This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the model. In particular, the nonlinear dynamic problem is transformed into an approximate static formulation, and simple regression methods are applied to obtain the solution in a fast and efficient way. The proposed method is validated by means of two measurement examples: the Wiener-Hammerstein benchmark problem and the identification of a crystal detector.
An example of NLSS models that have been successfully applied to identify several real-life systems is given by polynomial NLSS (PNLSS) models @cite_14 . In that approach, the nonlinear model is initialized simply by a linear model (BLA).
@cite_14
2060458267 2122538988 2782210340 2744067593
In this paper, we propose a method to model nonlinear systems using polynomial nonlinear state space equations. Obtaining good initial estimates is a major problem in nonlinear modelling. It is solved here by identifying first the best linear approximation of the system under test. The proposed identification procedure is successfully applied to measurements of two physical systems. Nonlinear principal component analysis is a novel technique for multivariate data analysis, similar to the well-known method of principal component analysis. NLPCA, like PCA, is used to identify and remove correlations among problem variables as an aid to dimensionality reduction, visualization, and exploratory data analysis. While PCA identifies only linear correlations between variables, NLPCA uncovers both linear and nonlinear correlations, without restriction on the character of the nonlinearities present in the data. NLPCA operates by training a feedforward neural network to perform the identity mapping, where the network inputs are reproduced at the output layer. The network contains an internal “bottleneck” layer (containing fewer nodes than input or output layers), which forces the network to develop a compact representation of the input data, and two additional hidden layers. The NLPCA method is demonstrated using time-dependent, simulated batch reaction data. Results show that NLPCA successfully reduces dimensionality and produces a feature space map resembling the actual distribution of the underlying system parameters. The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising meaningful models out of such observations in an automated fashion still remains an open problem. In this work, we put forth a machine learning approach for identifying nonlinear dynamical systems from data. Specifically, we blend classical tools from numerical analysis, namely the multi-step time-stepping schemes, with powerful nonlinear function approximators, namely deep neural networks, to distill the mechanisms that govern the evolution of a given data-set. We test the effectiveness of our approach for several benchmark problems involving the identification of complex, nonlinear and chaotic dynamics, and we demonstrate how this allows us to accurately learn the dynamics, forecast future states, and identify basins of attraction. In particular, we study the Lorenz system, the fluid flow behind a cylinder, the Hopf bifurcation, and the Glycoltic oscillator model as an example of complicated nonlinear dynamics typical of biological systems. Remaining Useful Life (RUL) of a component or a system is defined as the length from the current time to the end of the useful life. Accurate RUL estimation plays a critical role in Prognostics and Health Management(PHM). Data driven approaches for RUL estimation use sensor data and operational data to estimate RUL. Traditional regression based approaches and recent Convolutional Neural Network (CNN) approach use features created from sliding windows to build models. However, sequence information is not fully considered in these approaches. Sequence learning models such as Hidden Markov Models (HMMs) and Recurrent Neural Networks (RNNs) have flaws when modeling sequence information. HMMs are limited to discrete hidden states and are known to have issues when modeling long-term dependencies in the data. RNNs also have issues with long-term dependencies. In this work, we propose a Long Short-Term Memory (LSTM) approach for RUL estimation, which can make full use of the sensor sequence information and expose hidden patterns within sensor data with multiple operating conditions, fault and degradation models. Extensive experiments using three widely adopted Prognostics and Health Management data sets show that LSTM for RUL estimation significantly outperforms traditional approaches for RUL estimation as well as Convolutional Neural Network (CNN).