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IEEE SENSORS JOURNAL, VOL. 20, NO. 16, AUGUST 15, 2020 9359

A Fault Detection and Diagnosis System for

Autonomous Vehicles Based on Hybrid

Approaches

Yukun Fang , Haigen Min ,

Member, IEEE

, Wuqi Wang, Zhigang Xu ,

Member, IEEE

,

and Xiangmo Zhao ,

Member, IEEE

Abstract

—An accurate fault detection and diagnosis sys-

tem is of great importance for autonomous vehicles to prevent

the potential hazardous situations. In this paper, we propose

a fault detection and diagnosis system based on hybrid

approaches. First, to detect the state faults of the autonomous

vehicle, One-Class Support Vector Machine (SVM) method

is adopted to train the boundary curve which separates the

safe domain and unsafe domain. Meanwhile, a Kalman ﬁlter

observer is designed based on the linear kinematic vehicle

bicycle model to predict the current position of the vehicle,

and after obtaining the residuals between prediction and mea-

surement, Jarque-Bera test is applied to check the normality

of the residuals probability distribution to monitor whether

the trajectory deviates. Furthermore, we design a fuzzy system to distinguish the types of the detected faults based on a

modiﬁed neutral network, in which a membership functionlayer is added after the input layer. With the strong self-learning

ability of neutral network, the initial membership function of the fuzzy system is updated through black box test and can

indicate the probability of each fault type. Experiments on the real autonomous vehicle platform ‘Xinda’ and performance

comparison with other fault detectors validate the effectiveness of these methods and the usability of the fault detection

and diagnosis system.

Index Terms

—Fault detection and diagnosis for autonomous vehicles, one-class SVM, residuals distributioninference,

neutral network, black box test.

I. INTRODUCTION

OVER the past few years, automated driving technology

has attracted public attentions since its potential to

improve road trafﬁc efﬁciency and road capacity [1], [2].

However, safety issue for autonomous vehicles is still one

of the pain points that hinders the commercialization of self-

Manuscript received February 21, 2020; revised April 3, 2020;

accepted April 5, 2020. Date of publication April 14, 2020; date of current

version July 17, 2020. This work was supported in part by the National

Natural Science Foundation of China under Grant 61903046, in part by

the National Key Research and Development Program of China under

Grant 2019YFB1600100, in part by the Overseas Expertise Introduction

Project for Discipline Innovation under Grant B14043, and in part by

the Joint Laboratory for Internet of Vehicles, Ministry of Education-China

Mobile Communications Corporation, under Grant 213024170015. The

associate editor coordinating the review of this article and approving

it for publication was Dr. Marco J. da Silva.

(Corresponding authors:

Haigen Min; Xiangmo Zhao.)

The authors are with the School of Information Engineering, Chang’an

University, Xi’an 710064, China, and also with the Joint Laboratory

for Internet of Vehicles, Ministry of Education-China Mobile Communi-

cations Corporation, Xi’an 710064, China (e-mail: hgmin@chd.edu.cn;

xmzhao@chd.edu.cn).

Digital Object Identiﬁer 10.1109/JSEN.2020.2987841

driving. Thus, a fault detection and diagnosis (FDD) system

is vital to an autonomous vehicle.

A fault is deﬁned as an unpermitted deviation of at least

one characteristic property or parameter of the system from

the usual condition [3]. Faults can be classiﬁed as sensor

faults, actuator faults, and component or process faults [4],

[5]. Sensor faults emphasize the faults that lie in the input

module and actuator faults address the faults that lie in the

output module. While, component or process faults refer to

the faults that occur in other modules of the system or in the

support devices of the whole system, for example, the power

unit. For an autonomous vehicle, faults can be originated from

sensors [6], [7], like a sensor breakdown, or vehicle itself,

like mechanical faults. When faults occur, abnormality can be

reﬂected in various aspects such as the output of the system,

measured signals or data collected from sensors, etc.

There are three tasks to the fault diagnosis, including

fault detection, fault isolation, and fault identiﬁcation. Fault

detection is to check whether there is malfunction or fault

in the system, fault isolation is to locate the faulty com-

ponent and fault identiﬁcation is to determine the type of

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9360 IEEE SENSORS JOURNAL, VOL. 20, NO. 16, AUGUST 15, 2020

the faults [4]. The concept of redundancy is the core for

fault diagnosis to improve the reliability of the concerned

system, either hardware redundancy or analytical redundancy.

Hardware redundancy is to compare the data from duplicative

devices, which is reliable and is necessary for key component

but would be too costly and not practical to equip the whole

system. While, analytical redundancy uses mathematical and

statistical methods with some estimation techniques for fault

detection, isolation and identiﬁcation, which is the mainstream

for fault diagnosis. Generally, these analytical techniques

can be categorized as model-based approaches, signal-based

approaches and knowledge-based approaches [4], [8].

As early as 1976, Willsky presented the key concepts of

analytical redundancy for model-based fault detection and

diagnosis in [9], and model-based approaches can be further

categorized as parity equations [10], [11], parameter estimation

methods [12], and observer-based methods with Luenberger

observers [13] or Kalman ﬁlters [14]. In model-based methods,

the model of the process or the system should be available.

Based on the model, algorithms are deployed to monitor the

consistency between the measured outputs of the practical

system and the model-predicted outputs [4].

Signal-based methods utilize measured signals and these

methods assume that faults in the process are reﬂected in

the measured signals. By extracting the features from the

measured signals, diagnostic decision is made based on the

symptom (or pattern) analysis and prior knowledge on the

symptoms of the healthy systems [4]. In [15], a structured and

comprehensive overview of the research on anomaly detection

is provided, which focuses on ﬁnding patterns from data that

do not conform to expectation.

Since a priori known model or signal patterns are not

always possible to be obtained, the knowledge-based fault

diagnosis methods are developed. Knowledge-based methods,

also known as data-driven methods, require a large volume

of historic data to learn the features of a process or a

system. Based on the learned features, consistency between the

observed behavior of the operating system and the knowledge

base is checked to judge whether faults occur [8]. In [16],

comprehensive fault diagnostic methods were reviewed from

the data-driven perspective and in [17], some techniques have

been introduced, e.g., neural networks, fuzzy logic and support

vector machine (SVM), etc.

As for fault diagnosis for autonomous vehicles, some

researchers have implemented it from the perspective of sensor

data fusion. In [18], a federated sensor data fusion architecture

is proposed to deals with possible sensor faults and the

objective of this architecture is to isolate faulty sensors before

their data becomes integrated into the entire system. In [19],

Pous et al. proposes a fault detection architecture that use

measurements analytical redundancy and a non-linear transfor-

mation based on the multi-sensor data processing, including

the data from INS (Inertial Navigation System) sensor and

odometers.

It should be pointed out that approaches in each category

have their own speciﬁc advantages dealing with speciﬁc issues

but have their own constraints. For model-based approaches,

only a small amount of real-time data is needed to conduct

fault diagnosis but diagnosis performance of model-based

methods extremely depends on the explicitness of the model

that represent the input-output relationship. However, it is

often the case that an accurate model to describe a system or a

process is unavailable or very challenging to obtain in realistic

environment. Signal-based and knowledge-based approaches

do not require complete models but the performance of the

former can be greatly degraded by unknown input disturbances

[8] and the latter suffers high computational costs due to the

high dependency on the large amount of training data. Namely,

the quality of the measured signals or the collected data are

the key to these model-free methods.

Motivation of applying hybrid approaches is to take advan-

tages of each category to deal with different issues. Perception

to the circumstance and motion control of an autonomous

vehicle are two essential parts when discussing the process

of automatic driving [20]–[23]. Behaviors of the autonomous

vehicle can be modeled by various vehicle kinematic and

dynamics models according to different situations and the

knowledge of the environment can be obtained from the data

collected from sensors. Therefore, hybrid approaches that inte-

grate two or more fault diagnosis methods are more reasonable

when considering the design of a fault detection and diagnosis

system for autonomous vehicles. In this paper, several fault

diagnosis approaches are applied to deal with different issues.

Firstly, to detect whether there are state faults occurring, One-

Class SVM is adopted to train the boundary curve of the safe

domain and unsafe domain. Here, state of the autonomous

vehicle can be reﬂected on the velocity v, which indicates the

longitudinal features, and angular velocity ω, that indicates

the lateral features, and the state faults refer to the obvious

deviation of vand ωfrom the normal condition. Causes of

state faults can be originated from different subsystem, like

the breakdown of the dynamic system, brake system and

steering system etc. Then, considering that the trajectory in

a period of time for an autonomous vehicle can be predicted

by kinematic model, model-based approaches can be taken

into consideration to check whether there is a deviation of

vehicle trajectory. Thus, based on vehicle kinematic model,

a Kalman ﬁlter observer is designed to predict the position

of the autonomous vehicle in each test period and the ideal

trajectory is the predicted value of the Kalman ﬁlter. Then,

residuals between predicted values and measured values can

be obtained and through residuals distribution inference, tra-

jectory deviation can be detected. Further, we design a fuzzy

system to distinguish the types of the detected faults based on

a modiﬁed neutral network, in which a membership function

layer is added after the input layer. With the strong learning

ability of neural network, the initial membership function

given by prior experience is updated through black box test

and can indicate the probability of each fault type.

The main work and contribution of the paper are as follows:

1). We design a fault detection system and a fault probability

indicator speciﬁcally for autonomous vehicles using hybrid

approaches; 2). Membership function of the fuzzy system

is optimized by deploying neural network and black box

test technique, which greatly reduces the subjectivity of the

membership function.

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FAN G

et al.

: FDD SYSTEM FOR AUTONOMOUS VEHICLES BASED ON HYBRID APPROACHES 9361

Fig. 1. System framework of the fault detection and diagnosis system.

This paper is structured as follows. Section I illustrate

the deﬁnition of fault in literature and provide a compre-

hensive analysis of current fault diagnosis methods from the

perspective of analytical redundancy. Section II displays the

framework of the system and illustrates the methodologies.

In Section III, experiments are conducted to validate the effec-

tiveness of the proposed approaches and ﬁnally, in Section IV

we brieﬂy summarize our work in this paper.

II. SYSTEM FRAMEWORK AND METHODOLOGY

A. System Framework

The whole system is generally divided into two parts, i.e.

fault detection system and fault diagnosis system. Fault detec-

tion system can be further subdivided into state fault detector

and trajectory deviation detector. The former is responsible for

judging whether the state, i.e. velocity and angular velocity, is

normal, and the later checks whether the trajectory deviates.

Once faults are detected, fault diagnosis system is triggered

and classiﬁes the fault as ‘Moving Alarm’ (longitudinal prob-

lems) or ‘Steering Alarm’ (lateral problems). Readers can see

the detailed deﬁnition of the fault types in Section II, part

D, Deﬁnition 1 and Fig.1 shows the schematic of the system

framework.

Each subsystem is implemented with different approaches

but works cooperatively. One-Class SVM is applied to imple-

ment the state fault detector, and residuals distribution is used

to check the trajectory deviation. And, implementation for fault

probability indicator is based on neural network and black box

test techniques. The rest of this section will illustrate these

approaches in detail.

B. State Fault Detector

The autonomous vehicle works well for most of the time,

so the data collected from the sensors are mostly positive

samples, i.e. normal samples. For fault detection, the goal is

to identify whether there are faults or not and we can achieve

this goal by testing the new samples and checking whether it is

alike or not like the training samples. To cope with such prob-

lems that have only positive training samples or unbalanced

training samples, many One-Class Classiﬁers (OCCs) have

been proposed. In [24], Bose et al. review the basics of bound-

ary and autoencoder based extreme learning machine (ELM-

B and ELM-AE) as one class classiﬁer and adopt ELM-B

for machine health monitoring and anomaly detection in their

work. Gautam et al. present six OCC methods and thirteen

variants based-on ELM and online sequential ELM in [25].

And in [26], Martínez-Rego et al. compare several methods

widely used in fault detection applications, showing that SVM

based methodology is more robust. In this paper, One-Class

SVM is adopted as the anomaly detection algorithm.

One-Class SVM is a data-driven approach and often used

for novelty detection. The training data for this model is

extremely unbalanced, which matches the characteristic of

the data collected from the vehicle well. And in [27], Guo

compares One-Class SVM with other fault detection methods

through simulation and the result shows that One-Class SVM

can detect abrupt faults and slowly changed faults in real-time

and performs well on the small-sized samples.

The main idea of this algorithm is to separate all the data

points in the feature space from the origins with maximum

margin. The objective function deﬁned by Schölkopf et al [28].

is formulated as

min

w,ξi,ρ

1

2w2+1

µn

n

i=1

ξi−ρ

s.t.

(w·φ(xi)) ≥ρ−ξii=1,...,n

ξi≥0i=1,...,n(1)

where wis feature vector of the feature space in higher

dimension, ξiis slack variable that allows some data points to

lie within the margin, ρis the offset, µ∈(0,1) is the trade-

off parameter that control the boundary, nis the number of

samples, xiis the i-th input training data and φ(xi)is the non-

linear mapping function which maps the original data points

in low dimension to a higher dimension. Here, µis the most

important parameter mentioned in this algorithm, it sets the

upper boundary on the fraction of outliers and lower boundary

of the fraction of support vectors [29].

Our work is interested in the state of the autonomous vehicle

and we deﬁne the state vector

χ=[v,ω]T(2)

to reﬂect the state of the vehicle during the autonomous driving

process. Where vis the velocity of the vehicle, reﬂecting the

longitudinal state or features, ωis the angular velocity of

the vehicle, reﬂecting the lateral state or features. Feed the

model deﬁned by formula (1) with the samples collected from

the autonomous driving process using Gaussian Radial Base

Function (RBF) as the kernel function and adjust µand the

offset ρ, we can get a series of support vector αiby applying

Lagrange techniques. Thus, the decision function of the state

fault detection for the autonomous vehicle can be written as

f(χ) =sgn n

i=1

αi·exp −χ−χi2

2σ2−ρ(3)

where χis a new sample to be checked and χiis the i-th input

training data point, σ∈R is the parameter that determines the

radial range of the function. If the result of the newly tested

sample is negative, it can be an abnormal sample. Furthermore,

if negative results continually arise during the autonomous

driving process, we consider that the state of the vehicle does

not work well and requires to adopt safety strategy.

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9362 IEEE SENSORS JOURNAL, VOL. 20, NO. 16, AUGUST 15, 2020

Fig. 2. Schematic for a linear kinematic vehicle bicycle model.

C. Trajectory Deviation Detector

In practice, a single measurement alone sometimes can

generate unacceptable errors because of the noise and other

inaccurate disturbances. Kalman ﬁlter uses a series of observed

measurements over time, and through Kalman ﬁlter, the esti-

mation of unknown variables tends to be more precise than

those based on a single measurement. In the perspective of

fault detection, Kalman ﬁlter is a model-based method, and

in this paper, a Kalman ﬁlter observer is designed based on

the vehicle kinematic model to predict the current position

of the vehicle during the process of autonomous driving.

By analyzing the residuals between the predicted values and

the measured values, we can check whether the trajectory

deviates in a checking period.

1) Vehicle Kinematic Model:

Our research uses Kalman ﬁlter

observer to predict the current position. As mentioned above,

fault detection with Kalman ﬁlter is a model-based approach

for the speciﬁc research issue, and vehicle kinematic model

is the basis to design the Kalman ﬁlter. Here we choose

vehicle bicycle model to depict the kinematic features of the

autonomous vehicle.

For a linear kinematic vehicle bicycle model [21], longitu-

dinal, lateral and yaw motions of the vehicle should be taken

into consideration. As shown in Fig.2, in the inertial frame

XOY, (x,y)is the coordinate of the vehicle center, φis the

angle between the direction of the vehicle and the horizontal

direction X, with the center in the midpoint of the rear axle.

We deﬁne a linear system state (k)=[x,y,φ]T,andthe

discretized linear kinematic bicycle model can be obtained as

follows.

(k)=⎡

⎣

x(k)

y(k)

ϕ(k)⎤

⎦

=⎡

⎣

x(k−1)+t·v(k−1)cos(ϕ(k−1))

y(k−1)+t·v(k−1)sin(ϕ(k−1))

ϕ(k−1)+t·v(k−1)/ l·tan(δ (k−1)) ⎤

⎦(4)

where tis the sampling period, δrepresents the front wheel

steering angle, vrepresents the vehicle longitudinal velocity,

lrepresents the wheel base, and (k)represents the vehicle

state in the k−th step. In fact, φhas relationship with the yaw

angle of the autonomous vehicle and the yaw angle can be

directly obtained from the sensor. Therefore, φ(k−1) is known

at the k−th time step and the discretized linear kinematic

bicycle model can be simpliﬁed as

(k)=x(k)

y(k)

=1+λx(k−1)0

01+λy(k−1)·x(k−1)

y(k−1)(5)

where

λx(k−1)=t·v(k−1)·cos(ϕ(k−1))

x(k−1)λy(k−1)

=t·v(k−1)·sin(ϕ(k−1))

y(k−1)

2) Kalman Filter Observer Designing:

Kalman ﬁlter (KF) and

its modiﬁcations like extended Kalman ﬁlter (EKF) and the

unscented Kalman ﬁlter (UKF) has been widely used in system

state prediction [30]. These modiﬁed methods theoretically

perform better than Kalman Filter but the complexity and

computational cost are much higher. Considering the kinematic

model is linear and assuming that the background noise

is white Gaussian noise (WGN), we can just apply KF to

estimate the current position to simplify the designing and

reduce the computational cost.

Kalman ﬁlter is a recursive estimator, which means that only

the estimated state from the previous time and the current

measurement are needed to obtain the prediction for the

current state. Procedure for this algorithm can be generally

divided into two phases in each step, i.e., prediction and state

update [31].

a) Phase 1: Prediction:

(k|k−1)=F(k−1|k−1)+BU(k)(6)

P(k|k−1)=FP(k−1|k−1)F+Q(7)

where (k|k-1) is the predicted priori state at moment kbased

on the state at moment k-1, (k-1|k-1) is the state at moment

k-1, U(k)is the control input and Bis the control parameter

matrix. Since there is no control input and U(k)=0 here.

P(k|k-1) and P(k-1|k-1) are corresponding covariance matrix

of (k|k-1) and (k-1|k-1), respectively. Qis the process

noise covariance matrix, Fis the one step state-transition

matrix and is the coefﬁcient matrix in formula (5), and F

is the transposition of F.

b) Phase 2: State Update:

Kg(k)=P(k|k−1)H(HP(k|k−1)H+R)(8)

(k|k)=(k|k−1)+Kg(k)(Z(k)−H(k|k−1)) (9)

P(k|k)=(I−Kg(k)H)P(k|k−1)(10)

where Kg(k)is the Kalman gain at moment k,His the

measurement matrix and His the transposition of H,Ris

the observation noise matrix, Z(k)is the measurement value

at moment kand Irepresents identity matrix.

3) Residuals Distribution Inference:

Compared to the state

faults detection, trajectory deviation detection requires more

samples to conduct the distribution inference. In fact, state

faults emphasize the abnormality at an instant moment while

trajectory faults stress the abnormality of moving tendency.

FAN G

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: FDD SYSTEM FOR AUTONOMOUS VEHICLES BASED ON HYBRID APPROACHES 9363

Fig. 3. Explanation to different types of test period Tstate and Ttraj.

Settings of test period for state faults and trajectory faults are

various. As shown in Fig.3, note Tas a sampling period and

Nas the number of samples obtained in T,Tstate =lT as a test

period to detect state faults and Ttraj =LT as a test period to

detect trajectory deviation, where land Lare the adjustable

coefﬁcients. Thus, for state faults detection, lN samples are

used in each Tstate, and for trajectory deviation detection, LN

samples are used in each Ttraj.Ll.

There are many statistical inference methods that can be

considered to the distribution inference. χ2testing is a com-

monly used statistical tool to check whether the samples

accord to a speciﬁc distribution [7]. Besides, Kolmogorov-

Smirnov test, Shapiro-Wilk test and Jarque-Bera test etc.

are also frequently used methods to check the normal-

ity of the samples’ distribution [32]. Here we choose

Jarque-Bera test [33] to conduct the residuals distribution

inference. Motivations to use Jarque-Bera test primarily

lies in:

1) Approaches based on testing skewness and kurtosis are

comparatively sensitive to outliers [33];

2) Data of the residuals shows the symmetric long-tailed

feature.

The task we confront is fault detection and normality test

using Jarque-Bera test are comparatively more sensitive to

outliers than other methods. Besides, in the simulation study

conducted by Torabi et al. in [32], the result shows that Jarque-

Bera test is one of the most powerful methods for normality

test when the distribution is symmetric close to normal and

symmetric long tailed. The histogram shown in Fig.12 in the

next section is the preprocessing to the residuals data, which

shows the ‘symmetric close to normal’ and ‘symmetric long

tailed’ features aforementioned.

The null hypothesis H0for the Jarque-Bera test is that

the tested samples come from a normal distribution with

an unknown mean and variance. Since we assume that the

process noise and observation noise are both zero mean white

Gaussian noise, the residuals between the predicted values

from the Kalman ﬁlter observer and the measured values

from the sensor should be a zero mean Gaussian process

theoretically.

Jarque-Bera test assumes that samples from a normal dis-

tribution have an expected skewness of 0 and an expected

kurtosis of 3. By checking whether the tested samples have

the skewness and kurtosis matching a normal distribution,

the Jarque-Bera test can judge the normality of the tested

samples. Residuals distribution inference can provide refer-

ence for fault detection. If the residuals distribution has great

difference with the zero mean Gaussian distribution, we have

reasons to believe that the operation of the surveilled system is

abnormal.

D. Diagnosis System: Membership Function Training

Using Neural Network

If faults are already detected, further we want to explore

what factors have caused such faults. In real world, a fault or a

failure can be caused by several possible factors with a certain

probability. Assuming we have factor set Aand result set B

A={Ai|i=1,2,...m}B={Bi|i=1,2,...n}

where Aiis a possible cause that can lead to a result Bi.A

speciﬁc factor Aicausing a speciﬁc result Biis just partially

true since other factors can also cause the speciﬁc result. Thus,

we use fuzzy system to describe such indeﬁnite causality.

Membership function is the core of the fuzzy system.

It depicts the probability distribution with the change of the

variable we are interested in. Our purpose is to design a fuzzy

system that can indicate the probability of each factor that

leads to faults or failure. To simplify the design, we restrict

the result set Bto contain only one element, i.e. faults are

detected and the autonomous vehicle is in the wrong state.

As to factor set A, we deﬁne two types of factor that result in

fault:

Deﬁnition 1: Types of factor that lead to faults.

Moving Alarm: this type indicates that the longitudinal state

of the autonomous vehicle is probably abnormal;

Steering Alarm: this type indicates that the lateral state of

the autonomous vehicle is probably abnormal.

Such deﬁnition is based on the vehicle state. If the type is

determined, we can further explore which sub system of the

autonomous vehicle breaks down. The sub-system can be the

dynamic system, brake system, steering system or perception

system. However, we will not discuss fault isolation for the

sub-systems in this paper, and what we focus on is to get the

probability of each type if faults occur.

Formula (2) has deﬁned the state vector χ,wherevreﬂects

the longitudinal state and ωreﬂects the lateral state. If faults

do occur, they can be reﬂected via the two state variables.

Therefore, vand ωshould be the variables when designing the

membership function. According to some priori experience,

initial membership functions for each type are given as below:

Initial membership function for Moving Alarm:

M(v) =1

1+e−σv(ν−µv)(11)

Initial membership function for Steering Alarm:

M(ω) =1

1+e−σω(ω−µω)(12)

where µv,µωare the threshold for velocity and angular

velocity. If the velocity or the angular velocity is greater than

their threshold, it is possible that the state of the vehicle can

be abnormal. σv,σware the parameters that determine the

steepness of the transition zone from normal state to abnormal

state. The greater the parameter is, the steeper the transition

zone is. Fig.4 shows the general shape of the membership

function.

The initial membership function is given by our priori

experiences and we are not sure whether it can depict the

fault probability well. Besides, the threshold for membership

9364 IEEE SENSORS JOURNAL, VOL. 20, NO. 16, AUGUST 15, 2020

Fig. 4. Shape of the membership function, given μv=16.67, μω=25,

σv=σω=0.5.

Fig. 5. Structure schematic of the neural network.

function of ‘Moving Alarm’ differs with the change of angular

velocity ω, and vice versa. That means the membership

functions dynamically change with the state vector (Process

of membership functions dynamically changing is visualized

in Fig.16 in our experiment, introduced in the next section),

and the initial membership function just determine the general

shape.

To reduce the subjectivity and better reﬂect the real situation

with the membership function, we design a neural network to

update the membership function. The structure schematic of

the network is shown in Fig.5. and here, M(v) and M(ω) are

the membership function deﬁned in formula (11) and (12).

The schematic of the neural network shown in Fig.5 is

slightly different from the fully connected neural network. The

input layer just transfers the state vector to the next layer. The

hidden layer performs a nonlinear transformation with a ﬁxed

activation function, e.g., sigmoid function, Rectiﬁed Linear

Unit (ReLU) function, to map the input space onto a new

space. The output layer gives the result of the forward propa-

gation. Target output (or ‘label’) is [1,0]Tif the given input is a

normal datum, [0,1]Tif the given input is an abnormal datum.

Difference lies in the membership function layer, which is the

deformation of the normal hidden layer. Neurons in this layer

activate the input with membership function. Similar work has

been done in [34] and once the network is trained, the updated

membership function is represented by the trained network.

E. Diagnosis System: Black Box Testing for Parameters

Update

Neural network designed in the previous part can just judge

whether the input data are normal or not. It does not directly

update the parameters for the initial membership function.

To get the fault probability of each type, we require the

formulation or asymptotic formulation of the membership

functions. In order to achieve this, black box test is applied to

update the parameters of the membership functions.

Once we get the trained network, we regard it as a ‘black

box’ that can tell us whether the input vehicle state is nor-

mal or not. If the state is normal, the target output is [1,0]T,

otherwise [0,1]T. In formula (11) and (12),we illustrate that

µv,µωare the threshold for velocity and angular velocity.

Suppose that the state component ωis given, if there is a

velocity value vTh, where the target output transforms from

[1,0]Tto [0,1]T,thevTh is just the threshold µvfor the given

ω.Asωvaries, vTh differs. Therefore, vTh is dependent on

ω, formulated as:

vTh =f(ω) (13)

Similarly, critical value of angular velocity ωTh is dependent

on v,i.e.

ωTh =g(v) (14)

If f(ω) and g(v) are obtained, given a state [v, ω]T, the critical

values vTh and ωTh are conﬁrmed. That means the parameters

µvand µware obtained only if the state [v,ω]Tis given.

Supposing we have known the function f(ω) and g(v),

we plug them into (11) and (12) respectively in some extreme

situation where the M(v ) and M(ω) are known. Then, parame-

ters σv,σwcan be obtained. We deﬁne the ‘extreme situation’

where the velocity and the angular velocity reach up to the

upper boundary vup and ωup, respectively. Such situation is

absolutely in abnormality and the probability in fault state is

very close to 1, i.e.

lim

v→vup

M(v) =1,lim

ω→ωup

M(ω) =1

To get the value of σv,σw,weset M(v ) =1−ε1and

M(ω) =1−ε2in such extreme situation, where ε1,ε2∈R+

are very tiny positive numbers, then we can get

σv=

−ln 1

1−ε1−1

vup −f(ω) (15)

σω=

−ln 1

1−ε2−1

ωup −g(v) (16)

So, the core for parameters update is to ﬁnd f(ω) and g(v)

and we adopt grid search to ﬁnd the critical values vTh and

ωTh to ﬁt the function f(ω) and g(v ). Assuming we have

a two-dimension test matrix, one dimension is vthe other

is ω. Each dimension is equally divided with the same and

small stride. Thus, each element of the two-dimension matrix

is a state vector [v,ω]T. Feed the test matrix to the trained

network, or ‘black box’, we can get the output matrix that

indicates ‘normal’ or ‘abnormal’ of each state. Then, according

to the result of the output matrix, we can mark the critical

values in the test matrix, and ﬁnally, f(ω) and g(v) can

be obtained by ﬁtting and approximation in accord with the

distribution of the critical values.

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: FDD SYSTEM FOR AUTONOMOUS VEHICLES BASED ON HYBRID APPROACHES 9365

Fig. 6. ‘Xinda’ autonomous vehicle.

Fig. 7. The CAV Test Field and the driving path.

III. METHODOLOGY VALIDATION AND ANALYSIS

To evaluate the effectiveness of the approaches proposed

in the previous section, we collected the GPS data from the

autonomous vehicle ‘Xinda’ platform (showed in Fig.6)in

unmanned mode in The Connected Autonomous Vehicle Test

Field (The CAV Test Field, showed in Fig.7) of Chang’an

University.

One point to be addressed is that, some GPS data are

collected without passing through the tunnel and the data are

regarded as healthy data, while some GPS data are speciﬁcally

collected when the vehicle moves through the tunnel, and

the data are labeled as ‘abnormal’. With the collected GPS

data, we implement the methods as mentioned in the previous

section. The result and analysis will be illustrated in detail in

this section.

A. Data Preprocessing

The original GPS data (can be downloaded from IEEE

Dataport 1) contains several ﬁelds and we just extract the items

we need. These items include sampling moment, latitude,

longitude, yaw, vE and vN.HerevE and vN are the components

of the velocity value in due east and due north respectively.

Sampling period is 0.01s.

With the extracted data, the ﬁrst thing we do is data clean-

ing, including getting rid of incomplete records and duplicated

records etc. Then we will utilize the cleaned data to obtain the

items we require, i.e. Xand Ycoordinates in the orthogonal

plane coordinate system, yaw, velocity and angular velocity.

Velocity can be obtained by computing the quadratic sum of

1http://dx.doi.org/10.21227/5g7e-3475.

Fig. 8. Change of Trajectory, Yaw, Velocity and Angular Velocity during

the autonomous driving process in a single experiment. Here we apply

‘unwrap’ technique in MATLAB to avoid the absolute jumps between

consecutive time frames when visualize the Yaw data.

Fig. 9. Decision boundary found by One-Class SVM, given the trade-off

parameter μ=0.01, with Gaussian Radial Base Function (RBF) as the

kernel function.

vE and vN. Angular velocity can be obtained by computing

the difference quotient of the yaw in two successive time

frames (or sampling period). As to X,Ycoordinates in the

orthogonal plane coordinate system, some transformations of

coordinate techniques should be considered. Here we apply

Mercato projection to transform the latitude and longitude data

into X,Ycoordinates data, with the start point as the origin of

the orthogonal plane coordinate system. Fig.8, using normal

data, visualizes the items we obtained, reﬂecting the state

and trajectory changing of the vehicle during the autonomous

driving process.

B. Result and Analysis for One-Class SVM

One-Class SVM in our experiment is implemented to check

whether the state (described via velocity and angular velocity)

is normal. This method requires that all samples given are

positive, therefore we choose the GPS data of the autonomous

vehicle that do not pass through the tunnel as the training

data. After preprocessing, these data will be the input of

the algorithm to ﬁnd out the boundary that separate the safe

domain and unsafe domain, as shown in Fig.9.

From Fig.9, we can see that the frontier trained by One-

Class SVM (red solid line) is a ‘hard’ boundary that tightly ﬁts

9366 IEEE SENSORS JOURNAL, VOL. 20, NO. 16, AUGUST 15, 2020

Fig. 10. ROC curve of adopted method and other OCCs for fault

detection.

the training data. Obviously, it is an overﬁtting boundary since

there is almost no margin between the training data and the

boundary. Such boundary will be unusable in practice since it

will frequently trigger the alarm of fault. Therefore, we extend

the frontier conformally based on the learned boundary and

get a ‘soft’ boundary (orange dashed line). The blue area

shows the process of extension. Boundaries located in the

lighted-colored blue area have higher generalization ability

but, meanwhile, higher bias from the training data. And,

the criterion for conﬁrming the soft boundary is based on the

kinematic and dynamic knowledge that we know about the

‘Xinda’ autonomous vehicle.

The trigger mechanism is that if more than 100 state inputs

[v,ω]Tin two seconds (200 sampling periods) are out of the

soft boundary, the system judges that state faults occur. The

yellow dots are the abnormal test data generated by adding

Gaussian noise to some selected training data with the mean

values equal to 5.3876 for vand 1.4510 for ω, and standard

deviation values equal to 3.8284 for vand 3.7463 for ω.

Result shows that the soft boundary can separate most of

the abnormal samples from the safe domain (area inside the

orange dashed line). The red dots are some of the samples

from a training dataset for self-driving cars in Kaggle.2This

data set records some states of an autonomous car and we can

see from the result that our training result is, to some degree,

overﬁtting. However, different systems behave differently. This

soft boundary matches ‘Xinda’ well but may not ﬁts other

driverless cars. Therefore, for different studying object, we can

apply similar data-driven approaches but using its speciﬁc data

to train the decision boundary.

To estimate the performance of the classiﬁer, we add some

fault data (offset based on the healthy data) into the healthy

data and label them. Receiver Operating Characteristic (ROC)

curve is a widely used tool to estimate the performance of a

binary classiﬁer and we compare the method we adopt with

other One-Class Classiﬁers (OCCs) used to detect outliers and

the result is shown in Fig.10, where the true positive rate

2https://www.kaggle.com/roydatascience/training-car#driving_log.csv

Fig. 11. Overﬁtting validation of the One-Class SVM method.

(TPR) is also known as sensitivity or probability of detection

and the false positive rate (FPR) is also known as probability

of false alarm. For ROC curve, the closer to the upper left

corner the curve is, the better the classiﬁer performs. Another

measurement to the performance is the area under the ROC

curve (AUC), and the closer to 1 the AUC value is, the better

the classiﬁer performs. In Fig.10., the blue plot is the ROC

curve of the adopted method, the red one is the result of

Isolation Forest, the green one is the result of Autoencoder

[35] and the pink one is the result of extremely learning

machine based Autoencoder (ELM_AE) [36], [37]. We can

see that the blue curve is the closet one to the upper left corner

and the AUC values of adopted method, Isolation Forest,

Autoencoder and ELM_AE are 0.9501, 0.8892, 0.7585 and

0.7613 respectively.

As for the boundary obtained via One-Class SVM, the result

is overﬁtting based on one training data set. More samples

are collected to validate this assumption and the result is

shown in Fig.11. We can see that boundaries based on different

training data set are different but the region separated by these

boundaries are roughly the same.

To get a usable detector, we can collect the healthy data in

the daily experiment to optimize the decision boundary, or if

the data we can collect are limited, we can adopt the strategy

mentioned above to extend the frontier conformally based on

the learned boundary.

C. Result and Analysis for Residuals Distribution

Inference

The Kalman ﬁlter observer in our experiment is used to pre-

dict the current position of the autonomous vehicle. Residuals

between the predicted value and the measured value should

be a zero mean Gaussian distribution theoretically. Through

residuals distribution inference, we want to monitor whether

the moving tendency of the vehicle is normal. Fig.12 shows the

result in a single checking period to detect trajectory deviation.

From the Fig.12, we can conclude that, for the single

experiment, the residuals distribution is approximately in

accordance with a zero mean Gaussian distribution. In each

checking period, if the residuals distribution is zero mean

Gaussian, we believe there is no deviation for the trajec-

tory. All these conclusions above are addressed based on an

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: FDD SYSTEM FOR AUTONOMOUS VEHICLES BASED ON HYBRID APPROACHES 9367

Fig. 12. Residuals distribution inference in a single checking period to

detect trajectory deviation. The blue bar diagram is the histogram of the

samples in a checking period. The red solid line is the ﬁtting probability

density function.

Fig. 13. Gaussian distribution validation for background noise.

assumption that the background noise is Gaussian distribution.

Repeated experiments also validate such assumption. If the

noise sources are multitudinous and each source is indepen-

dent, such assumption is reasonable according to Central Limit

Theorem. Repeated experiments also validate such assumption

in our experimental environment. We randomly choose four

distribution inference results in different checking periods

from many tests, as shown in Fig.13 and the normality are

all established.

Gaussian noise assumption is tenable for most of the case

since the sources of background noise are numerous and

independent. If there is one or several dominant noise sources,

such assumption would not stand and trajectory deviation

monitor applied by residual probability distribution inference

is not available.

D. Membership Function Parameters Update

Once faults are detected, the probability of each factor

that caused such faults is the core issue we want to explore.

Standing on the point of safety, the greater the velocity

value or angular velocity value, the more possible that the

state of the vehicle is in abnormality, empirically. Therefore,

membership function of vor ωshould be S-shaped with the

Fig. 14. Structure and connection relationship of the designed network.

variable changing from small value to large value, logically.

Initial membership functions are given in accord with such

priori knowledge, shown in Fig.4. Here we set the initial

critical value µv=16.67m/s, µw=25◦/saccording to

the kinematic and dynamics features of ‘Xinda’ autonomous

vehicle and initialize the parameters σv=σw=0.5.

Such membership function is high of subjectivity and we

designed a special neural network, adding a ‘membership

function layer’ after the input layer, to optimize the mem-

bership function so that it can better reﬂect the probability

of each factor according to the real training data. Structure

and connection relationship of the network that we adopted is

shown in Fig.14.

This network has two inputs, i.e. the state vector [v,ω]T,

following the membership function layer where neurons in

this layer activate the inputs with membership function. There

are two hidden layers in this network and each hidden layer

has six neurons (structures similar to this can also work and

‘two hidden layers, 6 neurons each layer’ is the structure with

comparatively faster convergence speed), adopting sigmoid

function as the activation function. Output layer has two

neurons and the target output is [1,0]Tif the given training

sample is normal, otherwise [0,1]Tif the given training sample

is abnormal.

The input layer just transfers the input state vector to

next layer. Except the connections between input layer and

membership function layer are one-to-one, other connections

in this network are fully connected.

Training data for this network is a big issue to deal with. In

practice, we can easily collect a large amount of the normal

samples of the autonomous vehicle but can hardly obtain

abnormal samples. To ensure safety, we cannot deliberately

make the autonomous vehicle drive in an abnormal state just

for data collection. To cope with this problem, fault data can

be generated by two ways. First, as shown in Fig.7,thereisa

tunnel in the test ﬁeld. GPS signals will be blocked or there is a

multipath effect when the autonomous vehicle passes through

the tunnel. We collect the data in this environment as the fault

samples (In the tunnel, data from other sensors like LIDAR,

IMU (Inertial Measurement Unit) etc. will ensure the safety

of the autonomous vehicle). Another way to generate fault

9368 IEEE SENSORS JOURNAL, VOL. 20, NO. 16, AUGUST 15, 2020

Fig. 15. Fitting for vTh =fωand ωTh =gv.

samples is to add fault information artiﬁcially, for example,

adding background noise to the normal GPS signals with very

small SNR (Signal to Noise Ratio).

The Back-Propagation algorithm is adopted to train the net-

work, using Gradient Descent methods, with normal samples

labeled by [1,0]Tand abnormal samples labeled by [0,1]T.

We shufﬂe the normal samples and abnormal samples together

ﬁrst to avoid the bad inﬂuence brought by the label-sorted

inputs. Size of the state samples is about 30,000, among which

70% of the samples are used as the training data and the rest

30% as the testing data. When the error rate of the test data is

less than 0.01, we ﬁnished the training process and save the

weight parameters and bias parameters of the network.

Once the network is trained, the updated membership

function can be represented by the trained network, but we

still don’t know the formulation of the updated membership

function so that the probability of each factor that causes

faults cannot be ascertained. The updated membership function

should still be S-shaped and it can be formulated if the

parameters µv,µw,σv,σware ascertained. As illustrated in the

previous section II part E, the core for parameters determina-

tion is to ﬁnd the f(ω) (relationship between critical value of

velocity and angular velocity) and g(v) (relationship between

critical value of angular velocity and velocity). By applying

aforementioned black box test and ﬁtting techniques in section

II part E, ﬁtting results for vTh =f(ω) and ωTh =g(v) are

displayed in Fig.15.

Formalized expressions for the ﬁtting functions are

vTh =f(ω) =max(vTh)·1−1

1+e−2(ω−ωmid)(17)

ωTh =g(v) =max(ωTh)·1−1

1+e−2(v−vmid )(18)

where max(vTh)and max(ωTh)are maximum of vTh and ωTh

respectively, ωmid is the ωvalue where f(ω) =max(vTh)/2,

similarly vmid is the vvalue where g(v ) =max(ωTh)/2. Once

vTh and ωTh are obtained, σv,σωcan be solved according to

formula (15) and (16).

From the expressions (17) and (18) we can see that the

threshold is dynamically changing so that the membership

function is also dynamic. Such dynamic process is visualized

in Fig.16.

Fig. 16. Dynamically changing process for membership function M(ω)

and M(v).

TABLE I

SOME TEST RESULTS OF THE FAULTS PROBABILITY FOR EACH

FACTOR

Taking M(ω) in Fig.16. as an example, given different

velocity vas condition, the membership function indicates the

fault probability caused by angular velocity ωas ωchanging.

In fact, given any v,thevis corresponding with an M(ω)

curve and we just display several curves. Illustration for M(v)

is similar.

Up to now, all the parameters for the updated membership

function are ascertained, and the probability of faults for each

type is computed by formula (17) and (18) with the given

state [v,ω]T. Here are some test results, shown in TA B L E I

and TABL E I I .

TABL E I displays the fault probability of each factor based

on the training data from ‘Xinda’ and TABL E I I shows the

fault probability test of several samples from the public data

set in Kaggle.3In this public data set, all the samples are

obtained under the normal autonomous driving process.

Results from TA B LE I and TA BL E II show that the driving

behavior of ‘Xinda’ autonomous vehicle is, comparatively,

conservative. Such training results may match ‘Xinda’ very

well but may not ﬁt other autonomous vehicle. Design for a

fault detection and diagnosis system is usually for a speciﬁc

studying object or process, where we can apply similar data-

driven approaches but using its speciﬁc data to train the fault

detection and diagnosis system.

TABL E I gives us a reference to further explore the reasons

of a fault. If the ﬁrst value in TA B L E I is much higher than the

3https://www.kaggle.com/roydatascience/training-car#driving_log.csv

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: FDD SYSTEM FOR AUTONOMOUS VEHICLES BASED ON HYBRID APPROACHES 9369

TABLE II

TEST RESULT ON THE PUBLIC DATA SET

Fig. 17. Boundary Fault Probability Test. Here Hb-v means the fault

probability caused by factor v on the hard boundary, Hb-w means the

fault probability caused by factor ωon the hard boundary, Sb-v means

the fault probability caused by factor v on the soft boundary and Sb-w

means the fault probability caused by factor ωon the soft boundary.

second value, we can argue that the ‘Moving Alarm’ is under

the given state and we should focus on the factors that can

cause longitudinal faults, such as the dynamic system, brake

system etc. On the contrary, if the second value is much higher

than the ﬁrst value, it is more likely that it is ‘Steering Alarm’

under the given state and we should pay our attention to the

factors that can cause lateral faults, such as the steering system,

etc. If two values are both high, longitudinal and lateral factors

both contribute to the faults.

In Section III part B, we extend the hard boundary trained

by One-Class SVM to a soft boundary, given our prior

experience of ‘Xinda’ autonomous vehicle. Here we plug the

state vector on the boundary into formula (11) and (12) and

obtain the fault probability of each factor on the boundary,

shown in Fig.17. As we can see, the fault probability caused by

both vand ω(refer to ‘Moving Alarm’ and ‘Steering Alarm’

respectively) are not high on the hard boundary. If we use

this boundary as a warning line, it will cause a number of

false alarms. While, fault probability on the soft boundary

is comparatively higher and this curve is acceptable as an

alarm line in practice. Through checking the boundary fault

probability, we can optimize the learned frontier obtained from

One-Class SVM and get a usable and practical alarm line.

IV. CONCLUSION

In the last section of this paper, we will brieﬂy summarize

the work we have done. Purpose of this paper is to design a

fault detection and diagnosis system for autonomous vehicles.

Generally, methods for fault detection and diagnosis can be

categorized as model-based, signals-based and knowledge-

based. Considering the practical situation for autonomous

vehicles, hybrid approaches are applied. First, One-Class SVM

is adopted to detect whether there are state faults for the vehi-

cle. Then a Kalman ﬁlter is designed to obtain the residuals

between the predicted value and measured value so that the

distribution can be inferred. By checking the normality of

the residuals distribution, this fault detection system validates

whether the trajectory deviates in a checking period. Finally,

a fuzzy system is designed to explore the probability for each

possible factor that can cause faults, where the membership

function is obtained based on the implementation of the

neural network we constructed and the parameters of the

membership function are updated through black box test and

ﬁtting techniques.

As for the future work, one thing is the fault isolation.

We deﬁne the types of factors that lead to faults as ‘Moving

Alarm’ and ‘Steering Alarm’ to indicate longitudinal or lateral

state abnormality. Based on such classiﬁcation, we can further

explore which subsystem causes the fault. For example, if the

type is ‘Moving Alarm’, the fault can be generated from

dynamic system or brake system etc., while, if the type is

‘Steering Alarm’, problems can be caused by steering system

etc. If we can conﬁrm which subsystem caused faults, further

measures can be adopted to isolate the abnormal system and

ensure the safety of the autonomous vehicle. Another thing

should be addressed is the ELM based methods (ELM_AE

is one of the One-Class Classiﬁers shown in Fig.10.), which

show the characteristics of fast learning speed and good

generalization capability [37] and will be a group of reasonable

methods to optimize the training process of the neural network

based methods.

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Yukun Fang received the B.E. degree from

Chang’an University in 2019. He is currently

pursuing the Ph.D. degree with the School of

Information Engineering. From 2015 to 2019, he

majored in communication engineering with the

School of Information Engineering. His research

interests include fault detection and diagnosis

for systems, control theories for autonomous

vehicles, and game theory.

Haigen Min (Member, IEEE) received the B.S.,

M.S., and Ph.D. degrees from the Department

of Trafﬁc Information Engineering and Con-

trol, Chang’an University, China. He is cur-

rently a Lecturer with Chang’an University. His

research interests include high-precision local-

ization, environment perception, and cooperative

adaptive cruise control for connected and auto-

mated vehicles.

FAN G

et al.

: FDD SYSTEM FOR AUTONOMOUS VEHICLES BASED ON HYBRID APPROACHES 9371

Wuqi Wang is currently pursuing the degree in

software engineering with the School of Infor-

mation Engineering, Chang’an University. He is

currently preparing for his master’s degree with

the Department of Transportation Information

Engineering and Control, Chang’an University.

His doctoral research direction is autonomous

driving decision control based on reinforcement

learning.

Zhigang Xu (Member, IEEE) received the B.S.

degree in automation and the M.S. and Ph.D.

degrees in trafﬁc information engineering and

control from Chang’an University, China, in 2002,

2005, and 2012, respectively. He is currently a

Professor with Chang’an University. His research

focuses on connected and automated vehicle,

intelligent transportation systems, and nonde-

structive testing of infrastructures.

Xiangmo Zhao (Member, IEEE) received the

B.S. degree from Chongqing University, China,

in 1987, and the M.S. and Ph.D. degrees from

Chang’an University, China, in 2002 and 2005,

respectively. He is currently a Professor and

the Vice President of Chang’an University. He

has authored or coauthored over 130 publi-

cations. His research interests include intelli-

gent transportation systems, distributed com-

puter networks, wireless communications, and

signal processing. He has received many tech-

nical awards for his contribution to the research and development of

intelligent transportation systems.