Iterative observer-based state and parameter estimation for linear systems

The primary objective of this study is to develop a mathematical framework for failure prognostics and uncertainty management based on a state-space degradation model, where unknown parameters are present in the model. Joint state and parameter estimation is carried out by the Sequential Monte Carlo methods. Then, a degradation prediction with uncertainty limits is made. Sequential Monte Carlo methods for joint state and parameter estimation are reviewed, and the effectiveness of the techniques for the prognostics task is assessed. A performance comparison of these algorithms is made based on a numerical study. The results presented in this study show that the state-of-art SMC techniques can provide satisfactory results of joint state and parameter estimation for the prognostics task. The Particle Markov Chain Monte Carlo method provides relatively more accurate estimation results compared with other SMC methods while demanding more computing resources.

Investigation on drought characteristics such as severity, duration, and frequency is crucial for water resources planning and management in a river basin. While the methodology for multivariate drought frequency analysis is well established by applying the copulas, the estimation on the associated parameters by various parameter estimation methods and the effects on the obtained results have not yet been investigated. This research aims at conducting a comparative analysis between the maximum likelihood parametric and non-parametric method of the Kendall \(\tau \) estimation method for copulas parameter estimation. The methods were employed to study joint severity–duration probability and recurrence intervals in Karkheh River basin (southwest Iran) which is facing severe water-deficit problems. Daily streamflow data at three hydrological gauging stations (Tang Sazbon, Huleilan and Polchehr) near the Karkheh dam were used to draw flow duration curves (FDC) of these three stations. The \(Q_{75}\) index extracted from the FDC were set as threshold level to abstract drought characteristics such as drought duration and severity on the basis of the run theory. Drought duration and severity were separately modeled using the univariate probabilistic distributions and gamma–GEV, LN2–exponential, and LN2–gamma were selected as the best paired drought severity–duration inputs for copulas according to the Akaike Information Criteria (AIC), Kolmogorov–Smirnov and chi-square tests. Archimedean Clayton, Frank, and extreme value Gumbel copulas were employed to construct joint cumulative distribution functions (JCDF) of droughts for each station. Frank copula at Tang Sazbon and Gumbel at Huleilan and Polchehr stations were identified as the best copulas based on the performance evaluation criteria including AIC, BIC, log-likelihood and root mean square error (RMSE) values. Based on the RMSE values, nonparametric Kendall-\(\tau \) is preferred to the parametric maximum likelihood estimation method. The results showed greater drought return periods by the parametric ML method in comparison to the nonparametric Kendall \(\tau \) estimation method. The results also showed that stations located in tributaries (Huleilan and Polchehr) have close return periods, while the station along the main river (Tang Sazbon) has the smaller return periods for the drought events with identical drought duration and severity.

All-solid-state batteries (ASSBs) are considered to be the next generation of lithium-ion batteries. Physics-based models (PBMs) can effectively simulate the internal electrochemical reactions and provide critical internal states for battery management. In order to promote the onboard applications of PBMs for ASSBs, in this article, the parameter sensitivity of a typical PBM is analyzed, and a joint estimation method for states and parameters based on sigma-point Kalman filtering (SPKF) is proposed. First, to obtain accurate sensitivity analysis results, approaches from different principles, including local sensitivity, elementary effect test, and variance-based methods, are applied. Then, for the battery model based on partial differential equations, a nonlinear state-space model is constructed by using the finite-difference discretization method. Finally, the SPKF algorithm is employed to conduct the joint estimation of model parameters and lithium-ion concentrations. The results from constant current and dynamic cycles show that two parameters, namely maximum lithium-ion concentration and minimum lithium-ion concentration, have the most influence on the model results. The joint estimation method is validated in three different cases, and the mean absolute errors of the estimated voltage and state of charge (SOC) are below 2.1 mV and 1.5%, respectively.

In this paper a discrete-time iterative learning controller for single input single output systems is presented. The iterative learning controller works with a reduced sampling rate that ensures the reduction of an appropriate norm of the error trajectory from cycle to cycle and can cope with initial state error. Initial state error occurs when the initial state of the system is different from the initial state that is implicitly given by the reference trajectory. If the initial state changes for every learning iteration, then the controller cannot achieve ideal tracking but the error trajectory is bounded. Using two different sample times together with a potentially time variant learning gain improves the controller performance for dealing with initial state error. Simulation examples are presented to show the results of the proposed iterative learning controller with reduced sampling rate.

Clustered iterative stochastic ensemble method for multi-modal calibration of subsurface flow models

BackgroundParameter estimation is often the bottlenecking step in biological system modeling. For ordinary differential equation (ODE) models, the challenge in this estimation has been attributed to not only the lack of parameter identifiability, but also computational issues such as finding globally optimal parameter estimates over highly multidimensional search space. Recent methods using incremental estimation approach could alleviate the computational difficulty by performing the parameter estimation one-reaction-at-a-time. However, incremental estimation strategies usually require data smoothing and are known to produce biased parameter estimates.ResultsIn this article, we presented a new parameter estimation method called integrated flux parameter estimation (IFPE). We employed the integral form of the ODE such that we could compute the integral of reaction fluxes from time-series concentration data without data smoothing. Here, we formulated the parameter estimation as a nested optimization problem. In the outer optimization, we performed a minimization of model prediction errors over parameters associated with a subset of reactions labeled as independent. The dimension of the independent reaction subset was equal to the degrees of freedom in the calculation of integrated fluxes (IF) from concentration data. We selected the independent reactions such that given their IF values, the IFs of the remaining (dependent) reactions could be uniquely determined. Meanwhile, in the inner optimization, we estimated the model parameters associated with the dependent reactions, one-reaction-at-a-time, by minimizing the dependent IF prediction errors. We demonstrated the performance of the IFPE method using two case studies: a generalized mass action model of a branched pathway and a lin-log ODE model of Lactococcus lactis glycolytic pathway.ConclusionsThe IFPE significantly outperformed standard simultaneous parameter estimation in terms of computational efficiency and scaling. In comparison to incremental parameter estimation (IPE) method, the IFPE produced parameter estimates with significantly lower bias and did not require time-series data smoothing. The advantages of IFPE over the IPE however came at the cost of a small increase in the computational time.Electronic supplementary materialThe online version of this article (doi:10.1186/s12918-014-0127-x) contains supplementary material, which is available to authorized users.

In this paper, we present and evaluate dynamic dictionary-based estimation methods for joint model order and parameter estimation. In dictionary-based estimation, a continuous parameter space is discretized, and vector-valued dictionary elements are formed for specific parameter values. A linear combination of a subset of dictionary elements is used to represent the model, where the number of elements used is the estimated model order, and the parameters corresponding to the selected elements are the parameter estimates. In static-based methods, the dictionary is fixed; while in the dynamic methods proposed here, the parameter sampling, and hence the dictionary, adapt to the data. We propose two dynamic dictionary-based estimation algorithms in which the dictionary elements are dynamically adjusted to improve parameter estimation performance. We examine the performance of both static and dynamic algorithms in terms of probability of correct model order selection and the root mean-squared error of parameter estimates. We show that dynamic dictionary methods overcome the problem of estimation bias induced by quantization effects in static dictionary-based estimation, and we demonstrate that dictionary-based estimation methods are capable of parameter estimation performance comparable to the Cramér-Rao lower bound and to traditional ML-based model estimation over a wide range of signal-to-noise ratios.

Data assimilation is predominantly used for state estimation, combining observational data with model predictions to produce an updated model state that most accurately approximates the true system state whilst keeping the model parameters fixed. This updated model state is then used to initiate the next model forecast. Even with perfect initial data, inaccurate model parameters will lead to the growth of prediction errors. To generate reliable forecasts, we need good estimates of both the current system state and the model parameters. This article presents research into data assimilation methods for morphodynamic model state and parameter estimation. First, we focus on state estimation and describe implementation of a three‐dimensional variational (3D‐Var) data assimilation scheme in a simple 2D morphodynamic model of Morecambe Bay, UK. The assimilation of observations of bathymetry derived from synthetic aperture radar (SAR) satellite imagery and a ship‐borne survey is shown to significantly improve the predictive capability of the model over a 2‐year run. Here, the model parameters are set by manual calibration; this is laborious and is found to produce different parameter values depending on the type and coverage of the validation dataset. The second part of this article considers the problem of model parameter estimation in more detail. We explain how, by employing the technique of state augmentation, it is possible to use data assimilation to estimate uncertain model parameters concurrently with the model state. This approach removes inefficiencies associated with manual calibration and enables more effective use of observational data. We outline the development of a novel hybrid sequential 3D‐Var data assimilation algorithm for joint state‐parameter estimation and demonstrate its efficacy using an idealised 1D sediment transport model. The results of this study are extremely positive and suggest that there is great potential for the use of data assimilation‐based state‐parameter estimation in coastal morphodynamic modelling. Copyright © 2012 Royal Meteorological Society

Many existing software reliability models are based on the assumption of statistical independence among successive software failures. In reality, this assumption could be easily violated. In recent years, efforts have been made to relax this unrealistic assumption and a software reliability modeling framework considering failure correlation was developed by Goseva-Popstojanova and Trivedi. However, some important issues that are crucial to the proposed modeling framework to be used in practice remain unstudied, such as the method of estimation of model parameters. In this paper, we study the parameter estimation problem for the software reliability modeling framework developed in. We propose a relationship function among model parameters which could be essential to the reduction of the number of parameters to be estimated as well as to the reliability prediction using the proposed modeling framework. Two parameter estimation methods are developed based on deferent types of data available, using Maximum Likelihood Estimation (MLE) method. Simulation results preliminarily show that the accuracy of both proposed estimation methods seem to be satisfactory.

Motion recognition methods can distinguish body symbols and play an important role in real-time safety monitoring of pedestrians. In order to solve the problem of lack of data for deep learning-based action recognition models, a human motion synthesis method with hidden state initialization is proposed. Commonly used human motion synthesis methods utilize Recurrent Neural Network (RNN) to automatically generate subsequent motion sequences by taking several frames of motion data as input. In previous work, the initial hidden state of the RNN is usually set to zero or randomly initialized hidden state, resulting in a jump between the end frame of motion input and the first frame of motion synthesis, which affects the quality of the generated motion. To solve this problem, a method for estimating the initial hidden state estimation is proposed, which takes the initial hidden state as the independent variable, uses the objective function of the neural network as the optimization objective, and uses the gradient descent method to optimize the solution to obtain a suitable initial hidden state. The proposed motion model with initial hidden state estimation reduces the prediction error in the first frame by 63.51% and 6.90%, respectively, and the total error in 10 frames by 50.00% and the total errors of 10 frames were reduced by 50.00% and 4.89%, respectively. The experimental results show that the proposed motion model with initial hidden state estimation has better motion synthesis quality and motion prediction accuracy than the method without initial hidden state estimation; the proposed method improves the quality of motion synthesis by accurately estimating the first frame hidden state of the RNN human motion model, which can provide reliable data support for motion recognition models in real-time security monitoring.

The Pareto distribution has been introduced in Chapter 19. Also discussed there is a brief review of literature and methods of estimating its parameters. Further elaboration of the distribution is given in Chapter 20. Methods of parameter estimation were reviewed by Hosking and Wallis (1987). The methods of moments (MOM), maximum likelihood estimation (MLE) and probability weighted moments (PWM) were included in the review. Guo and Singh (1992) and Singh and Guo (1995) employed the principle of maximum entropy (POME) to develop a new competitive method of parameter estimation (Singh and Rajagopal, 1986) for the 3-parameter generalized Pareto (GP3) distribution and compared it with MOM, MLE and PWM using Monte Carlo simulated data The parameter estimates yielded by POME were either superior or comparable for high skewness.KeywordsRoot Mean Square ErrorMaximum Likelihood EstimationPareto DistributionGeneralize Pareto DistributionQuantile EstimationThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

In this work we develop some parameter and spectral estimation methods in Magnetic Resonance Spectroscopy Signals (MRS). We do this with a dual purpose: first, to enable the full estimation process for the constituent parameters of the time-domain msignal: Amplitude, frequency, damping constant and phase. Second, to generate the parameter estimation in the frequency domain in order to evaluate the effect of the application of time domain estimation methods [2].

Coarse-Fine Joint Target Parameter Estimation Method Based on AN-RSC in OFDM Passive Radar

A kernel functional representation of linear time-varying systems is employed in conjunction with B-spline functional approximation techniques to construct non-asymptotic state and parameter estimators for LTV systems. Total observability of the estimated system must be assumed. Practical identifiability conditions for parametric estimation are also stated. In the absence of output measurement noise the observer provides almost exact reconstruction of the system state and delivers high fidelity functional estimates of the time varying system parameters. It also shares the usual superior features of algebraic observers such as independence of the initial conditions of the system and good noise attenuation properties. Other advantages of the kernel and B-spline based identification of linear time-varying systems are elucidated.

This paper develops a hybrid strategy for identifying the nonlinear errors‐in‐variables (EIV) Wiener state‐space systems subjected to the unknown states. The Wiener nonlinear system with the noisy input is investigated, and a state‐space subsystem affected by the process disturbance is considered. The unbiased parameter estimation of the EIV Wiener systems with nonideal observations and polynomial nonlinearities is realized using the proposed bias‐compensated recursive least squares algorithm. Specifically, the estimated bias caused by the noisy measurements is eliminated, and the analytic formulas for estimating unmeasurable nonlinear intermediate variables are derived. Furthermore, based on the adaptive Kalman filtering principle, a state observer is designed to simultaneously estimate the subsystem states and the unknown noise variances in the estimated bias. The presented algorithms in the hybrid framework achieve the joint estimation of the parameters and states for EIV Wiener state‐space systems. The convergence analysis shows that the parameter estimates can converge to their true values. Finally, a numerical simulation and a quarter‐car model simulation demonstrate the effectiveness of the proposed algorithm.