FLEXFIS: A Robust Incremental Learning Approach for Evolving Takagi–Sugeno Fuzzy Models

Abstract

In this paper, we introduce a new algorithm for incremental learning of a specific form of Takagi-Sugeno fuzzy systems proposed by Wang and Mendel in 1992. The new data-driven online learning approach includes not only the adaptation of linear parameters appearing in the rule consequents, but also the incremental learning of premise parameters appearing in the membership functions (fuzzy sets), together with a rule learning strategy in sample mode. A modified version of vector quantization is exploited for rule evolution and an incremental learning of the rules' premise parts. The modifications include an automatic generation of new clusters based on the nature, distribution, and quality of new data and an alternative strategy for selecting the winning cluster (rule) in each incremental learning step. Antecedent and consequent learning are connected in a stable manner, meaning that a convergence toward the optimal parameter set in the least-squares sense can be achieved. An evaluation and a comparison to conventional batch methods based on static and dynamic process models are presented for high-dimensional data recorded at engine test benches and at rolling mills. For the latter, the obtained data-driven fuzzy models are even compared with an analytical physical model. Furthermore, a comparison with other evolving fuzzy systems approaches is carried out based on nonlinear dynamic system identification tasks and a three-input nonlinear function approximation example.Index Terms-Convergence to optimality, incremental clustering, robust evolving fuzzy models, static and dynamic process modeling, Takagi-Sugeno fuzzy systems.

Online active supervision of an evolving classifier for customized-gesture-command learning

“…DENFIS [42], eTS [6,43] and FLEXFIS [44] are among the first evolving fuzzy systems. A lot of similar fuzzy systems have been presented since then.…”

Identifying static and dynamic prediction models for NOx emissions with evolving fuzzy systems

“…f ac is a scaling parameter which can be tuned within a parameter grid search scenario (see Section 4). Condition (5) can be extended by treating the output dimension as a special case, and always evolving new clusters when the distance with respect to this dimension exceeds a pre-defined threshold (denoted as FLEXFIS Variant B in [25]). Here, however, we focus on the original native version FLEXFIS Variant A, as usually outperforming the B variant.…”

“…Our fuzzy modelling approach, called FLEXFIS, which is short for FLEXible Fuzzy Inference Systems [25], was originally developed for the incremental on-line case where single samples are recorded during on-line mode and the fuzzy system automatically updated based on these samples without using any prior (off-line or on-line recorded) samples. There, first the antecedent parts are updated and new rules evolved on demand by using Steps 1 to 4 as described above, and then the linear parameters are incrementally estimated in a single-pass manner by a recursive fuzzily weighted least squares approach (deduced from the recursive weighted least squares [33]) following the local learning spirit and defined by the following formulas:…”

“…However due to the specific adaptation of the learning gain as in (8) (decreasing with the number of samples), a monotonic decreasing behavior of the correction terms which are used in order to balance out the non-optimal solution can be achieved, finally bounding the deviation to optimality. For further details and proofs refer to [25].…”

An Evolving Neuro-Fuzzy System with Online Learning/Self-learning

“…The idea of evolving computational systems is very popular nowadays with Data Mining scientists [19][20][21][22][23][24][25][26]. Both the system's architecture and the amount of adjustable parameters are growing rapidly while processing data.…”