多传感器慢速采样下的快速残差生成器

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"基于多个慢速传感器的快速残差发生器" 这篇研究论文发表在IET Signal Processing期刊上，作者包括Hang Geng、Yan Liang、Xiaojing Zhang和Feng Yang，他们来自中国西北工业大学自动化学院。文章讨论了在多传感器系统中，如何利用多个慢速传感器进行快速故障检测的问题。研究的核心是一个基于因果约束的快速速率残差生成器，它从多传感器模型中建立起来。残差生成器是故障检测系统中的关键组件，它通过计算预期输出与实际输出之间的差异（即残差）来识别系统中的异常情况。在传统的故障检测方法中，如果传感器采样速率较低，可能无法实现快速的故障响应。该研究提出了一种新的解决方案，即通过设定一个带有因果约束的快速速率残差生成器，即使传感器的采样速度较慢，也能实现快速的故障检测。具体来说，论文中提到的残差生成器的参数是通过左特征向量分配的扰动解耦方法确定的。扰动解耦是一种控制理论技术，用于减少外部干扰对系统性能的影响。研究发现，能否成功实现扰动解耦与多速率传感器的采样特性有直接关系。这表明，不同的传感器采样频率会影响残差生成器的效果和系统的整体稳定性。论文中提供了一个数值实例，以证明所提出的快速残差生成器的有效性。通过这个实例，读者可以直观地理解该方法如何在实际系统中工作，并评估其在不同条件下的性能。 Nomenclature（符号表）部分列出了文章中使用的变量： - x：状态向量 - y：输出向量 - r：残差向量 - d：干扰向量 - I：单位矩阵 - 0：零矩阵 - K：增益矩阵 - T：因果约束矩阵 - diag{·}：块对角矩阵这篇论文提出了一个创新的方法，通过优化和调整基于慢速传感器的系统，能够在保持快速响应的同时，有效地检测系统故障。这对于工业控制、航空航天、电力系统等领域具有重要的应用价值，因为这些领域的传感器往往受限于采样速率，但快速的故障检测是至关重要的。

Published in IET Signal Processing

Received on 24th July 2013

Revised on 11th March 2014

Accepted on 28th March 2014

doi: 10.1049/iet-spr.2013.0296

ISSN 1751-9675

Fast-rate residual generator based on multiple

slow-rate sensors

Hang Geng, Yan Liang, Xiaojing Zhang, Feng Yang

School of Automation, Northwestern Polytechnical University, Xi’an, People’s Republic of China

E-mail: liangyan@nwpu.edu.cn

Abstract: This study puts forward the problem of fast-rate fault detection based on multiple slow-rate sensors. A fast-rate residual

generator with casuality constraint is established from the multi-sensor model. Parameters of the residual generator are determined

via disturbance-decoupling based on left eigenvector assignment. It is found that the condition of disturbance-decoupling is

related to the multi-rate sensor sampling nature. A numerical example is given to illustrate the effectiveness of the proposed

residual generator.

Nomenclature

x state vector

y output vector

r residual vector

d disturbance vector

I identity matrix

0 zero matrix

K gain matrix

T casuality constraint matrix

diag {·} a block diagonal matrix

superscript u, d, f refer to the control, disturbance and

fault, respectively

subscript i refers to the ith sensor

superscript −1 refers to the inverse operation

superscript T refers to the transpose operation

1 Introduction

Since the beginning of the 1970s, research on fault diagnosis

has gained increasing consideration world-wide in both

theory and applications [1–4]. The development was (and

still is) mainly stimulated by the trend of automation

towards more complexity and the growing demand for

higher availability and security of control systems [5–8].

In many complex systems, it is often unrealistic or

sometimes impossible to guarantee all physical signals

operating at one single-rate [9]. In this regard, standard

single-rate residual generators based on parity space and

observers were extended to the multi-rate case [10, 11].

Through converting a multi-rate sampled-data (MSD)

system into a linear time-invariant model with a slow

sampling rate, a residual generator was presented based on

parity space [12]. A residual generator for multi-rate

sampled-data systems was considered and the derived

performance index reﬂected the compromise between

sensitivity to faults and robustness to the unknown inputs

[13]. However, above the methods output the slow-rate

residual, which is not desirable in fast fault detection.

Considering the multi-rate sensor fault detection, a bank of

single-rate observers are derived, where the ith observer is

dedicated to the ith sensor [14]. The resultant detectability

condition seems too stringent by the fact that detecting the

ith sensor faults is just based on the ith sensor

measurements, instead of all sensors’ measurements. In

[15], an observer-based fault detection scheme was

designed for periodically time-varying systems (including

the multi-rate sampled-data system as a special case) based

on H

estimation approach. By optimising the predeﬁned

performance index, a fast-rate scheme for fault detection

was given to obtain an optimal parity space based residual

generator [16]. Later, the fast-rate residual generator was

achieved by optimising the performance index in H

∞

sense

under the causality constraint [17]. In [18], a uniﬁed fault

detection and isolation approach was modiﬁed to solve the

problem of residual generation to obtain a slow-rate residual

generator with causality constraint and an inverse lifting

operation was implemented for fast-rate residual generation.

However, to our best knowledge, a still open problem is

how to design a fast-rate fault residual decoupling with the

unknown disturbance based on multiple slow-rate sensors.

In this paper, a fast-rate residual generator based on

multiple slow-rate sensors is proposed. By lifting the

multi-rate multi-sensor model to a single-rate one, a residual

generator with causality constraint is obtained, whose

parameters are determined through decoupling the residual

with the disturbance based on the left eigenvector

assignment. It is found that the resultant decoupling

condition is related to the casuality constraint because of

the multi-rate nature.

The rest of this paper is organised as follows. The problem

under investigation is formulated in Section 2. The fast-rate

residual generator is established in Section 3. The

www.ietdl.org

878

The Institution of Engineering and Technology 2014

IET Signal Process., 2014, Vol. 8, Iss. 8, pp. 878–884

doi: 10.1049/iet-spr.2013.0296

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