论文标题
从黑框非线性状态空间模型开始使用多项式解耦来检索高度结构化的模型
Retrieving highly structured models starting from black-box nonlinear state-space models using polynomial decoupling
论文作者
论文摘要
非线性状态空间建模是一种非常强大的黑盒建模方法。多么强大的模型往往是复杂的，这是由大量参数描述的。在许多情况下，可解释性优于复杂性，这使得过于复杂的模型不适合或不需要。在这项工作中，通过从数据中检索更结构化的，简约的模型，而无需利用物理知识来降低此类模型的复杂性。该方法必不可少的是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的翻译，分为单变量非线性函数集。后者是根据张量分解计算的。结果表明，在非线性系统的描述中通常使用过多的自由度，而可以找到减少的表示。该方法产生高度结构化的状态空间模型，其中非线性所包含的单变量功能少，而性能损失有限。在以下模拟和实验上说明了结果：强制行驶振荡器，强制范德尔振荡器，Bouc-Wen滞后系统和锂离子电池模型。
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.
