Advances in Artificial Neural Systems

Advances in Artificial Neural Systems / 2013 / Article

Research Article | Open Access

Volume 2013 |Article ID 962734 | 12 pages | https://doi.org/10.1155/2013/962734

Fuzzified Data Based Neural Network Modeling for Health Assessment of Multistorey Shear Buildings

Academic Editor: Matt Aitkenhead
Received21 Nov 2012
Revised14 Feb 2013
Accepted15 Feb 2013
Published26 Mar 2013

Abstract

The present study intends to propose identification methodologies for multistorey shear buildings using the powerful technique of Artificial Neural Network (ANN) models which can handle fuzzified data. Identification with crisp data is known, and also neural network method has already been used by various researchers for this case. Here, the input and output data may be in fuzzified form. This is because in general we may not get the corresponding input and output values exactly (in crisp form), but we have only the uncertain information of the data. This uncertain data is assumed in terms of fuzzy number, and the corresponding problem of system identification is investigated.

1. Introduction

System identification methods in structural dynamics, in general, solve inverse vibration problems to identify properties of a structure from measured data. The rapid progress in the field of computer science and computational mathematics during recent decades has led to an increasing use of process computers and models to analyze, supervise, and control technical processes. The use of computers and efficient mathematical tools allows identification of the process dynamics by evaluating the input and output signals of the system. The result of such a process identification is usually a mathematical model by which the dynamic behaviour can be estimated or predicted. The system identification problem has been nicely explained in a recent paper [1]. The same statements from [1] are reproduced below for the benefit of the readers.

The study of structures dynamic behaviour may be categorized into two distinct activities: analytical and/or numerical modelling (e.g., finite element models) and vibration tests (e.g., experimental modal models). Due to different limitations and assumptions, each approach has its advantages and shortcomings. Therefore, in order to determine the dynamic properties of the structure, reconciliation processes including model correlation and/or model updating should be performed. Model updating can be defined as the adjustment of an existing analytical/numerical model in the light of measured vibration test. After adjustment, the updated model is expected to represent the dynamic behaviour of the structure more accurately as proposed by Friswell et al. [2]. With the recent advances in computing technology for data acquisition, signal processing, and analysis, the parameters of structural models may be updated from the measured responses under excitation of the structure. This procedure is achieved using system identification techniques as an inverse problem. The inverse problem may be defined as determination of the internal structure of a physical system from the system’s measured behaviour, or estimation of an unknown input that gives rise to a measured output signal according to Tanaka and Bui [3].

Comprehensive literature surveys have been provided on the subject of model updating of the structural systems by Alvin et al. [4], and Time series methods for fault detection and identification in vibrating structures were presented by Fassois and Sakellariou [5]. Shear buildings are among the most widely studied structural systems. Previous works on model updating of shear buildings rely mostly on using modal parameter identification and physical or structural parameter identification to drive the corresponding update procedures. As regards the publications, Marsi et al. [6] gave various methodologies for different types of problems in system identification. Various techniques for improving structural dynamic models were reviewed in a review paper by Ibanez [7], and studies made by Datta et al. [8] related to system identification of buildings done until that date were also surveyed. Some of the related publications may be mentioned as those of Loh and Tou [9] and Yuan et al. [10].

It is known that, the systems which may be modeled as linear, the identification problem often turns in to a non-linear optimization problem. This requires an intelligent iterative scheme to have the required solution. There exists various online and offline methods, namely, the Gauss-Newton, Kalman filtering and probabilistic methods such as maximum likelihood estimation, and so forth. However, the identification problem for a large number of parameters, following two basic difficulties are faced often:(i)objective function surface may have multiple maxima and minima, and the convergence to the correct parameters is possible only if the initial guess is considered as close to the parameters to be identified; (ii)inverse problem in general gives nonunique parameter estimates.To overcome these difficulties, researchers have developed various identification methodologies for the said problem by using powerful technique of Artificial Neural Network (ANN). Chen [11] presented a neural network based method for determining the modal parameters of structures from field measurement. Using the observed dynamic responses, he trained the neural network based on back-propagation technique. He then directly identified the modal parameters of the structure using the weight matrices of the neural network. In particular, Huang et al. [12] presented a novel procedure for identifying the dynamic characteristics of a building using a back-propagation neural network technique. Another novel neural network based approach has been presented by Kao and Hung [13] for detecting structural damage. A decentralized stiffness identification method with neural networks for a multidegree of freedom structure has been developed by Wu et al. [14]. Localized damage detection and parametric identification method with direct use of earthquake responses for large-scale infrastructures has also been proposed by Xu et al. [15]. A neural network based strategy by Xu et al. [16] was developed for direct identification of structural parameters from the time domain dynamic responses of an object structure without anyeigen value analysis.

System identification on the other hand tries to identify structural matrices of mass, damping and stiffness directly. Among various methodologies in this regard Chakraverty [17], Perry et al. [18], Wang [19], Yoshitomi and Takewaki [20], and Lu and Tu [21] developed different techniques to handle the system identification problems. Yuan et al. [10] developed a methodology that identifies the mass and stiffness matrices of a shear building from the first two orders of structural mode measurement. Koh et al. [22] proposed several Ga-based substructural identification methods, which work by solving parts of the structure at a time to improve the convergence of mass and stiffness estimates particularly for large systems. Chakraverty [17] proposed procedures to refine the methods of Yuan et al. [10] to identify the structural mass and stiffness matrices of shear buildings from the modal test data. The refinement was obtained using Holzer criteria. Tang et al. [23] utilized a differential evolution (DE) strategy for parameter estimation of the structural systems with limited output data, noise polluted signals, and no prior knowledge of mass, damping, or stiffness matrices. Recent works on model updating of multistory shear buildings for simultaneous identification of mass, stiffness, and damping matrices using two different soft-computing methods have been developed by Khanmirza et al. [1]. It may be seen from above that Artificial Neural Networks (ANNs) provide a fundamentally different approach to system identification. They have been successfully applied for identification and control of dynamics systems in various fields of engineering because of excellent learning capacity and high tolerance to partially inaccurate data.

It is revealed from the above literature review that various authors developed different identification methodologies using ANN. They supposed that the data obtained are in exact or crisp form. But in actual practice the experimental data obtained from equipments are with errors that may be due to human or equipment error, thereby giving uncertain form of the data. Although one may also use probabilistic methods to handle such problems. Then, the probabilistic method requires huge quantity of data which may not be easy or feasible. Thus in this paper, a minimum number of data are taken in fuzzified form to have the essence of the uncertainty. Accordingly, in this paper, identification methodologies for multistorey shear buildings have been proposed using the powerful technique of Artificial Neural Network (ANN) models which can handle fuzzified data. It is already mentioned that identification with crisp data is known and also neural network method has already been used by various researchers for this case. Here, the input and output data may be in fuzzified form. This is because in general we may not get the corresponding input and output values exactly (in crisp form), but we have only the uncertain information of the data. This uncertain data has been assumed to be in terms of fuzzy numbers.

In this paper, the initial design parameters, namely, stiffness and mass and so the frequency of the said problem is known. But after a large span of time, the structure may be subjected to various manmade and natural calamities. Then, the engineers want to know the present health of the structure by system identification methods. It is assumed that only the stiffness is changed and the mass remains the same. As such equipments are available to get the present values of the frequencies and using these one may get the present parameter values by ANN. But while doing the experiment, one may not get the exact values of the parameters. But we may get those values as uncertain, namely, in fuzzy form. So if sensors are placed to capture the frequency of the floors in fuzzy (uncertain) form, then those may be fed into the proposed new ANN model to get the present stiffness parameters in fuzzified form. In order to train the new ANN model, set of data are generated numerically beforehand. As such, converged ANN model gives the present stiffness parameter values in interval form for each floor. Thus, one may predict the health of the uncertain structure. Corresponding example problems have been solved, and related results are reported to show the reliability and powerfulness of the model.

2. Analysis and Modelling

System identification refers to the branch of numerical analysis which uses the experimental input and output data to develop mathematical models of systems which finally identify the parameters. The floor masses for this methodology are assumed to be , ], and the stiffness ],,  ,   are the structural parameters which are to be identified. It may be seen that all the mass and stiffness parameters are taken in fuzzy form. As such here for each mass , we have as the left value, as the centre value, and as the right value. Similarly for the stiffness parameter for each mass , we have as the left value, as the centre value, and as the right value. The n-storey shear structure is shown in Figure 1. Corresponding dynamic equation of motion for n-storey (supposed as n degrees of freedom) shear structure without damping may be written as where .

is mass matrix of the structure and is given by stiffness matrix of the structure and may be written as and are the vectors of displacement.

We will first solve the above free vibration equation for vibration characteristics, namely, for frequency and mode shapes of the said structural system in order to get the stiffness parameters in fuzzified form. Accordingly putting in free vibration equation (1), we get where are eigenvalues or the natural frequency and are mode shapes of the structure, respectively.

3. Basic Concept of Fuzzy Set Theory

Definition 1. Let be a universal set. Then, the fuzzy subset of is defined by its membership function which assigns a real number in the interval , to each element , where the value of at shows the grade of membership of in .

Definition 2. Given a fuzzy set in and any real number , then, the -cut or -level or cut worthy set of , denoted by , is the crisp set The strong -cut, denoted by , is the crisp set

Definition 3. A fuzzy number is a convex normalized fuzzy set of the real line whose membership function is piecewise continuous.

Definition 4. A triangular fuzzy number can be defined as a triplet . Its membership function is defined as Above TFN may be transformed to an interval form by -cut as

4. Operation of Fuzzy Number

In this section, we consider arithmetic operation on fuzzy numbers and the result is expressed in membership function: (1)Addition: (2)Subtraction: (3)Multiplication: (4)Division: (5)Minimum: (6)Maximum:

5. Artificial Neural Network (ANN) and Error-Back Propagation Training Algorithm (EBPTA) for Fuzzified Data

Traditional ANN and EBPTA are well known, but here for the sake of completeness, those are developed for fuzzy case. In ANN, the first layer is considered to be input layer and the last layer is the output layer. Between the input and output layers, there may be more than one hidden layer. Each layer will contain number of neurons or nodes (processing elements) depending upon the problem. These processing elements operate in parallel and are arranged in patterns similar to the patterns found in biological neural nets. The processing elements are connected to each other by adjustable weights. The input/output behavior of the network changes if the weights are changed. So, the weights of the net may be chosen in such a way so as to achieve a desired output. To satisfy this goal, systematic ways of adjusting the weights have to be developed to handle the fuzzified data which are known as training or learning algorithm. Neural network basically depends upon the type of processing elements or nodes, the network topology, and the learning algorithm. Here, error back-propagation training algorithm and feedforward recall have been used but to handle the uncertain system. The typical network is given in Figure 2.

In this Figure, , , and are input, hidden, and output layers, respectively. The weights between input and hidden layers are denoted by , and the weights between hidden and output layers are denoted by . Here, and .

Given training pairs where are input and are desired values for the given inputs, the error value is computed as for the present neural network as shown in Figure 2. The error signal terms of the output and hidden layers are written, respectively, as

Consequently, output layer weights and hidden layer weights are adjusted as where is the learning constant.

6. Results and Discussion

To investigate the present method here, examples of one- and two-storey shear structures are considered. So, for example, the floor masses for two-storey shear structure are ,  and the stiffnesses ,   are the structural parameters. Here, masses are assumed to be constant (as mentioned earlier). So, we will identify the stiffness parameter in fuzzy form using the fuzzy form of the frequency where frequency may be obtained from some experiments. In the following paragraphs, we have used the proposed method to identify the stiffness parameter for one-, two-, five-, and ten-storey frame structures. Here, we have considered the cases with crisp data for five- and ten-storeys and then fuzzified data for one- and two-storeys. The training data are also considered with the influence of noise, namely, in terms of triangular fuzzy number data. Accordingly we have considered the following four cases: Case(i): Five-storey shear structure with crisp data,Case(ii): Ten-storey shear structure with crisp data,Case(iii): Single-storey shear structure with fuzzified data,Case(iv): Double-storey shear structure with fuzzified data. Computer programs have been written and tested for variety of experiments for the above cases. For the first two cases, namely, Case(i) and Case(ii), the inputs are taken as the crisp frequency values and the outputs are the stiffness parameters which are also in crisp form. On the other hand, for Cases(iii) and (iv), the inputs are taken as the fuzzified frequency values and the outputs are the stiffness parameters again in fuzzified form in the developed Fuzzy Neural Network (FNN) algorithm.

For the first case, an example of a five-storey shear structure is taken where the masses are and the stiffness parameters are within the range , , , , and . A comparison between the desired and ANN values has been presented in Table 1. This table has been plotted in Figure 3.


Data
number
(Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des)

1181277.7318181472.368657722.6857880.654153111.56153114.81444531.813844120.921824304.530124387.4436
2195883.7223190579.193798497.336298529.639140890.778940714.233630510.588430636.656924013.411623815.5846
3110889.324112698.681697540.287897858.347456939.133356982.586135467.070935538.459727905.072327655.1679
4191334.6369191337.585674367.090674268.782458151.367858679.86530921.744430923.427827758.98327951.999
5162671.148163235.924690080.929190014.023453507.075853574.703131851.26331942.635621775.050921868.726
6109757.8778109754.040557034.339157094.316955073.90455154.802646360.940346469.156624899.561924897.644
7127671.411127849.821971003.128271088.064154999.75854862.649443688.961143896.572524554.259824455.862
8154429.3614154688.151998500.007395786.776348031.314847844.540436250.004736341.989627719.138926463.1301
9196399.16195750.683589751.902589610.366553100.037253109.557848498.010649004.44127950.536427093.6483
10193722.4668196488.853598520.88197974.621343228.92943423.733830822.026830688.921626813.963727546.8668

In Case(ii), an example for a ten-storey shear structure has been considered with constant masses similar to Case(i) and the stiffness parameters are in the range , . The desired and ANN values for   to   and   to   are compared in Tables 2(a) and 2(b), respectively.

(a)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des)

1116900.6563 114999.7254 23626.293 23947.0748 25255.905 24299.2141 29078.6982 29493.0391 27766.1413 28842.8102
2137413.4659 135922.821 22400.1311 21970.538 22076.7651 22160.1892 28671.6078 29898.7215 23928.6799 23185.2425
3174166.5579 171165.6706 26751.8243 27587.6627 28439.4836 28089.9027 28056.19 27636.7332 28909.5075 29349.7909
4185745.6345 187147.6518 28203.5977 29952.1598 23288.5994 23565.0893 25414.2964 25588.2055 24175.8385 24794.8455
5131376.8088 132868.9612 22531.4396 21865.7144 20887.9013 20732.4343 22490.5032 21838.4294 21747.4496 22317.9161
6174687.251 165011.8025 25813.5863 27811.4527 25015.1015 25909.9146 25615.7328 24979.4882 24612.1573 23962.9025
7185115.3655 197483.6148 24841.291 21957.9798 27352.9705 29101.8783 25184.1779 25178.456 27414.6225 27050.7748
8107439.5782 107596.7361 28408.1614 29923.5897 22079.0745 21937.6594 29361.5732 29942.4301 25283.6014 25585.5903
9164872.2954 158701.9167 25498.9862 28022.6157 26269.1879 24323.6779 28505.5766 28548.5168 27421.7863 27566.307
10134496.3197 136428.6869 23984.6699 23091.3643 26528.5422 27288.6387 20735.4877 20391.8449 26590.0291 26789.4101

(b)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des)

121170.0974 20899.5068 25777.6655 25605.5953 28204.3487 29899.5021 27503.4171 25859.8704 27163.5463 25814.4649
222417.1364 20549.7415 27621.6492 28654.3859 27612.505 28451.7819 28303.9996 29823.0322 22093.3505 22094.0508
329672.9685 29638.7013 25998.8211 27124.1481 22438.2305 21982.2179 26315.5549 26153.251 27684.8546 29019.9081
419962.2582 19656.5635 21156.2588 20166.7471 22269.5196 21950.7153 23818.7821 23766.1108 27240.5745 27020.6645
520161.805 20514.4829 25387.6098 28009.2088 23922.4631 23268.3965 27519.8427 28771.8175 23219.6412 23774.551
622307.0935 23043.4895 21527.1166 21425.0932 27311.6444 28803.3786 27670.7454 27848.5243 27234.7985 27349.5593
727804.4452 25801.9183 24442.8169 24784.7447 25319.1653 24711.0187 25870.6554 24649.5428 27640.8021 29541.0279
825509.2344 25309.6445 22738.1369 22568.3535 23936.8813 24039.6937 28924.1116 28139.7693 25172.6749 25428.1311
928341.8519 29012.0809 25380.1928 23690.9169 23071.1828 21792.3148 28034.5751 28984.4414 26519.4395 25401.0583
1027911.2912 29624.314 26475.8553 24319.8061 21306.3632 21696.0881 25327.5363 24074.5574 24485.2563 23343.2942

For Case(iii), the first example is that of a single-storey shear structure with masses and the stiffness parameters lie within the range , , and . A comparison between desired and the ANN values has been incorporated in Table 3. This table has been plotted in Figure 4. In the second example, a single-storey shear structure is considered with masses and the stiffness parameter varying within the range , , and  . Comparison between the desired and the ANN values is tabulated in Table 4 and is plotted in Figure 5.


Data
number
(Ann) (Des) (Ann) (Des) (Ann) (Des)

1124932.9319124189.1286135932.8213135095.2381191905.7285190281.611
2135763.4956140411.2146152464.2896151324.954191726.9669194488.719
3110291.5736109665.4525141591.1084140180.8034148514.9196149096.4092
4107394.0584107596.6692115134.7117113217.3293149119.797148935.2638
5124430.5911123991.6154134455.7107133781.941192947.0787194225.0591
6112574.5401112331.8935188853.0283190015.3846194542.4439195633.454
7120988.7913118390.7788138166.8698136934.6781157619.3944157540.8595
8108960.7756105997.9543113526.3083111130.2755126504.2017123995.2526
9124700.9011123497.9913143556.5197141726.7069179985.5092178035.2068
10105227.009104965.443135988.057135335.8571140612.991138983.8837


Data
number
(Ann) (Des) (Ann) (Des) (Ann) (Des)

162365.0341 62104.5643 67644.4378 67547.619 95458.8463 95145.8055
267613.8959 70215.6073 75826.931 75662.477 95893.1612 97249.3595
355005.0087 54842.7263 70556.3936 70090.4017 74368.7997 74553.2046
453128.7186 53798.3346 56947.542 56618.6646 74261.1768 74472.6319
562246.1626 61995.8077 66881.2194 66895.9705 96278.4523 97122.5295
655957.2602 56165.9467 94391.1219 95012.6923 97271.6645 97826.727
760056.7259 59195.3894 68223.7328 68472.3391 78385.7211 78780.4298
8 53587.3374 53008.9771 55747.5298 55570.1378 61968.3882 61997.6263
962126.6388 61758.9957 71196.546 70863.3535 89991.9346 89022.6034
1052238.7913 52482.7215 67702.5259 67677.9286 69679.1387 69496.9418

In Case(iv), the first example of a double-storey shear structure is considered where the masses are and the stiffness parameters varying within the range , , and , , and . The desired and ANN values have been compared in Tables 5(a) and 5(b). This table has also been shown in Figures 6(a) and 6(b). In the second example, a double-storey shear structure is implemented with masses and the stiffness parameters having the range , , and , , and . Comparison between the desired and ANN values are again incorporated in Tables 6(a) and 6(b). This table is plotted in Figures 7(a) and 7(b).

(a)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des)

1113258.5422113317.1008133858.2555133969.3413162741.2326162807.3359
2116526.66117338.8613128622.4646129208.408193447.2534195183.0465
3139119.0131139093.7802143501.0894143175.117191801.5675192053.204
4101316.7594101558.7126106512.8803105287.6998183040.5812183137.9743
5173554.7972173805.8096180269.037180336.4392198199.4731198416.3724
6105985.8857106047.1179117592.2043116726.841127688.8972126931.9426
7110472.1362110631.6345140132.9188139925.7771142461.6007142303.5615
8137120.3743137250.974152856.9037152687.5831155005.6994154807.0901
9119783.849119821.8403142480.6438141679.9468195824.6624194293.6984
10141708.5217141794.4104148654.6797148978.7638165370.4902165685.9891

(b)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des)

158488.0205 58566.0533 91472.5908 92796.1403 99954.016 99152.6233
251977.6459 51640.041 65679.199 65072.7474 85856.2114 82258.2268
369213.7504 68833.6105 77764.8854 78069.9896 85939.2478 85054.9378
460124.2902 59566.1848 83319.0924 83316.9426 93794.9834 94103.325
571317.3378 71432.6496 76748.5343 76956.3233 83930.3883 83468.7652
659384.591 59531.6634 73687.8221 74121.1031 85087.5853 84905.276
756031.7629 56050.5807 68215.603 68455.8273 83728.3652 83326.3957
858849.1438 58906.6227 72741.8224 73046.2969 79796.3231 79495.3742
957077.8681 56400.72 61035.9761 61329.384 95110.8992 99091.8975
1057858.7023 57830.2476 69404.8867 69250.9562 99433.354 99954.0197

(a)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des)

162193.4503 62149.2679 65871.2249 66562.894 69219.2648 69672.8181
271578.6175 71235.4748 71816.4848 72130.1157 83311.5254 83571.557
363514.5116 63533.5212 84447.6191 84399.8043 86708.0123 87062.8972
459459.7849 59872.6899 67907.0231 67971.4105 75148.6421 76002.6234
567809.323 67385.6336 85655.9802 86827.0037 91460.6917 91106.0592
657879.7498 57499.8627 69206.8111 69745.3738 71387.5577 71516.0705
777679.4222 79304.6034 83870.4195 84180.7933 93380.175 94408.5477
863484.2106 63107.2659 69028.8134 69579.1498 85313.0398 85212.3715
952329.6174 52222.7046 72316.9085 72125.2707 88399.7894 88475.7194
1050895.5951 50988.8812 69532.938 69859.5759 87547.575 87746.6634

(b)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des)

127396.6322 27507.0572 27776.8241 27698.5425 28078.4211 28085.141
221439.7109 21682.5355 27548.5904 27550.771 29081.9724 28275.8382
323717.5546 23773.9554 27948.7301 27919.6303 28617.4807 28629.8048
422090.0439 22160.1892 23180.7111 23205.2425 28962.7934 29908.7215
525086.5697 25154.2346 25465.6455 25360.6413 27961.1253 27904.0722
620724.6386 20919.5068 28645.592 28852.8102 29353.9707 29493.0391
720706.4881 21137.0574 23381.0249 23275.6543 25716.8788 25890.2606
821056.3736 21382.9255 21574.7879 21557.5235 26851.9289 26712.6437
922075.9397 22008.6282 24479.3131 24386.4498 27062.0237 26806.523
1024070.1411 24079.5484 25009.5776 24971.7702 28009.5803 28335.006

The training data with the influence of noise for two-storey shear structure in TFN form for five sets of data have been presented here. Accordingly, Figures 8(a) and 8(b) refer the fuzzy plot of frequency. Moreover, the Triangular Fuzzy Number (TFN) plots of identified stiffness are cited in Figures 9(a) and 9(b). Also for different alpha values such as , and , the comparison between the desired and ANN values with another five sets of data has been given in Tables 7(a), and 7(b), and 7(c).

(a)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des)

1 109470 109250 124660 123870 63676 63908 81668 81670
2 119370 119420 141760 141590 59687 59772 79075 78865
3 141840 141880 154360 154170 63017 63149 77680 77561
4 126590 126380 179820 178510 58265 57879 84888 87763
5 143790 143950 160360 160670 61323 61256 90425 90743

(b)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des)

1 111790 111390122640121830 66536 66826 79388 79513
2 125300 125280141300141110 62124 62253 75972 75891
3 144990 144970153930153750 65795 65976 76269 76271
4 131130 130750169150167990 59057 58865 78073 80211
5 145180 145390157010157330 63632 63541 84419 84602

(c)

Data number (Ann) (Des) (Ann) (Des) (Ann) (Des) (Ann) (Des)

1 115270 114590 119610 118770 70827 71203 75968 76278
2 134200 134070 140600 140400 65779 65975 71318 71430
3 149710 149600 153290 153110 69963 70218 74153 74336
4 137940 137310 153150 152200 60244 60344 67851 68882
5 147270 147540 152000 152320 67096 66967 75411 75392

7. Conclusion

Here, the procedure is demonstrated to identify stiffness parameters for multistorey shear structure using fuzzified data in ANN. The present study considers example problems of one-, two-, five-, and ten-storey shear structures. Identification study for five- and ten-storey shear structures has been done with crisp data. Then, fuzzified data has been considered for one- and two-storey shear structures for the present identification procedure. Initial design parameters, namely, stiffness and mass and so the frequency of the said problem is known in term of fuzzy numbers. The engineers want to know the present health of the structure by system identification methods. It is assumed that only the stiffness is changed and the mass remains the same. The present values of the frequencies may be obtained by available equipments, and using these, one may get the present parameter values by ANN. So, if sensors are placed to capture the frequency of the floors in fuzzy (uncertain) form, then, those may be fed into the proposed new ANN model to get the present stiffness parameters. The methods of one- and two-storey shear structures with fuzzified data may very well be extended for higher storey structures following the present procedure. As regards the influence of noise, it may be seen that the input and output data for two-storey shear structure are actually in terms of Triangular Fuzzy Number (TFN) which themselves dictate the noise in both monotonic increasing and decreasing senses. In order to train the new ANN model, set of data are generated numerically beforehand. As such, converged ANN model gives the present stiffness parameter values in fuzzified form for each floor. Thus, one may predict the health of the structure. Corresponding example problems (as mentioned) have been solved, and related results are reported to show the reliability and powerfulness of the model.

Acknowledgments

The authors would like to acknowledge funding from the Ministry of Earth Sciences, New Delhi, India. They are also thankful to the anonymous reviewers for their valuable suggestion to improve the paper.

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Copyright © 2013 Deepti Moyi Sahoo and S. Chakraverty. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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