MODEL STRUCTURE DETERMINATION FOR SYSTEM IDENTIFICATION VIA COMBINATION OF PHYSICAL LAW,KNOWLEDGE AND DATA

对于由或二阶微分方程表示的线性时不变多输入多输出连续系统，我们打算在本项目中开发一种确定模型的顺序和/或结构指标的方法，以及表征参数上的一般特征的参数化方案。通常，含噪声的测量数据没有足够的质量和数量来完全决定模型的结构，但却包含丰富的信息来参数化模型。因此，利用物理/化学规律的信息可能是一种非常有效的方法。然后，我们尝试开发一种方法，可以通过相互交叉验证和完成来提取高质量的信息。例如，从控制系统设计的角度来看，如果一个模型准确地代表了控制规范所要求的频域特性，那么这个模型就是合适的。通过这种方式，我们的主要工作是收集用户对模型的要求，主要从控制系统设计中挑选，并确定具有满足要求的参数化模型。我们已经尝试这样做，以便它们与物理/化学考虑的信息保持一致。具体考虑了最小二乘法在模型近似下的重新解释、数据滤波的影响、输入输出测量噪声下的估计、模型阶数确定问题、离散时间模型的单位脉冲响应序列与连续时间模型的脉冲响应序列之间的联系等问题。

For linear time invariant multi-input and multi-output continuous systems represented by or-dinary differential equations, we intended in this project to develop a method for determining order and/or structure indices of a model, and parametrization schemes which represent generic characteristics on parameters.Generally, measurement data with noise do not involve any sufficient quality or quantity which may completely determine a model structure, but contain rich information to parametrize a model. Hence exploiting the information for physical/chemical law may be a very effective way. We have then tried to develop an approach which may draw out high-quality informations via cross-validation and completion for each other. For instance, from viewpoint of control system design, a model is appropriate for the control system if the model represent exactly the characteristics in frequency domain required from control specification.In this way, our main job was to collect requests to models from users, pick up ones mainly from control system design, and determine a model having parametrization which satisfy the requests. We have tried to do it so that they are in harmony with the informations from physical/chemical considerations.More concretely, we considered the problem such as : reinterpretation of the Least Squares Method in view of the model approximation, the effect of data filtering, estimation under input and output measurement noise, model order determination problem, connection between the sequence of unit pulse response of discrete time model and the impulse response of a continuous time model.