Systematic Adaptive Fuzzy Logic Modelling of Complex Systems From Input-Output Data

Abstract

The complex nonlinear systems, which are difficult to be mathematically modelled, can be described by a fuzzy model. This article attempts to improve and to address the problems concerning the systematic fuzzy-logic modelling of multi-input-muiti-output (MIMO) systems, by introducing the following three concepts. 1) A generalized and parameterized reasoning mechanism constructed based on the weighted sum of the normalized defuzzified output value of each individual rule. Then the crisp outputs of the fuzzy model can be directly calculated from the crisp inputs using the parameterized reasoning mechanism. This reasoning mechanism is suitable for online learning and real-time control applications. 2) A gradient-descent based parameter adjustment to tune the parameters of reasoning mechanism (which are equal to the number of rules) instead of the existing heuristic complex parameter identification in the literature. 3) An improved method to select the main system input from all input candidates in the presence of singularity. The proposed systematic method of fuzzy modelling has the advantages of simplicity, flexibility, and high accuracy. The two example data, which have been widely used in the literature as benchmark, are used to evaluate the performance of the proposed method.

Development of an adaptive fuzzy logic-based inverse dynamic model for laser cladding process

“…According to the literature Turksen (1997), fuzzy modelling consists of building two essential components: (i) a knowledge-base consisting of a set of fuzzy rules and (ii) a reasoning mechanism, which is an inference procedure that derives conclusions from a set of fuzzy IF-THEN rule and known facts. In the most recent fuzzy modelling approach, the knowledge-base of a fuzzy model, which is a set of R rules, can be built by system identification using the input-output data of the systems (Sugeno and Yasukawa, 1993;Wang, 1992;Emami et al, 1998;Zeinali and Notash, 2005). Systematic fuzzy modelling can be summarized by the flowchart depicted in Fig.…”

“…Therefore, in order to generate the optimum number of rules, it is required to have a fuzzy partitioning method that relates the system inputs and outputs. The fuzzy partitioning based on clustering proposed by Sugeno and Yasukawa (1993) and was later improved by Emami et al (1998) and Zeinali and Notash (2005) addresses the problems discussed above. The central point of this partitioning approach is that the output space (output data) is partitioned using fuzzy c-mean (FCM) clustering method as a first step of rule generation, Fig.…”

“…The systematic fuzzy modelling method presented in this paper is based on the above portioning method and improved FCM clustering proposed in Zeinali and Notash (2005). Furthermore, the employed fuzzy modelling method uses a new parameterized reasoning mechanism which is also proposed by Zeinali and Notash (2005).…”

“…Fuzzy modelling method (Zadeh, 1973;Sugeno and Yasukawa, 1993) is one of the nonlinear black-box modelling methods which has a universal approximation capability (Wang, 1992). This method is widely used in the literature for modelling of different complex systems (Emami et al, 1998;Zeinali and Notash, 2005). Fuzzy model refers to the models consisting of fuzzy IF-THEN rules and fuzzy inference system.…”

“…In this paper, to address the above mentioned drawbacks, an improved version of the systematic fuzzy modelling method proposed by Zeinali and Notash (2005) is employed to construct the fuzzy inverse dynamic model of the process, which occasionally will be referred to as fuzzy model hereafter. As mentioned earlier, the fuzzy inverse dynamic model is required to calculate the scanning speed (i.e., control input) as a function of desired clad height, powder flow rate and laser power.…”