Parametric trends analysis of the critical heat flux based on artificial neural networks

Parametric trends of the critical heat flux (CHF) are analyzed by applying artificial neural networks (ANNs) to a CHF data base for upward flow of water in uniformly heated vertical round tubes. The analyses are performed from three viewpoints, i.e., for fixed inlet conditions, for fixed exit conditions, and based on local conditions hypothesis. Katto's and Groeneveld et al. dimensionless parameters are used to train the ANNs with the experimental CHF data. The trained ANNs predict the CHF better than any other conventional correlations, showing RMS errors of 8.9%, 13.1% and 19.3% for fixed inlet conditions, for fixed exit conditions, and for local conditions hypothesis, respectively. The parametric trends of the CHF obtained from those trained ANNs show a general agreement with previous understanding. In addition, this study provides more comprehensive information and indicates interesting points for the effects of the tube diameter, the heated length, and the mass flux. It is expected that better understanding of the parametric trends is feasible with an extended data base.     

Prediction of critical heat flux using ANFIS

The prediction of Critical Heat Flux (CHF) is essential for water cooled nuclear reactors since it is an important parameter for the economic efficiency and safety of nuclear power plants. Therefore, in this study using Adaptive Neuro-Fuzzy Inference System (ANFIS), a new flexible tool is developed to predict CHF. The process of training and testing in this model is done by using a set of available published field data. The CHF values predicted by the ANFIS model are acceptable compared with the other prediction methods. We improve the ANN model that is proposed by Vaziri et al. (2007) to avoid overfitting. The obtained new ANN test errors are compared with ANFIS model test errors, subsequently. It is found that the ANFIS model with root mean square (RMS) test errors of 4.79%, 5.04% and 11.39%, in fixed inlet conditions and local conditions and fixed outlet conditions, respectively, has superior performance in predicting the CHF than the test error obtained from MLP Neural Network in fixed inlet and outlet conditions, however, ANFIS also has acceptable result to predict CHF in fixed local conditions.     

神经网络在CHF预测中的应用

利用人工神经网络理论对均匀加热垂直上升圆管内的临界热流密度（ＣＨＦ）进行预测和参数趋势分析。本研究采用局部条件假设,并选用Ｃｒｏｅｎｅｖｌｄ的ＣＨＦ查询表数据为本文神经网络训练的样本,采用训练成功的网络预测ＣＨＦ值可以得到比常规方法更好的效果,其均方差为１４．９％。     

临界热流密度的人工神经网络预测法

本文成功地训练了3种用于预测临界热流密度(CHF)的人工神经网络,其输入参数分别是系统压力、质量流速、平衡含汽量;其输出参数是CHF.通过人工神经网络,分析了压力、流量、热平衡含汽量和进口过冷度对CHF的影响,且成功地将人工神经网络应用于CHF的预测中,预测结果与实验值符合很好.分析结果表明:人工神经网络训练的3种类型中,类型Ⅱ的预测精度最高,可达±10%.     

人工神经网络在圆管临界热流密度数据处理中的研究

利用人工神经网络理论对均匀加热垂直上升圆管内的临界热流密度(CHF)进行了预测。分别采用进口条件、出口条件以及局部条件假设，利用收集到的6941个CHF实验数据中的一半作为神经网络训练的样本，采用训练成功的网络预测CHF值可得到比常规方法更好的效果，其均方差分别为6．6％、10．39％和21．39％。     

Application of an Artificial Neural Network in Reactor Thermohydraulic Problem: Prediction of Critical Heat Flux

A new method for predicting Critical Heat Flux (CHF) with the Artificial Neural Network (ANN) method is presented in this paper. The ANNs were trained based on three conditions: type I (inlet or upstream conditions), II (local or CHF point conditions) and III (outlet or downstream conditions). The best condition for predicting CHF is type II, providing an accuracy of ±10%. The effects of main parameters such as pressure, mass flow rate, equilibrium quality and inlet subcooling on CHF were analyzed using the ANN. Critical heat flux under oscillation flow conditions was also predicted.     

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。      

Analysis of the critical heat flux in round vertical tubes under low pressure and flow oscillation conditions. Applications of artificial neural network

Artificial neural networks (ANNs) for predicting critical heat flux (CHF) under low pressure and oscillation conditions have been trained successfully for either natural circulation or forced circulation (FC) in the present study. The input parameters of the ANN are pressure, mean mass flow rate, relative amplitude, inlet subcooling, oscillation period and the ratio of the heated length to the diameter of the tube, L/D. The output is a nondimensionalized factor F, which expresses the relative CHF under oscillation conditions. Based on the trained ANN, the influences of principal parameters on F for FC were analyzed. The parametric trends of the CHF under oscillation obtained by the trained ANN are as follows: the effects of pressure below 500 kPa are complex due to the influence of other parameters. F will increase with increasing mean mass flow rate under any conditions, and will decrease generally with an increase in relative amplitude. F will decrease initially and then increase with increasing inlet subcooling. The influence curves of mean mass flow rate on F will be almost the same when the period is shorter than 5.0 s or longer than 15 s. The influence of L/D will be negligible if L/D>200. It is found that the minimum number of neurons in the hidden layer is a product of the number of neurons in the input layer and in the output layer.     

Prediction of critical heat flux for water flow in vertical round tubes using support vector regression model

This paper deals with ν-support vector regression (ν-SVR) based prediction model of critical heat flux (CHF) for water flow in vertical round tubes. The dataset used in this paper is obtained from available published literature. The dataset is partitioned into two independent sets, a training data set and a test data set, to avoid overfitting problem. To train the ν-SVR models with more informative data, the training data is selected using a subtractive clustering (SC) scheme, and then the remaining data is used as test data to evaluate the performance of the ν-SVR models. Next, the parametric trends of CHF are investigated using the ν-SVR models. The results obtained from the ν-SVR models are compared with those obtained from the radial basis function (RBF) network, which is a kind of artificial neural networks (ANNs). It is found that the results of the ν-SVR models are not only in better agreement with the experimental data than those of the RBF network, but also follow the general understanding. The analysis results indicate that the ν-SVR models can be successfully applied to CHF prediction.     

Application of artificial neural networks in analysis of CHF experimental data in round tubes

Artificial neural networks (ANNs) are applied successfully to analyze the critical heat flux (CHF) experimental data from some round tubes in this paper. A set of software adopting artificial neural network method for predicting CHF in round tube and a set of CHF database are gotten. Comparing with common CHF correlations and CHF look-up table, ANN method has stronger ability of allow-wrong and nice robustness. The CHF predicting software adopting artificial neural network technology can improve the predicting accuracy in a wider parameter range, and is easier to update and to use. The artificial neural nefwork method used in this paper can be applied to some similar physical problems.     

Classification and prediction of the critical heat flux using fuzzy theory and artificial neural networks

A new method to predict the critical heat flux (CHF) is proposed, based on the fuzzy clustering and artificial neural network. The fuzzy clustering classifies the experimental CHF data into a few data clusters (data groups) according to the data characteristics. After classification of the experimental data, the characteristics of the resulting clusters are discussed with emphasis on the distribution of the experimental conditions and physical mechanism. The CHF data in each group are trained in an artificial neural network to predict the CHF. The artificial neural network adjusts the weight so as to minimize the prediction error within the corresponding cluster. Application of the proposed method to the KAIST CHF data bank shows good prediction capability of the CHF, better than other existing methods.     

Numerical simulation and artificial neural network modeling of natural circulation boiling water reactor

Numerical simulation of natural circulation boiling water reactor is important in order to study its performance for different designs and under various off-design conditions. Numerical simulations can be performed by using thermal-hydraulic codes. Very fast numerical simulations, useful for extensive parametric studies and for solving design optimization problems, can be achieved by using an artificial neural network (ANN) model of the system. In the present work, numerical simulations of natural circulation boiling water reactor have been performed with RELAP5 code for different values of design parameters and operational conditions. Parametric trends observed have been discussed. The data obtained from these simulations have been used to train artificial neural networks, which in turn have been used for further parametric studies and design optimization. The ANN models showed error within ±5% for all the simulated data. Two most popular methods, multilayer perceptron (MLP) and radial basis function (RBF) networks, have been used for the training of ANN model. Sequential quadratic programming (SQP) has been used for optimization.     

基于神经网络与表决融合的核动力装置故障诊断方法

针对单神经网络（ANN）故障诊断方法的不足,将多神经网络诊断与表决融合方法结合起来,研究了基于多神经网络与表决融合的核动力装置故障诊断方法。在该方法中,多个不同类型的神经网络训练后用于核动力装置的故障诊断。选择对核动力装置安全有重要影响的运行参数作为各神经网络的输入变量,神经网络的输出是核动力装置的故障模式。用表决融合方法对不同神经网络的诊断结果进行融合,从而得到核动力装置故障诊断的最后结果。利用核动力装置典型的运行模式来验证所提出的诊断方法的效果。结果表明,与单神经网络相比,该方法可提高核动力装置故障诊断结果的精度和可靠性。     

Critical heat flux for finned and unfinned geometries under low flow and low pressure conditions

This paper presents the experiment and analysis for the critical heat flux (CHF) in a vertical annulus with finned and unfinned geometries under low flow and low pressure conditions. To consider the fin effect on CHF, the tests were performed on both finned heater and unfinned heater having same dimension as finned heater without fins. An analytical model was applied to estimate the heat flux and temperature distributions along the periphery of the finned geometry. The physical phenomena observed during the experiments are discussed and the parametric trends of the obtained data are examined to investigate the CHF characteristics for the finned geometry. A new correlation is proposed to predict the CHF for both finned and unfinned geometries at low flow and low pressure conditions. The developed correlation predicts the experimental data with an RMS error of 13.7%.     

基于神经网络方法的LOCA事故诊断

冷却剂丧失事故(Loss of Coolant Accident,LOCA)是核电厂安全分析中的一类典型事故,不同的破口位置和破口尺寸将直接影响到事故的处置和后果。为判断LOCA事故的破口位置和尺寸,可以借助于神经网络的模式识别功能。针对CPR1000核电系统,利用CATHARE软件建模并仿真不同破口位置和尺寸的LOCA事故,提取事故发生时的6类热工水力参数对BP(Back Propagation)神经网络、Elman神经网络、RBF(Radial Basis Function)神经网络和支持向量机进行训练,再将训练后的神经网络用于破口位置和尺寸的诊断。结果表明,在4种神经网络中,参数优化后的支持向量机对破口位置和尺寸的诊断准确率较高且诊断稳定性较好。在LOCA事故发生时,可以利用支持向量机获取破口的详细信息,辅助操纵员高效地处理事故。     

Comparison of correlations for predicting critical heat flux for uniformly heated vertical porous coated tubes at low pressure

The paper includes comparison of correlations for predicting critical heat flux for uniformly heated vertical porous coated tubes at pressure between 0.1 and 0.7 MPa. In this study, a total of 1120 data points of CHF (Critical heat flux) in uniformly heated vertical porous coated tubes were used. Accuracy of correlations was estimated by calculating average and RMS error with available experimental data, and a new correlation is presented. The new correlation predicts that the CHF data are significantly better than those currently available correlations, with average error 0.69% and RMS error 10.9%.     

An experimental study on the critical heat flux for low flow of water in a non-uniformly heated vertical rod bundle over a wide range of pressure conditions

An experimental study of the critical heat flux (CHF) has been performed for a water flow in a non-uniformly heated vertical 3 × 3 rod bundle under low flow and a wide range of pressure conditions. The experiment was especially focused on the parametric trends of the CHF and the applicability of the conventional CHF correlations to a return-to-power conditions of a main steam line break accident whose conditions might be a low mass flux, intermediate pressure, and a high inlet subcooling. The effects of the mass flux and pressure on the CHF are relatively large and complicated in the low pressure conditions. At a high mass flux or a low critical quality, the local heat flux at the CHF location sharply decreases with an increasing local critical quality. However, at a low mass flux or a high critical quality, the local heat flux at the CHF location shows a nearly constant value regardless of the increase of the critical quality. The CHF data at the very low mass flux conditions are correlated well by the churn-to-annular flow transition criterion or the flow reversal phenomena. Several conventional CHF correlations predict the present return-to-power CHF data with reasonable accuracies. However, the prediction capabilities become worse in a very low mass flux of below about 100 kg/(m² s).     

高流速下窄矩形通道内临界热流密度试验研究

在常压下,对具有窄间隙的矩形通道进行了下降流大流速临界热流密度试验研究。研究发现：大流速下临界热流密度随着流速的增加而呈线性增加,随出口含汽量的增加而减小Sudo公式的预测值较试验值要小在人口参数相同时。即相同的人口过冷度和质量流速式矩形通道的长度对临界热流密度的影响较小;如果从出口质量流速和出口含汽量来看,在相同的出口参数下,长度的增加将显著降低临界热流密度。     

Critical heat flux of water in vertical round tubes at low pressure and low flow conditions

An experimental study on critical heat flux (CHF) has been performed for water flow in vertical round tubes under low pressure and low flow (LPLF) conditions to provide a systematic data base and to investigate parametric trends. Totally 513 experimental data have been obtained with Inconel-625 tube test sections in the following conditions: diameter of 6, 8, 10 and 12 mm; heated length of 0.31.77 m; pressure of 106951 kPa; mass flux of 20277 kg m⁻² s⁻¹; and inlet subcooling of 50654 kJ kg⁻¹, thermodynamic equilibrium critical quality of 0.3231.251 and CHF of 1081598 kW m⁻². Flow regime analysis based on Mishima & Ishii’s flow regime map indicates that most of the CHF occurred due to liquid film dryout in annular-mist and annular flow regimes. Parametric trends are examined from two different points of view: fixed inlet conditions and fixed exit conditions. The parametric trends are generally consistent with previous understandings except for the complex effects of system pressure and tube diameter. Finally, several prediction models are assessed with the measured data; the typical mechanistic liquid film dryout model and empirical correlations of (Shah, M.M., 1987. Heat Fluid Flow 8 (4), 326–335; Baek, W.P., Kim, H.G., Chang, S.H., 1997. KAIST critical heat flux correlation for water flow in vertical round tubes, NUTHOS-5, Paper No. AA5) show good predictions. The measured CHF data are listed in Appendix B for future reference.     

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。