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Probabilistic neural network has successfully solved all kinds of engineering problems in various fields since it is proposed. In probabilistic neural network, Spread has great influence on its performance, and probabilistic neural network will generate bad prediction results if it is improperly selected. It is difficult to select the optimal manually. In this article, a variant of probabilistic neural network with self-adaptive strategy, called self-adaptive probabilistic neural network, is proposed. In self-adaptive probabilistic neural network, Spread can be self-adaptively adjusted and selected and then the best selected Spread is used to guide the self-adaptive probabilistic neural network train and test. In addition, two simplified strategies are incorporated into the proposed self-adaptive probabilistic neural network with the aim of further improving its performance and then two versions of simplified self-adaptive probabilistic neural network (simplified self-adaptive probabilistic neural networks 1 and 2) are proposed. The variants of self-adaptive probabilistic neural networks are further applied to solve the transformer fault diagnosis problem. By comparing them with basic probabilistic neural network, and the traditional back propagation, extreme learning machine, general regression neural network, and self-adaptive extreme learning machine, the results have experimentally proven that self-adaptive probabilistic neural networks have a more accurate prediction and better generalization performance when addressing the transformer fault diagnosis problem.

This study introduces a hybrid model that utilizes a model-based optimization method to generate training data and an artificial neural network (ANN)-based learning method to offer real-time exoskeleton support in lifting activities. For the model-based optimization method, the torque of the knee exoskeleton and the optimal lifting motion are predicted utilizing a two-dimensional (2D) human–exoskeleton model. The control points for exoskeleton motor current profiles and human joint angle profiles from cubic B-spline interpolation represent the design variables. Minimizing the square of the normalized human joint torque is considered as the cost function. Subsequently, the lifting optimization problem is tackled using a sequential quadratic programming (SQP) algorithm in sparse nonlinear optimizer (SNOPT). For the learning-based approach, the learning-based control model is trained using the general regression neural network (GRNN). The anthropometric parameters of the human subjects and lifting boundary postures are used as input parameters, while the control points for exoskeleton torque are treated as output parameters. Once trained, the learning-based control model can provide exoskeleton assistive torque in real time for lifting tasks. Two test subjects’ joint angles and ground reaction forces (GRFs) comparisons are presented between the experimental and simulation results. Furthermore, the utilization of exoskeletons significantly reduces activations of the four knee extensor and flexor muscles compared to lifting without the exoskeletons for both subjects. Overall, the learning-based control method can generate assistive torque profiles in real time and faster than the model-based optimal control approach.

Agriculture is the principal basis of livelihood that acts as a mainstay of any country. There are several changes faced by the farmers due to various factors such as water shortage, undefined price owing to demand–supply, weather uncertainties, and inaccurate crop prediction. The prediction of crop yield, notably paddy yield, is an intricate assignment owing to its dependency on several factors such as crop genotype, environmental factors, management practices, and their interactions. Researchers are used to predicting the paddy yield using statistical approaches, but they failed to attain higher accuracy due to several factors. Therefore, machine learning methods such as support vector regression (SVR), general regression neural networks (GRNNs), radial basis functional neural networks (RBFNNs), and back-propagation neural networks (BPNNs) are demonstrated to predict the paddy yield accurately for the Cauvery Delta Zone (CDZ), which lies in the eastern part of Tamil Nadu, South India. The performance of each developed model is examined using assessment metrics such as coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), mean squared error (MSE), mean absolute percentage error (MAPE), coefficient of variance (CV), and normalized mean squared error (NMSE). The observed results show that the GRNN algorithm delivers superior evaluation metrics such as R2, RMSE, MAE, MSE, MAPE, CV, and NSME values about 0.9863, 0.2295 and 0.1290, 0.0526, 1.3439, 0.0255, and 0.0136, respectively, which ensures accurate crop yield prediction compared with other methods. Finally, the performance of the GRNN model is compared with other available models from several studies in the literature, and it is found to be high while comparing the prediction accuracy using evaluation metrics.

This paper presents an intelligent predictive system designed to support real-time decision making in the control of rubber blend mixing processes. The core of the system is a General Regression Neural Network (GRNN), which accurately predicts key process parameters, such as viscosity (expressed as torque), temperature, and energy consumption across varying masses of the processed material. The model can evaluate the mixing progress based on the initial 10% of input data, allowing early intervention and process optimisation. Experimental validation was conducted using a Brabender Plastograph EC Plus with a natural rubber-based blend in the mass range of 60–75 g. The GRNN kernel width parameter (σ) was optimised through a 10-fold cross-validation. High predictive accuracy was confirmed by values of the coefficient of determination (R2) approaching 1, and consistently low values of the root mean square error (RMSE). This system offers a robust and scalable solution for intelligent process control, productivity enhancement, and quality assurance across diverse industrial applications, beyond rubber blending.

Software development effort estimation (SDEE) is one of the main tasks in software project management. It is crucial for a project manager to efficiently predict the effort or cost of a software project in a bidding process, since overestimation will lead to bidding loss and underestimation will cause the company to lose money. Several SDEE models exist; machine learning models, especially neural network models, are among the most prominent in the field. In this study, four different neural network models—multilayer perceptron, general regression neural network, radial basis function neural network, and cascade correlation neural network—are compared with each other based on: (1) predictive accuracy centred on the mean absolute error criterion, (2) whether such a model tends to overestimate or underestimate, and (3) how each model classifies the importance of its inputs. Industrial datasets from the International Software Benchmarking Standards Group (ISBSG) are used to train and validate the four models. The main ISBSG dataset was filtered and then divided into five datasets based on the productivity value of each project. Results show that the four models tend to overestimate in 80 % of the datasets, and the significance of the model inputs varies based on the selected model. Furthermore, the cascade correlation neural network outperforms the other three models in the majority of the datasets constructed on the mean absolute residual criterion.

The internal response mechanism of vegetation change in fragile high-altitude ecosystems is pivotal for ecological stability. This study focuses on the Lhasa River Basin (LRB) on the Tibetan Plateau (TP), a typical high-altitude fragile ecosystem where vegetation dynamics are highly sensitive to climate change and human activities. Utilizing MODIS surface reflectance data (MOD09Q1), a general regression neural network (GRNN) was applied to create a 250 m resolution fractional vegetation cover (FVC) dataset from 2001 to 2022, whose accuracy was verified with field survey data. Through methods like the Theil–Sen Median trend analysis, Mann–Kendall significance test, Hurst exponent, and geographical detector, the collaborative mechanism of 14 driving factors was systematically explored. Key conclusions are as follows: (1) The FVC in the LRB evolved in stages, first decreasing and then increasing, with 46.71% of the basin area expected to show an improvement trend in the future. (2) Among natural factors, elevation (q = 0.480), annual mean potential evapotranspiration (q = 0.362), and annual mean temperature (q = 0.361) are the main determinants of FVC spatiotemporal variation. (3) In terms of human activities, land use type has the highest explanatory power (q = 0.365) for FVC. (4) The interaction of two factors on FVC is stronger than that of a single factor, with the elevation–land use interaction being the most significant (q = 0.558). These results deepen our understanding of the interactions among vegetation, climate, and humans in fragile high-altitude ecosystems and provide a scientific basis for formulating zoned restoration strategies on the TP.

Precipitation water vapor (PWV) is an important parameter in numerical weather forecasting and climate research. However, existing PWV adjustment models lack comprehensive consideration of seasonal and geographic factors. This study utilized the General Regression Neural Network (GRNN) algorithm and Global Navigation Satellite System (GNSS) PWV in China to construct and evaluate European Centre for Medium-Range Weather Forecasts (ECMWF) Atmospheric Reanalysis (ERA5) PWV adjustment models for various seasons and subregions based on meteorological parameters (GMPW model) and non-meteorological parameters (GFPW model). A linear model (GLPW model) was established for model accuracy comparison. The results show that: (1) taking GNSS PWV as a reference, the Bias and root mean square error (RMSE) of the GLPW, GFPW, and GMPW models are about 0/1 mm, which better weakens the systematic error of ERA5 PWV. The overall Bias of the GLPW, GFPW, and GMPW models in the Northwest (NWC), North China (NC), Tibetan Plateau (TP), and South China (SC) subregions is approximately 0 mm after adjustment. The adjusted overall RMSE of the GLPW, GFPW, and GMPW models of the four subregions are 0.81/0.71/0.62 mm, 1.15/0.95/0.77 mm, 1.66/1.26/1.05 mm, and 2.11/1.35/0.96 mm, respectively. (2) The accuracy of the three models is tested using GNSS PWV, which is not involved in the modeling. The adjusted overall RMSE of the GLPW, GFPW, and GMPW models in the four subregions are 0.89/0.85/0.83 mm, 1.61/1.58/1.27 mm, 2.11/1.75/1.68 mm and 3.65/2.48/1.79 mm, respectively. As a result, the GFPW and GMPW models have better accuracy in adjusting ERA5 PWV than the linear model GLPW. Therefore, the GFPW and GMPW models can effectively contribute to water vapor monitoring and the integration of multiple PWV datasets.

In this study, we present a systematic scheme to identify the material parameters in constitutive model of hyperelastic materials such as rubber. This approach is proposed based on the combined use of general regression neural network, experimental data and finite element analysis. In detail, the finite element analysis is carried out to provide the learning samples of GRNN model, while the results observed from the uniaxial tensile test is set as the target value of GRNN model. A problem involving parameters identification of silicone rubber material is described for validation. The results show that the proposed GRNN-based approach has the characteristics of high universality and good precision, and can be extended to parameters identification of complex rubber-like hyperelastic material constitutive.

Flatness prediction is a critical technical concern in flatness feedforward control during strip cold rolling. This work realized a high-precision prediction of flatness for strip cold rolling by the data-driven and industrial Internet of Things (IIoT) technology and provided an effective mode for industrial data utilization. A flatness prediction model based on general regression neural network (GRNN) optimized by the differential evolutionary (DE) algorithm was proposed; an intact dataset was established by collecting data from the hot rolling and cold rolling production lines by developing a cross-process IIoT platform, and the proposed model and other common data-driven models are trained and tested based on that. The experiment results obtained based on a dataset with 50,000 samples show that the proposed model is feasible and can achieve accurate prediction of flatness during the strip cold rolling, and compared with the BP and SVM model, it has a better performance.

The general regression neural network (GRNN) allows testing of various events, wave paths, and site features as ground motion model (GMM) predictors. The GRNN is determined by all previous measurements, while this research aims to find the best conditional probability distribution fX|y of ground motion predictors given ground motion values. The fX|y is estimated by a kernel estimator. The GRNN was modified. Instead of the Euclidean distance of all predictors, we look for various metric spaces of predictors that minimize cross-validation error. This approach was used in the search for the GMM whose predictors include values describing focal mechanisms. Nodal plane angles were applied. GMMs containing different predictor configurations were compared. It was noticed that rake and strike nodal plane angles have an impact on the GRNN GMM while the dip angle does not. The databases of ground motions and events containing focal mechanisms, NGA-West2 and from Lubin Głogów Copper District in Poland, were used for the research.