# Heterogeneous Multi-Agent-Based Fault Diagnosis Scheme for Actuation System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Problem Description

#### 2.1. Multi-Agent Architecture

#### 2.2. Multi-Agent Model

## 3. Actuator Model

#### 3.1. Electro-Hydraulic Servo Actuator Model

#### 3.2. Electro-Hydrostatic Actuator Model

#### 3.3. Electro-Mechanical Actuator Model

## 4. Heterogeneous Multi-Agent-Based Fault Diagnosis

#### 4.1. FDI Parameters Design

- The augmented system (13) is stable;
- Interference and the control input have the least influence on the error signal ${r}_{i}\left(t\right)$;
- The fault has the greatest influence on the error signal ${r}_{i}\left(t\right)$;
- Each element of the error signal ${r}_{i}\left(t\right)$ is only sensitive to the specified special fault.

**Lemma**

**1**

**([30]).**Given a symmetric matrix$Z\in {S}_{m}$(${S}_{m}$represents the set of all symmetric matrices with$m\times m$dimensions), and matrices$U$and$V$with rank m of two columns, there is a matrix$X$without the structural constraints that satisfies:

**Theorem**

**1.**

**Proof of Theorem**

**1.**

**End of proof.**□

#### 4.2. Threshold Selection

- The influence of the model input signal on the error signal;
- The influence of the noise signal on the error signal.

## 5. Simulation

#### 5.1. Actuators without Faults

#### 5.2. Actuators with Faults

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 4.**Curves of the disturbances. (

**a**) Curve of disturbance input of Agent 1. (

**b**) Curve of disturbance input of Agent 2. (

**c**) Curve of disturbance input of Agent 3.

**Figure 5.**Curves of the error signals without faults. (

**a**) Curve of error signal without faults of Agent 1. (

**b**) Curve of error signal without faults of Agent 2. (

**c**) Curve of error signal without faults of Agent 3.

**Figure 6.**Curves of the faults. (

**a**) Curve of fault of Agent 1. (

**b**) Curve of fault of Agent 2. (

**c**) Curve of fault of Agent 3.

**Figure 7.**Curves of the error signals with faults (Agent 1). (

**a**) Curve of the error signal of Fault 1. (

**b**) Curve of the error signal of Fault 2. (

**c**) Curve of the error signal of Fault 3.

**Figure 8.**Curves of the error signals with faults (Agent 2). (

**a**) Curve of the error signal of Fault 1. (

**b**) Curve of the error signal of Fault 2. (

**c**) Curve of the error signal of Fault 3.

**Figure 9.**Curves of the error signals with faults (Agent 3). (

**a**) Curve of the error signal of Fault 1. (

**b**) Curve of the error signal of Fault 2. (

**c**) Curve of the error signal of Fault 3.

Value | 5 | 50 | 500 | 5000 | 50,000 | 5 × 10^{5} | 5 × 10^{6} | 5 × 10^{7} |

Result | NO | NO | NO | NO | NO | NO | OK | NO |

Value | 0.01 | 0.05 | 0.1 | 0.2 | 0.3 | 0.4 | 0.5 | 0.6 |

Result | OK | OK | OK | OK | OK | OK | OK | OK |

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**MDPI and ACS Style**

Cao, Y.; Li, T.; Li, Y.; Wang, X.
Heterogeneous Multi-Agent-Based Fault Diagnosis Scheme for Actuation System. *Actuators* **2022**, *11*, 113.
https://doi.org/10.3390/act11040113

**AMA Style**

Cao Y, Li T, Li Y, Wang X.
Heterogeneous Multi-Agent-Based Fault Diagnosis Scheme for Actuation System. *Actuators*. 2022; 11(4):113.
https://doi.org/10.3390/act11040113

**Chicago/Turabian Style**

Cao, Yuyan, Ting Li, Yang Li, and Xinmin Wang.
2022. "Heterogeneous Multi-Agent-Based Fault Diagnosis Scheme for Actuation System" *Actuators* 11, no. 4: 113.
https://doi.org/10.3390/act11040113