基于核方法的非線性系統(tǒng)辨識(shí)，均衡和信號(hào)分離及在故障診斷中的應(yīng)用
發(fā)布時(shí)間：2018-08-19 17:41
【摘要】：本論文在國(guó)家自然科學(xué)基金(50775208、51075372)、湖南省機(jī)械設(shè)備健康維護(hù)重點(diǎn)實(shí)驗(yàn)室開放基金(200904)和河南省教育廳自然科學(xué)基金(2008C460003)資助下,將核函數(shù)方法(Kernel Methods)應(yīng)用到非線性系統(tǒng)的辨識(shí),均衡和信號(hào)分離中,深入研究了基于核方法的機(jī)械故障診斷方法,并進(jìn)行了仿真對(duì)比與實(shí)驗(yàn)研究,取得了一些創(chuàng)新性成果。本文的主要內(nèi)容包括： 第一章,簡(jiǎn)述了本課題的研究意義,綜述了核函數(shù)方法及其在機(jī)械故障診斷中的國(guó)內(nèi)外研究現(xiàn)狀,概述了本文的主要內(nèi)容和創(chuàng)新之處。 第二章,論述了核函數(shù)的基礎(chǔ)理論,介紹了常用的核函數(shù),核函數(shù)的非線性映射以及構(gòu)造核函數(shù)的條件,為將核函數(shù)方法應(yīng)用到機(jī)械故障診斷中奠定理論基礎(chǔ)。這一章的內(nèi)容是整篇論文的理論基礎(chǔ)。 第三章,論述了核遞推最小二乘辨識(shí)思想和三種典型算法即ALD-KRLS、 SW-KRLS和FB-KRLS,通過(guò)仿真研究,比較了傳統(tǒng)最小二乘(LMS)辨識(shí)算法、遞推最小二乘(RLS)辨識(shí)算法和核遞推最小二乘(KRLS)辨識(shí)算法對(duì)非線性系統(tǒng)的辨識(shí)能力。仿真研究表明,不論是在辨識(shí)精度,穩(wěn)定性還是抗干擾性方面,KRLS辨識(shí)算法明顯優(yōu)于傳統(tǒng)LMS、RLS辨識(shí)法。在這三種典型的KRLS辨識(shí)算法,SW-KRLS法比其他兩種KRLS辨識(shí)算法獲得了更好的辨識(shí)效果。SW-KRLS法特別適用于時(shí)變非線性系統(tǒng)辨識(shí)。在此基礎(chǔ)上,提出了基于核遞推最小二乘辨識(shí)的機(jī)械故障方法,并應(yīng)用到轉(zhuǎn)子系統(tǒng)的故障診斷中,實(shí)驗(yàn)結(jié)果表明提出的方法是有效的。 第四章,針對(duì)傳統(tǒng)的自適應(yīng)均衡方法存在的不足,提出了一種基于KRLS的非線性系統(tǒng)自適應(yīng)均衡方法。該方法通過(guò)引入核函數(shù),將原始的非線性數(shù)據(jù)映射到高維特征空間,然后在高維特征空間中實(shí)施標(biāo)準(zhǔn)最小二乘算法。提出的方法并與傳統(tǒng)的非線性系統(tǒng)均衡方法進(jìn)行了對(duì)比分析,仿真研究表明,提出的方法優(yōu)于傳統(tǒng)的均衡方法,能很好的消除傳遞通道的影響,有效地提取出弱沖擊性成分。最后,將提出的方法應(yīng)用到轉(zhuǎn)子系統(tǒng)的弱沖擊性故障提取中,實(shí)驗(yàn)結(jié)果進(jìn)一步驗(yàn)證了提出的方法的有效性。 第五章,詳細(xì)論述了獨(dú)立分量分析、核函數(shù)獨(dú)立分量分析的基本思想和算法。KICA是一種非線性算法,它是將傳統(tǒng)ICA方法在高位特征空間中的推廣,它具有更加優(yōu)異的性能,可以解決一些經(jīng)典的ICA方法無(wú)法解決的難題,例如非線性混合的盲信號(hào)分離問(wèn)題。針對(duì)傳統(tǒng)的獨(dú)立分量分析在處理非線性混合的故障源分離的不足,提出了一種基于核獨(dú)立分量分析(KICA)的非線性混合的機(jī)械故障源盲分離方法,該方法利用核函數(shù)的優(yōu)點(diǎn),將信號(hào)從低維的非線性原始空間變換到高維線性特征空間,從而可以采用線性ICA方法進(jìn)行分離。仿真結(jié)果表明,與傳統(tǒng)的ICA方法相比,提出的方法在處理非線性混合的源盲分離具有明顯的優(yōu)勢(shì)。最后,將提出的方法應(yīng)用到軸承故障信號(hào)的盲分離中,實(shí)驗(yàn)結(jié)果進(jìn)一步驗(yàn)證了提出的方法的有效性。 第六章,總結(jié)了全文的工作,并提出了值得進(jìn)一步研究的一些問(wèn)題。
[Abstract]:In this paper, the Kernel Method is applied to the identification, equalization and signal separation of nonlinear systems with the support of the National Natural Science Foundation of China (50775208, 51075372), the Open Fund of Hunan Key Laboratory of Mechanical Equipment Health Maintenance (200904) and the Natural Science Foundation of Henan Education Department (2008C460003). Some innovative results have been obtained by comparing the simulation results with the experimental results. The main contents of this paper include:
In the first chapter, the research significance of this subject is briefly described, and the research status of kernel function method and its application in mechanical fault diagnosis at home and abroad is summarized.
In the second chapter, the basic theory of kernel function is discussed, and the common kernel function, the nonlinear mapping of kernel function and the conditions of constructing kernel function are introduced, which lays a theoretical foundation for applying kernel function method to mechanical fault diagnosis.
In the third chapter, the idea of kernel recursive least squares identification and three typical algorithms, namely ALD-KRLS, SW-KRLS and FB-KRLS, are discussed. Through simulation study, the identification ability of traditional least squares (LMS) identification algorithm, recursive least squares (RLS) identification algorithm and kernel recursive least squares (KRLS) identification algorithm for nonlinear systems are compared. The KRLS identification algorithm is superior to the traditional LMS and RLS identification algorithms in terms of identification accuracy, stability and anti-jamming. SW-KRLS identification algorithm achieves better identification results than the other two KRLS identification algorithms in the three typical KRLS identification algorithms. SW-KRLS method is especially suitable for time-varying nonlinear system identification. The mechanical fault diagnosis method based on kernel recursive least squares identification is applied to rotor system fault diagnosis. The experimental results show that the proposed method is effective.
In the fourth chapter, aiming at the shortcomings of the traditional adaptive equalization methods, an adaptive equalization method for nonlinear systems based on KRLS is proposed. By introducing kernel function, the original nonlinear data is mapped into the high-dimensional feature space, and then the standard least squares algorithm is implemented in the high-dimensional feature space. The simulation results show that the proposed method is superior to the traditional equalization method, and can eliminate the influence of the transmission channel and extract the weak impulsive components effectively. Finally, the proposed method is applied to extract the weak impulsive faults of the rotor system, and the experimental results are further validated. The effectiveness of the proposed method is also discussed.
In the fifth chapter, the basic idea and algorithm of independent component analysis and kernel function independent component analysis are discussed in detail. KICA is a nonlinear algorithm, which extends the traditional ICA method in high-level feature space. It has more excellent performance and can solve some difficult problems that classical ICA methods can not solve, such as nonlinear mixing blindness. Signal separation problem. In order to overcome the disadvantage of traditional independent component analysis (ICA) in dealing with nonlinear hybrid fault source separation, a nonlinear hybrid blind source separation method based on Kernel Independent Component Analysis (KICA) is proposed, which utilizes the advantages of kernel function to transform signals from low-dimensional nonlinear original space to high-dimensional lines. Compared with the traditional ICA method, the proposed method has obvious advantages in dealing with the source blind separation of nonlinear mixtures. Finally, the proposed method is applied to the blind separation of bearing fault signals. The experimental results further verify the proposed method. Effectiveness.
The sixth chapter summarizes the work of this paper and puts forward some questions worthy of further study.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TH165.3
[Abstract]:In this paper, the Kernel Method is applied to the identification, equalization and signal separation of nonlinear systems with the support of the National Natural Science Foundation of China (50775208, 51075372), the Open Fund of Hunan Key Laboratory of Mechanical Equipment Health Maintenance (200904) and the Natural Science Foundation of Henan Education Department (2008C460003). Some innovative results have been obtained by comparing the simulation results with the experimental results. The main contents of this paper include:
In the first chapter, the research significance of this subject is briefly described, and the research status of kernel function method and its application in mechanical fault diagnosis at home and abroad is summarized.
In the second chapter, the basic theory of kernel function is discussed, and the common kernel function, the nonlinear mapping of kernel function and the conditions of constructing kernel function are introduced, which lays a theoretical foundation for applying kernel function method to mechanical fault diagnosis.
In the third chapter, the idea of kernel recursive least squares identification and three typical algorithms, namely ALD-KRLS, SW-KRLS and FB-KRLS, are discussed. Through simulation study, the identification ability of traditional least squares (LMS) identification algorithm, recursive least squares (RLS) identification algorithm and kernel recursive least squares (KRLS) identification algorithm for nonlinear systems are compared. The KRLS identification algorithm is superior to the traditional LMS and RLS identification algorithms in terms of identification accuracy, stability and anti-jamming. SW-KRLS identification algorithm achieves better identification results than the other two KRLS identification algorithms in the three typical KRLS identification algorithms. SW-KRLS method is especially suitable for time-varying nonlinear system identification. The mechanical fault diagnosis method based on kernel recursive least squares identification is applied to rotor system fault diagnosis. The experimental results show that the proposed method is effective.
In the fourth chapter, aiming at the shortcomings of the traditional adaptive equalization methods, an adaptive equalization method for nonlinear systems based on KRLS is proposed. By introducing kernel function, the original nonlinear data is mapped into the high-dimensional feature space, and then the standard least squares algorithm is implemented in the high-dimensional feature space. The simulation results show that the proposed method is superior to the traditional equalization method, and can eliminate the influence of the transmission channel and extract the weak impulsive components effectively. Finally, the proposed method is applied to extract the weak impulsive faults of the rotor system, and the experimental results are further validated. The effectiveness of the proposed method is also discussed.
In the fifth chapter, the basic idea and algorithm of independent component analysis and kernel function independent component analysis are discussed in detail. KICA is a nonlinear algorithm, which extends the traditional ICA method in high-level feature space. It has more excellent performance and can solve some difficult problems that classical ICA methods can not solve, such as nonlinear mixing blindness. Signal separation problem. In order to overcome the disadvantage of traditional independent component analysis (ICA) in dealing with nonlinear hybrid fault source separation, a nonlinear hybrid blind source separation method based on Kernel Independent Component Analysis (KICA) is proposed, which utilizes the advantages of kernel function to transform signals from low-dimensional nonlinear original space to high-dimensional lines. Compared with the traditional ICA method, the proposed method has obvious advantages in dealing with the source blind separation of nonlinear mixtures. Finally, the proposed method is applied to the blind separation of bearing fault signals. The experimental results further verify the proposed method. Effectiveness.
The sixth chapter summarizes the work of this paper and puts forward some questions worthy of further study.
【學(xué)位授予單位】：鄭州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2012
【分類號(hào)】：TH165.3
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相關(guān)期刊論文 前10條
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