State estimator for multisensor systems with irregular sampling and time-varying delays

This article addresses the state estimation in linear time-varying systems with several sensors with different availability, randomly sampled in time and whose measurements have a time-varying delay. The approach is based on a modification of the Kalman filter with the negative-time measurement update strategy, avoiding running back the full standard Kalman filter, the use of full augmented order models or the use of reorganisation techniques, leading to a lower implementation cost algorithm. The update equations are run every time a new measurement is available, independently of the time when it was taken. The approach is useful for networked control systems, systems with long delays and scarce measurements and for out-of-sequence measurements.     

Distributed resilient estimation over sensor networks for nonlinear time‐delayed systems with stochastic perturbations

This paper is concerned with the distributed resilient estimation problem for a class of nonlinear time‐delayed systems subject to stochastic perturbations. The plant and the measurements are disturbed by two Gaussian white stochastic processes with known statistical information, respectively. In addition, a resilient estimator is designed for each node by means of the parameter uncertainties and Bernoulli‐distributed random variables. Then, a novel exponential‐bounded performance index is put forward to measure the disturbance rejection level of the distributed estimators against the external disturbances and the impact of the initial values. A new vector dissipation definition including multiple vectors of energy storage functions is established to deal with the time‐delay estimation error dynamics. Within the framework of local performance analysis inspired by this new definition of vector dissipation, sufficient conditions in terms of recursive linear matrix inequalities are constructed for each node to guarantee the desirable performance index. Next, a local optimization problem subject to a set of recursive linear matrix inequalities is presented for each node to minimize the upper bound in the performance index, where the calculations can be conducted on every node in a distributed manner and the estimator gains are also calculated. Finally, an illustrative simulation example is provided to verify the applicability of the proposed estimators.     

Particle filter with one-step randomly delayed measurements and unknown latency probability

In this paper, a new particle filter is proposed to solve the nonlinear and non-Gaussian filtering problem when measurements are randomly delayed by one sampling time and the latency probability of the delay is unknown. In the proposed method, particles and their weights are updated in Bayesian filtering framework by considering the randomly delayed measurement model, and the latency probability is identified by maximum likelihood criterion. The superior performance of the proposed particle filter as compared with existing methods and the effectiveness of the proposed identification method of latency probability are both illustrated in two numerical examples concerning univariate non-stationary growth model and bearing only tracking.     

Distributed consensus estimation for diffusion systems with missing measurements over sensor networks

In this paper, the problem of distributed consensus estimation with randomly missing measurements is investigated for a diffusion system over the sensor network. A random variable, the probability of which is known a priori, is used to model the randomly missing phenomena for each sensor. The aim of the addressed estimation problem is to design distributed consensus estimators depending on the neighbouring information such that, for all random measurement missing, the estimation error systems are guaranteed to be globally asymptotically stable in the mean square. By using Lyapunov functional method and the stochastic analysis approach, the sufficient conditions are derived for the convergence of the estimation error systems. Finally, a numerical example is given to demonstrate the effectiveness of the proposed distributed consensus estimator design scheme.     

State estimation for discrete-time Markov jump linear systems with multiplicative noises and delayed mode measurements

In this paper, the state estimation problem for discrete-time Markov jump linear systems affected by multiplicative noises is considered. The available measurements for the system under consideration have two components: the first is the model measurement and the second is the output measurement, where the model measurement is affected by a fixed amount of delay. Using Bayes' rule and some results obtained in this paper, a novel suboptimal state estimation algorithm is proposed in the sense of minimum mean-square error under a lot of Gaussian hypotheses. The proposed algorithm is recursive and does not increase computational and storage load with time. Computer simulations are carried out to evaluate the performance of the proposed algorithm.     

Adaptive Gaussian filters for nonlinear state estimation with one-step randomly delayed measurements

This paper proposes new algorithms of adaptive Gaussian filters for nonlinear state estimation with maximum one-step randomly delayed measurements. The unknown random delay is modeled as a Bernoulli random variable with the latency probability known a priori. However, a contingent situation has been considered in this work when the measurement noise statistics remain partially unknown. Due to unavailability of the complete knowledge of measurement noise statistics, the unknown measurement noise covariance matrix is estimated along with states following: (i) variational Bayesian approach, (ii) maximum likelihood estimation. The adaptation algorithms are mathematically derived following both of the above approaches. Subsequently, a general framework for adaptive Gaussian filter is presented with which variants of adaptive nonlinear filters can be formulated using different rules of numerical approximation for Gaussian integrals. This paper presents a few of such filters, viz., adaptive cubature Kalman filter, adaptive cubature quadrature Kalman filter with their higher degree variants, adaptive unscented Kalman filter, and adaptive Gauss–Hermite filter, and demonstrates the comparative performance analysis with the help of a nontrivial Bearing only tracking problem in simulation. Additionally, the paper carries out relative performance comparison between maximum likelihood estimation and variational Bayesian approaches for adaptation using Monte Carlo simulation. The proposed algorithms are also validated with the help of an off-line harmonics estimation problem with real data.     

Soft sensor design by multivariate fusion of image features and process measurements

This paper presents a multivariate data fusion procedure for design of dynamic soft sensors where suitably selected image features are combined with traditional process measurements to enhance the performance of data-driven soft sensors. A key issue of fusing multiple sensor data, i.e. to determine the weight of each regressor, is achieved through multivariate regression. The framework is described and illustrated with applications to cement kiln systems that are characterized by off-line quality measurements and on-line analyzers with limited reliability. Image features are extracted with a multivariate analysis technique from RGB pictures. The color information is also transformed to hue, saturation and intensity components. Both sets of image features are combined with traditional process measurements to obtain an inferential model by partial least squares (PLS) regression. A dynamic PLS model is obtained by filtering the original data block augmented with time lagged variables such that improved predictive performance of the quality variable results. Key issues regarding data preprocessing and extraction of suitable image features are discussed with a case study, the on-line estimation of nitrogen oxides (NOx) emission of cement kilns. On-site tests demonstrate improved performance over soft sensors based on conventional process measurements only.     

Development of a variable selection method for soft sensor using artificial neural network and nonnegative garrote

This paper developed a new variable selection method for soft sensor applications using the nonnegative garrote (NNG) and artificial neural network (ANN). The proposed method employs the ANN to generate a well-trained network, and then uses the NNG to conduct the accurate shrinkage of input weights of the ANN. This paper took Bayesian information criterion as the model evaluation criterion, and the optimal garrote parameter s was determined by v-fold cross-validation. The performance of the proposed algorithm was compared to existing state-of-art variable selection methods. Two artificial dataset examples and a real industrial application for air separation process were applied to demonstrate the performance of the methods. The experimental results showed that the proposed method presented better model accuracy with fewer variables selected, compared to other state-of-art methods.     

Robust distributed H∞ filtering over an uncertain sensor network with multiple fading measurements and varying sensor delays

In this paper, the problem of robust distributed H_∞ filtering is investigated for state‐delayed discrete‐time linear systems over a sensor network with multiple fading measurements, random time‐varying communication delays, and norm‐bounded uncertainties in all matrices of the system. The diagonal matrices, whose elements are individual independent random variables, are utilized to describe the multiple fading measurements. Furthermore, the Bernoulli‐distributed white sequences are introduced to model the random occurrence of time‐varying communication delays. In the proposed filtering approach, the stability of the estimation error system is first shown by the Lyapunov stability theory and the H_∞ performance is then achieved using a linear matrix inequality method. Finally, two numerical examples are given to show the effectiveness and performance of the proposed approach.     

state estimation with fading measurements,randomly varying nonlinearities and probabilistic distributed delays

In this paper, the state estimation problem is investigated for a class of discrete‐time stochastic systems in simultaneous presence of three network‐induced phenomena, namely, fading measurements, randomly varying nonlinearities and probabilistic distributed delays. The channel fading is characterized by the ?th‐order Rice fading model whose coefficients are mutually independent random variables with given probability density functions. Two sequences of random variables obeying the Bernoulli distribution are utilized to govern the randomly varying nonlinearities and probabilistic distributed delays. The purpose of the problem addressed is to design an state estimator such that the dynamics of the estimation errors is stochastically stable and the prespecified disturbance rejection attenuation level is guaranteed. Through intensive stochastic analysis, sufficient conditions are established under which the addressed state estimation problem is recast as a convex optimization one that can be solved via the semi‐definite program method. Finally, a simulation example is provided to show the usefulness of the proposed state estimation scheme. Copyright © 2014 John Wiley & Sons, Ltd.     

一种神经网络逆系统软仪表的数据预处理方法

为了解决神经网络逆系统软仪表对噪声敏感的问题，本文提出了一种数据预处理方法。该方法先采用两步判断法对数据进行一次处理，再用滑动平均滤波方法对数据进行二次处理，有效地滤除了噪声信号，比较精确地复现了原始信号。对红霉素发酵过程中的pH值过程变量进行了实验，结果表明了该算法的有效性和可行性。     

Assessing quality performance based on the on-line sensor measurements using neural networks

Rapidly evolving sensor technologies, which employ advanced techniques, such as lasers, machine vision, and pattern recognition, have the potential to greatly improve quality control activities in the finished product inspection and process monitoring. In this paper, a neural network model was developed to probe the dependence between the quality of finished product and sensor measurements which were collected to monitor the failure (sudden fracture) of a tool in the manufacturing process. A real case in mass production is employed to illustrate the modeling procedure. Utilizing the trained neural network, the quality information of finished product can be further obtained from the online tooling sensor measurements. The result reveals that the tooling sensor measurements not only can be employed to detect the process condition (wear out or sudden fracture) but also can provide valuable information to monitor the quality performance of finished product simultaneously.     

Development and application of soft sensor model for heterogeneous information of aluminum reduction cells

The soft sensor model for heterogeneous information is presented because of the difficulty of online acquiring heterogeneous information of aluminum reduction cells. Firstly many redundancy samples are optimized by Fuzzy C-Means in order to acquire classified samples. Then dynamic process of heterogeneous information of aluminum reduction cells is modeled by multiple neural networks. Finally soft sensor model for heterogeneous information of aluminum reduction cells is developed. The model was used in 320 KA prebaked aluminum reduction cells in Guangxi Branch of China Aluminum Corporation. The results indicate that there are three types of instabilities for aluminum reduction cells: single anode irrationality, parameters irrationality of heat balance and outside operations. Corresponding measures to eliminate the three types of instabilities for aluminum reduction cells are the following: raising the anode, adjusting the parameters of heat balance and improving the operation of changing anode and taping metal.     

Continuous output feedback stabilization for nonlinear systems based on sampled and delayed output measurements

This paper addresses the problem of output feedback stabilization for nonlinear systems with sampled and delayed output measurements. Firstly, sufficient conditions are proposed to ensure that a class of hybrid systems are globally exponentially stable. Then, based on the sufficient conditions and a dedicated construction continuous observer, an output feedback control law is presented to globally exponentially stabilize the nonlinear systems. The output feedback stabilizer is continuous and hybrid, and can be derived without discretization. The maximum allowable sampling period and the maximum delay are also given. At last, a numerical example is provided to illustrate the design methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling for soft sensor systems and parameters updating online

Soft sensor technology is an important means to estimate important process variables in real-time. Modeling for soft sensor system is the core of this technology. Most nonlinear dynamic modeling methods integrate the processes of building the dynamic and static relationships between secondary and primary variables, which limits the estimation accuracy for primary variables. To avoid the problem, a kind of soft sensor model consisting of a dynamic model in cascade with a static one is proposed. The model identification and update online are conducted in substep way. In order to improve the model update efficiency, two improved Gauss–Newton recursive algorithms, which avoid nonsingular covariance matrix, are proposed for time-invariant and time-variant soft sensor systems. The uniform convergence for dynamic model parameter and the existence of estimation deviations for static model parameters are proved for time-invariant soft sensor system. The parameters of time-variant soft sensor system would be boundedly convergent. Case study confirms that, on the basis of the proposed model and recursive algorithms, the dynamic and static characteristics of soft sensor system can be described efficiently, and the primary variables are ensured to be estimated accurately.     

Comparison of variable selection methods for PLS-based soft sensor modeling

Data-driven soft sensors have been widely used in both academic research and industrial applications for predicting hard-to-measure variables or replacing physical sensors to reduce cost. It has been shown that the performance of these data-driven soft sensors could be greatly improved by selecting only the vital variables that strongly affect the primary variables, rather than using all the available process variables. In this work, a comprehensive evaluation of different variable selection methods for PLS-based soft sensor development is presented, and a new metric is proposed to assess the performance of different variable selection methods. The following seven variable selection methods are compared: stepwise regression (SR), partial least squares with regression coefficients (PLS-BETA), PLS with variable importance in projection (PLS-VIP), uninformative variable elimination with PLS (UVE-PLS), genetic algorithm with PLS (GA-PLS), least absolute shrinkage and selection operator (Lasso), and competitive adaptive reweighted sampling with PLS (CARS-PLS). Their strengths and limitations for soft sensor development are demonstrated by a simulated case study and an industrial case study.     

Piecewise-continuous observers for linear systems with sampled and delayed output

The paper presents a new class of state observers for linear systems with sampled and delayed output measurements. These observers are derived using the theory of a particular class of hybrid systems called piecewise-continuous systems, and can be easily implemented. The performances of the piecewise-continuous observers are compared with the performances of state observers designed using the Lyapunov–Krasovskii techniques. A piecewise-continuous observer is designed and implemented to an experimental visual servoing platform.     

State estimation for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays

In this paper, the state estimation problem is investigated for a class of discrete nonlinear systems with randomly occurring uncertainties and distributed sensor delays. The norm-bounded uncertainties enter into the system in a randomly way, and such randomly occurring uncertainties (ROUs) obey certain Bernoulli distributed white noise sequence with known conditional probability. By constructing a new Lyapunov–Krasovskii functional, sufficient conditions are proposed to guarantee the convergence of the estimation error for all discrete time-varying delays, ROUs and distributed sensor delays. Subsequently, the explicit form of the estimator parameter is derived by solving two linear matrix inequalities (LMIs) which can be easily tested by using standard numerical software. Finally, a simulation example is given to illustrate the feasibility and effectiveness of the proposed estimation scheme.     

Optimal selection of soft sensor inputs for batch distillation columns using principal component analysis

In this paper, a novel methodology based on principal component analysis (PCA) is proposed to select the most suitable secondary process variables to be used as soft sensor inputs. In the proposed approach, a matrix is defined that measures the instantaneous sensitivity of each secondary variable to the primary variables to be estimated. The most sensitive secondary variables are then extracted from this matrix by exploiting the properties of PCA, and they are used as input variables for the development of a regression model suitable for on-line implementation.This method has been evaluated by developing a soft sensor that uses temperature measurements and a process regression model to estimate on-line the product compositions for a simulated batch distillation process. The identification of the optimal soft sensor inputs for this case study has been discussed with respect to the definition of the sensitivity matrix, the data sampling interval, the presence of measurement noise, and the size of the input set. The simulation results demonstrate that the proposed approach can effectively identify the size and configuration of the input set that leads to the optimal estimation performance of the soft sensor.