利用多项式解耦从黑箱非线性状态空间模型恢复高度结构化模型
Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling
摘要：
非线性状态空间建模是一种非常强大的黑箱建模方法。无论多么强大，最终的模型往往是复杂的，由大量的参数描述。在许多情况下，可解释性优于复杂性，使得过于复杂的模型不适合或不受欢迎。在这项工作中，这些模型的复杂性降低检索一个更结构化的，简约的模型，从数据，而不利用物理知识。该方法的关键是将通常在非线性状态空间模型中发现的所有多变量非线性函数转换为单变量非线性函数集。后者是从张量分解计算的。结果表明，通常是一个多余的自由度的描述中使用的非线性系统，而减少representations. The方法产生高度结构化的状态空间模型中的非线性包含在一个单一的单变量函数，与有限的性能损失。仿真和实验结果表明：强迫Duffing振荡器，强迫范德波尔振荡器，一个Bouc-Wen滞后系统，和锂离子电池模型。
英文摘要：
Nonlinear state-space modelling is a very powerful black-box modelling approach. However powerful, the resulting models tend to be complex, described by a large number of parameters. In many cases interpretability is preferred over complexity, making too complex models unfit or undesired. In this work, the complexity of such models is reduced by retrieving a more structured, parsimonious model from the data, without exploiting physical knowledge. Essential to the method is a translation of all multivariate nonlinear functions, typically found in nonlinear state-space models, into sets of univariate nonlinear functions. The latter is computed from a tensor decomposition. It is shown that typically an excess of degrees of freedom are used in the description of the nonlinear system whereas reduced representations can be found. The method yields highly structured state-space models where the nonlinearity is contained in as little as a single univariate function, with limited loss of performance. Results are illustrated on simulations and experiments for: the forced Duffing oscillator, the forced Van der Pol oscillator, a Bouc-Wen hysteretic system, and a Li-Ion battery model.
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