Multiple Nonlinear Regression Method Research Articles

A new method for the prediction of flash points for ternary miscible mixtures

The flash point is one of the most important physicochemical parameters used to characterize the fire and explosion hazard for flammable liquids. The flash points of ternary miscible mixtures with different components and compositions were measured in this study. Four model input parameters, being normal boiling point, the standard enthalpy of vaporization, the average number of carbon atoms and the stoichiometric concentration of the gas phase for mixtures, were employed and calculated based on the theory of vapor–liquid equilibrium. Both multiple linear regression (MLR) and multiple nonlinear regression (MNR) methods were applied to develop prediction models for the flash points of ternary miscible mixtures. The developed predictive models were validated using data measured experimentally as well as taking data on flash points of ternairy mixtures from the literature. Results showed that the obtained average absolute error of both the MLR and the MNR model for all the datasets were within the range of experimental error of flash point measurements. It is shown that the presented models can be effectively used to predict the flash points of ternary mixtures with only some common physicochemical parameters.

New Spot Weld Fatigue Criteria and Fatigue Data Editing Technique

Firstly, this paper presents new criteria for fatigue life prediction of spot weld. It starts with the presentation of the database used for this study. Then, two criteria for spot weld life prediction, based respectively on mechanical damage and fracture mechanics, are developed through a nonlinear multiple regression method of optimization. These criteria considerably improve the correlation between numerical and test results. Finally, an application of this study is led on a fatigue test of a full body-in-white with about 4000 spot welds.Secondly, this paper presents new fatigue data editing techniques. Existing fatigue data editing techniques are tested on a full body-in-white fatigue lifetime calculation. The load applied to the biw is complex, with several load application locations and directions. All the critical point have to be detected with the new strength signal. Existing fatigue data editing techniques are adapted and tested on a full body-in-white fatigue calculation. Since the time discretization point number of the new load signal obtained from the literature techniques is too high, two new fatigue data editing technique are developed and tested on a full body-in-white durability calculation. The damage values damages at both spot weld and sheet metal, predicted with these new simplified load signals, are close to the damages values calculated with the full load signal. In addition, the number of time discretization points is low, at least 4.2 inferior to the time discretization point number obtained with existing techniques.

Thermooxidative degradation of polyoxymethylene homo- and copolymer nanocomposites with hydroxyapatite: Kinetic and thermoanalytical study

In this paper thermooxidative degradation process of polyoxymethylene homo- and copolymer (POM)/hydroxyapatite nanocomposites has been studied. Kinetic analysis by Friedman, Ozawa–Flynn–Wall and multiple non-linear regression methods, as well as thermoanalytical studies using TG–MS and TG–FTIR method, were performed. TG results show that thermal stability of POM matrix significantly decreases with an increase of HAp nanoparticles concentration. The presence of higher HAp concentration changes mechanism of POM degradation, including its kinetics, which was demonstrated by a change of kinetic model from autocatalytic to phase-boundary or nth order reaction one. Hyphenated TG–MS and TG–FTIR data show that the main degradation product in the presence of higher amounts of HAp is formaldehyde, and formation of other degradation products – typical for POM thermoxidative degradation – is considerably diminished. Finally, mechanism of POM degradation in the presence of stoichiometric hydroxyapatite has been postulated.

Development of artificial neural networks and multiple regression models for the NATM tunnelling-induced settlement in Niayesh subway tunnel, Tehran

Here we investigate maximum settlement prediction of the Niayesh subway tunnel, excavated by employing the New Austrian Tunnelling Method in the Tehran metropolitan area, by several approaches, such as the semi-empirical method, linear and non-linear multiple regression method (MR), and finally by a programming Multi-Layered Perception (MLP) with a Back Propagation training algorithm. The geology at the site is mostly composed of conglomerates with pebbles and boulders. The maximum settlement is estimated based on the semi-empirical relations represented by several researchers. The input data set for MR and MLP models are soil characteristic [cohesion (C), internal friction angle (φ), elasticity modulus (E) and unit weight (Gs)], excavation depth (Z 0), soil type (S t) and PLAXIS 2D settlement prediction by the Hardening Soil model. Among all MLP and MR models, MLP models and especially model 6, the model based on E, Z, φ, Gs, C and S t variables, seem to be reliable and agreeable to numerical results. The performance of MR, MLP, and optimized MLP models are evaluated by comparing statistic parameters, including coefficient correlations (R), root mean square error (RMSE), mean error (ME) and Akaike information criterion (AIC), whose values for model 6 are 0.93, 1.66, 0.89 and 13.16, respectively. Therefore, compared to other MLP and MR models, the optimized MLP model shows a relatively high level of accuracy. Additionally, model 4, the model based on E, Z, φ and Gs variables, shows in MLP analysis that unit weight does not have significant effect on maximum settlement.

Soil infiltration based on bp neural network and grey relational analysis

Soil infiltration is a key link of the natural water cycle process. Studies on soil permeability are conducive for water resources assessment and estimation, runoff regulation and management, soil erosion modeling, nonpoint and point source pollution of farmland, among other aspects. The unequal influence of rainfall duration, rainfall intensity, antecedent soil moisture, vegetation cover, vegetation type, and slope gradient on soil cumulative infiltration was studied under simulated rainfall and different underlying surfaces. We established a six factor-model of soil cumulative infiltration by the improved back propagation (BP)-based artificial neural network algorithm with a momentum term and self-adjusting learning rate. Compared to the multiple nonlinear regression method, the stability and accuracy of the improved BP algorithm was better. Based on the improved BP model, the sensitive index of these six factors on soil cumulative infiltration was investigated. Secondly, the grey relational analysis method was used to individually study grey correlations among these six factors and soil cumulative infiltration. The results of the two methods were very similar. Rainfall duration was the most influential factor, followed by vegetation cover, vegetation type, rainfall intensity and antecedent soil moisture. The effect of slope gradient on soil cumulative infiltration was not significant.

Deformation Resistance of Alloy 2.25Cr1Mo0.25V of Heavy Cylinder for Hydrogenation Reactor

2.25Cr1Mo0.25V alloy steel of making heavy cylinder for hydrogenation reactor was taken as research subject. The compression experiment was carried out on Gleeble-3500 thermal simulator under different conditions of deformation temperature, strain rate and deformation degree. The relationship between deformation resistance and deformation temperature, strain rate, deformation degree was analyzed. Two different types (dynamic recovery and dynamic recristallization) of deformation resistance model were established through multiple nonlinear regression method. The relative error of deformation resistance between the calculated value and the measured value was under 10% and the maximum error of the rolling force between the calculated value and the measured value was 9.7%, which showed that this deformation resistant model was accurate and met industry requirements.

Predictive models for dynamic modulus using weighted least square nonlinear multiple regression model

The objectives of this paper are (1) to evaluate the dynamic modulus prediction models and (2) to develop an alternative prediction model using the nonlinear multiple regression method. A total of 14 field produced mixture types (in a total of 1314 measurements) with various designed traffic levels and aggregate sizes were used. Two prediction models, the Witczak prediction model developed in 2006 and the Hirsch model developed in 2003, were revised in this study. In addition, the revised Witczak prediction equation was simplified using fewer independent variables (11 variables instead of 21 variables); and values of the newly revised coefficients with improved accuracy for Hirsch model are presented in this paper. A new model using the weighted least square nonlinear multiple regression model (WLS NLR) was developed in this study. It was found that the WLS NLR has a better prediction when compared with other prediction models used in this study.

Developing rainfall intensity–duration–frequency relationship for two regions in Saudi Arabia

Intensity–duration–frequency (IDF) relationship of rainfall amounts is one of the most commonly used tools in water resources engineering for planning, design and operation of water resources projects. The objective of this research is to derive IDF relationship of rainfall at Najran and Hafr Albatin regions in the kingdom of Saudi Arabia (KSA). These relationships are useful in the design of urban drainage works, e.g. storm sewers, culverts and other hydraulic structures. Two common frequency analysis techniques were used to develop the IDF relationship from rainfall data of these regions. These techniques are: Gumbel and the Log Pearson Type III distribution (LPT III).An equation for estimating rainfall intensity for each region was derived using both techniques. The results obtained using Gumbel distribution are slightly higher than the results obtained using the LPT III distribution. Rainfall intensities obtained from these two methods showed good agreement with results from previous studies on some parts of the study area. The chi-square goodness-of-fit test was used to determine the best fit probability distribution. The parameters of the IDF equations and coefficient of correlation for different return periods (2, 5, 10, 25, 50 and 100) are calculated by using non-linear multiple regression method. The results obtained showed that in all the cases the correlation coefficient is very high indicating the goodness of fit of the formulae to estimate IDF curves in the region of interest.

Adsorption of methylene blue as a descriptor of C–S–H nanostructure

Abstract The adsorption of methylene blue (MB) on C–S–H surfaces (C/S ratios 0.60–1.80) and its dependence on C–S–H nanostructure was investigated. UV–VIS spectroscopy was used to obtain the adsorption–desorption isotherms at 23 °C, 35 °C and 50 °C. The character of the UV–VIS spectra and the nature of the C–S–H–MB interaction are discussed. Several sorption models including those due to Langmuir, Harkins–Jura, Halsey, Henderson, and Freundlich are fitted to the data using a non-linear multiple-regression method. Factors influencing the sorption of MB by C–S–H are discussed. The results demonstrated that the adsorption of MB molecules on C–S–H strongly depends on the nanostructural characteristics of C–S–H.

A Constitutive Model for Thixotropic Plastic Forming of Composites

A new constitutive model for semi-solid composites forming was derived with analyzing constitutive relationships of semi-solid metal and composites forming. Parameters in the constitutive model were determined by the multiple nonlinear regression method. A constitutive relationship of semi-solid SiCp/AZ61 composites thixotropic plastic forming was proposed. The calculated results were good agreement with the experimental ones. The proposed constitutive model has the higher forecast precision and practical significance. The construction of constitutive model provides references for the thixotropic forming theory, simulation and technology.

Joined Influences of Nonlinearity and Dilation on the Ultimate Pullout Capacity of Horizontal Shallow Plate Anchors by Energy Dissipation Method

The ultimate pullout capacity (UPC) and the shape modification factors of horizontal plate anchors were calculated by using upper-bound limit analysis, in which the assumptions of both a nonlinear failure criterion and the nonassociated flow rule were made upon the soil mass above the anchor plate. Three types of anchor plates, including strip anchors, circle anchors, and rectangle anchors, and the cor- responding failure mechanisms are taken into consideration. The anchor breakout factors were obtained according to the principle of virtual power, which was realized numerically by the nonlinear sequential quadratic programming algorithm. The shape modification factors for different kinds of anchors were given through a multiple nonlinear regression method. Numerical experiments demonstrate the validity of the solutions by reducing the solutions (nonlinear criterion and nonassociated flow rule) into their special cases (linear criterion and associated flow rule), which matches well with existing work. The dilation and nonlinearity of soil mass should be considered because it plays a remarkable role in the UPC of anchor plates. DOI: 10.1061/(ASCE)GM.1943-5622.0000075. © 2011 American Society of Civil Engineers. CE Database subject headings: Failures; Plates; Anchors; Pullout; Energy dissipation. Author keywords: Nonlinear failure criterion; Nonassociated flow rule; Plate anchors; Ultimate pullout capacity; Upper-bound theorem of limit analysis.

Using Hydraulic Parameters to Estimate Longitudinal Dispersion Coefficient in Open Channel

A comparative analysis of previous theoretical and empirical equations is applied to evaluate their behavior in predicting dispersion coefficient in open channel. A new simplified method for predicting dispersion coefficients using hydraulic parameters is developed. A nonlinear multiple regression method is prepared to derive a new equation of dispersion coefficient. This equation is proven to be superior in explaining dispersion coefficient of open channel more precisely, as compared to existing equations. Keywords: Longitudinal dispersion, hydraulic parameters, dispersion coefficients.

Proximate analysis based multiple regression models for higher heating value estimation of low rank coals

In this paper, multiple nonlinear regression models for estimation of higher heating value of coals are developed using proximate analysis data obtained generally from the low rank coal samples as-received basis. In this modeling study, three main model structures depended on the number of proximate analysis parameters, which are named the independent variables, such as moisture, ash, volatile matter and fixed carbon, are firstly categorized. Secondly, sub-model structures with different arrangements of the independent variables are considered. Each sub-model structure is analyzed with a number of model equations in order to find the best fitting model using multiple nonlinear regression method. Based on the results of nonlinear regression analysis, the best model for each sub-structure is determined. Among them, the models giving highest correlation for three main structures are selected. Although the selected all three models predicts HHV rather accurately, the model involving four independent variables provides the most accurate estimation of HHV. Additionally, when the chosen model with four independent variables and a literature model are tested with extra proximate analysis data, it is seen that that the developed model in this study can give more accurate prediction of HHV of coals. It can be concluded that the developed model is effective tool for HHV estimation of low rank coals.

Predicting intact rock strength for mechanical excavation using multivariate statistics, artificial neural networks, and regression trees

Mechanical rock excavation projects require uniaxial compressive strength (UCS) and static modulus of elasticity ( E) of the intact rock material. High-quality core specimens of proper geometry are needed for the direct determination of these parameters. However, it is not always possible to obtain suitable specimens from highly fractured and/or weathered rocks for this purpose. Therefore, models predicting UCS and E based on rock index tests and intact rock properties have become alternative methods. For this reason, this paper is concerned with the applications of artificial neural networks (ANN) and regression trees technique along with the principal components and factor analyses on the predictions of UCS and E of intact rocks from their other properties. For that purpose, data obtained from three different rock cutting projects have been subjected to a series of statistical analyses. Results of the principal components analysis have shown that the most of the variance in the data set can be explained by only three principal components. The principal component with the highest variance is mainly weighted on the dependent variables of UCS and E. Factor analysis has revealed that two common factors may summarize the data set instead of original seven variables. Subsequent bivariate correlation and curve fitting analyses revealed that NCB cone indenter test was the most reliable indirect test to estimate UCS and E for the rocks that were employed in this study. For this reason, NCB cone indenter hardness was used in building predictive models for UCS and E along with dry density and Shore scleroscope hardness. Two different pairs of models for UCS and E were developed using ANN and regression trees technique, which were then compared to those built by multiple nonlinear regression method. Evaluation of the graphical and numerical measures of the goodness of the fit statistics clearly indicated that respective ANN models were more acceptable for predicting UCS and E than multiple nonlinear regression models. However, regression tree technique has appeared to be the best in building predictive models for UCS and E amongst the other methods.

Numerical Simulation on Thixoforming of Wrought Magnesium Alloy

The thixoforming of wrought magnesium alloy was analyzed with computer numerical simulation based on rigid plastic/rigid viscoplastic finite element method. The simulated parameters were chosen and depended on the constitutive model of semi-solid AZ61 alloy that was established using the multiple nonlinear regression method in our prior literature. Thixo mechanical properties of semi-solid AZ61 alloy in high solid volume fraction were also analyzed. Behaviors of metal flow and temperature field were obtained, which were also compared with experimental data in literature. Research showed that the hard deformation magnesium alloy had great filling ability in semi-solid state, and the stress and strain distributions in workpiece after thixoforming were uniform. The semi-solid thixoforming technology has taken priority of the traditional processing.

Constitutive Model of Thixotropic Plastic Forming for Semi-Solid AZ61 Magnesium Alloy

Uniaxial compression tests on semi-solid AZ61 alloy fabricated by stain-induced activation (SIMA) process and the conventional casts were carried out using the Gleedle-1500 dynamic material testing machine. The relationships between stress and stain were analyzed. The numerical relationships among processing parameters (strain rate z ε& strain z ε temperature T liquid volume fraction L f ) and stress were studied. The proposed constitutive equation was established for semi-solid AZ61 magnesium alloy using the multiple nonlinear regression method. A scientific basic provided for both numerical simulation of processing process of semi- solid AZ61 alloy and rational choice and control of processing parameters.

Cure kinetics of epoxy resin used for advanced composites

AbstractThe cure kinetics of an epoxy resin used for the preparation of advanced polymeric composite structures was studied by isothermal differential scanning calorimetry (DSC). A series of isothermal DSC runs provided information about the kinetics of cure over a wide temperature range. According to the heat evolution behavior during the curing process, several influencing factors of isothermal curing reactions were evaluated. The results showed that the isothermal kinetic reaction of this epoxy resin followed an autocatalytic kinetic mechanism. In the latter reaction stage, the curing reaction became controlled mainly by diffusion. Cure rate was then modeled using a modified Kamal autocatalytic model that accounts for the shift from a chemically controlled reaction to a diffusion‐controlled reaction. The model parameters were determined by a nonlinear multiple regression method. Copyright © 2004 Society of Chemical Industry

Strength and ductility of laterally confined concrete columns

The objective of this study is to determine experimentally and analytically the magnitude of the strength enhancement of concrete confined by lateral ties. Sixty-five reinforced concrete columns with a 200 mm square cross section were tested. Experimental parameters include the compressive strength of concrete; the volumetric ratio, strength, and confinement type of rectilinear ties; and the distribution of longitudinal reinforcement bars. The confinement effects are explained by utilizing an effectively confined distance ratio. Tie stress caused by lateral concrete pressure is presented as a function of the volumetric ratio and configuration of ties, and the strength of concrete based on the experimental data and the nonlinear multiple regression method. Based on the empirical data and the nonlinear multiple regression method, this paper presents an empirical equation to determine the strength enhancement as a function of the tie stress, the effectively confined distance ratio, the volumetric ratio of ties, and the strength of concrete. The validity of the American Concrete Institute and Canadian Standards Association specifications for minimum tie spacing and the design of cross ties are examined.Key words: high-strength concrete, ductility, strength enhancement factor, confinement type of ties, volumetric ratio of ties, effectively confined distance ratio, nonlinear multiple regression method.

Stress–strain curve of laterally confined concrete

The objective of this study is to present a stress–strain relation of confined concrete from an empirical study of 65 columns. Experimental parameters include the strength of concrete, the volumetric ratio, strength, and confinement type of rectilinear ties, and the distribution of longitudinal bars. For the purpose of investigating confinement effects, an effectively confined distance ratio was introduced and the effects according to each parameter were analyzed. This paper provides an equation to determine the tie stress caused by lateral concrete pressure as an important index to measure confinement degree. Analyzing the experimental data by nonlinear multiple regression method, this study provides the empirical equations to determine the peak stress and its corresponding strain of confined concrete expressed by the tie stress, the effectively confined distance ratio, the strength of concrete, and the configuration of ties. Starting from the model proposed by Popovics, an empirical model for stress–strain curve of laterally confined concrete is developed by three coordinates, ( f cc, ε cc), (0.85 f cc, ε 0.85), and (0.3 f cc, ε 0.3). Comparison with other stress–strain curves illustrates the validity of the proposed relation.

Data mining for tunnel support stability: neural network approach

This paper presents a data mining approach to the prediction of tunnel support stability using artificial neural networks (ANN). The case data of a railway tunnel recently finished in Taiwan were used to establish the model. The main rock type was sedimentary rock. Rock mechanical and construction-related parameters with significant influences on support stability were filtered to train and test the ANN. Validation was also performed to show that the ANN outperformed the discriminant analysis and the multiple non-linear regression method in predicting tunnel support stability status.