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Soft Computing Technique in the Water Sector: Artificial Neural Network Approach
Published in Surendra Kumar Chandniha, Anil Kumar Lohani, Gopal Krishan, Ajay Krishna Prabhakar, Advances in Hydrology and Climate Change, 2023
Himanshu Panjiar, Ankit Chakravarti
Generalized regression algorithm is used in generalized regression neural network (GRNN). Generalized regression algorithm does not need iterative training as it approximates any arbitrary function between output and input vectors. This algorithm is directly drawing the function estimate from the training data. It is based on a standard statistical technique called kernel regression and used for the estimation of probability density function of continuous variables. GRNN was initially suggested by Specht in 1991 (Specht, 1991). GRNN consists of four layers, namely, input layer {xi; i = 1,2...} as first layer, pattern layer {pj; j = 1,2...} as second layer, summation layer {sk; k = 1,2...} as third layer, and an output layer (y) is the final layer as shown in Figure 4.12. The output layer can have single or multiple output nodes and that can be designed as per the requirement. One of the important points to be noted here is that each output node should be connected to two summation layer nodes (Specht, 1991).
Vulnerability Assessment
Published in James A. Momoh, Adaptive Stochastic Optimization Techniques with Applications, 2015
A powerful neural network model is the generalized regression neural network (GRNN) that has a simple architecture of four layers known as input, patterns, summation, and output (see Figure 10.2). The number of input units in the first layer is equal to independent factors or variables. The first layer is fully connected to the pattern layer, whose output is a measure of the distance of the input from the stored patterns. Each pattern layer unit is connected to two neurons in the summation layer, known as S-summation neuron and D-summation neuron. The S-summation neuron computes the sum of the weighted outputs of the pattern layer while the D-summation neuron calculates the unweighted outputs of the pattern neurons. For D-summation neuron, the connection weight is set to unity.
Evaluation of rural territorial functions: A case study of Henan Province, China
Published in Ai Sheng, Energy, Environment and Green Building Materials, 2015
Due to the interrelations and interactions of different territorial functions of the rural, the operations of each sub-function create a complicated system; thus, the widely used quantitative evaluation methods and linear modeling are not easily applicable to the sophisticated reality (Feng, 2003). the general regression neural network under rapid development recently provided a new approach in solving complicated problems of non-linear modeling. the general regression neural network has many advantages that traditional methods do not have: Network, for instance, can “imitate” and “memorize” any sophisticated “function” relation between the input and output variables, and it can process all kinds of vague and non-linear data (Li, 2004).
Predicting unregulated disinfection by-products in water distribution networks using generalized regression neural networks
Published in Urban Water Journal, 2021
Haroon R. Mian, Guangji Hu, Kasun Hewage, Manuel J. Rodriguez, Rehan Sadiq
The performance of developed GRNN models was evaluated considering various metrics, such as percentage (%) bad predictions, root mean square error (RMSE), and mean absolute error (MAE). Using a combination of error metrics is considered a reliable approach to evaluate models’ performance (Chai and Draxler 2014). These metrics were measured for both training and testing data. The % bad predictions measure the number of data points in percentage for which predicted concentration was different from the actual value. The bad predictions were determined by calculating the residual between the actual and predicted concentration. A higher residual value leads to a bad prediction, reflecting low model performance in terms of prediction. RMSE is a standard deviation of the residuals, which measures the spread of residuals. RMSE is calculated:
Predicting the pile static load test using backpropagation neural network and generalized regression neural network – a comparative study
Published in International Journal of Geotechnical Engineering, 2021
The general regression neural network applies regression to the input data using a probability density function. It is also a feedforward network consisting of four layers; input, pattern, summation, and output layers. All the attributes values are fed to the input layer as a vector. The pattern layer, consisting of units that store cluster centres, then receives these input. The cluster centres are determined using a particular clustering technique, such as the K-means. The objective of these centres is to group the sample inputs so that each group can be represented in one unit of the pattern layer measuring the distance of the input vector from the cluster centre (Specht 1991). The squares of all the differences between the values in a new vector and the cluster centres are summed and input to an activation function, which is an exponential function. The pattern layer produces an output, which is stored as two parts in the summation layer that consists of two units. The predicted value is produced in the output unit by computing the division of the stored values in the two summation units.
Artificial neural network models for global solar energy and photovoltaic power forecasting over India
Published in Energy Sources, Part A: Recovery, Utilization, and Environmental Effects, 2020
Gulnar Perveen, M. Rizwan, Nidhi Goel, Priyanka Anand
Generalized Regression Neural Network (GRNN): These networks are used for function approximation. To closely fit the data, a spread smaller than the typical distance between input vectors are used and smoothly fitting the data, a larger spread has been used.