Neural Networks: Training and Application to Nonlinear System Identification and Control

This dissertation investigates training neural networks for system identification and classification. The research contains two main contributions as follow:1. Reducing number of hidden layer nodes using a feedforward componentThis research reduces the number of hidden layer nodes and training time of neural networks to make them more suited to online identification and control applications by adding a parallel feedforward component. Implementing the feedforward component with a wavelet neural network and an echo state network provides good models for nonlinear systems.The wavelet neural network with feedforward component along with model predictive controller can reliably identify and control a seismically isolated structure during earthquake. The network model provides the predictions for model predictive control. Simulations of a 5-story seismically isolated structure with conventional lead-rubber bearings showed significant reductions of all response amplitudes for both near-field (pulse) and far-field ground motions, including reduced deformations along with corresponding reduction in acceleration response. The controller effectively regulated the apparent stiffness at the isolation level. The approach is also applied to the online identification and control of an unmanned vehicle. Lyapunov theory is used to prove the stability of the wavelet neural network and the model predictive controller. 2. Training neural networks using trajectory based optimization approachesTraining neural networks is a nonlinear non-convex optimization problem to determine the weights of the neural network. Traditional training algorithms can be inefficient and can get trapped in local minima. Two global optimization approaches are adapted to train neural networks and avoid the local minima problem. Lyapunov theory is used to prove the stability of the proposed methodology and its convergence in the presence of measurement errors. The first approach transforms the constraint satisfaction problem into unconstrained optimization. The constraints define a quotient gradient system (QGS) whose stable equilibrium points are local minima of the unconstrained optimization. The QGS is integrated to determine local minima and the local minimum with the best generalization performance is chosen as the optimal solution. The second approach uses the QGS together with a projected gradient system (PGS). The PGS is a nonlinear dynamical system, defined based on the optimization problem that searches the components of the feasible region for solutions. Lyapunov theory is used to prove the stability of PGS and QGS and their stability under presence of measurement noise

Neural Metamaterial Networks for Nonlinear Material Design

Nonlinear metamaterials with tailored mechanical properties have applications in engineering, medicine, robotics, and beyond. While modeling their macromechanical behavior is challenging in itself, finding structure parameters that lead to ideal approximation of high-level performance goals is a challenging task. In this work, we propose Neural Metamaterial Networks (NMN) -- smooth neural representations that encode the nonlinear mechanics of entire metamaterial families. Given structure parameters as input, NMN return continuously differentiable strain energy density functions, thus guaranteeing conservative forces by construction. Though trained on simulation data, NMN do not inherit the discontinuities resulting from topological changes in finite element meshes. They instead provide a smooth map from parameter to performance space that is fully differentiable and thus well-suited for gradient-based optimization. On this basis, we formulate inverse material design as a nonlinear programming problem that leverages neural networks for both objective functions and constraints. We use this approach to automatically design materials with desired strain-stress curves, prescribed directional stiffness and Poisson ratio profiles. We furthermore conduct ablation studies on network nonlinearities and show the advantages of our approach compared to native-scale optimization

On the smoothness of nonlinear system identification

We shed new light on the \textit{smoothness} of optimization problems arising in prediction error parameter estimation of linear and nonlinear systems. We show that for regions of the parameter space where the model is not contractive, the Lipschitz constant and $\beta$-smoothness of the objective function might blow up exponentially with the simulation length, making it hard to numerically find minima within those regions or, even, to escape from them. In addition to providing theoretical understanding of this problem, this paper also proposes the use of multiple shooting as a viable solution. The proposed method minimizes the error between a prediction model and the observed values. Rather than running the prediction model over the entire dataset, multiple shooting splits the data into smaller subsets and runs the prediction model over each subset, making the simulation length a design parameter and making it possible to solve problems that would be infeasible using a standard approach. The equivalence to the original problem is obtained by including constraints in the optimization. The new method is illustrated by estimating the parameters of nonlinear systems with chaotic or unstable behavior, as well as neural networks. We also present a comparative analysis of the proposed method with multi-step-ahead prediction error minimization

Neural networks for small scale ORC optimization

This study concerns a thermodynamic and technical optimization of a small scale Organic Rankine Cycle system for waste heat recovery applications. An Artificial Neural Network (ANN) has been used to develop a thermodynamic model to be used for the maximization of the production of power while keeping the size of the heat exchangers and hence the cost of the plant at its minimum. R1234yf has been selected as the working fluid. The results show that the use of ANN is promising in solving complex nonlinear optimization problems that arise in the field of thermodynamics

Design optimization applied in structural dynamics

This paper introduces the design optimization strategies, especially for structures which have dynamic constraints. Design optimization involves first the modeling and then the optimization of the problem. Utilizing the Finite Element (FE) model of a structure directly in an optimization process requires a long computation time. Therefore the Backpropagation Neural Networks (NNs) are introduced as a so called surrogate model for the FE model. Optimization techniques mentioned in this study cover the Genetic Algorithm (GA) and the Sequential Quadratic Programming (SQP) methods. For the applications of the introduced techniques, a multisegment cantilever beam problem under the constraints of its first and second natural frequency has been selected and solved using four different approaches