Fuzzy Logic System Analysis - Report Example

FUZZY LOGIC SYSTEM Introduction This report intends to analyse the reliability of a given machinery. The reliability of any complex system depends on the reliability of the individual components in it. Any complex system can be considered as a control system and can be analysed in many different ways. This report adopts the Fuzzy logic approach to analyse the given control system. This report introduces the concepts of fuzzy logic related to the given machinery. Later it deals with the analysis of the machine performance for a default machine using the fuzzy logic tool box in MATLAB. The results of the analysis for different input and output conditions are compared and finally the best conditions are derived for the best performance of the machine. The given system : The given control system is a manufacturing machinery whose reliability can be analysed through the performance of three parts namely part A, part B and part C present in that machine. In order to diagnose faults in the components there are three sensors associated with them namely sensor 1, sensor 2 and sensor 3. A fault in any one of the three components may require either a cheap or expensive repair. The recovery time, the time that it takes the machine to return to full working order after repair, is either quick or slow or takes an intermediate amount of time. The output values of the sensors are to be controlled in a specific manner to evaluate the condition on the three parts on a scale 0 ( representing good condition – okay ) to 1( representing faulty condition). Representing the machinery in MATLAB : The given machinery can be represented and analysed using the Fuzzy Logic Tool Box available in MATLAB. Fuzzy logic starts with the concept of a fuzzy set. A fuzzy set is a set without a crisp, clearly defined boundary. It can contain elements with only a partial degree of membership. For the given system fuzzy variables are defined for each sensor and each part. The fuzzy variables for each sensor contain three equally sized, linear shaped, overlapping fuzzy sets comprising high, medium and low. The fuzzy variable for each machine part also contains three equally sized, linear shaped, overlapping fuzzy sets comprising of faulty, unreliable and okay. To construct the default system, the Mamdani Fuzzy Inference System in MATLAB GUI has been used. Mamdanis method was among the first control systems built using fuzzy set theory. It was proposed in 1975 by Ebrahim Mamdani (Sabeghi and Naghibzadeh , 2006,). In the FIS editor the default methods for AND , OR, implication, aggregation and defuzzification have been used. Three inputs have been defined with names sens1, sens2, sens3. Three outputs have been defined namely part A, part B, part C. The default FIS is as shown in Fig. 1. Fig. 1. The FIS Editor for the Default system. The membership function editor takes into account the range of the sensors as Sensor 1: 0 – 40 Sensor 2: 20 – 120 Sensor 3: 50 – 200. The range of the output parts are chosen to be 0 to 1. The default ‘trimf’ has been chosen for the inputs and outputs of the default system. Fig. 2 shows the membership editor for the default system. Fig. 2 The membership editor for the default system. The rules of the given system are entered through the rules editor as displayed in fig.3. Analysis of the default System : The default system has been analysed by giving different values for the input like [ 20 70 125 ] which is the mid value of the inputs gives the output value of the three parts as [ 0.5 0.5 0.5 ]. [30 110 190 ] values of input gives the outputs as [ 0.361 0.138 0.188 ] as shown in Fig. 4. The output values for the input [ 30 110 190 ] are nearer the reliable range of operation of the machine which has 0 value as okay and 1 value as faulty. Hence the input values for the default system have been chosen to be [ 30 110 190 ]. Fig.3 the Rule Editor showing the rules for the Default system. Fig.4 the Rule Viewer showing the OUTPUT values of the Default System. Analysis for different TASKs : Task 1 – Modification of fuzzy approaches : The different Fuzzy approaches have been modified and the output has been noted for the chosen input set [ 30 110 190 ]. The output values for the different modified fuzzy methods are shown in Table1. Fuzzy Approach Part A output Part B output Part C output AND (prod) 0.426 0.148 0.167 OR (probor) 0.421 0.148 0.167 IMPLICATION (prod) 0.38 0.14 0.15 AGGREGATION SUM 0.38 0.15 0.17 PROBOR 0.39 0.15 0.169 DEFUZZIFICZTION bisector 0.42 0.12 0.13 Mom 0.38 0.0 0.15 Lom 0.77 0.0 0.03 som 0.0 0.0 0.0 Table 1. The output values for the different modified fuzzy methods It can be seen that the som ( Self Organised Maps) - defuzzification method gives the output values to be 0 ( zero ) that corresponds to reliable (okay) condition. Task 2 – Modification of input fuzzy sets : The membership functions of the original input sets are varied and the corresponding output are noted for the chosen input values of [ 30 110 190]. The output values for the different modified fuzzy sets are shown in Table 2. Member function for input fuzzy sets Part A output Part B output Part C output Trapmf 0.414 0.131 0.134 Gbellmf 0.42 0.14 0.146 Gaussmf 0.415 0.175 0.202 Gauss2mf 0.418 0.418 0.167 Sigmf 0.57 0.501 0.504 Dsigmf 0.45 0.297 0.321 Psigmf 0.45 0.29 0.32 smf 0.58 0.5 0.501 Table 2 . The output values for the different modified input fuzzy sets. It can be seen that the output approaches 0 ( zero), the reliable condition only for ‘trapmf’. Task 3 - Modification of input fuzzy sets : Here the membership functions of the original input sets are kept at default ‘trimf’ but the output sets varied and the corresponding output are noted for the chosen input values of [ 30 110 190]. The output values for the different modified fuzzy sets are shown in Table 3. Member function for output fuzzy sets Part A output Part B output Part C output Trampmf 0.343 0.119 0.167 Gbellmf 0.33 0.13 0.162 Gaussmf 0.359 0.133 0.162 Gauss2mf 0.334 0.113 0.162 Sigmf 0.5 0.5 0.5 Dsigmf 0.401 0.203 0.228 Psigmf 0.401 0.203 0.228 smf 0.5 0.5 0.5 Table 3. The output values for the different modified output fuzzy sets. It can be seen that gbellmf and gauss2mf give more effevtive outputs. Among them gauss2mf is more appropriate for reliable system parts. The most effective system possible : From the above analysis, it can be seen that the following are the requirements for the most appropriate reliable system The fuzzy approach has to be default AND, OR, implication, aggregation. But the defuzzification must be SOM. The membership function of input fuzzy set has to be trampmf. The membership function of output fuzzy set has to be gauss2mf. Based on these fuzzy conditions the final appropriate / effective system has been designed. The following fig.5 shows the FIS editor , fig.6 shows the membership function editor. The analysis of this system shows that the outputs are 0 ( zero) which corresponds to the reliable ( okay) condition for the same chosen input values of [ 30 110 190]. This output is shown in the rule view as in fig.7. Fig. 5 FIS Editor of the final reliable system. Fig. 6 The member function editor of output fuzzy set of the final reliable system. Fig.7 Output values of the final reliable system. Conclusion : This report discusses the fuzzy analysis of a given manufacturing machiney. The default system has been constructed earlier for the given fuzzy rules. Later the different fuzzy approaches, fuzzy sets have been changed to analyse the output values. A desired combination of these fuzzy conditions ie. SOM defuzification approach, trapmf for input fuzzy set, gauss2mf for output fuzzy set have been adopted to get the most appropriate reliable machine . References : 1. M. Sabeghi and Naghibzadeh , 2006, Deadline Vs Laxity as a decision parameter in Fuzzy Real Time Scheduling , 2nd IEEE International Conference on information , 2006. Read More