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Fuzzy Logic Based Modelling of Cast Component Properties
9th IFAC Conference on Manufacturing Modelling, Management and 9th IFAC Conference on Manufacturing Modelling, Management and Control 9th IFAC Conference on Manufacturing Modelling, Management and Control 9th IFAC Conference on Manufacturing Modelling, Management and online at www.sciencedirect.com Berlin, Germany, August 28-30, 2019 Available Control 9th IFAC Conference on Manufacturing Modelling, Management and Berlin, Germany, August 28-30, 2019 Control Berlin, Germany, August 28-30, 2019 Control Berlin, Germany, August 28-30, 2019 Berlin, Germany, August 28-30, 2019
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IFAC PapersOnLine 52-13 (2019) 1132–1137
Fuzzy Fuzzy Fuzzy Fuzzy Fuzzy He He He He He
Logic Based Logic Based Logic Based Logic Based Component Logic Based Component Component Component ∗ Component
Modelling of Modelling of Modelling of Modelling of Properties Modelling of Properties Properties Properties ∗ Properties
Cast Cast Cast Cast Cast
Tan ∗ Vladimir Tarasov ∗ Anders E. W. Jarfors ∗∗ Tan Tarasov W. Jarfors ∗∗ ∗ Anders ∗∗ ∗∗ E. Tan ∗∗ Vladimir Vladimir Tarasov Salem Seifeddine ∗∗ E. W. Jarfors ∗∗ ∗ Anders Salem Seifeddine Tan Tarasov Anders ∗∗ E. W. Jarfors ∗∗ ∗ Vladimir ∗ Salem Seifeddine Tan Vladimir Tarasov Anders ∗∗ E. W. Jarfors Salem Seifeddine ∗ Seifeddine Computer Science ∗∗ and Informatics, ∗ Department ofSalem ∗ Department of Computer Science and Informatics, of Computer J¨ Science and Informatics, School of Engineering, onk¨ oping University, ∗ Department School of Engineering, J¨ o nk¨ oping University, of and Informatics, ∗ Department School Engineering, J¨ onk¨ nk¨ ping University, Boxof1026, 551 11 J¨ oScience ooping, Sweden Department of Computer Computer Science and Informatics, Box 1026, 551 11 J¨ o nk¨ o ping, Sweden School of Engineering, J¨ o nk¨ o ping University, Boxof1026, 551 11 J¨ oonk¨ ooping, School Engineering, J¨ nk¨ ping Sweden University, Box o o ∗∗ Box 1026, 1026, 551 551 11 11 J¨ J¨ onk¨ nk¨ oping, ping, Sweden Sweden ∗∗ Department of Materials and Manufacturing , ∗∗ Department of Materials and Manufacturing , Department of Materials and Manufacturing of Engineering, J¨ onk¨ oping University, , ∗∗School of Engineering, J¨ onk¨ oping University, Department of Materials and Manufacturing ∗∗School School Engineering, J¨ nk¨ ping University, ,, Boxof1026, 11 J¨ oonk¨ ooping, Sweden Department of551 Materials and Manufacturing Box 1026, 551 11 J¨ o nk¨ o ping, Sweden School of Engineering, J¨ o nk¨ o ping University, Boxof1026, 551 11 J¨ oonk¨ ooping, School Engineering, J¨ nk¨ ping Sweden University, Box 1026, 551 11 J¨ o nk¨ o ping, Sweden Box 1026, 551 11 J¨ onk¨ oping, Sweden
Abstract: Digitalization of manufacturing requires building models to represent accumulated Abstract: Digitalization of manufacturing requires building models to represent accumulated Abstract: Digitalization manufacturing requiresThe building representmodels accumulated data and knowledge on theofproducts and processes. use ofmodels formal to knowledge allows data and knowledge on the products and processes. The use of formal knowledge models allows Abstract: Digitalization of manufacturing requires building models to represent data and knowledge on the products and processes. The use of formal knowledge models allows for increaseDigitalization of the automation level leading to more sustainable Casting is Abstract: of manufacturing requires building modelsmanufacturing. to represent accumulated accumulated for increase of the level leading to more sustainable manufacturing. Casting is data and on products and processes. The use formal knowledge models allows for increase the automation automation level leading more sustainable manufacturing. Casting is important forof different industries because it to offers a great of designing for weight data and knowledge knowledge on the the products and processes. The use of offreedom formal knowledge models allows important for different industries because it offers aa great freedom of for weight for increase the automation level leading to more sustainable manufacturing. Casting is important forof industries because it to offers great of designing designing for weight reduction. paper presents an approach modelling of freedom cast component properties that for increaseThis of different the automation level leading to more sustainable manufacturing. Casting is reduction. This paper presents an approach to modelling of cast component properties that important for different industries because it offers a great freedom of designing for weight reduction. paper an because approach modelling cast component properties that is based onThis fuzzy logic.presents The approach includes learning of of the fuzzy inference rulesforfrom the important for different industries it tooffers a great freedom of designing weight is based onThis fuzzy logic. The includes learning of of the fuzzy inference rules from the reduction. an approach modelling is based fuzzypaper logic.presents The approach approach includes learning thecast fuzzy inference properties rulesprocess fromthat the data. Theonconstructed fuzzy logic canto used toof tune thecomponent manufacturing to reduction. This paper presents an models approach tobe modelling of cast component properties that data. The constructed fuzzy logic models can be used to tune the manufacturing process to is based on fuzzy logic. The approach includes learning of the fuzzy inference rules from data. Theon constructed logic models can be used toof tune theofmanufacturing process to produces cast components with desired properties. The evaluation the resultsrules demonstrates is based fuzzy logic.fuzzy The approach includes learning the fuzzy inference from the the produces cast components with desired properties. The evaluation of the demonstrates data. The constructed logic models can used to tune process to produces cast components desired properties. Theand evaluation ofmanufacturing the results results demonstrates that the accuracy of thefuzzy twowith created models are be 3.58% respectively with the learned data. The constructed fuzzy logic models can be used to 3.15% tune the the manufacturing process to that the accuracy of the two created models are 3.58% and 3.15% respectively with the learned produces cast components with desired properties. The evaluation of the results demonstrates that accuracy of the twowith created models are 3.58% and 3.15% with the learned fuzzythe inference rules being identical to the manually created ones. respectively The presented approach can produces cast components desired properties. The evaluation of the results demonstrates fuzzy inference rules being identical to the manually created ones. The presented approach can that accuracy of two created models are and with fuzzy rules being manually created ones. respectively TheCopyright presented approach can the c the help the toinference automate the management cast component manufacturing. 2019learned IFAC that the accuracy of the the twoidentical createdofto models are 3.58% 3.58% and 3.15% 3.15% respectively with the learned c help to automate the management of cast component manufacturing. Copyright 2019 IFAC fuzzy inference rules being identical to the manually created ones. The presented approach can c 2019 IFAC help toinference automate thebeing management manufacturing. fuzzy rules identicaloftocast the component manually created ones. TheCopyright presented approach can cc 2019 help to automate the management of cast component manufacturing. Copyright IFAC © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. help to automate the management of cast component manufacturing. Copyright 2019 IFAC Keywords: knowledge modelling, fuzzy logic, fuzzy systems, mechanical properties prediction Keywords: Keywords: knowledge knowledge modelling, modelling, fuzzy fuzzy logic, logic, fuzzy fuzzy systems, systems, mechanical mechanical properties properties prediction prediction Keywords: knowledge modelling, fuzzy logic, fuzzy systems, mechanical properties prediction Keywords: knowledge modelling, fuzzy logic, fuzzy systems, mechanical properties prediction 1. INTRODUCTION be considered when designing for weight reduction (Jarfors 1. INTRODUCTION INTRODUCTION be considered when designing for weight reduction (Jarfors 1. be al., considered when et 2010; Tian etdesigning al., 2002;for Daiweight et al.,reduction 2003): (Jarfors 1. INTRODUCTION et al., 2010; Tian et al., 2002; Dai et al., 2003): be considered when designing for weight reduction et al., 2010; Tian et al., 2002; Dai et al., 2003): 1. INTRODUCTION considered when designing for weight reduction (Jarfors (Jarfors The new concept of Integrated and Intelligent Manufac- be (1) Part design: manufacturability, material selection, et al., 2010; Tian al., 2003): The new new concept concept of of Integrated Integrated and and Intelligent Intelligent ManufacManufacal.,Part 2010;design: Tian et etmanufacturability, al., 2002; 2002; Dai Dai et et al., al., 2003): selection, material The turing stresses the importance of machine intelligence in et(1) (1) Part design: manufacturability, material selection, process selection and castability, microstructural varituring stresses theofimportance importance of machine machine intelligence in The new Integrated Intelligent Manufacprocess selection and vari(1) manufacturability, material turing stresses the intelligence in the area ofconcept advanced (Chen, 2017). The new concept of manufacturing Integrated ofand andsystems Intelligent Manufacprocess selection and castability, castability, microstructural microstructural variationsdesign: due to design (1) Part Part design: manufacturability, material selection, selection, the area of advanced manufacturing systems (Chen, 2017). turing stresses the importance of machine intelligence in ations due to design process selection and castability, microstructural varithe of advanced manufacturing (Chen, 2017). Thearea technology is shifting towards asystems knowledge intensive turing stresses the importance of machine intelligence in ations due to design (2) Imperfections: melt processing related defects, casting process selection and castability, microstructural variThearea technology is shifting shifting towards aasystems knowledge intensive the of manufacturing (Chen, 2017). (2) Imperfections: melt processing related defects, casting ations due to design The technology towards knowledge intensive focus, while the isaccumulation of knowledge bases is still the area of advanced advanced manufacturing systems (Chen, 2017). (2) Imperfections: melt processing related defects, casting process defects ations due to design focus,technology while the the accumulation accumulation of knowledge knowledge bases is still still The shifting a intensive process (2) focus, of bases is beingtechnology awhile challenge.is of manufacturing requires The is Digitalization shifting towards towards a knowledge knowledge intensive process defects defectsmelt (2) Imperfections: Imperfections: melt processing processing related related defects, defects, casting casting being a challenge. Digitalization of manufacturing requires focus, while the accumulation of knowledge bases is still Although, deterministic models are instrumental for the process defects being a challenge. Digitalization of manufacturing requires construction of models to represent gathered data focus, while the accumulation of knowledge bases is and still Although, processdeterministic defects models are instrumental for the construction of models to represent gathered data and being a challenge. Digitalization of manufacturing requires deterministic models are instrumental forfrom the design of cast components, imperfections resulting construction models to represent gatheredThe data knowledge onofthe products and processes. useand of Although, being a challenge. Digitalization of manufacturing requires design of cast components, imperfections resulting from Although, deterministic models are instrumental for the knowledge on the products and processes. The use of construction of models to represent gathered data and design of cast components, imperfections resulting melt treatment and casting process inherently display deterministic models arewill instrumental forfrom the knowledge onofthe products and for processes. useand of Although, formal knowledge models increase ofdata the auconstruction models to allows represent gatheredThe melt treatment and casting process will inherently display design of cast components, imperfections resulting from formal knowledge models allows for increase of the auknowledge on the products and processes. The use of melt treatment and casting process will inherently display a stochastic e.g.imperfections oxide films being discrete of castbehaviour, components, resulting from formal knowledge allows for increase of the tomation level to more sustainable manufacturing. knowledge on leading the models products and processes. The useauof design aa stochastic behaviour, e.g. oxide films being melt treatment and process will inherently display tomation level leading to sustainable manufacturing. formal models allows for of the stochastic behaviour, oxide films being discrete discrete particles of varying size e.g. formed during processing that treatment and casting casting process will inherently display tomation leading to more more sustainable manufacturing. Dopico knowledge etlevel al. (2016) point out that theincrease degree of formal knowledge models allows for increase of automathe auau- melt of varying size formed during processing that aparticles stochastic behaviour, e.g. oxide films being discrete Dopico et al. (2016) point out that the degree of automatomation level leading to more sustainable manufacturing. of in varying sizelocations formed during that willstochastic end up discrete but not processing inbeing a repeatable behaviour, e.g. oxide films discrete Dopico etlevel al. point outinthat degree of strategy. automa- aparticles tion plays an (2016) important the the Industry 4.0 tomation leading to role more sustainable manufacturing. will end up in discrete locations but not in a repeatable particles of varying size formed during processing that tion plays an important role in the Industry 4.0 strategy. Dopico et al. (2016) point out that the degree of automawill end (Campbell, up discrete but not in a repeatable fashion 2011). Additional variations in part of in varying sizelocations formed during processing that tion plays an important role the Industry 4.0 strategy. The use of al. intelligent technologies can make real in particles Dopico et (2016) point outinthat the degree ofimpact automafashion (Campbell, 2011). Additional variations in part will end up in discrete locations but not in aa repeatable The use of intelligent technologies can make real impact in tion plays an important role in the Industry 4.0 strategy. fashion (Campbell, 2011). Additional variations in part quality and accuracy of a simulation will result from a will end up in discrete locations but not in repeatable The use ofmanufacturing intelligent technologies can make real in fashion advanced by supplying machines with the tion plays an important role in the Industry 4.0impact strategy. quality and accuracy of aa Additional simulation will result from a (Campbell, 2011). variations in part advanced manufacturing by supplying supplying machines with the the The use of intelligent technologies can make real impact in quality and accuracy of simulation will result from number of parameters that cannot be uncontrolled in a fashion (Campbell, 2011). Additional variations in part advanced manufacturing by machines with capability learn from the data can andmake reason next The use of to intelligent technologies realabout impact in quality number of parameters that cannot be uncontrolled in a and accuracy of a simulation will result from capability to learn from the data and reason about next advanced manufacturing by supplying machines with the number of parameters cannot be will uncontrolled in a foundry and (Raza et al., 2017). The quality of available data accuracy ofthat a simulation result from capability to learn from the data and machines reason about steps in production. advanced manufacturing by supplying withnext the quality foundry (Raza et The quality of data number of that cannot be uncontrolled in a steps in in production. production. capability to foundry (Raza et al., al., 2017). 2017). The quality of 1available available also affects prediction capabilities. Table providesdata of parameters parameters that cannot be uncontrolled inan a steps capability to learn learn from from the the data data and and reason reason about about next next number also affects prediction capabilities. Table 1 provides an foundry (Raza et al., 2017). The quality of available data Casting is important for different industries because it foundry steps in also affects capabilities. Table provides an examples of prediction material performance variation in a part. It (Raza et al., 2017). The quality of 1available data steps in production. production. Casting is important for different industries because it examples of material performance variation in a It capabilities. Table provides an Casting is important different industries it also offers a great freedom for of designing for weightbecause reduction examples of prediction material performance in a part. part. It showsaffects inherent variations due to thevariation location the tensile also affects prediction capabilities. Table 11 of provides an offers aa great great freedom for of designing designing for weight weightbecause reduction Casting is important different it shows inherent variations due to the location of the tensile of material performance variation in a part. It offers freedom of for reduction (Jarfors et 2010). The automotive sector is the largest Casting is al., important for different industries industries because it examples shows inherent variations due to the location of the tensile bar and variations from different foundries producing the examples of material performance variation in a part. It (Jarfors et al., 2010). The automotive sector is the largest offers great freedom of designing weight reduction bar and variations from different foundries producing the inherent variations due to the location of the tensile (Jarfors et al., 2010). The is the largest user ofa weight cast components . sector The performance of shows offers alight great freedom of automotive designing11 for for weight reduction bar and variations from different foundries producing the castinginherent (Sigworth, 2011). due to the location of the tensile shows variations user of light weight cast components The performance of (Jarfors et al., 2010). The automotive is the largest 1 . sector casting (Sigworth, 2011). and variations from user light weight cast components . sector The performance of bar a castofcomponent depends on several1 factors, which should (Jarfors et al., 2010). The automotive is the largest casting bar and(Sigworth, variations 2011). from different different foundries foundries producing producing the the a component depends on which user light cast .. The of To create models of cast components, it is necessary to (Sigworth, 2011). a cast castof on several several1 factors, factors, which should should user ofcomponent light weight weightdepends cast components components The performance performance of casting casting (Sigworth, 2011). To create models of cast components, it is necessary to a models ofand castincomplete components, is necessary to dealcreate with uncertain datait collected during a cast cast component component depends depends on on several several factors, factors, which which should should To deal with uncertain and incomplete data collected during To create models of cast components, it is necessary to The research reported in this paper has been financed by grant deal with uncertain and incomplete data collected during the manufacturing process. Fuzzy logic is one of the To create models of cast components, it is necessary to The research reported in this paper has been financed by grant the manufacturing process. Fuzzy logic is one of the deal with uncertain and incomplete data collected during #20170066 fromreported the Knowledge Foundation (Sweden). the manufacturing process. Fuzzy logic is one of the The research in this paper has been financed by grant proposed methods to manage uncertainty, imprecision and deal with uncertain and incomplete data collected during #20170066 fromreported the Foundation (Sweden). proposed methods toprocess. manage uncertainty, imprecision and 1 The the manufacturing Fuzzy logic is the research in thisvehicle paper sales has been financed by grant OICAs statistics of Knowledge worldwide http://www.oica.net/ #20170066 fromreported the Knowledge Foundation (Sweden). proposed methods manage uncertainty, imprecision and incompleteness of to data (Zadeh, 1973). Fuzzy logicof a the manufacturing process. Fuzzy logic is one one ofhas the research in thisvehicle paper sales has been financed by grant 1 The OICAs statistics of Knowledge worldwide http://www.oica.net/ #20170066 from the Foundation (Sweden). 1 incompleteness of data (Zadeh, 1973). Fuzzy logic has a proposed methods to manage uncertainty, imprecision and category/sales-statistics/ OICAs statistics of worldwide vehicle sales http://www.oica.net/ #20170066 from the Knowledge Foundation (Sweden). incompleteness of data (Zadeh, 1973). Fuzzy logic has proposed methods to manage uncertainty, imprecision anda 1 OICAs statistics of worldwide vehicle sales http://www.oica.net/ category/sales-statistics/ 1 OICAs statistics of worldwide vehicle sales http://www.oica.net/ incompleteness of data (Zadeh, 1973). Fuzzy logic has category/sales-statistics/ incompleteness of data (Zadeh, 1973). Fuzzy logic has a a category/sales-statistics/
category/sales-statistics/ 2405-8963 © 2019 2019, IFAC IFAC (International Federation of Automatic Control) Copyright 1149Hosting by Elsevier Ltd. All rights reserved. Copyright 2019 IFAC 1149Control. Peer review© responsibility of International Federation of Automatic Copyright © under 2019 IFAC 1149 Copyright © 2019 IFAC 1149 10.1016/j.ifacol.2019.11.348 Copyright © 2019 IFAC 1149
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Table 1. Range of properties for one alloy cast by different foundries using a standardised mould from which 5 samples were taken. The variation at each location illustrated the variation between the foundries producing the casting.(Sigworth, 2011) Location
UTS (MPa)
YS (MPa)
Ef (%)
1 2 3 4 5
235–276 231–283 252–297 259–314 248–293
166–242 166–242 162–173 166–269 162–173
1.8–4 1.5–4.5 3–7.7 3.5–9.5 3–7.5
Fig. 1. Fuzzy logic system
successful record of industrial applications of fuzzy control in managing complex non-linear systems (Precup and Hellendoorn, 2011). Moreover, mechanical properties such as hardness and roughness of cast and metallic materials have been modelled with the help of fuzzy logic (Shabani et al., 2015; Zalnezhad et al., 2013; Barzani et al., 2015; Iqbal et al., 2007). This paper presents an approach to modelling of cast component properties that is based on fuzzy logic. The approach includes learning of the fuzzy inference rules to predict yield strength from the data. The constructed fuzzy logic models can be used to tune the manufacturing process by varying the chemical composition and solidification rate and examining the resulting mechanical property values. In the remainder of the paper, fuzzy logic systems are introduced in Sect. 2 together with related work. Sect. 3 presents details of experimental work to collect the data. Sect. 4 describes knowledge modelling with fuzzy logic and automatic extraction of inference rules. The results are discussed in Sect. 5 and the conclusions are presented in Sect. 6.
Fig 1 shows high level structure of a Fuzzy Logic System (FLS). It contains four components: fuzzifier, inference rules, inference engine, and defuzzifier. The fuzzifier maps crisp numbers into fuzzy sets. Inference rules are a collection of IF-THEN statements, e.g. “IF x1 is fast and x2 is very low, THEN y is average.” They represent the subjective knowledge in an application (Mendel, 1995). The inference engine performs a certain inference procedure based on the rules and derives a conclusion. It maps input fuzzy sets into output fuzzy sets. In applications where crisp numbers must be obtained as the output, the defuzzification step is necessary. It maps output fuzzy sets into crisp numbers. In the fuzzifier and defuzzifier, membership functions are used to map crisp numbers into fuzzy linguistic terms and vice versa. Both membership functions and if-then rules can be either acquired from domain experts or learned from numerical data. Often it is expensive to query a domain expert, or there may be no experts available when the FLS is built. Methods to automatically extract membership functions and rules from numerical data without the help of human experts can be found in many work. In the present work the rules are derived from the data using a method adapted from the one proposed in (Wang and Mendel, 1992) and the membership functions are defined manually by a knowledge engineer after examining the experimental data.
2. FUZZY LOGIC SYSTEMS Fuzzy logic has long been applied to industrial problems with successful results (Precup and Hellendoorn, 2011). However, very few studies have applied fuzzy logic in casting and metal industry. Several papers have been published on predicting surface roughness and hardness of cast and metallic components and predicting mechanical properties of non-metallic materials. There are only limited attempts to predict mechanical properties, such as yield strength, of cast components, which is the focus of this paper and then in particular the aluminum alloy A356 and linking the performance to process and microstructural in-data (Tarasov et al., 2019). Other methods such as Bayesian theory and artificial neural networks (ANN) have also have been applied to model and predict mechanical properties of industry materials as powerful tools to deal with uncertainties. In contrast to these methods, which often result in an opaque model, “black box”, a fuzzy logic model is a highly interpretable ”grey box” when Mamdani-type fuzzy model is applied (Hellendoorn and Driankov, 2012). This makes the fuzzy logic approach especially interesting for industrial applications as soon as model transparency is often required by the stakeholders for the model to be used at a working place.
3. CASTING AND TENSILE TESTING EXPERIMENTS The first phase of the experiments included melt preparation and casting. Seven Al – 7%Si – 0.4%Mg alloys were melt in a resistance furnace. Each alloy was modified with approximately 200–250 ppm Sr. A 200◦ C preheated permanent copper mould was used to cast cylindrical rods, which were then inserted into the Bridgeman furnace. The rods were remelted for 20 min. at 710◦ C and directionally solidified afterwards. Different microstructures can be produced by changing the speed of the furnace during the passage of molten rod during the cooling channels. Three different coarsenesses of the microstructure were directionally solidified for the present investigation. Each one has Secondary Dendrite Arm Spacing (SDAS) of approximately 10, 25 or 50 µm. Water cooling was used for high furnace speeds, 3 mm/s and 0.3 mm/s corresponding to SDAS of 10 and 25 µm respectively. While air was the cooling media was used for the 0.03 mm/s velocity that corresponds to SDAS of 50 µm. The next phase was tensile testing of the bars with a gauge length of 50 mm and a diameter of 7 mm that were machined from the directionally solidified rods. The constant strain rate of 0.5 mm/min was applied using
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defined for resulting yield strength. The systems were implemented using a fuzzy logic toolbox 2 for SciPy 3 .
Fig. 2. Knowledge modelling to support manufacturing of cast components a Zwick/Roell Z100 machine equipped with a 100 kN load cell and a clip-on 20 mm gauge length extensometer. The tests were carried out until fracture in a sample, using three tensile test bars for each condition. Only samples representing the potential of the alloy in term of tensile properties are presented, since the proposed directional solidification technology has proven to deliver optimal tensile test results due to excellent feeding during solidification, revealing the potential of studied alloys. In total two series of experiments were conducted. The first series was conducted on specimens cast with the alloy A356 — Al – 7%Si – 0.4%Mg – 0.25%Fe with variation of Cu. The second series was based on alloy A356 — Al – 7%Si – 0.4%Mg with variation of Si. In both series the solidification rate of the samples was varied as described above. Each experiment generated a data set on cast specimens that included variation of the chemical composition of cast alloys, i.e., percentage of Cu or Si, and variation in the casting process, i.e., SDAS.
As described in Sect. 3, the experiments provided two data sets. Each data set contains a set of input-output data pairs, {(x11 , x12 ; y 1 ), (x21 , x22 ; y 2 ), . . .}, where x1 represents SDAS, x2 represents the percentage of Cu or Si, and y represents the output YS. The first data set contained 67 data points. The data were divided into two parts: a training data set with 46 data points and a test data set with 21 data points. The second data set contained 52 data points. This data set was divided into two parts: a training data set with 36 data points and a test data set with 16 data points. The training data sets were used to create the fuzzy logic models, i.e. to define the membership functions for input and output linguistic variables (Sect. 4.1) and to learn fuzzy inference rules (Sect. 4.2). The prediction accuracy of the created fuzzy models were evaluated with the help of the test data sets (Sect. 5). 4.1 Linguistic variables and membership functions The Gaussian type was chosen for the membership functions of all the input and output variables, as it was considered to be the most adequate by the domain experts. The parameters of the membership functions (i.e. σ, which controls the width of the ”bell” of the curve, and c, which defines the position of the centre of the curve peak) are identified based on the examination of the data sets. The typical number of membership functions for a variable is between three and seven (Zalnezhad et al., 2013; Barzani et al., 2015; Chiang et al., 2008). The number of five membership functions was chosen for most variables because it allowed for good coverage of the variable ranges from the data sets. Only the coarsenesses of microstructure was measured with three distinct values, which required three membership functions to represent them. The examination of the training data sets included two steps:
4. FUZZY LOGIC REPRESENTATION OF MECHANICAL PROPERTIES OF CAST COMPONENTS The overview of the approach to fuzzy logic modelling is shown in Fig 2. The process of manufacturing of cast components has several parameters such as the chemical composition of alloy or the rate of solidification. These parameters may affect the mechanical properties of cast components. The data collected during the manufacturing process is used to create a fuzzy logic system. This system provides the mapping between the input parameters and the output properties, and can predict values of yield strength and other mechanical properties. The predicted values together with the input parameters are utilised to improve the manufacturing process. In the current work, two fuzzy logic systems were built to predict yield strength of a cast component, as soon as two different additives, Cu and Si, were used. The created systems are based on multiple-input-single-output mamdani-type fuzzy model. There are two inputs for each fuzzy logic system: ”SDAS”, representing microstructure coarseness, and ”Cu”, representing the percentage of Cu (for the first data set), or ”Si”, representing the percentage of Si (for the second data set). The output is ”YS” was
(1) Compilation of the existing values of an input/output (a process parameter or mechanical property) in a list and sorting it to determine the range of the variable. (2) Partitioning of the value list into segments to determine the number of memberships functions (linguistic labels) for a variable and the parameters, i.e. σ and c, for each membership function. The size of each partition was chosen to encompass a few values and the overall partitioning were confirmed by the domain experts. The linguistic variables and membership functions for each variable are shown in Fig. 3. Finally, the utilised aggregation method was max and the defuzzification method was centroid. 4.2 Fuzzy inference rules For each fuzzy logic system a set of two-input one-output inference rules were generated. The rules were first identified as ”and” rules (i.e., logical conjunction, which is denoted as &) by a knowledge engineering expert. Then 2 3
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Fig. 3. Membership functions for the input and output parameters. For each function the x-axis indicates input values and the y-axis indicates their corresponding degree of membership. rules were automatically generated from the training data using a method adapted from the one proposed in Wang and Mendel (1992). The method consists of three steps:
Table 2. The fuzzy inference rules generated from the first training data set. No. 1 2 3 4 5 6 7 8 9 10 11
1) Generate a rule for each input-output data pair (x1 , x2 ; y) in training data: IF xi1 is A and xi2 is B, THEN y i is C, where µA (xi1 ), µB (xi2 ), and µC (y i ) are membership functions with the maximum membership degree for each respective value. For example, as shown in Fig 4, xi2 has degree 0.8 in ”little”, 0.2 in ”very little”, and 0 in other regions, therefore xi1 is considered to be ”little”. In Fig 4 xi1 is considered to be ”average”, and y i is considered to be ”average”. The rule obtained from the input-output data pair is: IF xi1 is average and xi2 is little, THEN y i is average. 2) Calculate a degree for each rule: D(rulei ) = µA (xi1 ) × µB (xi2 ) × µC (y)i
For example, the degree for the rule above is 0.48, since D(rulei ) = 1 × 0.8 × 0.6 = 0.48.
3) Generate the final list of rules
If there is more than one rule with the same antecedent, the rule that has the maximum degree is selected into the final list. For example, Rule 1: IF xi1 is A and xi2 is B, THEN y i is C1, and the degree for rule 1 is 0.48. Rule 2: IF xi1 is A and xi2 is B, THEN y i is C2, and the degree of rule 2 is 0.52 Then, rule 2 is selected into the final list of the rules, since it has higher degree than rule 1.
Antecedent (SDAS==coarse) & (Cu==very-little) (SDAS==fine) & (Cu==very-little) (SDAS==average) & (Cu==very-little) (SDAS==coarse) & (Cu==little) (SDAS==fine) & (Cu==little) (SDAS==average) & (Cu==little) (Cu==average) (Cu==much) (SDAS==fine) & (Cu==very-much) (SDAS==coarse) & (Cu==very-much) (SDAS==average) & (Cu==very-much)
Consequent (YS=very-low) (YS=low) (YS=low) (YS=low) (YS=average) (YS=average) (YS=average) (YS=average) (YS=high) (YS=high) (YS=very-high)
This method for learning rules from data is general, simple and straightforward. The method was implemented in Python. It performed fast. It significantly reduced the time and effort needed to built the systems. Tables 2 and 3 present the rules that were generated from the training data using the algorithm. The quality of the rules was evaluated by comparing to the sets of rules manually created by a knowledge engineer (which are presented in Tarasov et al. (2019)). The rules generated using the presented method are identical to the rules manually created. 5. EVALUATION OF THE MODEL ACCURACY The prediction accuracy of the constructed fuzzy logic systems was evaluated with the help of the test data sets. The evaluation results are presented in Table 4 for the first test data set and in Table 5 for the second test data set. The prediction error was measured using Mean Absolute Percentage Error (MAPE) (De Myttenaere et al., 2016). It is computed by dividing the absolute difference of the
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Fig. 4. The degrees of xi1 , xi2 and y i in membership functions. Table 4. Evaluation of the model accuracy for the first test data set
Table 3. The fuzzy inference rules generated from the second training data set. No. 1 2 3 4 5 6 7 8 9 10
Antecedent (SDAS==coarse) & (Si==little) (SDAS==coarse) & (Si==average) (SDAS==coarse) & (Si==much) (Si==very-little) (SDAS==average) (SDAS==coarse) & (Si==very-much) (SDAS==fine) & (Si==little) (SDAS==fine) & (Si==average) (SDAS==fine) & (Si==much) (SDAS==fine) & (Si==very-much)
Consequent (YS=very-low) (YS=very-low) (YS=very-low) (YS=low) (YS=low) (YS=low) (YS=average) (YS=high) (YS=very-high) (YS=very-high)
Sample AA13 AA23 AA33 AB13 AB22 AB32 AC11 AC21 AC31 AD13 AD23 AD33 AE12 AE32 AF31 AG14 AG23 AG33 AI12 AI23 AI32 MAPE
predicted and measured values by the absolute value of the measured value and averaging this ratio over the data. MAPE is given at the bottom of each table and it is 3.58% for the first fuzzy logic model and 3.15% for the second model. The first column in each table contains the designation of a casting component from the test data sets. Both tables show the percentage of Cu/Si and SDAS, which are the input values to the fuzzy logic models, as well as the measured value of yield strength in the next three columns. The values predicted by the fuzzy systems are shown in the fifth column of each table. The last column contains a (signed) percentage error for each pair of predicted and measured values.
This paper has proposed a fuzzy logic based approach to modelling of mechanical properties of cast components. The fuzzy logic models are constructed with the help of the data collected during the manufacturing process. The approach includes learning of the fuzzy inference rules from
SDAS 10 20 50 10 20 50 10 20 50 10 20 50 10 50 50 10 20 50 10 20 50
YS(M) 125.44 125.51 113.06 133.59 135.94 117.57 144.96 145.11 129.44 144.20 157.29 139.01 151.14 141.50 152.20 166.83 173.85 170.86 194.70 202.88 189.74
YS(P) 135.02 135.03 116.41 135.64 135.64 118.02 145.58 145.58 129.51 156.37 155.92 135.03 157.76 136.79 159.84 160.00 160.00 160.00 184.40 191.29 184.29
Err(%) 7.65 7.58 2.97 1.54 -0.22 0.39 0.43 0.33 0.05 8.13 -0.87 -2.86 4.29 -3.32 5.02 -4.10 -7.97 -6.36 -5.29 -2.9 -2.87 3.58
Table 5. Evaluation of the model accuracy for the second test data set Sample AIA13 AIA23 AIA33 AIB13 AIB23 AIB33 AIC13 AIC33 AID13 AID33 AIE13 AIE23 AIE32 AIF13 AIF23 AIF33 MAPE
The related work reports the prediction accuracy of the fuzzy logic based systems that is similar to the prediction errors of the constructed fuzzy logic systems. The prediction errors were also discussed with the domain experts, who considered the error level as acceptable. While the performance of the fuzzy logic systems is good, it is worth noting that this work is one of the first steps on modelling of yield strength of cast components. Small data sets were used to create the models. The prediction accuracy may be different if bigger data sets are used for the modelling. Moreover, the procedure of data collection at a particular lab or foundry could affect the performance of the fuzzy logic models due to variations in measurement accuracy or unaccounted differences in the cast process. One example of such variation is given in Table 1 . 6. CONCLUSIONS
Cu 0 0 0 0.6 0.6 0.6 1 1 1 1.5 1.5 1.5 1.7 1.7 2.5 3.5 3.5 3.5 5.5 5.5 5.5
Si 7 7 7 10 10 10 11.5 11.5 12.5 12.5 13 13 13 14.5 14.5 14.5
SDAS 10 20 50 10 20 50 10 50 10 50 10 20 50 10 20 50
YS(M) 125.44 125.51 113.06 161.20 132.35 108.67 168.94 115.77 180.14 110.40 176.33 136.41 110.99 176.03 128.38 118.65
YS(P) 127.61 127.61 127.52 148.63 130.16 110.95 168.0 110.61 173.80 111.11 175.82 130.88 110.90 176.19 130.45 127.36
Err(%) 1.74 1.67 12.79 -7.79 -1.65 2.09 -0.56 -4.45 -3.52 0.64 -0.29 -4.05 -0.08 -0.09 1.61 7.34 3.15
the data after manual creation of memberships functions. The created fuzzy logic systems map the casting process parameters to the mechanical properties of produced cast components and are capable of predicting particular values of yield strength. The fuzzy inference rules learned from the data are identical to the manually created rules. The evaluation of the accuracy of the two constructed knowledge models demonstrates the error level of 3.58%
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and 3.15% respectively, which is similar to the error level reported in the related work. The proposed approach to modelling of cast components can support the manufacturing process at foundries by providing formal models relating the input process parameters to the output cast properties. The use of such knowledge models can alleviate resource and time intensive tensile testing of cast components. Moreover, the biggest part of the model construction — extraction of fuzzy inference rules — can be automated. Hence, the proposed approach contributes to the digitalization of the foundry industry. Future work is two fold. Firstly, the fuzzy logic models will be extended by incorporating other mechanical properties of cast components, such as ultimate tensile strength, elongation to failure and Young’s modulus, which are of interest for industry stakeholders and are important for the management of cast component manufacturing. Secondly, various methods will be further explored to automate definition of membership functions and generation of fuzzy inference rules from training data. Many methods to automatically extract membership functions and rules from numerical data without the help of human experts can be found in literature. Different methods will be evaluated by using them to build fuzzy logic systems for predicting mechanical properties of cast components. The trade-off between interpretability and accuracy will also be studied when the models are built from empirical data. Furthermore, cooperating with industry stakeholders, more extensive laboratory test data are expected to be obtained for fuzzy logic modelling and evaluation in the future. REFERENCES Barzani, M.M., Zalnezhad, E., Sarhan, A.A., Farahany, S., and Ramesh, S. (2015). Fuzzy logic based model for predicting surface roughness of machined Al-Si-CuFe die casting alloy using different additives-turning. Measurement, 61(Supplement C), 150–161. doi:10.1016/ j.measurement.2014.10.003. Campbell, J. (2011). Complete Casting Handbook: Metal Casting Processes, Techniques and Design. Butterworth-Heinemann, Oxford. Chen, Y. (2017). Integrated and intelligent manufacturing: Perspectives and enablers. Engineering, 3(5), 588–595. doi:10.1016/j.eng.2017.04.009. Chiang, K.T., Liu, N.M., and Chou, C.C. (2008). Machining parameters optimization on the die casting process of magnesium alloy using the grey-based fuzzy algorithm. The International Journal of Advanced Manufacturing Technology, 38(3), 229–237. doi:10.1007/ s00170-007-1103-z. Dai, X., Yang, X., Campbell, J., and Wood, J. (2003). Effects of runner system design on the mechanical strength of Al-7Si-Mg alloy castings. Materials Science and Engineering: A, 354(1), 315–325. doi:10.1016/ S0921-5093(03)00021-2. De Myttenaere, A., Golden, B., Grand, B.L., and Rossi, F. (2016). Mean absolute percentage error for regression models. Neurocomputing, 192, 38–48. doi:10.1016/j. neucom.2015.12.114. Advances in artificial neural networks, machine learning and computational intelligence.
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Dopico, M., Gomez, A., De la Fuente, D., Garc´ıa, N., Rosillo, R., and Puche, J. (2016). A vision of industry 4.0 from an artificial intelligence point of view. In Proceedings on the International Conference on Artificial Intelligence (ICAI), 407–413. Hellendoorn, H. and Driankov, D. (2012). Fuzzy model identification: selected approaches. Springer Science & Business Media. Iqbal, A., He, N., Li, L., and Dar, N.U. (2007). A fuzzy expert system for optimizing parameters and predicting performance measures in hard-milling process. Expert Systems with Applications, 32(4), 1020–1027. doi:10. 1016/j.eswa.2006.02.003. Jarfors, A.E.W., Bejhem, M., Carlsson, T., Eliasson, A., Keife, H., Nicolescu, C.M., and Rundqvist, B. (2010). Tillverkningsteknologi. Studentlitteratur, Lund, 4th edition. Mendel, J.M. (1995). Fuzzy logic systems for engineering: a tutorial. Proceedings of the IEEE, 83(3), 345–377. Precup, R.E. and Hellendoorn, H. (2011). A survey on industrial applications of fuzzy control. Computers in Industry, 62(3), 213–226. Raza, M., Svenningsson, R., Irwin, M., F¨agerstr¨ om, B., and Jarfors, A.E. (2017). Effects of Process Related Variations on Fillablity Simulation of Thin-Walled IN718 Structures. Springer. Shabani, M.O., Rahimipour, M.R., Tofigh, A.A., and Davami, P. (2015). Refined microstructure of compo cast nanocomposites: the performance of combined neuro-computing, fuzzy logic and particle swarm techniques. Neural Computing and Applications, 26(4), 899– 909. doi:10.1007/s00521-014-1724-8. Sigworth, G. (2011). Understanding quality in aluminum castings. International Journal of Metalcasting, 5(1), 7–22. doi:10.1007/BF03355504. Tarasov, V., Tan, H., Jarfors, A.E., and Seifeddine, S. (2019). Fuzzy logic-based modelling of yield strength of as-cast a356 alloy. Neural Computing and Applications, 1–12. doi:10.1007/s00521-019-04056-5. Tian, C., Law, J., van der Touw, J., Murray, M., Yao, J.Y., Graham, D., and John, D.S. (2002). Effect of melt cleanliness on the formation of porosity defects in automotive aluminium high pressure die castings. Journal of Materials Processing Technology, 122(1), 82– 93. doi:10.1016/S0924-0136(01)01229-8. Wang, L.X. and Mendel, J.M. (1992). Generating fuzzy rules by learning from examples. IEEE Transactions on systems, man, and cybernetics, 22(6), 1414–1427. Zadeh, L.A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics, SMC-3(1), 28–44. doi:10.1109/TSMC.1973.5408575. Zalnezhad, E., Sarhan, A.A.D., and Hamdi, M. (2013). A fuzzy logic based model to predict surface hardness of thin film TiN coating on aerospace AL7075T6 alloy. The International Journal of Advanced Manufacturing Technology, 68(1), 415–423. doi:10.1007/ s00170-013-4738-y.
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Fuzzy Fuzzy Fuzzy Fuzzy Fuzzy He He He He He
Logic Based Logic Based Logic Based Logic Based Component Logic Based Component Component Component ∗ Component
Modelling of Modelling of Modelling of Modelling of Properties Modelling of Properties Properties Properties ∗ Properties
Cast Cast Cast Cast Cast
Tan ∗ Vladimir Tarasov ∗ Anders E. W. Jarfors ∗∗ Tan Tarasov W. Jarfors ∗∗ ∗ Anders ∗∗ ∗∗ E. Tan ∗∗ Vladimir Vladimir Tarasov Salem Seifeddine ∗∗ E. W. Jarfors ∗∗ ∗ Anders Salem Seifeddine Tan Tarasov Anders ∗∗ E. W. Jarfors ∗∗ ∗ Vladimir ∗ Salem Seifeddine Tan Vladimir Tarasov Anders ∗∗ E. W. Jarfors Salem Seifeddine ∗ Seifeddine Computer Science ∗∗ and Informatics, ∗ Department ofSalem ∗ Department of Computer Science and Informatics, of Computer J¨ Science and Informatics, School of Engineering, onk¨ oping University, ∗ Department School of Engineering, J¨ o nk¨ oping University, of and Informatics, ∗ Department School Engineering, J¨ onk¨ nk¨ ping University, Boxof1026, 551 11 J¨ oScience ooping, Sweden Department of Computer Computer Science and Informatics, Box 1026, 551 11 J¨ o nk¨ o ping, Sweden School of Engineering, J¨ o nk¨ o ping University, Boxof1026, 551 11 J¨ oonk¨ ooping, School Engineering, J¨ nk¨ ping Sweden University, Box o o ∗∗ Box 1026, 1026, 551 551 11 11 J¨ J¨ onk¨ nk¨ oping, ping, Sweden Sweden ∗∗ Department of Materials and Manufacturing , ∗∗ Department of Materials and Manufacturing , Department of Materials and Manufacturing of Engineering, J¨ onk¨ oping University, , ∗∗School of Engineering, J¨ onk¨ oping University, Department of Materials and Manufacturing ∗∗School School Engineering, J¨ nk¨ ping University, ,, Boxof1026, 11 J¨ oonk¨ ooping, Sweden Department of551 Materials and Manufacturing Box 1026, 551 11 J¨ o nk¨ o ping, Sweden School of Engineering, J¨ o nk¨ o ping University, Boxof1026, 551 11 J¨ oonk¨ ooping, School Engineering, J¨ nk¨ ping Sweden University, Box 1026, 551 11 J¨ o nk¨ o ping, Sweden Box 1026, 551 11 J¨ onk¨ oping, Sweden
Abstract: Digitalization of manufacturing requires building models to represent accumulated Abstract: Digitalization of manufacturing requires building models to represent accumulated Abstract: Digitalization manufacturing requiresThe building representmodels accumulated data and knowledge on theofproducts and processes. use ofmodels formal to knowledge allows data and knowledge on the products and processes. The use of formal knowledge models allows Abstract: Digitalization of manufacturing requires building models to represent data and knowledge on the products and processes. The use of formal knowledge models allows for increaseDigitalization of the automation level leading to more sustainable Casting is Abstract: of manufacturing requires building modelsmanufacturing. to represent accumulated accumulated for increase of the level leading to more sustainable manufacturing. Casting is data and on products and processes. The use formal knowledge models allows for increase the automation automation level leading more sustainable manufacturing. Casting is important forof different industries because it to offers a great of designing for weight data and knowledge knowledge on the the products and processes. The use of offreedom formal knowledge models allows important for different industries because it offers aa great freedom of for weight for increase the automation level leading to more sustainable manufacturing. Casting is important forof industries because it to offers great of designing designing for weight reduction. paper presents an approach modelling of freedom cast component properties that for increaseThis of different the automation level leading to more sustainable manufacturing. Casting is reduction. This paper presents an approach to modelling of cast component properties that important for different industries because it offers a great freedom of designing for weight reduction. paper an because approach modelling cast component properties that is based onThis fuzzy logic.presents The approach includes learning of of the fuzzy inference rulesforfrom the important for different industries it tooffers a great freedom of designing weight is based onThis fuzzy logic. The includes learning of of the fuzzy inference rules from the reduction. an approach modelling is based fuzzypaper logic.presents The approach approach includes learning thecast fuzzy inference properties rulesprocess fromthat the data. Theonconstructed fuzzy logic canto used toof tune thecomponent manufacturing to reduction. This paper presents an models approach tobe modelling of cast component properties that data. The constructed fuzzy logic models can be used to tune the manufacturing process to is based on fuzzy logic. The approach includes learning of the fuzzy inference rules from data. Theon constructed logic models can be used toof tune theofmanufacturing process to produces cast components with desired properties. The evaluation the resultsrules demonstrates is based fuzzy logic.fuzzy The approach includes learning the fuzzy inference from the the produces cast components with desired properties. The evaluation of the demonstrates data. The constructed logic models can used to tune process to produces cast components desired properties. Theand evaluation ofmanufacturing the results results demonstrates that the accuracy of thefuzzy twowith created models are be 3.58% respectively with the learned data. The constructed fuzzy logic models can be used to 3.15% tune the the manufacturing process to that the accuracy of the two created models are 3.58% and 3.15% respectively with the learned produces cast components with desired properties. The evaluation of the results demonstrates that accuracy of the twowith created models are 3.58% and 3.15% with the learned fuzzythe inference rules being identical to the manually created ones. respectively The presented approach can produces cast components desired properties. The evaluation of the results demonstrates fuzzy inference rules being identical to the manually created ones. The presented approach can that accuracy of two created models are and with fuzzy rules being manually created ones. respectively TheCopyright presented approach can the c the help the toinference automate the management cast component manufacturing. 2019learned IFAC that the accuracy of the the twoidentical createdofto models are 3.58% 3.58% and 3.15% 3.15% respectively with the learned c help to automate the management of cast component manufacturing. Copyright 2019 IFAC fuzzy inference rules being identical to the manually created ones. The presented approach can c 2019 IFAC help toinference automate thebeing management manufacturing. fuzzy rules identicaloftocast the component manually created ones. TheCopyright presented approach can cc 2019 help to automate the management of cast component manufacturing. Copyright IFAC © 2019, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. help to automate the management of cast component manufacturing. Copyright 2019 IFAC Keywords: knowledge modelling, fuzzy logic, fuzzy systems, mechanical properties prediction Keywords: Keywords: knowledge knowledge modelling, modelling, fuzzy fuzzy logic, logic, fuzzy fuzzy systems, systems, mechanical mechanical properties properties prediction prediction Keywords: knowledge modelling, fuzzy logic, fuzzy systems, mechanical properties prediction Keywords: knowledge modelling, fuzzy logic, fuzzy systems, mechanical properties prediction 1. INTRODUCTION be considered when designing for weight reduction (Jarfors 1. INTRODUCTION INTRODUCTION be considered when designing for weight reduction (Jarfors 1. be al., considered when et 2010; Tian etdesigning al., 2002;for Daiweight et al.,reduction 2003): (Jarfors 1. INTRODUCTION et al., 2010; Tian et al., 2002; Dai et al., 2003): be considered when designing for weight reduction et al., 2010; Tian et al., 2002; Dai et al., 2003): 1. INTRODUCTION considered when designing for weight reduction (Jarfors (Jarfors The new concept of Integrated and Intelligent Manufac- be (1) Part design: manufacturability, material selection, et al., 2010; Tian al., 2003): The new new concept concept of of Integrated Integrated and and Intelligent Intelligent ManufacManufacal.,Part 2010;design: Tian et etmanufacturability, al., 2002; 2002; Dai Dai et et al., al., 2003): selection, material The turing stresses the importance of machine intelligence in et(1) (1) Part design: manufacturability, material selection, process selection and castability, microstructural varituring stresses theofimportance importance of machine machine intelligence in The new Integrated Intelligent Manufacprocess selection and vari(1) manufacturability, material turing stresses the intelligence in the area ofconcept advanced (Chen, 2017). The new concept of manufacturing Integrated ofand andsystems Intelligent Manufacprocess selection and castability, castability, microstructural microstructural variationsdesign: due to design (1) Part Part design: manufacturability, material selection, selection, the area of advanced manufacturing systems (Chen, 2017). turing stresses the importance of machine intelligence in ations due to design process selection and castability, microstructural varithe of advanced manufacturing (Chen, 2017). Thearea technology is shifting towards asystems knowledge intensive turing stresses the importance of machine intelligence in ations due to design (2) Imperfections: melt processing related defects, casting process selection and castability, microstructural variThearea technology is shifting shifting towards aasystems knowledge intensive the of manufacturing (Chen, 2017). (2) Imperfections: melt processing related defects, casting ations due to design The technology towards knowledge intensive focus, while the isaccumulation of knowledge bases is still the area of advanced advanced manufacturing systems (Chen, 2017). (2) Imperfections: melt processing related defects, casting process defects ations due to design focus,technology while the the accumulation accumulation of knowledge knowledge bases is still still The shifting a intensive process (2) focus, of bases is beingtechnology awhile challenge.is of manufacturing requires The is Digitalization shifting towards towards a knowledge knowledge intensive process defects defectsmelt (2) Imperfections: Imperfections: melt processing processing related related defects, defects, casting casting being a challenge. Digitalization of manufacturing requires focus, while the accumulation of knowledge bases is still Although, deterministic models are instrumental for the process defects being a challenge. Digitalization of manufacturing requires construction of models to represent gathered data focus, while the accumulation of knowledge bases is and still Although, processdeterministic defects models are instrumental for the construction of models to represent gathered data and being a challenge. Digitalization of manufacturing requires deterministic models are instrumental forfrom the design of cast components, imperfections resulting construction models to represent gatheredThe data knowledge onofthe products and processes. useand of Although, being a challenge. Digitalization of manufacturing requires design of cast components, imperfections resulting from Although, deterministic models are instrumental for the knowledge on the products and processes. The use of construction of models to represent gathered data and design of cast components, imperfections resulting melt treatment and casting process inherently display deterministic models arewill instrumental forfrom the knowledge onofthe products and for processes. useand of Although, formal knowledge models increase ofdata the auconstruction models to allows represent gatheredThe melt treatment and casting process will inherently display design of cast components, imperfections resulting from formal knowledge models allows for increase of the auknowledge on the products and processes. The use of melt treatment and casting process will inherently display a stochastic e.g.imperfections oxide films being discrete of castbehaviour, components, resulting from formal knowledge allows for increase of the tomation level to more sustainable manufacturing. knowledge on leading the models products and processes. The useauof design aa stochastic behaviour, e.g. oxide films being melt treatment and process will inherently display tomation level leading to sustainable manufacturing. formal models allows for of the stochastic behaviour, oxide films being discrete discrete particles of varying size e.g. formed during processing that treatment and casting casting process will inherently display tomation leading to more more sustainable manufacturing. Dopico knowledge etlevel al. (2016) point out that theincrease degree of formal knowledge models allows for increase of automathe auau- melt of varying size formed during processing that aparticles stochastic behaviour, e.g. oxide films being discrete Dopico et al. (2016) point out that the degree of automatomation level leading to more sustainable manufacturing. of in varying sizelocations formed during that willstochastic end up discrete but not processing inbeing a repeatable behaviour, e.g. oxide films discrete Dopico etlevel al. point outinthat degree of strategy. automa- aparticles tion plays an (2016) important the the Industry 4.0 tomation leading to role more sustainable manufacturing. will end up in discrete locations but not in a repeatable particles of varying size formed during processing that tion plays an important role in the Industry 4.0 strategy. Dopico et al. (2016) point out that the degree of automawill end (Campbell, up discrete but not in a repeatable fashion 2011). Additional variations in part of in varying sizelocations formed during processing that tion plays an important role the Industry 4.0 strategy. The use of al. intelligent technologies can make real in particles Dopico et (2016) point outinthat the degree ofimpact automafashion (Campbell, 2011). Additional variations in part will end up in discrete locations but not in aa repeatable The use of intelligent technologies can make real impact in tion plays an important role in the Industry 4.0 strategy. fashion (Campbell, 2011). Additional variations in part quality and accuracy of a simulation will result from a will end up in discrete locations but not in repeatable The use ofmanufacturing intelligent technologies can make real in fashion advanced by supplying machines with the tion plays an important role in the Industry 4.0impact strategy. quality and accuracy of aa Additional simulation will result from a (Campbell, 2011). variations in part advanced manufacturing by supplying supplying machines with the the The use of intelligent technologies can make real impact in quality and accuracy of simulation will result from number of parameters that cannot be uncontrolled in a fashion (Campbell, 2011). Additional variations in part advanced manufacturing by machines with capability learn from the data can andmake reason next The use of to intelligent technologies realabout impact in quality number of parameters that cannot be uncontrolled in a and accuracy of a simulation will result from capability to learn from the data and reason about next advanced manufacturing by supplying machines with the number of parameters cannot be will uncontrolled in a foundry and (Raza et al., 2017). The quality of available data accuracy ofthat a simulation result from capability to learn from the data and machines reason about steps in production. advanced manufacturing by supplying withnext the quality foundry (Raza et The quality of data number of that cannot be uncontrolled in a steps in in production. production. capability to foundry (Raza et al., al., 2017). 2017). The quality of 1available available also affects prediction capabilities. Table providesdata of parameters parameters that cannot be uncontrolled inan a steps capability to learn learn from from the the data data and and reason reason about about next next number also affects prediction capabilities. Table 1 provides an foundry (Raza et al., 2017). The quality of available data Casting is important for different industries because it foundry steps in also affects capabilities. Table provides an examples of prediction material performance variation in a part. It (Raza et al., 2017). The quality of 1available data steps in production. production. Casting is important for different industries because it examples of material performance variation in a It capabilities. Table provides an Casting is important different industries it also offers a great freedom for of designing for weightbecause reduction examples of prediction material performance in a part. part. It showsaffects inherent variations due to thevariation location the tensile also affects prediction capabilities. Table 11 of provides an offers aa great great freedom for of designing designing for weight weightbecause reduction Casting is important different it shows inherent variations due to the location of the tensile of material performance variation in a part. It offers freedom of for reduction (Jarfors et 2010). The automotive sector is the largest Casting is al., important for different industries industries because it examples shows inherent variations due to the location of the tensile bar and variations from different foundries producing the examples of material performance variation in a part. It (Jarfors et al., 2010). The automotive sector is the largest offers great freedom of designing weight reduction bar and variations from different foundries producing the inherent variations due to the location of the tensile (Jarfors et al., 2010). The is the largest user ofa weight cast components . sector The performance of shows offers alight great freedom of automotive designing11 for for weight reduction bar and variations from different foundries producing the castinginherent (Sigworth, 2011). due to the location of the tensile shows variations user of light weight cast components The performance of (Jarfors et al., 2010). The automotive is the largest 1 . sector casting (Sigworth, 2011). and variations from user light weight cast components . sector The performance of bar a castofcomponent depends on several1 factors, which should (Jarfors et al., 2010). The automotive is the largest casting bar and(Sigworth, variations 2011). from different different foundries foundries producing producing the the a component depends on which user light cast .. The of To create models of cast components, it is necessary to (Sigworth, 2011). a cast castof on several several1 factors, factors, which should should user ofcomponent light weight weightdepends cast components components The performance performance of casting casting (Sigworth, 2011). To create models of cast components, it is necessary to a models ofand castincomplete components, is necessary to dealcreate with uncertain datait collected during a cast cast component component depends depends on on several several factors, factors, which which should should To deal with uncertain and incomplete data collected during To create models of cast components, it is necessary to The research reported in this paper has been financed by grant deal with uncertain and incomplete data collected during the manufacturing process. Fuzzy logic is one of the To create models of cast components, it is necessary to The research reported in this paper has been financed by grant the manufacturing process. Fuzzy logic is one of the deal with uncertain and incomplete data collected during #20170066 fromreported the Knowledge Foundation (Sweden). the manufacturing process. Fuzzy logic is one of the The research in this paper has been financed by grant proposed methods to manage uncertainty, imprecision and deal with uncertain and incomplete data collected during #20170066 fromreported the Foundation (Sweden). proposed methods toprocess. manage uncertainty, imprecision and 1 The the manufacturing Fuzzy logic is the research in thisvehicle paper sales has been financed by grant OICAs statistics of Knowledge worldwide http://www.oica.net/ #20170066 fromreported the Knowledge Foundation (Sweden). proposed methods manage uncertainty, imprecision and incompleteness of to data (Zadeh, 1973). Fuzzy logicof a the manufacturing process. Fuzzy logic is one one ofhas the research in thisvehicle paper sales has been financed by grant 1 The OICAs statistics of Knowledge worldwide http://www.oica.net/ #20170066 from the Foundation (Sweden). 1 incompleteness of data (Zadeh, 1973). Fuzzy logic has a proposed methods to manage uncertainty, imprecision and category/sales-statistics/ OICAs statistics of worldwide vehicle sales http://www.oica.net/ #20170066 from the Knowledge Foundation (Sweden). incompleteness of data (Zadeh, 1973). Fuzzy logic has proposed methods to manage uncertainty, imprecision anda 1 OICAs statistics of worldwide vehicle sales http://www.oica.net/ category/sales-statistics/ 1 OICAs statistics of worldwide vehicle sales http://www.oica.net/ incompleteness of data (Zadeh, 1973). Fuzzy logic has category/sales-statistics/ incompleteness of data (Zadeh, 1973). Fuzzy logic has a a category/sales-statistics/
category/sales-statistics/ 2405-8963 © 2019 2019, IFAC IFAC (International Federation of Automatic Control) Copyright 1149Hosting by Elsevier Ltd. All rights reserved. Copyright 2019 IFAC 1149Control. Peer review© responsibility of International Federation of Automatic Copyright © under 2019 IFAC 1149 Copyright © 2019 IFAC 1149 10.1016/j.ifacol.2019.11.348 Copyright © 2019 IFAC 1149
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Table 1. Range of properties for one alloy cast by different foundries using a standardised mould from which 5 samples were taken. The variation at each location illustrated the variation between the foundries producing the casting.(Sigworth, 2011) Location
UTS (MPa)
YS (MPa)
Ef (%)
1 2 3 4 5
235–276 231–283 252–297 259–314 248–293
166–242 166–242 162–173 166–269 162–173
1.8–4 1.5–4.5 3–7.7 3.5–9.5 3–7.5
Fig. 1. Fuzzy logic system
successful record of industrial applications of fuzzy control in managing complex non-linear systems (Precup and Hellendoorn, 2011). Moreover, mechanical properties such as hardness and roughness of cast and metallic materials have been modelled with the help of fuzzy logic (Shabani et al., 2015; Zalnezhad et al., 2013; Barzani et al., 2015; Iqbal et al., 2007). This paper presents an approach to modelling of cast component properties that is based on fuzzy logic. The approach includes learning of the fuzzy inference rules to predict yield strength from the data. The constructed fuzzy logic models can be used to tune the manufacturing process by varying the chemical composition and solidification rate and examining the resulting mechanical property values. In the remainder of the paper, fuzzy logic systems are introduced in Sect. 2 together with related work. Sect. 3 presents details of experimental work to collect the data. Sect. 4 describes knowledge modelling with fuzzy logic and automatic extraction of inference rules. The results are discussed in Sect. 5 and the conclusions are presented in Sect. 6.
Fig 1 shows high level structure of a Fuzzy Logic System (FLS). It contains four components: fuzzifier, inference rules, inference engine, and defuzzifier. The fuzzifier maps crisp numbers into fuzzy sets. Inference rules are a collection of IF-THEN statements, e.g. “IF x1 is fast and x2 is very low, THEN y is average.” They represent the subjective knowledge in an application (Mendel, 1995). The inference engine performs a certain inference procedure based on the rules and derives a conclusion. It maps input fuzzy sets into output fuzzy sets. In applications where crisp numbers must be obtained as the output, the defuzzification step is necessary. It maps output fuzzy sets into crisp numbers. In the fuzzifier and defuzzifier, membership functions are used to map crisp numbers into fuzzy linguistic terms and vice versa. Both membership functions and if-then rules can be either acquired from domain experts or learned from numerical data. Often it is expensive to query a domain expert, or there may be no experts available when the FLS is built. Methods to automatically extract membership functions and rules from numerical data without the help of human experts can be found in many work. In the present work the rules are derived from the data using a method adapted from the one proposed in (Wang and Mendel, 1992) and the membership functions are defined manually by a knowledge engineer after examining the experimental data.
2. FUZZY LOGIC SYSTEMS Fuzzy logic has long been applied to industrial problems with successful results (Precup and Hellendoorn, 2011). However, very few studies have applied fuzzy logic in casting and metal industry. Several papers have been published on predicting surface roughness and hardness of cast and metallic components and predicting mechanical properties of non-metallic materials. There are only limited attempts to predict mechanical properties, such as yield strength, of cast components, which is the focus of this paper and then in particular the aluminum alloy A356 and linking the performance to process and microstructural in-data (Tarasov et al., 2019). Other methods such as Bayesian theory and artificial neural networks (ANN) have also have been applied to model and predict mechanical properties of industry materials as powerful tools to deal with uncertainties. In contrast to these methods, which often result in an opaque model, “black box”, a fuzzy logic model is a highly interpretable ”grey box” when Mamdani-type fuzzy model is applied (Hellendoorn and Driankov, 2012). This makes the fuzzy logic approach especially interesting for industrial applications as soon as model transparency is often required by the stakeholders for the model to be used at a working place.
3. CASTING AND TENSILE TESTING EXPERIMENTS The first phase of the experiments included melt preparation and casting. Seven Al – 7%Si – 0.4%Mg alloys were melt in a resistance furnace. Each alloy was modified with approximately 200–250 ppm Sr. A 200◦ C preheated permanent copper mould was used to cast cylindrical rods, which were then inserted into the Bridgeman furnace. The rods were remelted for 20 min. at 710◦ C and directionally solidified afterwards. Different microstructures can be produced by changing the speed of the furnace during the passage of molten rod during the cooling channels. Three different coarsenesses of the microstructure were directionally solidified for the present investigation. Each one has Secondary Dendrite Arm Spacing (SDAS) of approximately 10, 25 or 50 µm. Water cooling was used for high furnace speeds, 3 mm/s and 0.3 mm/s corresponding to SDAS of 10 and 25 µm respectively. While air was the cooling media was used for the 0.03 mm/s velocity that corresponds to SDAS of 50 µm. The next phase was tensile testing of the bars with a gauge length of 50 mm and a diameter of 7 mm that were machined from the directionally solidified rods. The constant strain rate of 0.5 mm/min was applied using
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defined for resulting yield strength. The systems were implemented using a fuzzy logic toolbox 2 for SciPy 3 .
Fig. 2. Knowledge modelling to support manufacturing of cast components a Zwick/Roell Z100 machine equipped with a 100 kN load cell and a clip-on 20 mm gauge length extensometer. The tests were carried out until fracture in a sample, using three tensile test bars for each condition. Only samples representing the potential of the alloy in term of tensile properties are presented, since the proposed directional solidification technology has proven to deliver optimal tensile test results due to excellent feeding during solidification, revealing the potential of studied alloys. In total two series of experiments were conducted. The first series was conducted on specimens cast with the alloy A356 — Al – 7%Si – 0.4%Mg – 0.25%Fe with variation of Cu. The second series was based on alloy A356 — Al – 7%Si – 0.4%Mg with variation of Si. In both series the solidification rate of the samples was varied as described above. Each experiment generated a data set on cast specimens that included variation of the chemical composition of cast alloys, i.e., percentage of Cu or Si, and variation in the casting process, i.e., SDAS.
As described in Sect. 3, the experiments provided two data sets. Each data set contains a set of input-output data pairs, {(x11 , x12 ; y 1 ), (x21 , x22 ; y 2 ), . . .}, where x1 represents SDAS, x2 represents the percentage of Cu or Si, and y represents the output YS. The first data set contained 67 data points. The data were divided into two parts: a training data set with 46 data points and a test data set with 21 data points. The second data set contained 52 data points. This data set was divided into two parts: a training data set with 36 data points and a test data set with 16 data points. The training data sets were used to create the fuzzy logic models, i.e. to define the membership functions for input and output linguistic variables (Sect. 4.1) and to learn fuzzy inference rules (Sect. 4.2). The prediction accuracy of the created fuzzy models were evaluated with the help of the test data sets (Sect. 5). 4.1 Linguistic variables and membership functions The Gaussian type was chosen for the membership functions of all the input and output variables, as it was considered to be the most adequate by the domain experts. The parameters of the membership functions (i.e. σ, which controls the width of the ”bell” of the curve, and c, which defines the position of the centre of the curve peak) are identified based on the examination of the data sets. The typical number of membership functions for a variable is between three and seven (Zalnezhad et al., 2013; Barzani et al., 2015; Chiang et al., 2008). The number of five membership functions was chosen for most variables because it allowed for good coverage of the variable ranges from the data sets. Only the coarsenesses of microstructure was measured with three distinct values, which required three membership functions to represent them. The examination of the training data sets included two steps:
4. FUZZY LOGIC REPRESENTATION OF MECHANICAL PROPERTIES OF CAST COMPONENTS The overview of the approach to fuzzy logic modelling is shown in Fig 2. The process of manufacturing of cast components has several parameters such as the chemical composition of alloy or the rate of solidification. These parameters may affect the mechanical properties of cast components. The data collected during the manufacturing process is used to create a fuzzy logic system. This system provides the mapping between the input parameters and the output properties, and can predict values of yield strength and other mechanical properties. The predicted values together with the input parameters are utilised to improve the manufacturing process. In the current work, two fuzzy logic systems were built to predict yield strength of a cast component, as soon as two different additives, Cu and Si, were used. The created systems are based on multiple-input-single-output mamdani-type fuzzy model. There are two inputs for each fuzzy logic system: ”SDAS”, representing microstructure coarseness, and ”Cu”, representing the percentage of Cu (for the first data set), or ”Si”, representing the percentage of Si (for the second data set). The output is ”YS” was
(1) Compilation of the existing values of an input/output (a process parameter or mechanical property) in a list and sorting it to determine the range of the variable. (2) Partitioning of the value list into segments to determine the number of memberships functions (linguistic labels) for a variable and the parameters, i.e. σ and c, for each membership function. The size of each partition was chosen to encompass a few values and the overall partitioning were confirmed by the domain experts. The linguistic variables and membership functions for each variable are shown in Fig. 3. Finally, the utilised aggregation method was max and the defuzzification method was centroid. 4.2 Fuzzy inference rules For each fuzzy logic system a set of two-input one-output inference rules were generated. The rules were first identified as ”and” rules (i.e., logical conjunction, which is denoted as &) by a knowledge engineering expert. Then 2 3
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Fig. 3. Membership functions for the input and output parameters. For each function the x-axis indicates input values and the y-axis indicates their corresponding degree of membership. rules were automatically generated from the training data using a method adapted from the one proposed in Wang and Mendel (1992). The method consists of three steps:
Table 2. The fuzzy inference rules generated from the first training data set. No. 1 2 3 4 5 6 7 8 9 10 11
1) Generate a rule for each input-output data pair (x1 , x2 ; y) in training data: IF xi1 is A and xi2 is B, THEN y i is C, where µA (xi1 ), µB (xi2 ), and µC (y i ) are membership functions with the maximum membership degree for each respective value. For example, as shown in Fig 4, xi2 has degree 0.8 in ”little”, 0.2 in ”very little”, and 0 in other regions, therefore xi1 is considered to be ”little”. In Fig 4 xi1 is considered to be ”average”, and y i is considered to be ”average”. The rule obtained from the input-output data pair is: IF xi1 is average and xi2 is little, THEN y i is average. 2) Calculate a degree for each rule: D(rulei ) = µA (xi1 ) × µB (xi2 ) × µC (y)i
For example, the degree for the rule above is 0.48, since D(rulei ) = 1 × 0.8 × 0.6 = 0.48.
3) Generate the final list of rules
If there is more than one rule with the same antecedent, the rule that has the maximum degree is selected into the final list. For example, Rule 1: IF xi1 is A and xi2 is B, THEN y i is C1, and the degree for rule 1 is 0.48. Rule 2: IF xi1 is A and xi2 is B, THEN y i is C2, and the degree of rule 2 is 0.52 Then, rule 2 is selected into the final list of the rules, since it has higher degree than rule 1.
Antecedent (SDAS==coarse) & (Cu==very-little) (SDAS==fine) & (Cu==very-little) (SDAS==average) & (Cu==very-little) (SDAS==coarse) & (Cu==little) (SDAS==fine) & (Cu==little) (SDAS==average) & (Cu==little) (Cu==average) (Cu==much) (SDAS==fine) & (Cu==very-much) (SDAS==coarse) & (Cu==very-much) (SDAS==average) & (Cu==very-much)
Consequent (YS=very-low) (YS=low) (YS=low) (YS=low) (YS=average) (YS=average) (YS=average) (YS=average) (YS=high) (YS=high) (YS=very-high)
This method for learning rules from data is general, simple and straightforward. The method was implemented in Python. It performed fast. It significantly reduced the time and effort needed to built the systems. Tables 2 and 3 present the rules that were generated from the training data using the algorithm. The quality of the rules was evaluated by comparing to the sets of rules manually created by a knowledge engineer (which are presented in Tarasov et al. (2019)). The rules generated using the presented method are identical to the rules manually created. 5. EVALUATION OF THE MODEL ACCURACY The prediction accuracy of the constructed fuzzy logic systems was evaluated with the help of the test data sets. The evaluation results are presented in Table 4 for the first test data set and in Table 5 for the second test data set. The prediction error was measured using Mean Absolute Percentage Error (MAPE) (De Myttenaere et al., 2016). It is computed by dividing the absolute difference of the
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Fig. 4. The degrees of xi1 , xi2 and y i in membership functions. Table 4. Evaluation of the model accuracy for the first test data set
Table 3. The fuzzy inference rules generated from the second training data set. No. 1 2 3 4 5 6 7 8 9 10
Antecedent (SDAS==coarse) & (Si==little) (SDAS==coarse) & (Si==average) (SDAS==coarse) & (Si==much) (Si==very-little) (SDAS==average) (SDAS==coarse) & (Si==very-much) (SDAS==fine) & (Si==little) (SDAS==fine) & (Si==average) (SDAS==fine) & (Si==much) (SDAS==fine) & (Si==very-much)
Consequent (YS=very-low) (YS=very-low) (YS=very-low) (YS=low) (YS=low) (YS=low) (YS=average) (YS=high) (YS=very-high) (YS=very-high)
Sample AA13 AA23 AA33 AB13 AB22 AB32 AC11 AC21 AC31 AD13 AD23 AD33 AE12 AE32 AF31 AG14 AG23 AG33 AI12 AI23 AI32 MAPE
predicted and measured values by the absolute value of the measured value and averaging this ratio over the data. MAPE is given at the bottom of each table and it is 3.58% for the first fuzzy logic model and 3.15% for the second model. The first column in each table contains the designation of a casting component from the test data sets. Both tables show the percentage of Cu/Si and SDAS, which are the input values to the fuzzy logic models, as well as the measured value of yield strength in the next three columns. The values predicted by the fuzzy systems are shown in the fifth column of each table. The last column contains a (signed) percentage error for each pair of predicted and measured values.
This paper has proposed a fuzzy logic based approach to modelling of mechanical properties of cast components. The fuzzy logic models are constructed with the help of the data collected during the manufacturing process. The approach includes learning of the fuzzy inference rules from
SDAS 10 20 50 10 20 50 10 20 50 10 20 50 10 50 50 10 20 50 10 20 50
YS(M) 125.44 125.51 113.06 133.59 135.94 117.57 144.96 145.11 129.44 144.20 157.29 139.01 151.14 141.50 152.20 166.83 173.85 170.86 194.70 202.88 189.74
YS(P) 135.02 135.03 116.41 135.64 135.64 118.02 145.58 145.58 129.51 156.37 155.92 135.03 157.76 136.79 159.84 160.00 160.00 160.00 184.40 191.29 184.29
Err(%) 7.65 7.58 2.97 1.54 -0.22 0.39 0.43 0.33 0.05 8.13 -0.87 -2.86 4.29 -3.32 5.02 -4.10 -7.97 -6.36 -5.29 -2.9 -2.87 3.58
Table 5. Evaluation of the model accuracy for the second test data set Sample AIA13 AIA23 AIA33 AIB13 AIB23 AIB33 AIC13 AIC33 AID13 AID33 AIE13 AIE23 AIE32 AIF13 AIF23 AIF33 MAPE
The related work reports the prediction accuracy of the fuzzy logic based systems that is similar to the prediction errors of the constructed fuzzy logic systems. The prediction errors were also discussed with the domain experts, who considered the error level as acceptable. While the performance of the fuzzy logic systems is good, it is worth noting that this work is one of the first steps on modelling of yield strength of cast components. Small data sets were used to create the models. The prediction accuracy may be different if bigger data sets are used for the modelling. Moreover, the procedure of data collection at a particular lab or foundry could affect the performance of the fuzzy logic models due to variations in measurement accuracy or unaccounted differences in the cast process. One example of such variation is given in Table 1 . 6. CONCLUSIONS
Cu 0 0 0 0.6 0.6 0.6 1 1 1 1.5 1.5 1.5 1.7 1.7 2.5 3.5 3.5 3.5 5.5 5.5 5.5
Si 7 7 7 10 10 10 11.5 11.5 12.5 12.5 13 13 13 14.5 14.5 14.5
SDAS 10 20 50 10 20 50 10 50 10 50 10 20 50 10 20 50
YS(M) 125.44 125.51 113.06 161.20 132.35 108.67 168.94 115.77 180.14 110.40 176.33 136.41 110.99 176.03 128.38 118.65
YS(P) 127.61 127.61 127.52 148.63 130.16 110.95 168.0 110.61 173.80 111.11 175.82 130.88 110.90 176.19 130.45 127.36
Err(%) 1.74 1.67 12.79 -7.79 -1.65 2.09 -0.56 -4.45 -3.52 0.64 -0.29 -4.05 -0.08 -0.09 1.61 7.34 3.15
the data after manual creation of memberships functions. The created fuzzy logic systems map the casting process parameters to the mechanical properties of produced cast components and are capable of predicting particular values of yield strength. The fuzzy inference rules learned from the data are identical to the manually created rules. The evaluation of the accuracy of the two constructed knowledge models demonstrates the error level of 3.58%
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and 3.15% respectively, which is similar to the error level reported in the related work. The proposed approach to modelling of cast components can support the manufacturing process at foundries by providing formal models relating the input process parameters to the output cast properties. The use of such knowledge models can alleviate resource and time intensive tensile testing of cast components. Moreover, the biggest part of the model construction — extraction of fuzzy inference rules — can be automated. Hence, the proposed approach contributes to the digitalization of the foundry industry. Future work is two fold. Firstly, the fuzzy logic models will be extended by incorporating other mechanical properties of cast components, such as ultimate tensile strength, elongation to failure and Young’s modulus, which are of interest for industry stakeholders and are important for the management of cast component manufacturing. Secondly, various methods will be further explored to automate definition of membership functions and generation of fuzzy inference rules from training data. Many methods to automatically extract membership functions and rules from numerical data without the help of human experts can be found in literature. Different methods will be evaluated by using them to build fuzzy logic systems for predicting mechanical properties of cast components. The trade-off between interpretability and accuracy will also be studied when the models are built from empirical data. Furthermore, cooperating with industry stakeholders, more extensive laboratory test data are expected to be obtained for fuzzy logic modelling and evaluation in the future. REFERENCES Barzani, M.M., Zalnezhad, E., Sarhan, A.A., Farahany, S., and Ramesh, S. (2015). Fuzzy logic based model for predicting surface roughness of machined Al-Si-CuFe die casting alloy using different additives-turning. Measurement, 61(Supplement C), 150–161. doi:10.1016/ j.measurement.2014.10.003. Campbell, J. (2011). Complete Casting Handbook: Metal Casting Processes, Techniques and Design. Butterworth-Heinemann, Oxford. Chen, Y. (2017). Integrated and intelligent manufacturing: Perspectives and enablers. Engineering, 3(5), 588–595. doi:10.1016/j.eng.2017.04.009. Chiang, K.T., Liu, N.M., and Chou, C.C. (2008). Machining parameters optimization on the die casting process of magnesium alloy using the grey-based fuzzy algorithm. The International Journal of Advanced Manufacturing Technology, 38(3), 229–237. doi:10.1007/ s00170-007-1103-z. Dai, X., Yang, X., Campbell, J., and Wood, J. (2003). Effects of runner system design on the mechanical strength of Al-7Si-Mg alloy castings. Materials Science and Engineering: A, 354(1), 315–325. doi:10.1016/ S0921-5093(03)00021-2. De Myttenaere, A., Golden, B., Grand, B.L., and Rossi, F. (2016). Mean absolute percentage error for regression models. Neurocomputing, 192, 38–48. doi:10.1016/j. neucom.2015.12.114. Advances in artificial neural networks, machine learning and computational intelligence.
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Dopico, M., Gomez, A., De la Fuente, D., Garc´ıa, N., Rosillo, R., and Puche, J. (2016). A vision of industry 4.0 from an artificial intelligence point of view. In Proceedings on the International Conference on Artificial Intelligence (ICAI), 407–413. Hellendoorn, H. and Driankov, D. (2012). Fuzzy model identification: selected approaches. Springer Science & Business Media. Iqbal, A., He, N., Li, L., and Dar, N.U. (2007). A fuzzy expert system for optimizing parameters and predicting performance measures in hard-milling process. Expert Systems with Applications, 32(4), 1020–1027. doi:10. 1016/j.eswa.2006.02.003. Jarfors, A.E.W., Bejhem, M., Carlsson, T., Eliasson, A., Keife, H., Nicolescu, C.M., and Rundqvist, B. (2010). Tillverkningsteknologi. Studentlitteratur, Lund, 4th edition. Mendel, J.M. (1995). Fuzzy logic systems for engineering: a tutorial. Proceedings of the IEEE, 83(3), 345–377. Precup, R.E. and Hellendoorn, H. (2011). A survey on industrial applications of fuzzy control. Computers in Industry, 62(3), 213–226. Raza, M., Svenningsson, R., Irwin, M., F¨agerstr¨ om, B., and Jarfors, A.E. (2017). Effects of Process Related Variations on Fillablity Simulation of Thin-Walled IN718 Structures. Springer. Shabani, M.O., Rahimipour, M.R., Tofigh, A.A., and Davami, P. (2015). Refined microstructure of compo cast nanocomposites: the performance of combined neuro-computing, fuzzy logic and particle swarm techniques. Neural Computing and Applications, 26(4), 899– 909. doi:10.1007/s00521-014-1724-8. Sigworth, G. (2011). Understanding quality in aluminum castings. International Journal of Metalcasting, 5(1), 7–22. doi:10.1007/BF03355504. Tarasov, V., Tan, H., Jarfors, A.E., and Seifeddine, S. (2019). Fuzzy logic-based modelling of yield strength of as-cast a356 alloy. Neural Computing and Applications, 1–12. doi:10.1007/s00521-019-04056-5. Tian, C., Law, J., van der Touw, J., Murray, M., Yao, J.Y., Graham, D., and John, D.S. (2002). Effect of melt cleanliness on the formation of porosity defects in automotive aluminium high pressure die castings. Journal of Materials Processing Technology, 122(1), 82– 93. doi:10.1016/S0924-0136(01)01229-8. Wang, L.X. and Mendel, J.M. (1992). Generating fuzzy rules by learning from examples. IEEE Transactions on systems, man, and cybernetics, 22(6), 1414–1427. Zadeh, L.A. (1973). Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man, and Cybernetics, SMC-3(1), 28–44. doi:10.1109/TSMC.1973.5408575. Zalnezhad, E., Sarhan, A.A.D., and Hamdi, M. (2013). A fuzzy logic based model to predict surface hardness of thin film TiN coating on aerospace AL7075T6 alloy. The International Journal of Advanced Manufacturing Technology, 68(1), 415–423. doi:10.1007/ s00170-013-4738-y.
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