Multi-rate Measurements Research Articles

A multi-rate high-order dynamic twin-latent-variable probabilistic modeling and its process monitoring application

Quality-relevant process monitoring provides important guarantees for the safety of industrial operation, which is based on the assumption that data collection is complete and low-order autocorrelated. However, real industrial processes always exhibit complex characteristics such as multi-rate sampling and high-order dynamic, which pose great challenges for process monitoring. To this end, a multi-rate high-order dynamic twin-latent-variable probabilistic (MHDTVP) model is presented in this paper to extract data correlations among multi-rate measurements from quality-relevant and irrelevant perspectives. Moreover, to reveal the dynamics in the multi-rate sampling process, an autoregressive twin-latent-variable structure is designed to extract both quality-relevant and quality-irrelevant high-order dynamic features. In the MHDTVP model, parameters are trained through an efficient expectation maximization (EM) iteration framework. Finally, the performance conclusions of MHDTVP are validated with the Tennessee Eastman process (TEP) and Thermal Power Plant (TPP). The experimental results demonstrate that the proposed model exhibits superior monitoring efficiency for multi-rate dynamic processes compared to similar approaches.

Encryption-Decryption-Based State Estimation With Multirate Measurements Against Eavesdroppers: A Recursive Minimum-Variance Approach

This paper is concerned with the secure state estimation problem for a networked system with multi-rate measurements. The measurement data are transmitted to the estimator over a communication network, where an eavesdropper could intercept the transmitted information and generate the state estimates based on the overheard signals. In order to protect the privacy of the system state from information leakage, a novel encryptor is proposed to encrypt the measurement signals into codewords before being transmitted, and a decryptor is then adopted at the user side to decrypt the received codewords into the desired measurement signals, based on which a recursive state estimator is developed whose parameter is calculated by solving several coupled difference equations. Here, the secret key for decryption is available to the user but is unknown to the eavesdropper. The encryptor and the estimator are co-designed such that 1) at the user side, the estimation error covariance has an upper bound that is subsequently minimized in the sense of the matrix trace, where the uniform boundedness of the error covariance is also examined; and 2) at the eavesdropper side, the corresponding state estimation error is divergent. Two simulation examples are provided to demonstrate the effectiveness of our developed secure state estimation scheme.

Digital H∞ filter design for a low frequency multiple‐input multiple‐output system with multirate measurements

AbstractIn this article, a digital filter is designed for a low frequency multiple‐input multiple‐output (MIMO) system with multirate measurements from multiple samplers. A delay compensation is introduced to reduce estimation errors from the multiple samplers and a zero‐order holder. A single‐rate error system is obtained by converting the low frequency MIMO system using a discrete‐time lifting technique. A digital filter is proposed based on a delay‐partitioning method to guarantee asymptotic stability and performance for the single‐rate error system. A numerical example is provided to show effectiveness and superiority of the digital filter in low frequency domain.

GNSS-5G Hybrid Positioning Based on Multi-Rate Measurements Fusion and Proactive Measurement Uncertainty Prediction

The fifth-generation (5G) network can be used jointly with a global navigation satellite system (GNSS) to help relieve the problem of having few visible satellites in urban environments and achieve highly accurate localization. The 5G base stations (BSs) can provide range and angle measurements at a much higher rate than GNSS. However, this benefit has not been fully employed by existing GNSS-5G hybrid methods. In addition, the near–far effect of 5G BS causes a large dynamic range of the measurement noise uncertainty. This challenge has not been well dealt with by the existing adaptive noise estimation methods, resulting in the decline of positioning accuracy and system convergence. This work proposes a multiple-rate adaptive Kalman filter (MRAKF) for GNSS-5G hybrid positioning with a hybrid sequential fusing scheme. It supports the fusion of GNSS and 5G measurements at different data rates to better employ the high-rate 5G measurements. A distance-dependent model is derived to quantitatively characterize the effect of BS-user equipment (UE) distance over the measurement noise covariance, leading to a proactive measurement uncertainty prediction algorithm to adaptively adjust the observation noise covariance matrix. Furthermore, a switchover strategy is proposed to switch its positioning mode to avoid the impact of variation of available line of sight (LOS) BSs. Both simulations and a real driving test were carried out. Results show that the proposed MRAKF method significantly improves the positioning accuracy compared with the other four adaptive noise estimation methods and the standard EKF. It requires the lowest computation complexity among all adaptive methods in this work.

Multi-Rate Data Fusion for State and Parameter Estimation in (Bio-)Chemical Process Engineering

For efficient operation, modern control approaches for biochemical process engineering require information on the states of the process such as temperature, humidity or chemical composition. Those measurement are gathered from a set of sensors which differ with respect to sampling rates and measurement quality. Furthermore, for biochemical processes in particular, analysis of physical samples is necessary, e.g., to infer cellular composition resulting in delayed information. As an alternative for the use of this delayed measurement for control, so-called soft-sensor approaches can be used to fuse delayed multirate measurements with the help of a mathematical process model and provide information on the current state of the process. In this manuscript we present a complete methodology based on cascaded unscented Kalman filters for state estimation from delayed and multi-rate measurements. The approach is demonstrated for two examples, an exothermic chemical reactor and a recently developed model for biopolymer production. The results indicate that the the current state of the systems can be accurately reconstructed and therefore represent a promising tool for further application in advanced model-based control not only of the considered processes but also of related processes.

Kernel Generalization of Multi-Rate Probabilistic Principal Component Analysis for Fault Detection in Nonlinear Process

In practical process industries, a variety of online and offline sensors and measuring instruments have been used for process control and monitoring purposes, which indicates that the measurements coming from different sources are collected at different sampling rates. To build a complete process monitoring strategy, all these multi-rate measurements should be considered for data-based modeling and monitoring. In this paper, a novel kernel multi-rate probabilistic principal component analysis (K-MPPCA) model is proposed to extract the nonlinear correlations among different sampling rates. In the proposed model, the model parameters are calibrated using the kernel trick and the expectation-maximum (EM) algorithm. Also, the corresponding fault detection methods based on the nonlinear features are developed. Finally, a simulated nonlinear case and an actual pre-decarburization unit in the ammonia synthesis process are tested to demonstrate the efficiency of the proposed method.

Parameter estimation for nonlinear systems with multirate measurements and random delays

AbstractWe present an approach for parameter estimation with multirate measurements, with the slow measurements having variable time delays due to laboratory analysis, and also being functions of all the states during the sample collection. We formulate a particle filter‐based approach under the framework of the expectation maximization algorithm to develop the estimates. The effectiveness and applicability of the proposed method are demonstrated though a simulation example, a hybrid tank experiment and an industrial case study; in each case, the slow and fast measurements are for the same variable. We show that this approach results in improved parameter estimation when the information from the delayed measurements is fused with the fast measurement information.

State Estimation for Multirate Measurements in the Presence of Integral Term and Variable Delay

Measurements in the process industry can arrive with fast or slow sampling rates. Fast measurements, such as flowrate and temperature, are sampled frequently and are obtained instantly after sampling. The slow measurements, which are usually related to chemical quality variables such as product composition, are sampled infrequently and have some delay due to laboratory analysis. Moreover, sample collection for laboratory analysis may extend over a significant time interval, and the slow measurements are actually functions of all the states during the sampling period. Our objective is to develop a multirate state estimation method for this situation. We propose two methods to solve the problem: the exact Bayesian approach and the augmented state approach. In the exact Bayesian approach, the algorithm is developed by implementing the Bayes rule. In the augmented state approach, the system is reformulated by augmenting the current state with past information required for fusing the slow measurements and then applying general state estimation procedures. The performance of the proposed methods for state estimation is demonstrated through simulation and experimental studies and by comparison with methods that only use the fast measurements.

Filtering Design for Multirate Sampled-Data Systems

The problem of ${\mathcal {H}}_{\infty }$ filtering to estimate the unmeasurable states is investigated in this paper and the most general multirate measurements condition is taken into account. The main result of this paper is to give a method to design a filter, which can guarantee the stability of the resultant filtering error system with ${\mathcal {H}}_{\infty }$ performance. For a given system with multirate measurements, this paper first provides a method to convert this multirate design problem into an equivalent single-rate design problem. Then, it can be proved that the design approach of a required filter based on a linear matrix inequality is a sufficient and necessary condition. Lastly, two examples are utilized to demonstrate that this design approach is effective and applicable to estimate the unmeasurable states for the given system with multirate measurements.

Moving horizon estimation with multirate measurements and correlated noises

SummaryThis article is concerned with the moving horizon estimation (MHE) problem for a class of linear discrete‐time systems subject to multirate measurements and correlated noises. The sensors of the plant are grouped into two nodes with different sampling periods, which give rise to the multirate measurements. Under the effects of multirate measurements, the underlying system is then described by a periodic system with correlated noises. A MHE strategy is formulated and the corresponding analytical solution of the state estimation is derived by using the “completing the square” technique. Based on the lifting approach, the dynamics of the estimation error covariance is analyzed and the desired estimator parameters are obtained by solving a set of linear matrix inequalities. An illustrative example is given to show the effectiveness of our proposed MHE method.

Distributed output feedback control for multi-unit system with delayed multirate measurements

The aim of this work is to analyze output feedback distributed control framework based on model predictive control (MPC) for multi-unit systems with multirate and delayed measurements. Primary controlled variable(s) is sampled infrequently, and the measurement is available after a delay. The distributed, unit-specific estimators and controllers communicate through selective information transfer based on process knowledge. The distributed state estimator is designed based on sampled state augmentation method to efficiently compute improved state estimates on arrival of the delayed infrequent measurements. The multirate estimators are appropriately modified to incorporate the disturbance model to handle model-plant mismatch (MPM). The proposed implementation is analyzed using two case studies. A linearized, reactor-separator system is used to demonstrate that multirate estimation is required for offset-free tracking. A more complex variant of the reactor-separator system with recycle demonstrates the ability of nonlinear distributed estimator-MPC framework to incorporate infrequent and delayed primary measurements.

Modeling and Observer-Based Monitoring of RAFT Homopolymerization Reactions

Reversible addition–fragmentation chain–transfer (RAFT) polymerization of methyl methacrylate (MMA) is modeled and monitored using a multi-rate multi-delay observer in this work. First, to fit the RAFT reaction rate coefficients and the initiator efficiency in the model, in situ 1 H nuclear magnetic resonance (NMR) experimental data from small-scale (<2 mL) NMR tube reactions is obtained and a least squares optimization is performed. 1 H NMR and size exclusion chromatography (SEC) experimental data from large-scale (>400 mL) reflux reactions is then used to validate the fitted model. The fitted model accurately predicts the polymer properties of the large-scale reactions with slight discordance at late reaction times. Based on the fitted model, a multi-rate multi-delay observer coupled with an inter-sample predictor and dead time compensator is designed, to account for the asynchronous multi-rate measurements with non-constant delays. The multi-rate multi-delay observer shows perfect convergence after a few sampling times when tested against the fitted model, and is in fair agreement with the real data at late reaction times when implemented based on the experimental measurements.

Multirate Factor Analysis Models for Fault Detection in Multirate Processes

Generally, the measurements of modern industries are collected from different sources, which indicates that the traditional multivariate statistical process monitoring methods cannot be directly used in the multirate systems if one aims to utilize the complete multirate measurements. Hence, a set of multirate factor analysis models is developed for process modeling and fault detection purpose in the multirate processes. In the proposed model, the cross correlations are described and bounded by the common factors and the model parameters are calibrated using the expectation–maximum algorithms. Also, the proposed models are further discussed both from theoretical and geometric perspective. Finally, the proposed fault detection methods are tested by a simulated Tennessee–Eastman process and a real R2S anaerobic reactor unit in the wastewater treatment process.

Multiple probability principal component analysis for process monitoring with multi-rate measurements

To obtain the informative enough data from the modern chemical processes, various sensors and measuring instruments have been applied. Among them, both the online measurements and offline laboratory analyser results are collected and used for multivariate statistical process monitoring purpose. Hence, it indicates that the obtained measurements indeed contain different sampling rates due to the different demands of the control systems and the equipment constraints. To handle the multi-rate process monitoring problem, it is desirable to effectively integrate the measurements with different sampling rates. In this paper, a multiple probability principal component analysis (MPPCA) model is proposed for efficient collection of data and the improvement of the performance on model prediction and process monitoring. In the proposed model, it has been derived as a general form for any multi-rate systems and the model parameters are calibrated by the expectation–maximization algorithm. Based on it, several statistics are constructed for different sampling rates in the process monitoring scenario. Finally, two case studies are presented to show the effectiveness of the proposed method.

Development of a State Estimation Environment for the Optimal Control of a Mini-plant for the Hydroformylation in Microemulsions

A state estimation framework for a surfactant containing multiphase process for the hydroformylation of long-chained alkenes is presented. Firstly, available state estimation methods, such as the extended Kalman filter, the unscented Kalman filter and the particle filter are compared regarding their usability in processes with high model and measurement uncertainty. Subsequently, an MHE-based state estimation algorithm is introduced. This includes an approach, which handles the occurring multi-rate measurements by dividing the state estimation into two separate steps. Finally, the implementation is discussed regarding necessary requirements and the state estimation framework is applied within long-term real process operation in a mini-plant.

A high-accuracy constrained SINS/CNS tight integrated navigation for high-orbit automated transfer vehicles

High-accuracy and reliable autonomous navigation is increasingly crucial for automated transfer vehicles (ATV). This paper proposes a novel strapdown inertial navigation system/celestial navigation system (SINS/CNS) tight integration scheme aided by dynamic model constraints for high-orbit ATV to realize accurate and autonomous navigation. In this scheme, the complete weightlessness constraint in orbit is used to address the divergence of position and velocity caused by inaccurate accelerometer bias estimation problem encountered in the traditional SINS/CNS integration method, and the image point position-based tight integration model is derived to handle the adverse influence of time-varying attitude measurement noise due to changes of star geometry observed by a large-view-filed star sensor. Moreover, an information filter is devised to fuse the multi-rate measurements. The proposed algorithm is evaluated by a representative high-orbit ATV trajectory simulation, which indicates significant improvements in navigation accuracy compared with its traditional counterparts. The proposed algorithm can realize navigation accuracy enhancements without introducing additional sensors, strengthening its potentials in engineering application.

A Solution to Estimation Fusion for Multirate Measurements with Delays

This paper presents the distributed estimation fusion algorithms for a class of multirate multisensor systems with measurement delays. Different sensors uniformly sample measurements with different sampling rates and time delays. First, a new state-space model at the measurement sampling points is constructed and the original time delayed system is transformed to a delay-free one with correlated noises in limited time intervals to obtain the real-time estimation. Based on the new state-space model, the optimal local filter at the measurement sampling points is obtained for each single-sensor subsystem, and then the local estimator at the state update points is derived by using the predictor based on the filter at the measurement sampling points. Then, the estimation error cross-covariance matrices between any two local estimators are derived. Finally, the real-time distributed fusion estimator at the state update points is obtained based on the optimal fusion criterion weighed by matrices in the linear unbiased minimum variance sense. Besides, to avoid the correlation between system and measurement noises in the developed state-space model, a simple alternative but nonreal-time estimation fusion algorithm is also presented by employing dummy measurements. A numerical example is given to illustrate the effectiveness of the proposed algorithms.

Robust soft sensor development using multi-rate measurements

Two different types of measurements are often available for the key quality variables in process industries - (a) an accurate “slow-rate” laboratory measurements, and (b) a less accurate “fast-rate” online analyser measurements. Also, the analyser measurements are prone to fail due to hardware issues. Therefore, the main objective of this work is to present a novel approach for developing an accurate, fast-rate, inferential model of quality variables which is robust to outliers. For this purpose, we present a maximum likelihood based approach to integrate the multi-rate output data in the model building task, using Expectation Maximization algorithm. The efficacy of the proposed approach is demonstrated using a simulation example.

Application of MHE to large-scale nonlinear processes with delayed lab measurements

The paper addresses nonlinear estimation problems on nonlinear processes containing several lab measurements sampled slowly and with long delay, which is the usual case in industrial polymerization applications. A moving horizon estimation algorithm is developed to compute the theoretical optimal solution given the multi-rate measurements. In this algorithm, the MHE window is recalculated as the new lab measurement becomes available. Simulation studies on a polymerization process with plant model mismatch are performed. Observability analysis and estimation results of MHE with and without lab measurements show that lab measurements help identify the disturbances and can improve the performance of both estimation and closed-loop control.

Jump state estimation with multiple sensors with packet dropping and delaying channels

This work addresses the design of a state observer for systems whose outputs are measured through a communication network. The measurements from each sensor node are assumed to arrive randomly, scarcely and with a time-varying delay. The proposed model of the plant and the network measurement scenarios cover the cases of multiple sensors, out-of-sequence measurements, buffered measurements on a single packet and multirate sensor measurements. A jump observer is proposed that selects a different gain depending on the number of periods elapsed between successfully received measurements and on the available data. A finite set of gains is pre-calculated offline with a tractable optimisation problem, where the complexity of the observer implementation is a design parameter. The computational cost of the observer implementation is much lower than in the Kalman filter, whilst the performance is similar. Several examples illustrate the observer design for different measurement scenarios and observer complexity and show the achievable performance.