非线性系统辨识的多目标进化框架研究
Multi-Objective Evolutionary Framework for Non-linear System Identification: A Comprehensive Investigation
摘要：
本文提出了一个多目标的非线性系统结构选择框架，该框架由多项式NARX模型表示。该框架集成了多准则决策（MCDM），其中包括偏好处理，多目标进化算法（MOEAs）和后验选择的关键组成部分。为此，三个著名的MOEA，如NSGA-II，SPEA-II和MOEA/D进行了彻底的调查，以确定是否存在任何显着差异，其搜索性能。所有这些MOEA的各种定性和定量参数，如重组机制，交叉和突变概率的选择的敏感性，也进行了研究。这些问题进行了批判性的分析，考虑七个离散时间和连续时间基准非线性系统，以及非线性波浪力建模的实际案例研究。这项调查的结果表明，MOEA可以定制，以确定正确的非线性系统的结构。此外，通过频域分析已经确定，可以识别连续时间系统的多个有效离散时间模型。一个严格的统计分析的MOEA通过性能的甜蜜点在参数空间令人信服地表明，这些算法是强大的控制参数范围很广。
英文摘要：
The present study proposes a multi-objective framework for structure selection of nonlinear systems which are represented by polynomial NARX models. This framework integrates the key components of Multi-Criteria Decision Making (MCDM) which include preference handling, Multi-Objective Evolutionary Algorithms (MOEAs) and a posteriori selection. To this end, three well-known MOEAs such as NSGA-II, SPEA-II and MOEA/D are thoroughly investigated to determine if there exists any significant difference in their search performance. The sensitivity of all these MOEAs to various qualitative and quantitative parameters, such as the choice of recombination mechanism, crossover and mutation probabilities, is also studied. These issues are critically analyzed considering seven discrete-time and a continuous-time benchmark nonlinear system as well as a practical case study of non-linear wave-force modeling. The results of this investigation demonstrate that MOEAs can be tailored to determine the correct structure of nonlinear systems. Further, it has been established through frequency domain analysis that it is possible to identify multiple valid discrete-time models for continuous-time systems. A rigorous statistical analysis of MOEAs via performance sweet spots in the parameter space convincingly demonstrates that these algorithms are robust over a wide range of control parameters.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
