An ADT Life Prediction Method Based on the Wavelet-Packet Band Energy Yu Fan, Xiaoyang Li
School of Reliability and Systems Engineering Beihang University Beijing, C hina
[email protected],
[email protected]
Abstract- Vibration signal is often used as the monitoring data of electromechanical products health state. In order to solve the problem that ishow to use the vibration data collected from Accelerated Degradation Testing (ADT) to predict the life and reliability of electromechanical product under normal conditions, this paper studies the ADT life prediction methods based on wavelet packet band energy extraction. Firstly, based on the fact that
wavelet
packet
analysis
can
decompose
the
signal
in
frequency domain effectively and present all frequency domain features and details in time domain, ADT vibration data based wavelet packet band energy extraction is presented. Secondly, we propose a life prediction method combined the drift of Brownian motion (DBM) with band energy feature extraction. Finally, the application in the ADT of brush DC motor verified that the proposed method can effectively extract the features of the product life status and can accurately predict the life and reliability of the product under the normal conditions •. Keywords- feature
(Abstract)
extraction; wavelet packet band
energy
method; ADT; life Prediction.
I.
INTRODUCTION
As the rapid development of modern technology, industrial companies have to manufacture high-reliable and long-lifetime products in order to survive in the competitive market. The factors such as the limiting time and sample make traditional testing techniques to difficultly assess the reliability and life of these products. Accelerated Degradation Testing (ADT) has solved this problem by leading accelerated stress into the test, so it can quickly assess the life and reliability of products, shorten the development cycle, and reduce development costs. ADT has gradually become more and more popular in the reliability testing area. Nowadays, ADT is mainly applied in electronics, optoelectronics, microwave and other products. The mature performance parameters are mostly concrete and can be directly used to characterize the product state such as the power parameters. For example, the optical power of optoelectronic products [1], and the power gain of the microwave devices [2]. For electromechanical, hydraulic, mechanical and other products, the main factors of the depletion mode are usually fatigue, corrosion and wearing. The information of life and performance of such products are often included in the vibration response signal. Thus a certain feature extraction 978·14577-1911-0/12/$26.00 ©2012 IEEE
method can be used to extract the characteristic factors to reflect the life status changing of the products. Under the accelerated conditions, the depletion process will speed up and will be reflected by the vibration signal into its characteristic factors. C ombining feature extraction with ADT will be an effective way to predict the life of such products. The common vibration signals feature extraction method is time-frequency analysis methods, including short time Fourier transform [3], time-frequency distribution method [4], wavelet analysis method [5][6], etc. Wavelet analysis has excellent frequency characteristics and local properties, and the wavelet packet time-frequency energy analysis method can effectively extract the band energy as the feature information from the signal [7][8][9]. This provides an effective way for the vibration signal feature extraction [10]. Therefore, how to combine the vibration response of field testing that easier to monitor with the product life characteristic factors extracted by in-field ADT becomes a most important problem in engineering and research fields. Focusing this, this article will carry out the research of vibration signal ADT life prediction method based on wavelet packet frequency energy feature extraction method. II.
A.
ACCELERATED DEGRADATION TESTING
Basic Principles and Assumptions
ADT is an experimental technique and method on the basis of not changing failure mechanism, finding the relationship between product life and stress (the acceleration model), and using the products' performance degradation data under high (accelerated) stress level to extrapolate and predict the product life characteristics under normal stress level. Brownian motion has continuous time parameters and continuous space parameters, and is the most basic and simple and the most important stochastic process. On this basic, the Brownian motion with the drift term decomposed the displacement increment of the particle into the sum of the randomness of increment and the deterministic increment. DBM is very common in physics engineering field. For example, it can describe the thermal motion of molecules or the law of electron mobility motion and has practical significance very much. By given physical meaning to corresponding
MU33 I I
2012 Prognostics & System Health Management Conference (PHM-2012 Beijing)
coefficients, DBM can characterize many physical processes. So it can be used to describe the model of the product performance degradation process. Base on above background, some assumptions are given below: A SMP. 1 Degradation process is monotonic, i.e., the degradation damage cannot reverse; A SMP. 2 There are no failures appeared during ADT, i.e. the product performance has not degraded through the critical value; A SMP. 3 Under the normal stress level So and accelerated stress level S, < S2 < ... < Sk, the product performance degradation process yet) are subject to the DBM with degradation rate d(S/) and the drift parameter (JI, 1= 1, ... , k: (1) YI(/)=SIB(/)+d(S/)?1 Yo
1=[
Each product performance monitor time is til) (l = 1, ... , k;
) then during the test time
... , m/ ,
i = 1, ..., nl; j = 1,
the monitoring time is 11'1 I
:s; ... :s; II1111/ '
, the performance value is
YIij, the degradation incremental XII) = YIi(j+') - YII)' the time interval MIl)= tli(j+I)- til)' the log-likelihood function of C SADT is:
In L
I
k
oc - - L....
2(j
I
m'-'
""" L.... L.... , n,
/�, i�' j�'
Jl
[ x,, -exp [ a+bm" ( S / )]'I1I"J' /oj
!'J.t/ij
1
�27r(J12M
r
[ x-d(S/)·tl/j'l
l
2(JI'tll
ex p i - "----------''-
� J
A SMP. 5 The drift parameter depicts some sort of functional relationship between environmental stress and system performance variables change, so there are such relationship between the drift parameter and the stress level S/: (2)
III.
The pdf of DBM yet) fust passing the border a is as follows: e C""""""7 xp
en/hll
rJ(a-yo)-d(S)'I]' l i f 2(j I l J ,
A.
=
