Structure-optimizing identification of nonlinear systems using elitist particle filtering

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The identification of real-world physical and technical systems is a classical task in statistical signal theory, where the identification of systems with memory and a nonlinear relation between the model coefficients and the observations (so-called NIK models with memory) attracts increasing attention as a new research challenge. Such models are especially relevant for electromagnetic and electroacoustic transducers in a nonlinear operating mode (e.g., hysteresis, overload). Based on our own and other prior work, it seems very promising to develop methods for the structure-optimizing identification of NIK models with memory, where both coefficients and structure parameters (e.g., model order) of the nonlinear system are estimated simultaneously. In this project we aim at demonstrating that the EPFES (elitist particle filter based on evolutionary strategies) algorithm, as recently proposed by the group of the applicant, meets decisive requirements to considerably advance the state of the art. In contrast to classical linearization methods or local optimization techniques, the EPFES combines fundamental methods of machine learning and genetic algorithms to model coefficients as random variables and to evaluate realizations of these random variables (so-called particles) based on long-term fitness measures. While the EPFES algorithm has been successfully verified for the identification of time-varying memoryless systems, this proposal focuses on further generalizing the EPFES approach and combining the resulting algorithms with methods for model and structure optimization with the goal to develop a universal approach for structure-optimizing identification of NIK-models with memory. In work package 1, the heuristically motivated long-term evaluation underlying the EPFES approach shall be conceptually advanced by adopting techniques from other research areas (e.g., particle swarm optimization) to identify nonlinear systems with memory, such as neural networks with feedback or time delays. In work package 2, for further model optimization, explicit physical knowledge should be incorporated into the estimation procedure following the concept of significance-aware filtering. Furthermore, the structure-optimizing identification of nonlinear systems with memory should be investigated in work package 3 by comparing different combinations of competing model structures. Finally, the EPFES-based approach developed so far will be applied to multichannel system identification in work package 4 and considered in various transform domains, e.g., in the wave domain. Experimental verification of the developed estimation schemes will focus on tasks in the area of acoustic signal processing, which are characterized by highly challenging signal properties but also by significant practical relevance and relatively easy access to realistic data.