multiple linear regression

In this study, the temperature in friction stir welding of duplex stainless steel has been investigated. At first, temperature estimation was modeled and estimated at different distances from the center of the stir zone by the multivariate Lagrangian function. Then, the linear extrapolation method and multiple linear regression method were used to estimate the temperature outside the range and center of the stir zone. Temperature estimation is based on three parameters rotational speed, welding speed and distance from the center of stir zone. In the first method, by generalizing the multivariate Lagrangian method, the multivariate Lagrangian temperature function was generalized according to the above parameters. In the second method, in order to investigate the effect of the variables in the regression model, a comparison of two complete models and a reduced model based on the sum of squares errors was used. Then, by analyzing the multiple regression equations governing the output variable, a multiple linear regression function was introduced. Since the temperature of the stir zone is not measurable by the thermocouple, so in general the best fit curve for estimating the function is when the modeling is based on parameters that minimize the error function.To implement the multiple linear regression method, the error function was introduced to minimize the sum of the error squares and the error derivative was calculated in relation to the parameters of tool rotation speed, welding speed and distance from the center of the stir zone. Therefore, multiple linear regression method was considered as the basic method and as a criterion with other methods. According to the results obtained from the prediction in the center of the stir zone, the temperature difference in all three methods is desirable and negligible. The maximum temperature difference of multiple linear regression method with multivariate Lagrangian method in all nodes was 18.8 oC and multiple linear regression method with linear extrapolation method was 26.36 oC. Therefore, the multivariate Lagrangian interpolation method is less different than the linear extrapolation method in the center of the stir zone and is more accurate.

Stress concentration on the geometric discontinuities is one of the factors of structure failure. Nowadays, plates with holes are inseparable parts of designs and pieces, therefore studying the stress concentration caused by these holes is necessary to prevent structure failure. So the designer for presenting a design must be aware of the stress concentration in the hole and according to it design the basis. In this research, by using the regression method and on the basis of the mechanical properties of the materials and the radius of curvature in the corner of the hole, we try to present an explicit relation for estimating stress concentration in the orthotropic plates with quasi-square hole. This relation, in addition to easing the use and bypassing the hard and complex process of analytical solution, provides designer with the opportunity to calculate stress of perforated viscoelastic plates by using the effective module method or Boltzmann's superposition principle. At first, with analytical solution based on the Lekhnitskii method the stress values are calculated in many composite plates with quasi-square hole. Then, by using multiple linear regression and on the grounds of mechanical properties, is given an explicit relation for the stress concentration coefficient. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of 2%.

In this work tow simple approaches have been introduced to predict heat of explosion of high energetic materials. experimental heat of explosion of 74 energetic compound were collected from articles and this dataset was separated randomly into two groups، training and prediction sets، respectively، which were used for generation and evaluation of suitable models. Multiple linear regression (MLR) analysis was employed to select the best subset of descriptors and to build linear models; while nonlinear models were developed by means of artificial neural network (ANN). The obtained models with four descriptors involved show good predictive power for the test set: a squared correlation coefficient (R2) of 0. 798 and a standard error of estimation (s) of 606. 48 were achieved by the MLR model; while by the ANN model، R2 and SE were 0. 98 and 189. 4، respectively. Based on the large R2 -value and small SE values، significantly for ANN model، one can deduce that the predicted results are in good agreement with the measured values. Calculated heats of explosion are also compared with corresponding two famous cods، namely EDPHT and LOTUSE. It can be seen that the performance of the present models is better than these cods