Structure-optimizing identification of nonlinear systems using elitist particle filtering

现实世界物理和技术系统的识别是统计信号理论中的一个经典任务，其中具有记忆的系统的识别以及模型系数与观测值之间的非线性关系（所谓的具有记忆的NIK模型）作为一个新的研究挑战越来越受到关注。这种模型特别适用于非线性工作模式下的电磁和电声换能器（如迟滞、过载）。基于我们自己和其他先前的工作，开发具有记忆的NIK模型的结构优化识别方法似乎非常有前途，其中非线性系统的系数和结构参数（例如，模型阶数）同时估计。在这个项目中，我们的目标是证明EPFES（基于进化策略的精英粒子过滤器）算法，正如申请人小组最近提出的那样，满足了显著推进当前技术水平的决定性要求。与经典的线性化方法或局部优化技术相比，EPFES结合了机器学习和遗传算法的基本方法，将系数建模为随机变量，并基于长期适应度测量评估这些随机变量（所谓的粒子）的实现。EPFES算法已被成功验证用于时变无记忆系统的识别，本论文的重点是进一步推广EPFES方法，并将所得算法与模型和结构优化方法相结合，目标是开发一种具有记忆的nik模型结构优化识别的通用方法。在工作包1中，EPFES方法的启发式动机长期评估将通过采用其他研究领域的技术（例如，粒子群优化）在概念上推进，以识别具有记忆的非线性系统，例如具有反馈或时间延迟的神经网络。在工作包2中，为了进一步优化模型，应该将明确的物理知识纳入到遵循意义感知过滤概念的估计过程中。此外，在工作包3中，通过比较竞争模型结构的不同组合，研究具有记忆的非线性系统的结构优化识别问题。最后，到目前为止开发的基于epfes的方法将应用于工作包4中的多通道系统识别，并考虑在各种变换域中，例如在波域中。所开发的估计方案的实验验证将集中在声信号处理领域的任务上，这些任务的特点是具有高度挑战性的信号特性，但也具有重要的实际相关性和相对容易获得的实际数据。

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.