1. Why Intelligent Vehicles Must Monitor Inertial Sensor Health
As the primary device for acquiring information, sensors are the foundation on which a control system works reliably, safely and stably. When sensor performance degrades, when a fault occurs, or when a sensor fails, it will severely affect system monitoring and control, and can even cause incalculable losses. Sensor fault diagnosis is therefore especially important.
Intelligent driving technology for vehicles in highway environments covers three major scientific problems: perception and recognition of complex driving environments; planning and decision-making of driving behavior under uncertain conditions; and state estimation and optimal control of the vehicle in a dynamic environment. Judging whether the vehicle itself is working normally is done by analyzing the redundancy of its sensors.
Fault (Fault, Failure) generally refers to a state in which system equipment cannot complete its expected function under specified conditions. Fault diagnosis consists of two parts, detection and diagnosis: detection determines whether the system has developed a fault, while diagnosis determines which component has failed and what type of fault it is, that is, it determines the behavior pattern of each component.
2. The Landscape of Fault Diagnosis Methods: From Residual Signals to Data-Driven Approaches
Fault diagnosis methods usually have three basic elements: the model, the process measurements, and the fault signal. Different ways of acquiring and processing each element produce different fault diagnosis methods. Existing classifications usually divide fault diagnosis into three categories: signal-processing-based methods, model-based methods, and knowledge-based methods. Qualitative analysis and quantitative analysis are unified and complementary to each other.
2.1 Model-Based Methods: Constructing the Residual Signal
This method combines the mathematical model of the system with observable input and output variables to construct a suitable residual signal. By analyzing the residual signal the system can be diagnosed; this is the earliest fault diagnosis method to be applied. Their basic idea is to reconstruct the state of the controlled system, then compare it with the measurable variables to generate a residual sequence, and to perform statistical analysis on that residual sequence; with an appropriate model and statistical method, a fault can be detected.
2.2 Wavelet Transform: Capturing the Features of Non-Stationary Signals
Signal processing methods mainly use various signal processing techniques to analyze and process the measured signal, extracting time-domain or frequency-domain features of fault-related signals for fault diagnosis; they mainly include spectral analysis methods and wavelet transform methods. Once a fault occurs in the system, its measured signal often becomes non-stationary, and because the Fourier transform is a global transform it cannot effectively extract local features of the signal in the time-frequency domain. The wavelet transform, as an alternative to the Fourier transform, has good time-frequency analysis capability for non-stationary signals, and because it offers variable resolution, that variable resolution can effectively improve fault detection capability.
3. Hardware Redundancy vs. Software Redundancy: The Trade-off Between Two Engineering Routes
Sensor diagnosis technology separates the fault information of a sensor in real time through various data processing methods and issues an alarm quickly, so that when a sensor is about to fail or has already failed, it helps staff locate the fault source and eliminate it. In practice it is usually divided into hardware redundancy and software analysis redundancy.
Hardware redundancy: multiple sensors of the same type (usually 3 or more) measure the same system parameter, and a majority-voting rule identifies the faulty sensor. Hardware redundancy is simple in principle, does not depend on a mathematical model, and detects faults quickly, but because it requires more than 3 sensors of the same type measuring the same point, it needs more equipment, which raises cost, weight and maintenance expense.
Software redundancy: uses the redundant information of a sensor that is unrelated to the measured object to build its mathematical model, providing an analytical relationship between the sensor’s own output and the measured object in order to detect faults. This analytical relationship can be implemented in software and is convenient to use. However, a mathematical model of the system must be established, and it demands very high model reliability and accuracy, while in complex systems such a model is usually very hard to obtain.
4. Different-Precision Redundancy: Cutting Fault Diagnosis Cost with a High-Low Pairing
By using one high-precision and one low-precision sensor for redundancy, the low-precision sensor is low in cost and keeps the redundant hardware cost down, and digital processing methods are then applied to the redundant data. Relative to the original hardware redundancy, this method reduces cost; relative to software redundancy, it simplifies the difficulty of mathematical modeling of the system. Most of the methods above require sensors of the same type or comparable performance, and when the redundant sensors differ in precision, especially when the precision gap is large, their fault diagnosis performance drops significantly.
In sensor fault diagnosis the main principle is: minimize the influence of dynamic model uncertainty while maximizing the influence of the fault. Because different-precision redundant sensors have different precision, their steady-state errors are inconsistent, and the uncertainties of the individual sensors in the data redundancy are inconsistent. How to eliminate that inconsistency while amplifying the fault is the key to fault diagnosis.
4.1 Data Preprocessing for Low-Precision Sensors
Since the drawback of a low-precision sensor is low precision, reducing its uncertainty is the main task of data preprocessing. A sensor’s variance can be obtained from the device datasheet, so denoising the data can reduce its uncertainty, and the Kalman filter is very effective at denoising a signal and improving precision.
4.2 The Cyclic Kalman Filter Bank and the Innovation Criterion
Once the preprocessing of the sensor data is complete, m Kalman filters are designed for the data of m sensors, each using a different sensor measurement signal as its input. In this way a cyclic Kalman filter bank is established, and the method is simple and easy to model.
When a sensor is normal the innovation is zero; when a fault occurs the innovation becomes a non-zero function. When a sensor develops a fault, the innovation is no longer 0, so the detection rule follows: when no fault occurs the mean of the innovation is zero, and when a fault occurs the mean of the innovation is not zero. To locate the fault, a fault decision is needed: extract the innovation from the m filters and make a decision through fault estimation, so as to determine which sensor has failed.
Because the algorithm performs Kalman filtering twice, it is called the TSKF (Two Stages Kalman Filter) algorithm. The TSKF fault diagnosis algorithm processes time step k as follows: Step 1. preprocess the low-precision sensor signal to reduce uncertainty; Step 2. build the cyclic Kalman filter bank and filter the sensor data to produce the innovation; Step 3. process the innovation sequence to complete the fault diagnosis.
5. How Diagnosis Capability Is Maintained Under Strong Background Noise
A low-precision sensor’s noise intensity varies considerably as the environment changes, so a noise estimation algorithm is added in the data preprocessing stage to provide an effective measurement noise variance R(t). After the wavelet transform, the main energy of the signal is concentrated in the low-frequency sub-band at the large scale, while the high-frequency sub-band at the small scale concentrates coefficients of smaller amplitude and lower energy. Therefore, when external noise is fairly large, the coefficients of the highest-frequency sub-band can be regarded as noise, and the standard deviation of the noise can be estimated from those coefficients.
Experiments show that the false detection rate of the ordinary Kalman filtering method is large, while that of the two-stage Kalman filtering method is smaller; in particular, when the interference noise is greater than 1, the former’s false detection rate exceeds 50%. In particular, once the wavelet denoising and noise estimation steps are added, under a strong noise background the method still retains strong detection and diagnosis capability, and it has good economic practicality in real applications.
6. Multi-Rate Sensor Systems: Multi-Scale Kalman Filtering
In real applications, when several sensors of different types are used to acquire data, for example an accelerometer gives acceleration, GPS gives position information, and a gyroscope gives yaw angle and other information, but their sampling rates are not the same: an accelerometer can run at 1 kHz, a gyroscope can also reach several hundred hertz, while GPS runs at 6 Hz. Faced with such a system of inconsistent rates, how to effectively improve the accuracy of fault detection and diagnosis becomes the research problem.
In the multi-scale Kalman filtering process, the innovation represents the innovation occurring at scale j and time step k; when a fault occurs, the innovation represents the fault information at scale j, and that value can be used to locate which scale the fault appeared at, so as to determine which sensor has failed.
There are many kinds of navigation systems. Integrated navigation can draw on the strengths of each to offset the weaknesses of the others, which not only improves navigation accuracy but also gives the whole navigation system fault-tolerant capability and raises its reliability. An inertial navigation system is easily affected by errors and is better suited to measuring short-term changes in position and velocity, while the Global Positioning System (GPS) can provide accurate position and velocity information but is easily disturbed, especially in urban environments where high-rise buildings cause multipath reflection and its performance drops markedly.
7.1 The Difference Between Loosely Coupled and Tightly Coupled
In a loosely coupled system, the Kalman filter of the GPS receiver provides position and velocity; these are subtracted from the position and velocity given by the inertial system, and the difference enters the INS/GPS integrated Kalman filter, which suppresses the error of the inertial navigation system and calibrates it. In a tightly coupled scheme, the pseudorange and pseudorange rate measured by GPS, together with the satellite ephemeris, are all sent to a single INS/GPS integrated Kalman filter, which jointly estimates all observable system errors. The output of the filter is used to correct the inertial navigation system.
7.2 Judging a Fault from the Statistical Properties of the Innovation Sequence
The law of large numbers explains that stability is a property of many random phenomena in nature, and dynamic systems likewise possess stability. Obviously, when the system is in a stable state the innovation sequence satisfies the independent and identically distributed condition. When a sensor develops a fault, the statistical properties of the innovation sequence become abnormal, that is, the corresponding variance changes, so the fault can be detected and estimated.
Taking the absolute value of the innovation sequence, if that value exceeds γ times its variance estimate (γ > 1), then a fault is considered to have occurred at that moment; a confidence level is used to determine γ, for example if the confidence level is taken as 0.997 then γ is 3. Therefore, if the residual at the erroneous moment is corrected, the impact of the fault on the accuracy of the filter estimate can be reduced, thereby improving the filtering accuracy.
8. From Fault Diagnosis to Fault Prediction
Fault prediction combines fault diagnosis technology with event prediction technology. By predicting a fault in advance it gives early warning and improves the system’s ability to handle anomalies. Fault prediction and fault diagnosis differ in essence: fault diagnosis finds the cause and the faulty component from a fault phenomenon that has already appeared, whereas fault prediction uses existing knowledge and predictive reasoning to judge a fault that may occur.
When the state equation is nonlinear and the noise is not Gaussian white noise, the conditions for Kalman filtering are not satisfied, and divergence is very likely, so the Kalman filter fails. Once a sensor develops a fault it contains both discrete fault modes and continuous state variables, becoming a hybrid dynamic system, and the Kalman filter can no longer be used to handle it; the particle filter method, because it is not constrained by the Gaussian assumption and can estimate the state of a hybrid system, can be used for fault diagnosis in this situation.
9. A Few Points for Putting Fault Diagnosis into Engineering Practice
Adding some intelligent algorithms (neural networks, evolutionary computation and so on) to the fault diagnosis methods of a redundant sensor system improves the adaptability of the algorithm and further raises the accuracy of fault diagnosis. The ultimate purpose of a fault diagnosis system is to guarantee that the controller runs safely, reliably and stably, and to ensure safe and reliable operation of the system through fault compensation and fault-tolerant control.