multiple linear regression

In this paper, grey wolf optimization (GWO) and multiple linear regression (MLR) models have been utilized to estimate the maximum surface settlement (Smax) and trough width (i) of settlement profile due to the tunnel excavation. The results show the superiority of the GWO algorithm compared to the MLR model and similar empirical models. Moreover, the importance study and the correlation matrix of the datasets reveal that thrust force and cohesion are the most important variables on Smax and i, respectively. On the other hand, the tunnel diameter and Poisson ratio are the least important variables on Smax and i, respectively .

At present, the Equivalent Passenger Car Unit (PCU) values, proposed by other international guides, are used in the design and analysis of signalized intersections in Iran. It is likely that this would produce a negative impact of the accuracy of capacity analysis used for these intersections as the geometric design, behavioral attributes and vehicle characteristics are different here. Hence, it was decided to estimate the PCU values for buses, minibuses and motorcycles at Iranian signalized intersections using a multiple linear regression in this study. The required field data was collected from 9 intersections located at Isfahan and Yazd cities and the regression analysis was then performed on the data using SPSS software. Thereby, the PCU values for the motorcycles, minibuses and buses were obtained as 0.46, 1.45 and 2.53. Finally, an overall average PCU value of 2.13 was obtained for the heavy vehicles. The results could be used as the best estimate of PCU values for the similar Iranian signalized intersections.

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.

In this paper, we try to use a multiple linear regression method to explicitly describe the explicit relation between the stress concentration coefficient of plates containing elliptic openings in terms of mechanical properties and the angle of rotation of openness. First, the stress concentration coefficient for a lot of composites was calculated by analytical method based on the mixed variable method and using different values of the mechanical properties of the composites. Using the obtained data, using the regression method Multiple Linear The explicit relation was used to estimate the stress concentration coefficient in unbounded composite plates containing elliptic openings under tensile load. It is important to note that several factors affect the concentration of tension around the openness. Therefore, by correct selection of these parameters, it can be significantly reduced the stress concentration and increased the structural strength. One of these factors is the angle of rotation of openness, which is discussed in this article. In addition to the ease of use, the proposed relationship, by eliminating complex and complex analytical solutions, saves time and allows the designer to obtain the desired parameters to achieve the desired stress. The results showed that the regression model was able to estimate the coefficient of stress concentration with an error of less than 1 percent.

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%.

The construction and maintenance of structural pavement was a high-cost problem in last decade. The mechanical properties of self compacting concrete (SCC) required important factors .From its mechanical properties, the compressive strength (CS) is necessary to investigate experimental and computational intelligence analysis in construction materials. Developing models with accurate estimation for this key property caused to saving costs and time and producing an optimal blend. Because of the many advantages, using of SCC in structures is increasing. Construction of precast-prefabricated components, with the use of concrete has also recently been considered. Concrete properties have significant role in precast-prefabricated girders behavior. Exact prediction of these properties is the base of member’s analysis and design. The main purpose of this study is presents new formulation to estimate the compressive strength of self-compacting concrete containing rice husk ash (RHA) using robust variant of genetic programming, namely gene expression programming (GEP) method. To evaluate the performance of the GEP-based proposed model, prediction was also done using classical data driven methods named artificial neural network (ANN) and multiple linear regression (MLR) models.  A large and reliable experimental database containing the results of 156 compressive strength of SCC incorporating RHA is collated through an extensive review of the literature. The performance of proposed models of CS is then assessed using the database, and the results of this evaluation are presented using selected performance measures. New expressions for the estimation of CS of SCC are developed based on the database. To evaluate the modeling performances of the proposed GEP models for CS, different statistical metrics were used. Correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE) were used as the measure of precision. The results showed that the models developed using the aforementioned methods have accuracy over 90 percent in prediction of CS of SCC. The results of testing datasets are compared to experimental results and their comparisons demonstrate that the GEP model (R=0.94, RMSE= 4.308 and MAE=4.916) outperforms ANN (R=0.92, RMSE= 5.136 and MAE=5.624) and MLR (R=0.89, RMSE= 8.212 and MAE=9.472). Proposed models have a strong potential to predict compressive strength of self compacting concrete incorporating rice husk ash with great precision. The importance of different input parameters is also given for predicting the compressive strengths at various ages using gene expression programming. Performed sensitivity analysis to assign effective parameters on compressive strength indicates that cementitious binder content is the most effective variable in the mixture. The assessment results present that the performance of the proposed models are in close agreement with the experimental results. Moreover, the new GEP-based formulation provides improved estimates of the compressive strength of SCC compared to ANN and MLR models. The proposed design equation can readily be used for pre-design purposes or may be used as a fast check on deterministic solutions.

In sustainable management of solid waste, decreasing construction waste generation is an important step. In developing countries, modern construction techniques are not adopted as in developed countries and contractors follow wasteful manners when utilizing building materials. The result is building material waste which unfavorably aects environment. At the same time, it is considered an earnest concern and a solemn environmental problem all over the world requiring a reliable database to be managed, whereas investigations done by the authors imply that no ocial organization maintains any related authenticated data, making thriving construction waste management policies too dicult to be dened and implemented in Tehran, Iran. In this article, variables aecting materials waste were derived from accessible reviewed literature, then using the rst questionnaire survey quantities of variables were collected for thirty two representative residential buildings in Tehran. Primary analysis showed that cement is wasted more than other studied materials (about 8.6% by weight). Due to huge amounts of energy and raw materials used in production of cement and pertained destructive eects on environment such as air pollutants emission, cement waste reduction leads to emission abatement and cost saving. This is why cement waste was targeted to be diminished in this paper. After quantifying cement waste versus dependent variables of this study, it was resulted that \lump sum" contract is preferable to \cost plus" contract in terms of cement waste. Furthermore, designing smaller buildings with more stories is suggested instead of bigger buildings with fewer stories. Since no construction waste reduction policy is implemented in Iran so far, authors conducted a subsequent questionnaire survey to evaluate dierent waste reduction policies. As a result, dening a nancial-based incentive plan ranked the rst in order of preference based on opinions of construction experts. Therefore, a nancial-based incentive plan was structured. This plan was proven to be both viable economically and justiable environmentally. These suggestions could be proposed to Tehran municipality to be implementable in sustainable residential building projects.

The purpose of this paper is to present a new model based on the multiple regression method for estimating stress concentration factor of a quasi-triangular hole in composite lamina. One of the important applications of providing stress distribution around holes in terms of mechanical properties is the use of these relationships in the stress analysis of perforated viscoelastic plate using the effective modulus method or Boltzmann's superposition principle. First, using different values of the mechanical properties of the composites plates, and employing an analytical solution based on the complex variable method, the stress concentration factor of quasi-triangular hole is calculated for a number of these materials. Then, using multiple linear regression, An explicit expression for the stress concentration factor is given in terms of mechanical properties. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of less than 1%. An important point in this article is the reduction of the calculations by applying the aforementioned relations. In other papers in this field, hard and complex calculations were used to obtained the stress concentration factors, but with the help of the relation of this paper, it is to calculate the stress concentration factor with having the mechanical properties of the plate.

One of the concerns of designers of engineering structures is structural failure due to stress concentration caused by geometric discontinuities in the structures. Therefore, by considering that perforated composite plates are used in most engineering structures, their study is very important. The purpose of this paper is to present a new model based on the regression method for estimating stress concentration factor of a circular hole in orthotropic plates. One of the important applications of providing stress distribution around holes in terms of mechanical properties is the use of these relationships in the stress analysis of perforated viscoelastic plate using the effective modulus method or Boltzmann's superposition principle. First, using different values of the mechanical properties of the composites plates, and employing an analytical solution based on the complex variable method, the stress concentration factor of circular hole is calculated for a number of these materials. Then, using multiple linear regression, an explicit expression for the stress concentration factor is given in terms of mechanical properties. The results show that the multiple regression model is able to predict the circumferential stress with a maximum error of less than 1%.

Nowadays, the world is facing to increasing loss of fossil resources, energy crisis and environmental problems. On the other hand, diesel engines due to wide application in various sectors such as transport, agriculture, industry, etc., are the main sources of emissions and fuel consumption. Accurate measurement of fuel consumption and engine pollution is time-consuming and costly. Hence, the main objective of this study was to develop proper linear regression models of some important performance parameters of ITM285 tractor engine based on engine torque and engine speed. Experiments were carried out in 11 levels of primary engine speed (1063, 1204, 1346, 1488, 1629, 1771, 1818, 1913 and 2054 rpm) by 10 N.m steps of torque from zero (no load) to full load. The measured parameters include fuel consumption mass flow, exhaust temperature, instantaneous engine speed, maximum and mean exhaust opacities. Four different linear regression models were used to estimate the parameters. The results of regression models performance evaluation showed that quadratic model had the highest efficiency and the lowest RMSE for all parameters. The maximum and minimum effects of engine torque were on exhaust temperature and instantaneous engine speed, respectively; while, this result was completely reverse for primary engine speed. The results of regression models evaluation showed a high adaptation between the output of each model and the desired output. Also, the fuel mass flow and exhaust temperature were highly correlated to the maximum and mean exhaust opacity with correlation coefficients of 0.96 and 0.99, respectively.