Prediction of Superconductivity for Oxides Based on Structural Parameters and Artificial Neural Network Method

Superconductive properties for oxides were predicted by artificial neural network (ANN) method with structural and chemical parameters as inputs. The predicted properties include superconductivity for oxides, distributed ranges of the superconductive transition temperature (Tc) for complex oxides, and Tc values for cuprate superconductors. The calculated results indicated that the adjusted ANN can be used to predict superconductive properties for unknown oxides.

Estimation of Tsunami Run-up Height by Three Artificial Neural Network Methods

Tsunami ran-up height is a significant parameter for dimensions of coastal structures. In the present study, tsunami run-up heights are estimated by three different Artificial Neural Network （ANN） models, i.e. Feed Forward Back Propagation （FFBP）, Radial Basis Functions （RBF） and Generalized Regression Neural Network （GRNN）. As the input for the ANN configuration, the wave height （H） values are employed. It is shown that the tsunami ran-up height values are closely approximated with all of the applied ANN methods. The ANN estimations are slightly superior to those of the empirical equation. It can be seen that the ANN applications are especially significant in the absence of adequate number of laboratory experiments. The results also prove that the available experiment data set can be extended with ANN simulations. This may be helpful to decrease the burden of the experimental studies and to supply results for comparisons.

Artificial Neural Network Method Based on Expert Knowledge and Its Application to Quantitative Identification of Potential Seismic Sources

In this paper,an approach is developed to optimize the quality of the training samples in the conventional Artificial Neural Network(ANN)by incorporating expert knowledge in the means of constructing expert-rule samples from rules in an expert system,and through training by using these samples,an ANN based on expert-knowledge is further developed.The method is introduced into the field of quantitative identification of potential seismic sources on the basis of the rules in an expert system.Then it is applied to the quantitative identification of the potential seismic sources in Beijing and its adjacent area.The result indicates that the expert rule based on ANN method can well incorporate and represent the expert knowledge in the rules in an expert system,and the quality of the samples and the efficiency of training and the accuracy of the result are optimized.

Fractal Solitons, Arbitrary Function Solutions, Exact Periodic Wave and Breathers for a Nonlinear Partial Differential Equation by Using Bilinear Neural Network Method

This paper extends a method, called bilinear neural network method(BNNM), to solve exact solutions to nonlinear partial differential equation. New, test functions are constructed by using this method. These test functions are composed of specific activation functions of single-layer model,specific activation functions of "2-2" model and arbitrary functions of "2-2-3" model. By means of the BNNM, nineteen sets of exact analytical solutions and twenty-four arbitrary function solutions of the dimensionally reduced p-gB KP equation are obtained via symbolic computation with the help of Maple. The fractal solitons waves are obtained by choosing appropriate values and the self-similar characteristics of these waves are observed by reducing the observation range and amplifying the partial picture. By giving a specific activation function in the single layer neural network model, exact periodic waves and breathers are obtained. Via various three-dimensional plots, contour plots and density plots,the evolution characteristic of these waves are exhibited.

A New Artificial Neural Network Method for Solving Schrodinger Equations on Unbounded Domains

The simulation for particle or soliton propagation based on linear or nonlinear Schrodinger equations on unbounded domains requires the computational domain to be bounded,and therefore,a special boundary treatment such as an absorbing boundary condition(ABC)or a perfectly matched layer(PML)is needed so that the reflections of outgoing waves at the boundary can be minimized in order to prevent the destruction of the simulation.This article presents a new artificial neural network(ANN)method for solving linear and nonlinear Schrodinger equations on unbounded domains.In particular,this method randomly selects training points only from the bounded computational space-time domain,and the loss function involves only the initial condition and the Schrodinger equation itself in the computational domainwithout any boundary conditions.Moreover,unlike standard ANNmethods that calculate gradients using expensive automatic differentiation,this method uses accurate finitedifference approximations for the physical gradients in the Schrodinger equation.In addition,a Metropolis-Hastings algorithm is implemented for preferentially selecting regions of high loss in the computational domain allowing for the use of fewer training points in each batch.As such,the present training method uses fewer training points and less computation time for convergence of the loss function as compared with the standard ANN methods.This new ANN method is illustrated using three examples.

VPVnet:A Velocity-Pressure-Vorticity Neural Network Method for the Stokes’Equations under Reduced Regularity

We present VPVnet,a deep neural network method for the Stokes’equa-tions under reduced regularity.Different with recently proposed deep learning meth-ods[40,51]which are based on the original form of PDEs,VPVnet uses the least square functional of thefirst-order velocity-pressure-vorticity(VPV)formulation([30])as loss functions.As such,onlyfirst-order derivative is required in the loss functions,hence the method is applicable to a much larger class of problems,e.g.problems with non-smooth solutions.Despite that several methods have been proposed recently to reduce the regularity requirement by transforming the original problem into a corresponding variational form,while for the Stokes’equations,the choice of approximating spaces for the velocity and the pressure has to satisfy the LBB condition additionally.Here by making use of the VPV formulation,lower regularity requirement is achieved with no need for considering the LBB condition.Convergence and error estimates have been established for the proposed method.It is worth emphasizing that the VPVnet method is divergence-free and pressure-robust,while classical inf-sup stable mixedfinite elements for the Stokes’equations are not pressure-robust.Various numerical experiments including 2D and 3D lid-driven cavity test cases are conducted to demon-strate its efficiency and accuracy.

Simultaneous Determination of Iron and Manganese in Water Using Artificial Neural Network Catalytic Spectrophotometric Method

A new analytical method using Back-Propagation (BP) artificial neural network and kinetic spectrophotometry for simultaneous determination of iron and magnesium in tap water, the Yellow River water and seawater is established. By conditional experiments, the optimum analytical conditions and parameters are obtained. Levenberg-Marquart (L-M) algorithm is used for calculation in BP neural network. The topological structure of three-layer BP ANN network architecture is chosen as 15-16-2 (nodes). The initial value of gradient coefficient μ is fixed at 0.001 and the increase factor and reduction factor of μ take the default values of the system. The data are processed by computers with our own programs written in MATLAB 7.0. The relative standard deviation of the calculated results for iron and manganese is 2.30% and 2.67% respectively. The results of standard addition method show that for the tap water, the recoveries of iron and manganese are in the ranges of 98.0%-104.3% and 96.5%-104.5%, and the RSD is in the range of 0.23%-0.98%; for the Yellow River water (Lijin district of Shandong Province), the recoveries of iron and manganese are in the ranges of 96.0%-101.0% and 98.7%-104.2%, and the RSD is in the range of 0.13%-2.52%; for the seawater in Qingdao offshore, the recoveries of iron and manganese are in the ranges of 95.3%-104.8% and 95.3%-104.7%, and the RSD is in the range of 0.14%-2.66%. It is found that 21 common cations and anions do not interfere with the determination of iron and manganese under the optimum experimental conditions. This method exhibits good reproducibility and high accuracy in the determination of iron and manganese and can be used for the simultaneous determination of iron and manganese in tap water and natural water. By using the established ANN- catalytic spectrophotometric method, the iron and manganese concentrations of the surface seawater at 11 sites in Qingdao offshore are determined and the level distribution maps of iron and manganese are drawn.

Linearization Learning Method of BP Neural Networks

Feedforward multi layer neural networks have very strong mapping capability that is based on the non linearity of the activation function, however, the non linearity of the activation function can cause the multiple local minima on the learning error surfaces, which affect the learning rate and solving optimal weights. This paper proposes a learning method linearizing non linearity of the activation function and discusses its merits and demerits theoretically.

An Artificial Neural Network-Based Response Surface Method for Reliability Analyses of c-φ Slopes with Spatially Variable Soil

This paper presents an artificial neural network（ANN）-based response surface method that can be used to predict the failure probability of c-φslopes with spatially variable soil.In this method,the Latin hypercube sampling technique is adopted to generate input datasets for establishing an ANN model;the random finite element method is then utilized to calculate the corresponding output datasets considering the spatial variability of soil properties;and finally,an ANN model is trained to construct the response surface of failure probability and obtain an approximate function that incorporates the relevant variables.The results of the illustrated example indicate that the proposed method provides credible and accurate estimations of failure probability.As a result,the obtained approximate function can be used as an alternative to the specific analysis process in c-φslope reliability analyses.

The application of neural networks to comprehensive prediction by seismology prediction method

BP neural networks is used to mid-term earthquake prediction in this paper. Some usual prediction parameters of seismology are used as the import units of neural networks. And the export units of neural networks is called as the character parameter W_0 describing enhancement of seismicity. We applied this method to space scanning of North China. The result shows that the mid-term anomalous zone of W_0-value usually appeared obviously around the future epicenter 1~3 years before earthquake. It is effective to mid-term prediction.

Online Gradient Methods with a Punishing Term for Neural Networks

Online gradient methods are widely used for training the weight of neural networks and for other engineering computations. In certain cases, the resulting weight may become very large, causing difficulties in the implementation of the network by electronic circuits. In this paper we introduce a punishing term into the error function of the training procedure to prevent this situation. The corresponding convergence of the iterative training procedure and the boundedness of the weight sequence are proved. A supporting numerical example is also provided.

A Study on the Convergence of Gradient Method with Momentum for Sigma-Pi-Sigma Neural Networks

In this paper, a gradient method with momentum for sigma-pi-sigma neural networks (SPSNN) is considered in order to accelerate the convergence of the learning procedure for the network weights. The momentum coefficient is chosen in an adaptive manner, and the corresponding weak convergence and strong convergence results are proved.

The Complex System Modeling Method Based on Uniform Design and Neural Network

In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the modeling samples and obtain the overall information of the system;for the purpose of modeling the system or its characteristics, the artificial neural network is used to construct the model. Experiment indicates that this method can model the complex system effectively.

Structural Reliability Analysis Based on Support Vector Machine and Dual Neural Network Direct Integration Method

Aiming at the reliability analysis of small sample data or implicit structural function,a novel structural reliability analysis model based on support vector machine(SVM)and neural network direct integration method(DNN)is proposed.Firstly,SVM with good small sample learning ability is used to train small sample data,fit structural performance functions and establish regular integration regions.Secondly,DNN is approximated the integral function to achieve multiple integration in the integration region.Finally,structural reliability was obtained by DNN.Numerical examples are investigated to demonstrate the effectiveness of the present method,which provides a feasible way for the structural reliability analysis.

TIME SERIES NEURAL NETWORK FORECASTING METHODS

This paper has discussed the possibility and key problem to construct the neural network time series model, and three time series neural network forecasting methods has been proposed, i. e. a neural network nonlinear time series model, a neural network multi-dimension time series model and a neural network combining predictive model. These three methods are applied to real problems. The results show that these methods are better than the traditional one. Furthermore, the neural network methods are compared with the traditional method, and the constructed model of intellectual information forecasting system is given.

DOBD Algorithm for Training Neural Network: Part I. Method

Overfitting is one of the important problems that restrain the application of neural network. The traditional OBD (Optimal Brain Damage) algorithm can avoid overfitting effectively. But it needs to train the network repeatedly with low calculational efficiency. In this paper, the Marquardt algorithm is incorporated into the OBD algorithm and a new method for pruning network-the Dynamic Optimal Brain Damage (DOBD) is introduced. This algorithm simplifies a network and obtains good generalization through dynamically deleting weight parameters with low sensitivity that is defined as the change of error function value with respect to the change of weights. Also a simplified method is presented through which sensitivities can be calculated during training with a little computation. A rule to determine the lower limit of sensitivity for deleting the unnecessary weights and other control methods during pruning and training are introduced. The training course is analyzed theoretically and the reason why DOBD algorithm can obtain a much faster training speed than the OBD algorithm and avoid overfitting effectively is given.

A New Method for Evolving Artificial Neural Networks Using Genetic Algorithm

In this paper, a new neuroevolution algorithm (NEGA) for simultaneous evolution of both architectures and weights of neural networks is described. A whole new network encoding method is shown. The competing conventions problem is solved absolutely. Heuristic methods are used to constrain the topology mutation probability and the trend of mutation kind choice. Also, the niching method is used to protect the network topologies evolution. The experiment results show the efficiency and rapidity of NEGA forcefully.

Determination of penetration depth at high velocity impact using finite element method and artificial neural network tools

Determination of ballistic performance of an armor solution is a complicated task and evolved significantly with the application of finite element methods(FEM) in this research field.The traditional armor design studies performed with FEM requires sophisticated procedures and intensive computational effort,therefore simpler and accurate numerical approaches are always worthwhile to decrease armor development time.This study aims to apply a hybrid method using FEM simulation and artificial neural network(ANN) analysis to approximate ballistic limit thickness for armor steels.To achieve this objective,a predictive model based on the artificial neural networks is developed to determine ballistic resistance of high hardness armor steels against 7.62 mm armor piercing ammunition.In this methodology,the FEM simulations are used to create training cases for Multilayer Perceptron(MLP) three layer networks.In order to validate FE simulation methodology,ballistic shot tests on 20 mm thickness target were performed according to standard Stanag 4569.Afterwards,the successfully trained ANN(s) is used to predict the ballistic limit thickness of 500 HB high hardness steel armor.Results show that even with limited number of data,FEM-ANN approach can be used to predict ballistic penetration depth with adequate accuracy.

Load Reduction Test Method of Similarity Theory and BP Neural Networks of Large Cranes

Static load tests are an important means of supervising and detecting a crane＇s lift capacity. Due to space restrictions, however, there are difficulties and potential danger when testing large bridge cranes. To solve the loading problems of large-tonnage cranes during testing, an equivalency test is proposed based on the similarity theory and BP neural networks. The maximum stress and displacement of a large bridge crane is tested in small loads, combined with the training neural network of a similar structure crane through stress and displacement data which is collected by a physics simulation progressively loaded to a static load test load within the material scope of work. The maximum stress and displacement of a crane under a static load test load can be predicted through the relationship of stress, displacement, and load. By measuring the stress and displacement of small tonnage weights, the stress and displacement of large loads can be predicted, such as the maximum load capacity, which is 1.25 times the rated capacity. Experimental study shows that the load reduction test method can reflect the lift capacity of large bridge cranes. The load shedding predictive analysis for Sanxia 1200 t bridge crane test data indicates that when the load is 1.25 times the rated lifting capacity, the predicted displacement and actual displacement error is zero. The method solves the problem that lifting capacities are difficult to obtain and testing accidents are easily possible when 1.25 times related weight loads are tested for large tonnage cranes.

Calibration Method of Magnetometer Based on BP Neural Network

Due to the influence of processing technology and environmental factors, there are errors in attitude measurement with the three-axis magnetometer, and the change of parameters during the operation of the magnetometer in orbit will have a great impact on the measurement accuracy. This paper studies the calibration method of magnetometer based on BP neural network, which reduces the influence of model error on calibration accuracy. Firstly, the error model of the magnetometer and the structural characteristics of the BP neural network are analyzed. Secondly, the number of hidden layers and hidden nodes is optimized. To avoid the problem of slow convergence and low accuracy of basic BP algorithm, this paper uses the Levenberg Marquardt backpropagation training method to improve the training speed and prediction accuracy and realizes the on-orbit calibration of magnetometer through online training of the neural network. Finally, the effectiveness of the method is verified by numerical simulation. The results show that the neural network designed in this paper can effectively reduce the measurement error of magnetometer, while the online training can effectively reduce the error caused by the change of magnetometer parameters, and reduce the measurement error of magnetometer to less than 10 nT.