A DecisionMaking Methodology Based on Expert Systems Applied to Machining Tools Condition Monitoring
Abstract
:1. Introduction
1.1. Expert Systems as Complementary Elements in DecisionSupport Systems
1.2. Expert Systems in Machining Applications
1.3. Hierarchization Processes
2. Materials and Methods
2.1. Definition of the Methodology
2.2. Implementation of the Methodology
2.2.1. First Expert System
2.2.2. Hierarchization of the Aggressiveness Factors
 First, a group of experts participates in the processes of the evaluation and hierarchization of a set of values, associated to the aggressiveness factors, taking into account a specific set of criteria. The results of such evaluations are expressed using vague fuzzy numbers [62] because of their capabilities, not just for modeling qualitative linguistic environments with higher accuracy, but also for extending uncertainty by controlling the determination of the membership functions. This allows for working on intervals in which it can be considered that the evaluations performed on the different values may have a membership degree that is independent of the function that links them to their respective criteria. Thus, for example, a certain value would not have a precise membership function that determines the degree to which it belongs, for instance, to the correct accomplishment of a criterion, but instead it would have an interval wherein such membership function could be contained. In the specific case of this work, the values to be hierarchized are the aggressiveness factors, while the associated criteria are the process variables. Furthermore, the vague number will describe the interval wherein the membership function that represents the membership of the aggressiveness factor in the risk associated with one of the input variables will lie. There will be, therefore, a vague number for each input value associated to each aggressiveness factor. In conclusion, these vague numbers will represent how close the corresponding aggressiveness factor is to belonging to a function that describes the risk associated with an input value. The evaluation results issued by each expert are stored in a matrix, named the Vague Fuzzy Decision Matrix, which may differ depending on the expert in charge of its elaboration.
 Afterwards, a set of weights associated with the experts and the criteria is defined, thus allowing us to prioritize those that show a higher importance level. For example, in the case of the experts, it allows us to distinguish those with more expertise, or in the case of the criteria, to identify those with a higher impact on the tool’s lifespan. For the determination of the experts’ weights, a sequential process will be followed. In this way, each expert will first perform a selfassessment, after which they will assess their colleagues, always using a 0–100 scoring scale. Once these assessments are obtained, the mean value of the scores for each expert will be calculated, thus determining their respective weights. In the case of the criteria’s weights, the different experts will assess their respective importance for and influence on the tool’s lifespan, determining the weight of each criterion using the median value, a metric that is more robust when faced with extreme values, because the determination of the influence of the dominant criteria can be equally valued, no matter who the expert is.
 Making use of a series of operators derived from the Intuitionistic Fuzzy Set concept [62,74], which are applicable to vague numbers as these are essentially intuitionistic fuzzy numbers [63], it is possible to perform an aggregation and a subsequent defuzzification of the vague numbers that compose the previously defined matrices (the Vague Fuzzy Decision Matrix). Such operators, among which the Intuitionistic Fuzzy Weighted Geometric (IFWG) operator, the Intuitionistic Fuzzy Ordered Weighted Geometric (IFOWG) operator, and the Intuitionistic Fuzzy Hybrid Geometric (IFHG) operator [67] are perhaps the most representative, allow us to group all the matrices into a new Collective Vague Fuzzy Decision Matrix, and after that, to generate the Aggregate Vague Values associated with each alternative. Using those values, it is possible to calculate a score for each aggressiveness factor, and thus to determine the hierarchization depending on the value of the weight obtained. The hierarchization will be performed by calculating the scores value of the aggregate vague numbers that represent each aggressiveness factor. These score values will lie within the [−1, 1] interval [75], with “1” indicating that the corresponding aggressiveness factor has to belong to the risk function of each of the input variables.
Implementation of the Hierarchization Process
2.2.3. Determination of the Global Aggressiveness Factor
2.2.4. Capture and Processing of the Machining Process Audio Signals
 Step 1—The centroids are calculated for the audio signal spectrum every 0.5 s, both for the current audio sample and for the reference sample stored in the database;
 Step 2—The difference function between the centroid functions associated with each audio sample is determined;
 Step 3—Once the centroid graphs for the spectra of both signal samples have been established, it is possible to calculate the difference between them, and later to determine the area associated with a given time interval;
 Step 4—After that, the median value is calculated for the different areas obtained, and a value is determined that represents the distortion associated with the spectrum, taking into account that the ideal median value should be close to zero.
2.2.5. Second Expert System
2.2.6. Strategy for the Reinforcement of the Knowledge Base
2.2.7. Calculation of the Diagram and Interpretation of the Risk
 For Tool Risk values lower than or equal to 60%, i.e., diagram thicknesses smaller than 60% of the diameter of its base, it will be understood that the work conditions do not involve relevant excesses in tool wear, and therefore there is little effect on the tool’s lifespan;
 For Tool Risk values in the 60–80% range of the diagram’s base diameter, it will be understood that the work conditions should be checked, as they might produce the early wear of the tool and a certain shortening of its lifespan;
 For Tool Risk values equal to or above 80%, it will be understood that the work conditions are inadequate, and must be changed at once.
3. Case Study
3.1. First Expert System
3.2. Hierarchization of the Aggressiveness Factors
3.2.1. Calculation of the Diagram and Interpretation of the Risk
3.2.2. Definition of the Weights of the Criteria and the Experts
3.2.3. Application of Operators
3.3. Determination of the Global Aggressiveness Factor
3.4. Capture and Processing of the Machining Audio Signals
3.5. Second Expert System
3.6. Strategy for the Reinforcement of the Knowledge Base
3.7. Calculation of the Diagram and Risk Interpretation
3.8. Validation
4. Discussion
 Expert systems: The use of expert systems, with respect to other prediction models used in artificial intelligence, such as machine learning or deep learning algorithms, and even classic statistical inference models, presents a differential advantage resulting from the use of symbolic reasoning for the creation of its knowledge base and its inference mechanism. In the face of normal computational reasoning, based on the identification of the statistical relevance of the collected data, and implemented by means of different algorithms such as random forest, Naïve Bayes, and different types of neural networks and evolutional programming approaches, symbolic reasoning possesses the ability to model knowledge based on symbols, such as in common language. On the other hand, the conceptualization of expert systems facilitates the diversification of the knowledge derived from information sources—in this case experts from the machining field—as well as generalizing its formalization [78], which allows and simplifies the appropriate use of machines by staff members possessing different skill and expertise levels in the field of study. This will result in a reduction in the machine’s dependence on its operator’s skills, and in the incorporation of external expertise and knowledge into the control of the machining process. Expert systems also help to reduce the uncertainty that is inherent to the machine condition assessment process itself, both the random or epistemic, and that associated to the vagueness that is present in human language [79]. It is of interest to mention that the inference engine used by the expert systems could be a different one, in this way making possible the incorporation of other engines or algorithms, which endows it with greater versatility and adaptability.
 Vague fuzzy sets: The use of multicriteria models is common in decisionmaking stages, where a decisionmaker must determine the ranking of a collection of alternatives according to some criteria in order to select the best option. As was already mentioned in the subsection “1.3. Hierarchization processes”, new approaches have been developed in the last few decades incorporating new abilities that allow for solving some of the limitations that affect the “classic” models. In this work, a choice was made for the use of vague fuzzy sets to determine the hierarchization of the factors presenting a larger impact on the tool’s lifespan, which allows us to construct an error verification protocol that is specific to each machine. The use of this approach allows for not only limiting the random and epistemic [79,80] uncertainty in the scoring process, but also for controlling the hierarchization process itself [67]. Even if it is true that other multicriteria methods exist that allow one to manage uncertainty in an implicit way, the choice of using vague fuzzy numbers is a novelty in the field of study.
Relevance to the Field of Study
5. Conclusions
 It allows one to evaluate the machine’s condition, addressing the different qualitative and qualitative factors that are associated with its usual operation and failure, this being of help to its operators, regardless of whether they are experts or not;
 It reduces the issues associated with a late/premature tool change, which might result in excessive costs to the company, as well as in other potential losses or damages;
 It establishes a standard tool condition evaluation process.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
Abbreviations
AI  Artificial intelligence. 
AF  Aggressiveness factor. 
Specific Aggressiveness Factors  
ACAF  Axial Cutting Depth Aggressiveness Factor. 
CFRAF  Cutting Feed Rate Aggressiveness Factor. 
CFFAF  Cutting Fluid Flow Aggressiveness Factor. 
CSAF  Cutting Speed Aggressiveness Factor. 
InsertAF  Insert’s Cumulated Work Time Aggressiveness Factor. 
CNC  Computer Numerical Control. 
IFHG  Intuitionistic Fuzzy Hybrid Geometric. 
IFOWG  Intuitionistic Fuzzy Ordered Weighted Geometric. 
IFWG  Intuitionistic Fuzzy Weighted Geometric. 
OWG  Ordered Weighted Geometric. 
WG  Weighted Geometric. 
References
 Saptaji, K.; Gebremariam, M.A.; Azhari, M.A.B.M. Machining of Biocompatible Materials: A Review. Int. J. Adv. Manuf. Technol. 2018, 97, 2255–2292. [Google Scholar] [CrossRef]
 Santos, M.C.; Machado, A.R.; Sales, W.F.; Barrozo, M.A.S.; Ezugwu, E.O. Machining of Aluminum Alloys: A Review. Int. J. Adv. Manuf. Technol. 2016, 86, 3067–3080. [Google Scholar] [CrossRef]
 Hovsepian, P.E.; Luo, Q.; Robinson, G.; Pittman, M.; Howarth, M.; Doerwald, D.; Tietema, R.; Sim, W.M.; Deeming, A.; Zeus, T. TiAlN/VN Superlattice Structured PVD Coatings: A New Alternative in Machining of Aluminium Alloys for Aerospace and Automotive Components. Surf. Coat. Technol. 2006, 201, 265–272. [Google Scholar] [CrossRef]
 Byrne, G.; Dornfeld, D.; Inasaki, I.; Ketteler, G.; König, W.; Teti, R. Tool Condition Monitoring (TCM)—The Status of Research and Industrial Application. CIRP Ann.—Manuf. Technol. 1995, 44, 541–567. [Google Scholar] [CrossRef]
 Ji, W.; Wang, L. Industrial Robotic Machining: A Review. Int. J. Adv. Manuf. Technol. 2019, 103, 1239–1255. [Google Scholar] [CrossRef][Green Version]
 Zhou, C.; Guo, K.; Yang, B.; Wang, H.; Sun, J.; Lu, L. Singularity Analysis of Cutting Force and Vibration for Tool Condition Monitoring in Milling. IEEE Access 2019, 7, 134113–134124. [Google Scholar] [CrossRef]
 Kurada, S.; Bradley, C. A Review of Machine Vision Sensors for Tool Condition Monitoring. Comput. Ind. 1997, 34, 55–72. [Google Scholar] [CrossRef]
 Ambhore, N.; Kamble, D.; Chinchanikar, S.; Wayal, V. Tool Condition Monitoring System: A Review. Mater. Today Proc. 2015, 2, 3419–3428. [Google Scholar] [CrossRef]
 Rehorn, A.G.; Jiang, J.; Orban, P.E. StateoftheArt Methods and Results in Tool Condition Monitoring: A Review. Int. J. Adv. Manuf. Technol. 2005, 26, 693–710. [Google Scholar] [CrossRef]
 Mohanraj, T.; Shankar, S.; Rajasekar, R.; Sakthivel, N.R.; Pramanik, A. Tool Condition Monitoring Techniques in Milling Processa Review. J. Mater. Res. Technol. 2020, 9, 1032–1042. [Google Scholar] [CrossRef]
 Serin, G.; Sener, B.; Ozbayoglu, A.M.; Unver, H.O. Review of Tool Condition Monitoring in Machining and Opportunities for Deep Learning. Int. J. Adv. Manuf. Technol. 2020, 109, 953–974. [Google Scholar] [CrossRef]
 Ruitao, P.; Pang, H.; Jiang, H.; Hu, Y. Study of Tool Wear Monitoring Using Machine Vision. Autom. Control Comput. Sci. 2020, 54, 259–270. [Google Scholar] [CrossRef]
 Dou, J.; Xu, C.; Jiao, S.; Li, B.; Zhang, J.; Xu, X. An Unsupervised Online Monitoring Method for Tool Wear Using a Sparse AutoEncoder. Int. J. Adv. Manuf. Technol. 2020, 106, 2493–2507. [Google Scholar] [CrossRef]
 Fong, K.M.; Wang, X.; Kamaruddin, S.; Ismadi, M.Z. Investigation on Universal Tool Wear Measurement Technique Using ImageBased CrossCorrelation Analysis. Meas. J. Int. Meas. Confed. 2021, 169, 108489. [Google Scholar] [CrossRef]
 Teti, R.; Jemielniak, K.; O’Donnell, G.; Dornfeld, D. Advanced Monitoring of Machining Operations. CIRP Ann.—Manuf. Technol. 2010, 59, 717–739. [Google Scholar] [CrossRef][Green Version]
 Sick, B. OnLine and Indirect Tool Wear Monitoring in Turning with Artificial Neural Networks: A Review of More than a Decade of Research. Mech. Syst. Signal Process. 2002, 16, 487–546. [Google Scholar] [CrossRef]
 Shi, X.; Wang, R.; Chen, Q.; Shao, H. Cutting Sound Signal Processing for Tool Breakage Detection in Face Milling Based on Empirical Mode Decomposition and Independent Component Analysis. JVC/J. Vib. Control 2015, 21, 3348–3358. [Google Scholar] [CrossRef]
 Burstein, F.; Holsapple, C.W. Handbook on Decision Support Systems 1; Springer: Berlin, Germany, 2008. [Google Scholar]
 Burstein, F.; Holsapple, C.W. Handbook on Decision Support Systems 2; Springer: Berlin, Germany, 2008. [Google Scholar]
 Bonczek, R.H.; Holsapple, C.W.; Whinston, A.B.; Carter, H. Foundations of Decision Support Systems; Academic Press: New York, NY, USA, 1981. [Google Scholar]
 Hevner, A.R.; Chatterjee, S. Design Research in Information Systems: Theory and Practice; Springer: New York, NY, USA, 2010; ISBN 9781441961075. [Google Scholar]
 Lucas, P.J.F.; van der Gaag, L.C. Principles of Expert Systems; AddisonWesley: Wokingham, UK, 1991; ISBN 0201416409. [Google Scholar]
 Krishnamoorthy, C.S.; Rajeev, S. Artificial Intelligence and Expert Systems for Engineers; CRC Press: Boca Raton, FL, USA, 1996. [Google Scholar]
 Liao, S.H. Expert System Methodologies and Applicationsa Decade Review from 1995 to 2004. Expert Syst. Appl. 2005, 28, 93–103. [Google Scholar] [CrossRef]
 Sol, H.G.; Takkenberg, C.A.T.; de Vries Robbé, P.F. Expert Systems and Artificial Intelligence in Decision Support Systems. In Proceedings of the Second Mini Euroconference, Lunteren, The Netherlands, 17–20 November 1985. [Google Scholar]
 Kumar, Y.; Jain, Y. Research Aspects of Expert System. Int. J. Comput. Bus. Res. 2012, 1, 1–11. [Google Scholar]
 Myers, W. Introduction to Expert Systems. IEEE Expert 1986, 1, 100–109. [Google Scholar] [CrossRef]
 Buchanan, B.G. Expert Systems: Working Systems and the Research Literature. Expert Syst. 1986, 3, 32–50. [Google Scholar] [CrossRef]
 Todd, B.S. An Introduction to Expert Systems; Oxford University Computing Laboratory: Oxford, UK, 1992. [Google Scholar]
 Merritt, D. Building Expert Systems in Prolog; Springer: New York, NY, USA, 1989; ISBN 9781461389132. [Google Scholar]
 ComesañaCampos, A.; CasalGuisande, M.; CerqueiroPequeño, J.; BouzaRodríguez, J.B. A Methodology Based on Expert Systems for the Early Detection and Prevention of Hypoxemic Clinical Cases. Int. J. Environ. Res. Public Health 2020, 17, 8644. [Google Scholar] [CrossRef]
 CasalGuisande, M.; ComesañaCampos, A.; CerqueiroPequeño, J.; BouzaRodríguez, J.B. Design and Development of a Methodology Based on Expert Systems, Applied to the Treatment of Pressure Ulcers. Diagnostics 2020, 10, 614. [Google Scholar] [CrossRef] [PubMed]
 Grosan, C.; Abraham, A. RuleBased Expert Systems. Intell. Syst. Ref. Libr. 2011, 17, 149–185. [Google Scholar] [CrossRef]
 Berzal, F. Redes Neuronales & Deep Learning; Independently Published: Granada, Spain, 2018; ISBN 1731265387. [Google Scholar]
 Jackson, P. Introduction to Expert Systems; AddisonWesley Publishing Co., Inc.: Wokingham, UK, 1986. [Google Scholar]
 Leondes, C.T. Expert Systems: The Technology of Knowledge Management and Decision Making for the 21st Century; Academic Press: San Diego, CA, USA, 2002; ISBN 9780124438804. [Google Scholar]
 Hevner, A.R.; March, S.T.; Park, J.; Ram, S. Design Science in Information Systems Research. MIS Q. Manag. Inf. Syst. 2004, 28, 75–105. [Google Scholar] [CrossRef][Green Version]
 Elangovan, M.; Ramachandran, K.I.; Sugumaran, V. Studies on Bayes Classifier for Condition Monitoring of Single Point Carbide Tipped Tool Based on Statistical and Histogram Features. Expert Syst. Appl. 2010, 37, 2059–2065. [Google Scholar] [CrossRef]
 Elangovan, M.; Devasenapati, S.B.; Sakthivel, N.R.; Ramachandran, K.I. Evaluation of Expert System for Condition Monitoring of a Single Point Cutting Tool Using Principle Component Analysis and Decision Tree Algorithm. Expert Syst. Appl. 2011, 38, 4450–4459. [Google Scholar] [CrossRef]
 Mesina, O.S.; Langari, R. A NeuroFuzzy System for Tool Condition Monitoring in Metal Cutting. J. Manuf. Sci. Eng. Trans. ASME 2001, 123, 312–318. [Google Scholar] [CrossRef]
 Saglam, H.; Unuvar, A. Tool Condition Monitoring in Milling Based on Cutting Forces by a Neural Network. Int. J. Prod. Res. 2003, 41, 1519–1532. [Google Scholar] [CrossRef]
 Li, S.; Elbestawi, M.A. Tool Condition Monitoring in Machining by Fuzzy Neural Networks. J. Dyn. Syst. Meas. Control Trans. ASME 1996, 118, 665–672. [Google Scholar] [CrossRef]
 Patange, A.D.; Jegadeeshwaran, R.; Dhobale, N.C. Milling Cutter Condition Monitoring Using Machine Learning Approach. IOP Conf. Ser. Mater. Sci. Eng. 2019, 624, 012030. [Google Scholar] [CrossRef]
 Zaloha, V.O.; Zinchenko, R.M.; Honshchyk, A.V. ANFIS Building Methodology for the Task of Cutting Tool Condition Diagnosis Using Matlab Software. Key Eng. Mater. 2014, 581, 466–471. [Google Scholar]
 Silva, R.G.; Reuben, R.L.; Baker, K.J.; Wilcox, S.J. Tool Wear Monitoring of Turning Operations by Neural Network and Expert System Classification of a Feature Set Generated from Multiple Sensors. Mech. Syst. Signal Process. 1998, 12, 319–332. [Google Scholar] [CrossRef]
 Aralikatti, S.S.; Ravikumar, K.N.; Kumar, H.; Shivananda Nayaka, H.; Sugumaran, V. Comparative Study on Tool Fault Diagnosis Methods Using Vibration Signals and Cutting Force Signals by Machine Learning Technique. SDHM Struct. Durab. Health Monit. 2020, 14, 127–145. [Google Scholar] [CrossRef]
 Zuperl, U.; Cus, F.; Balic, J. Intelligent Cutting Tool Condition Monitoring in Milling. J. Achiev. Mater. Manuf. Eng. 2011, 49, 477–486. [Google Scholar]
 Lin, X.; Zhou, B.; Zhu, L. Sequential Spindle CurrentBased Tool Condition Monitoring with Support Vector Classifier for Milling Process. Int. J. Adv. Manuf. Technol. 2017, 92, 3319–3328. [Google Scholar] [CrossRef]
 Hwang, C.L.; Yoon, K. Multiple Attribute Decision Making: Methods and Applications A StateoftheArt Survey; Springer: Berlin/Heidelberg, Germany, 1981; ISBN 9783642483189. [Google Scholar]
 Miller, G.A. The Magical Number Seven, plus or Minus Two: Some Limits on Our Capacity for Processing Information. Psychol. Rev. 1956, 63, 81–97. [Google Scholar] [CrossRef][Green Version]
 Pugh, S. Concept Selection—A Method That Works. In Proceedings of the International Conference on Engineering Design, Heurista, Zürich, Rome, Italy, 9–13 August 1981; pp. 497–506. [Google Scholar]
 Pugh, S. Total Design: Integrated Methods for Successful Product Engineering; AddisonWesley: Wokingham, England, 1991. [Google Scholar]
 Saaty, T.L. How to Make a Decision: The Analytic Hierarchy Process. Eur. J. Oper. Res. 1990, 48, 9–26. [Google Scholar] [CrossRef]
 Marsh, E.; Slocum, A.H.; Otto, K.N. Hierarchical Decision Making in Machine Design; Technical Report; MIT Precision Engineering Research Center: Cambridge, MA, USA, 1993. [Google Scholar]
 Behzadian, M.; Khanmohammadi Otaghsara, S.; Yazdani, M.; Ignatius, J. A Stateof theArt Survey of TOPSIS Applications. Expert Syst. Appl. 2012, 39, 13051–13069. [Google Scholar] [CrossRef]
 Opricovic, S.; Tzeng, G.H. Compromise Solution by MCDM Methods: A Comparative Analysis of VIKOR and TOPSIS. Eur. J. Oper. Res. 2004, 156, 445–455. [Google Scholar] [CrossRef]
 Brans, J.P.; Vincke, P.; Mareschal, B. How to Select and How to Rank Projects: The Promethee Method. Eur. J. Oper. Res. 1986, 24, 228–238. [Google Scholar] [CrossRef]
 Behzadian, M.; Kazemzadeh, R.B.; Albadvi, A.; Aghdasi, M. PROMETHEE: A Comprehensive Literature Review on Methodologies and Applications. Eur. J. Oper. Res. 2010, 200, 198–215. [Google Scholar] [CrossRef]
 Dyer, J.S. Maut—Multiattribute Utility Theory. In Multiple Criteria Decision Analysis: State of the Art Surveys; Springer: New York, NY, USA, 2005; Volume 78, pp. 265–295. ISBN 9780387230672. [Google Scholar]
 Zadeh, L.A. Fuzzy Sets. Inf. Control 1965, 8, 338–353. [Google Scholar] [CrossRef][Green Version]
 Bellman, R.E.; Zadeh, L.A. DecisionMaking in a Fuzzy Environment. Manag. Sci. 1970, 17, B141–B164. [Google Scholar] [CrossRef]
 Gau, W.L.; Buehrer, D.J. Vague Sets. IEEE Trans. Syst. Man Cybern. 1993, 23, 610–614. [Google Scholar] [CrossRef]
 Bustince, H.; Burillo, P. Vague Sets Are Intuitionistic Fuzzy Sets. Fuzzy Sets Syst. 1996, 79, 403–405. [Google Scholar] [CrossRef]
 Xu, Z. MultiPerson MultiAttribute Decision Making Models under Intuitionistic Fuzzy Environment. Fuzzy Optim. Decis. Mak. 2007, 6, 221–236. [Google Scholar] [CrossRef]
 Atanassov, K. Intuitionistic Fuzzy Sets. In Proceedings of the VII ITKR’s Session, Sofia, Bulgaria, 7–9 June 1983. [Google Scholar]
 Atanassov, K.T. Intuitionistic Fuzzy Sets. Fuzzy Sets Syst. 1986, 20, 87–96. [Google Scholar] [CrossRef]
 Xu, Z.; Yager, R.R. Some Geometric Aggregation Operators Based on Intuitionistic Fuzzy Sets. Int. J. Gen. Syst. 2006, 35, 417–433. [Google Scholar] [CrossRef]
 Xu, Z. An Overview of Methods for Determining OWA Weights. Int. J. Intell. Syst. 2005, 20, 843–865. [Google Scholar] [CrossRef]
 Mamdani, E.H.; Assilian, S. An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller. Int. J. ManMach. Stud. 1975, 7, 1–13. [Google Scholar] [CrossRef]
 Mamdani, E.H. Advances in the Linguistic Synthesis of Fuzzy Controllers. Int. J. ManMach. Stud. 1976, 8, 669–678. [Google Scholar] [CrossRef]
 Mamdani, E.H. Application of Fuzzy Logic to Approximate Reasoning Using Linguistic Synthesis. IEEE Trans. Comput. 1977, C–26, 1182–1191. [Google Scholar] [CrossRef]
 Ross, T.J. Fuzzy Logic with Engineering Applications, 3rd ed.; John Wiley & Sons, Ltd.: Chichester, UK, 2010; ISBN 9781119994374. [Google Scholar]
 GRANTA EduPack, Formerly CES EduPack: Materials Education Support  Ansys. Available online: https://www.ansys.com/products/materials/grantaedupack (accessed on 29 December 2020).
 Atanassov, K.T. Intuitionistic Fuzzy Sets; PhysicaVerlag Heidelberg: Heidelberg, Germany, 1999; ISBN 9783790824636. [Google Scholar]
 Chen, S.M.; Tan, J.M. Handling Multicriteria Fuzzy DecisionMaking Problems Based on Vague Set Theory. Fuzzy Sets Syst. 1994, 67, 163–172. [Google Scholar] [CrossRef]
 Chai, T.; Draxler, R.R. Root Mean Square Error (RMSE) or Mean Absolute Error (MAE)?Arguments against Avoiding RMSE in the Literature. Geosci. Model Dev. 2014, 7, 1247–1250. [Google Scholar] [CrossRef][Green Version]
 Dubovikov, K. Managing Data Science; Packt Publishing Ltd.: Birmingham, UK, 2019; ISBN 9781838826321. [Google Scholar]
 Pfeifer, R.; Lüthi, H.J. Decision Support Systems and Expert Systems: A Complementary Relationship? In Expert Systems and Artificial Intelligence in Decision Support Systems; Springer: Dordrecht, The Netherlands, 1987; pp. 41–51. [Google Scholar]
 Thunnissen, D.P. Propagating and Mitigating Uncertainty in the Design of Complex Multidisciplinary Systems; California Institute of Technology: Pasadena, CA, USA, 2005. [Google Scholar]
 Herrmann, J.W. Engineering Decision Making and Risk Management; John Wiley & Sons, Inc.: Hoboken, NJ, USA, 2015; ISBN 9781118919330. [Google Scholar]
Machining Process 


Aggressiveness Factors Associated to the Machining Parameters  

Input Data—Antecedents  Output Data—Consequents  
Factors  Range  Factors  Range 
Cutting speed (CS)  0–1000 m/min  CSAF  0–10 
Cutting feed rate (CFR)  0–1 mm/turn  CFRAF  
Axial cutting depth (AD)  0–10 mm  ADAF  
Cutting fluid flow (CFF)  0–100%  CFFAF  
Insert’s cumulated work time (insert)  0–100 min  InsertAF  
Machinability of the material  0–5  * AF (aggressiveness factor) * The denomination of the output data indicator consists of two parts. The term on the left of the dash refers to the input variable, while the term on the right of the dash, AF, refers to the aggressiveness factor. For example, CSAF refers to the cutting speed aggressiveness factor.  
Membership functions of the antecedents  Membership functions of the consequents  
Cutting speed (CS)  * In the initial configuration of the inference system, the membership functions of the consequents, that is, of the particular aggressiveness factors for each parameter, are the same, thus only a graph is shown.  
Cutting feed rate (CFR)  
Axial cutting depth (AD)  Initial configuration  
 
Cutting fluid flow (CFF)  Subset of the 45 fuzzy rules
 
Insert’s cumulated work time (insert)  
Machinability of the material  
Intuitionistic Fuzzy Set  Vague Fuzzy Set 

${A}_{I}=\left\{\langle x,{\mu}_{A}\left(x\right),{v}_{A}\left(x\right)\rangle \mid x\in X\right\}$  ${A}_{V}=\left\{\langle x,\left[{t}_{A}\left(x\right),1{f}_{A}\left(x\right)\right]\rangle \mid x\in X\right\}$ 
${\mu}_{A}\left(x\right)+{v}_{A}\left(x\right)\le 1$  ${t}_{A}\left(x\right)+{f}_{A}\left(x\right)\le 1$ 
Aggressiveness Factors Associated with the Machining Parameters  

Input Data—Antecedents  Output Data—Consequents  
Factors  Range  Factors  Range 
Global aggressiveness factor (AF Global)  −1 through 1  Tool risk  0–100 
Sound processing and comparison output (Delta_area_centroid)  0 5000  
Membership functions of the antecedents  Membership functions of the consequent  
Global aggressiveness factor (AF Global)  
Sound processing and comparison output (Delta_area_centroid)  Initial configuration  
 
Subset of the 9 fuzzy rules

Machining Process  

Process  Lathe machining 
Tool  
Designation  DNMG 15 06 08MR 2025 
Insert thickness  6.35 mm 
Cumulated work time of the old insert  30 min 
Cumulated work time of the new insert  0 min 
General Variables of the Machining Process  
Cutting speed  150 m/min 
Cutting feed rate  0.2 mm/turn 
Axial cutting depth  1 mm 
Cutting fluid flow  0% 
Insert’s cumulated work time  30 min 
Material to be machined  
Material  Aluminium 
Machinability  4.5 
Cutting Speed Aggressiveness Factor  Cutting Feed Rate Aggressiveness Factor  Axial Cutting Depth Aggressiveness Factor  Cutting Fluid Flow Aggressiveness Factor  Insert’s Cumulated Work Time Aggressiveness Factor 

2.3733  2.1582  2.1582  5  5 
E_{1}  A_{1}  A_{2}  A_{3}  A_{4}  A_{5}  

${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  
C_{1}  1  1  0.5  0.9  0.5  0.8  0.6  0.8  0.8  1 
C_{2}  0.6  0.9  1  1  0.6  0.9  0.5  0.7  0.8  1 
C_{3}  0.5  0.8  0.4  0.7  1  1  0.7  0.8  0.8  1 
C_{4}  0.7  1  0.6  0.9  0.2  0.3  1  1  0.8  1 
C_{5}  0.8  0.9  0.6  0.8  0.6  0.7  0.6  0.9  1  1 
E_{2}  A_{1}  A_{2}  A_{3}  A_{4}  A_{5}  

${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  
C_{1}  0.9  1  0.8  0.9  0.6  0.7  0.5  0.9  0.6  0.9 
C_{2}  0.4  0.8  0.8  1  0.7  1  0.4  0.6  0.4  0.8 
C_{3}  0.6  0.7  0.5  0.9  0.9  1  0.8  1  0.7  0.9 
C_{4}  0.7  0.9  0.7  0.9  0.3  0.5  0.7  0.9  0.6  0.9 
C_{5}  0.5  0.7  0.7  1  0.4  0.9  0.4  1  0.9  1 
A_{1}  A_{2}  A_{3}  A_{4}  A_{5}  

${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  ${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  
C_{1}  0.979  1.000  0.549  0.900  0.519  0.779  0.579  0.819  0.755  0.979 
C_{2}  0.553  0.879  0.956  1.000  0.619  0.919  0.478  0.679  0.696  0.956 
C_{3}  0.519  0.779  0.418  0.736  0.979  1.000  0.719  0.837  0.779  0.979 
C_{4}  0.700  0.979  0.619  0.900  0.217  0.332  0.931  0.979  0.755  0.979 
C_{5}  0.728  0.856  0.619  0.837  0.553  0.736  0.553  0.919  0.979  1.000 
${\mathit{t}}_{\tilde{\mathit{a}}}$  $1{\mathit{f}}_{\tilde{\mathit{a}}}$  

A_{1}  0.68  0.89 
A_{2}  0.60  0.86 
A_{3}  0.52  0.70 
A_{4}  0.64  0.86 
A_{5}  0.81  0.98 
Rank  $\mathit{S}\left(\tilde{\mathit{a}}\right)$ 

A_{5}  0.793 
A_{1}  0.564 
A_{4}  0.495 
A_{2}  0.459 
A_{3}  0.214 
Aggressiveness Factors  

Experts  Cutting Speed  Cutting Feed Rate  Axial Cutting Depth  Cutting Fluid Flow  Insert’s Cumulated Work Time  Total 
Expert A  25%  5%  5%  25%  40%  100% 
Expert B  20%  15%  10%  20%  35%  100% 
Expert C  20%  10%  10%  30%  30%  100% 
Expert D  20%  15%  15%  40%  10%  100% 
Expert E  30%  25%  5%  20%  20%  100% 
Methodology  22%  18%  8%  20%  32%  100% 
Experts  RMSE  RMSE Mean Value 

Expert A  7%  7.2% 
Expert B  2%  
Expert C  6%  
Expert D  14%  
Expert E  7% 
Method/System  Efficiency  Scalability  Inference  Learning  Adaptability 

Elangovan et al. [39]  The proposed system is based in the use of a decision trees classifier. It does not manage uncertainty.  The system is not scalable.  It uses statistical inference instead of symbolic reasoning.  The system incorporates knowledge in a way that is subsidiary to its classification process.  The system could not be easily used for monitoring other machine types, as it would require generating a preliminary dataset. 
          
Mesina and Langari [40]  The authors use a neurofuzzy system, which does manage uncertainty.  The system is not scalable.  It uses statistical inference and symbolic reasoning.  The system incorporates knowledge by means of a training process.  The system could not be easily used for monitoring other machine types, as it would require generating a training dataset. 
=    =      
Saglam and Unuvar [41]  The proposed system is based in the use of a neural network, which implicitly manages uncertainty in a probabilistic way.  The system is not scalable.  The system uses statistical inference instead of symbolic reasoning.  The system incorporates new knowledge in the process of training the architecture.  The system could not be easily used for monitoring other machine types, as it would require a training dataset. 
=          
Patange et al. [43]  The proposed system is based in the use of decision trees and random forest, which do not manage uncertainty.  The system is not scalable.  It uses statistical inference instead of symbolic reasoning.  The system incorporates knowledge in a subsidiary way to its classification process.  The system could not be easily used for monitoring other machine types. It would require a training dataset. 
          
Aralikatti et al. [46]  The proposed system is based in the use of machine learning techniques, including the use of the Naïve Bayes classifier. A probabilistic approach is applied to uncertainty control.  The system is not scalable.  The proposed system uses statistical inference instead of symbolic reasoning.  The system incorporates knowledge in a subsidiary way to its classification process.  The system could not be easily used for monitoring other machine types. It requires a training dataset. 
=          
Lin et al. [48]  The proposed system is based on a least squares support vector machine (LSSVM) classifier. It does not manage uncertainty in the starting data.  The system is not scalable.  The proposed system uses statistical inference instead of symbolic reasoning.  The system incorporates knowledge in a way that is subsidiary to its classification process.  The system could not be easily used for monitoring other machine types. It would require a training dataset. 
          
Proposed system  The proposed system manages uncertainty by means of the use of nonprobabilistic approaches.  The proposed system is scalable. It is possible to modify the calculation and inference modules.  The proposed system uses deductive symbolic reasoning.  The system has the capability of modeling and incorporating new knowledge. Additionally, it is provided with a reinforcement module, by means of which it is possible to correct its behavior as the system is being used.  The system could easily be adapted to the monitoring of other machine types. It does not require a training process. 
Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. 
© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
CasalGuisande, M.; ComesañaCampos, A.; Pereira, A.; BouzaRodríguez, J.B.; CerqueiroPequeño, J. A DecisionMaking Methodology Based on Expert Systems Applied to Machining Tools Condition Monitoring. Mathematics 2022, 10, 520. https://doi.org/10.3390/math10030520
CasalGuisande M, ComesañaCampos A, Pereira A, BouzaRodríguez JB, CerqueiroPequeño J. A DecisionMaking Methodology Based on Expert Systems Applied to Machining Tools Condition Monitoring. Mathematics. 2022; 10(3):520. https://doi.org/10.3390/math10030520
Chicago/Turabian StyleCasalGuisande, Manuel, Alberto ComesañaCampos, Alejandro Pereira, JoséBenito BouzaRodríguez, and Jorge CerqueiroPequeño. 2022. "A DecisionMaking Methodology Based on Expert Systems Applied to Machining Tools Condition Monitoring" Mathematics 10, no. 3: 520. https://doi.org/10.3390/math10030520