Optimization and Parameters Estimation in Ultrasonic Echo Problems Using Modified Artificial Bee Colony Algorithm

Journal of Bionic Engineering 12 (2015) 160–169

Optimization and Parameters Estimation in Ultrasonic Echo Problems Using Modified Artificial Bee Colony Algorithm Jinghua Zhou, Xiaofeng Zhang, Guangbin Zhang, Dongmei Chen Ultrasonic Key Laboratory of Shaanxi Province, College of Physics and Information Technology, Shaanxi Normal University, Xi’an, Shaanxi 710119, China

Abstract The patterns of ultrasonic backscattered echoes represent valuable information pertaining to the geometric shape, size, and orientation of the reflectors as well as the microstructure of the propagation path. Accurate estimation of the ultrasonic echo pattern is essential in determining the object or propagation path properties. This paper proposes a parameter estimation method for ultrasonic echoes based on Artificial Bee Colony (ABC) algorithm which is one of the most recent swarm intelligence based algorithms. A modified ABC (MABC) algorithm is given by adding an adjusting factor to the neighborhood search formula of traditional ABC algorithm in order to enhance its performance. The algorithm could overcome the impact of different search range on estimation accuracy to solve the multi-dimensional parameter optimization problems. The performance of the MABC algorithm is demonstrated by numerical simulation and ultrasonic detection experiments. Results show that MABC not only can accurately estimate various parameters of the ultrasonic echoes, but also can achieve the optimal solution in the global scope. The proposed algorithm also has the advantages of fast convergence speed, short running time and real-time parameters estimation. Keywords: artificial bee colony algorithm, swarm intelligence, global optimization, ultrasonic echoes, ultrasonic testing Copyright © 2015, Jilin University. Published by Elsevier Limited and Science Press. All rights reserved. doi: 10.1016/S1672-6529(14)60110-4

1 Introduction Using ultrasonic pulse echoes to perform nondestructive detection is an important method in industrial nondestructive detection and biomedical engineering[1–6]. The purpose of this method is that, through the analysis of detected target echoes to determine the physical characteristics of the reflective targets, such as geometric shape, size and other information on the transmission path[7–10]. It is essential to estimate ultrasonic echo parameters accurately and quickly for ultrasonic nondestructive testing. So far, many methods have been used to estimate the parameters of ultrasonic echo. In 1998, Femmam and M’Sirdi applied the nonlinear method to the study of ultrasonic nondestructive testing and biological tissue characterization, and used the wavelet transform method to study the ultrasonic target echo[11]. In 2001, Demirli and Saniie systematically discussed the nonlinear methods and used Gauss-Newton algorithm to estimate ultrasonic echo parameters[12–14]. But the estiCorresponding author: Xiaofeng Zhang E-mail: [email protected]

mated results of Gauss-Newton algorithm may be a local optimum point rather than a global optimum point because that the results usually depend on the selection of the initial values. In order to solve the problem that the estimation results depend on the initial values, Zhou et al. applied the Ant Colony Optimization (ACO) algorithm to Gaussian echo model and successfully estimated the ultrasonic echo parameters[15]. This algorithm not only overcomes the disadvantage that parameter estimation results depend on the initial values, but also has high estimation accuracy. However, the algorithm is prone to stagnation in parameter estimation. In order to solve complex real world optimization problems, some efficient and effective algorithms have been introduced such as particle swarm optimization, ACO, artificial fish school algorithm, shuffled frog leaping algorithm and artificial bee colony algorithm[15,26–29]. Swarm means the collective behavior of insect or animal groups in nature such as fish, birds, ants and bees. Swarm intelligence optimization algorithms

Zhou et al.: Optimization and Parameters Estimation in Ultrasonic Echo Problems Using Modified Artificial Bee Colony Algorithm

are widely used to solve the optimization problems in many fields in view of their superiority. Compared with traditional methods, swarm intelligence algorithms have obvious advantages in solving global optimization problems, such as short computing time and high precision. ABC algorithm is a new optimization algorithm of bionic intelligence which simulates the behavior of honey bees to solve practical optimization problems. ABC algorithm was introduced by Karaboga in 2005[16], and he did further researches on ABC algorithm in the following years[17–23]. Compared to genetic algorithm[24,25], particle swarm optimization[26,27], ACO algorithm[15,28,29] and other swarm intelligence, ABC algorithm has more superior optimal performance and has been successfully applied in various fields such as digital filtering, target recognition and cluster analysis[19,30,31]. However, similar to other swarm intelligence algorithms, ABC algorithm still has some challenges to overcome. When solving multidimensional parameters optimization problem, the range of different parameters will influence the search step length of the employed bees. This paper presents a new algorithm which is called Modified Artificial Bee Colony (MABC) algorithm to estimate the parameters of ultrasonic echo based on a new search formula. The new search formula can control the search step length of each parameter of multivariable problems. The rest of this paper is organized as follows: in section 2, the general aspects of ABC are discussed and the MABC algorithm is proposed. Section 3 describes the mathematical model of ultrasonic echo. In section 4, the MABC algorithm is applied to the ultrasonic echoes estimation problems and finally, section 5 presents the conclusions of this work.

2 Modified ABC algorithm for multidimensional ultrasound parameters estimation 2.1 ABC algorithm The theory of ABC algorithm has been clearly expressed by Akay and Karaboga[21]. In a real bee colony, some tasks are performed by specialized individuals; while in ABC algorithm, foraging artificial bees are classified into three groups, namely, employed bees, onlooker bees, and scout bees. The ABC algorithm begins with a population of randomly generated food sources. The responsibility of an employed bee is to

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collect the nectar information of a food source and pass the information to an onlooker via a special dance in the hive. Then depending on the nectar information, an onlooker determines whether to recognize a food source and make further search of this food source. When a food source is abandoned, a scout randomly searches for a new food source. In the ABC algorithm, each solution to the problem under consideration is called a food source and represented by an n dimensional real-valued vector where the fitness of the solution corresponds to the nectar amount of the associated food resource[21,32,33]. In ABC algorithm, each food source represented by the position is a possible solution for the problem under consideration. The scout bees generate a set of xi in the initialization of the algorithm[16], let xi =[ xi1, xi2, …, xiD] represent the ith food source and solutions are generated by Eq. (1): xij = lb j + rand(0,1)(ub j − lb j ),

(1)

where i = 1, … , N/2, j = 1, …, D, D represents the vector dimension of the location of food source, lbj and ubj are the lower and upper bounds of the jth parameter of the solution i. After generated the initial food sources, evaluate[16] each food source by Eq. (2): ⎧ 1 / (1 + fi ) fiti = ⎨ ⎩ 1 + abs( f i )

fi ≥ 0 , fi < 0

(2)

where fi is the objective function value of the corresponded solution i. After the initialization evaluation, all bees begin to repeat the cycle of the search progress; each employed bee is associated with only one food source and searches a new food source[16] in the neighborhood by Eq. (3): vij = xij + φij ( xij − xkj ),

(3)

where φij is a random number in [−1, 1], k = 1…N/2, j=1, …, D, vi is a new food source, xi is the current food source, xk is a neighbor food source and k is a randomly chose that has to be different from i. After all employed bees completed neighborhood search, onlooker bees get the nectar amount of food sources in the hive through a special dance of employed bees. Then onlooker bees choose food source depending on the nectar amount of food source, and the probability[16] of the solution i can be expressed as:

pi =

fit

∑

i N /2 i =1

fiti

,

(4)

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where fiti is the quality of the current food source i which is corresponding to the nectar amount of the food source i. When a food source is abandoned by employed bee and onlooker bee, the scout bee randomly generate a new food source to replace the abandoned one. There are two control parameters using ABC algorithm to estimate parameters. They are colony size N and the global cycle numbers M, respectively. Setting food sources = employed bees = onlooker bees = N/2. The specific steps of the ABC algorithm are[16]: Step 1: Generate initial food sources xi, i =1, 2, 3, … , N/2; Step 2: Evaluate initial food sources and set initial value of the global cycle=1; Step 3: Repeat; Step 4: Generate new food source vi for each employed bee by Eq. (3), and calculate the fitness by Eq.(2); Step 5: Choose new food source of each employed bees by greedy selection; Step 6: Calculate the probability value of xi(pi) by Eq. (4); Step 7: Onlooker bee select food source according to pi from the food sources selected and calculate the fitness; Step 8: Choose new food source of each onlooker bee by greedy selection; Step 9: If a food source is abandoned, replace it with a randomly generated food source by a scout using Eq. (1); Step 10: Memorize the best food source achieved so far, cycle= cycle +1; Step 11: Until cycle= M. 2.2 MABC Algorithm Compared with traditional algorithms, ABC algorithm can faster find the optimal solution of complex problems and jump out of local optimal solutions with fewer setting parameters. However, when solving multidimensional parameter problem, the search step of the algorithm depends on the difference of two vector parameters due to that different parameter ranges make the search step with greater randomness and affect the convergence speed and search accuracy. In order to overcome this shortcoming, we improve the search by changing the search method of the employed bees and

onlooker bees. The new searching formula is expressed as: vij = xij + u ( xij − xkj )(r − 0.5),

(5)

where vi is a new solution (food source), u is the adjusting factor, j means the jth parameter of the solution vector i, xkj is the jth parameter of the solution vector k, r is a random number in [0, 1]. u can be expressed as: ⎧ ub j − lb j ⎪ 2 u = ⎨ (ub j − lb j ) ⎪1 − (ub − lb ) j j ⎩

ub j − lb j ≥ 1

,

(6)

ub j − lb j < 1

Δb = ubj−lbj is the difference between the upper and lower bounds of the jth parameter. When the scope of the different parameters is not agreement, Δb will determine the search step which affects the search speed and accuracy. When Δb changes, the bigger Δb will give Eq. (6) a smaller coefficient while the smaller Δb with give a bigger coefficient. By using u to control the step size, the new searching formula can improve the accuracy of search. The flowchart of the MABC algorithm shows in Fig. 1.

3 Ultrasonic echo model and objective function 3.1 Ultrasonic echo model The transducer impulse echo forms the basis function for the backscattering echo model. A Gaussian model is used to simulate the magnitude spectrum of the transducer impulse echo, which is centered about the center frequency of the transducer and covers the frequency bandwidth of the transducer[12]. The impulse response of the ultrasonic transducer is expressed as: 2

x(t ) = e−ατ cos(2πf c t ).

(7)

Using this ideal model of transducer for ultrasonic measurement, the spectrum model of ultrasonic transducer response is represented by: 2

s (θ; t ) = β e−α (t −τ ) cos[2πf c (t − τ ) + ϕ ].

(8)

The parameter vector θ = [β α τ fc φ] is the characteristic parameter vector of ultrasonic echo, which have intuitive meanings for the ideal surface reflector in a homogeneous propagation path. Where, β is the amplitude coefficient with unit V, α is the bandwidth

Zhou et al.: Optimization and Parameters Estimation in Ultrasonic Echo Problems Using Modified Artificial Bee Colony Algorithm

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Noise should be included in the model because the signals are corrupted by the noise in the practical measurement[12–14]. By characterized the noise as additive White Gaussian Noise (WGN), the actual echo can be modeled as:

Generate initial solutions

Evaluate the solutions

y (t ) = s (θ ; t ) + n(t ).

Do neighborhood search and generate new solutions by employed bees

(9)

where n(t) is the noise. When the number of reflectors is known, the Gaussian model can be used to set up the multiple echoes model[12]. The K-superimposed Gaussian echoes are modeled as:

Calculate the fitness of new solutions

K

Apply greedy selection

yk (t ) = ∑ s (θk ; t ) + n(t ),

(10)

k =1

Calculate selecting probabilities of solutions for onlooker bees

where θk defines the shape and location of each echo. 3.2 Objective function Before using the MABC algorithm to estimate the parameter vector in the model of ultrasonic echo, we need a reasonable objective function. The objective function established by the least squares method can be expressed as:

Do neighborhood search and generate new solutions by onlooker bees

Calculate the fitness of new solutions

Apply greedy selection No Memorize the best solution

Is there an abandoned solution? Yes No

Replace it with a new solution by the scout bee

Are termination conditions satisfied? Yes Final solution

Fig. 1 Flowchart of MABC algorithm.

factor with unit (MHz)2, τ is the arrival time with the unit μs, fc is the center frequency with unit MHz, φ is the phase with unit rad. Because of its Gaussian shaped envelope, this model is referred to as the Gaussian echo wavelet.

N

M

i =1

m =1

f (θ ) = ∑ [ x(i ) − ∑ s (θ m ; ti )]2 ,

(11)

where N is the number of discrete points in a period, M is the multiplicity of echoes, s(θm; ti) is the echo function of parameter vector, x(i) is the echo data obtained by the experimental measurements. The parameter vector corresponding to the echoes by seeking the minimum of f(θ).

4 Results and discussion In order to verify the performance of the MABC algorithm for ultrasonic echo parameters estimation, we estimate the parameters of ultrasonic echo based on the Gaussian echo model in the Signal-to-Noise Ratio (SNR) of 20 dB, 10 dB and 0 dB, respectively. Computer simulation platform configurations are: Pentium (R) Dual-Core E5700 Processor, CPU Clock Speed 3.00GHz, Internal Storage 2.0 GB, Microsoft Windows XP professional 32-bit systems, MATLAB7.1.0 Version. 4.1 The parameters estimation of single ultrasonic echo The parameters of the MABC algorithm are: colony size N = 20, local circle times L = 25, global circle times

Journal of Bionic Engineering (2015) Vol.12 No.1

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M = 100. Ultrasonic echo parameter settings and parameter estimation results are shown in Table 1, where the abbreviations lb and ub represent the lower and upper bounds of the search range, avg is the average value of the estimation results and std is the standard deviation. The abbreviations are also used in the other tables of this paper. Take the first group of the initial values, the initial waveforms and the estimated waveforms of ultrasonic echoes for different SNR are shown in the Fig. 2. The simulation results show that the estimation errors of MABC algorithm are small. The algorithm can accurately estimate every parameters of the ultrasonic echo for different SNR. When the initial values deviate from the true value and the SNR decrease, the estimated error is increasing, but it still can estimate all parameters of the echoes. Compared with the traditional algorithms[34] (Gauss-Newton algorithm, simulated annealing algorithm), MABC algorithm overcomes the disad-

vantage of initial value dependent and it can improve the calculation accuracy. To verify the superiority of the MABC algorithm in ultrasonic echo parameter estimation, we compare the MABC algorithm with traditional ABC algorithm and ACO algorithm. These three algorithms are simulated under the same initial value, maximum number of iterations and the objective function. The simulation results for different SNR are shown in Table 2. The numerical results show that the computation time of the three algorithms increase with the decrease in the SNR and the estimated accuracies decline with it. For different SNR, the MABC algorithm has higher precision and about half of computation time of ACO algorithm. The estimation accuracies and the computing time of MABC algorithm are better than that of ABC algorithm. So MABC algorithm is more suitable for the real-time estimation of echo parameters. When SNR is 20 dB, the

Table 1 Parameter estimation results of single echo under different SNR

β

1.0000

Search range lb ub 0.5000 1.5000

α

25.0000

12.5000

37.5000

24.2624

0.7376

26.3227

1.3227

28.0764

3.0764

τ

1.0000

0.5000

1.5000

0.9917

0.0083

0.9840

0.0160

0.9751

0.0249

f

5.0000

2.5000

7.5000

4.9033

0.0967

4.8010

0.1990

5.3387

0.3387

φ

1.0000

0.5000

1.5000

0.9480

0.0520

0.8678

0.1322

0.8191

0.1809

Parameters

True values

SNR = 20 dB avg std 0.9591 0.0409

SNR = 10 dB avg std 1.1172 0.1172

SNR = 0 dB avg std 1.2190 0.2190

Table 2 The comparison of estimated performance for ACO, ABC and MABC under different SNR of single echo SNR

20 dB

10 dB

0 dB

Search range

ACO

ABC

MABC

Parameters

True values

lb

ub

avg

std

avg

std

avg

std

β

1.0000

0.9000

1.1000

0.9912

0.0088

0.9917

0.0083

0.9925

0.0075

α

25.0000

22.5000

27.5000

25.1739

0.1739

25.1255

0.1255

24.8806

0.1194

τ

1.0000

0.9000

1.1000

0.9969

0.0031

1.0013

0.0013

1.0008

0.0008

f

5.0000

4.5000

5.5000

5.0186

0.0186

5.0180

0.0180

4.9871

0.0129

φ

1.0000

0.9000

1.1000

0.9909

0.0091

1.0076

0.0076

0.9984

0.0016

Runtime (s)

--

--

--

5.3899

2.7579

2.7366

β

1.0000

0.9000

1.1000

1.0427

0.0427

0.9674

0.0326

0.9817

0.0183

α

25.0000

22.5000

27.5000

23.7772

1.2228

25.8791

0.8795

24.7027

0.2973

τ

1.0000

0.9000

1.1000

0.9923

0.0077

1.0070

0.0070

1.0027

0.0027

f

5.0000

4.5000

5.5000

4.8948

0.1052

4.9180

0.0820

5.0838

0.0838

φ

1.0000

0.9000

1.1000

0.9208

0.0792

0.9300

0.0700

1.0103

0.0103

Runtime (s)

--

--

--

5.3978

2.7685

2.7440

β

1.0000

0.9000

1.1000

1.1000

0.1000

1.0960

0.0960

1.0398

0.0398

α

25.0000

22.5000

27.5000

26.6739

1.6739

26.4661

1.4661

25.6693

0.6693

τ

1.0000

0.9000

1.1000

0.9871

0.0129

0.9891

0.0109

0.9921

0.0079

f

5.0000

4.5000

5.5000

4.8276

0.1724

4.8408

0.1592

5.1345

0.1345

φ

1.0000

0.9000

1.1000

0.9020

0.0980

0.9249

0.0751

1.0410

0.0410

Runtime (s)

--

--

--

5.5516

2.7921

2.7673

Zhou et al.: Optimization and Parameters Estimation in Ultrasonic Echo Problems Using Modified Artificial Bee Colony Algorithm Estimated waveform Amplitude (V)

Amplitude (V)

Initial waveform 2 0 −2

0

0.5

1 t (us)

1.5

2

1 0 −1

0

0.5

1

(a) SNR=20 dB

Amplitude (V)

Amplitude (V)

0

0.5

1

2

Estimated waveform

2

0

1.5

t (us)

Initial waveform

−2

165

1.5

2

1 0 −1

0

0.5

1

t (us)

1.5

2

t (us) (b) SNR=10 dB Estimated waveform Amplitude (V)

Amplitude (V)

Initial waveform 5 0 −5

0

0.5

1

1.5

2

t (us)

1 0 −1

0

0.5

1

1.5

2

t (us) (c) SNR=0 dB

Fig. 2 The initial waveforms and estimated waveforms of single echo under different SNR.

convergence curves of the three algorithms changed with the numbers of cycles are shown in Fig. 3. By comparing the convergence curves of the three algorithms in Fig. 3, we find that the convergence rates of three algorithms are quick at the beginning. Impacted by the pheromone, the convergence curve of ACO algorithm fluctuates in the vicinity of the optimal solution. While the ABC and MABC algorithm can further convergence under the conditions of the current optimal value until it reaches the optimal value. Compared to 9

ACO ABC MABC

8 7 6 5 4 3

0

10

20

30

40 50 60 70 Number of cycles, N

80

90

100

Fig. 3 Convergence curves of three algorithms for single ultrasonic echo.

ABC algorithm, the MABC algorithm has higher calculation accuracy. Therefore, MABC algorithm is better than ABC algorithm and ACO algorithm in estimating parameters of ultrasonic echoes. 4.2 The parameters estimation for triple ultrasonic echoes Set the parameters of the MABC algorithm as: colony size N = 30, local circle times L = 30, global circle times M = 200. We estimate the parameters of triple ultrasonic echoes and the estimation results are shown in Table 3. When SNR is 10 dB, the initial waveform and estimated waveform are shown in Fig. 4. The simulation results show that MABC algorithm can estimate the parameters accurately for triple ultrasonic echoes. To further demonstrate the superiority of MABC, the estimated results of three algorithms under the same initial conditions were compared. The simulation results are shown in Table 4 and the convergence curve of the three algorithms for triple ultrasonic echoes is shown in Fig. 5. From Table 4 and Fig. 5 we conclude that MABC algorithm has the shortest computation time and the

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Convergence curve

Amplitude (V)

100

ACO ABC MABC

Amplitude (V)

Objective function, f(θ)

90 80 70 60 50 40 30 20 10 0 0

20

40

60

80 100 120 140 Number of cycles, N

160

180

Fig. 5 Convergence curves of three algorithms for triple ultrasonic echoes.

Fig. 4 The initial waveform and estimated waveform of triple ultrasonic echoes.

Table 3 Parameter estimation results of triple echoes under different SNR: search range big deviation from true values Search range lb ub

SNR = 20 dB avg std

SNR = 10 dB avg std

SNR = 0 dB avg std

Parameters

True values

β1 α1

0.9000 10.0000

0.7000 8.0000

1.1000 12.0000

0.8867 9.9516

0.0133 0.0484

0.8757 10.8445

0.0243 0.8445

0.8656 11.1020

0.0344 1.1020

τ1

1.5000

1.3000

1.7000

1.5027

0.0027

1.5046

0.0046

1.5097

0.0097

f1

5.0000

4.0000

6.0000

5.0323

0.0323

4.7384

0.2616

5.6027

0.6027

φ1

1.0000

0.8000

1.2000

0.9829

0.0171

1.0304

0.0304

1.1541

0.01541

β2

1.0000

0.8000

1.2000

0.9792

0.0208

0.9580

0.0420

1.0861

0.0861

α2

9.0000

7.0000

11.0000

9.0778

0.0778

9.1896

0.1896

9.3194

0.3194

τ2

2.0000

1.8000

2.2000

1.9953

0.0047

2.0092

0.0092

2.0193

0.0193

f2

7.0000

6.0000

8.0000

6.9896

0.0104

6.9437

0.0563

6.9055

0.0945

φ2

0.0000

−0.2000

0.2000

−0.0392

0.0392

0.0677

0.0677

0.0921

00921

β3

0.8000

0.6000

1.0000

0.7929

0.0071

0.8122

0.0122

0.8294

0.0294

α3

8.0000

6.0000

10.0000

8.0200

0.0200

7.8416

0.1584

8.3567

0.3567

τ3

2.5000

2.3000

2.7000

2.4958

0.0042

2.4864

0.0136

2.4741

0.0259

f3

6.0000

5.0000

7.0000

5.9795

0.0205

5.9147

0.0853

6.1648

0.1648

φ3

0.0000

−0.2000

0.2000

−0.0110

0.0110

−0.0225

0.0225

0.0464

0.0464

Table 4 The comparison of estimated performance ACO, ABC and MABC under 20 dB of triple echoes Search range lb ub

Parameters

True values

β1 α1

20.0000 1.0000

19.0000 0.9000

τ1

8.0000

f1

1.0000

φ1

200

ACO

ABC

MABC avg std

avg

std

avg

std

21.0000 1.1000

20.7083 0.9957

0.7083 0.0043

20.2375 0.9988

0.2375 0.0012

19.9808 0.9989

0.0192 0.0011

7.0000

9.0000

8.0624

0.0624

8.0394

0.0394

7.9862

0.0138

0.9000

1.1000

0.9764

0.0236

0.9914

0.0086

1.0066

0.0066

1.0000

0.9000

1.1000

1.0097

0.0097

1.0052

0.0052

0.9963

0.0037

β2

15.0000

14.0000

16.0000

15.3917

0.3917

14.8585

0.1415

15.0059

0.0059

α2

1.4000

1.3000

1.5000

1.3943

0.0057

1.4033

0.0033

1.3985

0.0015

τ2

5.0000

4.0000

6.0000

5.2240

0.2240

4.9217

0.0783

4.9453

0.0547

f2

0.8000

0.7000

0.9000

0.8772

0.0772

0.8334

0.0334

0.8104

0.0104

φ2

0.8000

0.7000

0.9000

0.8655

0.0655

0.7848

0.0152

0.8077

0.0077

β3

10.0000

9.0000

11.0000

9.3466

0.6534

10.4962

0.4962

10.2263

0.2263

α3

1.9000

1.8000

2.0000

1.8355

0.0645

1.8952

0.0048

1.9017

0.0017

τ3

3.0000

2.0000

4.0000

2.7292

0.1708

3.1354

0.1354

3.1113

0.1113

f3

0.6000

0.5000

0.7000

0. 5144

0.0856

0.5623

0.0377

0.6132

0.0132

φ3

0.7000

0.6000

0.8000

0.7172

0.0172

0.7107

0.0107

0.6915

0.0085

Runtime (s)

--

--

--

31.8371

23.5386

20.9644

Zhou et al.: Optimization and Parameters Estimation in Ultrasonic Echo Problems Using Modified Artificial Bee Colony Algorithm

highest estimation accuracy comparing with ACO algorithm and ABC algorithm for multiple echoes estimation. 4.3 The parameters estimation of experimental ultrasonic echo To verify the practicality of the MABC algorithm, the parameters of the experimental echo is estimated by MABC algorithm. Ultrasound pulse echo signals were obtained from a water immersion ultrasonic NDT system illustrated in Fig. 6. The experiment conditions are: the thickness of the solid aluminum block sample is 3.0 cm; the frequency of the ultrasonic probe is 4 MHz. The MABC algorithm is used to estimate the parameters of the ultrasonic experimental echo. The estimated results are [β α τ fc φ] = [2.1355 2.3752 9.5335 3.9872 0.1017]. Experimental waveform of the pulse-echo test and the estimated waveform are shown in Fig. 7. The known aluminum sound velocity is 6305 m·s−1, then the thickness of the aluminum block can be

Pulser/Receiver

Ultrasonic transducer Water Sample

— — — — — — — — — —

–— –— –— –— –— –— –— –— –— –—

–— –— –— –— –— –— –— –— –— –—

–— –— –— –— –— –— –— –— –— –—

– – – – – – – – – –

167

calculated by the estimation arrival time is 3.0054 cm, which is basically the same to the true value of the sample. The double echoes experiment conditions are: the thickness of the solid aluminum block sample is 1.0 cm, and the thickness of the solid copper block sample is 0.2 cm; the frequency of the ultrasonic probe is 7.5 MHz. The estimated parameters of the double ultrasonic experimental echoes based on MABC algorithm are shown in Table 5. Experimental waveform and the estimated waveform are shown in Fig. 8. The estimation results of arrival time are τ1= 3.1792 us and τ2= 3.9917 us, respectively. The sound velocity of aluminum and copper are 6305 m·s−1 and 5010 m·s−1, respectively. The thickness of the aluminum block calculated by the estimation result is 1.0022 cm and the calculated thickness of the copper block is 0.2035 cm, which are basically the same to the true value of the samples. From Table 5 and Fig. 8, we can see that the parameters of double experiment echoes can be estimate accurately by MABC algorithm, and the estimated echoes are similar to the original waveforms. Table 5 Parameter estimation results of double echoes

Digital oscilloscope

β2

α1

τ1

f1

φ1

lb

2.0000

4.5000

3.0000

7.0000

3.0000

ub

4.0000

5.5000

4.0000

8.0000

4.0000

2.7503

4.9982

3.1792

7.4992

3.7019

θ Search range

Estimated values Computer

Search range

Fig. 6 Schematic of the experimental configuration for ultrasonic immersion test.

β2

α2

τ2

f2

φ2

lb

1.0000

4.5000

4.0000

7.0000

1.0000

ub

2.0000

5.5000

5.0000

8.0000

3.0000

1.1897

4.9954

3.9917

7.5065

1.8972

θ

Estimated values

Experimental waveform

4 2 0 −2 −4

2.5

3

2.5

3

4

3.5

4 t (us) Estimated waveform

4.5

2 0 −2 −4

Fig. 7 The experimental waveform and estimated waveform of single ultrasonic echo.

3.5

t (us)

4

4.5

Fig. 8 The experimental waveform and estimated waveform of double ultrasonic echoes.

168

Journal of Bionic Engineering (2015) Vol.12 No.1 Breast tissue characterization using FARMA modeling of

5 Conclusions In this paper we develop a modified artificial bee colony algorithm to estimate the parameters of ultrasonic echoes based on nonlinear Gauss echo model. The search formula is modified by introducing an adjusting factor into the search formula of traditional ABC algorithm. Using adjustment factor to control the step size, the new algorithm can improve the search accuracy. The algorithm is validated by numerical simulation and ultrasonic detection experiments. The parameters estimation results show the MABC algorithm can get the global optimal solution of the ultrasonic echoes parameters for single and multiple echoes and has higher estimation accuracy even the initial value much deviate from the true values. MABC algorithm can obtain stable echo parameters under different SNR conditions. By comparing the MABC algorithm with the traditional ABC and ACO algorithm, we conclude that the MABC algorithm has a faster convergence speed and short computing time, which is more suitable for real-time detection of ultrasonic echo.

Acknowledgments A part of this study was supported by the Fundamental Research Funds for the Central Universities (Grant No. GK201302049) ， the Funds of the Xi’an Science Technology Bureal (CX12166(3)), and the Natural Science Funds of Shaanxi Province (2012JM1013).

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