Multivariate Nonlinear Model Research Articles

Statistical Modeling of NaCl and FeSO4 Pretreatment Effect on Refractory Copper Ore Leaching

Black copper oxides, a significant copper resource, present challenges in leaching due to their refractory nature and complex mineralogical composition. This study investigates the sulfation dynamics of the reductive leaching process of black copper ores with the purpose of increasing the copper leaching, focusing on the influences of time and the addition of NaCl and FeSO4 on sulfation behavior. Experiments were designed to replicate industrial conditions using oxidized minerals from the Codelco Salvador hydrometallurgy plant. Multivariate nonlinear regression models and response surface methodology were employed to analyze sulfation behavior. The findings demonstrate that analytical acid consumption (AAC) exerts a consistently positive and statistically significant effect on sulfation across the sampled domain, while NaCl and FeSO₄ also influence the process. However, variations in their levels showed limited impact. Time was significant only within the 24–48 h range. The optimized model predicted maximum sulfation at 60 h with 60% AAC, 90 g NaCl, and 42 g FeSO₄, with strong alignment between the observed and predicted values. These insights emphasize the importance of pretreatment methods, including sulfuric acid curing and NaCl addition, in improving leaching efficiency.

Construction of a Compound Model to Enhance the Accuracy of Hepatic Fat Fraction Estimation with Quantitative Ultrasound.

Background: we evaluated regression models based on quantitative ultrasound (QUS) parameters and compared them with a vendor-provided method for calculating the ultrasound fat fraction (USFF) in metabolic dysfunction-associated steatotic liver disease (MASLD). Methods: We measured the attenuation coefficient (AC) and the backscatter-distribution coefficient (BSC-D) and determined the USFF during a liver ultrasound and calculated the magnetic resonance imaging proton-density fat fraction (MRI-PDFF) and steatosis grade (S0-S4) in a combined retrospective-prospective cohort. We trained multiple models using single or various QUS parameters as independent variables to forecast MRI-PDFF. Linear and nonlinear models were trained during five-time repeated three-fold cross-validation in a retrospectively collected dataset of 60 MASLD cases. We calculated the models' Pearson correlation (r) and the intraclass correlation coefficient (ICC) in a prospectively collected test set of 57 MASLD cases. Results: The linear multivariable model (r = 0.602, ICC = 0.529) and USFF (r = 0.576, ICC = 0.54) were more reliable in S0- and S1-grade steatosis than the nonlinear multivariable model (r = 0.492, ICC = 0.461). In S2 and S3 grades, the nonlinear multivariable (r = 0.377, ICC = 0.32) and AC-only (r = 0.375, ICC = 0.313) models' approximated correlation and agreement surpassed that of the multivariable linear model (r = 0.394, ICC = 0.265). We searched a QUS parameter grid to find the optimal thresholds (AC ≥ 0.84 dB/cm/MHz, BSC-D ≥ 105), above which switching from a linear (r = 0.752, ICC = 0.715) to a nonlinear multivariable (r = 0.719, ICC = 0.641) model could improve the overall fit (r = 0.775, ICC = 0.718). Conclusions: The USFF and linear multivariable models are robust in diagnosing low-grade steatosis. Switching to a nonlinear model could enhance the fit to MRI-PDFF in advanced steatosis.

Prediction of manhole-cover skid-resistance performance using decision trees and regression analysis

This study conducts skid-resistance coefficient tests on 3,600 manhole covers and collects data on various influencing factors, such as surface conditions, pattern types, starting zones, turning zones, usage duration, wheel track locations, and surrounding traffic volume. A preliminary classification analysis of the data is performed using decision trees to identify key factors affecting manhole-cover skid resistance. Subsequently, a multivariate nonlinear regression model is applied to examine the impact of these factors on the target variables. By integrating decision trees and nonlinear regression in a hybrid modeling approach, the study aims to reveal complex patterns in the data and generate reliable predictive results. The decision-tree analysis using non-continuous variables reveals that manhole covers located at turns and starting zones, and those with worn surfaces are more likely to fail to meet safety standards for skid resistance. The multivariate nonlinear regression model, which compares the predicted values against the actual British Pendulum Number (BPN) test results, achieves an accuracy of 82.9%.

Effect of biochar content and particle size on mechanical and water absorption properties of landscaping waste/polylactic acid composites

The high-value utilization of landscaping waste to produce wood-plastic composites provides a promising approach to waste management, yet remains a challenge. In this study, wood-plastic composites were prepared using landscaping waste and polylactic acid (PLA) through an extrusion-molding process, with biochar (BC) as the reinforcing material. First, the effects of biochar content (0.5 %, 1 %, 2 %, 3 %, 4 %) and particle size (100mesh, 300mesh, 800mesh, 1200 mesh) on the physico-mechanical and dynamic thermo mechanical properties of the composites were analyzed. A multivariate nonlinear model was employed to fit the flexural properties of the composites. Additionally, the water absorption properties were investigated under immersion conditions at three different temperatures (20°C, 35°C, 50°C). The results demonstrated that biochar significantly improved the interfacial compatibility between landscaping waste and PLA, enhancing the mechanical properties of this composite. When the biochar content was 1 % and particle size was 100 mesh, flexural strength reached 25.16 MPa, respectively, representing increases of 19.20 % over composites without biochar, while the change in impact strength was small. In addition, the water absorption process of composites with 1 % BC were well fitted by Fick's law. SEM morphology observation indicated that interfacial bonding was reduced after water absorption, which was consistent with the test results. Combined with Arrhenius equation and Fick's law, the water absorption model of the composites at each water immersion temperature was obtained, which can predict the water absorption behavior at 60°C.

Prediction of Sunspot Activity Based on Differential Evolution Algorithm and BP Neural Network Model

In this research report, the prediction method of sunspot activity is deeply discussed, and a variety of statistical and data science models are used to make comprehensive prediction. Research focuses include the start time and duration of the solar maximum in the solar cycle, as well as the prediction of the number and area of sunspots. By capturing the periodicity of solar activity, Pearson correlation coefficient is used to analyze the relationship between the maximum solar activity and the number of sunspots, and the adaptive multivariate nonlinear regression-BP neural network model and particle swarm optimization BP neural network are combined to make high-precision prediction. The research results provide a scientific basis for the prediction of space weather, ionospheric state and communication system reliability.

Research on cross regional green certificate bilateral distributed robust trading strategy based on Bayesian theory

To ensure the effective implementation of the compulsory green certificate transaction in China, a multi-participant cross-regional green certificate bilateral transaction model considering the relevant technical characteristics of the unit is proposed to solve the problems such as the mismatch between the supply and demand of green certificates and the reduction of the transaction plan by the grid operation constraints in the current green certificate transaction. To mobilize the initiative of participants, the model adopts the bilateral transaction of free negotiation. To balance the interests of transaction participants, the paper analyzes the complex interaction of multi participants in cross-regional bilateral transactions by using cooperative game theory. Simultaneously, the model considers multiple uncertainties among participants and takes into account the correlation of photovoltaic power in multiple periods. Based on the distributed robust theory, the multivariate nonlinear model and mixed-effect model of Bayesian are proposed to construct the fuzzy sets of the probability distribution for wind and photovoltaic power. On this basis, the paper analyzes the strategic behaviors of multi participants affected by uncertainty factors in the cross-regional green certificate bilateral trade through a numerical example, and quantitatively analyzes the sensitivity of each participant’s transaction plan affected by uncertainty factors. The results show that the degree of competition will affect the strategic behavior and income of the participants, and the full cooperation mode can not only avoid the risk of fluctuations in the transaction price and transaction power within the alliance but also stabilize the supply and demand of green certificate transactions.

Enhancing Sensing Performance of Capacitive Sensors Using Kirigami Structures.

Capacitive sensors have widespread applications in human-machine interaction, Internet of Things, and smart home systems due to their low cost, high sensitivity, and ease of integration. However, improving the sensitivity and sensing distance of capacitive sensors remains a challenging issue. This study proposes a novel capacitive sensor design method based on Kirigami structures, which enhances sensor performance by introducing specific cutting patterns into the conductive layer to leverage edge effects. Through experimental testing and statistical analysis, we systematically investigated the influence of Kirigami geometric parameters on sensor sensitivity and sensing distance. We designed and fabricated 12 different Kirigami structures, including circular flower patterns, array patterns, layered pointed flower patterns, and circular strip structures, and compared them with traditional non-cut structures. The results show that Kirigami structures significantly improved sensor performance. Compared to traditional sensors without Kirigami structures, optimally designed Kirigami capacitive sensors demonstrated approximately a 3-fold increase in sensitivity and up to 170 percent extension in sensing distance. Multivariate regression analysis and nonlinear models revealed complex relationships between Kirigami structural parameters and sensor performance. Notably, the circular strip (three-layer) structure exhibited the best performance, possibly due to its maximization of edge effects and optimization of electric field distribution. This study provides new design insights for developing high-performance capacitive sensors, with potential applications in improving smart home systems and indoor activity monitoring for solitary elderly individuals.

Analytical Figures of Merit in Univariate, Multivariate, and Multiway Calibration: What Have We Learned? What Do We Still Need to Learn?

ABSTRACTAn overview of the status of the research in analytical figures of merit is provided, including all calibration scenarios from univariate to multivariate and multiway analytical protocols. Both linear and nonlinear multivariate models are considered. Starting with the simplest multivariate model, inverse least‐squares regression, the basic concepts of sensitivity, sample leverage, and limit of detection are introduced. The extension to other multivariate models is discussed, as well as to nonlinear models based on radial basis functions, kernel partial least‐squares, and multilayer feed‐forward artificial neural networks. Finally, multiway calibration models are discussed, including multilinear decomposition models such as parallel factor analysis (PARAFAC) and multivariate curve resolution–alternating least‐squares (MCR‐ALS). In the latter case, recent developments concerning the pervasive phenomenon of rotational ambiguity are discussed. Unfinished works and areas where further research efforts are needed to develop closed‐form expressions and to fully understand their meaning are included.

Effect of flow rate and condenser cooling water temperature on product yield of coconut trunk sawdust pyrolysis liquid smoke

Liquid smoke is a product resulting from the pyrolysis of biomass waste that contains chemical compounds with various applications, such as food preservatives, natural pesticides, and raw materials for the chemical industry. Liquid smoke is a by-product of simultaneous pyrolysis. To maximize the yield of liquid smoke while minimizing mass loss that could potentially pollute the environment, the simultaneous pyrolysisreactor needs to operate under optimal condensation conditions. This study observed two condensation parameters: the flow rate and the cooling water temperature of the condenser, using the case study of pyrolysis of biomass waste from coconut trunk sawdust. Pyrolysis was conducted at a temperature of 400°C for 2.5 hours, varying the flow rate of the cooling water in the condenser (1, 2, 2.5, 3, and 3.5 liters/minute)and the temperature of the cooling water (10°C, 20°C, 25°C, and 30°C). A multivariable nonlinear mathematical model was obtained, relating the yield of liquid smoke (y; %) to the water temperature parameter (x1) and the flow rate of the cooling water in the condenser (x2), which is expressed as y = 6.68 + 1.89x1 – 0.04x1² – 0.41x1x2 + 13.06x2 – 0.89x2². It was concluded that the optimal condensation conditions consist of a flow rate and cooling water temperature of 2 liters/minute and 20°C, respectively, yielding a maximum of 36% liquid smoke, 33% charcoal, and a minimum mass loss of 31%. Based on the coefficient values in the obtained mathematical model, it can also be concluded that the more dominant parameter affecting the yield of liquid smoke is the flow rate of the cooling water in the condenser, with a coefficient value of 13.06. An effective condensation system can enhance the conversion efficiency of pyrolysis vapour into liquid smoke and minimize potential pollution, demonstrating significant potential in processing biomass waste into valuable products, such as liquid smoke and charcoal, while being more environmentally friendly and energy-efficient.

Study on the Law and Influencing Factors of Spontaneous Imbibition in Chang 7 Reservoir of Ordos Basin

Abstract This paper examines the imbibition and oil displacement process of fracturing fluid in a laboratory setting, focusing on the Chang 7 tight oil reservoir block in Ordos Basin. The study investigates the capability of different imbibition fluid systems to alter wettability and reduce interfacial tension. Additionally, it explores the imbibition and oil displacement abilities of cores with varying levels of wettability and permeability focusing on the imbibition equilibrium time, imbibition recovery rate, and the imbibition recovery multiplier. The reasons for these results were also examined. A multivariate nonlinear regression model is established to analyze the relationship between imbibition recovery, capillary radius, wettability angle, and interfacial tension. Additionally, neural network analysis is employed to determine the significance of these influencing factors. The findings from this research provide theoretical guidance for enhancing understanding of imbibition mechanisms and improving recovery rates in tight oil reservoirs.

Geopolitical risks and energy transition: the impact of environmental regulation and green innovation

This study examines the impact of geopolitical risk on energy transition, focusing on the moderating roles of environmental regulations and green innovation within OECD countries. By employing a multivariate linear and nonlinear regression model, we identify a substantial positive effect of geopolitical risk on energy transition. Our analysis indicates that stronger environmental regulations and advancements in green innovation significantly amplify this effect. Through threshold effect bootstrap sampling tests, we detect a nonlinear relationship between geopolitical risk and energy transition at varying levels of environmental regulation and green innovation. We also explore lag effects, revealing that the influence of geopolitical risk on energy transition grows stronger over time. The inclusion of interaction terms in our analysis further clarifies the moderating influences of environmental regulation and green innovation. Utilizing a range of geopolitical risk indicators and regression methods, our findings are robust, consistently highlighting the proactive role of geopolitical risk in fostering energy transition. These insights highlight the importance of integrated strategies that harness environmental regulations and technological innovation to facilitate a resilient and efficient energy transition in the face of challenges posed by geopolitical uncertainties.

Prediction of thermal protection performance and empirical study of flame-retardant cotton based on a combined model

Thermal protection performance (TPP) is an important index to evaluate the performance of firefighting clothing. The purpose of this work is to build a model to predict the TPP values of fabrics with fewer variables. Two properties of flame-retardant cotton were tested with TPP values under different air gaps, and the correlations between these properties were also analyzed. A combined model was established by integrating multivariate nonlinear regression model and gradient boosting regression tree model. Then the combined model was compared with these two single models. The results showed that the correlation coefficients between gram weight and thickness of fabric and TPP value were 0.833 and 0.837, respectively, indicating a strong correlation. The correlation coefficient between air gap and TPP value was 0.304, indicating a weak correlation. In predicting the thermal protective performance of flame-retardant cotton, this study employed a multivariate nonlinear regression model, a Gradient Boosting Regression Tree (GBRT) model, and a combined model. After comparing various evaluation metrics, it was finally decided to adopt the combined model for predicting the thermal protective performance values of flame-retardant cotton. This method improved the prediction accuracy of thermal protective performance, facilitating the promotion and application of the combined model. Furthermore, when exploring the thermal protective performance of flame-retardant cotton, the use of fewer variables to establish the prediction model can not only significantly simplify the complex structure of the model but also greatly enhance the analysis efficiency, ensuring the efficiency and precision of the research process.

Field strength prediction of 220 kV cable oil terminal defects based on multivariate nonlinear regression model

During the installation of a cable oil terminal, it is easy to leave scratches on the main insulation owing to uneven forces when removing the semi-conductive layer. Scratch defects cause field intensity distortion, which leads to partial discharge and insulation failure. This study attempts to establish a simulation model of a 220 kV cable terminal to determine the effect of the length, depth, and position of the scratch on the maximum field strength at the defect. The simulation and experiment demonstrate that the maximum field strength at the defect increases with greater length and decreases as the depth increases. Therefore, a prediction method for the terminal defect field strength based on a multivariate nonlinear regression model was proposed in this study. When the defect is located at 20 mm from the root of the stress cone, the maximum field strength is 14.5 MV/m when the length and depth are 2 mm and 1 mm, respectively. The maximum field strength at the defect was predicted based on the length, depth, and position of the scratch defect to evaluate the severity of the defect.

Retrograde orbits associated separatrices in perturbed restricted three-body problem

This study develops single and multivariate nonlinear regression models for predicting Jacobi constant related to separatrix associated with simply symmetric retrograde periodic orbits in the framework of CRTBP with and without perturbations effects. These models are constructed using data from real and hypothetical systems considering that the parameter of mass is independent variable, while the Jacobi constant is displayed as a function of mass and oblateness parameters. Third-degree polynomials from single-variable regression and fourth-degree polynomials from multivariate regression accurately predict the Jacobi constant for given mass and oblateness values, facilitating the identification of separatrices in the PSS without intensive construction efforts. Error analysis confirms the model’s high accuracy across all parameters values. Additionally, chaos detection techniques, including the SALI, GALI, and Lyapunov exponent methods, along with bifurcation analysis, are employed to identify the regions of local and global chaos.

Forecasting the output of high-tech industry in China: A novel nonlinear grey time-delay multivariable model with variable lag parameters

Under the rapidly developing economy in China, accurate forecasting holds vital significance for policymaking and operational planning within the high-tech industry. However, the influencing factors affecting the output, accompanied by the time-delay effect, could be nonlinear, and uncertain. Thereby, this paper proposes a new nonlinear grey multivariable model with time-varying lag parameters. To be specific, the newly designed time delay function and power exponent are introduced, which can significantly enhance the adaptability and flexibility of the proposed method. The Grey Wolf Optimization algorithm is utilized to calculate the dynamic time lag parameters and power exponent to improve the prediction reliability. Furthermore, this new approach is applied to predict the high-tech industry’s output in China, Shanghai Municipality, and the Eastern Region, with due consideration given to the time-delay effect between input factors and outputs. To assess its efficacy, some leading models are selected for comparison to the proposed model. Furthermore, the utilization of Monte-Carlo simulation, the Probability Density Analysis, and the simulations are used to demonstrate the robustness and stability of this new method. The findings show that the proposed model is a feasible and applicable approach for prediction, exhibiting outstanding accuracy.

Predicting vulnerability through hybrid modeling combining GAM and XGBoost - A case of affected population vulnerability to tropical cyclone in Hainan Province

Tropical cyclones are one of the most destructive natural disasters, frequently occurring in the southeastern coastal areas of China, causing huge losses. Accurate characterization and prediction of negative impacts are necessary to minimize impact on coastal cities. However, a complex interaction between hazard intensity and other drivers is involved in the impact of some extreme tropical cyclones, which are often worthy of attention. In this study, a quantitative vulnerability assessment model of tropical cyclones considering the mutual relation between hazard intensity and environmental drivers was developed using the generalized additive model (GAM), random forest (RF), and extreme gradient boosting (XGBoost) for the case of Hainan Province, China. In the testing dataset, the root mean squared error of the optimal model was 0.1393, and the mean absolute percentage error of the optimal model was 35.2 % for spikes in the affected population rate. The spikes in the affected population rate were predicted well by the hybrid model jointly considering nonlinear multivariable regression models and undersampling machine learning methods.

Prediction technology of mine water inflow based on entropy weight method and multiple nonlinear regression theory and its application

Mine water inflow is an important basis for the formulation of mining plans and the utilization of groundwater resources. The mine water inflow is the result of the combined influence of many factors. The weight value of the influencing factors is calculated by the entropy method, and the order of importance of the factors is: precipitation > mining depth > cumulative mined-out area > aquifer thickness > mining area > mining height. The optimal univariate nonlinear regression model of mine water inflow to each influencing factor is obtained by factor scatter analysis and Matlab function programming. On this basis, combined with the weight values of factors, a multivariate nonlinear regression prediction model of mine water inflow based on weighting is innovatively established, which overcomes the defect that the traditional water inflow prediction method that cannot reflect the relative importance differences of various influencing factors. The multivariate weighted nonlinear regression model is used to predict the mine water inflow of typical coal mines, and the prediction results are compared with the linear regression model and the measured value. The results show that the prediction model of mine water inflow based on weighted multivariate nonlinear regression is accurate higher, with higher practical application value.

The association between preoperative serum cholinesterase and all-cause mortality in geriatric patients with hip fractures: a cohort study of 2387 patients

ObjectiveThis study is to evaluate the association between preoperative cholinesterase levels and all-cause mortality in geriatric hip fractures.MethodsElderly patients with hip fractures were screened between Jan 2015 and Sep 2019. Demographic and clinical characteristics of patients were collected. Linear and nonlinear multivariate Cox regression models were used to identify the association between preoperative cholinesterase levels and mortality in these patients. Analyses were performed using EmpowerStats and the R software.ResultsTwo thousand three hundred eighty-seven patients were included in this study. The mean follow-up period was 37.64 months. Seven hundred eighty-seven (33.0%) patients died due to all-cause mortality. Preoperative cholinesterase levels were 5910 ± 1700 U/L. Linear multivariate Cox regression models showed that preoperative cholinesterase level was associated with mortality (HR = 0.83, 95% CI: 0.78–0.88), P < 0.0001) for every 1000 U/L. However, the linear association was unstable, and nonlinearity was identified. A cholinesterase concentration of 5940 U/L was an inflection point. When preoperative cholinesterase level < 5940 U/L, the mortality decreased by 28% for every 1000 U/L increase in cholinesterase (HR = 0.72, 95%CI: 0.66–0.79, P < 0.0001). When cholinesterase was > 5940 U/L, the mortality was no longer decreased with the rise of cholinesterase (HR = 1.01, 95%CI: 0.91–1.11, P = 0.9157). We found the nonlinear association was very stable in the propensity score-matching sensitive analysis.ConclusionsPreoperative cholinesterase levels were nonlinearly associated with mortality in elderly hip fractures, and cholinesterase was a risk indicator of all-cause mortality.Trial registrationThis study is registered on the website of the Chinese Clinical Trial Registry (ChiCTR: ChiCTR2200057323) (08/03/2022).

Exploring capelin (Mallotus villosus) population dynamics using Empirical Dynamic Modelling (EDM)

Capelin (Mallotus villosus) populations on the Newfoundland shelf collapsed in the early 1990s, coinciding with a regime shift and greatly reduced capelin and groundfish biomasses which both persist to this day. The biphasic nature of this stock’s history suggest it may experience nonlinear dynamics, which are difficult to predict using linear models. This study explores the application of Empirical Dynamic Modelling (EDM) nonlinear, nonparametric time series forecasting tools to capelin biomass data, seeking to detect nonlinear dynamics, compare performance of linear and nonlinear multivariate predictive models, identify drivers of capelin biomass using convergent cross-mapping, and measure the sign and strength of capelin species interactions. We found capelin dynamics were nonlinear, and multivariate EDM predictive models returned equal or improved model diagnostics to linear models in most situations. We identified long-term climate dynamics and timing of sea ice retreat as the primary drivers of capelin dynamics, but some indications of potential top-down effects from Greenland halibut were also detected. Atlantic cod biomass, and capelin catch were investigated as potential drivers of capelin dynamics, but both were found more likely to be driven by capelin dynamics. Overall, our results support the idea that capelin dynamics are mostly bottom-up driven, and that capelin itself is a driver of its predators, suggesting that the overall ecosystem may be largely bottom-up driven. This study also clearly identifies the utilities of EDM as a complementary tool for stock assessments by detecting and forecasting nonlinear stock dynamics, and identifying and characterizing relationships between stock biomass and the factors which drive it.

Nearly Instantaneous Time-Varying Reproduction Number for Contagious Diseases-a Direct Approach Based on Nonlinear Regression.

While the world recovers from the COVID-19 pandemic, another outbreak of contagious disease remains the most likely future risk to public safety. Now is therefore the time to equip health authorities with effective tools to ensure they are operationally prepared for future events. We propose a direct approach to obtain reliable nearly instantaneous time-varying reproduction numbers for contagious diseases, using only the number of infected individuals as input and utilisingthe dynamics of the susceptible-infected-recovered (SIR) model. Our approach is based on a multivariate nonlinear regression model simultaneously assessing parameters describing the transmission and recovery rate as a function of the SIR model. Shortly after start of a pandemic, our approach enables estimation of daily reproduction numbers. It avoids numerous sources of additional variation and provides a generic tool for monitoring the instantaneous reproduction numbers. We use Norwegian COVID-19 data as case study and demonstrate that our results are well aligned with changes in the number of infected individuals and the change points following policy interventions. Our estimated reproduction numbers are notably less volatile, provide more credible short-time predictions for the number of infected individuals, and are thus clearly favorable compared with the results obtained by two other popular approaches used for monitoring a pandemic. The proposed approach contributes to increased preparedness to future pandemics of contagious diseases, as it can be used as a simple yet powerful tool to monitor the pandemics, provide short-term predictions, and thus support decision making regarding timely and targeted control measures.