Application Of Grey Prediction Model With Hyperbolic Sine Driving Term In Physical Tensile Strength

The tensile strength of materials is an important mechanical performance indicator for testing mechanical products,and has important value in evaluating mechanical parts.However,as the temperature continues to rise,obtaining the tensile strength value of the tested material becomes increasingly difficult.In order to estimate the tensile strength value of the material at high temperatures,this thesis regards the mechanical properties of the material as a grey system and combines the grey prediction model to calculate the tensile strength value of the material at high temperatures.This paper mainly focuses on the following three aspects of research.(1)The application of continuous grey prediction model with hyperbolic sine driving term in physical tensile strength.This thesis proposes a continuous grey prediction model SinHGM(1,1)with hyperbolic sine driving term based on the traditional grey prediction model GM(1,1).The ordinary differential equation theory,grey modeling technology,least square estimation and other methods are used to analyze the model,and the feasibility of the model is verified through specific examples.Subsequently,the new model was used to calculate the tensile strength values of steel 8620 quenched in oil,and the tensile strength values at different temperatures were obtained.Finally,the SinHGM(1,1)model was used to calculate the original data of four sets of tensile strength,and the calculation results showed that the new model had significant errors in the four sets of tensile strength data.Based on this,we analyzed the causes of significant errors from the modeling mechanism of the continuous grey prediction model SinHGM(1,1).(2)The application of a discrete grey prediction model with hyperbolic sine driving term in physical tensile strength.The continuous grey prediction model SinHGM(1,1)has inconsistent whitening differential equations and grey basic forms,which can lead to internal errors in the model and affect its accuracy.Based on the SinHGM(1,1)model,this paper proposes a discrete grey prediction model SinHDGM(1,1)with hyperbolic sinusoidal driving term from a discrete to discrete perspective,and derives specific expressions for the model’s time response function and linear parameters.The feasibility of the model was verified with specific examples.Subsequently,the model was applied to calculate the tensile strength value of steel C1144 quenched in water,and the results showed that the model outperformed the traditional grey prediction model.Finally,the discrete model was used to calculate four sets of original tensile strength data,and the calculation results showed some improvement compared to the SinHGM(1,1)model,but the error was still significant,and further improvement of the model’s accuracy was needed.(3)The application of a new information grey prediction model for hyperbolic sinusoidal driving term in physical tensile strength.Note the situation where the weights of all data in the SinHGM(1,1)and SinHDGM(1,1)models are all 1.In order to further improve the accuracy of the model,this paper introduces the concept of new information priority accumulation into the grey prediction model of hyperbolic sine driven terms,and proposes a new grey prediction model,NISinHGM(1,1).After obtaining the expressions of the system time response function and linear parameters,an optimization problem with data weights as decision variables was established,and the optimal decision variable values were selected through the dragonfly optimization algorithm.Similarly,the feasibility of the new model was specifically validated using the urban supply of natural gas as an example.Next,the model was used to calculate the original data of four sets of tensile strength,and the calculation results showed that the accuracy of the new model was higher than that of the first two models.Finally,the numerical values of the material’s tensile strength at high temperatures were predicted.