- 上一篇：非线性循环行为混杂纤维混凝土结构墙英文文献和中文翻译
- 下一篇：对木桥的负载和阻力系数的校准英文文献和中文翻译
Animportant assumption behind the method is that some inputvariables in a multiple regression do not have an importantexplanatory effect on the response. Stepwise regression keepsonly the statistically significant terms in the model. Finally,the R2and (RootMean Square Error) RMSE values are calcu-lated for each model.Several precautions are taken into consideration to ensureintegrity of the model as follows [18]:(1) The signs of the multiple linear regression coef-ficients should agree with the signs of the sim-plelinear regression of the inpidual independentvariables and agree with intuitive engineeringjudgment. (2) There should be no multicollinearity among thefinal selected independent variables; and(3) The model with the smallest number of indepen-dent variables, minimum RMSE, and highest R2value is selected.ANN modelsIn general, ANNs consist of three layers, namely, the input, thehidden and the output layers. In the input layer, the input vari-ables of the problems are situated. The output layer containsthe output variables of what is being modeled. In statisticalterms, the input layer contains the independent variables andthe output layer contains the dependent variables. The nodesbetween successive layers are connected by links each carryinga weight that quantitatively describes the strength of thoseconnections, thus denoting the strength of one node to affectthe other node [13].ANNs typically start out with randomized weights for alltheir neurons. This means that they do not know anythingand must be trained to solve the particular problem for whichthey are intended. When a satisfactory level of performance isreached the training is ended and the network uses theseweights to make a decision [19].The experience in this field is extracted from Semeida [20].In his research, the multi-layer perceptron (MLP) neuralnetwork models give the best performance of all models. Inaddition, this network is usually preferred in engineering appli-cations because many learning algorithm might be used inMLP. One of the commonly used learning algorithms inANN applications is back propagation algorithm (BP), whichwas also used in this research (NeuroSolutions 7) [21].The overall data set of 41 sites is pided into a trainingdata set and a testing data set.This partition was done randomly with roughly 85% of thedata used for training and 15%of the total data used for testing.Model performances are RMSE and R2for testing and trainingdata set in one hand and for all data set in the other hand [22].Results and discussionLinear regression modelsThere are four models that are statistically significant with V85after stepwise regression using SSPS Package. All of the vari-ables are significant at the 5% significance level (95% confi-dence level) for these four models. In other words, (P-value)is <0.05 for all independent variables. Finally, many modelsare excluded due to poor significance with V85. Therefore,the best models are as follows (shown in Fig. 1).Model ð1Þ V85 ¼ 68:01 þ 2:515ðMWÞðR2¼ 0:2; and RMSE ¼ 18:9Þð2ÞModel ð2Þ V85 ¼ 36:51 þ 24:889ðSWÞðR2¼ 0:501; and RMSE ¼ 14:8Þð3ÞModel ð3Þ V85 ¼ 63:03 23:893ðSAÞþ 15:36ðSWÞðR2¼ 0:732; and RMSE ¼ 10:93Þð4ÞModel ð4Þ V85 ¼ 44:6 25:3ðSAÞþ 12:3ðSWÞþ 0:273ðPSLÞð5ÞðR2¼ 0:761; and RMSE ¼ 10:32ÞInvestigation of the previous results shows that: Model 4 is the best for all models and contains themaximum number of variables. In addition, it hasthe best R2, and the lowest RMSE for all models. The negative sign of the coefficient for SA means thatthe V85 decreases with the existence of side access.The drivers are to be careful when they see side accesssigns ahead; consequently, they decrease their speeds.This is consistent with logic. In addition, the coeffi-cient of this variable is 25.3 which indicating thestrong effect of SA on decreasing V85 in the Egyptianhighways. It should be noted that this variable wasnot effective in the previous studies out of Egypt. The positive sign of the coefficient for SWmeans that theV85 increases with the increase of SW. In other word, thewider right shoulder width encourages the driver toincrease his speeds if he is not restricted by other vehicles.The coefficient of this variable is+12.3 which indicatingits strong effect on increasing V85 comparable withHimes and Donnell [10] as equals to +7.44.