Data filtering-based least squares iterative algorithm for Hammerstein nonlinear systems by using the model decomposition

This paper focuses on the iterative identification problems for a class of Hammerstein nonlinear systems. By decomposing the system into two fictitious subsystems, a decomposition-based least squares iterative algorithm is presented for estimating the parameter vector in each subsystem. Moreover, a data filtering-based decomposition least squares iterative algorithm is proposed. The simulation results indicate that the data filtering-based least squares iterative algorithm can generate more accurate parameter estimates than the least squares iterative algorithm

Recursive search-based identification algorithms for the exponential autoregressive time series model with coloured noise

This study focuses on the recursive parameter estimation problems for the non-linear exponential autoregressive model with moving average noise (the ExpARMA model for short). By means of the gradient search, an extended stochastic gradient (ESG) algorithm is derived. Considering the difficulty of determining the step-size in the ESG algorithm, a numerical approach is proposed to obtain the optimal step-size. In order to improve the parameter estimation accuracy, the authors employ the multi-innovation identification theory to develop a multi-innovation ESG (MI-ESG) algorithm for the ExpARMA model. Introducing a forgetting factor into the MI-ESG algorithm, the parameter estimation accuracy can be further improved. With an appropriate innovation length and forgetting factor, the variant of the MI-ESG algorithm is effective to identify all the unknown parameters of the ExpARMA model. A simulation example is provided to test the proposed algorithms

Parameter estimation algorithm for multivariable controlled autoregressive autoregressive moving average systems

This paper investigates parameter estimation problems for multivariable controlled autoregressive autoregressive moving average (M-CARARMA) systems. In order to improve the performance of the standard multivariable generalized extended stochastic gradient (M-GESG) algorithm, we derive a partially coupled generalized extended stochastic gradient algorithm by using the auxiliary model. In particular, we divide the identification model into several subsystems based on the hierarchical identification principle and estimate the parameters using the coupled relationship between these subsystems. The simulation results show that the new algorithm can give more accurate parameter estimates of the M-CARARMA system than the M-GESG algorithm

Gradient-based iterative parameter estimation for bilinear-in-parameter systems using the model decomposition technique

The parameter estimation issues of a block-oriented non-linear system that is bilinear in the parameters are studied, i.e. the bilinear-in-parameter system. Using the model decomposition technique, the bilinear-in-parameter model is decomposed into two fictitious submodels: one containing the unknown parameters in the non-linear block and the other containing the unknown parameters in the linear dynamic one and the noise model. Then a gradient-based iterative algorithm is proposed to estimate all the unknown parameters by formulating and minimising two criterion functions. The stochastic gradient algorithms are provided for comparison. The simulation results indicate that the proposed iterative algorithm can give higher parameter estimation accuracy than the stochastic gradient algorithms

State filtering and parameter estimation for two input two output systems with time delay

This paper focuses on presenting a new identification algorithm to estimate the parameters and state variables for two-input two-output dynamic systems with time delay based on canonical state space models. First, the related input-output equation is determined and transformed into an identification oriented model, which does not involve in the unmeasurable states, and then a residual based least squares identification algorithm is presented for the estimations. After the parameters being estimated, the system states are subsequently estimated by using the estimated parameters. Through theoretical analysis, the convergence of the algorithm is derived to provide assurance for applicability. Finally, a selected simulation example is given for a meaningful case study to show the effectiveness of the proposed algorithm

Prospective Lifetables: Life Insurance Pricing and Hedging in a Stochastic Mortality Environment

In life insurance, actuaries have traditionally calculated premiums and reserves using a deterministic mortality intensity, which is a function of the age of the insured only. Over the course of the 20th century, the population of the industrialized world underwent a major mortality transition, with a dramatic decline in mortality rates. The mortality decline has been dominated by two major trends: a reduction in mortality due to infectious diseases affecting mainly young ages, and a decrease in mortality at old ages. These mortality improvements have to be taken into account to price long-term life insurance products and to analyse the sustainability of social security systems. In this paper, we argue that pricing and reserving for pension and life insurance products requires dynamic (or prospective) lifetables. We briefly review classic and recent projection methods and adopt a Poisson log-bilinear approach to estimate Portuguese Prospective Lifetables. The advantages of using dynamic lifetables are twofold. Firstly, it provides more realistic premiums and reserves, and secondly, it quantifies the risk of the insurance companies associated with the underlying longevity risks. Finally, we discuss possible ways of transferring the systematic mortality risk to other parties.

State filtering-based least squares parameter estimation for bilinear systems using the hierarchical identification principle

This study presents a combined parameter and state estimation algorithm for a bilinear system described by its observer canonical state-space model based on the hierarchical identification principle. The Kalman filter is known as the best state filter for linear systems, but not applicable for bilinear systems. Thus, a bilinear state observer (BSO) is designed to give the state estimates using the extremum principle. Then a BSO-based recursive least squares (BSO-RLS) algorithm is developed. For comparison with the BSO-RLS algorithm, by dividing the system into three fictitious subsystems on the basis of the decomposition–coordination principle, a BSO-based hierarchical least squares algorithm is proposed to reduce the computation burden. Moreover, a BSO-based forgetting factor recursive least squares algorithm is presented to improve the parameter tracking capability. Finally, a numerical example illustrates the effectiveness of the proposed algorithms

Hierarchical gradient- and least squares-based iterative algorithms for input nonlinear output-error systems using the key term separation

This paper considers the parameter identification problems of the input nonlinear output-error (IN-OE) systems, that is the Hammerstein output-error systems. In order to overcome the excessive calculation amount of the over-parameterization method of the IN-OE systems. Through applying the hierarchial identification principle and decomposing the IN-OE system into three subsystems with a smaller number of parameters, we present the key term separation auxiliary model hierarchical gradient-based iterative algorithm and the key term separation auxiliary model hierarchical least squares-based iterative algorithm, which are called the key term separation auxiliary model three-stage gradient-based iterative algorithm and the key term separation auxiliary model three-stage least squares-based iterative algorithm. The comparison of the calculation amount and the simulation analysis indicate that the proposed algorithms are effective. (c) 2021 The Franklin Institute. Published by Elsevier Ltd. All rights reserved

Identification of the nonlinear systems based on the kernel functions

Constructing an appropriate membership function is significant in fuzzy logic control. Based on the multi-model control theory, this article constructs a novel kernel function which can implement the fuzzification and defuzzification processes and reflect the dynamic quality of the nonlinear systems accurately. Then we focus on the identification problems of the nonlinear systems based on the kernel functions. Applying the hierarchical identification principle, we present the hierarchical stochastic gradient algorithm for the nonlinear systems. Meanwhile, the one-dimensional search methods are proposed to solve the problem of determining the optimal step sizes. In order to improve the parameter estimation accuracy, we propose the hierarchical multi-innovation forgetting factor stochastic gradient algorithm by introducing the forgetting factor and using the multi-innovation identification theory. The simulation example is provided to test the proposed algorithms from the aspects of parameter estimation accuracy and prediction performance