Solution Properties for Pertubed Linear and Nonlinear Integrals Equations

In this study we consider perturbative series solution with respect to a parameter {\epsilon} > 0. In this methodology the solution is considered as an infinite sum of a series of functional terms which usually converges fast to the exact desired solution. Then we investigate perturbative solutions for kernel perturbed integral equations and prove the convergence in an appropriate ranges of the perturbation series. Next we investigate perturbation series solutions for nonlinear perturbations of integral equations of Hammerstein type and formulate conditions for their convergence. Finally we prove the existence of a maximal perturbation range for non linear integral equations

Machine Learning Approach for Rapid Estimation of Five-Day Biochemical Oxygen Demand in Wastewater

Improperly managed wastewater effluent poses environmental and public health risks. BOD evaluation is complicated by wastewater treatment. Using key parameters to estimate BOD in wastewater can improve wastewater management and environmental monitoring. This study proposes a BOD determination method based on the Artificial Neural Networks (ANN) model to combine Chemical Oxygen Demand (COD), Suspended Solids (SS), Total Nitrogen (T-N), Ammonia Nitrogen (NH4-N), and Total Phosphorous (T-P) concentrations in wastewater. Twelve different transfer functions are investigated, including the common Hyperbolic Tangent Sigmoid (HTS), Log-sigmoid (LS), and Linear (Li) functions. This research evaluated 576,000 ANN models while considering the variable random number generator due to the ten alternative ANN configuration parameters. This study proposes a new approach to assessing water resources and wastewater facility performance. It also demonstrates ANN’s environmental and educational applications. Based on their RMSE index over the testing datasets and their configuration parameters, twenty ANN architectures are ranked. A BOD prediction equation written in Excel makes testing and applying in real-world applications easier. The developed and proposed ANN-LM 5-8-1 model depicting almost ideal performance metrics proved to be a reliable and helpful tool for scientists, researchers, engineers, and practitioners in water system monitoring and the design phase of wastewater treatment plants

Forecast of Airblast Vibrations Induced by Blasting Using Support Vector Regression Optimized by the Grasshopper Optimization (SVR-GO) Technique

Air overpressure (AOp) is an undesirable environmental effect of blasting. To date, a variety of empirical equations have been developed to forecast this phenomenon and prevent its negative impacts with accuracy. However, the accuracy of these methods is not sufficient. In addition, they are resource-consuming. This study employed support vector regression (SVR) optimized with the grasshopper optimizer (GO) algorithm to forecast AOp resulting from blasting. Additionally, a novel input selection technique, the Boruta algorithm (BFS), was applied. A new algorithm, the SVR-GA-BFS7, was developed by combining the models mentioned above. The findings showed that the SVR-GO-BFS7 model was the best technique (R2 = 0.983, RMSE = 1.332). The superiority of this model means that using the seven most important inputs was enough to forecast the AOp in the present investigation. Furthermore, the performance of SVR-GO-BFS7 was compared with various machine learning techniques, and the model outperformed the base models. The GO was compared with some other optimization techniques, and the superiority of this algorithm over the others was confirmed. Therefore, the suggested method presents a framework for accurate AOp prediction that supports the resource-saving forecasting methods

Forecast of Airblast Vibrations Induced by Blasting Using Support Vector Regression Optimized by the Grasshopper Optimization (SVR-GO) Technique

Air overpressure (AOp) is an undesirable environmental effect of blasting. To date, a variety of empirical equations have been developed to forecast this phenomenon and prevent its negative impacts with accuracy. However, the accuracy of these methods is not sufficient. In addition, they are resource-consuming. This study employed support vector regression (SVR) optimized with the grasshopper optimizer (GO) algorithm to forecast AOp resulting from blasting. Additionally, a novel input selection technique, the Boruta algorithm (BFS), was applied. A new algorithm, the SVR-GA-BFS7, was developed by combining the models mentioned above. The findings showed that the SVR-GO-BFS7 model was the best technique (R2 = 0.983, RMSE = 1.332). The superiority of this model means that using the seven most important inputs was enough to forecast the AOp in the present investigation. Furthermore, the performance of SVR-GO-BFS7 was compared with various machine learning techniques, and the model outperformed the base models. The GO was compared with some other optimization techniques, and the superiority of this algorithm over the others was confirmed. Therefore, the suggested method presents a framework for accurate AOp prediction that supports the resource-saving forecasting methods

Deep Neural Networks for the Estimation of Masonry Structures Failures under Rockfalls

Although the principal aim of the rockfall management is to prevent rock boulders from reaching the buildings instead of the buildings resisting the boulder impacts, there usually exists a residual risk that has to be assessed, even when structural protection measurements are taken. The evaluation of the expected damage of buildings due to rockfalls using empirical data from past events is not always possible, as transferring and applying damage observations from one area to another can be unrealistic. In order to simulate potential rockfall scenarios and their damage on buildings, numerical methods can be an alternative. However due to their increased requirements in expertise and computational costs, their integration into the risk analysis is limited, and simpler tools to assess the rockfall vulnerability of buildings are needed. This paper focuses on the application of artificial intelligence AI methods for providing the expected damage of masonry walls which are subjected to rockfall impacts. First, a damage database with 672 datasets was created numerically using the particle finite element method and the finite element method. The input variables are the rock volume (VR), the rock velocity (RV), the masonry wall (t) and the masonry tensile strength fm. The output variable is a damage index (DI) equal to the percentage of the damaged wall area. Different AI algorithms were investigated and the ANN LM 4-21-1 model was selected to optimally assess the expected wall damage. The optimum model is provided here (a) as an analytical equation and (b) in the form of contour graphs, mapping the DI value. Known the VR and the RV, the DI can be directly used as an input for the vulnerability of masonry walls into the quantitative rockfall risk assessment equation

Novel Fuzzy-Based Optimization Approaches for the Prediction of Ultimate Axial Load of Circular Concrete-Filled Steel Tubes

An accurate estimation of the axial compression capacity of the concrete-filled steel tubular (CFST) column is crucial for ensuring the safety of structures containing them and preventing related failures. In this article, two novel hybrid fuzzy systems (FS) were used to create a new framework for estimating the axial compression capacity of circular CCFST columns. In the hybrid models, differential evolution (DE) and firefly algorithm (FFA) techniques are employed in order to obtain the optimal membership functions of the base FS model. To train the models with the new hybrid techniques, i.e., FS-DE and FS-FFA, a substantial library of 410 experimental tests was compiled from openly available literature sources. The new model’s robustness and accuracy was assessed using a variety of statistical criteria both for model development and for model validation. The novel FS-FFA and FS-DE models were able to improve the prediction capacity of the base model by 9.68% and 6.58%, respectively. Furthermore, the proposed models exhibited considerably improved performance compared to existing design code methodologies. These models can be utilized for solving similar problems in structural engineering and concrete technology with an enhanced level of accuracy