Computational Predictions for Predicting the Performance of Structure

Introduction

Fire is one of the possible scenarios for all structures, especially after an earthquake. The structural strength is reduced during fire by increasing the temperature; thus, the analysis of the structural behavior subjected to fire is one of the important topics in structural engineering. The analysis of structural elements against fire and post-fire earthquake for each structural element in detail can be done using FEA; however, these types of analysis by FEM take a long time because of their complexity. For this issue, prediction models, such as regression models, Gene Expression Programming (GEP), Machine Learning (ML) methods, Deep Learning (DL) methods, hybrid models, and ensemble models, can be used to save time and cost of calculation. Furthermore, using the prediction models, by changing the time of fire, temperature, and loading, the new design parameters can be selected. On the other hand, the results of the analyses can be used for many designs. In addition, using a prediction model, the optimized design can be estimated. This project will utilize three distinct methods, each of which will be the subject of a separate workshop.

What is the effect of fire on the structural behavior?

The possibility of fire is related to many factors; however, one of the possible scenarios refers to the fire after an earthquake because of a breaking in the electricity and gas pipe. The steel elements of the structure lose their strength at high temperatures, especially after 600 ^oC.  For reinforced concrete (RC) members and composite structures, the losing in strength occurs later than the steel structures. In other words, the concrete and cover of the reinforcement bar play the role of protection for steel and reinforcement bars, respectively.

Why conduct a parametric study?There is no specific standard, equation, reference book, or design book for the simulation of the steel and RC element subjected to fire and post-fire earthquake. The references suggested the material behavior only for the steel and concrete at rising temperatures. As a result, the simulation of structural elements subjected to fire and post-fire earthquake is a complex analysis and needs significant time and cost for simulation. There are many design parameters that influence the performance of steel and RC elements subjected to fire and post-fire earthquake; therefore, many samples should be simulated with various design parameters to specify the effect of the design parameters on the sample behavior, although using some method, like , the number of samples can be decreased. The Taguchi method is used by SPSS software.

How many samples should be simulated?

The number of samples is related to the number of design parameters and their levels that should be changed in the study. The levels can be specified according to requirements, reality, and standards. For example, the required sample numbers for a parametric study with four six variables should be at least 729 samples. The design parameters include the dimensions of structural elements, strength of steel and concrete, ratio of steel reinforcement bars, temperature, time of fire, and static and dynamic loads.

Simulating samples using FEA with ABAQUSABAQUS is a strong software for the simulation of complex problems by FEA, especially for multi-loading conditions. To simulate composite castellated steel bars, RC connections, and steel connections, the members of the structure should be defined and simulated truly. After developing and validating the FEA model, the samples, which are specified in the last section, should be simulated and analyzed. The Johnson-Cook model is used for the simulation of the steel plate. Von Mises is used in the simulation of the samples. Von Mises stress is a value used to determine if a given material will yield or fracture. It is mostly used for ductile materials, such as metals. The von Mises yield criterion states that if the von Mises stress of a material under load is equal to or greater than the yield limit of the same material under simple tension, then the material will yield. Overall, 180 composite castellated steel beams under static loads and fire, 63 steel connections under post-fire earthquake, and 132 RC connections under post-fire earthquake are simulated using ABAQUS.

Simulating FEA results using Artificial Intelligence (AI)

In recent years, prediction approaches have been developed to present alternative computational methods with lower costs and time in calculation. In addition, by these methods, the optimal design can be specified quickly, and the behavior of all design parameters can be analyzed in a second instead of a complex and long analysis. The surrogate models, which are present in this package, include regression models, Gene Expression Programming, adaptive network-based fuzzy inference system (ANFIS), and ensemble models. The ensemble model is a combination of some models that keep some features of their single models. The FEA dataset includes training datasets and testing datasets that should be specified randomly. After training the models using the training datasets, the models should predict the behavior of composite castellated steel beams under static loads and fire, the steel connections under post-fire earthquake, and the RC connections under post-fire earthquake. All models can be compared based on the time and cost of calculation and accuracy. However, the accuracy of models is compared by the statistical parameters and error terms that include the coefficient of determination, root mean square error (RMSE), normalized square error (NMSE), fractional bias, maximum positive error, maximum negative error, distribution of errors, and mean absolute error. MATLAB is used for this part.

Method 1: Using SPSS to generate the samples with various parameters

The samples and the variation in design parameters should be logical and based on the standards and reality. To optimize the number of samples for simulation, the Taguchi approach is used by .

Method 2: Using ABAQUS to validate a FEA model and simulation of all models

ABAQUS is used to validate an FEA model. To validate a sensitivity analysis should be conducted. After that, using the validated FEA model, the behavior of samples subjected to fire or post-fire earthquake is simulated.

Method 3: Using ABAQUS to validate a FEA model and simulation of all models

MATLAB is used to develop AI methods, including regression methods, GEP, ANFIS, and ensemble methods. The statistical parameters and error terms are calculated by one of these software.

Workshop 1: Design a parametric study and optimize the number of samples in a parametric study

In this workshop, first, the effective factors in designing the samples for a parametric study are presented. An appropriate parametric study should consider all effective variables; thus, specifying the effective variables for each parametric study is important. Although by increasing the number of samples, the accuracy of analysis will be increased, the time and cost of analysis will be increased; therefore, in the second part of this workshop, Taguchi as a method for designing a parametric study is explained to optimize the number of samples, although it keeps the accuracy of analysis for a big data.

Workshop 2:  FE modeling of composite castellated steel beam under fire and steel and RC connections under post-fire earthquake and validation

In this Workshop, the simulation of composite castellated steel beam under fire and steel and RC connections under post-fire earthquake is explained step by step in ABAQUS, and after that, six samples that refer to four experimental studies are simulated by ABAQUS. The validation of the FEA model is very important for each FEA model. Therefore, in the end, the validation of the FEA model using mesh sensitivity analysis and comparing the results of FEA with experimental results is presented.

Workshop 3:  Simulation of the behavior of composite castellated steel beam under fire and steel and RC connections under post-fire earthquake by AI models

Using regression models, GEP, Machine Learning (ML), Deep Learning (DL), hybrid, and ensemble models, the behavior of SPSW and RCSW is estimated. For using these methods, the dataset, which is the collection of design parameters, loading conditions, and the response of composite castellated steel beams under fire and steel and RC connections under post-fire earthquakes, is separated randomly into two groups, including training and testing datasets. The training dataset is used to train the surrogate models, and after that, the models are used to predict the response of the composite castellated steel beam under fire and steel and RC connections under post-fire earthquake according to design parameters and loading and fire conditions. The statistical parameters and error terms are used to compare the model in this Workshop.