Neural Network Software for Dam-Reservoir-Foundation Interaction

International Conference on Intelligent Computational Sstems (ICICS') Jan. 7-, Dubai Neural Network Software for Dam-Reservoir-Foundation Interaction Abdolreza Joghataie, Mehrdad Shafiei Dizai, Farzad Shafiei Dizai Abstract A software has been developed to use artificial neural networks (ANNs) for the modelling of nonlinear hsteretic response of concrete gravit dams under earthquake loading when reservoir and foundation interactions are included. The neural network which is designed for a given dam has been called the "Neuro-modeller" of that dam. Pine flat dam has been studied as example problem. Firstl using an analsis software, the dam has been analzed under different earthquakes to collect a large number of data for training the "Neuro-modeller" which has then been used for the analsis of the dam under other earthquakes. Numerical tests using other earthquakes have been done to verif the capabilities of the neuromodeller, all of which have been successful. Kewords Concrete gravit dam, Dam-Reservoir-Foundation Interaction, Hsteresis, Neuro-modeller, Nonlinear response. M I. INTRODUCTION ODELLING complicated nonlinear hsteretic response behavior of concrete gravit dams, under earthquake and hdrodnamic loading due to the impact of earthquake on reservoir when water and foundation interaction has been included, has been considered of great importance []-[].Various tpes of mathematical models for numerical nonlinear hsteretic analsis of concrete gravit dams have been presented [7]-[5]. Although considering dam-reservoir-foundation interaction will lead to greater accurac in the result, it makes the nonlinear analsis more complicated and time-consuming. An aim of this stud has been to decrease the time required for the analsis. Another disadvantage of numerical methods in analzing concrete gravit dams is their poor accurac. Another purpose of this stud has been to investigate the possibilit to use neural networks to enhance the precision. A new neural network is designed and trained which is called neuro-modeller. In this new neural network there is no need to define nonlinear parameters or different nonlinear models for concrete neither to model dam-reservoirfoundation interaction in that the neural network learns the dnamic nonlinear behavior of the dam and works similar to Abdolreza Joghataie is Associate Professor in Civil Engineering Department, Sharif Universit of Technolog, Azadi Avenue, Tehran, Iran (corresponding author, e-mail: oghatae@sharif.edu). Mehrdad Shafiei Dizai is Former Graduate Student in Civil Engineering Department, Sharif Universit of Technolog, Azadi Avenue, Tehran, Iran. (email: mehrdad_shafiei@ahoo.com). Farzad Shafiei Dizai is Former Graduate Student in Civil Engineering Department, Iran Universit of science &Technolog, Tehran, Iran. the numerical analsis software to estimate the dam behavior from the input it receives about the past response of the dam. The results obtained from dnamic analsis b the neuromodeler of Pine Flat dam have been compared with the results obtained from the finite element software, NSAG-DRI []. The comparison has proven the noteworth potential of neural networks in learning and analzing the nonlinear dnamic behavior of Pine Flat dam. II. SMEARED CRACK MODEL For numerical modeling of the nonlinear hsteretic behavior of concrete gravit dams, NSAG-DRI software and smeared crack model have been used. Figure shows the basics of analsis b this method []-[]. Fig. Smeared crack model, (a) smeared crack in pine flat concrete gravit dam after it has been subected to El Centro earthquake, (b) Stress-strain diagram and damage energ, (c) Hsteretic loading and unloading in stress-strain curve (drawn based on []), (d) profile of deformation under El Centro earthquake, (e) A -node element in the smeared crack model []-[]. III. ARTIFICIAL NEURAL NETWORKS Neural networks are parallel processing sstems developed based on our knowledge about how the natural brain functions. Figure shows the general structure of a multi laer feed forward neural network (MLFFNN) composed of several processing units called neurons. Ever neuron acts as a processor. Neurons are attached to each other b wire-like connections. The nodes in a laer are attached to the nodes in their neighboring laers. The variable coefficients are called connection weights. The first laer on the left is called the input laer and the last laer is called the output laer. There are man references on the theoretic principles and application 9

International Conference on Intelligent Computational Sstems (ICICS') Jan. 7-, Dubai of neural networks, []-[7]. Also there is a vast number of works on the application of neural networks in structural engineering such as []-[]. (a) Fig. Architecture of a MLFFNN IV. THE FINITE ELEMENT MESH USED IN NUMERICAL MODELING OF DAMS NSAG-DRI is a software developed for two dimensional finite element numerical nonlinear dnamic analsis of concrete gravit dams. Fig. 3 shows the finite element mesh used for Pine Flat, dam considering dam-reservoir-foundation interaction []. (b) Fig. Crack profiles for Pine Flat dam from different earthquakes: (a) El Centro, (b) Taft VI. NONLINEAR DYNAMIC ANALYSIS OF CONCRETE GRAVITY DAMS The nonlinear dnamic analsis of Pine Flat dam considering dam-reservoir-foundation interaction has been conducted b using NSAG-DRI under near-field and far-field earthquakes of various frequenc content. The aim has been to show that the "neuro-modeller" can successfull work in ver complex nonlinear conditions. Fig. 3 Cross section of Pine Flat dam and corresponding finite element mesh for its analsis V. CRACK PROFILE AND PROPAGATION IN DAMS After nonlinear analsis of Pine Flat dam under a number of different earthquakes, their crack profiles have been as shown in Figure. A. Nonlinear Analsis Dnamic nonlinear analsis of the dam has been carried out under a white noise earthquake for seconds. The time histor of white noise earthquake acceleration used in the training of the neuro-modeler has been as shown in Figure 5. Acceleration (g)... -. -. -. 5 5 time (sec) Fig. 5 Time histor of White noise earthquake Also seconds of the results of dnamic nonlinear response of Pine Flat dam under the white noise earthquake has been shown in Figure a. The output has been used to train the neuro-modeller. Also Pine Flat dam has been analzed under different tpes of earthquakes including El Centro, Taft and Corrolitos. The analsis of nonlinear 3

International Conference on Intelligent Computational Sstems (ICICS') Jan. 7-, Dubai response for the displacement of crest of the dam under different tpes of earthquakes has been as shown in Figures b to d. 7 5 3 - - - - - White Noise earthquake Taft earthquake (a) (b) Finite Element Analsis Neural Network laer, sigmoid function neurons have been used. The activation function of the input and output nodes has been linear. Input nodes: The input vector has included: i = displacement of the crest of the dam at time step i, i = velocit of the crest of the dam at time step i, i=,,,, and X = the histor of earth acceleration. Output nodes: the output laer has contained the displacement and velocit at the end of the time step. The total number of input nodes has been. The output vector has included: i+ = displacement of the crest of the dam at time step i+, = velocit of the crest of the dam at time step i+. i+ - - - (c) El Centro earthquake 7 5 3 - - -3 Corrolitos earthquake (d) time (sec) Fig. comparing results of nonlinear analsis b neuron-modeller and finite element method when the dam has been subected to: (a) White Noise, (b) Taft, (c) El Centro and (d) Corrolitos earthquakes. VII. DESIGN OF NEURO-MODELLER First the neuro-modeler has been designed and then evaluated. Because the input-output data has been nonlinear, sigmoid function has been used for the activation function of the hidden neurons of the neural network. A. Determination of architecture Training of the neuro-modeler is carried out b means of the back propagation algorithm. The input-output vectors for designing the neuro-modeler have been obtained through numerical analsis of finite element b NSAG-DRI software under a white noise earthquake. The criterion to stop the training of the neural network has been the mean square error (MSE). Designing a neural network b trail and error is as detailed in Figure 7. The neuro-modeler is composed of input and output laers and a hidden laer. The number of input and output nodes has been 5 and, respectivel. In the hidden Fig. 7 Neuro-modeller architecture VIII. NEURO-MODELLER AND MODELLING HYSTERETIC BEHAVIOR OF DAMS Multi laer feed forward neural network with back propagation algorithm has static structure in nature and it has limited capabilit to learn nonlinear records. Hence the suffer from disadvantages, because in such neural networks there is no internal memor. Multi laer feed forward neural networks (MLFFNN) are not capable of modeling and learning hsteretic cclic behavior because the lack memor. For a neural network to learn hsteretic ccles it should have a memor. Two forms of memories can be considered for the neural networks: first, a memor located inside the neuron and second, to provide a side memor b feeding back information from the output to the input of the neural network [5]-[]. In this stud the second form, i.e. providing a side memor for the network has been used. IX. TRAINING OF NEURO-MODELLER To train the neuro-modeller b means of data obtained from the result of analsis b finite element method, seconds of the analsis results b NSAG-DRI software, under a white noise earthquake with the intervals of.s, has been used. 3

International Conference on Intelligent Computational Sstems (ICICS') Jan. 7-, Dubai On the other hand, to train the neuro-modeler the input-output pairs have been generated based on the data collected from the analsis of the dam, using NSAG-DRI software under the white noise earthquake acceleration. To generate the training pairs, Δt=.s was selected. As a result, the number of input-output pairs to train the neuro-modeler has been. Hence the analsis time and sampling periods have been and. seconds respectivel. The neuro-modeller has been trained on the information gained from the nonlinear analsis of Pine Flat dam under the white-noise earthquake. Graphs for the training error of the neuro-modeler have been drawn in Figure, where the horizontal axis represents the number of training ccles and the vertical axis refers to the mean square error (MSE). After training ccles, the error converges to.. To calculate the error of the neural network, Equation has been used. In this equation, N stands for the number of training pairs, is for the target value and shows the amount obtained from the neural network [9]-[]. The obective function to be minimized is the Mean Square Error (MSE) following Equation : N MSE = = ( ) () N where MSE = Mean Square Error of training or testing. Mean Square Error (MSE).E-.E-.E-3 White noise earthquake.e- 5 5 Training ccles Fig. MSE (Mean Square Error) of training versus training ccles. X. ANALYSIS BY MEANS OF NEURO-MODELLER The trained neuro-modeller has been able to analsis the dam response, so that at each time step, onl inputs about the earthquake excitation has been needed. Figure 9 shows schematicall the analsis algorithm where and refer to displacement and velocit of the crest of the dam at the beginning of analsis. XI. TESTING DESIGNED NEURO-MODELLER After the training has been over and its successful learning under white noise earthquake, the neuro-modeller has been tested on a number of other earthquakes including El Centro, Taft and Corrolitos, where predictions b the neuro-modeler have been compared with the target values. The neuromodeller has been evaluated under different tpes of earthquakes with various frequenc content. The predictions have been recorded throughout the time. The output of the neuro-modeler has been fed back to the neuro-modeler to be used in the prediction of the next time step. The result obtained from the analsis b means of the neuro-modeller and numerical method of finite element has been shown in Figure b dotted and solid lines respectivel. As Figure shows, the neuro-modeller has analzed the concrete gravit dam successfull under different tpes of earthquakes. XII. CONCLUSION In this stud, a new software has been presented for dnamic analsis of concrete gravit dams with nonlinear behavior b taking into account the dam-reservoir-foundation interaction. Multi laer feed forward neural networks have been used for dnamic analsis of dams. Because of the training abilit of neural network sstems there is no need to specif the dnamic parameters of the dam and/or to specif basic prperties of the nonlinear model. To approve the efficienc of this method, Pine Flat dam with nonlinear behavior has been analzed under various tpes of earthquakes as well as b means of the new neural network based method. A neuro-modeller has been trained and then used to analze the dam under different earthquakes. The results have been compared with the results from using NSAG-DRI software where it has been shown that the neuromodeller has been capable of providing results similar to those of NSAG-DRI. However once the neuro-modeller has been trained, it could analze the dam under other earthquakes in a considerabl much lower time. Fig. 9 Schematic presentation of using "Neuro-modeller" in analsis of Pine Flat dam Technolog for partiall supporting this research. ACKNOWLEDGMENT The writers would like to thank the deput of higher education and deput of research of Sharif Universit of 3

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