**1. Introduction**

In a nuclear power plant (NPP), accurate situation awareness of key systems, structures, and components (SSCs) is important for safety, reliability, and economics which are key drivers for operation. However, faults and failures can occur in sensors and equipment, which can lead to unexpected shutdown of the power reactors. Such situations may compromise the safety and reliability of the SSCs and result in risk and economic losses that may amount to hundreds of thousands of Euros [1]. For example, in United State of America, the economic loss as a result of shutting down a NPP is approximately \$1.25 million per day [2]. Thus, if unnecessary shutdown of the system as a result of faults and failures can be prevented, economic loss due to shutdown can be minimized. Therefore, it is of paramount importance to improve the situation awareness of SSCs in NPPs in order to ensure that their faults and failures are detected early, which can be achieved through online signal analysis techniques [3–6], and fault detection and diagnosis (FDD) methods [7–13]. There are several techniques of signal analysis, fault detection, and fault diagnostics, which can be classified into two main categories: model-based

[14–17] and data-driven [18–22] methods. The model-based approaches require understanding of the target system's physical structure in order to develop a mathematical model of system response for the purpose of FDD. Data-driven techniques, instead, use the historical data measured by the installed sensors and collected overtime during system' operation to develop an empirical model. In both cases, the developed model can, then, be applied to the target SSC for on-line signal analysis, monitoring, and FDD during operation, from which the condition of the SSC can be retrieved and sent to the human operator/maintenance engineer as alert or alarm, in case of any fault or failure has occurred in the SSC. Based on the status of the SSC, necessary operator action or maintenance intervention can be performed on the SSC to avoid undesired conditions during operation. Adopting these methods in NPP come with several benefits, including [23]:


The recent advancement in data analysis and computational efficiency are motivating the nuclear and other industries to apply CBM for allowing early mitigation, minimizing unplanned shutdown, increasing safety, and reducing maintenance costs. A simple CBM strategy is a scheme that monitors the target component via a fault detection system that continuously collects data from sensors installed on the target component [24], makes a detection decision based on the collected information, provides to operators the condition of the component (normal or abnormal), and triggers an alarm in case of abnormal conditions, which alert the decision makers, for example, stakeholders, operators, and maintenance engineers, for deciding whether or not an intervention on a maintenance action is required on the component.

**Figure 1** illustrates an architecture of the fault detection system considered in this work, which is based on an empirical model for signal reconstruction. Typically, as shown in **Figure 1**, a fault detection system is a decision tool based on (i) the model that reconstructs the values of on-line signals expected in normal conditions; and (ii) the residual calculator that analyses the differences between the measured on-line signal values and the reconstructed values, whereby an alarm is triggered if the residuals are statistically deviated from the allowable range representative of normal conditions.

Several empirical models have been developed and used for signal reconstruction. Such techniques include kernel regression (KR)—a special and simple form of Gaussian process regression (GPR) (which has been adapted for signal reconstruction as an auto-associative kernel regression (AAKR) [20] in nuclear industry),

*Fault Detection by Signal Reconstruction in Nuclear Power Plants DOI: http://dx.doi.org/10.5772/intechopen.101276*

**Figure 1.** *A typical fault detection system.*

auto-associative artificial neural networks (AANNs) [25–27], principal component analysis (PCA) [28–33], multivariate state estimation technique (MSET) [34, 35], Parzen estimation [36], support vector machines [37, 38], evolving clustering method [39], partial least squares (PLS) [40], and fuzzy logic systems [41–45]. However, most data-driven models are developed under steady state plant operation, whereas it is fundamental to have signal validation and monitoring during transient operation as well, considering the fact that most industrial systems' operations are time-varying. Transient operations are any non-steady state, timevarying conditions, which includes start-up, shutdown, and load-following modes of the system, whose time-series data are characterized by an explicit order dependency between observations—a time dimension.

In general, model-based approaches provide valid FDD techniques and are a powerful way to investigate FDD issues in highly dynamic and time-varying systems. However, the high performance of model-based FDD is often achieved at the cost of highly complex process modeling that requires sophisticated system design procedures [46]. Consequently, there is the need for low-complexity data-driven algorithms that could be used for time-varying analysis of the transient operation of the process system. In this respect, AAKR has proven superior to PCA [47] and is less computationally demanding than AANN. AAKR is typically trained to reconstruct the output of its own input under normal conditions. It has been successfully used in actual NPP steady-state operations for instrument channel calibration and condition monitoring [48]. It is a nonparametric technique for estimating a regression function. Unlike parametric models, AAKR relies on the data to determine the model structure.

However, some drawbacks of AAKR, such as spillover effects and robustness issues, can lead to missed alarms or delays in fault detection, and to a difficulty in correctly identifying the sensor variable responsible for a fault that is detected [49]. In order to address these drawbacks, a robust distance measure has been proposed, based on removing the largest elemental difference that contributes to the Euclidean distance metric so as to enable the model to correctly predict sensor values [50]. In [51], a modified AAKR has been proposed, based on a similarity measure between the observational data and historical data, with a pre-processing step that projects both the observed and historical data into a new space defined by a penalty vector.

Although those modifications have improved the AAKR performance, the underlining structure of the AAKR is still based on the traditional unilateral kernel regression and lacks temporal information, which makes its application inappropriate for signal analysis during transient operation because only the current query vector affects the model. Any previous information leading to the current query signals vector is completely ignored. Although this procedure is acceptable and even preferable for many applications, it is not acceptable for transient operations, in which the previous information directly affects the next data point [52, 53].

Recently, a weighted-distance based auto associative bilateral kernel regression (AABKR) for on-line monitoring during process transient operations has been proposed [54] and successfully applied to start-up transient data from an NPP [54, 55]. The AABKR captures both the spatial and temporal information in the data. The time dimension of these kinds of time-series data is, in fact, a structure that provides additional information. The AABKR systematically distributes the weights along the time dimension, using a weighted-distance algorithm that captures temporal dependences in the data [54, 55]. The weighted-distance algorithm uses a derivative-based comparator for the identification of a 'time position index' (the position of the nearest vector, within the historical data vectors, to the current on-line query observation) [54], which directly eliminates the use of on-line time input to the model.

However, when applied to data from steady-state, the performance of the AABKR in terms of correct fault diagnosis (i.e., the identification of the sensor variable responsible for the fault) is not satisfactory, as the fault, in most cases, is detected in both faulty and fault-free sensor signals [54, 55]. After thorough examination, it has been observed that [54]: (1) the AABKR suffers significantly from the spillover effect; (2) the effect is the result of the wrong identification of the 'time position index' by derivatives; and (3) the values of derivatives approximated from a typical steady-state process are, obviously, constants (and nearly zeroes) for most of the data points, particularly, when the process change in time is almost negligible, resulting in wrong identification of the 'time position index'.

It is worth noting that, a correct identification of time position index is crucial for the temporal weighted-distance algorithm that captures the temporal correlation in the data. The consequence of this effect is that, if a fault occurs, it might indeed be detected but, with an incorrect fault diagnosis of the variable responsible for that fault.

Motivated by these observations, we here propose a modified AABKR for efficient on-line monitoring, applicable not only in transient process operations but also in steady-state operations. We develop new algorithms, based on dynamic time warping (DTW), for the identification of temporal dependencies in the data [55]. To evaluate the performance of the proposed methods, we use both synthetic data from a numerical process and real-time data collected from a pressurized water reactor power plant.
