Non-crossing Quantile Regression Neural Network as a Calibration Tool for Ensemble Weather Forecasts

Despite the maturity of ensemble numerical weather prediction(NWP),the resulting forecasts are still,more often than not,under-dispersed.As such,forecast calibration tools have become popular.Among those tools,quantile regression(QR)is highly competitive in terms of both flexibility and predictive performance.Nevertheless,a long-standing problem of QR is quantile crossing,which greatly limits the interpretability of QR-calibrated forecasts.On this point,this study proposes a non-crossing quantile regression neural network(NCQRNN),for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing.The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer,which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer,through a triangular weight matrix with positive entries.The empirical part of the work considers a solar irradiance case study,in which four years of ensemble irradiance forecasts at seven locations,issued by the European Centre for Medium-Range Weather Forecasts,are calibrated via NCQRNN,as well as via an eclectic mix of benchmarking models,ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models.Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration,amongst all competitors.Furthermore,the proposed conception to resolve quantile crossing is remarkably simple yet general,and thus has broad applicability as it can be integrated with many shallow-and deep-learning-based neural networks.

Predicting uniaxial compressive strength of tuff after accelerated freeze-thaw testing: Comparative analysis of regression models and artificial neural networks

Ignimbrites have been widely used as building materials in many historical and touristic structures in the Kayseri region of Türkiye. Their diverse colours and textures make them a popular choice for modern construction as well. However, ignimbrites are particularly vulnerable to atmospheric conditions, such as freeze-thaw cycles, due to their high porosity, which is a result of their formation process. When water enters the pores of the ignimbrites, it can freeze during cold weather. As the water freezes and expands, it generates internal stress within the stone, causing micro-cracks to develop. Over time, repeated freeze-thaw (F-T) cycles lead to the growth of these micro-cracks into larger cracks, compromising the structural integrity of the ignimbrites and eventually making them unsuitable for use as building materials. The determination of the long-term F-T performance of ignimbrites can be established after long F-T experimental processes. Determining the long-term F-T performance of ignimbrites typically requires extensive experimental testing over prolonged freeze-thaw cycles. To streamline this process, developing accurate predictive equations becomes crucial. In this study, such equations were formulated using classical regression analyses and artificial neural networks (ANN) based on data obtained from these experiments, allowing for the prediction of the F-T performance of ignimbrites and other similar building stones without the need for lengthy testing. In this study, uniaxial compressive strength, ultrasonic propagation velocity, apparent porosity and mass loss of ignimbrites after long-term F-T were determined. Following the F-T cycles, the disintegration rate was evaluated using decay function approaches, while uniaxial compressive strength (UCS) values were predicted with minimal input parameters through both regression and ANN analyses. The ANN and regression models created for this purpose were first started with a single input value and then developed with two and three combinations. The predictive performance of the models was assessed by comparing them to regression models using the coefficient of determination (R2) as the evaluation criterion. As a result of the study, higher R2 values (0.87) were obtained in models built with artificial neural network. The results of the study indicate that ANN usage can produce results close to experimental outcomes in predicting the long-term F-T performance of ignimbrite samples.

Regression Method for Rail Fastener Tightness Based on Center-Line Projection Distance Feature and Neural Network

In the railway system,fasteners have the functions of damping,maintaining the track distance,and adjusting the track level.Therefore,routine maintenance and inspection of fasteners are important to ensure the safe operation of track lines.Currently,assessment methods for fastener tightness include manual observation,acoustic wave detection,and image detection.There are limitations such as low accuracy and efficiency,easy interference and misjudgment,and a lack of accurate,stable,and fast detection methods.Aiming at the small deformation characteristics and large elastic change of fasteners from full loosening to full tightening,this study proposes high-precision surface-structured light technology for fastener detection and fastener deformation feature extraction based on the center-line projection distance and a fastener tightness regression method based on neural networks.First,the method uses a 3D camera to obtain a fastener point cloud and then segments the elastic rod area based on the iterative closest point algorithm registration.Principal component analysis is used to calculate the normal vector of the segmented elastic rod surface and extract the point on the centerline of the elastic rod.The point is projected onto the upper surface of the bolt to calculate the projection distance.Subsequently,the mapping relationship between the projection distance sequence and fastener tightness is established,and the influence of each parameter on the fastener tightness prediction is analyzed.Finally,by setting up a fastener detection scene in the track experimental base,collecting data,and completing the algorithm verification,the results showed that the deviation between the fastener tightness regression value obtained after the algorithm processing and the actual measured value RMSE was 0.2196 mm,which significantly improved the effect compared with other tightness detection methods,and realized an effective fastener tightness regression.

Prediction of the undrained shear strength of remolded soil with non-linear regression,fuzzy logic,and artificial neural network

This study aims to predict the undrained shear strength of remolded soil samples using non-linear regression analyses,fuzzy logic,and artificial neural network modeling.A total of 1306 undrained shear strength results from 230 different remolded soil test settings reported in 21 publications were collected,utilizing six different measurement devices.Although water content,plastic limit,and liquid limit were used as input parameters for fuzzy logic and artificial neural network modeling,liquidity index or water content ratio was considered as an input parameter for non-linear regression analyses.In non-linear regression analyses,12 different regression equations were derived for the prediction of undrained shear strength of remolded soil.Feed-Forward backpropagation and the TANSIG transfer function were used for artificial neural network modeling,while the Mamdani inference system was preferred with trapezoidal and triangular membership functions for fuzzy logic modeling.The experimental results of 914 tests were used for training of the artificial neural network models,196 for validation and 196 for testing.It was observed that the accuracy of the artificial neural network and fuzzy logic modeling was higher than that of the non-linear regression analyses.Furthermore,a simple and reliable regression equation was proposed for assessments of undrained shear strength values with higher coefficients of determination.

Incorporating Lasso Regression to Physics-Informed Neural Network for Inverse PDE Problem

Partial Differential Equation(PDE)is among the most fundamental tools employed to model dynamic systems.Existing PDE modeling methods are typically derived from established knowledge and known phenomena,which are time-consuming and labor-intensive.Recently,discovering governing PDEs from collected actual data via Physics Informed Neural Networks(PINNs)provides a more efficient way to analyze fresh dynamic systems and establish PEDmodels.This study proposes Sequentially Threshold Least Squares-Lasso(STLasso),a module constructed by incorporating Lasso regression into the Sequentially Threshold Least Squares(STLS)algorithm,which can complete sparse regression of PDE coefficients with the constraints of l0 norm.It further introduces PINN-STLasso,a physics informed neural network combined with Lasso sparse regression,able to find underlying PDEs from data with reduced data requirements and better interpretability.In addition,this research conducts experiments on canonical inverse PDE problems and compares the results to several recent methods.The results demonstrated that the proposed PINN-STLasso outperforms other methods,achieving lower error rates even with less data.

RBF neural network regression model based on fuzzy observations

A fuzzy observations-based radial basis function neural network （FORBFNN） is presented for modeling nonlinear systems in which the observations of response are imprecise but can be represented as fuzzy membership functions. In the FORBFNN model, the weight coefficients of nodes in the hidden layer are identified by using the fuzzy expectation-maximization （ EM ） algorithm, whereas the optimal number of these nodes as well as the centers and widths of radial basis functions are automatically constructed by using a data-driven method. Namely, the method starts with an initial node, and then a new node is added in a hidden layer according to some rules. This procedure is not terminated until the model meets the preset requirements. The method considers both the accuracy and complexity of the model. Numerical simulation results show that the modeling method is effective, and the established model has high prediction accuracy.

Identification of dynamic systems using support vector regression neural networks

A novel adaptive support vector regression neural network （SVR-NN） is proposed, which combines respectively merits of support vector machines and a neural network. First, a support vector regression approach is applied to determine the initial structure and initial weights of the SVR-NN so that the network architecture is easily determined and the hidden nodes can adaptively be constructed based on support vectors. Furthermore, an annealing robust learning algorithm is presented to adjust these hidden node parameters as well as the weights of the SVR-NN. To test the validity of the proposed method, it is demonstrated that the adaptive SVR-NN can be used effectively for the identification of nonlinear dynamic systems. Simulation results show that the identification schemes based on the SVR-NN give considerably better performance and show faster learning in comparison to the previous neural network method.

Study on the Model of Excessive Staminate Catkin Thinning of Proterandrous Walnut Based on Quadratic Polynomial Regression Equation and BP Artificial Neural Network

The excessive staminate catkin thinning （emasculation） of proterandrous walnut is an important management measure for improving yield. To improve the excessive staminate catkin thinning efficiency, the model of quadratic polynomial regression equation and BP artificial neural network was developed. The effects of ethephon, gibberel in and mepiquat on shedding rate of staminate catkin of pro-terandrous walnut were investigated by modeling field test. Based on the modeling test results, the excessive staminate catkin thinning model of quadratic polynomial regression equation and BP artificial neural network was established, and it was validated by field test next year. The test data were divided into training set, vali-dation set and test set. The total 20 sets of data obtained from the modeling field test were randomly divided into training set （17） and validation set （3） by central composite design （quadric rotational regression test design）, and the data obtained from the next-year field test were divided into the test set. The topological struc-ture of BP artificial neural network was 3-5-1. The results showed that the pre-diction errors of BP neural network for samples from the validation set were 1.355 0%, 0.429 1% and 0.353 8%, respectively; the difference between the predicted value by the BP neural network and validated value by field test was 2.04%, and the difference between the predicted value by the regression equation and validated value by field test was 3.12%; the prediction accuracy of BP neural network was over 1.0% higher than that of regression equation. The effective combination of quadratic polynomial stepwise regression and BP artificial neural network wil not only help to determine the effect of independent parameter but also improve the prediction accuracy.

Nonparametric Statistical Feature Scaling Based Quadratic Regressive Convolution Deep Neural Network for Software Fault Prediction

The development of defect prediction plays a significant role in improving software quality. Such predictions are used to identify defective modules before the testing and to minimize the time and cost. The software with defects negatively impacts operational costs and finally affects customer satisfaction. Numerous approaches exist to predict software defects. However, the timely and accurate software bugs are the major challenging issues. To improve the timely and accurate software defect prediction, a novel technique called Nonparametric Statistical feature scaled QuAdratic regressive convolution Deep nEural Network (SQADEN) is introduced. The proposed SQADEN technique mainly includes two major processes namely metric or feature selection and classification. First, the SQADEN uses the nonparametric statistical Torgerson–Gower scaling technique for identifying the relevant software metrics by measuring the similarity using the dice coefficient. The feature selection process is used to minimize the time complexity of software fault prediction. With the selected metrics, software fault perdition with the help of the Quadratic Censored regressive convolution deep neural network-based classification. The deep learning classifier analyzes the training and testing samples using the contingency correlation coefficient. The softstep activation function is used to provide the final fault prediction results. To minimize the error, the Nelder–Mead method is applied to solve non-linear least-squares problems. Finally, accurate classification results with a minimum error are obtained at the output layer. Experimental evaluation is carried out with different quantitative metrics such as accuracy, precision, recall, F-measure, and time complexity. The analyzed results demonstrate the superior performance of our proposed SQADEN technique with maximum accuracy, sensitivity and specificity by 3%, 3%, 2% and 3% and minimum time and space by 13% and 15% when compared with the two state-of-the-art methods.

Multivariate adaptive regression splines and neural network models for prediction of pile drivability

Piles are long, slender structural elements used to transfer the loads from the superstructure through weak strata onto stiffer soils or rocks. For driven piles, the impact of the piling hammer induces compression and tension stresses in the piles. Hence, an important design consideration is to check that the strength of the pile is sufficient to resist the stresses caused by the impact of the pile hammer. Due to its complexity, pile drivability lacks a precise analytical solution with regard to the phenomena involved.In situations where measured data or numerical hypothetical results are available, neural networks stand out in mapping the nonlinear interactions and relationships between the system’s predictors and dependent responses. In addition, unlike most computational tools, no mathematical relationship assumption between the dependent and independent variables has to be made. Nevertheless, neural networks have been criticized for their long trial-and-error training process since the optimal configuration is not known a priori. This paper investigates the use of a fairly simple nonparametric regression algorithm known as multivariate adaptive regression splines（MARS）, as an alternative to neural networks, to approximate the relationship between the inputs and dependent response, and to mathematically interpret the relationship between the various parameters. In this paper, the Back propagation neural network（BPNN） and MARS models are developed for assessing pile drivability in relation to the prediction of the Maximum compressive stresses（MCS）, Maximum tensile stresses（MTS）, and Blow per foot（BPF）. A database of more than four thousand piles is utilized for model development and comparative performance between BPNN and MARS predictions.

Optimization of causative factors using logistic regression and artificial neural network models for landslide susceptibility assessment in Ujung Loe Watershed, South Sulawesi Indonesia

Landslide susceptibility maps(LSMs) play a vital role in assisting land use planning and risk mitigation. This study aims to optimize causative factors using logistic regression(LR) and an artificial neural network(ANN) to produce a LSM. The LSM is produced with 11 causative factors and then optimized using forward-stepwise LR(FSLR), ANN, and their combination(FSLR-ANN) until eight causative factors were found for each method. The ANN method produced superior validation results compared with LR. The ROC values for the training data set ranges between 0.8 and 0.9. On the other hand, validation with the percentage of landslide fall into LSM class high and very high, ANN method was higher(92.59%) than LR(82.12%). FSLR-ANN with nine causative factors gave the best validation results with respect to area under curve(AUC) values, and validation with the percentage of landslide fall into LSM class high and very high. In conclusion, ANN was found to be better than LR when producing LSMs. The best Optimization was combination of FSLR-ANN with nine causative factors and AUC success rate 0.847, predictive rate 0.844 and validation with landslide fall into high and very high class with 91.30%. It is an encouraging preliminary model towards a systematic introduction of FSLR-ANN model for optimization causative factors in landslide susceptibility assessment in the mountainous area of Ujung Loe Watershed.

Prediction of kiwifruit firmness using fruit mineral nutrient concentration by artificial neural network(ANN) and multiple linear regressions(MLR)

Many properties of fruit are influenced by plant nutrition. Fruit firmness is one of the most important fruit characteristics and determines post-harvest life of the fruit, in recent decades, artificial intelligence systems were employed for developing predictive models to estimate and predict many agriculture processes. In the present study, the predictive capabilities of multiple linear regressions （MLR） and artificial neural networks （ANNs） are evaluated to estimate fruit firmness in six months, including each of nutrients concentrations （nitrogen （N）, potassium （K）, calcium （Ca） and magnesium （Mg）） alone （P1）, com- bination of nutrients concentrations （P2）, nutrient concentration ratios alone （P3）, and combination of nutrient concentrations and nutrient concentration ratios （P4）. The results showed that MLR model estimated fruit firmness more accuracy than ANN model in three datasets （P1, P2 and P4）. However, the application of P3 （N/Ca ratio） as the input dataset in ANN model improved the prediction of fruit firmness than the MLR model. Correlation coefficient and root mean squared error （RMSE） were 0.850 and 0.539 between the measured and the estimated data by the ANN model, respectively. Generally, the ANN model showed greater potential in determining the relationship between 6-mon-fruit firmness and nutrients concentration.

Prediction of uniaxial compressive strength and modulus of elasticity for Travertine samples using regression and artificial neural networks

Uniaxial Compressive Strength (UCS) and modulus of elasticity (E) are the most important rock parameters required and determined for rock mechanical studies in most civil and mining projects. In this study, two mathematical methods, regression analysis and Artificial Neural Networks (ANNs), were used to predict the uniaxial compressive strength and modulus of elasticity. The P-wave velocity, the point load index, the Schmidt hammer rebound number and porosity were used as inputs for both meth-ods. The regression equations show that the relationship between P-wave velocity, point load index, Schmidt hammer rebound number and the porosity input sets with uniaxial compressive strength and modulus of elasticity under conditions of linear rela-tions obtained coefficients of determination of (R2) of 0.64 and 0.56, respectively. ANNs were used to improve the regression re-sults. The generalized regression and feed forward neural networks with two outputs (UCS and E) improved the coefficients of determination to more acceptable levels of 0.86 and 0.92 for UCS and to 0.77 and 0.82 for E. The results show that the proposed ANN methods could be applied as a new acceptable method for the prediction of uniaxial compressive strength and modulus of elasticity of intact rocks.

Predicting the growth performance of growing-finishing pigs based on net energy and digestible lysine intake using multiple regression and artificial neural networks models

Backgrounds:Evaluating the growth performance of pigs in real-time is laborious and expensive,thus mathematical models based on easily accessible variables are developed.Multiple regression(MR)is the most widely used tool to build prediction models in swine nutrition,while the artificial neural networks(ANN)model is reported to be more accurate than MR model in prediction performance.Therefore,the potential of ANN models in predicting the growth performance of pigs was evaluated and compared with MR models in this study.Results:Body weight(BW),net energy(NE)intake,standardized ileal digestible lysine(SID Lys)intake,and their quadratic terms were selected as input variables to predict ADG and F/G among 10 candidate variables.In the training phase,MR models showed high accuracy in both ADG and F/G prediction(R^(2)_(ADG)=0.929,R^(2)_(F/G)=0.886)while ANN models with 4,6 neurons and radial basis activation function yielded the best performance in ADG and F/G prediction(R^(2)_(ADG)=0.964,R^(2)_(F/G)=0.932).In the testing phase,these ANN models showed better accuracy in ADG prediction(CCC:0.976 vs.0.861,R^(2):0.951 vs.0.584),and F/G prediction(CCC:0.952 vs.0.900,R^(2):0.905 vs.0.821)compared with the MR models.Meanwhile,the“over-fitting”occurred in MR models but not in ANN models.On validation data from the animal trial,ANN models exhibited superiority over MR models in both ADG and F/G prediction(P<0.01).Moreover,the growth stages have a significant effect on the prediction accuracy of the models.Conclusion:Body weight,NE intake and SID Lys intake can be used as input variables to predict the growth performance of growing-finishing pigs,with trained ANN models are more flexible and accurate than MR models.Therefore,it is promising to use ANN models in related swine nutrition studies in the future.

Comparison of Artificial Neural Networks,Geographically Weighted Regression and Cokriging Methods for Predicting the Spatial Distribution of Soil Macronutrients(N,P,and K)

Soil macronutrients(i.e. nitrogen(N), phosphorus(P), and potassium(K)) are important soils components and knowing the spatial distribution of these parameters are necessary at precision agriculture. The purpose of this study was to evaluate the feasibility of different methods such as artificial neural networks(ANN) and two geostatistical methods(geographically weighted regression(GWR) and cokriging(CK)) to estimate N, P and K contents. For this purpose, soil samples were taken from topsoil(0–30 cm) at 106 points and analyzed for their chemical and physical parameters. These data were divided into calibration(n = 84) and validation(n = 22). Chemical and physical variables including clay, p H and organic carbon(OC) were used as auxiliary soil variables to estimate the N, P and K contents. Results showed that the ANN model(with coefficient of determination R^2 = 0.922 and root mean square error RMSE = 0.0079%) was more accurate compared to the CK model(with R^2 = 0.612 and RMSE = 0.0094%), and the GWR model(with R^2 = 0.872 and RMSE = 0.0089%) to estimate the N variable. The ANN model estimated the P with the RMSE of 3.630 ppm, which was respectively 28.93% and 20.00% less than the RMSE of 4.680 ppm and 4.357 ppm from the CK and GWR models. The estimated K by CK, GWR and ANN models have the RMSE of 76.794 ppm, 75.790 ppm and 52.484 ppm. Results indicated that the performance of the CK model for estimation of macro nutrients(N, P and K) was slightly lower than the GWR model. Also, the accuracy of the ANN model was higher than CK and GWR models, which proved to be more effective and reliable methods for estimating macro nutrients.

Prediction of Shear Wave Velocity Using Artificial Neural Network Technique, Multiple Regression and Petrophysical Data: A Case Study in Asmari Reservoir (SW Iran)

Shear wave velocity has numerous applications in geomechanical, petrophysical and geophysical studies of hydrocarbon reserves. However, data related to shear wave velocity isn’t available for all wells, especially old wells and it is very important to estimate this parameter using other well logging. Hence, lots of methods have been developed to estimate these data using other available information of reservoir. In this study, after processing and removing inappropriate petrophysical data, we estimated petrophysical properties affecting shear wave velocity of the reservoir and statistical methods were used to establish relationship between effective petrophysical properties and shear wave velocity. To predict (VS), first we used empirical relationships and then multivariate regression methods and neural networks were used. Multiple regression method is a powerful method that uses correlation between available information and desired parameter. Using this method, we can identify parameters affecting estimation of shear wave velocity. Neural networks can also be trained quickly and present a stable model for predicting shear wave velocity. For this reason, this method is known as “dynamic regression” compared with multiple regression. Neural network used in this study is not like a black box because we have used the results of multiple regression that can easily modify prediction of shear wave velocity through appropriate combination of data. The same information that was intended for multiple regression was used as input in neural networks, and shear wave velocity was obtained using compressional wave velocity and well logging data (neutron, density, gamma and deep resistivity) in carbonate rocks. The results show that methods applied in this carbonate reservoir was successful, so that shear wave velocity was predicted with about 92 and 95 percents of correlation coefficient in multiple regression and neural network method, respectively. Therefore, we propose using these methods to estimate shear wave velocity in wells without this parameter.

Forecasting model of residential load based on general regression neural network and PSO-Bayes least squares support vector machine

Firstly,general regression neural network(GRNN) was used for variable selection of key influencing factors of residential load(RL) forecasting.Secondly,the key influencing factors chosen by GRNN were used as the input and output terminals of urban and rural RL for simulating and learning.In addition,the suitable parameters of final model were obtained through applying the evidence theory to combine the optimization results which were calculated with the PSO method and the Bayes theory.Then,the model of PSO-Bayes least squares support vector machine(PSO-Bayes-LS-SVM) was established.A case study was then provided for the learning and testing.The empirical analysis results show that the mean square errors of urban and rural RL forecast are 0.02% and 0.04%,respectively.At last,taking a specific province RL in China as an example,the forecast results of RL from 2011 to 2015 were obtained.

Electricity price forecasting using generalized regression neural network based on principal components analysis

A combined model based on principal components analysis (PCA) and generalized regression neural network (GRNN) was adopted to forecast electricity price in day-ahead electricity market. PCA was applied to mine the main influence on day-ahead price, avoiding the strong correlation between the input factors that might influence electricity price, such as the load of the forecasting hour, other history loads and prices, weather and temperature; then GRNN was employed to forecast electricity price according to the main information extracted by PCA. To prove the efficiency of the combined model, a case from PJM (Pennsylvania-New Jersey-Maryland) day-ahead electricity market was evaluated. Compared to back-propagation (BP) neural network and standard GRNN, the combined method reduces the mean absolute percentage error about 3%.

Risk factors and prediction of acute kidney injury after liver transplantation:Logistic regression and artificial neural network approaches

BACKGROUND Acute kidney injury(AKI)has serious consequences on the prognosis of patients undergoing liver transplantation.Recently,artificial neural network(ANN)was reported to have better predictive ability than the classical logistic regression(LR)for this postoperative outcome.AIM To identify the risk factors of AKI after deceased-donor liver transplantation(DDLT)and compare the prediction performance of ANN with that of LR for this complication.METHODS Adult patients with no evidence of end-stage kidney dysfunction(KD)who underwent the first DDLT according to model for end-stage liver disease(MELD)score allocation system was evaluated.AKI was defined according to the International Club of Ascites criteria,and potential predictors of postoperative AKI were identified by LR.The prediction performance of both ANN and LR was tested.RESULTS The incidence of AKI was 60.6%(n=88/145)and the following predictors were identified by LR:MELD score>25(odds ratio[OR]=1.999),preoperative kidney dysfunction(OR=1.279),extended criteria donors(OR=1.191),intraoperative arterial hypotension(OR=1.935),intraoperative massive blood transfusion(MBT)(OR=1.830),and postoperative serum lactate(SL)(OR=2.001).The area under the receiver-operating characteristic curve was best for ANN(0.81,95%confidence interval[CI]:0.75-0.83)than for LR(0.71,95%CI:0.67-0.76).The root-mean-square error and mean absolute error in the ANN model were 0.47 and 0.38,respectively.CONCLUSION The severity of liver disease,pre-existing kidney dysfunction,marginal grafts,hemodynamic instability,MBT,and SL are predictors of postoperative AKI,and ANN has better prediction performance than LR in this scenario.

Risk based security assessment of power system using generalized regression neural network with feature extraction

A comprehensive risk based security assessment which includes low voltage, line overload and voltage collapse was presented using a relatively new neural network technique called as the generalized regression neural network (GRNN) with incorporation of feature extraction method using principle component analysis. In the risk based security assessment formulation, the failure rate associated to weather condition of each line was used to compute the probability of line outage for a given weather condition and the extent of security violation was represented by a severity function. For low voltage and line overload, continuous severity function was considered due to its ability to zoom in into the effect of near violating contingency. New severity function for voltage collapse using the voltage collapse prediction index was proposed. To reduce the computational burden, a new contingency screening method was proposed using the risk factor so as to select the critical line outages. The risk based security assessment method using GRNN was implemented on a large scale 87-bus power system and the results show that the risk prediction results obtained using GRNN with the incorporation of principal component analysis give better performance in terms of accuracy.