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  本文選題：相空間重構(gòu) + 遺傳算法　； 參考：《天津理工大學(xué)》2017年碩士論文

【摘要】：非線性動力系統(tǒng)是由確定的動力系統(tǒng)產(chǎn)生的復(fù)雜行為。對于結(jié)構(gòu)已知的非線性動力系統(tǒng),可以根據(jù)動力特性建立非線性動力系統(tǒng)模型。大部分的非線性動力系統(tǒng)很難建立一個精確的數(shù)學(xué)模型。但是,根據(jù)觀測到的時間序列值,可以近似的擬合出一個非線性動力系統(tǒng)模型。本文對結(jié)構(gòu)已知與結(jié)構(gòu)未知的非線性動力系統(tǒng)模型進(jìn)行研究。首先對非線性動力系統(tǒng)進(jìn)行分析,包括系統(tǒng)穩(wěn)定性、倍周期分岔性、混沌特性進(jìn)行研究。重點研究了相空間重構(gòu)理論,分別使用互信息法和飽和關(guān)聯(lián)維數(shù)法來確定相空間重構(gòu)的參數(shù)。相空間重構(gòu)理論為建立非線性預(yù)測模型奠定基礎(chǔ)。對于結(jié)構(gòu)已知的非線性動力系統(tǒng),根據(jù)動力系統(tǒng)特性,建立非線性動力系統(tǒng)模型。對于可以求出解析式的非線性動力系統(tǒng)模型,采用粒子群方法求解最優(yōu)模型參數(shù),仿真實驗表明,該方法比傳統(tǒng)的求解方法具有更高的預(yù)測精度。對于難以求出解析式的非線性動力系統(tǒng)模型,采用Newmark和Wilson計算方法,求解非線性動力系統(tǒng)模型的瞬態(tài)解析,仿真實驗表明,當(dāng)積分步長很短時,該方法具有很高的預(yù)測精度。對于結(jié)構(gòu)未知的非線性動力系統(tǒng),對常用的自適應(yīng)預(yù)測模型和局域預(yù)測模型進(jìn)行研究。在相空間中,構(gòu)建Volterra自適應(yīng)預(yù)測模型。為了提高Volterra自適應(yīng)預(yù)測模型預(yù)測精度,采用群體智能的遺傳算法,通過交叉、變異、選擇等方法求解模型最優(yōu)參數(shù),實驗表明該方法改進(jìn)模型的學(xué)習(xí)能力,加快收斂速度,提高了預(yù)測精度。在相空間中,構(gòu)建基于粒子濾波優(yōu)化的局域線性預(yù)測模型。在局域線性預(yù)測模型中,使用歐氏距離和相關(guān)系數(shù)結(jié)合的方法來選擇鄰近點,根據(jù)鄰近點構(gòu)建局域線性預(yù)測模型,并采用粒子濾波方法求解最優(yōu)模型參數(shù),實驗表明該方法較局域線性表模型和局域神經(jīng)網(wǎng)絡(luò)模型,具有更高的預(yù)測精度。
[Abstract]:Nonlinear dynamic system is a complex behavior produced by a definite dynamic system. For the known nonlinear dynamic system, the nonlinear dynamic system model can be established according to the dynamic characteristics. It is difficult for most nonlinear dynamic systems to establish an accurate mathematical model. However, according to the observed time series, we can approximate fit a nonlinear dynamic system model. In this paper, the nonlinear dynamic system model with known structure and unknown structure is studied. Firstly, the nonlinear dynamical system is analyzed, including system stability, period doubling bifurcation and chaos characteristics. The theory of phase space reconstruction is mainly studied. Mutual information method and saturation correlation dimension method are used to determine the parameters of phase space reconstruction. The theory of phase space reconstruction lays a foundation for the establishment of nonlinear prediction model. According to the characteristics of the dynamic system, the nonlinear dynamic system model is established for the known nonlinear dynamic system of the structure. The particle swarm optimization (PSO) method is used to solve the optimal model parameters for the analytical nonlinear dynamic system model. The simulation results show that the proposed method has higher prediction accuracy than the traditional method. For the nonlinear dynamic system model which is difficult to be solved, Newmark and Wilson calculation methods are used to solve the transient analysis of the nonlinear dynamic system model. The simulation results show that the method has a high prediction accuracy when the integral step is very short. For nonlinear dynamical systems with unknown structures, adaptive prediction models and local prediction models are studied. Volterra adaptive prediction model is constructed in phase space. In order to improve the prediction accuracy of Volterra adaptive prediction model, the genetic algorithm of swarm intelligence is used to solve the optimal parameters of the model by means of crossover, mutation and selection. The experiments show that this method improves the learning ability of the model and accelerates the convergence speed. The prediction accuracy is improved. A local linear prediction model based on particle filter optimization is constructed in phase space. In the local linear prediction model, the Euclidean distance and the correlation coefficient are combined to select the adjacent points, the local linear prediction model is constructed according to the adjacent points, and the particle filter method is used to solve the optimal model parameters. Experiments show that this method has higher prediction accuracy than local linear table model and local neural network model.
【學(xué)位授予單位】：天津理工大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O19

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本文編號：1995189