The construction and approximation of feedforward neural network with hyperbolic tangent function

In this paper, we discuss some analytic properties of hyperbolic tangent function and estimate some approximation errors of neural network operators with the hyperbolic tan- gent activation function. Firstly, an equation of partitions of unity for the hyperbolic tangent function is given. Then, two kinds of quasi-interpolation type neural network operators are con- structed to approximate univariate and bivariate functions, respectively. Also, the errors of the approximation are estimated by means of the modulus of continuity of function. Moreover, for approximated functions with high order derivatives, the approximation errors of the constructed operators are estimated.

Vibration suppression for rotating space slender flexible structures based on novel deformation description and NNSMC controller with hyperbolic tangent function

Rotating Space Slender Flexible Structures(RSSFS)are extensively utilized in space operations because of their light weight,mobility,and low energy consumption.To realize the accurate space operation of the RSSFS,it is necessary to establish a precise mechanical model and develop a control algorithm with high precision.However,with the application of traditional control strategies,the RSSFS often suffers from the chattering phenomenon,which will aggravate structure vibration.In this paper,novel deformation description is put forward to balance modeling accuracy and computational efficiency of the RSSFS,which is better appropriate for real-time control.Besides,the Neural Network Sliding Mode Control(NNSMC)strategy modified by the hyperbolic tangent(tanh)function is put forward to compensate for modeling errors and reduce the chattering phenomenon,thereby improving the trajectory tracking accuracy of the RSSFS.Firstly,a mathematical model for the RSSFS is developed according to the novel deformation description and the vibration theory of flexible structure.Comparison of the deformation accuracy between different models proves that the novel modeling method proposed has high modeling accuracy.Next,the universal approximation property of the Radial Basis Function(RBF)neural network is put forward to determine and compensate for modeling errors,which consist of higher-order modes and the uncertainties of external disturbances.In addition,the tanh function is proposed as the reaching law in the conventional NNSMC strategy to suppress driving torque oscillation.The control law of modified NNSMC strategy and the adaptive law of weight coefficients are developed according to the Lyapunov theorem to guarantee the RSSFS stability.Finally,the simulation and physical experimental tests of the RSSFS with different control strategies are conducted.Experimental results show that the control law according to the novel deformation description and the modified NNSMC strategy can obtain accurate tracking of the rotation and reduce the vibration of the RSSFS simultaneously.

An artificial neural network visible mathematical model for real-time prediction of multiphase flowing bottom-hole pressure in wellbores

Accurate prediction of multiphase flowing bottom-hole pressure(FBHP)in wellbores is an important factor required for optimal tubing design and production optimization.Existing empirical correlations and mechanistic models provide inaccurate FBHP predictions when applied to real-time field datasets because they were developed with laboratory-dependent parameters.Most machine learning(ML)models for FBHP prediction are developed with real-time field data but presented as black-box models.In addition,these ML models cannot be reproduced by other users because the dataset used for training the machine learning algorithm is not open source.These make using the ML models on new datasets difficult.This study presents an artificial neural network(ANN)visible mathematical model for real-time multiphase FBHP prediction in wellbores.A total of 1001 normalized real-time field data points were first used in developing an ANN black-box model.The data points were randomly divided into three different sets;70%for training,15%for validation,and the remaining 15%for testing.Statistical analysis showed that using the Levenberg-Marquardt training optimization algorithm(trainlm),hyperbolic tangent activation function(tansig),and three hidden layers with 20,15 and 15 neurons in the first,second and third hidden layers respectively achieved the best performance.The trained ANN model was then translated into an ANN visible mathematical model by extracting the tuned weights and biases.Trend analysis shows that the new model produced the expected effects of physical attributes on FBHP.Furthermore,statistical and graphical error analysis results show that the new model outperformed existing empirical correlations,mechanistic models,and an ANN white-box model.Training of the ANN on a larger dataset containing new data points covering a wider range of each input parameter can broaden the applicability domain of the proposed ANN visible mathematical model.