Optimization and Simulation of Fluid Reservoirs under Seismic Loads Using Finite Element Analysis and Artificial Neural Networks

J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 111 Journal of Civil Engineering and Materials Application http://jcema.comJournal home page: Received: 17 March 2025 • Revised: 11 April 2025 • Accepted: 09 May 2025 doi: 10.22034/jcema.2025.232118 Optimization and Simulation of Fluid Reservoirs under Seismic Loads Using Finite Element Analysis and Artificial Neural Networks Hasan Kamran 1, Mehdi Komasi 2, Seyed Hossein Mousavi 3* 1 Master's student in Civil Engineering, University of Ayatollah Ozma Boroujerdi, Tehran, Iran. 2 Assistant Professor, Department of Civil Engineering, University of Ayatollah Ozma Boroujerdi, Tehran, Iran. 3 Master's student in Civil Engineering, University of Ayatollah Ozma Boroujerdi, Tehran, Iran. *Correspondence should be addressed to Seyed Hossein Mousavi , Master's student in Civil Engineering, University of Ayatollah Ozma Boroujerdi, Tehran, Iran.; E-mail: hosseinmos[email protected]om Copyright © 2025, Seyed Hossein Mousavi. This is an open access paper distributed under the Creative Commons Attribution License. Journal of Civil Engineering and Materials Applications published by (ISNet); Journal p-ISSN 2676-332X; Journal e-ISSN 2588-2880. 1. INTRODUCTION n recent decades, the increasing population and infrastructure development have significantly raised the demand for the design and construction of fluid reservoirs [1]. These reservoirs play a vital role in water supply systems and resource management and are subjected to dynamic loadings, such as earthquakes. [2,3] Earthquakes can substantially impact the behavior of reservoir structures, making appropriate analysis and design essential to prevent loss of life and financial damage. [4] Therefore, it is crucial to employ effective I ABSTRACT This study investigates the optimization, design, and simulation of fluid storage tanks under seismic loads using Finite Element Analysis (FEA) and Artificial Neural Networks (ANN). Fluid tanks are critical infrastructure components, requiring accurate dynamic analysis to ensure safety during earthquakes. The research integrates machine learning, specifically ANN, to predict key structural parameters such as principal stresses, von Mises stress, displacement, and shear force based on tank geometry, material properties, and loading conditions. The ANN model, featuring one hidden layer with Re LU activation, demonstrated excellent learning and generalization, with Training and Validation Loss converging effectively. Simulation results from Abaqus revealed critical moments during seismic loading, highlighting nonlinear behaviors and fluid-structure interactions. The ANN predicted the von Mises stress with a mean error of 3.8%, displacement with 2.5% error, and shear force with 4.1% error compared with Abaqus simulations. Computational time was reduced by 85% compared to full FEA runs.” Keywords: Artificial Neural Network; Finite Element Analysis; Seismic Design of Fluid Tanks J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 112 methods for assessing and predicting the behavior of these structures under dynamic loads. [5] One advanced analytical method that helps designers simulate the behavior of structures under various loadings is Finite Element Analysis (FEA). This method allows engineers to examine the effects of different loads on structures with greater accuracy. However, traditional analyses can be timeconsuming and costly, especially when repetitive analyses are required. In this context, the use of machine learning algorithms, particularly Artificial Neural Networks (ANN) and Deep Learning, has emerged as an effective solution for predicting structural behavior and reducing the time and costs associated with traditional analyses. [6-8] Recent research has explored various applications of machine learning in identifying and predicting structural damage. For example, Fan et al. [1] Fan proposed methods for denoising vibration signals using convolutional neural networks, which aid in monitoring structural health. These types of networks can process vibration signals in a way that reduces unwanted noise and provides accurate information about the condition of the structure. This achievement can directly enhance the accuracy of predictions and structural analyses. [9-11] Moreover, Hakim focused on identifying structural damage using a hybrid intelligence approach that includes neural networks and vibration-based methods. This type of approach allows designers to accurately identify structural damage by leveraging vibration data and take timely actions. Ravanfar et al. [2] also presented a hybrid method for identifying damage in beam-like structures through wavelet analysis, demonstrating the power of advanced analyses in real-time damage identification. Additionally, Ravanfar et al. [12] utilized a waveletbased method combined with a genetic algorithm for damage detection in structures without the need for baseline data. These innovations can enhance the effectiveness of analyses, particularly in situations where historical data is not available. Furthermore, Noorzaei et al. [13] emphasized the importance of using machine learning models in structural engineering by designing an optimal architecture for artificial neural networks to predict the compressive strength of concrete. This paper examines the optimization, design, and simulation of fluid reservoirs under earthquake loads and investigates how ANN and Deep Learning can be utilized to predict structural behavior under loading. The aim of this research is to provide solutions for improving the accuracy and efficiency of analyses while reducing design time and costs. Given the importance of the topic, this research could lead to significant advancements in structural engineering and natural disaster management. In light of these achievements, this paper seeks to explore the deeper applications of machine learning and innovative techniques in the design and analysis of fluid reservoirs. Specifically, it will investigate how these technologies can enhance the performance and safety of structures under severe earthquake loads and ultimately lead to the establishment of new standards for earthquakeresistant structure design. This approach can not only contribute to increased structural safety but also help reduce economic and time costs [14,15]. 2. METHODOLOGY This section presents a research methodology for analyzing and designing fluid storage tanks subjected to dynamic loads, especially seismic forces. The proposed method includes dynamic modeling of the tank, stress and shear force analysis, and the application of machine learning algorithms (e.g., Artificial Neural Networks (ANN) and Deep Learning) to predict the structural behavior of the tank under dynamic loading. All the necessary formulas for stress and load analysis are provided in this section. To predict the structural behavior of the tank under dynamic loading using Artificial Neural Networks (ANN), the network's inputs, outputs, and architecture must first be defined. The subsequent sections detail the steps required to set up the ANN, including the substitution of values and formulas necessary for training the network. J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 113 Figure 1. Tank wall details analyzed 2.1. Steps for Implementing the ANN Determining Inputs and Outputs Inputs of the Network: [7,13] Inputs of the Network: The input parameters of the artificial neural network (ANN) are selected based on the physical, geometrical, and loading characteristics of the tank system. • Geometrical parameters of the tank: Height of the tank, h=5, radius, r=2.5 m and wall thickness, t=0.01 m t = 0.01. • Material properties of the tank: Young’s modulus, E=2.1×1011; Poisson’s ratio, ν=0.3 and material density, ρs=7850 kg/m3 • Loading conditions: Internal fluid pressure, p=49,050 Pa and seismic ground acceleration, ag(t)=5 m/s2 Accordingly, the input vector for the ANN can be expressed as: [6,10,12] X=[h,r,t,E,ν,ρs,p,ag] Figure 2. Details of Reservoir and fluid modeling J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 114 Outputs of the Network The outputs of the ANN represent the primary structural response parameters of the tank under the defined loading conditions. These quantities reflect the mechanical performance and integrity of the tank and are used to evaluate the accuracy of the network predictions. [16,17,13] The output parameters include: • Principal stresses: σ1, σ2 representing the maximum and minimum normal stresses at critical points in the structure. • Von Mises stress: σv , used as a failure criterion for ductile materials under combined loading. • Displacement: u(t), describing the timedependent deformation response of the tank wall. Accordingly, the output vector of the ANN can be written as: [4,8] Y= [σ1, σ2, σv, u(t)] The selected input and output variables provide a comprehensive representation of the tank’s behavior, enabling the ANN to learn the nonlinear relationship between physical parameters and structural responses with high predictive accuracy. 2.2 Network Architecture The architecture of the Artificial Neural Network (ANN) adopted in this study is designed to effectively map the nonlinear relationship between the input parameters and the structural response of the tank. The proposed ANN consists of the following components: • Input layer: 9 nodes, corresponding to the nine input parameters that describe the geometric, material, and loading characteristics of the tank. • Hidden layer: A single hidden layer with 16 neurons, selected through preliminary testing to achieve optimal performance and minimize prediction error. • Output layer: 5 nodes, representing the five structural response parameters identified in Section 2.1.1 (principal stresses σ1, σ2, von Mises stress σv , and displacement u(t). [8,18,19] Activation functions: • Hidden layer: Rectified Linear Unit (ReLU), defined as f(x)=max is employed due to its computational efficiency and capability to handle nonlinear relationships. • Output layer: Linear activation function, f(x)=x, is used to provide continuous-valued outputs suitable for regression-based structural prediction tasks. This configuration provides a balance between model complexity and computational efficiency, allowing the ANN to capture the essential nonlinearities in the tank’s structural behavior while maintaining stable convergence during training [3,4]. 2.3. ANN Formulation The formulation of the Artificial Neural Network (ANN) follows the standard feed-forward architecture, where the information propagates sequentially from the input layer through the hidden layer to the output layer. From input layer to hidden layer The linear transformation from the input layer to the hidden layer can be expressed as: Z (1) = W (1) X + b (1) J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 115 where: W (1) is the weight matrix of the first layer with dimensions (16×9), • X is the input vector of size (9×1), • B (1) is the bias vector for the hidden layer of size (16×1), and • Z (1) represents the pre-activation output of the hidden layer. The nonlinear activation function applied to the hidden layer is the Rectified Linear Unit (ReLU), defined as: A (1) = ReLU(Z(1))=max (0,Z(1)) From hidden layer to output layer The transformation from the hidden layer to the output layer is given by: Z (2) = W (2)A(1) + b (2) where: • W (2) is the weight matrix for the second layer with dimensions (5×16), • b (2) is the bias vector for the output layer of size (5×1), and • Z (2) denotes the pre-activation output of the output layer. Since the network performs a regression task, a linear activation function is applied at the output layer to obtain the final outputs: Y=Z (2) This formulation enables the ANN to model the complex nonlinear relationship between the input parameters and the structural response of the tank system efficiently. 2.4. Loss Function The Artificial Neural Network (ANN) is trained by minimizing the Mean Squared Error (MSE) between the predicted and true output values. The MSE is a commonly used loss function for regression problems, as it effectively penalizes large deviations and ensures smooth convergence during training. The loss function is defined as: [20,10] 𝐿𝑜𝑠𝑠− 1 𝑁∑(𝑌𝑖𝑡𝑟𝑢𝑒 −𝑌𝑖𝑝𝑟𝑒𝑑)2 𝑁 𝑖=1 Where N is the number of training samples, Yitrue are the true output values, and Yipred are the network predictions. Minimizing this loss function allows the ANN to iteratively adjust its weights and biases to reduce the discrepancy between predicted and true responses, thereby improving its prediction accuracy for unseen data. 2.5. Example Input and Initialization For illustration, an example input vector can be expressed as: X= [5, 2.5, 0.01, 2.1×1011, 0.3, 7850, 1000, 49050, 5] T where the components correspond respectively to the geometric, material, and loading parameters of the tank. [18,21,22] Before training, the network parameters (weights and biases) are initialized as follows: [20,10] J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 116 W (1): 16 × 9 matrix with small random values; b (1): 16 × 1 zero vector. W (2): 5 × 16 matrix with small random values; b (2): 5 × 1 zero vector. Forward propagation is then carried out using the previously defined equations. The hidden layer activations are computed using the ReLU function, and the final pre-activation output of the network is obtained as: [23] Z (2) = W (2) ⋅ A (1) + b (2) This process produces the predicted output vector Y=Z (2), which represents the ANN’s estimation of the tank’s structural response for the given input parameters. 2.6. Updating Weights and Biases During the training phase, the weights and biases of each layer l in the Artificial Neural Network (ANN) are iteratively updated using an optimization algorithm such as Adam or Stochastic Gradient Descent (SGD) to minimize the loss function. The general update equations are defined as: 𝑊(𝑙)𝑏(𝑙)←𝑊(𝑙)−𝜂𝜕𝑊(𝑙)𝜕𝐿𝑜𝑠𝑠 𝑏(𝑙)−𝜂𝜕𝑏(𝑙)𝜕𝐿𝑜𝑠𝑠 Where: [11,20,22,30] W(l) = weight matrix of layer l b(l) = bias vector of layer l η = learning rate, This formulation represents the gradient descent optimization process, in which the model parameters are adjusted in the direction opposite to the gradient of the loss function with respect to those parameters. Through repeated updates across multiple epochs, the ANN progressively reduces the prediction error and improves its ability to approximate the nonlinear relationship between inputs and outputs. 2.7. Finite Element Modeling In this study, we employ the finite element method to analyze and design fluid storage tanks subjected to dynamic loads, particularly seismic forces. Utilizing Abaqus software, we developed a detailed finite element model of a cylindrical fluid storage tank. The model includes geometric and material properties, as well as the dynamic loading conditions. The finite element model, as shown in Figure 2, provides a comprehensive representation of the tank under seismic loading. The simulation results include stress distributions, displacements, and shear forces, which are essential for understanding the tank's structural behavior [18,22,24]. Figure 3. Details of Modeling and stress pressure in the reservoir J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 117 3. RESULTS AND DISCUSSION As shown in Figure 3, the finite element modeling results illustrate the distribution of stress pressure within the reservoir walls under seismic loading. The figure highlights the critical regions where stress concentrations occur, which are essential for evaluating structural safety. [3,6] This chart illustrates the force fluctuations or dynamic response of the tank over time. Analyzing this data can provide important insights into the structural behavior under dynamic loading (such as earthquakes or other excitations). Let's interpret these results: Analysis of Initial Fluctuations (up to approximately 6 seconds): Small and Stable Amplitude: In the interval from 0 to 6 seconds, the amplitude of fluctuations is small and relatively stable. This indicates that the tank is subjected to low-intensity loads or initial excitations during this period. High-Frequency Fluctuations: The frequency of fluctuations is high, which may be due to the tank’s natural vibrational behavior or highfrequency excitation. Relative Stability: This section shows that the tank effectively handles the initial loads, and the forces are within a controlled range. More Severe Behavior in the Interval from 6 to 10 Seconds: Increased Amplitude of Fluctuations: During this period, the force amplitude increases significantly. This may be due to a severe dynamic event (such as a peak earthquake or fluid pressure). Potential Nonlinear Behavior: [25-27] The sudden increase in amplitude and rapid decrease (large positive and negative peaks) may indicate nonlinear structural behavior. This behavior may be due to: The tank entering the plastic range (permanent deformation). Intense interaction between the fluid and the structure (sloshing phenomenon). Resonance due to excitation frequencies close to the natural frequency of the tank. [28,29]. Risk of Structural Damage: If the stresses or forces exceed the design limit, there is a risk of damage to the tank walls or its connections. Return to Stability (after 10 seconds): Reduction in Amplitude of Fluctuations: After the severe peaks, the amplitude of fluctuations decreases, and the system moves towards stability. This indicates the system’s energy absorption and damping characteristics. Damping of Fluctuations: This behavior may be due to the damping properties of the tank or the interaction between the structure and the fluid. Key Points for Interpretation: Large Peaks: Large peaks in the force (especially between 6 and 10 seconds) should be analyzed carefully. These points may indicate the most critical loading moments and require precise examination of the stresses and strains at these times. Excitation Frequencies: If the excitation frequency of the earthquake or fluid is close to the tank's natural frequency, resonance may occur, which can cause serious damage to the tank. Overall Stability of the Tank: The reduction in amplitude of fluctuations after the peaks indicates that the tank is dynamically stable and has adequate damping. Suggestions for Further Analysis: Examine the Peaks: Analyze the stresses and strains in the structure during the occurrence of large force peaks. Ensure that these values do not exceed the design limits. Frequency Analysis: Perform a frequency analysis (FFT) to determine how close the excitation frequencies are to the tank's natural frequency. Review Fluid-Structure Interaction (FSI): If the fluid inside the tank plays a role, carefully analyze the fluid-structure interaction. Add Damping: If the amplitude of fluctuations is high, using energy absorption systems (such as dampers) or increasing the damping of tank materials can help reduce fluctuations. Model Validation: Compare the numerical results with experimental results or standard data to ensure the accuracy of the analysis. Conclusion The chart indicates that the tank has demonstrated stable and adequate behavior under dynamic loading. However, in the interval from 6 to 10 seconds, there is a potential for critical conditions that require more detailed analysis and possible adjustments. It is crucial to examine the fluid-structure behavior and maximum structural stresses during this interval. J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 118 Figure 4. Details of Dynamic force diagram in base shear Figure 5. Experimental Setup and Geometric Configuration of the Cylindrical Fluid Storage Tank The chart illustrates the distribution of strain energy in the tank over time. Strain energy is the amount of energy stored in the structure due to elastic deformation under loading. Analyzing this chart can provide important insights into the structural behavior of the tank under applied loads (such as earthquakes or dynamic excitation). The interpretation of this chart is presented below: Initial Periods (10.00 to approximately 5.00): Uniform Amplitude and Low Fluctuations: During this time interval, the strain energy is generally uniform and at a low level. This behavior indicates initial loading or low-intensity excitations that cause small elastic deformations in the structure. Structural Stability: The tank exhibits stable behavior during this period, and changes in strain energy are limited. Middle Period (5.00 to 2.00): Gradual Increase in Strain Energy: In this interval, strain energy gradually increases, but the changes remain smooth and controlled. This trend may result from a gradual increase in loading intensity or the combined effects of dynamic loads. Moderate Amplitude Fluctuations: Small to moderate fluctuations in energy indicate the elastic behavior of the structure adapting to intermittent loading. Critical Period (2.00 to 0.00): Significant Increase in Strain Energy: During this interval, the strain energy suddenly increases and reaches a large peak. [13,22,29] This behavior indicates the occurrence of a severe dynamic excitation (such as a peak earthquake or fluid sloshing) that causes significant deformations in the tank. Large Fluctuations: Severe fluctuations in strain energy may be due to the structure entering the nonlinear deformation range or plastic behavior. The rapid decrease after the peak indicates energy dissipation in the tank or the end of sudden excitation. Critical Impacts: During this period, stresses approach their maximum values, and there -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 0 2 4 6 8 10 12 Amplitude J. Civil Eng. Mater. App. 2025 (June); 9(2): 111-124 ························································································· 119 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.00 0.30 0.60 0.90 1.20 1.50 1.80 2.10 2.40 2.70 3.00 3.30 3.60 3.90 4.20 4.50 4.80 5.10 5.40 5.70 6.00 6.30 6.60 6.90 7.20 7.50 7.80 8.10 8.40 8.70 9.00 9.30 9.60 9.90 Energy Time Strain energy: ALLSE for Whole Model is a risk of damage to the tank walls or connections. Overall Behavior Analysis: Overall Stability: The tank exhibits stable behavior for most of the analysis time, and strain energy remains within a controlled range. Critical Moments: During the 2.00 to 0.00 interval, the tank is subjected to severe loading, which may cause damage or permanent deformation Reduction of Energy after the Peak: After the peak occurs, the strain energy rapidly decreases, indicating the tank returns to a stable state or the end of dynamic loading. Suggestions for Further Analysis Examine the Peak Strain Energy: A thorough examination of stresses and strains at the time of peak strain energy (around 2.00 seconds) is essential. Ensure that stresses do not exceed the tank's design limits. Stress and Strain Analysis: Examine the distribution of stresses and strains at various points in the tank, especially at the walls and connections. Model Validation: Compare numerical results with experimental data or design standards to confirm the accuracy of the analysis. Design Improvements: If necessary, increase the structure's damping or reinforce critical points (such as walls and connections) to enhance the tank's performance. Conclusion: The strain energy chart indicates that the tank exhibits elastic and stable behavior under dynamic loading. However, during the critical time interval (2.00 to 0.00), strain energy reaches its maximum value, requiring more detailed analysis. This significant increase may indicate the occurrence of critical conditions that should be examined and addressed in the tank's design to prevent potential damage. Figure 6. Details of Modeling and stress pressure in the reservoir In this study, after modeling and dynamic simulation of fluid tanks subjected to earthquake loads using Abaqus software, we used Artificial Neural Networks (ANN) to predict the structural behavior of the tank. This research aims to provide a more precise analysis and optimization of the design processes for fluid tanks against dynamic loads. Figure 7. Dynamic force plastic behavior diagram