本文選題：多新息辨識 + 遞階辨識��； 參考：《江南大學(xué)》2017年博士論文

【摘要】：多新息辨識通過推廣單新息修正理念,擴(kuò)展辨識新息的維數(shù),充分利用新息作為有用信息能改善參數(shù)估計和狀態(tài)估計精度的特性,提高辨識效果。論文研究多新息辨識方法及其收斂性,選題具有理論意義和學(xué)術(shù)價值。論文主要工作如下。(1)針對Box-Jenkins系統(tǒng),利用隨機(jī)鞅理論分析了輔助模型多新息廣義增廣隨機(jī)梯度算法的收斂性,在持續(xù)激勵的條件下,證明了參數(shù)估計收斂于真實參數(shù)。為了減少有色噪聲對系統(tǒng)參數(shù)估計的影響,通過線性濾波器對觀測數(shù)據(jù)進(jìn)行濾波,提出了基于數(shù)據(jù)濾波的多新息廣義增廣隨機(jī)梯度算法,提高了多新息辨識算法在同等新息長度下的參數(shù)辨識精度。進(jìn)一步,將提出的算法推廣到多變量Box-Jenkins系統(tǒng)的辨識。(2)針對雙線性參數(shù)系統(tǒng),利用過參數(shù)化技術(shù)將系統(tǒng)的輸出表達(dá)成觀測數(shù)據(jù)與參數(shù)乘積的線性組合,結(jié)合多新息辨識理論與負(fù)梯度搜索,推導(dǎo)了基于過參數(shù)化模型的多新息隨機(jī)梯度算法。為了避免過參數(shù)化導(dǎo)致的冗余參數(shù)問題,利用遞階辨識理論,推導(dǎo)了遞階多新息隨機(jī)梯度算法,并從理論上分析了算法的性能。為了獲取更高的參數(shù)估計精度,將數(shù)據(jù)濾波技術(shù)與多新息辨識理論相結(jié)合,提出了有色噪聲干擾下雙線性參數(shù)系統(tǒng)基于數(shù)據(jù)濾波的多新息隨機(jī)梯度算法。進(jìn)一步,將提出的算法推廣用于估計多變量雙線性參數(shù)系統(tǒng)的參數(shù)。(3)針對輸入非線性狀態(tài)空間系統(tǒng),基于動態(tài)線性子系統(tǒng)的能觀測性規(guī)范型,導(dǎo)出了系統(tǒng)的辨識模型,其特征是既含有線性子模塊和非線性輸入的參數(shù)乘積,又含有不可量測的系統(tǒng)狀態(tài)。針對上述特點,將辨識模型分解為兩個子模型,信息向量中未知狀態(tài)用估計的狀態(tài)代替以估算系統(tǒng)參數(shù),根據(jù)量測數(shù)據(jù)和已計算的參數(shù)估計,利用Kalman濾波原理估計系統(tǒng)的狀態(tài),執(zhí)行交互運算,提出了基于Kalman濾波的遞階多新息隨機(jī)梯度算法,實現(xiàn)系統(tǒng)參數(shù)和狀態(tài)的聯(lián)合估計。進(jìn)而在設(shè)計狀態(tài)觀測器的基礎(chǔ)上,利用數(shù)據(jù)濾波技術(shù),推導(dǎo)了基于狀態(tài)觀測器和數(shù)據(jù)濾波的多新息辨識算法,提高參數(shù)估計精度。論文對提出的一些辨識方法都利用數(shù)值例子進(jìn)行了仿真研究,驗證了提出方法的性能,對幾個重要辨識算法在理論上進(jìn)行了收斂性能分析。
[Abstract]:By popularizing the idea of single innovation correction and extending the dimension of identification innovation, multi-innovation identification can improve the accuracy of parameter estimation and state estimation by fully utilizing innovation as useful information and improve the identification effect. This paper studies the multi-innovation identification method and its convergence, the topic has theoretical significance and academic value. The main work of this paper is as follows: (1) for Box-Jenkins system, the convergence of generalized augmented stochastic gradient algorithm with auxiliary model is analyzed by means of stochastic martingale theory. Under the condition of continuous excitation, the convergence of parameter estimation to real parameters is proved. In order to reduce the influence of colored noise on the parameter estimation of the system, a generalized augmented stochastic gradient algorithm with multiple innovations based on data filtering is proposed by using linear filter to filter the observed data. The parameter identification accuracy of the multi-innovation identification algorithm under the same innovation length is improved. Furthermore, the proposed algorithm is extended to the identification of multivariable Box-Jenkins systems. (2) for bilinear parametric systems, the output of the system is expressed as a linear combination of the observed data and the product of the parameters by using the over-parameterization technique. Based on the multi-innovation identification theory and the negative gradient search, a multi-innovation stochastic gradient algorithm based on the over-parameterized model is derived. In order to avoid the redundant parameter problem caused by over-parameterization, the hierarchical multi-innovation stochastic gradient algorithm is derived by using hierarchical identification theory, and the performance of the algorithm is analyzed theoretically. In order to obtain higher precision of parameter estimation, a multi-innovation stochastic gradient algorithm based on data filtering for bilinear parametric systems with colored noise interference is proposed by combining the data filtering technique with the theory of multi-innovation identification. Furthermore, the proposed algorithm is extended to estimate the parameters of multivariable bilinear parameter systems. (3) for input nonlinear state space systems, an identification model is derived based on the observability canonical form of dynamic linear subsystems. Its characteristic is that it contains not only the parameter product of linear submodule and nonlinear input, but also the unmeasurable state of the system. In view of the above characteristics, the identification model is decomposed into two sub-models. The unknown state in the information vector is replaced by the estimated state to estimate the system parameters, and the state of the system is estimated by the Kalman filter principle according to the measured data and the calculated parameters. A hierarchical multi-innovation stochastic gradient algorithm based on Kalman filter is proposed to realize the joint estimation of system parameters and states. Based on the design of the state observer, the multi-innovation identification algorithm based on the state observer and the data filter is derived by using the data filtering technology to improve the precision of parameter estimation. In this paper, some of the proposed identification methods are simulated with numerical examples to verify the performance of the proposed method, and the convergence performance of several important identification algorithms is analyzed theoretically.
【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2017
【分類號】：N945.14

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