# Model-Based Fault Diagnosis of Actuators in Electronically Controlled Air Suspension System

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Modeling and Failure Analysis of ECAS System

#### 2.1. Modeling of Vehicle Height Adjustment System in ECAS System

_{s}is the sprung mass of the whole vehicle, kg; ${\ddot{x}}_{s}$ is the vertical acceleration of the body center of mass; F

_{1}, F

_{2}, F

_{3}, and F

_{4}are the forces on the front left, rear left, front right, and rear right body, respectively, N; I

_{y}is the moment of inertia of the car body around the Y-axis, km∙m

^{2}; $\ddot{\theta}$ is the pitch angular acceleration, rad/s

^{2}; a and b are the distance from the center of mass of the car body to the front and rear axles, m; I

_{x}is the moment of inertia of the car body around the X-axis, km∙m

^{2}; $\text{}\ddot{\phi}$ is the roll angular acceleration, rad/s

^{2}; and d is the 1/2 tread, m.

_{0}is the initial volume of the air spring, m

^{3}; and ΔV is the rate of change of air spring volume, m

^{3}/m.

^{3}; ĸ is the adiabatic coefficient of air; R is the gas constant, N∙m/(kg∙K); T is the internal temperature of the air spring, °C; and q

_{m}is the gas mass flow rate when charging and discharging the air spring, kg/s.

#### 2.2. Actuator Failure Analysis and Modeling

_{d}is the flow coefficient; A is the flow area of the valve port, m

^{2}; D is the duty cycle; ΔP is the difference between input pressure and output pressure, P

_{a}; and ρ is the gas density, kg/m

^{3}.

_{f}is as follow:

_{f}can be expressed as:

## 3. Fault Diagnosis of ECAS System Based on Adaptive Threshold

#### 3.1. Fault Diagnosis System Architecture Based on KEFs

_{k}is the filter gain matrix. Process noise ω and measurement noise ν are mutually uncorrelated Gaussian white noise. The probability distribution characteristics are as follows:

_{k}is the process noise covariance matrix, and R

_{k}is the measurement noise covariance matrix. The EKF algorithm is shown in Figure 5, where ${F}_{k}=\frac{\partial f\left({x}_{k}\right)}{\partial {x}_{k}}|{x}_{k}={\widehat{x}}_{k},\text{}{H}_{k}=\frac{\partial h\left({x}_{k}\right)}{\partial {x}_{k}}|{x}_{k}={\widehat{x}}_{k},\text{}{\Gamma}_{k}=\frac{\partial f\left({x}_{k}\right)}{\partial {\omega}_{k}}|{x}_{k}={\widehat{x}}_{k},\text{}{\widehat{z}}_{k}=h\left({\widehat{x}}_{k,\text{}k-1}\right)$.

#### 3.2. Calculation of Adaptive Threshold

- Linearization error

- 2.
- Parameter uncertainty error

**c**calculates the acceptable deviation.

#### 3.3. Fault Detection

_{i}

^{(j)}is the output estimated residual, i is the extended Kalman filter number (i = 1 − 4), and j is the measurement output number. j = 1, 2, 3 represent the height change of the air spring, the vertical acceleration at the four corners of the body, and the internal air pressure of the air spring, respectively. Actuators 1–4 represent the front left, rear left, front right, and rear right air spring solenoid valves, respectively. Taking the residual r as the fault detection indicator, there are three fault detection indicators, including the air spring height estimation residual r

_{i}

^{(1)}and the vertical acceleration estimation residual error at the four corners of the car body r

_{i}

^{(2)}, and the air spring pressure estimation residual r

_{i}

^{(3)}. Each extended Kalman filter will produce the above three fault detection indicators (that is, r

_{i}

^{(1)}, r

_{i}

^{(2)}and r

_{i}

^{(3)}). Comparing the fault detection index with the adaptive threshold h, it can be detected whether the actuator has a fault.

_{i}

^{(j)}= 1; when the detection index value is less than the detection threshold, the actuator has not failed. The corresponding detection index r

_{i}

^{(j)}is equal to 0.

#### 3.4. Simulation and Analysis

_{2}

^{(1)}, r

_{2}

^{(2)}and r

_{2}

^{(3)}output by EKF2 all exceeds the adaptive threshold. The residual outputs by other filters still fluctuate around zero or are less than the adaptive threshold. According to Figure 7 and the residual characteristics in Table 2, the front left air spring solenoid valve is malfunctioning. The fault detection time is 11.1 s, 10.4 s, and 10.1 s, respectively. If one of r

_{2}

^{(1)}, r

_{2}

^{(2)}and r

_{2}

^{(3)}exceeds the threshold, it is considered that a fault has occurred. Therefore, the actuator failure was detected at 10.1 s.

_{1}

^{(1)}, r

_{1}

^{(2)}, r

_{1}

^{(3)}all exceed the adaptive threshold. The residual outputs by other filters are still smaller than the adaptive threshold, and the fault detection time is 11.4 s, 10.6 s, and 10.4 s, respectively. Therefore, the actuator failure is detected at 10.4 s. According to Figure 7 and the residual characteristic Table 2, it can be judged that the rear left air spring solenoid valve is malfunctioning.

## 4. Design and Simulation of Active Fault Tolerant Control

#### 4.1. Design of Active Fault Tolerant Control

_{0}of the controller is replaced so that the duty ratio of the solenoid valve is increased, and the height change rate of the air spring corresponding to the faulty solenoid valve is increased. This can improve the inconsistency of air spring changes at the four corners and, ultimately, increase the vehicle height adjustment speed, as well as improve the body posture.

#### 4.2. Simulation of Active Fault Tolerant Control

## 5. Hardware In-Loop Simulation System

#### 5.1. Hardware Platform

#### 5.2. Results and Analysis

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

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**Figure 6.**Changes of fault detection indicators under Fault 1: (

**a**) Fault detection index r

_{i}

^{(1)}and threshold h1; (

**b**) Fault detection index r

_{i}

^{(2)}and threshold h2; (

**c**) Fault detection index r

_{i}

^{(3)}and threshold h3.

**Figure 7.**Change of fault detection index under Fault 2: (

**a**) Fault detection index r

_{i}

^{(1)}and threshold h1; (

**b**) Fault detection index r

_{i}

^{(2)}and threshold h2; (

**c**) Fault detection index r

_{i}

^{(3)}and threshold h3.

**Figure 9.**Performance comparison before and after fault tolerant control under Fault 1 (stuck): (

**a**) Relative height of mass center; (

**b**) Pitch angle; (

**c**) Roll angle.

**Figure 10.**Performance comparison before and after fault tolerant control under Fault 2 (constant gain): (

**a**) Relative height of mass center; (

**b**) Pitch angle; (

**c**) Roll angle.

**Figure 13.**Performance comparison before and after fault tolerant control under Fault 1: (

**a**) Relative height of mass center; (

**b**) Pitch angle; (

**c**) Roll angle.

**Figure 14.**Performance comparison before and after fault tolerant control under Fault 2: (

**a**) Relative height of mass center; (

**b**) Pitch angle; (

**c**) Roll angle.

Event | Symbol | Description |
---|---|---|

Basic event | The lowest level event that does not need to be ascertained | |

No extended Events | Events that have little impact on the top event or whose cause cannot be known temporarily | |

Result Event | Contains top and middle events that are always at the outputs | |

Transfer symbol | This event indicates information transfer and avoids drawing repetition | |

Logic symbol: and gate | Output events only occur when all input events occur | |

Logical symbols: or doors | As long as one of the input events occurs, the output event occurs |

Residual | r_{1}^{(1)} | r_{2}^{(1)} | r_{3}^{(1)} | r_{4}^{(1)} | r_{1}^{(2)} | r_{2}^{(2)} | r_{3}^{(2)} | r_{4}^{(2)} | r_{1}^{(3)} | r_{2}^{(3)} | r_{3}^{(3)} | r_{4}^{(3)} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

No Failure | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Actuator 1 failure | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 |

Actuator 2 failure | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 |

Actuator 3 failure | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 |

Actuator 4 failure | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 |

Fault Number | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|

Moment of failure/s | 8 | ||||

Fault behavior | n | 0 | 0.2 | 0.4 | 0.6 |

δ | 0 | 0 | 0 | 0 |

Fault Type | Fault Tolerance Measures |
---|---|

No fault | The original controller is adopted |

Constant gain fault | Online adjustment of controller parameters |

Stuck fault | Close all solenoid valves and stop height adjustment |

Fault Number | Performance Index | Failure (No Fault Tolerance) | Fault Tolerant Control | Improvement Range |
---|---|---|---|---|

2 | Height adjustment time (s) | 25.5 | 21.6 | 15.3% |

Peak pitch angle (RAD) | 0.0009 | 43.8% | ||

Peak roll angle (RAD) | 0.0024 | 0.0015 | 37.5% | |

3 | Height adjustment time (s) | 24.2 | 20.4 | 15.7% |

Peak pitch angle (RAD) | 0.0094 | 0.001 | 89.4% | |

Peak roll angle (RAD) | 0.0063 | 0.0013 | 79.4% | |

4 | Height adjustment time (s) | 20.8 | 19.2 | 7.7% |

Peak pitch angle (RAD) | 0.0027 | 0.0011 | 59.3% | |

Peak roll angle (RAD) | 0.0017 | 0.0012 | 29.4% |

Fault Number | Performance Index | Failure (No Fault Tolerance) | Fault Tolerant Control | Improvement Range |
---|---|---|---|---|

2 | Height adjustment time (s) | 25.5 | 21.6 | 15.3% |

Peak pitch angle (RAD) | 0.0018 | 0.001 | 44.4% | |

Peak roll angle (RAD) | 0.0025 | 0.0016 | 36% | |

3 | Height adjustment time (s) | 24.2 | 20.4 | 15.7% |

Peak pitch angle (RAD) | 0.0091 | 0.00098 | 89.2% | |

Peak roll angle (RAD) | 0.0061 | 0.0016 | 73.8% | |

4 | Height adjustment time (s) | 20.8 | 19.2 | 7.7% |

Peak pitch angle (RAD) | 0.003 | 0.0012 | 60% | |

Peak roll angle (RAD) | 0.0017 | 0.0013 | 23.5% |

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**MDPI and ACS Style**

Jiang, X.; Xu, X.; Shan, H.
Model-Based Fault Diagnosis of Actuators in Electronically Controlled Air Suspension System. *World Electr. Veh. J.* **2022**, *13*, 219.
https://doi.org/10.3390/wevj13110219

**AMA Style**

Jiang X, Xu X, Shan H.
Model-Based Fault Diagnosis of Actuators in Electronically Controlled Air Suspension System. *World Electric Vehicle Journal*. 2022; 13(11):219.
https://doi.org/10.3390/wevj13110219

**Chicago/Turabian Style**

Jiang, Xinwei, Xing Xu, and Haiqiang Shan.
2022. "Model-Based Fault Diagnosis of Actuators in Electronically Controlled Air Suspension System" *World Electric Vehicle Journal* 13, no. 11: 219.
https://doi.org/10.3390/wevj13110219