用小區合併法建立非線性ARMAX程序之線性模型網路

線性模型網路把數個線性模型配上適用函數後連結成網路結構來描述非線性系統的行為，適用函數代表對應的線性模型在系統資訊空間的適用範圍，此範圍可以代表該系統的特定操作區。建構線性模型網路時會把系統資訊空間分割成許多個小區，小區內的系統行為以線性模型描述，於是複雜的非線性模型建構問題就被轉換成簡單的線性模型建構問題。然而如何分割資訊空間是一個不適定或無定解的最佳化問題，沒有理論解析方法可以求得唯一解，實用上可以採用局部線性模型樹演算法逐一試探符合預設條件的分割方式，但是每一次試探分割都要考慮整個系統資訊空間的數據，導致演算量龐大而且耗時。本論文提出小區合併演算法，預先把系統資訊空間分割成許多基本小區，再把線性模型相近的小區合併成大區，因為每一次合併只需要考慮相關小區的數據，因此能夠減少演算複雜度也可以節省演算時間。本論文針對能夠以非線性外因輸入自回歸移動平均模型(NARMAX)描述之非線性程序，用小區合併演算法分割其系統資訊空間並建立對應的各個外因輸入自回歸移動平均模型(ARMAX)，最後構成描述該非線性程序的線性模型網路。幾個具有代表性的實例模擬結果顯示，在模型精確度相當的情況下，小區合併演算法的演算量遠少於局部線性模型樹演算法，因此確定小區合併演算法的建模效率比較優越。

關鍵字

線性模型網路；小區合併演算法；局部線性模型樹；非線性外因輸入自回歸移動平均模型

並列摘要

A linear model network links several local linear models with validity functions to describe nonlinear behaviors. Each validity function locates a specific operating region of the nonlinear system, on which a local linear model is sufficient to describe the behavior. Dividing the information space of the system into suitable regions is critical in constructing the linear model network. However, it is an ill-posed optimization problem that lacks a theoretical approach to find the solution. Recently, the local linear model tree algorithm was shown able to find a sub-optimal solution of dividing the information space and identifying the local linear models. However, any decision of extending a branch on the tree involves in calculations of the entire set of data that brings huge computation burden. This thesis presents the region aggregation algorithm (RAA) to lessen the computation burden. The RAA divides the information space evenly into tiny regions so that on any region the system behavior can be described by a local linear model. Then the algorithm tries to merge neighboring regions into a larger region by fitting a local linear model with the data out of these regions. For each trial of merge the calculation only concerns data out of these neighboring regions rather than the entire information space. We apply the RAA to construct linear model networks for processes said nonlinear autoregressive-moving-average model with exogenous inputs (NARMAX). Each local linear model of the network is an autoregressive-moving-average model with exogenous inputs (ARMAX) that can be identified by the auto-regression technique. The simulation results of several benchmark nonlinear processes show that the performance of the RAA is significantly better than that of the local linear model tree algorithm.

並列關鍵字

Linear model network ； the region aggregation algorithm ； the local linear model tree algorithm ； ARMAX

參考文獻

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國際替代計量

用小區合併法建立非線性ARMAX程序之線性模型網路

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