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Regularization Of Inverse Problems

Parameter estimation for a controlled autoregressive autoregressive moving average system based on a recursive framework

In this paper, we consider the identification of RBF-type models with nonsmooth constraint, where the parameters can be partitioned into a linear part and a nonlinear part. Taking advantage of this special structure, we design a variable projection-based parameter estimation algorithm for the optimization of the RBF-type models with nonsmooth constraint. The proposed algorithm decomposes the original optimization problem into an inner subproblem and an outer subproblem. The linear parameters are eliminated by solving the easier solved inner problem, resulting in a reduced function that only contains nonlinear parameters. Then we separately utilize the proximal gradient method to optimize the linear parameters and trust region method to optimize the remaining nonlinear parameters. Simulation results on synthetic data and real-world data confirm the efficiency and effectiveness of the proposed algorithm. 

A variable projection-based parameter estimation algorithm for the nonsmooth separable nonlinear problems

In this paper, we consider the identification of RBF-type models with nonsmooth constraint, where the parameters can be partitioned into a linear part and a nonlinear part. Taking advantage of this special structure, we design a variable projection-based parameter estimation algorithm for the optimization of the RBF-type models with nonsmooth constraint. The proposed algorithm decomposes the original optimization problem into an inner subproblem and an outer subproblem. The linear parameters are eliminated by solving the easier solved inner problem, resulting in a reduced function that only contains nonlinear parameters. Then we separately utilize the proximal gradient method to optimize the linear parameters and trust region method to optimize the remaining nonlinear parameters. Simulation results on synthetic data and real-world data confirm the efficiency and effectiveness of the proposed algorithm.

To effectively predict the mechanical dispatch reliability (MDR), the artificial neural networks method combined with aircraft operation health status parameters is proposed, which introduces the real civil aircraft operation data for verification, to improve the modeling precision and computing efficiency. Grey relational analysis can identify the degree of correlation between aircraft system health status (such as the unscheduled maintenance event, unit report event, and services number) and dispatch release and screen out the most closely related systems to determine the set of input parameters required for the prediction model. The artificial neural network using radial basis function (RBF) as a kernel function, has the best applicability in the prediction of multidimensional, small sample problems. Health status parameters of related systems are used as the input to predict the changing trend of MDR, under the artificial neural network modeling framework. The case study collects real operation data for a certain civil aircraft over the past five years to validate the performance of the model which meets the requirements of the application. The results show that the prediction quadratic error Ep of the model reaches 6.9 × 10−8. That is to say, in the existing operating environment, the prediction of the number of delay ＆ cancel events per month can be less than once. The accuracy of RBF ANN, BP ANN and GA-BP ANN are compared further, and the results show that RBF ANN has better adaptability to such multidimensional small sample problems. The efforts of this paper provide a highly efficient method for the MDR prediction through aircraft system health state parameters, which is a promising model to enhance the prediction and controllability of the dispatch release, providing support for the construction of the civil aircraft operation system. 

Mechanical Dispatch Reliability Prediction for Civil Aircraft Considering Operational Parameters

The radial basis function network-based state-dependent autoregressive (RBF-AR) model has been widely used in modeling and prediction of nonlinear time series. The parameter identification of RBF-AR model can be reformulated as a separable nonlinear least squares problem. The variable projection (VP) algorithm has been proven to be valuable in solving such problems. However, for ill-posed problems, the classical VP algorithm usually yields unstable models. In this paper, we consider a novel regularized separable algorithm that takes advantage of the VP method and the expectation–maximization (EM) method. The proposed algorithm utilizes the VP algorithm to optimize the nonlinear parameters and automatically picks out the regularization parameters during the search process. Numerical results on real-world data and synthetic time series confirm the effectiveness of the proposed algorithm.

A novel expectation–maximization-based separable algorithm for parameter identification of RBF-AR model

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A novel expectation–maximization-based separable algorithm for parameter identification of RBF-AR model