Steady-state Data Reconciliation Research Articles

A multiscale data reconciliation approach for sensor fault detection

When used separately on the sensor data of the processes like nuclear reactors, the data reconciliation with fault detection and isolation strategy gives noise-corrupted estimates, and the wavelet transformation gives erroneous inferences about the operating point of the process under sensor fault conditions. Aiming to solve these challenging problems, a hybrid multi-scale data reconciliation scheme that combines data reconciliation with the wavelet transform is proposed in this work. The proposed method uses the steady-state data reconciliation framework under the assumption of consistent algebraic relationships among the wavelet coefficient data. The role of multivariate techniques in obtaining the algebraic relationships, online detection and isolation of sensor faults, orthogonal decomposition, and reconciliation of the wavelet coefficients data is demonstrated. It is shown that the reconciled estimates obtained from this method very closely represent the true behavior of the process as problems with respect to random noise, high-frequency components due to process faults, sensor faults, and the influence of sensor faults on the signal estimates are alleviated. The effectiveness of this method is quantitatively established when applied to the ex-core neutron detector data of the advanced heavy water reactor in various simulations.

Nonlinear Model Identification and Data Reconciliation Using Kernel Principal Component Regression

Reconciliation of process data is an important preprocessing technique, the main purpose of which is to obtain accurate estimates of variables and model parameters. Reconciliation requires a process model which is generally developed using first principles. For many complex processes, the development of such models is difficult and time-consuming. In this work we propose a novel alternative method for steady state data reconciliation of nonlinear processes which does not require a functional model between variables to be specified a priori. A nonlinear model relating the variables is developed from a given data set, while simultaneously obtaining accurate estimates of the measured variables. The method we propose combines concepts drawn from Kernel Principal Components Regression with an error-in-variables model parameter estimation technique. Simulation studies demonstrate that the proposed approach is able to improve the accuracy of measured variables. The identified nonlinear model is also useful for reconciling future measurements of the process.

Sensor Network Robustness Using Model-Based Data Reconciliation for Continuous Tablet Manufacturing

Advances in continuous manufacturing in the pharmaceutical industry necessitate reliable process monitoring systems that are capable of handling measurement errors inherent in all sensor technologies and detecting measurement outliers to ensure operational reliability. The purpose of this work was to demonstrate data reconciliation (DR) and gross error detection methods as real-time process management tools to accomplish robust process monitoring. DR mitigates the effects of random measurement errors, while gross error detection identifies nonrandom sensor malfunctions. DR is an established methodology in other industries (i.e., oil and gas) and was recently investigated for use in drug product continuous manufacturing. This work demonstrates the development and implementation of model-based steady-state data reconciliation on 2 different end-to-end continuous tableting lines: direct compression and dry granulation. These tableting lines involve different equipment and sensor configurations, with sensor network redundancy achieved using equipment-embedded sensors and in-line process analytical technology tools for the critical process parameters and critical quality attributes. The nonlinearity of the process poses additional challenges to solve the steady-state data reconciliation optimization problem in real time. At-line and off-line measurements were used to validate the framework results.

Steady-State Data Reconciliation Framework for a Direct Continuous Tableting Line.

Reliable process monitoring in real-time remains a challenge for the pharmaceutical industry. Dealing with random and gross errors in the process measurements in a systematic way is a potential solution. In this paper, we present a process model-based framework, which for given sensor network and measurement uncertainties will predict the most likely state of the process. Thus, real-time process decisions, whether for process control or exceptional events management, can be based on the most reliable estimate of the process state. Reliable process monitoring is achieved by using data reconciliation (DR) and gross error detection (GED) to mitigate the effects of random measurement errors and non-random sensor malfunctions. Steady-state data reconciliation (SSDR) is the simplest forms of DR but offers the benefits of short computational times. We also compare and contrast the model-based DR approach (SSDR-M) to the purely data-driven approach (SSDR-D) based on the use of principal component constructions. We report the results of studies on a pilot plant-scale continuous direct compression-based tableting line at steady-state in two subsystems. If the process is linear or mildly nonlinear, SSDR-M and SSDR-D give comparable results for the variables estimation and GED. SSDR-M also complies with mass balances and estimate unmeasured variables. SSDR successfully estimates the true state of the process in presence of gross errors, as long as steady state is maintained and the redundancy requirement is met. Gross errors are also detected while using SSDR-M or SSDR-D. Process monitoring is more reliable while using the SSDR framework.

Enhancement of performance monitoring of a coal-fired power plant via dynamic data reconciliation

Wide-range and frequent operation changes have become a common phenomenon with thermal power plants in the context of fast penetration of intermittent renewable power. Performance monitoring at transient states is more important to the safety and high efficiency of power plants. Data quality is essential for conducting dynamic performance monitoring, and dynamic data reconciliation (DDR) provides great potential to enhance quality of measured data at transient states. In this paper, a moving window based approach to dynamic data reconciliation is proposed for a real coal-fired power plant using high sampling operational data. Firstly, dynamic characteristics of the system are discussed, taking account of the equipment accumulation in DDR problems. Results of case studies indicate that the data accuracy of measured mass flow parameters are enhanced effectively after DDR, and better results are obtained with the increasing time window size. Comparison with steady state data reconciliation approach is also carried out to indicate the enhanced effect of the DDR approach for the performance monitoring of a real power plant.

Expectation Maximization Approach for Simultaneous Gross Error Detection and Data Reconciliation Using Gaussian Mixture Distribution

Process measurements play a significant role in process identification, control, and optimization. However, they are often corrupted by two types of errors, random and gross errors. The presence of gross errors in the measurements affects the reliability of optimization and control solutions. Therefore, in this work, we characterize the measurement noise model using a Gaussian mixture distribution, where each mixture component denotes the error distribution corresponding to random error and gross error, respectively. On the basis of this assumption, we propose a maximum likelihood framework for simultaneous steady-state data reconciliation and gross error detection. Since the proposed framework involves the noise mode as a hidden variable denoting the existence of gross errors in the data, it can be solved using the expectation maximization (EM) algorithm. This approach does not require the parameters of the error distribution model to be preset, rather they are determined as part of the solution. Several...

Numerical Aspects of Data Reconciliation in Industrial Applications

Data reconciliation is a model-based technique that reduces measurement errors by making use of redundancies in process data. It is largely applied in modern process industries, being commercially available in software tools. Based on industrial applications reported in the literature, we have identified and tested different configuration settings providing a numerical assessment on the performance of several important aspects involved in the solution of nonlinear steady-state data reconciliation that are generally overlooked. The discussed items are comprised of problem formulation, regarding the presence of estimated parameters in the objective function; solution approach when applying nonlinear programming solvers; methods for estimating objective function gradients; initial guess; and optimization algorithm. The study is based on simulations of a rigorous and validated model of a real offshore oil production system. The assessment includes evaluations of solution robustness, constraint violation at convergence, and computational cost. In addition, we propose the use of a global test to detect inconsistencies in the formulation and in the solution of the problem. Results show that different settings have a great impact on the performance of reconciliation procedures, often leading to local solutions. The question of how to satisfactorily solve the data reconciliation problem is discussed so as to obtain improved estimates.

Concurrent reconciliation of chemical and mineral assays for mineral processing circuits

The steady-state data reconciliation of mineral processing plants has traditionally depended on chemical assays of samples collected from various streams in the plant. In some cases, additional information in the form of size assays and size-wise chemical assays have been employed to improve the reconciliation problem. Reconciliation algorithms, in addition to making the measured data consistent with the basic conservation principles, also help in predicting the material flow rates in different streams. This information helps the process engineer to identify and troubleshoot problem areas, and further use it to optimize the plant's performance. If all the minerals present in the ore system are known (established through X-Ray Diffraction), the chemical formulae of the minerals provide the relationship between the chemical assays and mineral composition. In this communication, first we propose an approach to estimate the mineral composition from the measured chemical assays for a given sample or stream. It is then extended to a plant-wide concurrent data reconciliation methodology, involving both the chemical assays and mineral composition. This concurrent data reconciliation procedure provides estimates of mineral composition around the plant even when mineral composition measurements are not available. This additional information will help the plant engineers to track and improve their plant's behavior more intuitively. When mineral compositions are measured (for example, through QEMSCAN) they can be reconciled along with chemical assays. The methodology is demonstrated with data from batch and semi-batch laboratory studies on selective dispersion-flocculation of iron ore slimes.

Application of Data Reconciliation and Fault Detection and Isolation of Ion Chambers in Advanced Heavy Water Reactor

In a nuclear reactor, e.g. Advanced Heavy Water Reactor, a large number of neutron flux detectors are used for measurement of core flux based on which different monitoring, control and protection functions are performed. Changes in ambient and operating conditions of these detectors result in deviations from the nominal signals. These deviations, termed as faults, lead to erroneous inferences about the operation of the reactor. In order to ensure that such faults do not hamper the intended functionality, adequate degree of redundancy is provided in the detectors and the signal that deviates considerably from the signals of other detectors is rejected. However, it would be desirable to develop a method to continuously monitor the detectors for occurrence of faults and isolate the faulty reading based on more formal and systematic approach. In addition to occasional faults, there might also be random errors resulting from various sources. This paper aims at detection and isolation of faults in Ion Chambers of Advanced Heavy Water Reactor and minimization of random errors in the signal data with the help of a Data Reconciliation based scheme. This scheme makes use of the process constraint models developed from the multivariate statistical techniques, viz., Principal Component Analysis and Iterative Principal Component Analysis combined with Iterative Measurement Test method of Fault Detection and Isolation. Development of constraint models relies on data from Ion Chambers in the form of current signals from their amplifiers. These signals are functions of the neutron fluxes at their respective locations. Such data were generated for four representative situations of the reactor operation with the help of the mathematical model of the reactor and the amplifier models associated with the Ion Chambers. To these data, various additive biases were applied, subsequently, Data Reconciliation and Fault Detection and Isolation are attempted within the ambit of linear steady-state Data Reconciliation and the results are presented. The study establishes the efficacy of Iterative Principal Component Analysis and Iterative Measurement Test for Data Reconciliation and Fault Detection and Isolation of Ion Chamber signals in a nuclear reactor.

Selecting proper uncertainty model for steady-state data reconciliation – Application to mineral and metal processing industries

Data reconciliation is widely applied in mineral and metal processing plants to improve information quality. Imprecision, unreliability and incompleteness of measurements are common problems motivating the implementation of the technique. Current practices rely on mass and energy conservation constraints to estimate the underlying steady-state values of process variables. Typically, the Gaussian context is assumed and a Maximum-Likelihood estimator is selected. The performance of such an estimator depends on the covariance matrices used to characterize model and measurement uncertainties. In practice, determining these covariance matrices is a challenging task that is often overlooked. Using inappropriate uncertainty models, based on simplistic or improper hypotheses, can lead to unexpected underperformances. The objective of the paper is to illustrate the impact of correctly selecting uncertainty covariance matrices for steady-state data reconciliation. Different case-studies involving a combustion chamber, a hydrocyclone, a flotation circuit, and a separation unit are used for investigating the sensitivity of the algorithm to the structure of covariance matrices. An example based on Monte-Carlo simulations is presented to assess the importance of assigning right values to variance terms. Simulation results show that the adjustment of uncertainty covariance matrices has a significant influence on the precision of estimates and reveal that some common tuning practices can have detrimental effects.

Role of Steady State Data Reconciliation in Process Model Development

In chemical and hydrocarbon industry operational efficiency is improved by model-based solutions. Historical process data plays an important role in the identification and verification of models utilized by these tools. Since most of the used information are measured values, they are affected by errors influencing the quality of these models. Data reconciliaton aims the reduction of random errors to enhance the quality of data used for model development resulting in more reliable process simulators. This concept is applied to the development and validation of the complex process model and simulator of an industrial hydrogenation system. The results show the applicability of the proposed scheme in industrial environment.

The importance of uncertainty covariance tuning for steady-state data reconciliation in mineral and metal processing

Data reconciliation is widely applied in metallurgical plants for steady-state estimation of process variables. Algorithms are mainly based on mass and energy conservation equations that could be mostly extracted from process flow diagrams. An important difficulty is to characterize uncertainties about the plant behavior. Usually, the Gaussian context is assumed and a Maximum-Likelihood estimator is retained. In practice, tuning the weighting matrix, i.e. selecting the variances of modeling and measurement errors, is a challenging task that is sometimes overlooked. The objective of the paper is to illustrate the impact of correctly choosing uncertainty covariance matrices. Effects of matrix structures are investigated to assess the sensitivity of data reconciliation to uncertainty. Analyses are supported by simulation of basic case-studies including a combustion chamber, a hydrocyclone, a flotation circuit and a separation unit. Results show that adjustment of the uncertainty covariance matrix has a significant impact on the precision of estimates. A correct selection is highly valuable for subsequent uses of reconciled data.

Steady-state data reconciliation for absorption refrigeration systems

In this paper data reconciliation is applied to the steady-state operational data of a single-effect ammonia/water absorption chiller. The methodology includes the detection of steady-state, the application of systematic degrees of freedom analysis (in order to determine a suitable set of measured input variables for the absorption chiller model), and data reconciliation of the measurements (which included the treatment of gross errors). The reconciliation problem was solved using a two stage sequential approach in which the objective function is minimized in Matlab and the absorption chiller is simulated in the Engineering Equation Solver (EES). The Modified Iterative Measurement Test was used to detect the measurements that contain gross errors. This methodology makes it possible to identify and eliminate the sources of gross errors, and to obtain performance calculations that are in agreement with the laws of conservation.

Data reconciliation and variable classification by null space methods

General steady-state data reconciliation with both measured and un-measured variables is treated through theoretical vector space methods. Instead of solving the initial equality constrained optimization problem, a parametrized regular least squares regression onto the null space of the Jacobian matrix of the constraining equations is performed, yielding adjusted estimates of process variables. Additionally the full structure of the Jacobian, through its singular value decomposition, is exploited in order to state classification rules for the process variables with regards to redundancy and observability as well as to obtain estimates of observable variables. The method is exemplified by applying it to a small process monitoring network for which mass balance provides the physical constraints. Furthermore, the covariance matrix of the adjustments is used in order assist in the design of an improved network with respect to the number of flow-meters required so that reliable estimates of the process variables can be obtained.

Hematocele

Data reconciliation is widely applied in mineral and metal processing plants to improve information quality. Imprecision, unreliability and incompleteness of measurements are common problems motivating the implementation of the technique. Current practices rely on mass and energy conservation constraints to estimate the underlying steady-state values of process variables. Typically, the Gaussian context is assumed and a Maximum-Likelihood estimator is selected. The performance of such an estimator depends on the covariance matrices used to characterize model and measurement uncertainties. In practice, determining these covariance matrices is a challenging task that is often overlooked. Using inappropriate uncertainty models, based on simplistic or improper hypotheses, can lead to unexpected underperformances. The objective of the paper is to illustrate the impact of correctly selecting uncertainty covariance matrices for steady-state data reconciliation. Different case-studies involving a combustion chamber, a hydrocyclone, a flotation circuit, and a separation unit are used for investigating the sensitivity of the algorithm to the structure of covariance matrices. An example based on Monte-Carlo simulations is presented to assess the importance of assigning right values to variance terms. Simulation results show that the adjustment of uncertainty covariance matrices has a significant influence on the precision of estimates and reveal that some common tuning practices can have detrimental effects.

Impact of plant dynamics on the performance of steady-state data reconciliation

This paper studies the impact of plant dynamics on the performance of steady-state data reconciliation for processes operating in stationary mode. Data reconciliation can effectively reduce effects of measurement errors on process variables estimation. This has greatly motivated the use of steady-state observers in the process industry. However, processes are operating under unsteady-state conditions and the fundamental hypothesis of steady-state is not respected. The objective of the paper is to develop criteria for assessing the impact of stationary disturbances on estimates quality and therefore to propose applicability indices for steady-state data reconciliation methods in disturbed plants. A generic criterion based on generalized variance is given and criteria are proposed for plant performance indicators using variance reduction in specific state-space directions. The various applicability indices are illustrated through a material balance example for a simulated mineral separation circuit and the steady-state approach is compared to an optimal stationary data reconciliation method.

A new framework for data reconciliation and measurement bias identification in generalized linear dynamic systems

This article describes a new framework for data reconciliation in generalized linear dynamic systems, in which the well-known Kalman filter (KF) is inadequate for filtering. In contrast to the classical formulation, the proposed framework is in a more concise form but still remains the same filtering accuracy. This comes from the properties of linear dynamic systems and the features of the linear equality constrained least squares solution. Meanwhile, the statistical properties of the framework offer new potentials for dynamic measurement bias detection and identification techniques. On the basis of this new framework, a filtering formula is rederived directly and the generalized likelihood ratio method is modified for generalized linear dynamic systems. Simulation studies of a material network present the effects of both the techniques and emphatically demonstrate the characteristics of the identification approach. Moreover, the new framework provides some insights about the connections between linear dynamic data reconciliation, linear steady state data reconciliation, and KF. © 2009 American Institute of Chemical Engineers AIChE J, 2010

Soft sensors based on nonlinear steady-state data reconciliation in the process industry

In this article, recent practical experiences of soft sensor projects based on data reconciliation in the process industry are reported. The discussed items comprise the steady-state detection, the gross error detection, the initial value generation, and remarks on the implementation of this method. Two practical examples are presented from the area of process industry. The first is a representative soft sensor application to provide consistent measurements for data monitoring. The second is a soft sensor application which uses a rigorous model to estimate concentrations in a distillation column.

STEADY-STATE BILINEAR DATA RECONCILIATION DEALING WITH SCHEDULING

Mass balance model for steady-state linear data reconciliation is insufficient, especially when short-term scheduling is performed on hybrid systems. Scheduling-equations are established and used as addition to the model. A new formulation of data reconciliation is thus proposed as steady-state bilinear data reconciliation. In this way, the redundancy degree is increased and the solvability of data reconciliation is improved. Simulation results demonstrate the efficiency and consistency of the proposed approach.

Comparison of steady state and integral dynamic data reconciliation

This paper is devoted to the comparison of the performance of integral approach to dynamic data reconciliation and steady state data reconciliation. It is shown that in the absence of biases and leaks, the performance of both approaches is similar. Moreover, it is proven that once the appropriate variance is chosen, both methods are identical in the absence of accumulation terms. Finally, an analysis is made on how large the discrepancies are when there are accumulation terms.