Measured Output Probability Density Functions Research Articles

Fault Detection for Non-Gaussian Stochastic Systems with Time-Varying Delay

Fault detection (FD) for non-Gaussian stochastic systems with time-varying delay is studied. The available information for the addressed problem is the input and the measured output probability density functions (PDFs) of the system. In this framework, firstly, by constructing an augmented Lyapunov functional, which involves some slack variables and a tuning parameter, a delay-dependent condition for the existence of FD observer is derived in terms of linear matrix inequality (LMI) and the fault can be detected through a threshold. Secondly, in order to improve the detection sensitivity performance, the optimal algorithm is applied to minimize the threshold value. Finally, paper-making process example is given to demonstrate the applicability of the proposed approach.

Constrained discrete-time PI controller design for output PDFs of stochastic systems with time delays

This article presents a new proportional-integral (PI) tracking control strategy for non-Gaussian stochastic systems based on a square root B-spline model for the output probability density functions (PDFs). Following the square root B-spline approximation to the measured output PDF, a non-linear discrete-time dynamical model can be established between the control input and the weights related to the PDFs. It is noted that the PDF tracking is transformed to a constrained dynamical tracking control problem for weight dynamics. For the non-linear discrete-time weight model including time-delay terms and exogenous disturbances, convex linear matrix inequality optimisation algorithms are used to design a generalised PI controller such that stabilisation, state constraint and tracking performance can be guaranteed simultaneously. Furthermore, in order to enhance the robustness, the peak-to-peak measure index is applied to optimise the tracking performance. Simulations are given to demonstrate the efficiency of the proposed approach.

Delay-dependent fault detection and diagnosis using B-spline neural networks and nonlinear filters for time-delay stochastic systems

A new fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (PDFs) of the system. The square-root B-spline neural networks is used to formulate the output PDFs with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Delay-dependent criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. It is shown that this new criterion can provide higher sensitivity performance than the existing result. Simulations are given to demonstrate the efficiency of the proposed approach.

Observer-based optimal fault detection using PDFs for time-delay stochastic systems

This paper concerns the problem of fault detection (FD) for general stochastic systems with time delays. Different from the classical FD problem, the available information for the FD is the input and the measured output probability density functions (PDFs) of the system. Based on this, firstly, square root B-spline expansions technique is applied to model the PDFs so that the concerned FD problem is transformed into a nonlinear FD problem subject to the weight dynamical systems. Secondly, by using the FD observer as residual generator and guaranteed cost performance index as objective function, design of the FD observer is formulated as an optimization problem. A delay-dependent condition to solve this problem is established in terms of the feasibility of linear matrix inequality (LMI). Moreover, in order to improve FD performance, the guaranteed cost algorithm is applied to optimal observer design. Finally, two examples are given to demonstrate the applicability of the proposed approach.

Observer-Based Optimal Fault Detection and Diagnosis Using Conditional Probability Distributions

A new optimal fault detection and diagnosis (FDD) scheme is studied in this paper for the continuous-time stochastic dynamic systems with time delays, where the available information for the FDD is the input and the measured output probability density functions (pdf's) of the system. The square-root B-spline functional approximation technique is used to formulate the output pdf's with the dynamic weightings. As a result, the concerned FDD problem can be transformed into a robust FDD problem subjected to a continuous time uncertain nonlinear system with time delays. Feasible criteria to detect and diagnose the system fault are provided by using linear matrix inequality (LMI) techniques. In order to improve FDD performances, two optimization measures, namely guaranteed cost performance and H <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">infin</sub> performance, are applied to optimize the observer design. Simulations are given to demonstrate the efficiency of the proposed approach

Fault detection and diagnosis for general stochastic systems using B-spline expansions and nonlinear filters

This paper presents a new fault detection and diagnosis (FDD) algorithm for general stochastic systems. Different from the classical FDD design, the distribution of system output is supposed to be measured rather than the output signal itself. The task of such an FDD algorithm design is to use the measured output probability density functions (PDFs) and the input of the system to construct a stable filter-based residual generator such that the fault can be detected and diagnosed. For this purpose, square root B-spline expansions are applied to model the output PDFs and the concerned problem is transformed into a nonlinear FDD algorithm design subjected to a nonlinear weight dynamical system. A linear matrix inequality based solution is presented such that the estimation error system is stable and the fault can be detected through a threshold. Moreover, an adaptive fault diagnosis method is also provided to estimate the size of the fault. Simulations are provided to show the efficiency of the proposed approach.

PID controller design for output PDFs of stochastic systems using linear matrix inequalities

This paper presents a pseudo proportional-integral-derivative (PID) tracking control strategy for general non-Gaussian stochastic systems based on a linear B-spline model for the output probability density functions (PDFs). The objective is to control the conditional PDFs of the system output to follow a given target function. Different from existing methods, the control structure (i.e., the PID) is imposed before the output PDF controller design. Following the linear B-spline approximation on the measured output PDFs, the concerned problem is transferred into the tracking of given weights which correspond to the desired PDF. For systems with or without model uncertainties, it is shown that the solvability can be casted into a group of matrix inequalities. Furthermore, an improved controller design procedure based on the convex optimization is proposed which can guarantee the required tracking convergence with an enhanced robustness. Simulations are given to demonstrate the efficiency of the proposed approach and encouraging results have been obtained.

Estimating unknown probability density functions for random parameters of stochastic ARMAX systems

Different from existing parameter estimation algorithms where the values of parameters are required to be estimated, this paper presents a new method to estimate the unknown probability density functions of random parameters for non-Gaussian dynamic stochastic systems. The System is represted by an ARMAX model, where the parameters and the system noise term are random processes that are characterized by their unknown probability density functions. Under the assumption that each random parameter and the noise term are independent and are identically distributed sequece, a simple mathematical relationship is established between the measured output probability density function of the system and the unknown probability density functions of the random parameters and noise term. The mement generating function in probability theory has been used to transfer the multiple convolution integration into a simple algebraic operation. An identification algorithm is then established that estimates these unknown probability density functions of the parameters and the noise term by using the measured output probability density functions and the system input.

Detect and Diagnose Unexpected Changes in the Output Probability Density Functions for Dynamic Stochastic Systems: An Identification Based Approach

In parallel to the recently developed observer based fault detection algorithm (Wang, 1998), this paper presents an identification based fault detection and diagnosis approach for the output probability density function for unknown time-invariant stochastic systems. The fault is assumed to be the unexpected changes of the system physical parameters which affect the shape of the output probability density functions of the system. In this context, the measured control input directly affects the distribution of the system output in some probability sense. An on-line parameter estimation algorithm is constructed using the measured output probability density functions of the system. Based upon the same type of dynamic model proposed by Wang (1997, 1998), a functional weighted integration of the output probability density function is employed in the evaluation of the residual signals for both fault detection and diagnosis purposes. An applicability study of the proposedalgorithm to the detection of the unexpected changes of the solid flocculation in paper making is included, where a simulated example is employed to illustrate the use of the developed algorithm and encourage results have been obtained.