Multivariate Nonlinear Regression Model Research Articles

Mathematical model for multivariate nonlinear prediction of SMD of X-type swirl pressure nozzles

X-type swirl pressure nozzle is a new type of nozzle with the spin core structure. Due to its superior atomization characteristics, it has been widely applied in the field of spraying dust suppression in recent years. Sauter mean diameter (hereinafter referred to as SMD) is an important indicator to evaluate the atomization characteristics and dust suppression performance of nozzles. In order to build the SMD prediction model for this type of nozzles, based on the independently designed spray experiment platform, the interaction law between the nozzle SMD and the four influence factors is obtained through the orthogonal design method. On this basis, a mathematical model for predicting the nozzle SMD is built using the multivariate nonlinear regression method. The results show that SMD increases with the increase of axial distance, absolute radial distance value and nozzle diameter, but decreases with the increase of feed water pressure. The primary and secondary sequence of the four factors affecting SMD is: feed water pressure > axial distance > nozzle diameter > radial distance. The fitting values of the multivariate nonlinear regression model are basically the same with the experimental values, with the relative error of less than 3.50% and the average relative error of only 1.35%, which can be used for the theoretical calculation of the SMD of the X-type swirl pressure nozzles. The multivariate nonlinear prediction model built in this study can provide guidance for the design and selection of such spraying dust suppression schemes as nozzle outlet diameter, feed water pressure and nozzle layout, etc. for the field engineering application of such nozzles.

Future trends in social inequalities in obesity in England, Wales and Scotland.

Previous studies have shown persistent or increasing socioeconomic inequalities in obesity in many European countries. The aim of this study was to project trends in social inequalities in obesity to 2035 in male and female adults (aged 16+) in the UK to ascertain if the gap is widening or narrowing. BMI data for the UK were extracted from the Health Survey for England (2004-14), Scottish Health Survey (2008-14) and the Welsh Health Survey (2004-14), respectively. A non-linear multivariate regression model was fitted to cross-sectional risk factor data to create longitudinal projections to 2035 stratified by sex, and occupational status or education level. Individuals in routine and manual jobs are projected to have the highest prevalence of obesity by 2035 and to experience the highest increases in obesity prevalence to 2035. Social inequalities based on occupation are projected to widen (except in English females). Social inequalities based on education are projected to decrease (except in Welsh females). A population strategy of prevention focused on the structural determinants of obesity is needed to change the trajectory of obesity prevalence trends and to tackle health inequalities.

Influential factors on water footprint: A focus on wheat production and consumption in virtual water import and export regions

Agriculture is a key sector and a major consumer of water resources; therefore, a clear understanding of the agricultural water demand for crop production and consumption is imperative for addressing water scarcity problems, particularly in water export regions. This study provides new insights into the influential factors driving the changes in the agricultural production water footprint (WFprod) and consumption water footprint (WFcon) in the net water import and net water export regions. The WFprod and WFcon of wheat are evaluated in Beijing city (the net water import region) and Heilongjiang province (the net water export region) over the period 1996–2015. The statistical significances of the influential factors, i.e., climate change, gross domestic product, population, dietary demand and technology update are determined using a multivariate linear regression model (LRM) and nonlinear regression model (NLRM). The results indicate that the gross domestic product and population were the dominant positive influential factors, whereas technology update and dietary demand were the dominant negative influential factors affecting the changes in the WFprod and WFcon in the net water import region. In the net water export region, technology update was the dominant negative influential factor affecting the changes in the WFprod and WFcon. Climate change did not contribute significantly to the changes in the WFprod and WFcon of wheat; however, it was an important factor (especially precipitation for the green WF with an average relative importance of more than 22% and the blue WF with an average relative importance of more than 15%) affecting the changes in the WFprod and WFcon of the crop. An in-depth analysis of the influential factors that contribute to the changes in the WFs is fundamentally important for decision-makers to develop countermeasures and strategic planning implementations to mitigate water resource pressure in China.

The Application of Cobb-Douglas Function in Forecasting the Duration of Internet Public Opinions Caused by the Failure of Public Policies

Gushes of Internet public opinions may trigger unexpected incidents that significantly affect social security and stability, especially for ones caused by the failure of public policies. Therefore, forecasting this kind of Internet public opinions is of great significance. The duration could be cited as one of the most direct indicators that can reflect the severity of a specific Internet public opinion case. Based on this background, this paper aims to find the factors that may affect the duration of Internet public opinions, and accordingly proposes a model that can accurately predict the duration before the release of public policies. Specifically, an index system including 8 factors by considering four dimensions, namely, object, environment, reality (offline), and the network (online), is established. In addition, based on the dataset containing 23 typical Internet public opinion cases caused by the failure of public policies, 9 prediction models are gained by applying the multivariate linear regression model, multivariate nonlinear regression model, and the Cobb-Douglas function.

Morbid obesity in the UK: A modelling projection study to 2035.

Background: Morbid obesity (body mass index ⩾40 kg/m2) carries a higher risk of non-communicable disease and is associated with more complex health issues and challenges than obesity body mass index ≥30kg/m2 and <40kg/m2, resulting in much higher financial implications for health systems. Although obesity trends have previously been projected to 2035, these projections do not separate morbid obesity from obesity. This study therefore complements these projections and looks at the prevalence and development of morbid obesity in the UK. Methods: Individual level body mass index data for people aged >15 years in England, Wales (2004-2014) and Scotland (2008-2014) were collated from national surveys and stratified by sex and five-year age groups (e.g. 15-19 years), then aggregated to calculate the annual distribution of healthy weight, overweight, obesity and morbid obesity for each age and sex group. A categorical multi-variate non-linear regression model was fitted to these distributions to project trends to 2035. Results: The prevalence of morbid obesity was predicted to increase to 5, 8 and 11% in Scotland, England and Wales, respectively, by 2035. Welsh women aged 55-64 years had the highest projected prevalence of 20%. In total, almost five million people are forecast to be classified as morbidly obese across the three countries in 2035. Conclusions: The prevalence of morbid obesity is predicted to increase by 2035 across the three UK countries, with Wales projected to have the highest rates. This is likely to have serious health and financial implications for society and the UK health system.

Parametric analysis of external and internal factors influence on building energy performance using non-linear multivariate regression models

The energy efficiency is one of the most important issues nowadays; the problem with the buildings heating is especially relevant for Ukraine. The aim of the paper is to develop a convenient tool building energy performance analysis based on regression model for internal air temperature prediction, depending on a number of internal and external influential factors. The external climatic factors, such as outside air temperature, wind speed and direction, solar heat gains depending on building fenestration surfaces orientation, are considered. Internal factors include heating load, number of floors, air exchange rate etc. In order to achieve the goal, a room dynamic simulation model is created in the EnergyPlus software. A number of simulations are carried out based on the created building energy model. The individual and aggregate selected factors influence on inside air temperature change is considered. The general structure of the multivariate nonlinear regression model for inside air temperature determination is analyzed and selected. Constant coefficients are obtained for each selected influencing factor, and verification of the received nonlinear regression model is performed based on simulation data using January climatic data from the IWEC file. The adequacy of the obtained regression model is estimated by the corrected determination coefficient (R2 = 0.981) and Fisher's criterion (F = 1324.3), which indicates the high accuracy of the obtained multivariate nonlinear regression. The proposed approach for regression model creation can be used for other architectural and thermal properties of building envelope.

Pedestrian-level wind conditions in the space underneath lift-up buildings

Lift-up buildings are advantageous in improving the wind circulation in a congested and compact city. However, the wind conditions in the void underneath a lift-up building, also known as the lift-up area, are vital for wind comfort of occupants of lift-up buildings. This study tested 28 lift-up buildings in a boundary layer wind tunnel to assess the influence of key design parameters; height and width of the main structure, and height, width, depth, and the shape of the central core on the wind conditions in the lift-up area. The results of the analyses show a significant influence of building height on the magnitude of wind speeds in the lift-up area while the width of the central core controls the area with low wind speeds. Tall buildings with short lift-up cores have small areas with acceptable pedestrian wind comfort, which can be increased by adopting corner modifications for the central core. The area of acceptable pedestrian wind comfort increases in oblique wind directions as the areas of high (>3.5 m s−1) and low (<1.5 m s−1) wind speeds are decreased. Finally, a non-linear second-order multivariable regression model is developed to predict pedestrian wind comfort in the lift-up area.

Particulate matter estimation over a semi arid region Jaipur, India using satellite AOD and meteorological parameters

The present study estimates ground-level Respirable Particulate Matter (RSPM) by the combined use of satellite remote sensing Aerosol Optical Depth (AOD) at 550 nm (AODMODIS or MODIS AOD) and ground-based meteorological measurements from April-2010 to March-2014 over Jaipur, semi-arid region in North-western, India.The satellite MODIS Level 2.0 AOD is used in developing multi-regression statistical models to estimate RSPM values over the study area. The relationship between particulate matter (PM) and AOD depends on size distribution, particle composition and vertical profile of aerosols. Thus, for optimal representation of MODIS AOD, the factors like Height of Planetary Boundary Layer (HPBL) and meteorological parameters has been considered in all regression models in the present study as surrogates. The performance of regression models is analyzed on the basis of descriptive statistical measures i.e. Normalised Mean Square Error (NMSE), Correlation (R), Factor of two observations (FA2), and Fractional Bias (FB). The nonlinear multi-regression model (MODEL V) performed better than other models for our study period and region on the basis of statistical analysis (R = 0.80, NMSE = 0.01, FB = 0.0, FA2 = 100). The coefficients obtained from MODEL V were again used over Jodhpur and found to perform better than other models.The study is further extended to find out the Air Quality Index (AQI) category over Jaipur. The average RSPM obtained from Rajasthan Pollution Control Board (RPCB) observations and those of model estimated values come under the “Moderately Polluted” category as per Indian air quality standards.

Inequalities in smoking and obesity in Europe predicted to 2050: Findings from the EConDA project.

The aim of this study was to project educational inequalities in obesity and smoking prevalence to 2050 based on past obesity and smoking trends by education level. Data on obesity (body mass index ≥ 30) and smoking prevalence (current smokers) by education level (tertiary education and less than tertiary) from nationally representative cross-sectional surveys were collected for the following six countries participating in the Economics of Chronic Diseases project (EConDA): England, Finland, Lithuania, the Netherlands, Poland (obesity only) and Portugal (obesity only). A nonlinear multivariate regression model was fitted to the data to create longitudinal projections to 2050. Inequalities were measured with a prevalence ratio and a prevalence difference using projected obesity/smoking prevalence. Educational inequalities in obesity prevalence are projected to increase in Finland, Lithuania and England for men, and in Lithuania and Poland for women, by 2050. Obesity prevalence is projected to increase faster among the more advantaged groups in England, Portugal, Finland and the Netherlands among women, and Portugal and the Netherlands among men, narrowing inequalities. In contrast to obesity, smoking prevalence is projected to continue declining in most of the countries studied. The decline is projected to be faster in relative terms among more advantaged groups; therefore, relative educational inequalities in smoking prevalence are projected to increase in all countries. Widening educational inequalities in obesity and smoking prevalence are expected in several European countries if current trends in obesity and smoking prevalence are unaltered. This will impact on inequalities in morbidity and mortality of associated diseases such as diabetes, coronary heart disease and chronic obstructive pulmonary disease.

Applying chemometrics to predict metallurgical niobium recovery in weathered ore

Abstract Niobium metallurgical recovery measures how much of the metal content in the ore is separated in the concentrate after the mineral processing stages. This information can be obtained through laboratory tests with ore samples obtained during drilling. Thereunto, representative ore samples are subjected to tests mimicking the ore concentration processing flow, but these experiments are time consuming and costly. The main objective of this study was to develop a more efficient way to obtain the metallurgical recovery information from ore samples. Based on the development of chemometrical studies, the chemical components currently analyzed in the ore with correlation to the metallurgical recovery were identified. These correlated variables were used to build a nonlinear multivariate regression model to explain the response variable, i.e. metallurgical recovery. The Principal Component Analysis was used in this work to define which chemical variables contribute most to explain the metallurgical recovery phenomenon. The Second order regression equation (Response Surface) was the most suitable methodology to explain the metallurgical niobium recovery and was created by the interaction of the five most important chemical variables. After the exclusion of outliers, the linear regression coefficient between the metallurgical recovery calculated and the metallurgical recovery analyzed was 82.59%. The use of the second order regression equation contributes to reduce the amount of experimental analysis to assess the geometallurgical niobium ore response, promoting the reduction of costs for metallurgical characterization of the ore samples. The methodology proposed proved to be efficient, maintaining an adequate precision in the forecasted response.

Hydrologic performance of bioretention in an expressway service area.

Bioretention can be an effective measure for stormwater treatment. However, there is a lack of systematic analysis of the impact of bioretention design parameters on hydrologic performance. Herein, SWMM and RECARGA models were applied to generate the typical annual rainfall runoff and simulate the water balance of the bioretention system in an expressway service area. The purpose of the investigation was to identify key design parameters for the bioretention system and delineate the priorities in developing the design. Results showed that the average groundwater recharge ratios for bioretention basins with and without an underdrain were 58.29% and 92.27%, respectively, the average overflow ratios were 4.13% and 4.19%, the average evapotranspiration ratios were 4.48% and 4.47%, and the average outflow ratio for bioretention with an underdrain was 33.94%. The ratio of the bioretention area to drainage area, and the saturated infiltration rates of planting soil and native soil were the main factors influencing water balance, while the underdrain diameter and gravel layer depth exerted little effect. Based on the impact analysis, multivariate nonlinear regression models of runoff reduction rate for two types of bioretention basin were established, which both exhibited high determination coefficients and acceptable Nash-Sutcliffe coefficients.

基于响应面法的离体皮肤组织激光融合切口性能多元非线性回归模型

基于响应面法的离体皮肤组织激光融合切口性能多元非线性回归模型

Quantitative Analysis of Magnesium in Soil by Laser-Induced Breakdown Spectroscopy Coupled with Nonlinear Multivariate Calibration

Laser-induced breakdown spectroscopy (LIBS) coupled with the nonlinear multivariate regression method was applied to analyze magnesium (Mg) contents in soil. The plasma was generated using a 100 mJ Nd:YAG pulsed laser, and the spectra were acquired using a multi-channel spectrometer integrated with a CCD detector. The line at 383.8 nm was selected as the analysis line for Mg. The calibration model between the intensity of characteristic line and the concentration of Mg was constructed. The traditional calibration curve showed that the concentration of Mg was not only related to the line intensity of itself, but also to other elements in soil. The intensity of characteristic lines for Mg (Mg I 383.8 nm), manganese (Mn) (Mn I 403.1 nm), and iron (Fe) (Fe I 407.2 nm) were used as input data for nonlinear multivariate calculation. According to the results of nonlinear regression, the ternary nonlinear regression was the most appropriate of the studied models. A good agreement was observed between the actual concentration provided by inductively coupled plasma mass spectrometry (ICP-MS) and the predicted value obtained using the nonlinear multivariate regression model. The correlation coefficient between predicted concentration and the measured value was 0.987, while the root mean square error of calibration (RMSEC) and root mean square error of prediction (RMSEP) were reduced to 0.017% and 0.014%, respectively. The ratio of the standard deviation of the validation to the RMSEP increased to 8.79, and the relative error was below 1.21% for nine validation samples. This indicated that the multivariate model can obtain better predicted accuracy than the calibration curve. These results also suggest that the LIBS technique is a powerful tool for analyzing the micro-nutrient elements in soil by selecting calibration and validation samples with similar matrix composition.

Study on optimization method of test conditions for fatigue crack detection using lock-in vibrothermography

In this paper, the lock-in vibrothermography (LVT) is utilized for defect detection. Specifically, for a metal plate with an artificial fatigue crack, the temperature rise of the defective area is used for analyzing the influence of different test conditions, i.e. engagement force, excitation intensity, and modulated frequency. The multivariate nonlinear and logistic regression models are employed to estimate the POD (probability of detection) and POA (probability of alarm) of fatigue crack, respectively. The resulting optimal selection of test conditions is presented. The study aims to provide an optimized selection method of the test conditions in the vibrothermography system with the enhanced detection ability.

Comparisons of Faulting-Based Pavement Performance Prediction Models

Faulting prediction is the core of concrete pavement maintenance and design. Highway agencies are always faced with the problem of lower accuracy for the prediction which causes costly maintenance. Although many researchers have developed some performance prediction models, the accuracy of prediction has remained a challenge. This paper reviews performance prediction models and JPCP faulting models that have been used in past research. Then three models including multivariate nonlinear regression (MNLR) model, artificial neural network (ANN) model, and Markov Chain (MC) model are tested and compared using a set of actual pavement survey data taken on interstate highway with varying design features, traffic, and climate data. It is found that MNLR model needs further recalibration, while the ANN model needs more data for training the network. MC model seems a good tool for pavement performance prediction when the data is limited, but it is based on visual inspections and not explicitly related to quantitative physical parameters. This paper then suggests that the further direction for developing the performance prediction model is incorporating the advantages and disadvantages of different models to obtain better accuracy.

A laboratory study on mix design to properly resemble a jointed brittle rock

In this paper attempts have been done to create a mortar with relatively high uniaxial compressive strength (UCS), easy casting, high flexibility, instant hardening, low cost and easy availability. The main use of this material is to physically model the mechanical behavior of jointed rock-like blocks. The effect of four parameters such as joint roughness coefficient (JRC), bridge length (L), bridge angle (γ) and joint inclination (θ) on UCS of non-persistent jointed blocks were studied. For this purpose, 35 cylindrical specimens with a broad range of plaster content (P) and cement content (C) in different ages were tested. In order to increase the strength of blocky specimens, some retarder and lubricant were used. The results showed that using 3 wt. % (Weight percent) lubricant MGAR106 and 0.05 wt. % Retarder decreases water content by 12.5% and increases plaster and cement content of 8.3% and 4.17 % respectively. Consequently, UCS of blocky specimens increased by 284.33%. In order to formulize the effect of P/C content and the age of cylindrical specimens (A) on UCS, Multivariate Non-linear Regression (MNR) and Bayesian Regularized Artificial Neural Network (BRANN) models were deployed. The results showed that BRANN approach can provide more exact predictions of the specimen UCS than MNR model. Moreover, P/C content had more influence on UCS than the specimen age. Finally the UCS tests on blocky specimens indicated that increasing JRC, bridge length and bridge angle increases UCS and it takes its minimum ate joint inclination of 60°. Furthermore, the capability of produced material to model cracking behaviour of jointed blocks was approved.

Ecophysiological responses of young mangrove species Rhizophora apiculata (Blume) to different chromium contaminated environments

Many mangrove forests have suffered from the contaminated environments near industrial areas. This study addresses the question how these environments influence the renewal of mangrove forests. To this end ecophysiological responses of the young mangrove species Rhizophora apiculata (Blume) grown under combinations of the factors heavy metals (here chromium), nutrition and soil/water environment were analyzed. We tested the hypothesis that soil/water conditions and nutrient status of the soil strongly influence the toxic effect of chromium. Seedlings of R. apiculata were grown in three different soil/water environments (natural saline soil with brackish water, salt-leached soil with fresh water and salt-leached-sterilized soil with fresh water) treated with different levels of chromium and NPK fertilizer. The system was inundated twice a day as similar to natural tidal condition in the mangrove wetland in the south of Vietnam. The experiments were carried out for 6months. Growth data of root, leaf and stem, root cell number and stomata number were recorded and analyzed. Results showed that growth of R. apiculata is slower in natural saline soil/water condition. The effect of chromium and of nutrients respectively depends on the soil/water condition. Under high concentrations of chromium, NPK fertilizer amplifies the toxic effect of chromium. Stomata density increases under chromium stress and is largest under the combination of chromium and salty soil/water condition. From the data a nonlinear multivariate regression model was derived capturing the toxicity threshold of R. apiculata under different treatment combinations.

Flotation column performance optimisation based on imperialist competitive algorithm

Optimisation in flotation columns is an important factor that influences the recovery and the grade of concentrate from the column. A column flotation process is a nonlinear, multi-variable problem with changeable parameters that traditional methods have difficulty optimising. Finding the optimum values of the column flotation variables is difficult due to the presence of many variables, large size of the search space, and many constraints. In this study, a novel optimisation method is presented based on a socio-politically motivated strategy, called imperialist competitive algorithm (ICA) which is paired with the multivariate non-linear regression (MNLR) model of the column flotation metallurgical performance as fitness function to optimise the operation parameters of flotation column in order to produce the optimum grade and recovery with respect to control parameter. The designed ICA system uses the practical data of pilot plant located in Sarcheshmeh copper complex. The results indicate that the proposed ICA finds accurately the best values of flotation column model parameters with error 1.36 × 10-16.

Does physical exposure throughout working life influence chair-rise performance in midlife? A retrospective cohort study of associations between work and physical function in Denmark

ObjectivesOur aim was to study associations between physical exposures throughout working life and physical function measured as chair-rise performance in midlife.MethodsThe Copenhagen Aging and Midlife Biobank (CAMB) provided data about...

Application and comparison of RNN, RBFNN and MNLR approaches on prediction of flotation column performance

Evaluation of grade and recovery plays an important role in process control and plant profitability in mineral processing operations, especially flotation. The accurate measurement or estimation of these two parameters, based on the secondary variables, is a critical issue. Data-driven modeling techniques, which entail comprehensive data analysis and implementation of machine learning methods for system forecast, provide an attractive alternative. In this paper, two types of artificial neural networks (ANNs), namely radial basis function neural network (RBFNN) and layer recurrent neural network (RNN), and also a multivariate nonlinear regression (MNLR) model were employed to predict metallurgical performance of the flotation column. The training capacity and the accuracy of these three above mentioned types of models were compared. In order to acquire data for the simulation, a case study was conducted at Sarcheshmeh copper complex pilot plant. Based on the root mean squared error and correlation coefficient values, at training and testing stages, the RNN forecasted the metallurgical performance of the flotation column better than RBF and MNLR models. The RNN could predict Cu grade and recovery with correlation coefficients of 0.92 and 0.9, respectively in testing process.