<sup>4</sup> ¼ ð Þ 331:3 (2)

<sup>¼</sup> ð Þ ð Þ <sup>302</sup>:<sup>3</sup> ;ð Þ <sup>323</sup>:<sup>3</sup> ;ð Þ <sup>347</sup>:<sup>1</sup> ;ð Þ <sup>331</sup>:<sup>3</sup> can be considered as

implements IF-THEN rule base obtained from fuzzy clustering of data.

physical model but by using fuzzy logic-based mathematical model.

3.1 Synthesis of Ti-Ni-Pd alloys with given characteristics

sition and the corresponding characteristics is shown in Table 2.

3. Material synthesis of Ti-Ni-X alloys by using ideal vector of

inference is mainly based on composition of a fuzzy input information on material constituents (and other conditions) and fuzzy relation which describes fuzzy IF-THEN rules. A different approach to fuzzy reasoning also exists and is applied in case of scarce rule base. This is based on fuzzy inference by using similarity of fuzzy input information and antecedents of existing fuzzy rules; a resulting output is then

1,…, B<sup>0</sup>

computed as linear interpolation of fuzzy rule consequents.

By using fuzzy inference, optimal values B<sup>0</sup>

the ideal vector of characteristics <sup>B</sup><sup>∗</sup> <sup>¼</sup> <sup>B</sup><sup>∗</sup>

to compute optimal values B<sup>0</sup>

Fuzzy Logic

characteristics

Thus, <sup>B</sup><sup>∗</sup> <sup>¼</sup> <sup>B</sup><sup>∗</sup>

considered big data:

80

IF Ni is L and Pd is A2

IF Ni is Aand Pd is A1

IF Ni is H2 and Pd is L1

IF Ni is H1 and Pd is L2

IF Ni is VH and Pd is VH

an ideal solution.

<sup>1</sup> ; B<sup>∗</sup> <sup>2</sup>; B<sup>∗</sup> 3

THEN Mf is A and Ms is A and As is aand Af is A

THEN Mf is L and Ms is L and Af is L and As is L

THEN Mf is L and Ms is L2 and Af is L2 and As is L

THEN Mf is VL and Ms is VL and As is Land Af isVL,

THEN Mf is H and Ms is H and Af is VH and As is VH The codebooks for inputs are shown in Tables 3 and 4.

The codebooks for the outputs are shown in Tables 7–10.

The linguistic approximation of the inputs is shown in Tables 5 and 6.

A big data fragment on Ti-Ni-Pd alloy composition [22].


#### Table 3.

Codebook for input 1 (Ni).


#### Table 4.

Codebook for input 2 (Pd).


#### Table 5.

Linguistic terms for input 1 (Ni).


#### Table 6.

Linguistic terms for input 2 (Pd).


the computational synthesis based on the fuzzy model uncovers the following alloy composition: Ni is about 19%, Ti is about 51%, and Pd is about 30% with the characteristics Mf = 347.78, about Ms = 364.86, about Af = 382.17, and As = 375.22.
