基于模拟退火算法的船用核动力装置故障诊断研究

针对核动力装置故障诊断存在的诊断精度低等问题,提出了一种基于模拟退火算法和概率因果模型相结合的故障诊断方法.首先根据故障样本集和概率因果理论建立动态多故障诊断模型,将复杂系统的多故障诊断转换成非线性规划问题.利用模拟退火算法对该问题进行求解,并建立了诊断测试系统.测试结果表明,方法能有效避免误诊、漏诊现象,可用于复杂核动力装置的动态多故障诊断.     

基于模拟退火算法的船用核动力装置故障诊断研究北大核心

针对核动力装置故障诊断存在的诊断精度低等问题,提出了一种基于模拟退火算法和概率因果模型相结合的故障诊断方法.首先根据故障样本集和概率因果理论建立动态多故障诊断模型,将复杂系统的多故障诊断转换成非线性规划问题.利用模拟退火算法对该问题进行求解,并建立了诊断测试系统.测试结果表明,方法能有效避免误诊、漏诊现象,可用于复杂核动力装置的动态多故障诊断.     

多气源天然气管网运行优化问题的混合整数规划模型及其算法

对于多气源天然气管网运行优化问题,文章首先引入了刻画压缩机开关的0-1整数变量,并对非线性的管道压降方程进行了合理的松弛化处理,建立了更符合实际的非线性混合整数规划模型.其次,基于序列线性化的思想,设计了一种求解该模型的序列混合整数线性化算法.最后,在不同规模的天然气管网系统中进行了多方面的对比实验.实验结果表明,新模型及求解算法能够有效降低成本、减少压缩机能耗,并且所需求解时间大大减少.     

基于时域配点法的充液储箱系统多模态方程求解

采用时域配点法研究了充液储箱系统多模态方程的稳态周期解.在模型求解过程中,利用牛顿迭代法求解了配点法得到的非线性代数方程组,而牛顿迭代的初值来自谐波平衡法求解得到的低阶谐波近似.数值仿真结果验证了时域配点法的有效性,并验证以二倍激励频率为基频的第二模态的假设形式更为有效.最终通过对比谐波系数数量级提出一种更为简洁有效的模态表达形式.     

免疫粒子群优化算法在农业水资源优化配置中的应用

求解农业水资源优化配置模型(高维非线性优化模型),较常采用大系统分解协调原理和动态规划相结合的方法,这样减少了变量个数,便于优化求解,但协调的过程需要多次从低阶模型中返回信息,而且对于每层的寻优求解过程存在难以克服的矛盾.采用标准的粒子群优化算法则优化程度不易保证并容易陷入局部最优,优化结果对初始种群依赖性较强.因此应用免疫进化算法对标准粒子群优化算法进行改进并应用于灌区农业水资源优化配置模型的求解.算例分析表明,免疫粒子群算法为求解高维复杂的优化配置问题提供了新思路.     

非线性电路和系统的故障诊断——一种新理论和方法

本文提出了关于非线性电路和系统的故障诊断的一种新理论——Volterra泛函级数理论,并以此为基础,发展了非线性电路和系统故障诊断的故障方程递归法和故障证明的决策法。它们是两种SAT方法,不但大大减小了仿真的工作量,而且适于线性与非线性系统、硬故障和软故障、参数识别和故障隔离。同时它们又是完全解析的频域中的符号法,因而适于任意动态非线性系统。     

谱HS投影算法求解非线性单调方程组

借助谱梯度法和HS共轭梯度法的结构, 建立一种求解非线性单调方程组问题的谱HS投影算法. 该算法继承了谱梯度法和共轭梯度法储存量小和计算简单的特征, 且不需要任何导数信息, 因此它适应于求解大规模非光滑的非线性单调方程组问题. 在适当的条件下, 证明了该算法的收敛性, 并通过数值实验表明了该算法的有效性.     

求时滞Volterra积分系统最优控制问题近似解的一个迭代算法

对一类典型的复杂系统—含多个非线性时滞的Volterra积分系统,给出其控制作用受限(硬约束)最优控制问题近似解的一个迭代算法,证明了该算法是well-defined的,并在一定的条件下证得了算法的收敛性.     

微分变换法求解二维非线性Volterra积分微分方程

为了解决二维非线性Volterra积分微分方程的求解问题,本文给出微分变换法.利用该方法将方程中的微分部分和积分部分进行变换,这样简化了原方程,进而得到非线性代数方程组,从而将原问题转换为求解非线性代数方程组的解,使得计算更简便.文中最后数值算例说明了该方法的可行性和有效性.     

基于Volterra自适应方法的水文混沌时间序列预测

Volterra泛函级数能够描述具有响应和记忆功能的非线性行为,一般用于非线性系统因果关系点对的预测,把Volterra自适应方法应用于水文混沌时间序列的预测研究是一个有意义的工作。论文针对水文系统的复杂性,基于混沌动力系统相空间重构技术,构建了水文混沌时间序列Volterra自适应预测方法,并采用NLMS算法调整滤波器参数,并就模型进行仿真计算,讨论了模型参数对预测精度的影响。直门达水文站月蒸发量混沌时间序列预测实验表明,水文混沌时间序列Volterra自适应预测方法,具有较好的预测精度和效果,拓展了水文预测报方法的研究途径。     

On the Relation between Energy-Conserving Low-Order Models and a System of Coupled Generalized Volterra Gyrostats with Nonlinear Feedback

In this paper we first prove the equivalence between the system of coupled Volterra gyrostats and a special class of energy-conserving low-order models. We then extend the definition of the classical Volterra gyrostat to include nonlinear feedback, resulting in a class of generalized Volterra gyrostats. Using this new class of gyrostats as a basic building block, we present an algorithm for converting a general class of energy-conserving low-order models that routinely arise in fluid dynamics, turbulence, and atmospheric sciences into a system of coupled generalized Volterra gyrostats with nonlinear feedback.      

A new nonlinear blind source separation method with chaos indicators for decoupling diagnosis of hybrid failures: A marine propulsion gearbox case with a large speed variation

The normal operation of propulsion gearboxes ensures the ship safety. Chaos indicators could efficiently indicate the state change of the gearboxes. However, accurate detection of gearbox hybrid faults using Chaos indicators is a challenging task and the detection under speed variation conditions is attracting considerable attentions. Literature review suggests that the gearbox vibration is a kind of nonlinear mixture of variant vibration sources and the blind source separation (BSS) is reported to be a promising technique for fault vibration analysis, but very limited work has addressed the nonlinear BSS approach for hybrid faults decoupling diagnosis. Aiming to enhance the fault detection performance of Chaos indicators, this work presents a new nonlinear BSS algorithm for gearbox hybrid faults detection under a speed variation condition. This new method appropriately introduces the kernel spectral regression (KSR) framework into the morphological component analysis (MCA). The original vibration data are projected into the reproducing kernel Hilbert space (RKHS) where the instinct nonlinear structure in the original data can be linearized by KSR. Thus the MCA is able to deal with nonlinear BSS in the KSR space. Reliable hybrid faults decoupling is then achieved by this new nonlinear MCA (NMCA). Subsequently, by calculating the Chaos indicators of the decoupled fault components and comparing them with benchmarks, the hybrid faults can be precisely identified. Two specially designed case studies were implemented to evaluate the proposed NMCA-Chaos method on hybrid gear faults decoupling diagnosis. The performance of the NMCA-Chaos was compared with state of art techniques. The analysis results show high performance of the proposed method on hybrid faults detection in a marine propulsion gearbox with large speed variations.     

Algorithm with asymptotically optimal accuracy for solving the nonlinear Volterra integral equation

A direct algorithm is proposed for solving the nonlinear Volterra integral equation of the second kind (with Hammerstein kernel) by reduction to a system of linear algebraic equations. The accuracy of the algorithm is asymptotically optimal if the original functions satisfy the Lipschitz condition. Error bounds are obtained for the algorithm in this class of functions.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 57, pp. 33–39, 1985.     

Systems of nonlinear Volterra integro-differential equations

An efficient method based on operational Tau matrix is developed, to solve a type of system of nonlinear Volterra integro-differential equations (IDEs). The presented method is also modified for the problems with separable kernel. Error estimation of the new schemes are analyzed and discussed. The advantages of this approach and its modification is that, the solution can be expressed as a truncated Taylor series, and the error function at any stage can be estimated. Methods are applied on the four problems with separable kernel to show the applicability and efficiency of our schemes, specially for those problems at broad intervals.     

Rolling element bearing diagnosis based on probability box theory

Feature extraction leads to the loss of statistical information of raw data and ignores the sampling uncertainty and the fluctuations in the signal over time in mechanical fault diagnosis. In this paper, novel modeling methods for mechanical signals based on probability box theory were proposed to solve the above problem. First, the type of random distribution of the bearing signals were analyzed. Then, a Dempster-Shafer structure was obtained to establish a probability box model. To address the identification difficulty of the type of random distribution for the bearing signals, a second probability box model was established based on a vector consisting of features from the bearing signals. If the data are not found to follow a random distribution, a third modeling method based on the definition of probability boxes was proposed. The effectiveness and applicability of the three proposed models were compared with experimental data from rolling element bearings. The combination of probability box theory and mechanical fault diagnosis theory can open up a new research direction for mechanical fault diagnosis.     

Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the taylor expansion method

This paper presents a new and an efficient method for determining solutions of the linear second kind Volterra integral equations system. In this method, the linear Volterra integral equations system using the Taylor series expansion of the unknown functions transformed to a linear system of ordinary differential equations. For determining boundary conditions we use a new method. This method is effective to approximate solutions of integral equations system with a smooth kernel, and a convolution kernel. An error analysis for the proposed method is provided. And illustrative examples are given to represent the efficiency and the accuracy of the proposed method.     

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.     

Multiparameter regularization for Volterra kernel identification via multiscale collocation methods

Identification of the Volterra system is an ill-posed problem. We propose a regularization method for solving this ill-posed problem via a multiscale collocation method with multiple regularization parameters corresponding to the multiple scales. Many highly nonlinear problems such as flight data analysis demand identifying the system of a high order. This task requires huge computational costs due to processing a dense matrix of a large order. To overcome this difficulty a compression strategy is introduced to approximate the full matrix resulted in collocation of the Volterra kernel by an appropriate sparse matrix. A numerical quadrature strategy is designed to efficiently compute the entries of the compressed matrix. Finally, numerical results of three simulation experiments are presented to demonstrate the accuracy and efficiency of the proposed method.     

Volterra series approximation for rational nonlinear system

Rational nonlinear systems are widely used to model the phenomena in mechanics, biology, physics and engineering. However, there are no exact analytical solutions for rational nonlinear system. Hence, the approximate analytical solutions are good choices as they can give the estimation of the states for system analysis, controller design and reduction. In this paper, an approximate analytical solution for rational nonlinear system is derived in terms of the solution of a polynomial system by Volterra series theory. The rational nonlinear system is transformed to a singular polynomial system with finite terms by adding some algebraic constraints related to the rational terms. The analytical solution of singular polynomial system is approximated by the summation of the solutions of Volterra singular subsystems. Their analytical solutions are derived by a novel regularization algorithm. The first fourth Volterra subsystems are enough to approximate the analytical solution to guarantee the accuracy. Results of numerical experiments are reported to show the effectiveness of the proposed method.     

基于故障树和混沌粒子群算法的锻压机床故障诊断方法

锻压机床由于生产效率高和材料利用率高的特点,被广泛应用于各领域.然而,锻压机床发生故障时,其故障种类繁多、故障数据量大,所以对锻压机床故障源的快速、准确诊断较困难.针对该问题,文章提出一种将故障树分析法和混沌粒子群算法相融合的方法,对锻压机床的故障源进行故障诊断.该方法是先通过故障树分析法对锻压机床的故障进行分析从而得到故障模式及其故障概率,然后由得到的故障模式和已知的故障维修经验分析归纳出故障模式的学习样本,再根据得到的故障概率运用混沌粒子群算法的遍历性快速、准确地诊断出锻压机床发生故障的精确位置.文章提出的方法以锻压机床的伺服系统为例进行了故障诊断实验,将该实验结果与遗传算法、粒子群算法进行对比.实验结果表明,文章的算法在锻压机床伺服系统的故障诊断中准确度更高、速度更快.