滤波方法及其在非线性系统故障诊断中的应用研究
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摘要
随着武器装备和机电系统对于可靠性和安全性要求的不断提高,故障检测、隔离和辨识技术发挥着越来越重要的作用。然而现代武器装备越来越复杂,其表现形式之一就是很多系统和工作过程都表现出较强的非线性,并且受到非高斯噪声和各种不确定因素的影响,导致这些系统的故障诊断面临较大的困难。非线性滤波方法是解决非线性系统故障诊断问题的重要技术途径之一,然而传统的滤波方法一般基于线性化和高斯假设,这在一定程度上影响了滤波精度和非线性系统故障诊断的准确率。如何突破传统方法的不足,进而提高非线性系统故障诊断的准确率,是亟待解决的关键问题之一。
本文正是在“十五”部委级预先研究项目的资助和实际工程项目的需求牵引下,重点借助“近似概率”的新颖非线性滤波方法和多源异类信息融合技术,开展了提高诊断准确率的深入研究。主要研究内容包括:
1.针对线性化和建模误差对非线性系统故障诊断准确率的影响问题,深入研究了U-卡尔曼滤波器(Unscented Kalman Filter, UKF)的改进策略和故障决策方法。为了在建模误差时加强对非线性系统故障状态的跟踪能力,提高故障诊断和辨识的精度,通过增加残差的正交性约束,提出了两种各具特色的强跟踪UKF算法,为非线性系统参数偏差型故障的准确诊断奠定了基础:(1)通过将渐消因子求解转换为多元无约束非线性最优化问题,提出了DFP(Daviden-Fletcher-Powell)寻优强跟踪UKF;(2)提出了带多重渐消因子的快速近似强跟踪UKF算法,大大降低了运算代价,适合于维数较高的非线性系统。在此基础上,给出了基于UKF及其改进算法的非线性系统故障诊断策略和实现流程,并对其中的滤波器选择和应用范围等问题进行了分析和讨论。仿真结果表明,采用UKF和强跟踪UKF,相对于基于EKF的故障诊断方法,能降低线性化误差和建模误差的影响,提高故障诊断和辨识的准确率。
2.深入研究了非高斯噪声下非线性系统故障诊断的粒子滤波方法。为了实现非高斯噪声下多维观测系统的故障检测,分别针对观测各元素独立和相关两种不同的情况,通过定义观测量的独立同均匀分布的条件累积分布函数,基于Parzen窗平滑和Chi-Square检测,进而提出了两种检测统计量和检测算法。为了提高故障检测的速度,采用混合粒子集表达后验概率分布,并由Monte Carlo数值方法优化得到各粒子集的加权值,据此提出了基于估计窗的快速故障检测算法。在此基础上,给出了基于联合估计和似然比策略实现故障诊断的方法和流程。结果表明,在非高斯噪声影响下,新方法能有效提高非线性系统故障检测和诊断的准确率,并能改善检测的实时性。
3.在利用非线性系统输入输出信息的基础上,为了融合系统其它多源信息提高诊断的准确率,深入研究了多知识体融合故障诊断方法。
(1)为了实现系统融合时的动态案例推理,提出了一种新的动态案例表达方法,利用系统特性集、征兆集和特征集混合模型作为案例的条件属性;接着通过定义案例组员的四种不同属性和相似性度量方法,提出了非线性系统动态案例的综合相似度计算策略。
(2)提出了多知识体融合模型中模型、案例和规则三种证据体的基本可信度分配方法。
(3)针对D-S证据理论用于决策级融合时存在的冲突问题,首次定义了证据重要度的概念引入偏好调节,据此定义了冲突修正项,并提出了一种新的证据合成公式,具有简单实用的优点。
4.以某型直升机飞行控制系统为对象,将全文所研究的技术和方法进行了整体应用和验证。首先建立了直升机飞行控制系统的小扰动线性模型和非线性动力学模型,应用结果表明在高斯和非高斯噪声影响下,UKF和粒子滤波器能提高故障检测的准确率。建立了某型直升机并联舵回路实验子系统,应用本文研究的非线性滤波技术和多知识体融合方法,设计并实现了故障诊断系统,实验结果表明,故障检测和诊断的准确率和综合品质得到了有效提高。
Along with the increasing requirement of reliability and safety of weapon equipments and mechantronic systems, fault detection, isolation(FDI) are playing very important role. While modern weapon equipments are becoming more and more complex, and one trait is that many systems and processes are nonlinear and disturbed by random noises and many kinds of uncertainty, which cause the accurate fault diagnosis to be very difficult. Among various techniques, nonlinear filtering method is an important method for the fault diagnosis of nonlinear systems. However, traditional filtering methods are mainly based on linearization or Gaussian hypothesis, which may influence the filtering precision and lead to low diagnosis accuracy rate(DAR), thus block their engineering application. How to break through the drawbacks of traditional methods and improve the DAR of nonlinear systems has been a key research content.
Supported by the National Defense Advanced Research Project and required by practical engineering project, this dissertation aims at the four influence factors that are linearization error, modeling error, Gaussian hypothesis error and low information usage rate. The new nonlinear filtering based on the“probability approximation”concept and multi-source information fusion technology are adopted to improve the accuracy rate. The main contents are as follows:
1. As to the fault diagnosis problem of nonlinear systems in Gaussian noise, the Unscented Kalman Filter(UKF) and fault decision methods are deeply studied and improved. By adding the orthogonal restriction to the residuals of nonlinear systems with modeling error, two different strong tracking UKF methods are proposed in order to enhance the tracking ability of faulty state and improve the precision of fault identification, thus lay a foundation to parameter bias type fault diagnosis for nonlinear systems: (1) By transforming the forgetting matrix to multi-dimensional nonlinear optimization problem with no restriction, the DFP(Daviden-Fletcher-Powell) strong tracking UKF is proposed; (2) The quick approximate strong tracking algorithm with multiple forgetting factors is proposed to reduce the calculation cost, which is suitable for high dimension nonlinear system. Furthermore, the fault detection and diagnosis strategy and realization flow are presented based on UKF and its improved algorithms, the filter selection and application range are analyzed and discussed. Simulation results show that the UKF and strong tracking UKF can reduce the influence of linearization error and modeling error compared to the traditional method, the diagnosis and identification accuracy rate is consequently improved.
2. The fault diagnosis problem of nonlinear systems in non-Gaussian noise is deeply studied. In order to detect the fault of multi-dimensional systems in non-Gaussian noise with independent and dependent observation elements respectively,by defining independent and identical condition accumulative distribution function of observations, two new detection statistics variable and detection methods are proposed based on the Parzen window smoothing and Chi-Square detection. In order to increase the detection speed, by using mixing particle sets to express the posterior probability distribution and adopting the Monte Carlo numerical methods to calculate the mixing weights, the fast fault detection algorithm is proposed based on the estimate window method. Furthermore, the fault diagnosis strategy and realization flow are presented by joint estimation and likelihood ratio methods. Simulation results demonstrate the effectiveness of the new methods.
3. In order to improve the DAR of nonlinear systems by multi-source information fusion besides the input and output information, the multi-knowledge fusion method is deeply studied.
(1) A multi-knowledge fusion model is proposed, and a new dynamic case expression methods is then proposed in order to realize the case based reasoning for the fusion realization. In the following, a case representation method is proposed by treat the system characteristics set, symptom set and feature set as the case conditional attributes. Then the synthetic similarity measure method for case retrieve is proposed.
(2) The three basic probability assignment methods of model, case and rule evidence are proposed for multi-knowledge fusion model.
(3) As to the problem of evidence confliction of D-S evidence theory for decision level fusion, the“evidence importance”concept is firstly defined to import the partiality adjustment, then the conflict modification term is defined, thus a new combination method is proposed with the advantage of simpleness and practicality.
4. The application of DAR improvement technologies are applied to the helicopter flight control systems. The small perturbation linearization model and nonlinear model are established, and the application results show that disturbed by Gaussian and non-Gaussian noises respectively, UKF and particle filters can improve the accuracy rate of fault detection. Then the parallel rudder loop experiment sub-system are established, the fault diagnosis systems are designed and realized by the studied techniques in this thesis, the experiment results indicate that the DAR and the diagnosis performance are improved effectively.
本文正是在“十五”部委级预先研究项目的资助和实际工程项目的需求牵引下,重点借助“近似概率”的新颖非线性滤波方法和多源异类信息融合技术,开展了提高诊断准确率的深入研究。主要研究内容包括:
1.针对线性化和建模误差对非线性系统故障诊断准确率的影响问题,深入研究了U-卡尔曼滤波器(Unscented Kalman Filter, UKF)的改进策略和故障决策方法。为了在建模误差时加强对非线性系统故障状态的跟踪能力,提高故障诊断和辨识的精度,通过增加残差的正交性约束,提出了两种各具特色的强跟踪UKF算法,为非线性系统参数偏差型故障的准确诊断奠定了基础:(1)通过将渐消因子求解转换为多元无约束非线性最优化问题,提出了DFP(Daviden-Fletcher-Powell)寻优强跟踪UKF;(2)提出了带多重渐消因子的快速近似强跟踪UKF算法,大大降低了运算代价,适合于维数较高的非线性系统。在此基础上,给出了基于UKF及其改进算法的非线性系统故障诊断策略和实现流程,并对其中的滤波器选择和应用范围等问题进行了分析和讨论。仿真结果表明,采用UKF和强跟踪UKF,相对于基于EKF的故障诊断方法,能降低线性化误差和建模误差的影响,提高故障诊断和辨识的准确率。
2.深入研究了非高斯噪声下非线性系统故障诊断的粒子滤波方法。为了实现非高斯噪声下多维观测系统的故障检测,分别针对观测各元素独立和相关两种不同的情况,通过定义观测量的独立同均匀分布的条件累积分布函数,基于Parzen窗平滑和Chi-Square检测,进而提出了两种检测统计量和检测算法。为了提高故障检测的速度,采用混合粒子集表达后验概率分布,并由Monte Carlo数值方法优化得到各粒子集的加权值,据此提出了基于估计窗的快速故障检测算法。在此基础上,给出了基于联合估计和似然比策略实现故障诊断的方法和流程。结果表明,在非高斯噪声影响下,新方法能有效提高非线性系统故障检测和诊断的准确率,并能改善检测的实时性。
3.在利用非线性系统输入输出信息的基础上,为了融合系统其它多源信息提高诊断的准确率,深入研究了多知识体融合故障诊断方法。
(1)为了实现系统融合时的动态案例推理,提出了一种新的动态案例表达方法,利用系统特性集、征兆集和特征集混合模型作为案例的条件属性;接着通过定义案例组员的四种不同属性和相似性度量方法,提出了非线性系统动态案例的综合相似度计算策略。
(2)提出了多知识体融合模型中模型、案例和规则三种证据体的基本可信度分配方法。
(3)针对D-S证据理论用于决策级融合时存在的冲突问题,首次定义了证据重要度的概念引入偏好调节,据此定义了冲突修正项,并提出了一种新的证据合成公式,具有简单实用的优点。
4.以某型直升机飞行控制系统为对象,将全文所研究的技术和方法进行了整体应用和验证。首先建立了直升机飞行控制系统的小扰动线性模型和非线性动力学模型,应用结果表明在高斯和非高斯噪声影响下,UKF和粒子滤波器能提高故障检测的准确率。建立了某型直升机并联舵回路实验子系统,应用本文研究的非线性滤波技术和多知识体融合方法,设计并实现了故障诊断系统,实验结果表明,故障检测和诊断的准确率和综合品质得到了有效提高。
Along with the increasing requirement of reliability and safety of weapon equipments and mechantronic systems, fault detection, isolation(FDI) are playing very important role. While modern weapon equipments are becoming more and more complex, and one trait is that many systems and processes are nonlinear and disturbed by random noises and many kinds of uncertainty, which cause the accurate fault diagnosis to be very difficult. Among various techniques, nonlinear filtering method is an important method for the fault diagnosis of nonlinear systems. However, traditional filtering methods are mainly based on linearization or Gaussian hypothesis, which may influence the filtering precision and lead to low diagnosis accuracy rate(DAR), thus block their engineering application. How to break through the drawbacks of traditional methods and improve the DAR of nonlinear systems has been a key research content.
Supported by the National Defense Advanced Research Project and required by practical engineering project, this dissertation aims at the four influence factors that are linearization error, modeling error, Gaussian hypothesis error and low information usage rate. The new nonlinear filtering based on the“probability approximation”concept and multi-source information fusion technology are adopted to improve the accuracy rate. The main contents are as follows:
1. As to the fault diagnosis problem of nonlinear systems in Gaussian noise, the Unscented Kalman Filter(UKF) and fault decision methods are deeply studied and improved. By adding the orthogonal restriction to the residuals of nonlinear systems with modeling error, two different strong tracking UKF methods are proposed in order to enhance the tracking ability of faulty state and improve the precision of fault identification, thus lay a foundation to parameter bias type fault diagnosis for nonlinear systems: (1) By transforming the forgetting matrix to multi-dimensional nonlinear optimization problem with no restriction, the DFP(Daviden-Fletcher-Powell) strong tracking UKF is proposed; (2) The quick approximate strong tracking algorithm with multiple forgetting factors is proposed to reduce the calculation cost, which is suitable for high dimension nonlinear system. Furthermore, the fault detection and diagnosis strategy and realization flow are presented based on UKF and its improved algorithms, the filter selection and application range are analyzed and discussed. Simulation results show that the UKF and strong tracking UKF can reduce the influence of linearization error and modeling error compared to the traditional method, the diagnosis and identification accuracy rate is consequently improved.
2. The fault diagnosis problem of nonlinear systems in non-Gaussian noise is deeply studied. In order to detect the fault of multi-dimensional systems in non-Gaussian noise with independent and dependent observation elements respectively,by defining independent and identical condition accumulative distribution function of observations, two new detection statistics variable and detection methods are proposed based on the Parzen window smoothing and Chi-Square detection. In order to increase the detection speed, by using mixing particle sets to express the posterior probability distribution and adopting the Monte Carlo numerical methods to calculate the mixing weights, the fast fault detection algorithm is proposed based on the estimate window method. Furthermore, the fault diagnosis strategy and realization flow are presented by joint estimation and likelihood ratio methods. Simulation results demonstrate the effectiveness of the new methods.
3. In order to improve the DAR of nonlinear systems by multi-source information fusion besides the input and output information, the multi-knowledge fusion method is deeply studied.
(1) A multi-knowledge fusion model is proposed, and a new dynamic case expression methods is then proposed in order to realize the case based reasoning for the fusion realization. In the following, a case representation method is proposed by treat the system characteristics set, symptom set and feature set as the case conditional attributes. Then the synthetic similarity measure method for case retrieve is proposed.
(2) The three basic probability assignment methods of model, case and rule evidence are proposed for multi-knowledge fusion model.
(3) As to the problem of evidence confliction of D-S evidence theory for decision level fusion, the“evidence importance”concept is firstly defined to import the partiality adjustment, then the conflict modification term is defined, thus a new combination method is proposed with the advantage of simpleness and practicality.
4. The application of DAR improvement technologies are applied to the helicopter flight control systems. The small perturbation linearization model and nonlinear model are established, and the application results show that disturbed by Gaussian and non-Gaussian noises respectively, UKF and particle filters can improve the accuracy rate of fault detection. Then the parallel rudder loop experiment sub-system are established, the fault diagnosis systems are designed and realized by the studied techniques in this thesis, the experiment results indicate that the DAR and the diagnosis performance are improved effectively.
引文
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