УДК 620.179.16
ULTRASONIC SIGNALS PROCESSING BASE ON PARAMETERS ESTIMATION
Zhang Qi, Yang Guang, Que Peiwen Institution of Automatic Detection, Shanghai Jiaotong University, Shanghai
200240, P. R. China
ОБРАБОТКА УЛЬТРАЗВУКОВЫХ СИГНАЛОВ НА ОСНОВЕ ДАННЫХ О ЗАДЕРЖКЕ
Жень Ки, Йанг Гуанг, Ку Пейвен Институт автоматического детектирования, Шанхайский университет Джаотонь, Шанхай 200240, КНР
Многие способы обработки сигналов, такие как интегральные преобразования, выделение параметров и подобные им, могут применяться для обработки у. з. А-сканов. Способ выделения параметров эхосигнала предположительно может сжимать А-сканы. Данный алгоритм производит разложение анализируемых сигналов на элементарные функции в соответствии с библиотекой образов и выделяет наиболее значимую компоненту из представленного сигнала. Для аппроксимации у. з. сигналов используется библиотека моделей высокочастотных гауссовых импульсов. Обработка производится с помощью генетического алгоритма. Представлены результаты компьютерного моделирования, которые демонстрируют эффективность предлагаемого метода.
Abstract: Many techniques, such as transform-domain techniques, parameter extraction techniques and so on, have been applied to process the ultrasonic 1D signal. Parameter extraction techniques using Matching Pursuit (MP) has been proposed to compress 1D ultrasonic signal. MP algorithm can iteratively decompose the analysed ultrasonic signal into elementary functions, called dictionary and select the best matched functions to represent original signal. In this paper, Gaussian echo model function is used as MP dictionary to represent ultrasonic signal. Genetic Algorithm (GA) is applied to estimate parameters of the elementary functions in the dictionary which can best represent the ultrasonic signal. Computer simulation and experimental results were performed to evaluate the efficiency of the proposed method.
Key words: matching pursuit, Genetic Algorithm, Gaussian echo model function, parameter estimation.
I. INTRODUCTION
The compression and noise cancellation of the ultrasonic nondestructive inspection signal are the significant problem in the nondestructive evaluation of the materials. The ultrasonic waves reflected or diffracted from flaws or boundaries can provide useful information on its integrity. But in practice, in addition to ultrasonic signals carrying desired information, noises are often carried in ultrasonic signals. Because of these noises it is very difficult to identify the ultrasonic defect signal. At the same time, modern ultrasonic detecting devices usually generate vast amounts of data and require huge data storage capacity. Thus ultrasonic signal data compression is always required to decrease the storage requirements.
With the ultrasonic nondestructive insprction development many signal processing techniques, such as transform-domain techniques: 1-D discrete cosine transform (DCT), Walsh-Hadamard transform (WHT), and discrete wavelet transforms [1, 2, 3]; parameter extraction techniques: matching pursuit (MP) algorithm [4], Maximum Likelihood Estimation (MLE) algorithm [5, 6] and continuous wavelet transform (CWT) parameter estimation methods [7]; another techniques: linear predictive coding [8], split spectrum processing (SSP) [9] techniques, neural network technique [10, 11], have been used to ultrasonic inspection echo signal. They can be applied to denoise the ultrasonic signal, compress the signal, recognize and class the flaws.
In this paper, parameter extraction techniques are mainly discussed. In reference [6], ultrasonic pulse-echo can be modeled as:
/(0; t) = pe-a(i-T)2cos(2n/c(i - t) + i);
0 = [pa/i], (1)
where 0 represents the parameter vector including the parameters, amplitude (P), bandwidth factor (a), time of arrival (t), center frequency (/c), and phase (i). It is a Gaussian echo model. So, ultrasonic echo signal can be represented by a set of parameters vectors, each set of parameter vectors having 5 parameters. The number of parameter vectors is much smaller than the number of the original sampled signal. Thus, if the parameters are recorded, the ultrasonic signal can be effectively compressed. Accordingly, the key point is to efficiently estimate the parameters vectors that best represent original ultrasonic signal.
MP is an iterative algorithm, introduced by Mallat and Zhang [12], which can decompose any given signal into a set of waveforms or atoms each providing compact time-frequency description of original signal according to its correlative frequency, time and amplitude properties. This algorithm has been applied for ultrasonic signal denoising, compression and approximation [2, 13]. Jin-Chul Hong [14] adopted a two-stage MP strategy based on Gabor dictionary and Chirp function dictionary to extract useful waves out of noisy signal in guide-wave based damage inspection, respectively. Using MP algorithm, it usually requires to properly utilize elementary functions or vectors to compose the dictionary for searching process. The elementary functions or vectors are called atoms. When the atoms of MP are elementary functions, it is difficult to estimate the basic parameters of the function. In reference [6], the Least-Squares (LS) estimation was used to obtain the values of the parameter vector. Because genetic algorithm (GA) can estimate the values of the parameter vector, MP based on GA was proposed in this paper.
GA is a numerical optimization method based on the concepts of genetics and natural selection [15]. It is an efficient technique to optimize difficult functions in large search spaces. It can escape from local minima and find near-optimal solutions for large-scale optimization problems with multiple local maxima. Thus GA is good candidate to estimate the values of ultrasonic echo parameters.
In this paper, MP based GA is applied to estimate the parameters of atom functions that best represent the detected ultrasonic signal. Parameter estimation method for the observed ultrasonic signal representing can be expressed in the following model
' M
y(t) = X / (9m; t) + V(t). (2)
m=1
The first term denotes the desired signal and the second term represents the noise. MP and GA algorithm are introduced in section 2, and the process of MP based GA is described in section 3. In section 4 simulation signals and experimental results have testified the efficiency of this method.
II. MATCHING PURSUIT
Matching pursuit is an adaptive algorithm. It can iteratively decompose a signal / in the Hilbertspaceto H a linear combination of atoms drawn from a complete dictionary D = {g; i = 0, 1, ..., L}, such as iigJI = 1, where L is the dictionary number of elements, such that finite linear combinations of the atoms are dense in H. Then, signal / is
M-1
/ = Xa mgm + RM/> (3)
m=0
where am is the appropriate expansion coefficient, the largest inner product between gm and analyzed signal, gm is the time-frequency atoms, RMf is the residual vector.
The first step in the MP algorithm is to search the dictionary for an atom g0 correlated best with the signal f. The atom g0 owning the largest inner product with analyzed signal is chosen, then
f = f, go>go + Rf. (4)
The next step is to find the best correlated atom with the residue Rf
Rf = {Rf, gi>gi+ Rf. (5)
If set R0f=f, then in a general case can be written as
Rmf {Rmf, gm>gm + Rm+1f. (6)
The original signal f is decomposed into a sum of dictionary elements that are chosen to best match its residues like function (3).
III. GENETIC ALGORITHM
GA is an adaptive search technique that can find out near-optimal solutions of large-scale optimization with multiple local maxima. GA has been used to estimate parameters, such as reference [16, 17]. It is simple and easy to estimate the parameters of the signals. In particular, they do not require fixing an initial value for model parameters to be estimated.
Ultrasonic pulse-echo can be represented by Gaussian echo model. The Gaussian echo model function has a parameter vector having five basic parameters. The values of the parameters are estimated by GA. The simple GA is described as follows: Firstly, a random initial population has been created; Secondly, candidates are selected into the crossover pool iteratively; Thirdly, new candidates are generated by the crossover operator. If the crossover fails to work, one of the individuals is selected randomly and mutated by the mutation operator; Fourthly, candidates are ranked according to their fitness value. Finally, the second, third, and fourth steps are repeated until the stopping rule is satisfied [18].
IV. MATCHING PURSUIT BASED ON GENETIC ALGORITHM
Gaussian echo model function is used as the dictionary of MP algorithm. MP searches the best matched Gaussian echo model function to the original signal. Then, this function can be subtracted from the original signal to get the signal residue. The parameters of the function are evaluated by genetic algorithm. The evaluation function takes an important role in developing a good simulation in the genetic algorithm. The main idea of the proposed algorithm is that the atom gm owning the inner product with residual vector, namely {Rmf, gm>, is regarded as fitm-ness function of the genetic algorithm. Therefore, the fitmnessm function is defined as follows
F = {Rmf, gm> m = 0, 1, 2... (7)
That is to find the atom gm owning the largest inner product with Rm f using genetic algorithm. The atom gm is defined as
gm(t) = KJm.e"am(t-Tm)2 cos (2f(t - Tm) + 4m). (8)
K is the normalized coefficient.
m
K _ gm) /Q\
The MP algorithm based on GA can be summarized in the following computational steps:
1. Create a random population of chromosomes.
2. Set fitness function.
3. Compute fitness value for all individuals.
4. Evaluate the fitness value, if it satisfied the stopping rule, go to step 7, if not, continue.
5. Apply crossover operator on population individuals.
6. Apply Mutation operator on pop
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