This article describes the implementation of the Hidden Markov Models for identification of exploitation conditions of the automobile tire by means of analyzing tire noise while car driving. This requires the development of special recognition algorithms of tire noise and cleaning of the signal from the background noise, it can be done by means of extraction of the clean signal from the noise by adaptive filters and by pattern recognition methods, typically used in speech recognition, to recognize a tire noise corresponding to a particular operating condition. In this way, we can diagnose the condition of a tire while car driving, which will reduce overloaded tire wear, due to improper use to a minimum and help prevent accidents as a result of tire failure.
The problem of the road transport accidents, caused by the failure of
automobile tire, is one of the most important ones for traffic safety. A key reason for
the failure of automobile tire is its increased wear as the result of improper
use. It may be caused by many factors: the collapse of the incorrect angles of
convergence, high or low tire pressure, overheating, etc. It is impossible to
control all the factors, influencing the dynamics of tires while driving, and,
therefore, there is a need for a comprehensive new indicator. We think that
this indicator is the sound of tires. There is a lot of research of tire dynamics
in the field of automobile safety. In general, models of tire/road noise can be
divided into four major types. The first type includes statistical models. A
popular example of this approach is introduced in the article by Sandberg, U.
and Descornet, G. [
First, it is necessary to clear the tire signal from the background noise. It can
be done by using adaptive filters. In our research we use adaptive filter, based
on the least mean square algorithm [
The acoustic signal ( ), which contains the tire signal ( ) and noise ( ) is recorded by the first microphone, which is installed near the tire. The pattern of noise ( ) is recorded by the second microphone, which is located near the engine of the automobile. There is a correlation between ( ) and ( ). The output of the adaptive filter will contain the measure of the noise ̂ ( ). The error of the filter will contain a clear tire acoustic signal ̂ ( ). The spectrogram of the clear tire signals which we received as the results of the experiments (the experiments are described in Section 4) is shown in Fig 2. The frequency range of the clean acoustic signals of the tire is between 4005000 Hz. 2.2
The next step is the feature extraction. The purpose of this step is to
parameterize the raw tire signal waveforms into sequences of feature vectors. Here
we use both FFT-based and LPC-based analysis with the purpose to identify
which approach is better for the tire noise coding. The feature techniques are
based on the widely known methods MFCC and LPCC [
We use the left-right HMM with seven hidden states (see Fig.4) for identification of the tires exploitation condition. The first and the last states ( and ) are not emitted as we need these nodes to create composed HMM (see Fig.5). Here – number of hidden states of the model ( =7); trix of the transition probabilities: [ ] – the ma(1) - hidden state of the HMM ( ) at the moment ; – next state of HMM; – actual state of HMM; ( ) – observation probability; – feature vectors of the tire noise.
–exploitation conditions of the tire 3.2
For HMM training we use the same method as for speech recognition [
Using maximum likelihood we estimate the matrix of transitions between the states in the hidden part of the model. After that we estimate the mean ̂ and the matrix of covariance ̂ by means of these formulas: ( | ( ) ( ) where T – is a number of the feature vectors; Then we can calculate the observation probability of the feature vectors of the tire noise: ( ) √( ) |̂ | ( ̂ ) ̂ ( ̂ ) Where n – is a dimensionality of the feature vectors.
It is necessary to estimate corresponding probability for each state, and to use
the Viterbi algorithm [
The next step is to create Gaussian mixtures [
) ( ( ) Re-estimation of the mean and covariance matrix is: (2) (3) (4) (5) (6) (7) ̂ where
– is the number of the observation vectors.
The weights of the Gaussian mixture components are: (8) (9) (10) (11) (12) given (13) (14) We re-estimate the parameters of the model until provements of the model parameters. ( ) stop getting im3.3
We use the Viterbi decoding [
( ) ( ) ( ) ( ) (
) ( )( ̂ ̂
) )( ( ) ( ) ( ) The maximum likelihood for observing sequence of vectors the HMM model: to ( ) ( ) As for the re-estimation case, the direct computation of likelihoods leads to underflow, so it will be better to compute log likelihood: ( ) ( ) ( ) ( ( ) This algorithm can be visualized as searching the best path through a matrix, where the vertical dimension represents the states of the HMM and the horizontal dimension represents the frames of the tire noise. Each large dot in the picture represents the log probability of observing that frame at that time and each arc between dots corresponds to the log transition probability. The log probability of any path is computed simply by summing the log transition probabilities and the log output probabilities along that path. The paths grow from left-to-right, column-by-column. At time t, each partial path ( ) is known for all states , hence, equation 14 can be used to compute ( ),thereby, extending the partial paths by one time frame. 4 4.1
We carried out field tests with the purpose to record the tire noise while car
driving with different exploitation conditions of the tire. Our experiment is
based on the standards ISO 10844 [
We made three different experiments. For each experiment we used 405 records of the tire noise, the total duration of 1 hour 41 minute 15 seconds for HMM training. To evaluate the efficiency of the system we used 50 records, a total duration of 12 minutes 30 seconds. As we can see in table 1 the accuracy of our method for the tire pressure is 88,2%; for the automobile speed - 95,7%; and for both the speed and tire pressure - 75%. We have found the correlation between the tire noise and the tire exploitations characteristics. The cleaning mechanism, based on adaptive filters, and the recognition mechanism, based on the HMM have shown prospective results. We found out that the performance of the recognition system depends on exploitation parameters. They show better results for the automobile speed than for the tire pressure identification. Moreover, we have also discovered, that the performance of the recognition system runs low when more than one parameter are identified. 6