**5.2 Start-up transient operations in nuclear power plants**

The real-time nuclear simulator data used in [54] is taken here to test the applicability of the proposed methods in transient operations. The data is collected from the simulator without any faults during heating from the cool-down mode (start-up operation). The simulator was designed to reproduce the behavior of a three loop pressurized water reactor (PWR) and to carry out various operational modes, such as start-up, preoperational tests, preheating, hot start-up, cold shutdown, power control, and the operational conditions in steady and accident states. **Figure 13** shows a basic three-loop PWR which is just an illustration of a real process. Six sensors' process signals from the reactor coolant system (RCS) were selected for monitoring during the start-up operation: S1 (cold leg temperature), S2 (core exit temperature), S3 (hot leg temperature), S4 (safety injection flow), S5 (residual heat removal flow), and S6 (sub-cooling margin temperature). The data consist of 1000 observations sequentially collected at constant time intervals of 1 s.

Because these data are fault-free, we first used the entire 1000 observations to train the method and to determine the optimal model parameters using 10-fold cross-validation. Then, we simulated an abnormal condition within these data for use as the testing data set for model evaluation. To effectively examine the fault

**Figure 13.** *Schematic diagram of three loops PWR reactor coolant system [60].*

detection capability of the proposed method, we conducted a thousand-runs Monte Carlo simulation experiment, in which the fault magnitude was a random number sampled from a bimodal uniform distribution, *U*ð Þ ½ � �10, �2 ∪½ � 2, 10 , and added to a signal. In this case, the sensor signal in fault at any time step of the Monte Carlo simulation was random uniformly sampled among the six possible sensor signals.

Summary statistics for the alarm rates from AAKR, AABKR, and the modified AABKR from the thousand-runs Monte Carlo simulation experiment are presented in **Table 2**. The mean values of the distributions of the alarm rates are depicted in


#### **Table 2.**

*Alarm rates (%) of a thousand-runs Monte Carlo simulation in start-up data.*

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

**Figure 14.** *Means of the alarm rates in start-up process operating condition.*

**Figure 14**. The mean values of the distributions of the TARs are 61.4, 99.8, and 95.3% for AAKR, AABKR, and the modified AABKR, respectively. While the mean values of the distributions of the FDRs are 84.57, 99.86, and 99.99% for AAKR, AABKR, and the modified AABKR, respectively. From the results, the performance of both AABKR and the modified AABKR is better than that of AAKR. On average, the TAR from AABKR is slightly higher than that of the modified AABKR. However, there is no significant difference between the FDR of the AABKR and that of the modified AABKR. Thus, for single-sensor faults, the modified AABKR, on average, has performance similar to that of the AABKR, and can be used to validate the sensors'states during transient operations, with the benefit of eliminating the use of derivatives entirely, thereby extending the applicability to steady-state process operation.
