Multiple Nonlinear Regression Method Research Articles

Prediction of cetane numbers of pure biodiesels based on various fuel properties using multiple non-linear correlations

Biodiesel has received considerable attention in recent years owing to its advantages over diesel fuel. Density, viscosity, flash point, heating value, and cetane number are among the most critical fuel properties of biodiesel. In the literature, using multiple linear regression, machine learning methods, and group contribution methods, some correlations have been derived to predict the cetane number of pure biodiesels depending on their properties (composition of fatty acid esters, number of carbon atoms, number of double bonds, molecular weight of the fatty acid esters, chain length, saponification number, iodine value, etc.). However, fewer researchers have attempted to establish a correlation between cetane number and other important fuel properties. Therefore, this study aims to employ multiple non-linear regression method for predicting the cetane number of pure biodiesels depending on the density, viscosity, flash point, and heating value. To obtain correlations, experimental data on fuel properties from the literature covering 100 different biodiesels (methyl and ethyl esters) were collected. The prediction performances of the suggested multiple non-linear correlations were compared to the multiple linear correlation frequently suggested in the literature. Reliable correlations with errors lower than 5% and high coefficient of determination values (r2) were derived.

Study of main factors influencing unsteady-state temperature drop in oil tank storage under dynamic thermal environment coupling

With the increasing oil demand, the construction of oil energy reserves in China needs to be further strengthened. However, given that there has been no research on the main influencing factors of crude oil temperature drop in storage tanks under actual dynamically changing environments, this paper considers the influence of dynamic thermal environment and internal crude oil physical properties on the fluctuating changes in crude oil temperature. A theoretical model of the unsteady-state temperature drop heat transfer process is developed from a three-dimensional perspective. According to the temperature drop variation law of crude oil storage tank under the coupling effect of various heat transfer modes such as external forced convection, thermal radiation, and internal natural convection, the external dynamic thermal environment influence zone, the internal crude oil physical property influence zone, and the intermediate transition zone of the tank are proposed. And the multiple non-linear regression method is used to quantitatively characterize the influence of external ambient temperature, solar radiation, wind speed, internal crude oil density, viscosity, and specific heat capacity on the temperature drop of crude oil in each influencing zone. The results of this paper not only quantitatively explain the main influencing factors of the oil temperature drop in the top, wall, and bottom regions of the tank, but also provide a theoretical reference for oil security reserves under a dynamic thermal environment.

New Correlation for Predicting Undersaturated Oil Compressibility for Mishrif Reservoir in the Southern Iraqi Oil Fields

Reservoir fluids properties are very important in reservoir engineering computations such as material balance calculations, well testing analyses, reserve estimates, and numerical reservoir simulations. Isothermal oil compressibility is required in fluid flow problems, extension of fluid properties from values at the bubble point pressure to higher pressures of interest and in material balance calculations (Ramey, Spivey, and McCain). Isothermal oil compressibility is a measure of the fractional change in volume as pressure is changed at constant temperature (McCain). The most accurate method for determining the Isothermal oil compressibility is a laboratory PVT analysis; however, the evaluation of exploratory wells often require an estimate of the fluid behavior prior to obtaining a representative reservoir sample. Also, experimental data is often unavailable.Empirical correlations are often used for these purposes.This paper developed a new mathematical model for calculating undersaturated oil compressibility using 129 experimentally obtained data points from the PVT analyses of 52 bottom hole fluid samples from Mishrif reservoirs in the southern Iraqi oil fields. The new undersaturated oil compressibility correlation developed using Statistical Analysis System (SAS) by applying nonlinear multiple regression method. It was found that the new correlation estimates undersaturated oil compressibility of Mishrif reservoir crudes in the southern Iraqi oil fields much better than the published ones. The average absolute relative error for the developed correlation is 7.16%.

Streamflow Prediction Study with Sequential Gauging Station Data Using Multiple Nonlinear Regression Method

Nehir akım verilerinin sürekli olması su kaynakları üzerine inşa edilecek yapıların tasarımı aşamalarında oldukça önemlidir. Geçmiş zaman kayıtlı akım verileri ele alındığında eksik akımların söz konusu olduğu görülebilmektedir. Dolayısı ile hidrometeorolojik olarak eşdeğer gözlem istasyonu verileri kullanılarak literatürde farklı yöntemlerle tahmin çalışmaları yapılmaktadır. Bu çalışmada hidrolojik süreçlerin lineer olmayan özellik göstermeleri nedeniyle Çoklu Doğrusal Olmayan Regresyon (ÇDOR) metodu ile akım tahmini değerlendirmeleri gerçekleştirilmiştir. Uygulama yeri olarak Seyhan ve Doğu Akdeniz Havzaları’ndaki aynı akarsu güzergahında yer alan ardışık akım gözlem istasyonları tercih edilmiştir. Çalışma sonucunda; 1729 nolu gözlem istasyonunun bağımsız; 1721 ve 1730 nolu istasyonların önceki 6 ay verilerinin ise bağımlı değişkenleri oluşturduğu modellemeler hem eğitim hem de test aşamaları için en yüksek korelasyon ve en düşük hata değerlerini vermiştir. 1829 nolu istasyonun bağımsız değişken; 1820 ve 1830 istasyonlarının ise bağımlı değişken olduğu model yapılarında sırasıyla 1 önceki ay ve 3 önceki ay giriş verilerinde en iyi sonuçlar görülmüştür. 1829-1830 istasyonları ile elde edilen Model-3 eğitim sonucu belirlilik katsayısı (R2) 0.943 olup, test sonucu ise 0.969 dolaylarında ortaya çıkmıştır. Bu modelde Ortalama Karesel Hata (OKH) sıfıra çok yakın olduğu için tüm modeller açısından en iyi değerlendirme kriteri olarak tespit edilmiştir.

Effect of Spraying Polyurea on the Anti-Blast Performance of the Ultra-High Performance Concrete Slab.

Recently, polyurea has been applied to improve the anti-blast performance of metal plates, masonry walls, and concrete structures. However, the strengthening effectiveness of polyurea on ultra-high performance concrete (UHPC) slabs with an overall response is still unclear. Hence, this paper examined the strengthening effectiveness of polyurea on the anti-blast performance of UHPC slabs under near-field explosion by the finite element (FE) method. First, a benchmark finite element model for UHPC and polyurea-UHPC (PUHPC) slabs under blast loading was established and validated by field blast tests, with scaled distances ranging from 0.4 m/kg1/3 to 0.8 m/kg1/3. After that, parametric analysis was conducted to fully understand the strengthening effectiveness of polyurea on the anti-blast performance of the UHPC slab. Factors including the scaled distance, polyurea thickness, span-to-depth ratio of the slab, and longitudinal reinforcement ratio were considered. The results showed that (1) spraying polyurea on the rear face of the UHPC slab can reduce the width of cracks and mitigate the damage of specimens; (2) the strengthening effectiveness of polyurea on the UHPC slab became prominent when the UHPC slab suffered a larger maximum deflection; (3) in terms of the deflection and energy absorption capacity of PUHPC slabs, the optimum thickness of sprayed polyurea was determined to be 8 mm to 12 mm; and (4) by adopting the multiple nonlinear regression method, a prediction formula was developed to quickly obtain the end rotation of the UHPC slab strengthened with polyurea under near-field explosions.

Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression

Abstract This article applies multiple nonlinear regression methods to establish a forecasting model for the load characteristics of air conditioning in shopping malls at different times. Based on Python data, determine the functional relationship of refrigerant parameters concerning pressure and temperature. The article uses kernel smoothing estimation technology to calculate the room temperature probability density distribution of users participating in DLC to characterize the user’s comfort. The article’s research results show that the average error between the regression analysis results of refrigerant parameters and the reference value is within 1%. This model is suitable for medium and long-term load forecasting. It has high prediction accuracy for the sudden change trend with a turning point.

Statistical Modelling of Carbonation Process in Reinforced Concrete Structure.

In order to quantitatively analyze the factors affecting the carbonation of reinforced concrete structures, the carbonation coefficient model is established based on 1834 groups of test data from natural carbonation and indoor accelerated tests in this paper. The main factors considered in the statistical model are the environmental temperature, the concentration of carbon dioxide, relative humidity, water–cement ratio, fly ash replacement, compressive strength of 28 days, curing time, compaction type, exposure to a salt environment, and environmental exposure classes. Based on the multiple nonlinear regression method, the carbonation coefficient model is fitted in two sections according to the different environmental exposures of the concrete structure. To analyze the applicability of the formula, the statistical formulas of relative humidity less than 70% and relative humidity higher than 70% are verified by the test data, and satisfactory results are obtained. Based on the quantitative analysis of the statistical model, the specific effects of relative humidity, strength, carbon dioxide content, fly ash, and curing time on concrete carbonation are clarified. The results show that the factors affecting carbonation are also different with different humidity values in the exposed environment of the concrete structure. When the relative humidity of the exposed environment is less than 70%, the parameters that have a great impact on concrete carbonation are fly ash replacement, compressive strength of 28 days, relative humidity, and the concentration of carbon dioxide. Among them, fly ash replacement, relative humidity, and the concentration of carbon dioxide can promote the carbonation of concrete. When the relative humidity of the exposed environment is higher than 70%, the parameters that have a great impact on concrete carbonation are the concentration of carbon dioxide, relative humidity, compressive strength of 28 days, curing time, and exposure classes. Only the concentration of carbon dioxide is conducive to the carbonation of concrete, and relative humidity has a very significant effect on concrete carbonation.

Analysis and prediction of uniaxial compressive strength of icy lunar regolith under extreme temperature

Water ice exists in the permanently shadowed region (PSR) of the moon. It can become a vital survival material for the lunar base and provide fuel for the moon to make the moon a relay station for deep space exploration. For in-situ sampling and detection of lunar water ice, the design of sampling equipment has to consider the mechanical properties of the icy lunar regolith (ILR) to be broken during the drilling process. According to the mineral and chemical composition of the soil in the PSR, basalt rocks and anorthosite rocks are selected as two basic raw materials to simulate lunar soil. Multiple sets of ILR simulated samples are prepared with different raw material ratios (five kinds), water content (5–25 wt%), dry density (bulk density, excluding water, 1.45–1.97 g/cm3), and temperature (−240 to −10 °C). Uniaxial compressive strength (UCS) tests are carried out on these samples. A comprehensive mapping model between the UCS and the above four factors is constructed using multiple nonlinear regression methods. Based on the existing remote sensing data, the relationships or hypotheses of the subsurface dry density, temperature, and water content with depth are given. Furthermore, the UCS and drillability grade of ILR are predicted to change with depth. The results show that the ratio of raw materials has far less influence on the UCS than the other three factors. When the sample temperature is lower than −180 °C, the degree of influence of temperature changes on the UCS is significantly reduced. The UCS of the sample increases nonlinearly with the increase of dry density. The samples have an extreme strength value in the saturated water content state. This study provides a standard for the design of the equipment for drilling detection of water ice and lays a foundation for presetting operating procedures of the drilling tool.

Prediction model for maximum shear displacement of pipe joints with preexisting defects based on finite element–multiple nonlinear regression method

AbstractUnder the coupling effect of the defects inside and around pipes, the shear displacement of the joints of old concrete pipes fallen into disrepair usually shows an accelerated deterioration trend, and its excessive value can lead to structural damage or fluid leakage. Therefore, developing a prediction model for the maximum shear displacement of concrete drainage pipe joints with preexisting defects is of crucial significance. To this end, this work selects internal corrosion and erosion voids as the typical defects inside and around old pipes, establishes 300 sets of three‐dimensional fine finite element (FE) models of the concrete drainage pipes with corrosion and void, and verifies the reliability of the developed FE model by the full‐scale tests. Based on the verified FE data, a prediction model is successfully proposed for the assessment of the maximum shear displacement of the concrete drainage pipe joints with corrosion and void defects. Moreover, parameter sensitivity analysis is carried out to reveal their relative contribution to the maximum shear displacement of pipe joints. The results show that the model proposed herein has the ability to accurately predict the maximum shear displacement of the pipe joints. The maximum and minimum relative error between the value predicted by the proposed model and the one computed by the FE model is also 12.4% and 4.8% respectively. Moreover, the traffic load with a contribution of 28.7% has the greatest impact on the maximum shear displacement of pipe joints.

Structural Design Optimization and Prestress Simulation of the Laminate-Containment Launcher

The laminate-containment launcher is a high-efficiency electromagnetic railgun launcher (EMRL), which uses a laminate structure to reduce eddy current loss. However, the research on the design optimization of the laminate-containment launcher with prestress and mass as the goal is rarely mentioned. In this article, some key parameters of the laminate-containment launcher—the magnitude of interference $s$ , the axial thickness of the steel laminate $t_{s}$ and insulation laminate $t_{i}$ , the thickness of inner glass fiber $r_{g}$ , and the radial thickness of the laminate $r_{l}$ —are studied. On this basis, the influence of the five parameters on the hoop stress of the rail is fitted as a function by using the multiple nonlinear regression method. Then, the maximum hoop stress $f_{\mathrm {1max}}$ and the maximum hoop stress difference $f_{\mathrm {2max}}$ of the rail are calculated by using a nonlinear programming algorithm. Finally, the maximum hoop stress $f_{\mathrm {1max}}$ , the maximum hoop stress difference $f_{\mathrm {2max}}$ , and the maximum mass $f_{\mathrm {3max}}$ are taken as the reference values, and the optimal solution of the multiobjective function is obtained by using the weighted nonlinear programming algorithm. The results can be described as follows: the hoop stress of the rail changes linearly with the increase of the magnitude of interference, while the hoop stress changes approximately quadratic with the change of other parameters. Through the optimization of nonlinear programming algorithm with weighted form, the optimal design under different weighted values is obtained, which has a small error compared with the calculation results of ANSYS. The important characteristic that the hoop stress of the laminate-containment launcher presents wavy variation along the axial direction is obtained by numerical simulation. These results can provide theoretical guidance for the structural design of the laminate-containment launcher.

Research on Food Security system and Optimization method based on multiple regression Analysis

Considering that the current model of the world food system puts efficiency and profit first, many people still go hungry and seriously pollute the environment. In this paper, the multiple nonlinear regression method is used to optimize the existing food system. Firstly, the food security evaluation system is established, and the global food security situation in recent years is obtained by calculating FSSI. Then, the model of influencing factors of food security is established, and the relationship between food system security index and various factors is obtained by multiple nonlinear regression, on this basis, fairness and sustainability index are obtained by the same method, and the existing food system is optimized. After analyzing the current situation of countries with different standards, we have formulated a series of intelligent optimization policies for them. Finally, by comparing the change trend of the index before and after optimization, it is found that the optimized index can reach the ideal value more quickly.

Regression models for sediment transport in tropical rivers.

The investigation of sediment transport in tropical rivers is essential for planning effective integrated river basin management to predict the changes in rivers. The characteristics of rivers and sediment in the tropical region are different compared to those of the rivers in Europe and the USA, where the median sediment size tends to be much more refined. The origins of the rivers are mainly tropical forests. Due to the complexity of determining sediment transport, many sediment transport equations were recommended in the literature. However, the accuracy of the prediction results remains low, particularly for the tropical rivers. The majority of the existing equations were developed using multiple non-linear regression (MNLR). Machine learning has recently been the method of choice to increase model prediction accuracy in complex hydrological problems. Compared to the conventional MNLR method, machine learning algorithms have advanced and can produce a useful prediction model. In this research, three machine learning models, namely evolutionary polynomial regression (EPR), multi-gene genetic programming (MGGP) and M5 tree model (M5P), were implemented to model sediment transport for rivers in Malaysia. The formulated variables for the prediction model were originated from the revised equations reported in the relevant literature for Malaysian rivers. Among the three machine learning models, in terms of different statistical measurement criteria, EPR gives the best prediction model, followed by MGGP and M5P. Machine learning is excellent at improving the prediction distribution of high data values but lacks accuracy compared to observations of lower data values. These results indicate that further study needs to be done to improve the machine learning model's accuracy to predict sediment transport.

Modification of D-W model for corrosion rate of shale gas pipeline under the synergistic corrosion of SRB and CO2

Purpose The purpose of this paper is to develop an equation for the synergistic corrosion of SRB and CO2 based on the D-W model. Design/methodology/approach The bacterial types in the a and ß pipelines were studied by the most probable number method, and the corrosion morphology of L360 in pipeline water samples was studied by surface analysis. The corrosion rate of L360 was studied using the weight loss method. The gray correlation method was used to calculate the degree of correlation between the influencing factors of corrosion under the synergistic effect of CO2 and SRB. The curve obtained from PIPESIM software and experiments data was then fitted using multiple non-linear regression method by MATLAB software. Findings The equation was used to predict the corrosion of the ß pipeline for verification, and it was found that seven out of ten excavation sites were within a 20% error range. Originality/value Using the gray correlation method, an equation that considers synergistic corrosion of SRB and CO2 has been developed based on the D-W model. The equation could be used to predict the corrosion rate of shale gas gathering pipelines through SRB and CO2 synergistic corrosion.

High-Temperature Behavior and Constitutive Modeling of MS1180 High-Strength Steel

The flow behavior analysis of MS1180 steel at high-temperature was carried out by the stress–strain data which were obtained through isothermal uniaxial tensile tests with Gleeble-3800 thermal simulator. The temperature range is 600 °C~900 °C and the strain rate is varied from 0.005 s−1 to 0.02 s−1. A modified Johnson-Cook (JC) constitutive model of MS1180 steel considering the mutual effect of deformation parameters was proposed applying multiple nonlinear regression method. The calculated stress values obtained by the modified constitutive equations and the experimental ones were compared with each other. The average relative error is less than 5% and correlation coefficient is greater than 0.95. The results verified that the modified constitutive equations has good prediction accuracy for the flow stress of MS1180.

Stochastic optimization and modeling of high-velocity impact tests on high-temperature carbon\u2013carbon composites

In this study, it is intended to optimize a high-velocity impact case of a composite plate. The case selected from literature focused on the failure response of advanced carbon–carbon (C/C) composites under high-velocity impacts. Based on the stochastic optimization method, three unique models are introduced within the present study's scope as dimensionless damage areas of front and back sides and the composite impact energy response. The difference between the equations found in the present study and the base study is the number of variables. Obtained prediction models consist of only the tests' input variables; thus, these models can be considered the essential prediction functions of high-velocity impact response of C/C composites under high temperatures. Multiple nonlinear regression method is used for objective functions of the optimization problem. Since the determination coefficient values have been found quite similar to the ones in the literature, the presented models can be considered successful in predicting the results. By utilizing the novel regression functions presented in this study, the damaged areas are minimized. Without the necessity of experimental research, further predictions can be made by operating the models found in the present study.

Study on the effect of polymer viscosity and Darcy velocity on relative permeability curves in polymer flooding

Relative permeability curves in polymer flooding are important parameters to reflect the two-phase flow performance in reservoir rocks, which have important application in numerical simulation, reservoir engineering and prediction of crude oil production. Although the researches on the relative permeability curves in polymer flooding have made some progress at present, the relative permeability curves used in these researches are generally obtained by traditional experiment methods (steady-state method and unsteady-state method) or microscopic pore-scale modeling method. However, these methods are incapable of considering the physicochemical properties (i.e. rheology, residual resistance factor, adsorption and diffusion) of polymer completely. In this paper, a numerical inversion method based on automatic history matching is used to determine relative permeability curves in polymer flooding. The method performs automatic history matching by Levenberg-Marquardt (LM) algorithm on the unsteady-state experimental results and the predicted results of the numerical simulation model. As the physic-chemical properties of polymer solution have been fully taken into account in the numerical simulation model by far, the method makes up for the shortcomings of the traditional methods. Based on the inversed relative permeability curves, the effects of polymer viscosity and Darcy velocity in the rheo-thinning regime on relative permeability curves are then studied respectively. The results show that polymer viscosity and Darcy velocity in the rheo-thinning regime have little influence on the shape of oil relative permeability curve, but have obvious influence on the shape of water relative permeability curve. The deviation between the water relative permeability curve of polymer flooding and the one of water flooding increases linearly with the increase of polymer viscosity and decreases in power function with the increase of Darcy velocity in the rheo-thinning regime. At last, the prediction model of relative permeability curves under the influence of polymer viscosity and Darcy velocity in the rheo-thinning regime is established by multiple nonlinear regression method. The verification results show that this prediction model is reliable and can be used to predict the relative permeability curves at different polymer viscosities and Darcy velocities in the rheo-thinning regime.

Artificial neural networks training via bio-inspired optimisation algorithms: modelling industrial winding process, case study

This research provides a study on how the weights of artificial neural networks (ANNs) can be automatically updated by applying bio-inspired algorithms, particularly using the particle swarm optimisation (PSO) algorithm, grasshopper optimisation algorithm (GOA) and grey wolf optimisation (GWO). These evolutionary computation algorithms were used to evolve the synaptic weights of ANNs to find a particular architecture of ANNs. The developed nonlinear models were targeted to the identification of a particular nonlinear prediction system, an industrial winding process, as a case study. These new models were referred, respectively, to as ANN-PSO, ANN-GOA and ANN-GWO. The proposed models were compared with other linear and nonlinear conventional models including least square error and multiple nonlinear regression methods, respectively, as well as other state-of-the-art models including multilayer perceptron-type NNs, radial basis function and recurrent local linear neuro-fuzzy. The performance of the developed models was assessed using several metric criteria. Comparison of the proposed ANN-PSO, ANN-GOA and ANN-GWO models with other traditional and state-of-the-art models asserts the efficacy of the proposed modelling approaches.

Cyclic Behavior Assessment of Steel Bar Hysteretic Dampers Using Multiple Nonlinear Regression Approach

Isolators prevent the transfer of earthquake energy to the structure and reduce its relative displacement by increasing the time period of the structure. Most isolators have low damping and hence, in some cases, the auxiliary dampers can play an important role in the increased damping and reduced displacement of the isolation system. In this paper, a new type of steel bar hysteretic dampers (SBHDs) as the auxiliary damper was studied and evaluated in the isolation systems. For this purpose, 1650 numerical models of SBHDs were constructed based on a laboratory sample with the bars of different length, number, and cross section. Also, the role of each of these geometric parameters in the seismic behavior of the dampers was evaluated using the hysteresis curves and the corresponding ideal bilinear curves. Owing to the deficiency of the analytical solutions in the estimation of the nonlinear behavior of SBHDs and to increase their accuracy, some models were proposed using the multiple nonlinear regression (MNLR) methods. The proposed relations can be used to obtain the displacements and the forces corresponding to the first yield point and the ultimate point, ductility ratio, elastic stiffness, post-yield stiffness, effective stiffness, and dissipated energy. The results showed that the proposed equations are able to estimate the cyclic behavior of SBHDs with the proper accuracy and well consistency, and can be used with full confidence.

Developing the digital twin of the economic, financial, information and logistics inter-cluster cooperation mechanism

Subject. This article deals with the issues related to the use of digital twins in order to manage innovation and industrial clusters and the liaison between them. Objectives. The article aims to develop a digital twin model of inter-cluster cooperation within a Federal district of Russia. The Volga (Privolzhsky) Federal District is considered a case study. Methods. For the study, we used a multiple non-linear regression method and a fast simulated annealing (FSA). Results. The article offers and describes a designed digital twin model of inter-cluster cooperation mechanism. Conclusions and Relevance. When reallocating investment and human resources within one federal district, the interests of the population of innovation and industrial clusters should be taken into account, as only just an increase in fixed investment does not always lead to the growth of the region's population. The use of the digital twin model of inter-cluster cooperation mechanism will help avoid premature unreasonable management decisions of the public-policy level regarding the further development of innovation-industrial clusters.

Time-temperature-cure process window of epoxy-vinyl ester resin for applications in liquid composite moulding processes

In this work, a methodology is proposed to develop time–temperature-cure process window of an epoxy-vinyl ester resin using cure kinetics. The cure kinetics of a commercially available epoxy-vinyl ester resin formulated for Liquid Composite Molding (LCM) processing was studied by Differential Scanning Calorimetry (DSC) under isothermal conditions over a specific range of temperature. For isothermal curing reactions performed at 50, 60, and 70 °C, several influencing factors were evaluated using the heat evolution behavior of curing process. Several cure kinetic models were tested to describe the cure kinetics of epoxy-vinyl ester resin. Comparisons of the model solutions with our experimental data showed that the modified Kamal and Sourour three parameter model was capable of capturing both the degree of cure and the curing rate qualitatively and quantitatively. The model parameters were evaluated by a non-linear multiple regression method and the temperature dependence of the kinetic rate constants thus obtained has been determined by fitting to the Arrhenius equation. The model parameters were extrapolated to operate able time- temperature profiles and resin cure evolution behavior was determined.