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首页> 外文期刊>Automatica >IDENTIFICATION OF NON-LINEAR SYSTEMS USING EMPIRICAL DATA AND PRIOR KNOWLEDGE - AN OPTIMIZATION APPROACH
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IDENTIFICATION OF NON-LINEAR SYSTEMS USING EMPIRICAL DATA AND PRIOR KNOWLEDGE - AN OPTIMIZATION APPROACH

机译：利用经验数据和先验知识识别非线性系统的一种优化方法

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The choice of a parametric model structure in empirical and semi-empirical non-linear modeling is usually viewed as an important and critical step. However, it is known that by augmenting the least-squares identification criterion with a term that imposes a penalty on the non-smoothness of the model, an optimal non-parametric model can be found explicitly. The optimal non-parametric model will depend on the particular form of the penalty, which can be looked upon as a priori knowledge, or the desired properties of the model. In this paper these results are extended in several directions: (i) we show how useful types of prior knowledge other than smoothness can be included as a term in the criterion or as a constraint, and how this influences the optimal model; (ii) dynamic models and a general prediction error penalty are considered; (iii) we present a practical numerical procedure for the identification of a close to optimal semi-parametric model. The numerical approach is motivated by the difficulty of deriving the optimal non-parametric model if there are complicated constraints or penalty terms in the criterion; and finally (iv) we discuss determination of the appropriate model complexity through selecting weights on the different penalties on the basis of empirical data. Since the optimal non-parametric model is identified using an augmented optimization criterion, and all prior knowledge and desired model properties may be specified through the augmented optimization criterion, it is the choice of this criterion that is critical in this approach. This elevates the empirical and semi-empirical modeling problems to a more transparent and engineering-friendly level than is achieved by directly specifying a parametric model structure. Hence, our results shed some more light on modern non-linear empirical modeling approaches like radial basis-functions, splines and neural networks. In addition to providing a fundamental insight into the role of different kinds of prior knowledge, this high-level formulation is also attractive from a practical point of view, as it lies closer to engineering thinking, and less guesswork is required. The flexibility and power of this approach are illustrated with a semi-realistic simulation example. [References: 38]
机译：在经验和半经验非线性建模中，参数模型结构的选择通常被视为重要而关键的步骤。然而，已知通过用对模型的非光滑度施加惩罚的项来扩展最小二乘识别标准，可以明确地找到最优的非参数模型。最佳的非参数模型将取决于惩罚的特定形式，可以将其视为先验知识或模型的期望属性。在本文中，这些结果在多个方向上进行了扩展：（i）我们展示了如何将平滑度以外的有用先验知识类型包括在准则中或作为约束项，以及这如何影响最优模型; （ii）考虑动态模型和一般的预测误差惩罚; （iii）我们提出了一种实用的数值程序，用于识别接近最佳的半参数模型。如果准则中存在复杂的约束或惩罚项，则难以获得最佳非参数模型，这是数值方法的动机。最后（iv）我们讨论了根据经验数据，通过选择不同罚分的权重来确定合适的模型复杂度。由于最佳非参数模型是使用增强优化准则来识别的，并且可以通过增强优化准则来指定所有先验知识和所需模型属性，因此在此方法中至关重要的是选择该准则。与直接指定参数模型结构相比，这将经验和半经验建模问题提升到更加透明和工程友好的水平。因此，我们的结果为现代非线性经验建模方法（如径向基函数，样条和神经网络）提供了更多启示。除了提供对各种先验知识的作用的基本了解之外，从实际的角度来看，这种高级表述也很有吸引力，因为它更接近于工程学思维，并且所需的猜测更少。通过半现实的仿真示例说明了此方法的灵活性和强大功能。 [参考：38]

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