Sequential point estimation based on U-statistics

This paper discusses a sequential procedure to estimate an estimable parameter of the underlying unkown distribution function. The estimator is based on the corresponding U-statistic. Under appropriate regularity conditions the regret is shown to be bounded. A second order approximation is provided for the expectation of the stopping time used.     

Nonlinear stochastic modeling to improve state estimation in process monitoring and control

State estimation from plant measurements plays an important role in advanced monitoring and control technologies, especially for chemical processes with nonlinear dynamics and significant levels of process and sensor noise. Several types of state estimators have been shown to provide high‐quality estimates that are robust to significant process disturbances and model errors. These estimators require a dynamic model of the process, including the statistics of the stochastic disturbances affecting the states and measurements. The goal of this article is to introduce a design method for nonlinear state estimation including the following steps: (i) nonlinear process model selection, (ii) stochastic disturbance model selection, (iii) covariance identification from operating data, and (iv) estimator selection and implementation. Results on the implementation of this design method in nonlinear examples (CSTR and large dimensional polymerization process) show that the linear time‐varying autocovariance least‐squares technique accurately estimates the noise covariances for the examples analyzed, providing a good set of such covariances for the state estimators implemented. On the estimation implementation, a case study of a chemical reactor demonstrates the better capabilities of MHE when compared with the extended Kalman filter. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Constrained particle filtering methods for state estimation of nonlinear process

Increasingly in practical applications, nonlinearity, non‐Gaussianity, and constraint must be considered to obtain good state estimation. A constrained particle filter (PF) approach for state estimation, which involves three alternative strategies to impose the constraints on the prior particles, posterior particles, and state estimation has been proposed. First, to impose constraints on prior particles, a constrained Gibbs sampling method with a constrained inverse transform sampling is proposed to restrict sampling within the constraint region under cases of both univariate and coupling constraints. Second, to ensure validity of posterior particles, resampling is confined to the valid prior particles and the violated ones are discarded, which results in a similar formulation as the existing acceptance/rejection constrained PF method in literature. Third, if the state estimation violates the constraint, different from the existing methods that either discard all violated particles or accept all of them by projecting them onto the constraint region, the proposed method makes a balance between the prior and the likelihood function by adjusting the weights of violated and valid particles, respectively. Compared with the existing methods, the proposed method provides better physical interpretation and involves no restrictive assumptions about the distributions. Simulation results demonstrate effectiveness of the proposed methods. © 2014 American Institute of Chemical Engineers AIChE J, 60: 2072–2082, 2014     

Subsystem decomposition of process networks for simultaneous distributed state estimation and control

An appropriate subsystem configuration is a prerequisite for a successful distributed control/state estimation design. Existing subsystem decomposition methods are not designed to handle simultaneous distributed estimation and control. In this article, we address the problem of subsystem decomposition of general nonlinear process networks for simultaneous distributed state estimation and distributed control based on community structure detection. A systematic procedure based on modularity is proposed. A fast folding algorithm that approximately maximizes the modularity is used in the proposed procedure to find candidate subsystem configurations. Two chemical process examples of different complexities are used to illustrate the effectiveness and applicability of the proposed approach. © 2018 American Institute of Chemical Engineers AIChE J, 65: 904–914, 2019     

Parameter estimation in models with hidden variables : An application to a biotech process

Biological processes are often characterised by significant nonlinearities, noisy measurements and hidden process variables. The dynamic behaviour of such processes can be represented by stochastic differential equations obtained from physical laws. We propose a Bayesian algorithm for parameter estimation in stochastic nonlinear biological processes with unmeasured (or hidden) variables. The proposed algorithm, involves drawing random samples iteratively from a posterior density functions of the parameters and the hidden variables. A Bayesian sampling techniques is used to approximate these posterior density functions. Both Metropolis–Hastings algorithm and Gibbs sampling are used for sample generation. The algorithm is extended to handle multiple data sets and missing observations. The algorithm is applied to an experimental data set collected from an algal bioreactor system. © 2011 Canadian Society for Chemical Engineering     

Subsystem decomposition and distributed state estimation of nonlinear processes with implicit time-scale multiplicity

In this work, we propose a subsystem decomposition approach and a distributed estimation scheme for a class of implicit two-time-scale nonlinear systems. Taking the advantage of the time scale separation, these processes are decomposed into fast subsystem and slow subsystem according to the dynamics. In the proposed method, an approach that combines the approximate solutions obtained from both the fast and slow subsystems to form a composite solution of the original system is proposed. Also, based on the fast and slow subsystems, a distributed state estimation scheme is proposed to handle the implicit time-scale multiplicity. In the proposed design, an extended Kalman filter (EKF) is designed for the fast subsystem and a moving horizon estimator (MHE) is designed for the slow subsystem. In the design, the slow subsystem is only required to send information to the fast subsystem one-directionally. The fast subsystem estimator does not send out any information. The estimators use different sampling times, that is, fast sampling of the fast state variables is considered in the fast EKF and slow sampling of the slow state variables is considered in the slow MHE. Extensive simulations based on a chemical process are performed to illustrate the effectiveness and applicability of the proposed subsystem decomposition and composite estimation architecture.     

Lyapunov‐based MPC with robust moving horizon estimation and its triggered implementation

In this work, we consider moving horizon state estimation (MHE)‐based model predictive control (MPC) of nonlinear systems. Specifically, we consider the Lyapunov‐based MPC (LMPC) developed in (Mhaskar et al., IEEE Trans Autom Control. 2005;50:1670–1680; Syst Control Lett. 2006;55:650–659) and the robust MHE (RMHE) developed in (Liu J, Chem Eng Sci. 2013;93:376–386). First, we focus on the case that the RMHE and the LMPC are evaluated every sampling time. An estimate of the stability region of the output control system is first established; and then sufficient conditions under which the closed‐loop system is guaranteed to be stable are derived. Subsequently, we propose a triggered implementation strategy for the RMHE‐based LMPC to reduce its computational load. The triggering condition is designed based on measurements of the output and its time derivatives. To ensure the closed‐loop stability, the formulations of the RMHE and the LMPC are also modified accordingly to account for the potential open‐loop operation. A chemical process is used to illustrate the proposed approaches. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4273–4286, 2013     

Dictionary‐based estimation of spectra for wide‐gamut color imaging

With the widespread use of commercialized wide‐gamut displays, the demand for wide‐gamut image content is increasing. To acquire wide‐gamut image content using camera systems, color information should be accurately reconstructed from recorded image signals for a wide range of colors. However, it is difficult to obtain color information accurately, especially for saturated colors, if conventional color cameras are used. Spectrum‐based color image reproduction can solve this problem; however, bulky spectral imaging systems are required for this purpose. To acquire spectral images more conveniently, a new spectral imaging scheme has been proposed that uses two types of data: high spatial‐resolution red, green, and blue (RGB) images and low spatial‐resolution spectral data measured from the same scene. Although this method estimates spectral images with high overall accuracy, the error becomes relatively large when multiple different colors, especially those with high saturation, are arranged in a small region. The main reason for this error is that the spectral data are utilized as low‐order spectral statistics of local spectra in this method. To solve this problem, in this study, a nonlinear estimation method based on sparse and redundant dictionaries was used for spectral image estimation—where the dictionary contains a number of spectra—without loss of information from the low spatial‐resolution spectral data. The estimated spectra are represented by a mixture of a few spectra included in the dictionary. Therefore, the respective feature of every spectrum is expected to be preserved in the estimation, and the color saturation is also preserved for any region. Experiments performed using the simulated data showed that the dictionary‐based estimation can be used to obtain saturated colors accurately, even when multiple colors are arranged in a small region. © 2011 Wiley Periodicals, Inc. Col Res Appl, 2013     

Simultaneous model selection and parameter estimation for lithium‐ion batteries: A sequential MINLP solution approach

Equivalent circuit model (ECM) is a practical and commonly used tool not only in state of charge (SOC) estimation but also in state of health (SOH) monitoring for lithium‐ion batteries (LIBs). The functional forms of circuit parameters with respect to SOC in ECM are usually empirical determined, which cannot guarantee to obtain a compact and simple model. A systematical solution framework for simultaneous functional form selection and parameter estimation is proposed. A bi‐objective mixed‐integer nonlinear programming (MINLP) model is first constructed. Two solution approaches, namely the explicit and implicit methods, are then developed to balance model accuracy and model complexity. The former explicitly treats the model complexity as a constraint and the latter implicitly embeds the model complexity into the objective as a penalty. Both approaches require sequential solution of the transformed MINLP model and an ideal and nadir ideal solutions‐based criterion is utilized to terminate the solution procedure for determining the optimal functional forms, in which ideal solution and nadir ideal solution represent the best and worst of each objective, respectively. Both explicit and implicit approaches are thoroughly evaluated and compared through experimental pulse current discharge test and hybrid pulse power characterization test of a commercial LIB. The fitting and prediction results illustrate that the proposed methods can effectively construct an optimal ECM with minimum complexity and prescribed precision requirement. It is thus indicated that the proposed MINLP‐based solution framework, which could automatically guide the optimal ECM construction procedure, can be greatly helpful to both SOC estimation and SOH monitoring for LIBs. © 2015 American Institute of Chemical Engineers AIChE J, 62: 78–89, 2016     

由块段估计误差引起的矿石损失和贫化的量化估计方法

给出了由块段估计误差引起的矿石损失的贫化的量化估计方法,开发编制了计算机程序,并以实例说明其具体应用。     

Optimal periodic forcing of nonlinear chemical processes for performance improvements

Unsteady-state periodic operations can improve the optimal steady-state performance of nonlinear chemical processes. To examine if the optimal periodic operation is proper and to obtain the optimal forcing functions subject to various control and state constraints it is suggested in this paper to convert the problems into a form which is suitable for constrained nonlinear programming. The adopted numerical optimization method is based on employing the control parametrization technique and is thus capable of dealing with the problem of multiple input forcings and obtaining optimal forcing functions and/or parameters while subject to general constraints. Besides, it provides information about to what extent the process performance can be improved by adopting the optimal periodic control.     

Sequential minimum risk point estimation (MRPE) methodology for a normal mean under Linex loss plus sampling cost: First-order and second-order asymptotics

Abstract

We have designed a sequential minimum risk point estimation (MRPE) strategy for the unknown mean of a normal population having its variance unknown too. This is developed under a Linex loss plus linear cost of sampling. A number of important asymptotic first-order and asymptotic second-order properties' characteristics have been developed and proved thoroughly. Extensive sets of simulations tend to validate nearly all of these asymptotic properties for small to medium to large optimal fixed sample sizes.     

基于粒子滤波联合估计的气相聚乙烯质量指标在线估计

针对气相聚乙烯生产中各种复杂的工况造成在线估计精度下降的现象,基于乙烯聚合机理并利用特征建模方法建立了聚乙烯质量指标预测模型,结合扩展卡尔曼滤波,提出了粒子滤波联合估计方法,即将状态和修正系数组成增广状态向量,实现对质量指标预测模型的在线滤波修正,并分析了基于粒子滤波估计的收敛性。所提方法在中石化某气相聚乙烯装置的长周期运行结果证实了所提方法的可行性和有效性,为实施聚乙烯装置的先进控制奠定了基础。     

ON THE MAXIMUM ENTROPY PROPERTY OF NONLINEAR AUTOREGRESSIONS

Abstract. The assumption of a linear autoregressive model for time series has often been justified on the basis of a maximum entropy principle. The purpose of this short note is to point out that the class of nonlinear autoregressions is also characterized by a maximum entropy property.     

Maximum likelihood estimation of noise covariance matrices for state estimation of autonomous hybrid systems

A critical aspect of developing Bayesian state estimators for hybrid systems, that involve a combination of continuous and discrete state variables, is to have a reasonably accurate characterization of the stochastic disturbances affecting their dynamics. Recently, Bavdekar et al. (2011) have proposed a maximum likelihood (ML) based framework for estimation of the noise covariance matrices from operating input–output data when an EKF is used for state estimation. In this work, the ML framework is extended to estimation of the noise covariance matrices associated with autonomous hybrid systems, and, to a wider class of recursive Bayesian filters. Under the assumption that the innovations generated by an estimator form a white noise sequence, the proposed ML framework computes the noise covariance matrices such that they maximize the log-likelihood function of the estimator innovations. The efficacy of the proposed scheme is demonstrated through the simulation and experimental studies on the benchmark three-tank system.     

Eigenspectra for flocculation quality estimation

We present an image analysis algorithm for flocculation quality estimation in high-solids slurries, and demonstrate its performance using inline process images of oil sands tailings flocculation. While a skilled human operator can often successfully evaluate such images, variations in feed as well as the lack of isolated flocs or spatial reference-points inherent in a high-solids slurry can cause conventional image analysis techniques to fail. We overcome these challenges by recasting the images in Fourier space, discarding phase information, and applying an eigenfaces-inspired image recognition algorithm to the resulting spectra. Each image is represented using a few projection coefficients onto an orthogonal basis and evaluated using likelihood-based classification schemes. This algorithm shows a high degree of success evaluating the flocculation quality of 129 batch and inline flocculation experiments (5,610 images total) utilizing feed tailings from two different oil sand producers at a variety of feed dilutions and flocculant dosing levels.     

Illuminant estimation for object recognition

Comparing colour histograms of images has been shown to be a powerful technique for discriminating among large sets of images. However, these histograms depend not only on the properties of imaged objects but also on the illumination under which the objects are captured. If this illumination dependence is not accounted for prior to constructing the colour histograms, colour‐based image indexing will fail when illumination changes. This failure can be addressed by correcting the RGBs in an image to corresponding RGBs representing the same scene but under a standard reference illuminant prior to constructing the histograms. To perform this correction of RGBs, it is necessary to have a measurement or, more commonly, an estimate of the illumination in the original scene. Many authors have proposed illuminant estimation (or colour constancy) algorithms to obtain such an estimate. Unfortunately, the results of colour histogram matching experiments under varying illumination conditions have shown that existing estimation algorithms do not provide a sufficiently good estimate of the scene illuminant to enable this approach to work. In this article we report on the results of our repetition of those experiments, but this time using a new illuminant estimation algorithm—the so‐called color by correlation approach, which has been shown to afford significantly better performance than previous algorithms. The results of this new experiment show that when this new algorithm is used to preprocess images, a significant improvement in colour histogram matching performance is achieved. Indeed, performance is close to the theoretically optimal level of performance, that is, close to that which can be obtained using actual measurements of the scene illumination. © 2002 Wiley Periodicals, Inc. Col Res Appl, 27, 260–270, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/col.10064     

Uncertainty estimation in colour measurement

A current concern in modern metrology is the estimation of uncertainties of measurement in a more consistent manner than applied in the past. This article derives analytical expressions for uncertainties in (x,y), (u,v), and (u′,v′) chromaticity coordinates derived both from direct spectral measurements and from filtered tristimulus colorimeter measurements. Correlations between the tristimulus responses are included. Correlation coefficients are estimated for both broad‐ and narrow‐band sources. Conclusions are drawn for accuracy requirements for spectral matching and for signal‐to‐noise ratios to achieve a particular uncertainty. Specific examples are given for traffic signal lights, light‐emitting diodes, and a luminance standard. © 2000 John Wiley & Sons, Inc. Col Res Appl, 25, 349–355, 2000