This paper describes a novel approach to sensor and actuator integrity monitoring. Multiple sensor and actuator faults can be detected and isolated. Most importantly, fault magnitudes can be correctly estimated. Our approach is robust to disturbance and does not require additional sensors.

In hydrologic modeling, various uncertainty sources may arise due to simplification/representation of real-world spatially distributed processes into the modeling framework, such as uncertainty due to model structure, initial conditions and input errors. One approach that is currently gaining attention to reduce model uncertainty is by optimally combining multiple models. The rationale behind this approach is that optimal weights could be derived for each model during the model combination process so that the developed multimodel predictions will result in improved predictability. Another approach—data assimilation—is gaining popularity in reducing uncertainty by deriving updated initial conditions recursively from the current available observations to reduce overall uncertainty by minimizing the error covariance matrix of state variables. In this paper, an experimental design is proposed to test the performance of both approaches, multimodel combination and data assimilation, in improving the hydrologic prediction at daily and monthly time scales. The experimental design is constructed on a synthetic basis such that the ‘true’ model structure and streamflow values are known. We evaluated the performance of multimodel combination and data assimilation through the experimental design at monthly and daily time scales, then compare how uncertainty due to initial conditions and hydrologic model can be dominant at the respective time scales. For the multimodel combination, we combined the models by evaluating the model performance conditioned on the predictor state. For data assimilation, the Ensemble Kalman Filter (EnKF) was adopted to test its usefulness through the same experimental design. Results from the synthetic study showed that under increased model uncertainty, the multimodel algorithm consistently performed better than the single model predictions and the EnKF algorithm in terms of all performance measures at monthly time scale. However, under daily time scale, the multimodel algorithm did not performing better than the EnKF algorithm in most of the model uncertainty cases. Findings from the synthetic study was also consistent upon application in predicting streamflow at daily and monthly time scales for a watershed in North Carolina.

Regional water supply systems undergo surplus and deficit conditions due to differences in inflow characteristics as well as due to their seasonal demand patterns. This study proposes a framework for regional water management by proposing an interbasin transfer (IBT) model that uses climate‐information‐based inflow forecast for minimizing the deviations from the end‐of‐season target storage across the participating pools. Using the ensemble streamflow forecast, the IBT water allocation model was applied for two reservoir systems in the North Carolina Triangle Area. Results show that interbasin transfers initiated by the ensemble streamflow forecast could potentially improve the overall water supply reliability as the demand continues to grow in the Triangle Area. To further understand the utility of climate forecasts in facilitating IBT under different spatial correlation structures between inflows and between the initial storages of the two systems, a synthetic experiment was designed to evaluate the framework under inflow forecast having different skills. Findings from the synthetic study can be summarized as follows: (a) inflow forecasts combined with the proposed IBT optimization model provide improved allocation in comparison to the allocations obtained under the no‐transfer scenario as well as under transfers obtained with climatology; (b) spatial correlations between inflows and between initial storages among participating reservoirs could also influence the potential benefits that could be achieved through IBT; (c) IBT is particularly beneficial for systems that experience low correlations between inflows or between initial storages or on both attributes of the regional water supply system. Thus, if both infrastructure and permitting structures exist for promoting interbasin transfers, season‐ahead inflow forecasts could provide added benefits in forecasting surplus/deficit conditions among the participating pools in the regional water supply system.

Droughts experienced by regional water supply systems often result due to reduced streamflow/precipitation potential which could occur due to varying exogenous climatic conditions such as tropical sea surface temperature (SST). Similarly, water supply systems can also experience frequent shortages in supply due to increased water demand resulting from urbanization and population growth in the region. The goal of this study is to identify a sustainable way of managing triangle area's two major reservoir systems while in the meantime improving the water supply reliability for its urban area. In this study, streamflow forecasts downscaled from climate forecasts for the winter season is developed to explore the potential for inter-basin transfer between Falls Lake of the Neuse River basin and Jordan Lake in the Cape Fear River basin. Using the 3-month ahead ensembles of streamflow forecasts, the reservoir simulation model estimates the probability of meeting the end of the season target storage for the two systems. Comparing these two probabilities, various scenarios of inter-basin transfers between the two systems are analyzed in such a way that the water quality releases from both systems are not endangered. Results show that by introducing inter-basin transfer, the reliability of the water supply for the triangle area could be increased, which would help in developing regional drought management strategies.

This paper proposes a new scheme to detect and isolate model-plant mismatch (MPM) for multivariate dynamic systems. The background of our study is the increasing demands on MPM detection and isolation for performance assessment of model predictive controllers (MPCs). In this paper, the MPM problem is formulated in terms of discrete-time state space models which are widely used in MPCs. Three MPM detection indices (MDIs) are proposed to detect the MPM. Also a logic framework is proposed to isolate the system matrices that have MPM. A numerical example is presented to demonstrate the applicability of the proposed scheme.

This paper proposes a novel subspace approach towards direct identification of a residual model for fault detection and isolation (FDI) in a system with non-uniformly sampled multirate (NUSM) data without any knowledge of the system. From the identified residual model, an optimal primary residual vector (PRV) is generated for fault detection. Furthermore, by transforming the PRV into a set of structured residual vectors, fault isolation is performed. The proposed algorithms have been applied to an experimental pilot plant with NUSM data for sensor FDI, where different types of faults are successfully detected and isolated, fully validating the practicality and utility of the developed theory.

The first part of the paper is the development of a data-driven Kalman filter for a non-uniformly sampled multirate (NUSM) system. Algorithms for both one-step predictor and filtering are developed and analysis of stability and convergence is conducted in the NUSM framework. The second part of the paper investigates a Kalman filter-based methodology for unified detection and isolation of sensor, actuator, and process faults in the NUSM system with analysis on fault detectability and isolability. Case studies using data respectively collected from a pilot experimental plant and a simulated system are conducted to justify the practicality of the proposed theory.

This paper first develops data-driven Kalman filters for non-uniformly sampled multirate systems. Then a novel methodology of fault detection and isolation for such systems is proposed. The proposed scheme is applied to a pilot scale experimental plant, where a successful case study on FDI is conducted.

This paper proposes a novel scheme of sensor/actuator fault detection and isolation (FDI) for multivariate dynamic systems in the presence of process uncertainties, including model-plant-mismatch and process disturbances. Given an estimated model that can be biased from the true one, the primary residual vector (PRV), for detecting faults in output sensors, can be made completely insensitive to process uncertainties under certain conditions. For detecting faults in actuators, the PRV can be made almost insensitive to the process uncertainties. Numerical and experimental examples justify the effectiveness of the proposed scheme, where comparison with an existing robust FDI scheme is conducted.

This paper considers fault detection and isolation (FDI) in a non-uniformly sampled multirate system. By extending the Chow-Willsky scheme from single rate systems to multirate systems, one generates a primary residual vector (PRV) for fault detection. Further, by structuring the PRV to have different sensitivity/insensitivity to different faults, fault isolation is performed. The power of the proposed FDI scheme is illustrated via numerical examples.

A novel approach is proposed towards on-line and real-time detection and isolation of parametric faults in a multivariable linear continuous-time (CT) system. The problem of fault detection and isolation (FDI) is formulated in terms of a CT state space model. Since parameters in a CT model usually have simple relationships with physical parameters of the system, isolating parametric faults in the CT model can lead to the isolation of undesired changes in the physical parameters. Isolating parametric faults is very challenging, because even in a linear time-invariant system, the fault model can be time-varying and random. To obtain a constant fault model, many existing parametric FDI schemes have to make unrealistical assumptions. Our proposed FDI approach can generate an optimal primary residual vector (PRV), in which the fault model is constant without making any assumptions. To isolate faults, the PRV is transformed into a set of structured residual vectors (SRVs), where one SRV is made insensitive to a specified subset of faults, but most sensitive to other faults. The proposed approach is successfully applied to detection and isolation of undesired changes in the physical parameters of a simulated continuously stirred tank process.

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach.

This paper proposes a novel approach to detection and isolation of faulty sensors in multivariate dynamic systems. After formulating the problem of sensor fault detection and isolation in a dynamic system represented by a state space model, we develop the optimal design of a primary residual vector for fault detection and a set of structured residual vectors for fault isolation using an extended observability matrix and a lower triangular block Toeplitz matrix of the system. This work is, therefore, a vector extension to the earlier scalar-based approach to fault detection and isolation. Besides proposing a new algorithm for consistent identification of the Toeplitz matrix from noisy input and output observations without identifying the state space matrices {A, B, C, D} of the system, the main contributions of this newly proposed fault detection and isolation scheme are: (1) a set of structured residual vectors is employed for fault isolation; (2) after determination of the maximum number of multiple sensors that are most likely to fail simultaneously, a unified scheme for isolation of single and multiple faulty sensors is proposed; and (3) the optimality of the primary residual vector and the structured residual vectors is proven. We prove the advantage of our newly proposed vector-based scheme over the existing scalar element-based approach for fault isolation and illustrate its practicality by simulated and experimental evaluation on a multivariate pilot scale, computer interfaced system.

Online monitoring of multivariable processes is crucial to operational safety, and product quality For this, multivariable statistical analysis methods, such as principal component analysis (PCA), partial least squares, and canonical Variate analysis have been widely applied. However, felt, recursive monitoring techniques have been developed for fully, dynamic and time-varying processes. Recursive PCA has been successfully applied to monitor static time-varying processes, but does not work for fully dynamic processes. Dynamic PCA has been developed, but its recursive variant is not available. Many processes operate in dynamic states and are often time-varying and the time-varying property includes the variation of parameters and of process structure, e.g., the change of model order. A novel approach to the adaptive monitoring of multivariate dynamic and time-varing processes by, the recursive multichannel instrumental variable (IV) lattice filters was developed using the errors-in-variables (EIV) state space model to represent a dynamic process. To show the relationship between EIV state-space representation of the process and a multichannel IV lattice filter, the lattice filter was used to generate a residual vector for process monitoring. By using lattice filters ability of recursively updating the process model both in time and order, a real time, on-line algorithm was used to update the residual vector with newly sampled process data, including a practical approach to recursive determination of time process model order. Based on the residual vector, the Hotelling T-2 statistic and the associated confidence limits are used as the monitoring index. The proposed scheme was evaluated on a simulation example and a pilot plant to support the theoretical results.

This paper proposes a novel scheme for the generation of primary residual vector (PRV) for sensor or actuator fault detection and isolation (FDI) in multivariate dynamic systems. The PRV, which is used for fault detection purpose, is designed to be insensitive to process uncertainties, including model–plant mismatch (MPM) and process disturbances. To generate the PRV, we do not need a precise system model. Instead, all we need is an estimate of the system model, which may be biased from the true model. Under the condition that the number of process uncertainties is less than the number of outputs, the generated PRV can be made perfectly insensitive to process uncertainties. Even when this condition does not hold, the most important elements in the process uncertainties can still be decorrelated from the PRV. A numerical example to demonstrate the theory is given. The newly proposed approach is compared with existing robust FDI schemes, e.g., the Chow–Willsky scheme.

Since most physical processes are continuous-time by nature, knowledge of system models in continuous-time domain is indispensable for diagnosis of process faults. This paper proposes a novel subspace-based approach towards identification of fault diagnosis-relevant models in multivariate dynamic continuous-time systems from sampled noisy data. A numerical example is given to demonstrate the validity of the theory.

A novel method proposed detects and identifies faulty sensors in dynamic systems using a subspace identification model. A consistent estimate of this subspace model was obtained from noisy input and output measurements by using errors-in-variables subspace identification algorithms. A parity vector was generated, which was decoupled from the system state, leading to a model residual for fault detection. An exponentially weighted moving average (EWMA) filter was applied to the residual to reduce false alarms due to noise. To identify faulty sensors, a dynamic structured residual approach with maximized sensitivity is proposed which generates a set of structured residuals, each decoupled from one subset of faults but most sensitive to others. All the structured residuals are also subject to an EWMA filtering to reduce the noise effect. Confidence limits for filtered structured residuals were determined using statistical inferential techniques. Other indices like generalized likelihood ratio and cumulative variance were compared to identify different types of faulty sensors. The fault magnitude was then estimated based on the model and faulty data. Data from a simulated 4 × 4 process and an industrial waste-water reactor were used to test the effectiveness of this method, where four types of sensor faults, including bias, precision degradation, drift, and complete failure, were tested.

In this paper, we make a comparison between dynamic principal component analysis (PCA) and errors-in-variables (EIV) subspace model identification (SMI) and establish consistency conditions for the two approaches. We first demonstrate the relationship between dynamic PCA and SMI. Then we show that when process variables are corrupted by measurement noise dynamic PCA fails to give a consistent estimate of the process model in general whether or not process noise is present. We then propose an indirect dynamic PCA approach for the consistent estimate of the process model resorting to EIV SMI algorithms. Consistent dynamic PCA models are obtained with and without process disturbances. Additional features of the indirect approach include (i) easy determination of the number of lagged variables in the model; (ii) determination of the number of significant process disturbances; and (iii) consistent estimate of the dynamic PCA models with and without process disturbances. We conduct two simulation examples and an industrial case study to support our theoretical results, where the relationship between dynamic PCA and EIV SMI is numerically verified.

This paper proposes a novel vector-based approach towards isolation of faulty sensors in multivariate dynamic processes. The main contributions are: (1) a set of structured residual vectors is employed for fault isolation; (2) a unified scheme for isolation of single and multiple faulty sensors is proposed; and (3) the optimality of fault detection and isolation is proven.

While principal component analysis (PCA) has found wide application in process monitoring, slow and normal process changes often occur in real processes, which lead to false alarms for a fixed-model monitoring approach. In this paper, we propose two recursive PCA algorithms for adaptive process monitoring. The paper starts with an efficient approach to updating the correlation matrix recursively. The algorithms, using rank-one modification and Lanczos tridiagonalization, are then proposed and their computational complexity is compared. The number of principal components and the confidence limits for process monitoring are also determined recursively. A complete adaptive monitoring algorithm that addresses the issues of missing values and outlines is presented. Finally, the proposed algorithms are applied to a rapid thermal annealing process in semiconductor processing for adaptive monitoring.