Model Identification with Fuzzy Neural Networks and T-S Model

Application of Fuzzy Neural Networks and T-S Model in System Identification

Fuzzy neural networks represent an intelligent algorithm that combines the advantages of fuzzy logic and neural networks, capable of handling uncertainty and nonlinear problems. The T-S (Takagi-Sugeno) model, as a special form of fuzzy system, simplifies complex system modeling through local linearization.

T-S Model Structural Characteristics The T-S model consists of premise parameters (corresponding to the condition part of fuzzy rules) and consequent parameters (corresponding to the output part of rules). Premise parameters partition the input space through membership functions, while consequent parameters typically employ linear expressions. This "fuzzy premise + linear consequent" structure maintains both the semantic interpretability of fuzzy systems and computational efficiency.

Core Steps for Model Identification Premise Parameter Identification: Automatically determines fuzzy partitioning of input space using clustering algorithms (e.g., Fuzzy C-Means - FCM) without manual rule preset. Implementation typically involves calculating cluster centers and membership degrees through iterative optimization. Consequent Parameter Identification: Determines coefficients for linear sub-models using optimization methods like least squares estimation, which can be implemented through matrix operations (pinv(X)*Y in MATLAB). Parameter Collaborative Optimization: Employs hybrid learning algorithms (e.g., gradient descent combined with least squares) to synchronously adjust premise and consequent parameters. This often involves alternating between structure learning (premise) and parameter learning (consequent).

Advantages and Application Scenarios Compared to traditional methods, T-S fuzzy neural networks' hybrid learning mechanism effectively handles dynamic system identification problems, particularly suitable for: Industrial process control with high nonlinearity Scenarios with noisy input-output data Adaptive systems requiring online updates

In practical applications, attention should be paid to the selection of premise parameter quantity - too few may lead to insufficient modeling accuracy, while too many may cause overfitting issues. Code implementation often requires cross-validation to determine optimal rule numbers.