=Paper=
{{Paper
|id=Vol-1145/paper7
|storemode=property
|title=Identification of Exploitation Conditions of the Automobile Tire while Car Driving by Means of Hidden Markov Models
|pdfUrl=https://ceur-ws.org/Vol-1145/paper7.pdf
|volume=Vol-1145
|dblpUrl=https://dblp.org/rec/conf/ysip/TananaevSK14
}}
==Identification of Exploitation Conditions of the Automobile Tire while Car Driving by Means of Hidden Markov Models==
https://ceur-ws.org/Vol-1145/paper7.pdf
Identification of Exploitation Conditions of the
Automobile Tire while Car Driving by Means of Hidden
Markov Models
Denis Tananaev, Galina Shagrova, Victor Kozhevnikov
North-Caucasus Federal University, Stavropol, Russia
d.d.tananaev@gmail.com,g_shagrova@mail.ru,
viktor_kozhevnikov@inbox.ru
Abstract. 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 particu-
lar 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.
Keywords: Hidden Markov models, Adaptive filters, tire noise, pattern recog-
nition, feature extraction
1 Introduction
The problem of the road transport accidents, caused by the failure of automo-
bile 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. [1]. The second type is composed of physical models. The
58 Identification of Exploitation Conditions
examples of such a modeling approach are analysed in the book by Kropp, W.
[2]. The third type of models for tire/road noise is hybrid theoretical models.
The examples of hybrid theoretical models are described by De Roo, F., Ger-
retsen, E. and Hamet, J.F., Klein, P. [3, 4]. Finally, statistical models can be
extended with pre or post processing, based on well-known physical relations,
often derived from theoretical models. The examples of hybrid statistical
models are introduced by Beckenbauer, T. and Kuijpers A. [5]. We think the
disadvantage of these models is that they only describe the noise generation
mechanisms of the tire, independently of the condition of the tire. In contrast,
we attempt to model dependencies between tire sounds and tire conditions,
based on the hypothesis that the operational status of the tire is reflected in its
noise characteristics. We must develop dedicated recognition algorithms of
tire noise and also algorithms of clearing up the signal of the background
noise. It can be done by means of extraction of the clean signal from the noise
by adaptive filters and pattern recognition to classify a tire noise as corre-
sponding to a particular operating condition.
2 Data Preparation
2.1 Adaptive Filtering
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 [6], which is realized in the Matlab Sim-
ulink (see Fig.1).
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 spectro-
gram of the clear tire signals which we received as the results of the experi-
ments (the experiments are described in Section 4) is shown in Fig 2.
Denis Tananaev, Galina Shagrova and Victor Kozhevnikov 59
Fig. 1. The scheme of adaptive filter from Matlab Simulink
Fig. 2. The tire signals spectrogram
The frequency range of the clean acoustic signals of the tire is between 400-
5000 Hz.
2.2 Feature Extraction
The next step is the feature extraction. The purpose of this step is to parame-
terize 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 [7] which are often
used for speech recognition. We process the signal with the frame size 25
msec and frame period 10 msec (Fig.3).
60 Identification of Exploitation Conditions
Fig. 3. Framing of the waveforms of the tire acoustic signal
The tire noise feature vectors were parameterized as follows: if the target pa-
rameters are MFCC, we use as the energy component. We use a Hamming
window in FFT. The filterbank has 26 channels. In output we receive 12+1
( ) coefficients. The performance of the tire noise recognition system can be
enhanced by adding time derivatives (delta and acceleration coefficients) to
the basic static parameters [7]. If the target parameters are LPCC, we use
linear prediction of the 14th order. The filterbank size is 22 channels and in
output we receive 12 coefficients. Then we add delta and acceleration. After
feature extraction procedure we have 39 dimensional MFCC vectors or if we
use the LPCC method - 36 dimensional vector.
3 HMM Training and Recognition
3.1 Topology of the HMM
We use the left-right HMM with seven hidden states (see Fig.4) for identifica-
tion 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).
Denis Tananaev, Galina Shagrova and Victor Kozhevnikov 61
Fig. 4. The left-right HMM for identification of the tire exploitation condition
Here – number of hidden states of the model ( =7); – the ma-
trix of the transition probabilities:
[ ] (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.
Fig. 5. Composed HMM; –exploitation conditions of the tire
3.2 HMM Training
For HMM training we use the same method as for speech recognition [7]. We
record a training database of the tire noise which relate to every exploitation
condition of the tire. It is necessary to make 3-5 recordings of the tire noise
62 Identification of Exploitation Conditions
10-15 seconds long for every exploitation condition with the purpose to create
the robust recognition system. Then for each exploitation condition of the tire
we initialize one HMM with seven hidden states.
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:
̂ (2)
̂ ( )( ) (3)
where T – is a number of the feature vectors;
Then we can calculate the observation probability of the feature vectors of the
tire noise:
( ̂ ) ̂ ( ̂ )
( ) (4)
√( ) |̂ |
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 [7] for reassigning the observation vectors for each state.
We re-estimate model parameters in this way until we stop getting their im-
provements.
The next step is to create Gaussian mixtures [9]. It is necessary to
create a robust system of the tire exploitation condition recognition.
We use the Baum – Welch [8] algorithm to define ( ) – the probability of
observation vector being in the particular state. Here is the number of train-
ing data After that, we re-estimate the parameters of the model.
The observation probability ( ) is:
( ) ( ) (5)
( ) ( )
( ) (6)
√( ) | |
Re-estimation of the mean and covariance matrix is:
( )
(7)
( )
Denis Tananaev, Galina Shagrova and Victor Kozhevnikov 63
where – is the number of the observation vectors.
( )( ̂ )( ̂ )
̂ (8)
( )
The weights of the Gaussian mixture components are:
( )
(9)
( )
We re-estimate the parameters of the model until ( ) stop getting im-
provements of the model parameters.
3.3 Recognition
We use the Viterbi decoding [7] for the tire noise recognition (Fig.6). This
algorithm could be used to find the maximum likelihood state sequence of
HMM and identify the tire exploitation condition. Let ( ) represent the
maximum likelihood of the observing tire noise vectors to in state j at
time t. This likelihood can be computed efficiently using the following re-
cursion:
() () ( ) (10)
where
( ) (11)
() ( ) (12)
The maximum likelihood for observing sequence of vectors to given
the HMM model:
( ) () (13)
As for the re-estimation case, the direct computation of likelihoods leads to
underflow, so it will be better to compute log likelihood:
() () ( ) ( ( ) (14)
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 hori-
zontal dimension represents the frames of the tire noise.
64 Identification of Exploitation Conditions
Fig. 6. – Scheme of the Viterbi decoding
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 com-
pute ( ),thereby, extending the partial paths by one time frame.
4 Experiments and Results
4.1 Experiments
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 [10] and ISO 13325:2003 [11], which de-
termine the conditions for the tire noise measurement, but we included the
following changes:
The noise of the tire was measured with the engine working
Microphones were installed near the front right wheel (Fig.7) with the
purpose to provide adaptive filtering of the background noise
Denis Tananaev, Galina Shagrova and Victor Kozhevnikov 65
Fig. 7. – Scheme of the microphones’ positions, during field tests: a) Upside view b). Front
view
We recorded the tire noise with three different speeds of the automobile 20,
40 и 60 km per hour and three different pressure levels: 1.9, 2.1 and 2.3 at-
mospheres. The automobile used for field tests was Mitsubishi L200 (year of
construction: 2011), with new tires 265/75R16.
4.2 Evaluation
We made three different experiments. For each experiment we used 405 rec-
ords of the tire noise, the total duration of 1 hour 41 minute 15 seconds for
HMM training.
Table 1. The experiment results
Features HMM (1 HMM (8 HMM (16
Gaussian) Gaussian Gaussian
mixtures) mixtures)
The results of the tire pressure identification
LPC/LPCEPSTRA 78% 87.5% 88.2%
MFCC 68% 77.4% 78.2%
The results of the automobile’s speed identification
LPC/LPCEPSTRA 81.2% 94.3% 95.7%
MFCC 78.6% 89.4% 91.8%
The results of the identification of the tire speed and pressure
LPC/LPCEPSTRA 61.4% 74.7% 75%
MFCC 58.6% 59.4% 61.9%
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 meth-
od for the tire pressure is 88,2%; for the automobile speed - 95,7%; and for
both the speed and tire pressure - 75%.
66 Identification of Exploitation Conditions
5 Conclusions
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 ex-
ploitation 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 pa-
rameter are identified.
6 References
1. Sandberg, U. and Descornet, G. (1980). Road surface influence on tire/road noise– part I &
II. Proceedings of INTERNOISE 1980, Miami, Florida.
2. Kropp, W. (1989). Structure-borne sound on a smooth tyre. Applied Acoustics, 26, 181-
192.
3. De Roo, F. and Gerretsen, E. (2000). TRIAS - tyre road interaction acoustic simulation
model. Proceedings of INTERNOISE 2000, Nice, Italy.
4. Hamet, J.F. and Klein, P. (2000). Road texture and tire noise. Retrieved April 10, 2006
fromhttp://www.inrets.fr/ur/lte/publications/publications-pdf/web-hamet/in00_674.pdf.
5. Beckenbauer, T. and Kuijpers, A. (2001). Prediction of pass-by levels depending on road
surface parameters by means of a hybrid model. Proceedings of INTERNOISE 2001, The
Hague, the Netherlands.
6. Deacons, V. (2009). MATLAB 6: 5 SP1/7/7 SP1 / SP2 + Simulink 7 5/6 Tools artificial in-
telligence and bioinformatics Monograph Imprint: Moscow: SOLON-PRESS, 2009.
7. Steve Young, Gunnar Evermann, Phil Woodland [and others]. The HTK Book. Cambridge
University Engineering Department. 2001-2002
8. Rabiner, L. R. A tutorial on Hidden Markov Models and Selected Applications in Speech
Recognition / L. R. Rabiner // Proceedings of the IEEE. Vol. 77. February 1989. № 2. P.
257 – 284.
9. McLachlan, G. and Peel, D. Finite Mixture Models. NewYork: Wiley Interscience, 2000.
10. ISO 10844:2011 .Acoustics - Specification of test tracks for measuring noise emitted by
road vehicles and their tyres / By International Organization for Standardization (ISO).
Geneva: ISO, 2011
11. ISO 13325:2003 Tyres - Coast-by methods for measurement to tyre-to-road sound emis-
sion / By International Organization for Standardization (ISO). Geneva: ISO, 2003.