Nuclear Engineering Division
Nuclear Engineering Division










Reactors designed by Argonne National Laboratory

Nuclear Reactors designed by Argonne



Multivariate State Estimation Technique (MSET)


Brief Description

The Multivariate State Estimation Technique (MSET) is a software system for real-time process monitoring. It provides system operators with timely and reliable information regarding the conformance of process behavior, as inferred from sensor readings, with the expected behavior based on past observation. It employs highly effective, patented techniques to: (1) generate an analytical estimate of sensor signals on the basis of actual sensor readings and previously learned correlations among them, and (2) analyze the statistical characteristics of the time series obtained by taking the difference between each measured signal and its numerically generated counterpart to determine, at the earliest possible time, whether the process is behaving as expected or anomalously. The reliability, sensitivity and efficiency of MSET have been demonstrated for a wide variety of process monitoring, signal validation, and sensor operability surveillance applications.

Benefits and Advantages

By providing timely and reliable indication of the health of a process, MSET can reduce the need to replace, service or re-calibrate instruments and components, thereby increasing system availability and lowering maintenance costs. Moreover, MSET's ability to detect and annunciate incipient faults at an early stage enables the operator to optimize the scheduling of corrective actions so that the adverse consequences of the malfunction are minimized. Finally, for cases where it can be established that sensor failure (and not a component malfunction) is responsible for the anomalous behavior, MSET's analytically generated estimate of what the sensor indication should be can be used as a substitute for the erroneous signal, and counterproductive tampering with the process itself can be avoided.

MSET screenshotMSET screenshot

It has been demonstrated that MSET possesses significant advantages in sensitivity, reliability, flexibility and computational efficiency over alternative process surveillance approaches currently available. Such alternatives include simple threshold limits, parity-space methods, and techniques employing other state estimates methods such as Kalman filters and artificial neural networks.

Technical Concepts

MSET consists of the following two major components:

  • State estimation model, designed to (a) use examples of the sensor readings characterizing the normal operating state of the system to learn, during a training stage, the correlations among these signals, and (b) generate an accurate estimate, during the on-line monitoring stage, of what each signal "should be" based on the latest set of sensor readings and the previously learned correlations among them.
  • Fault detection model, employing the Sequential Probability Ratio Test (SPRT) to analyze the residual time series obtained by subtracting each measured signal from its numerically generated counterpart. By performing statistical hypothesis tests on these residual time series, SPRT makes a determination, at the earliest possible time, of whether the process is behaving as expected or anomalously. This determination is made subject to user specified probabilities for false alarms and missed alarms.

The training of MSET requires the user to collect vectors of sensor readings for a set of operating conditions that encompass normal operating states of the system being monitored. It is necessary that these sensor readings have some degree of mutual correlation. To reduce the training effort, MSET employs the sensor readings corresponding to an optimal subset of the operating states to learn the normal correlations, including lead-lag dependencies, among these readings. This training procedure requires only models computing effort, and it is performed once-and-for-all (for a specified range of normal operating states) in advance of the on-line monitoring phase.

Using the results of the training model, MSET analyzes process data on-line. For each monitoring time step, MSET computes a combination of the training data that optimally explains the current set of measured data. This analytically derived vector of sensor data is then subtracted from the measured vector to generate a "residual signal" for each sensor. Taken collectively, the residual signals computed by MSET indicate the current deviation of the system from its normal operating configuration. Moreover, the residual for each individual signal may indicate an anomaly in that sensor or in the physical quantity it measures.

To provide the earliest possible indication of process anomalies, MSET employs the SPRT to detect changes over time in the statistical characteristics of the residual signals. Instead of a simple threshold limit that signals a fault when the residual exceeds some threshold values, the SPRT technique performs statistical hypothesis tests on the mean and variance of the residuals. These tests are conducted on the basis of user specified false-alarm and missed-alarm probabilities, allowing the user to control the likelihood of missed fault detection or false alarms. It has been demonstrated that the decision test based on the SPRT has an optimality property, namely that there is no other procedure with a lower error probability or a shorter time to annunciation for subtle anomalies, provided the noise carried by the monitored signal is random and Gaussian. For residual signals exhibiting serial correlation, MSET employs a filtering method to remove the serially correlated component of the signal and ensure that the data analyzed by SPRT are more nearly random and Gaussian.

Nuclear Plant Applications

MSET was initially demonstrated at the DOE-owned reactor EBR-II, where it was shown to detect coolant pump abnormalities at extremely early stages of degradation (well in advance of actual damage) and to provide reliable "virtual" replacement signals for degraded and irreplaceable sensors (e.g., primarily coolant flow meter). MSET has also been successfully used for light water reactor (LWR) signal validation applications at the Florida Power Corporation Crystal River 3 nuclear power station. During the testing of MSET at the Crystal River 3 Plant, a number of sensor problems were detected and identified. For example, a subtle discrepancy in a primary loop flow channel was identified that could not be detected by visual examination of the data or by existing monitoring systems; subsequent examination of the instrument string found a degrading component which was replaced. Had this problem not been identified, the resulting failure would have necessitated replacing the entire instrument string, including the sensor, to avoid plant shutdown.

In addition to this on-line sensor validation capability, the Crystal River testing also demonstrated the capability of MSET to address two other generic LWR issues: (1) identification and accommodation of Venturi flow meter degradation, and (2) detection of loss of time response capabilities of Rosemount pressure transmitters. With respect to the first issue, fouling of Venturi flow meters results in an erroneously high indication of the feedwater flow rate, which forces a corresponding reduction in plant power. This sensor-related problem causes a net power penalty of nearly 2% over a typical pressurized water reactor (PWR) operating cycle and a corresponding loss of revenue. MSET can detect this type of degradation and provide a virtual replacement signal that could be used to maintain and justify full power operation. The second problem of loss of time response is a potential safety issue in that failure of the Rosemount sensor systems (e.g., due to leaks or blockages in the capillary tubing connecting the sensor to the measurement location) leads to a response time degradation that might prevent or delay detection of plant transients. Because the signal in this case appears to be normal, conventional surveillance methods based on threshold tests applied to the signal's mean value would not detect its degradation. MSET's ability to address this problem was verified for the pressurizer level sensory system in Crystal River 3; a loss of time response failure was identified approximately three months before plant operators noticed any anomaly.


A list of patents related to the MSET software is available. All patents were issued by the US Patents Office.

Last Modified: Wed, February 5, 2014 6:31 PM

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Office of Technolofy Transfer:

For more information:

Dr. Rick Vilim
Engineering Analysis Dept.
Plant Analysis and Control Section
Fax: +1 630-252-4620

R. Vilim


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