A genetic fuzzy radial basis function neural network for structural health monitoring of composite laminated beams

Expert Systems with Applications 38 (2011) 11837–11842

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Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa

A genetic fuzzy radial basis function neural network for structural health monitoring of composite laminated beams Shi-jie Zheng ⇑, Zheng-qiang Li, Hong-tao Wang Aeronautical Science Key Lab of Smart Materials and Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China

a r t i c l e

i n f o

Keywords: Genetic algorithm Fuzzy logic RBF neural network Structural health monitoring

a b s t r a c t In this paper, a new neural network learning procedure, called genetic fuzzy hybrid learning algorithm (GFHLA) is proposed for training the radial basis function neural network (RBFNN). The method combines the genetic algorithm and fuzzy logic to optimize the centers and widths of the RBFNN, and the linear least-squared method is used to adjust the neural network connection weights. The modal frequencies of a glass/epoxy laminates beam with varying assumed delamination sizes and locations were computed using finite element method and fed into the genetic fuzzy RBF neural network to predict the delamination location and its extent. The simulation demonstrates that the neural network based on GFHLA is robust and promising. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction In the past decade, composite materials have been widely used in aerospace industry, automotive, civil engineering applications and many other sectors owe to their high specific strength to weight ratio and excellent corrosion resistance. However, the anisotropy and lack of homogeneity of composite materials result in various and complex damage mechanisms (Bois, Herzog, & Hochard, 2007). In a composite structure, one can observe microcracking, ply fractures (transverse cracks), delaminations, and laminate fractures Delamination, which is probably the most frequently occurring damage mode found in the composites because of the lack of reinforcement in the through-the-thickness direction, is readily caused by low energy impact as well as fatigue loading in the in-service condition. Delamination may lead to the severe degradation of the mechanical behavior of structures due to the loss of structural integrity. Deterioration of structures becomes a critical issue in regard to both safety and economic concerns (Zhou & Sim, 2002; Zou & Tong, 2000). Deterioration itself is inevitable, but online detection of the location and severity of structural damages is of great significance for providing solutions to ensure public safety and reliability of in-service structures in many important fields by means of detecting damage before serious and expensive degradation consequences occur. In the study of nonlinear mapping relationships between the structural damage indices and various damage statuses, soft computing techniques, such as the artificial neural network (Amraoui & Lieven, 2004; Chakraborty,

⇑ Corresponding author. Tel.: +86 25 84893466; fax: +86 25 84892294. E-mail address: [email protected] (S.-j. Zheng). 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.03.072

2005; Rafiq, Bugmann, & Easterbrook, 2001; Reddy & Ganguli, 2003; Steve et al., 2002; Zheng, Wang, & Liu, 2005), fuzzy logic (Ganguli, 2002; Sawyer & Rao, 2000; Taha & Lucero, 2005) and genetic algorithm (Au, Cheng, Tham, & Bai, 2003; Borges, Barbosa, & Lemonge, 2007; Lee & Wooh, 2005; Ling, Lau, Cheng, & Jin, 2005), have been increasingly utilized owing to their excellent pattern recognition capability. Artificial neural network (ANN), fuzzy logic and genetic algorithm (GA) are three different intelligence technologies that attempt to emulate human intelligence, but use different means. Each of the previous techniques has its own advantages and drawbacks. For example, neural networks actually can learn correctly from data and generalize highly nonlinear mapping among different domains, but they are opaque to the user and their reasoning capabilities are very poor. On the other hand, relying on IF-THEN rules and logical inference the fuzzy logic can explain its reasoning. They follow the same way that human beings use to make decisions in real life, namely, they use linguistic models. Such linguistic models have highly reasoning and nonlinear mapping capabilities. However, fuzzy systems lack the ability of learning and cannot adjust themselves to adapt a new environment. Both ANN and fuzzy logic can be considered as two different information processing systems, i.e. classifiers and controllers; however this is not the case for GA. The highly parallel searching nature of the GA provide them also with the properties of searching multi-peak spaces without suffering from the local minima problem associated with the hillclimbing methods. Also, GA is not dependent on continuity of the parameter space. Although GA cannot be used alone as modeling techniques, it is quite efficient when used with other modeling techniques. The fact that the previous three intelligence technologies can complement each other makes the idea of combining them

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Fig. 1. The flow chart of the RBFNN algorithm.

in hybrid models is widely accepted (Hefny, Bahnasawi, Abdel Wahab, & Shaheen, 1999). Hybrid intelligent systems based on different integration schemes of neural network, fuzzy logic and genetic algorithm have received much attention recently. The aim, of course, is to improve the performance of the artificial intelligent (AI) systems with the less possible drawbacks. Most of the work done in such an area is directed towards building hybrid intelligent models in which two of the previous intelligence technologies are integrated together, namely, combining GA with fuzzy logic (Pawar & Ganguli, 2007), GA with ANN (Suh, Shim, & Kim, 2000) or ANN with fuzzy logic (Nyongesa, Otieno, & Rosin, 2001). In the present paper, the above-mentioned three intelligence technologies are integrated together, a fuzzy radial basis function neural network is determined and the Fuzzy Cmeans clustering algorithm (FCM) is combined with genetic algorithm to determine optimize parameter of the neural network. 2. Genetic fuzzy RBFNN algorithm The present method for designing and training the RBFNN classifier involves two steps: (1) RBFNN structure determination and initialization and (2) RBFNN parameters adjustment. Fig. 1 shows the flow chart of the RBFNN structure determination and its

parameters’ optimization, while the corresponding solutions for each step are presented in the following. 2.1. Structure of the Fuzzy RBFNN As mentioned before, in this paper, the premise part of the system uses a fuzzy neural network (FNN). Fig. 2 shows the structure of FNN. In this figure, FNN is designed by implementing space partitioning in terms of individual variables. In this case, we are concerned with a granulation carried out in terms of fuzzy sets define in each input variable. Layer 1. The six inputs are the first six bending modal frequencies. The nodes in this layer just transmit input values to the next layer directly. Layer 2. This layer serves as fuzzifier layer, which maps input xi into fuzzy set Ai,j. A set of nodes are used here to obtain the membership grade of fuzzy subset of the input variable. Here, the number of fuzzy number is chosen 3. For the ith fuzzy set on the jth external input, the following Gaussian membership function is used:

  ujipj ¼ exp ðxpj  cji Þ2 =r2ji ;

i ¼ 1; 2; 3;

p ¼ 1; 2; . . . NT :

x1 y1 x2 y2

ð1Þ

Here NT is the amount of training samples; cij and rij are the center and width of the Gaussian membership function of the fuzzy set Aij, respectively. Layer 3. This is the fuzzy reasoning layer, which performs IFcondition reasoning by a product operation. There are totally 36 nodes in this layer. Each node at layer three is a rule node and represents one fuzzy rule. Product operator is used here. The firing strength of each rule is computed as follows:

apk ¼ x6

j ¼ 1; 2; . . . 6;

6 Y

ujipj ;

k ¼ 1; 2;    ; 36

i ¼ 1; 2; 3:

ð2Þ

j¼1

Layer 4. This layer is used for normalizing the input data from layer three.

Fig. 2. Topology structure of the fuzzy RBFNN.

a a pk ¼ P36pk : i¼1 api

ð3Þ

S.-j. Zheng et al. / Expert Systems with Applications 38 (2011) 11837–11842

Layer 5. The fifth layer is the output of RBF fuzzy neural network, the output is

ypi ¼

36 X

 pk ; wik a

i ¼ 1; 2:

ð4Þ

k¼1

After plugging the NT training data into Eq. (4), a more compact matrix form is obtained as follows:

aW ¼ Y;

ð5Þ

where a is the matrix of the firing strength of all rules, W is the output connection weight matrix, Y is the output matrix, where the dimensions of a, W and Y are NT  36, 36  2 and NT  2, respectively. Eq. (5) is an over determined problem and generally there is no exact solution. Instead, a least squares estimate (LSE) of W, W⁄, is sought to minimize the squared error ||aW Y||2. This is a standard problem that forms the grounds for linear regression, adaptive filtering and signal processing. The most well-known formula for W⁄ uses the pseudo-inverse of W:

W ¼ ðaT  aÞ1 aT Y;

ð6Þ

T

T

1

2.2. Fuzzy clustering and initialization RBF centers In the RBFNN structure, a clustering technique associates a cluster to each RBF units. Bezdek (1981) introduced several clustering algorithms based on fuzzy set theory and an extension of the leastsquares error criterion. Most analytical fuzzy clustering approaches are derived from Bezdeck’s FCM (Abe, Thawonmas, & Kayama, 1999; Bezdek, 1981). FCM is a data clustering algorithm that each data point is associated with a cluster through a membership degree. This technique partitions a collection of NT data points into r fuzzy groups and finds a cluster center in each group, such that a cost function of a dissimilarity measure is minimized. The algorithm employs fuzzy partitioning such that a given data point can belong to several groups with a degree specified by membership grades between 0 and 1. A fuzzy r-partition of input feature vector is represented by a matrix U = [lik], where the entries satisfy the following constraints:

lik 2 ½0; 1; 1 6 i 6 3; 1 6 k 6 NT ; lik ¼ 1; 1 6 k 6 NT :

ð7Þ ð8Þ

i¼1

U can be used to describe the cluster structure of X by interpreting lik as the degree of membership of lik to cluster i. The object of FCM is to find the matrices U = [uik] and C = [cij], representing the cluster centers, which allow to minimize the following cost function:

JðU; c1 ; . . . ; cc Þ ¼

c X

Ji ¼

i¼1

under the constraint :

NT c X X i¼1

3 X i¼1

2

um ij dij ;

ð9Þ

j¼1

uij ¼ 1;

where Dist2(k, i) = ||xk  Ci||2 is the distance between the pattern xk and the cluster center ci, m 2 [1, +1) is a weighting exponent called fuzzifier, C = {c1, c2 , . . . , cr} is the vector of the cluster centers, and dik is the distance between xk and the ith cluster. Bezdek (1981) proved that if m >= 1; then U and C minimize Jm(U, C) only if their entries are computed as follows:

PN T

m j¼1 uij xj

ci ¼ PN T

ð11Þ

m j¼1 uij

and

uij ¼

1 : Pc  dij 2=ðm1Þ

ð12Þ

k¼1 dkj

The conventional FCM algorithm consists of a series of iterations alternating between Eqs. (11) and (12). This algorithm converges to either a local minimum or a saddle point of J(U, C). In the present paper, the FCM algorithm is combined with genetic algorithm to determine optimize centers of membership function.

T

where a is the transpose of a, and (a a) a is the pseudo-inverse of a, if a T a is non-singular. While (6) is concise in notation, it is expensive in computation when dealing with the matrix inverse and, moreover, it becomes ill defined if aT a is singular. As a result, we employ sequential formulas to compute the LSE of W. This sequential method of LSE is more efficient. A detailed explanation of this method is beyond the aims of the present paper and details about it can be found in the reference written by Jang (1993). While the center and width of the Gaussian membership function of the fuzzy set Aij are presented in the following.

3 X

11839

8j ¼ 1; . . . ; NT ;

ð10Þ

2.3. Genetic fuzzy hybrid learning algorithm 2.3.1. Coding Coding aims to build the relationship between the problem and the individual in genetic algorithms. If the problems are expressed by coding strings, these strings are called an individual or a chromosome. Each individual represents a variable or a part of the problem which is needed to be optimized. In this paper, the centers of the Gaussian membership function are needed to be optimized by the GA. In the present case, each cluster centers has three linguistic variables and the real number coding is used. So each chromosome has eighteen genes and each gene denote one center Cij of the Gaussian membership function for the ith fuzzy set on the jth external input. 2.3.2. Initial population A population contains a number of individuals. As regards the specification of, there is a higher probability that a larger population will require fewer generations to evolve, i.e. fewer steps in the optimization process before arriving at the optimal solution, although with the increased population size the total processing computer overhead is not necessarily reduced as a consequence. Here, the size n is chosen 200. The initial population is produced by following steps: Step 1: Initially the membership matrix is constructed using random values between 0 and 1; such that constrains (7)–(9) are satisfied. Step 2: For each cluster i (i = 1, 2, 3), the fuzzy cluster centers ci are calculated using Eq. (11), and then this group of fuzzy cluster centers cij (i = 1, 2, 3; j = 1, 2, . . . , 6) is coded into an individual. Step 3: Steps 1–2 are repeated to produce 200 individuals. 2.3.3. Fitness function Our objective is to make the hidden centers as few as possible selected under the given accuracy. So the designing of the fitness function should ensure less hidden centers selected and less sum errors. In this paper, the fitness function of GA was designed as follows:

( Fi ¼

ðJ þ 2rÞ  J i

if

J i < J þ 2r i ¼ 1; 2; . . . ; 200

0

otherwise;

ð13Þ

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where J is the mean value of the objective function (Eq. (9)) corresponding to every chromosome of the current population; r the standard deviation; Ji the value of the objective function (Eq. (9)) corresponding to the ith chromosome. From Eq. (13), the idea is that the closer a chromosome comes to solve the problem; the higher fitness value is obtained. For a population, the individual with the highest fitness value is the winner of this generation. After the centers of the Gaussian membership function are determined, the width rij of the jth cluster for the ith input variable is calculated using

r2ij ¼

X

jjxi  cij jj2 =mij ;

ð14Þ

mij

where mij is the amounts of the ith input variables of all samples belongs to cluster j. 2.3.4. Genetic operators There are mainly three genetic operations, including, selection, crossover and mutation operations. These genetic operations have key effects on the performances of the genetic algorithm. 2.3.4.1. Reproduction. In this study, we use the roulette-wheel selection method—a simulated roulette is spun—for this selection process. The response fitness value of every individual is pi (i = 1, 2, . . . , N). According to the pi, a roulette wheel is divided into N parts. Here, N is the population size. In the selection operation, spinning the roulette wheel, if a consulted point lies in the ith sector, we will choose the ith individual. Obviously the area of the sector is larger, and then the probability that the consulted point lies in the sector, is more. This indicates that the better an individual’s fitness is, the more likely it is to be selected. An individual is probabilistically selected from the population on the basis of its fitness and the selected individual is then copied into the next generation of the population without any change. In this paper, a so-called elitist version of the genetic algorithm was employed whereby the best individual in the current generation is promoted directly to the next generation without undergoing any alteration or mutation. This variation ensures that the fittest member of each successive generation must be either equal or represent an improvement on the currently best candidate. Thus in this application the parameters of RBF neural networks will always converge through successive iterations. 2.3.4.2. Crossover and mutation. In order to facilitate the GA evolution cycle, the crossover and mutation operators are required. Selection directs the search toward the best existing individuals but does not create any new individuals. In nature, an offspring has two parents and inherits genes from both. The main operator working on the parents is the crossover operator, the operation of which occurred for a selected pair with a crossover rate pc. In each new population, there are pc  N individuals which are needed crossover operations. In the crossover step, we also keep the same number of chromosomes for each group. After this operation, the individuals with poor performances are replaced by the newly produced offspring. For selected two chromosomes (parents) from the population, the crossover will be done in two steps: (1) the binary part string representing the control neurons and the real number encoding part string representing the parametric neurons will do crossover separately; (2) the control part uses the traditional one single point crossover with a uniform probability distribution. While the parametric part utilizes linear combination crossover technique, for any two individuals x1 and x2, the new offspring is generated by the linear combination expressed as



x01 ¼ ax2 þ ð1  aÞx1 ; x02 ¼ ax1 þ ð1  aÞx2 ;

ð15Þ

where a 2 [0, 1], is a random real number. The mutation operator is always used to keep the diversity of population. Like the crossover, for each selected chromosome from the population, the string of the control neurons and the string of the parametric neurons mutate separately. A simple point mutation is used in control part and the operator exchanges with a given probability each term in parametric part with a randomly selected term in the corresponding complementary subset of the string. 2.3.4.3. Active operational rates settings. The choice of an optimal probability operation rate for crossover and mutation is a controversial debate for both analytical and empirical investigations. The increase of crossover probability would cause the recombination of building blocks to rise, and at the same time, it also increases the disruption of good chromosomes. On the other hand, should the mutation probability increase, this would transform the genetic search into a random search, but would help to reintroduce the lost genetic search. The present paper utilized a dynamically variable crossover and mutation rate which was dependent upon the spread of fitness

 Pc ¼ Pm ¼

Pc1  ðPc1  Pc2 Þðf 0  fav g Þ=ðfmax  fav g Þ f 0 P fav g Pc1 f 0 < f av g ;  Pm1  ðPm1  Pm2 Þðfmax  f Þ=ðfmax  fav g Þ f P fav g Pm1

f < fav g ;

ð16Þ ð17Þ

where Pc1, Pc2, Pm1 and Pm2 are set as 0.9, 0.6, 0.1 and 0.001, respectively. fmax is the maximum fitness value of the current population; f0 the larger fitness value between the two parents in the crossover stage; f the fitness value of the mutated individual; favg the mean value of the fitness of the current population. 3. Neural networks implementation 3.1. Finite element modeling In this paper, the 8-node element was adopted to compute the eigenfrequencies of a delaminated beam, the element has four nodes at each of its top (f = +1) and bottom faces (f = 1), respectively. The initial coordinate vector X and the displacement vector U are interpolation in the standard manner,

Xðn; g; fÞ ¼

4 X

Ni ðn; gÞðfþ X i þ f X 4þ1 Þ

i1

¼ N ðn; gÞX þ fN ðn; gÞX;

Uðn; g; fÞ ¼

4 X

ð18Þ

N i ðn; gÞðfþ X i þ f X 4þ1 Þ

i1

¼ N ðn; gÞU þ fN ðn; gÞU;

ð19Þ

N0i s

where are the two-dimensional bilinear interpolation functions, (n, g, f) are the natural or isoparametric coordinates, N0 s are self-defined. X is the nodal counterpart of X and U is the nodal counterpart of U. Moreover,

1 f ¼ ð1 þ fÞ; 2 þ

1 f ¼ ð1  fÞ; 2 

8 9 X > < 1> = .. X¼ ; . > ; > : X8

8 9 U > < 1> = .. U¼ : . > ; > : U8 ð20Þ

From the definition of strain, the covariant strain can be expressed as follows:

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L L1

Orientation - Degrees Degrees Degrees Degrees - Degrees Degrees Degrees Degrees - Degrees Degrees Degrees Degrees

L2

h

Composite Beam Model Midplane Delamination Fig. 3. Composite beam with delamination.

eij ¼ ðXT;i U;j þ XT;j U;i Þ=2

ð21Þ

in which i, j = n, g, f. In order to circumvent shear and trapezoidal lockings, the natural transverse normal and shear strains are modified by ANS (Zheng, Wang, & Chen, 2004) as:

1n 1þn cfg jn¼1;g¼0;f¼0 þ cfg jn¼1;g¼0;f¼0 ; 2 2 1g 1þg c~fn ¼ cfn jn¼0;g¼1;f¼0 þ cfn jn¼0;g¼1;f¼0 ; 2 2

c~fg ¼

where Te is the strain transformation matrix. For frequency analysis, the elemental mass and stiffness matrices are derived and then assembled to form the global mass and stiffness matrix. Note that all external forces are zero in the eigenvalue analysis and in the particular case of zero damping; a standard eigenvalue equation can then be written as:

ðK  x2 MÞu ¼ 0;

~eff ¼ N1 eff jn¼1;g¼1 þ N2 eff jn¼1;g¼1 þ N3 eff jn¼1;g¼1 þ N4 eff jn¼1;g¼1 : As the material properties are often defined in a local orthogonal frame (x, y, z), it is necessary to obtain the local physical strains from the ones with respect to (n, g, f). It will be assumed that the zaxis is perpendicular to the mid-surface of the shell. Hence the relation between the nature coordinate infinitesimal strains and the local physical strains is:

e ¼ f exx eyy ezz cxy czx cyz gT ¼ T e f enn egg ~eff cng c~fn c~g1 gT ; ð22Þ

ð23Þ

where M and K are the global mass and stiffness matrices. The modal frequencies of a 600  60  3 mm cantilever beam with varying assumed delamination sizes and locations were computed using the above-mentioned element model. This laminated beam studied here consisted of 12 unidirectional glass/epoxy plies with the sequence [0°/45°/90°/45°/0°/45°/90°/45°/0°/45°/90°/ 45°], its material properties of the laminae are E1 = 19.40 MPa, E2 = 12.25 MPa, E3 = 9.35 MPa, G12 = 3.52 GPa, G13 = 3.59 GPa, G23 = 3.57 GPa, m12 = 0.091, m13 = 0.165, m23 = 0.266, q = 1.96  103 Kg/m3. An assumed delamination was constant across the entire beam width and was in the beam midplane as shown in Fig. 3, where L1 represents the delamination location, L2 the delamination size. The different delamination sizes varied from 30 to 60 mm in intervals of 5 mm and the damage location for each delamination size varied from 330.6 to 530.6 mm in intervals of

Table 1 Parts of calculated modal frequencies of a delaminated beam. Delamination location

Delamination size

Modal frequency 1

2

3

4

5

6

350.6

30.0 35.0 40.0 45.0 50.0

5.0058 5.0057 5.0055 5.0053 5.0049

30.7418 30.7372 30.7317 30.7261 30.7187

88.3015 88.2322 88.1610 88.0897 88.0195

176.6926 176.1442 175.4750 174.6850 173.7462

288.1887 286.5265 284.5081 282.1435 279.4623

433.6779 429.8870 425.7135 421.3227 416.9144

410.6

30.0 35.0 40.0 45.0 50.0

5.0060 5.0059 5.0058 5.0056 5.0054

30.7483 30.7400 30.7307 30.7196 30.7066

88.4834 88.4372 88.3968 88.3631 88.3342

177.7150 177.2410 176.7484 176.2558 175.7724

288.1689 286.4177 284.3400 281.9555 279.2941

440.2425 438.9904 437.3906 435.3473 432.4346

460.6

30.0 35.0 40.0 45.0 50.0

5.0062 5.0061 5.0061 5.0060 5.0059

30.7622 30.7548 30.7474 30.7372 30.7252

88.4911 88.4449 88.3920 88.3313 88.2582

177.9939 177.8359 177.7243 177.6314 177.5570

289.0791 287.7929 286.2792 284.5675 282.6679

438.1210 435.7038 432.0259 427.7220 423.2616

510.6000

30.0 35.0 40.0 45.0 50.0

5.0063 5.0063 5.0063 5.0062 5.0062

30.7836 30.7799 30.7752 30.7706 30.7650

88.6471 88.6028 88.5489 88.4854 88.4103

178.5237 178.3285 178.0961 177.7987 177.4455

290.4445 289.8607 289.2077 288.5053 287.7533

438.9904 437.3645 435.4778 433.3475 431.0347

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Table 2 Genetic fuzzy RBF neural network output.

P1 P2 P3 P4 P5

Acknowledgments

Delamination Delamination Predicted Predicted size location size location

Predicted error

35 45 52.5 57.5 55

6.5815 4.1240 6.4505 3.0683 0.5501 4.8446 3.5457 3.9686 6.4942 5.6081

400.6 475.6 460.6 488.1 505.6

37.3035 47.9027 52.7888 55.4612 51.9225

417.1207 461.0074 438.2856 507.4708 421.6296

Size

Location

5 mm. Sets of the first six bending modal frequencies for 288 delamination cases were found. For the finite element analysis, delaminations were modeled by pairs of nodes with the same coordinates but different node numbers (except for the delamination starting and ending points) (Zheng, 2004). Table 1 shows the modal frequencies for some kinds of delamination sizes and location. 3.2. Training the neural network The training of the radial basis function neural network was accomplished using the 288 sets of modal frequencies and their associated delamination characteristics as calculated by finite element analysis. Five sets of the 283 generated data were reserved for testing the convergence of the RBF neural network and were not used for training. Instead of presenting these data directly to the network, it may be necessary to normalize the input and output data. Scaling of the inputs to the range [1, 0] greatly improves the training speed. A simple linear normalization function within the values of negative one to zero is adopted in this paper

XSi ¼ ðX Si  X i max Þ=ðX i max  X i max Þ;

ð24Þ

where XSi is the ith component of the Sth sample and XSi is the normalized value of variable XSi, Ximax and Ximin are the maximum and minimum values of the ith component of all samples, respectively. Ultimately, the five sets of reserved modal frequencies were input into the neural network and the results shown in Table 2 demonstrate that the genetic fuzzy RBF neural network can successfully predict the delamination parameters (size and location) of the composite beams. For the delaminated beam, the average difference of delamination size and location between the actual and predicted values is 4.7% and 4.3%, respectively. Training data from a more accurate analysis may improve the results. Further work is in progress and will be reported subsequently. 4. Conclusion This paper presents a novel learning algorithm for the RBFNN with applications in the structural health monitoring system. The proposed algorithm combines the merits of the fuzzy logic theory, neural networks, and genetic algorithms (GA), in which the genetic algorithm plays a central role. The FCM algorithm is combined with genetic algorithm and the linear least-squared method to determine optimal parameters of the neural network. A finite element analysis is used to obtained simulated modal frequencies. These simulated glass/epoxy parameters are fed into the genetic fuzzy RBF neural network. The delamination location and size were predicted successfully. The simulation demonstrates that the neural network based on GFHLA is robust and promising.

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