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Neural Network Models: Applications and Advancements
Neural Network Models in Finite Element Analysis
Neural network (NN) based constitutive models are increasingly being integrated into finite element (FE) analysis to solve boundary value problems. These models are particularly adept at capturing non-linear material behavior and can continuously learn from additional material response data. Unlike traditional plasticity models, NN constitutive models do not require special integration procedures or a material stiffness matrix, making them more versatile and easier to implement in FE analysis.
Stability of Clifford-Valued Neural Networks
The global exponential stability of Clifford-valued neural networks (NNs) with time-varying delays and impulsive effects has been a subject of recent research. By addressing the non-commutativity of Clifford numbers, researchers have developed a model that can be divided into real-valued sub-models. Using Lyapunov–Krasovskii functional and linear matrix inequality techniques, new conditions for the stability of these NN models have been formulated and validated through numerical simulations.
Neural Networks in Ecological Modeling
In ecological studies, neural networks (NNs) have shown superior performance over multiple regression (MR) models, especially in capturing non-linear relationships. For instance, in modeling the relationship between the density of brown trout spawning sites and habitat characteristics, NNs achieved a significantly higher R² value compared to MR models, demonstrating their effectiveness in ecological predictive modeling.
Wind Turbine Output Power Estimation
Neural networks have been effectively used to model the non-linear behavior of wind turbines for output power estimation. By using inputs such as wind speed average, standard deviation, and past output power, NN models have been able to predict wind turbine energy production with high accuracy. The optimal NN configuration identified in this context was an 8-5-1 structure, which provided mean square errors of less than 1%.
Control of Nonlinear Structural Systems
A neural network (NN) based approach has been developed to control nonlinear structural systems by combining H∞ control performance with Tagagi-Sugeno (T-S) fuzzy control. This method uses linear matrix inequality (LMI) techniques derived from Lyapunov theory to design a fuzzy-model-based H∞ control. The approach has been successfully applied to stabilize a nonlinearly tuned mass damper system, demonstrating strong robustness against modeling errors and external excitations.
Neural Networks in Mathematical Programming Problems
Neural networks (NNs) are increasingly being applied to solve complex mathematical programming problems (MPPs). These models, inspired by biological neurons, offer a new computational approach to optimization problems characterized by objective functions and constraints. The use of NNs in MPPs has been extensively reviewed, highlighting their potential to address various optimization challenges and suggesting new research directions for future studies.
Adaptive Neural Networks for Structural Model Updating
An adaptive neural network (NN) model has been proposed for updating structural models. This model uses a feedforward architecture and is trained with data from finite-element analyses. By adaptively retraining the NN model online, it is possible to reduce discrepancies between measured and predicted modal parameters. This methodology has been successfully applied to a suspension bridge model, significantly improving the accuracy of the structural parameters.
Physics-Informed Neural Networks for Fluid Modeling
Non-Newtonian physics-informed neural networks (nn-PINNs) have been developed to model complex fluid behaviors. These models solve coupled partial differential equations (PDEs) that describe the fluid's response to different deformation fields. By leveraging automatic differentiation in neural networks, nn-PINNs can accurately capture the behavior of various complex fluids without the need for mesh generation, making them highly effective for industrial and natural applications.
Building Neural Network Models from Empirical Data
A structured methodology for building neural network (NN) models from empirical engineering data has been proposed. This approach emphasizes the importance of defining the modeling task, understanding the theoretical capabilities of NNs, and using advanced methods like stacked generalization and ensemble modeling to improve model quality. An example of this methodology in action is the modeling of marine propeller behavior, which demonstrated significant improvements in model accuracy.
Conclusion
Neural network models are proving to be powerful tools across various fields, from finite element analysis and ecological modeling to wind turbine power estimation and structural control. Their ability to handle non-linear relationships and continuously learn from new data makes them invaluable for solving complex real-world problems. As research continues to advance, the applications and effectiveness of neural networks are expected to expand even further.
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