Collapse moment estimation by support vector machines for wall-thinned pipe bends and elbows

The collapse moment due to wall-thinned defects is estimated through support vector machines with parameters optimized by a genetic algorithm. The support vector regression models are developed and applied to numerical data obtained from the finite element analysis for wall-thinned defects in piping systems. The support vector regression models are optimized by using both the data sets (training data and optimization data) prepared for training and optimization, and its performance verification is performed by using another data set (test data) different from the training data and the optimization data. In this work, three support vector regression models are developed, respectively, for three data sets divided into the three classes of extrados, intrados, and crown defects, which is because they have different characteristics. The relative root mean square (RMS) errors of the estimated collapse moment are 0.2333% for the training data, 0.5229% for the optimization data and 0.5011% for the test data. It is known from this result that the support vector regression models are sufficiently accurate to be used in the integrity evaluation of wall-thinned pipe bends and elbows.     

Effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load

The objective of this study was to investigate the effect of local wall thinning on the collapse behavior of pipe elbows subjected to a combined internal pressure and in-plane bending load. This study evaluated the global deformation behavior and collapse moment of the elbows, which contained various types of local wall-thinning defects at their intrados or extrados, using three-dimensional elastic–plastic finite element analysis. The analysis results showed that the global deformation behavior of locally wall-thinned elbows was largely governed by the mode of the bending and the elbow geometry rather than the wall-thinning parameters, except for elbows with considerably large and deep wall thinning that showed plastic instabilities induced by local buckling and plastic collapsing in the thinned area. The reduction in the collapse moment with wall-thinning depth was considerable when local buckling occurred in the thinned areas, whereas the effect of the thinning depth was small when ovalization occurred. The effects of the circumferential thinning angle and thinning length on the collapse moment of elbows were not major for shallow wall-thinning cases. For deeper wall-thinning cases, however, their effects were significant and the dependence of collapse moment on the axial thinning length was governed by the stress type applied to the wall-thinned area. Typically, the reduction in the collapse moment due to local wall thinning was clearer when the thinning defect was located at the intrados rather than the extrados, and it was apparent for elbows with larger bend radius.     

Amorphous pocket model based on the modified heat transport equation and local lattice collapse

The experimental data of Thompson and Walker [D.A. Thompson, R.S. Walker, Radiat. Eff. 36 (1978) 91], which show an ion mass dependence of the number of displaced atoms after heavy ion impacts on silicon, are analyzed with various simulation models. Solution of the heat transport equation with nuclear energy deposition from binary collision simulation as input does not yield the desired ion mass dependence, even when varying the melting condition. A lattice collapse model, requiring a minimum density of point defects locally, also gives too weak an ion mass dependence if the input is directly taken from binary collision simulations. Only when both models are combined, i.e. when the molten atoms from the solution of the heat transport equation are used as input for the lattice collapse model, good agreement with the experimental results is obtained. We also find that molecular dynamics simulations disagree with the experimental data.     

Sensor monitoring using a fuzzy neural network with an automatic structure constructor

The performance of fuzzy neural networks applied to sensor monitoring strongly depends on the selection of input signals. A large number of input signals may be involved to estimate an output signal for failure detection. However, as the number of input signals increases, the required training time increases exponentially and the uncertainty of the model increases significantly due to the irrelevant and/or the redundant inputs. In this paper, a fuzzy neural network with an optimal structure constructor has been successfully developed to achieve a reliable and efficient sensor monitoring system. A fuzzy neural network is used to estimate an output signal from the selected input signals. Correlation analysis and genetic algorithm (GA) are combined for automatic input selection. In addition, the optimal number of fuzzy rules is accomplished automatically by the GA integrated along with the automatic input selection. The status of sensor health is determined by applying sequential probability ratio test to the residuals between the measured signals and the estimated signals. The proposed sensor monitoring system has been validated by using a variety of sensor signals acquired from Yonggwang units 3 and 4 pressurized water reactors.     

Prediction of residual stress in the welding zone of dissimilar metals using data-based models and uncertainty analysis

Since welding residual stress is one of the major factors in the generation of primary water stress-corrosion cracking (PWSCC), it is essential to examine the welding residual stress to prevent PWSCC. Therefore, several artificial intelligence methods have been developed and studied to predict these residual stresses. In this study, three data-based models, support vector regression (SVR), fuzzy neural network (FNN), and their combined (FNN + SVR) models were used to predict the residual stress for dissimilar metal welding under a variety of welding conditions. By using a subtractive clustering (SC) method, informative data that demonstrate the characteristic behavior of the system were selected to train the models from the numerical data obtained from finite element analysis under a range of welding conditions. The FNN model was optimized using a genetic algorithm. The statistical and analytical uncertainty analysis methods of the models were applied, and their uncertainties were evaluated using 60 sampled training and optimization data sets, as well as a fixed test data set.     

基于数据挖掘技术的组件核子密度预测研究

采用DRAGON程序对9600个样本进行计算,并以235U、238U、239Pu、241Pu、137Cs、244Cm以及154Nd核素的核子密度为预测参数,选用线性回归模型、基于决策树构建的回归树模型、多层感知机（MLP）模型和随机森林模型开展模型训练,选用皮尔逊相关系数（PCC）、平均绝对误差（MAE）、相对绝对误差（RAE）、相对均方根误差（RRSE）评价模型的拟合效果;利用训练好的模型在测试集中对目标核素进行预测,通过相对误差评价其预测精度。结果表明,训练数据模型的时间均在3 s以内;通过选取的参数的评价可得,对于所有预测核素,在4种模型中训练效果最佳的为MLP模型,其相关性均在0.999以上;MLP模型对所有的预测核素的预测平均偏差小于1%。本文初步验证了数据挖掘技术在组件核子密度预测方面的可行性。      

Calculation of the power peaking factor in a nuclear reactor using support vector regression models

Local power density (LPD) at the hottest part of a hot nuclear fuel rod should be estimated accurately to confirm that the rod does not melt. The power peaking factor (PPF) is defined as the highest LPD divided by the average power density in the reactor core. In this paper, the PPF is calculated by support vector regression (SVR) models using numerous measured signals from the reactor cooling system. SVR models are regression analysis models using a kernel function for artificial neural networks. Their neural network weights are found by solving a quadratic programming problem under linear constraints. SVR models are trained using a training data set and then verified against another test data set. The proposed SVR models were applied to the first fuel cycle of the Yonggwang nuclear power plant unit 3. The root mean square errors of the SVR model, with and without in-core neutron flux sensor signal inputs, were 0.1113% and 0.0968%, respectively. This level of errors is sufficiently low for use in LPD monitoring.     

Residual stress prediction of dissimilar metals welding at NPPs using support vector regression

Residual stresses are an important factor in the component integrity and life assessment of welded structures. In this paper, a support vector regression (SVR) method is presented to predict the residual stress for dissimilar metal welding according to various welding conditions. Dissimilar welding joint between nozzle and pipe is regarded in the analyses since it has been known to be highly susceptible to Primary Water Stress Corrosion Cracking (PWSCC) in the primary system of a nuclear power plant (NPP). The residual stress distributions are predicted along two straight paths of a weld zone: a pipe flow path on the inner weld surface and a path connecting two centers of the inner and outer surfaces of a weld zone of a pipe. Four SVR models are developed for four numerical data groups which are split according to the two end section constraints and the two prediction paths and the SVR models are optimized by a genetic algorithm. The SVR models are trained by using a data set prepared for training, optimized by using an optimization data set, and verified by using a test data set independent of the training data and the optimization data. It is known that the SVR models are sufficiently accurate to be used in the integrity evaluation by predicting the residual stress of dissimilar metal welding zones.     

Density limit disruption prediction using a long short-term memory network on EAST

Disruption prediction using a long short-term memory (LSTM) algorithm has been developed on EAST, due to its inherent advantages in time series data processing. In the present work, LSTM is used as the model and the AUC (area under receiver operation characteristic curve) is used as the evaluation index. When the model is trained on data from the plasma current flattop phase and tested on data from the same period multiple times, the highest AUC is 0.8646 and the training time is about 6900 s per epoch. For comparison, the last 1000 ms of the flattop phases are intercepted as short time sequences. When the model is trained on data from short time sequences and tested on data from the same period, the highest AUC is increased to 0.9379 and the training time is restricted to 36 s per epoch. When the best model trained on the short time sequences is applied to the flattop phase for testing, the AUC is up to 0.9189. The experiment results show that it is possible for LSTM to train the model on data from short time sequences and migrate the model to the entire flattop phase, with a shorter training time and higher AUC value.     

基于频域数据注意力机制的核电厂水泵故障模式识别模型研究

针对核电厂水泵共性的异常振动、转子部件摩擦与磨损等故障模式,利用水泵最容易获取的泵壳加速度信号的频域数据为输入,提出了一种结合卷积神经网络和注意力网络的频域数据注意力机制方法,并建立了核电厂水泵故障模式识别模型。研究结果表明:相对于传统方法,利用频域数据作为输入、基于频域数据注意力网络算法建立的水泵故障模式识别模型输入的数据长度更短,能够有效提升模型训练的效率,该故障模式识别模型在测试集上的故障模式识别准确率达到100%,优于其他基于深度学习算法建立的故障诊断模型,证明了本文提出方法的优势。      

Proposal of limit moment equation applicable to planar/non-planar flaw in wall thinned pipes under bending

In this paper, a limit bending moment equation applicable to all types of planar and non-planar flaws in wall-thinned straight pipes under bending was proposed. A system to rationally classify the planar/non-planar flaws in wall-thinned pipes was suggested based on experimental observations focused on the fracture mode. The results demonstrate the importance of distinguishing between axial and circumferential long flaws in wall-thinned pipes.     

Experimental evaluation of the effect of local wall thinning on the failure pressure of elbows

This study performed a series of burst tests using real-scale elbow specimens containing simulated local wall thinning to evaluate the effects of wall-thinning defects on the failure pressure of pipe bends and elbows. The tests were conducted under simple internal pressure at ambient temperature. The experiments included various wall-thinning geometries with different thinning depths, lengths, and circumferential angles, as well as various thinning locations such as extrados, intrados, and full-circumference. The failure pressure decreased exponentially with increasing axial thinning length and decreased almost linearly with increasing thinning depth. These tendencies are similar to those observed for wall-thinned straight pipe. The failure pressure also decreased and gradually saturated with increasing circumferential thinning angle, unlike the results of wall-thinned straight pipe. All specimens failed by bulging, followed by cracking. The axial crack always occurred at the center of the wall-thinned area in the extrados and intrados wall-thinning cases. For the full-circumference wall-thinning case, however, the crack location and pattern were dependent on the axial thinning length. A comparison of the failure pressure with the results of existing models showed that the existing models were excessively conservative in all cases and could not properly predict the dependence of failure pressure on the wall-thinning geometry.     

Adaptive fuzzy model based predictive control of nuclear steam generators

Poor control of U-tube steam generators (UTSG) in a nuclear power plant can lead to frequent reactor shutdowns or damage of turbine blades. The dynamics of steam generator vary as power level changes. There is, therefore, a need to systematically design a suitable controller for all power levels. In this paper, we employ the concepts of both predictive control and fuzzy set theory to design an appropriate control for UTSG water level. The controller has three main parts: (1) a TSK fuzzy model used for predicting the future behavior of UTSG, (2) a recursive algorithm to estimate parameters of this model and (3) a model predictive controller used to obtain optimal input control sequence. Simulation results show that the proposed controller has a remarkable performance for tracking the step and ramp reference trajectories while at the same time it is robust against steam flowrate changes.     

A semi-linguistic fuzzy approach to multi-actor decision-making: Application to aggregation of experts' judgments

In the present work, a semi-linguistic fuzzy algorithm is proposed to obtain the fuzzy weighting values for multi-criterion, multi-alternative performance evaluation problem, with application to the aggregated estimate in the aggregation process of multi-expert judgments. The algorithm framework proposed is composed of the hierarchical structure, the semi-linguistic approach, the fuzzy R-L type integral value, and the total risk attitude index. Depending on a linguistic/numerical scale conversion table, linguistic matrices of the importance weights and the preference ratings, assigned by multiple decision-makers, are converted to trapezoidal fuzzy numbers. Using the fuzzy preference index, computed through arithmetic operation on fuzzy numbers, for each alternative, the weighting value is yielded by the convex combination of the R-L type integral values using the Liou/Wang method and the total risk attitude index. In this work, extending the Chang/Chen method for triangular fuzzy numbers, the total risk attitude is devised for a trapezoidal fuzzy number system. Based on the fuzzy numbers assigned by multiple decision-makers at the data input stage, the total risk attitude index can be evaluated in terms of individual risk attitude indices for the importance weight and preference rating. To illustrate the single actor application of the algorithm proposed, a case problem available in literature is studied in connection to the weighting value evaluation of three-alternative (i.e., the aggregation of three-expert judgments) under seven-criterion. To investigate the effect of fuzzy models, the evaluation results such as overall utility value, aggregation weighting value, and aggregated estimate obtained using the present fuzzy model are compared with those for other fuzzy models based on the Kim/Park method, the Liou/Wang method, and the Chang/Chen method. It is found that the weight ranking of alternatives is independent of the aggregation models used. In addition, the effect of conversion scales is studied in assigning conversion scale systems available in literature. Furthermore, a multi-actor application associated with four decision-makers is illustrated by choosing heterogeneous scale system.     

Small-sample modeling method for nonstationary reactor noise analysis

A method of time-series analysis, applicable to nonstationary data, was developed to be used as a tool for surveillance and diagnosis of nuclear power plants. In this method, the nonstationary data are divided into a set of consecutive blocks and a parametric model, called the autoregressive (AR) model, is estimated for each of the blocks. The model parameters are determined by a least-squares algorithm based on the Householder transformation, which ensures a high numerical stability even when the number of samples used for model determination is small. Time-dependent variations of the statistical properties of the measured noise data are characterized by the blockwise evolution of the noise signatures derived from the AR models. As an empirical evaluation, the method was applied to data generated by simulation, and to data obtained from a BWR also. The advantages of the present method over the conventional AR method in numerical stability, spectral resolution and detectability of anomalies have been demonstrated through the analysis of these sample problems.     

基于高斯过程回归的临界热流密度预测

准确地预测临界热流密度（CHF）对于反应堆的安全和运行十分重要。针对现有人工神经网络（ANNs）预测方法所存在的缺点,提出一种基于高斯过程回归（GPR）的CHF预测方法。首先对获取的当地条件下CHF数据进行预处理,将数据划分为训练集和测试集;然后,利用训练数据对GPR模型进行训练,并得到最优超参数;再利用训练好的GPR模型对CHF进行预测,并将结果与径向基神经网络（RBFNN）进行比较,同时分析了重要参数对CHF的影响趋势。结果表明,与RBFNN相比,GPR模型的预测结果具有更高的预测精度和更小的误差,且与对应的实验值吻合较好,其参数趋势符合通用的趋势变化规律。      

基于决策树的堆芯物理参数预测研究

反应堆堆芯核设计涉及大量方案的搜索与详细计算,缩短方案搜索时间有利于提高核设计效率。数据挖掘技术通过对大量数据进行学习与模式识别,可实现核设计方案物理参数的快速预测,更快地筛选出可行的备选堆芯方案。本文基于数据挖掘的决策树4种算法：C4.5、RepTree、Random Forest及Random Tree,在计算时以燃料富集度、含可燃毒物燃料棒数量及含量作为自变量,以寿期内k_eff不均匀系数偏差（KUCD）、径向功率不均匀系数偏差（RPNCD）、径向中子通量不均匀系数偏差（RFNCD）、堆芯寿期（CL）作为目标函数,构成目标函数符合度（CPF）,利用大量已知核设计参数的组件及堆芯设计方案作为数据挖掘训练集,构建数据挖掘模型,并用于对未知核设计参数的组件方案集合（测试集）进行CPF快速预测。结果表明,4种算法利用训练集构建数据挖掘模型的时间在0.6 s以内,各算法的交叉验证精度均在0.7以上,其中C4.5算法对CPF预测精度最高;对测试集方案的核设计参数预测中,单个方案的预测时间均在0.9 s以内,而Random Forest算法对CPF等于4的预测效果最好。     

Failure probability assessment of wall-thinned nuclear pipes using probabilistic fracture mechanics

The integrity of nuclear piping system has to be maintained during operation. In order to maintain the integrity, reliable assessment procedures including fracture mechanics analysis, etc., are required. Up to now, this has been performed using conventional deterministic approaches even though there are many uncertainties to hinder a rational evaluation. In this respect, probabilistic approaches are considered as an appropriate method for piping system evaluation. The objectives of this paper are to estimate the failure probabilities of wall-thinned pipes in nuclear secondary systems and to propose limited operating conditions under different types of loadings. To do this, a probabilistic assessment program using reliability index and simulation techniques was developed and applied to evaluate failure probabilities of wall-thinned pipes subjected to internal pressure, bending moment and combined loading of them. The sensitivity analysis results as well as prototypal integrity assessment results showed a promising applicability of the probabilistic assessment program, necessity of practical evaluation reflecting combined loading condition and operation considering limited condition.     

A neuro-fuzzy controller for axial power distribution an nuclear reactors

A neuro-fuzzy control algorithm is applied for the core power distribution in a pressurized water reactor. The inputs of the neural fuzzy system are composed of data from each region of the reactor core. Rule outputs consist of linear combinations of their inputs (first-order Sugeno-Takagi type). The consequent and antecedent parameters of the fuzzy rules are updated by the backpropagation method. The reactor model used for computer simulations is a two-point xenon oscillation model based on the nonlinear xenon and iodine balance equations and the one group, one-dimensional neutron diffusion equation having nonlinear power reactivity feedback. The reactor core is axially divided into two regions, and each region has one input and one output and is coupled with the other region. The interaction between the regions of the reactor core is treated by a decoupling scheme. This proposed control method exhibits very fast response to a step or a ramp change of target axial offset without any residual flux oscillations between the upper and lower halves of the reactor core.     

Application of a self-organizing fuzzy logic controller to nuclear steam generator level control

In this paper, the self-organizing fuzzy logic controller is investigated for the water level control of a steam generator. In comparison with conventional fuzzy logic controllers, this controller performs the control task with no initial control rules; instead, it creates control rules and tunes input membership functions based on the performance criteria as the control behavior develops, and also modifies its control structure when uncertain disturbance is suspected. Selected tuning parameters of the self-organizing fuzzy logic controller are updated on-line in the learning algorithm, by a gradient descent method. This control algorithm is applied to the water level control of a steam generator model developed by Irving et al. The computer simulation results confirm the good performance of this control algorithm for all power ranges. This control algorithm can be expected to be used for the automatic control of a feedwater control system in a nuclear power plant with digital instrumentation and control systems.