本文選題：系統(tǒng)辨識(shí) + 隨機(jī)梯度　； 參考：《江南大學(xué)》2017年博士論文

【摘要】：輸入非線性系統(tǒng)由一個(gè)靜態(tài)無記憶的非線性模塊串聯(lián)一個(gè)動(dòng)態(tài)線性系統(tǒng)構(gòu)成,通過構(gòu)建不同形式的非線性模塊可以滿足不同工程的需要,也正因?yàn)槠浣Y(jié)構(gòu)的靈活性和實(shí)用性,受到人們廣泛的關(guān)注.輸入非線性系統(tǒng)存在未知參數(shù)的乘積項(xiàng),常用的過參數(shù)化算法會(huì)引入大量冗余參數(shù),不適用于多變量輸入非線性系統(tǒng)的參數(shù)辨識(shí).在這樣的背景下,論文選題“基于關(guān)鍵項(xiàng)分離的輸入非線性系統(tǒng)參數(shù)辨識(shí)”,具有重要的理論意義和研究?jī)r(jià)值.取得的研究成果如下.1.針對(duì)標(biāo)量輸入非線性系統(tǒng)的參數(shù)空間存在兩個(gè)參數(shù)集的乘積項(xiàng),而常用的過參數(shù)化算法將參數(shù)乘積項(xiàng)作為獨(dú)立待辨識(shí)參數(shù)進(jìn)行辨識(shí),從而導(dǎo)致一個(gè)可產(chǎn)生冗余參數(shù)估計(jì)的問題,論文采用關(guān)鍵項(xiàng)分離技術(shù),將系統(tǒng)的輸入輸出之間復(fù)雜的映射關(guān)系分解成兩部分,一種是直觀的外部映射關(guān)系,另一種是隱含但明確的內(nèi)部映射關(guān)系,從而得到一個(gè)無冗余參數(shù)的辨識(shí)模型.進(jìn)一步,將提出的方法推廣到多變量輸入非線性系統(tǒng).2.針對(duì)輸入非線性系統(tǒng)的辨識(shí)模型中包含未知的關(guān)鍵項(xiàng)、噪聲項(xiàng)和中間項(xiàng)導(dǎo)致辨識(shí)參數(shù)困難,采取輔助模型辨識(shí)思想,在實(shí)現(xiàn)辨識(shí)算法的過程中,將信息向量中的未知項(xiàng)用其估計(jì)值代替,并利用相應(yīng)的辨識(shí)算法得到參數(shù)估計(jì),然后利用得到的參數(shù)估計(jì)估算未知項(xiàng)的估計(jì),不斷循環(huán)得到滿意的辨識(shí)結(jié)果.3.針對(duì)多變量輸入非線性系統(tǒng)存在結(jié)構(gòu)復(fù)雜、參數(shù)空間維數(shù)高、各通道間存在耦合等特點(diǎn)導(dǎo)致遞推算法辨識(shí)效率低下的問題,利用模型分解的方法,將系統(tǒng)分解為兩個(gè)或多個(gè)子系統(tǒng),并結(jié)合遞階辨識(shí)理論,實(shí)現(xiàn)子系統(tǒng)參數(shù)之間的交互估計(jì),最后將遞推辨識(shí)算法推廣到多變量輸入非線性系統(tǒng).4.在上述基礎(chǔ)上,根據(jù)最小二乘原理和梯度搜索方法,推導(dǎo)了多變量輸入非線性系統(tǒng)的最小二乘迭代算法和梯度迭代算法.不同于遞推辨識(shí)算法,迭代算法利用采集到的一組輸入輸出數(shù)據(jù),進(jìn)行反復(fù)迭代運(yùn)算,更充分地利用了數(shù)據(jù),因而具有更快的收斂速度和更高的辨識(shí)精度.論文最后對(duì)提出的參數(shù)辨識(shí)算法都用計(jì)算機(jī)進(jìn)行仿真,驗(yàn)證其有效性,并對(duì)不同的參數(shù)辨識(shí)算法進(jìn)行了比較分析.
[Abstract]:The input nonlinear system is composed of a static memoryless nonlinear module in series and a dynamic linear system. By constructing different forms of nonlinear modules, it can meet the needs of different projects, and also because of the flexibility and practicability of its structure. Received widespread attention. There is a product term of unknown parameters in the input nonlinear system. The commonly used overparameterization algorithm will introduce a large number of redundant parameters, which is not suitable for parameter identification of multivariable input nonlinear systems. Under this background, it is of great theoretical significance and research value to select the topic of "input nonlinear system parameter identification based on the separation of key terms". The results of the research are as follows. There are two product terms of two parameter sets in the parameter space of scalar input nonlinear system. The commonly used over-parameterization algorithm identifies the parameter product as an independent parameter to be identified, which leads to a problem of redundant parameter estimation. In this paper, the key item separation technique is used to decompose the complex mapping relationship between the input and output of the system into two parts, one is the intuitionistic external mapping relationship, the other is the implicit but explicit internal mapping relationship. Thus, an identification model with no redundant parameters is obtained. Furthermore, the proposed method is extended to multivariable input nonlinear systems. In view of the difficulty of identifying parameters caused by the unknown key items in the identification model of input nonlinear system, the noise term and the intermediate term lead to the difficulty of identification parameters, the idea of auxiliary model identification is adopted, and the identification algorithm is realized. The unknown term in the information vector is replaced by its estimated value, and the parameter estimation is obtained by using the corresponding identification algorithm. Then, the estimated unknown term is estimated by the obtained parameter estimation, and the satisfactory identification result is obtained continuously. In view of the complex structure of multivariable input nonlinear system, the high dimension of parameter space and the coupling between different channels, the recursive algorithm is inefficiently identified, and the method of model decomposition is used to solve the problem. The system is decomposed into two or more subsystems, and the interactive estimation of the subsystem parameters is realized by combining the hierarchical identification theory. Finally, the recursive identification algorithm is extended to the multivariable input nonlinear system .4. On the basis of the above, the least squares iterative algorithm and gradient iterative algorithm for multivariable input nonlinear systems are derived according to the least square principle and gradient search method. Different from the recursive identification algorithm, the iterative algorithm makes use of a collection of input and output data to iterate over and over again, making full use of the data, so it has faster convergence speed and higher identification accuracy. At the end of the paper, the algorithms of parameter identification are simulated by computer to verify its validity, and the different parameter identification algorithms are compared and analyzed.
【學(xué)位授予單位】：江南大學(xué)
【學(xué)位級(jí)別】：博士
【學(xué)位授予年份】：2017
【分類號(hào)】：N945.14

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