Orthogonal least squares methods and their application to non-linear system identification
TLDR
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram- Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed.Abstract:
Identification algorithms based on the well-known linear least squares methods of gaussian elimination, Cholesky decomposition, classical Gram-Schmidt, modified Gram-Schmidt, Householder transformation, Givens method, and singular value decomposition are reviewed. The classical Gram-Schmidt, modified Gram-Schmidt, and Householder transformation algorithms are then extended to combine structure determination, or which terms to include in the model, and parameter estimation in a very simple and efficient manner for a class of multivariate discrete-time non-linear stochastic systems which are linear in the parameters.read more
Citations
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Model Estimation of Cerebral Hemodynamics Between Blood Flow and Volume Changes: A Data-Based Modeling Approach
TL;DR: It is shown that the relationship between the changes in CBF and CBV can be described using a parsimonious autoregressive with exogenous input model structure using a regularized total least-squares (RTLS) method to solve an error-in-the-variables problem.
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Improved Structure Optimization for Fuzzy-Neural Networks
TL;DR: First, a method is developed to select the most significant rules, along with a refinement stage to remove unnecessary correlations, and an improved information criterion is then proposed to find an appropriate number of inputs and rules to include in the model, leading to a balanced tradeoff between interpretability and accuracy.
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A nonlinear identification method to study effective connectivity in functional MRI.
TL;DR: This approach is nonlinear and does not rely on a priori specification of a model that contains structural information of neuronal populations, instead it relies on a nonlinear autoregressive exogenous model and nonlinear system identification theory; the model's nonlinear connectivities are determined using a least squares method.
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Wavelets-based non-linear model for real-time daily flow forecasting in Krishna River
R. Maheswaran,Rakesh Khosa +1 more
TL;DR: In this paper, a wavelet Volterra coupled (WVC) model was applied for daily inflow forecasting at Krishna Agraharam, Krishna River, India, and the relative performance of the WVC model was compared with regular artificial neural networks (ANN), wavelet-artificial neural network (WA-ANN), and other baseline models such as auto-regressive moving average with exogenous variables (ARMAX) for lead times of 1-5 days.
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A two-stage blind deconvolution strategy for bearing fault vibration signals
TL;DR: A novel approach to identify and restore periodic transients due to bearing faults through a deconvolution process based on sparsity is introduced, based on an adapted Continuous Single Best Replacement algorithm.
References
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Book
Applied Regression Analysis
Norman R. Draper,Harry Smith +1 more
TL;DR: In this article, the Straight Line Case is used to fit a straight line by least squares, and the Durbin-Watson Test is used for checking the straight line fit.
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Singular value decomposition and least squares solutions
Gene H. Golub,C. Reinsch +1 more
TL;DR: The decomposition of A is called the singular value decomposition (SVD) and the diagonal elements of ∑ are the non-negative square roots of the eigenvalues of A T A; they are called singular values.
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Linear regression analysis
TL;DR: In this paper, the authors take into serious consideration the further development of regression computer programs that are efficient, accurate, and considered an important part of statistical research, and provide up-to-date accounts of computational methods and algorithms currently in use without getting entrenched in minor computing details.
Journal ArticleDOI
Input-output parametric models for non-linear systems Part II: stochastic non-linear systems
TL;DR: Recursive input-output models for non-linear multivariate discrete-time systems are derived, and sufficient conditions for their existence are defined.