The integrity of a reactor pressure vessel (RPVs) is essential for the safe, efficient, and prolonged operation of nuclear power plants, but RPVs are subjected to extreme conditions, including high temperature, pressure, and neutron radiation. Given these conditions can lead to material degradation over time, accurate prediction of the remaining useful life (RUL) of RPVs is crucial for preventing catastrophic failures, as well as optimising maintenance schedules, and extending the lifespan of the components. Traditional methods for assessing the RUL of RPVs often rely on periodic inspections and deterministic models, which can be costly, time-consuming, and sometimes do not capture the complex nature of the various degradation mechanisms. A research paper by Raisa Bentay Hossain, K. Kobayashi, and S. B. Alam, titled: ‘Sensor degradation in nuclear reactor pressure vessels: the overlooked factor in remaining useful life prediction’ explores a novel technique for more accurate RUL predictions of reactor pressure vessels. The paper was first published in the Nature Partner Journal (npj) Materials Degradation.
The authors note that while advances in sensor technology have significantly enhanced the ability to monitor the condition of RPVs in real time, the precision of these forecasts depends on sensor condition. The same adverse conditions that threaten RPV integrity can also degrade sensors resulting in drift, increased noise, and complete failure. These characteristics can in turn result in inaccurate data collection and undermine the accuracy of any RUL predictions. The authors therefore argue that when developing algorithms for estimating RUL, it is essential to consider sensor degradation too. Their work seeks to transform how sensor degradation is assessed within the nuclear industry by highlighting the often-overlooked role of sensor health in accurate predictions of material states.
Neutron embrittlement and sensor decay
Ensuring the reliability and longevity of a system or component requires a thorough understanding of its RUL, which can be significantly influenced by conditions encountered during the component’s life cycle. Failures in accurate monitoring, caused by incorrect sensor readings, can directly impact RUL estimation. Despite the critical role of sensors in monitoring system health, the impact of degraded sensors on system health monitoring has been relatively overlooked. Monitoring sensor performance and assessing the impact of their health condition on observation data is vital. The presence of sensor degradation complicates the task of obtaining accurate information on the health of monitored components like RPVs, highlighting the importance of robust sensor health management in monitoring systems.
Improvements in the prediction of RUL for nuclear components have advanced understanding of their longevity and reliability by focusing on developing machine learning models and artificial intelligence techniques. However, a notable gap in these studies is the lack of consideration for sensor degradation and their dependency on extensive historical training data, which is challenging to obtain in the nuclear industry context.
Using Kalman Filter (KF) for RUL prediction is a well-established practice as it can effectively address multiple limitations in current methods of estimating RUL for RPVs. KFs accurately model dynamic and non-linear systems by integrating system equations that capture underlying physical processes, overcoming the challenges of inaccurate representation. Additionally, KFs efficiently use limited training data, employing techniques like transfer learning to mitigate extensive data requirements typical in machine learning approaches.
The authors consider neutron embrittlement as the primary cause of degradation in RPV materials and model this degradation as a mathematical Weiner Process, also called Brownian motion. Neutron embrittlement is a process affected by radiation damage and various environmental variables, which results in a complex, non-linear, and non-monotonic degradation pattern for RPV steel. Neutron embrittlement is a multifaceted phenomenon characterized by radiation damage, microstructural alterations, and changes in material properties due to the continuous absorption of neutrons over time. This degradation process is profoundly influenced by variables such as neutron fluence, temperature, and the detailed composition of the steel. The interplay of these factors results in a degradation pattern that is inherently non-linear and non-monotonic, making it challenging to model using simplistic continuous processes. These complexities necessitate advanced modelling approaches that can capture the nuanced behaviour of RPV steel under the influence of neutron embrittlement. However, for the sake of computational simplicity, the authors opted for a Wiener Process-based model, which while fundamentally simplistic, possesses the versatility to encapsulate non-linear and non-monotonic degradation patterns observed in neutron-embrittled RPV steel.
The study aimed to develop a sensor degradation model and integrate that with Remaining Useful Life prediction algorithms, producing a framework for comprehensive health evaluation of nuclear systems, structures, and components by explicitly quantifying the impact of sensor health deterioration. The RPV is used as a critical case study to illustrate this framework by modelling the effects of neutron embrittlement under the harsh operational conditions of nuclear power plants.
Modelling sensor decay to predict RPV life
Having developed an appropriate model for sensor degradation and integrated that within an RUL algorithm a real-life case study was used to provide a practical demonstration of the methodology.
The data was collected from a report on the results of the examination of Capsule W which monitors the effects of neutron irradiation on the Ameren-owned Callaway Unit 1 in Missouri, USA. Capsule W is the fifth removed from the reactor and tested in a continuing surveillance programme of reactor pressure vessel materials under actual operating conditions. Capsule W was removed at 25.75 Effective Full Power Years (EFPY) and post-irradiation mechanical tests of the Charpy V-notch and tensile specimens were performed. The report presents a detailed analysis to determine the neutron radiation environment within both the reactor pressure vessel and surveillance capsules. In the analysis, fast neutron exposure parameters in terms of fast neutron fluence (E >1.0 MeV) and iron atom displacements (dpa) were established on a plant- and fuel-cycle-specific basis. The authors used the iron atom displacement data for degradation analysis. The observed degradation data received from the sensors combines both system and sensor degradation and is the only data available. The observed data is categorised into two distinct segments. The initial 20 data points represent the iron atom displacement observed over 20 operating cycles, equivalent to fuel cycles. The subsequent data points project into the future, spanning intervals of 32, 35, 40, 48, 54, and 60 EFPY.
Considering use of the maximum likelihood estimation (MLE) method for estimating system and sensor parameters, the quantity of available data points assumes critical significance. In general, as the sample size (number of data points) increases, MLE tends to provide more accurate and reliable parameter estimates. To address this issue, the authors employed interpolation techniques, enabling additional data points to be inserted to increase the density of data including an additional data point representing the initial state, where the iron atom displacement is zero at time zero.
Comparing the real data path with the simulated Wiener Process shows the real dataset closely adheres to the characteristics of a Wiener process.
Since actual sensor degradation data was not available the authors employed simulated data to represent sensor degradation with a drift parameter η set to a value of 3.00 × 10−4 and diffusion parameter δ set to 7.00 × 10−4. The simulated sensor degradation data was then subtracted from the observed data to obtain the system degradation data. The plot illustrates the observed measurements, simulated sensor degradation data, and calculated system degradation data and suggests that all three data paths adhere to a Wiener process.
The system state estimation achieved through the application of the Kalman filter provides a comparison between the degradation levels obtained from the measurement data and the estimation. The authors argue that the close resemblance signifies the effectiveness of this approach but add that it is worth noting that the slight disparities can be attributed to variances in the true and estimated parameters, given the uncertainty associated with the real parameter values.
More accurate useful life prediction
The subsequent degradation measurement and prediction of system failure over time is shown in Figure 1, below, which illustrates the actual degradation measurements of a system component as a function of time, along with a predefined failure threshold. The intersection of the degradation curve with the failure threshold line marks the critical point where the component is assumed to have failed, which in this example case occurs at approximately 15 EFPY with a degradation level of 0.015 dpa. This is the point at which the system may require maintenance or replacement.
The failure threshold is a pre-specified value that defines when the system is considered to have failed and the remaining useful life (RUL) is the amount of time that the system is expected to remain operational. The RUL Kalman filter equations developed by the authors can be used to predict the probability that the system will fail within a certain period of time. This information can then be used to make informed decisions about system maintenance and replacement. For example, if the probability of the system failing within the next week is 10%, scheduling a maintenance inspection may be prudent. Or, if the probability of the system failing within the next year is 50%, we may want to start planning for a replacement.
This study tackles a critical and often-neglected factor in RPV health assessment: the effects of sensor degradation on RUL predictions. By meticulously quantifying this impact, the research addresses a hidden vulnerability in conventional RPV monitoring and underscores the need for degradation-aware predictive models.
In this case the Wiener process is applied to the nuclear domain, modelling the stochastic deterioration of RPVs. This marks a departure from deterministic models, enabling a more realistic representation of the complex and often unpredictable degradation mechanisms at play in harsh nuclear environments. The utilisation of the Wiener process offers flexibility that accommodates the complexities of degradation under nuclear reactor conditions, providing a significant advance over previous modelling approaches. Applying adaptive Kalman filter algorithms for RUL estimation in nuclear power plants (NPPs) tackles the unique challenges of NPP monitoring, allowing for dynamic refinement of RUL predictions as new sensor data becomes available. By harnessing real-world surveillance capsule data this empirical foundation significantly enhances the robustness and reliability of these degradation models, bridging the gap between theory and the complex realities of nuclear component aging.
In this work the authors demonstrate the importance of incorporating sensor degradation into remaining useful life (RUL) predictions for critical nuclear reactor pressure vessels. The findings also quantify the substantial errors that sensor degradation introduces into RUL estimations. By explicitly modelling sensor degradation in tandem with neutron embrittlement, the paper outlines the influence of sensor deterioration on nuclear component health evaluations. The authors note that future research endeavours will be to investigate sensor fusion techniques to further enhance the robustness of health assessments. Additionally, the integration of sensor degradation models into a comprehensive predictive maintenance framework promises to transform nuclear industry maintenance practices.
