Nonlinear Regression Models Research Articles

A comparative study of linear and nonlinear regression models for blood glucose estimation based on near-infrared facial images from 760 to 1650 nm wavelength

A comparative study of linear and nonlinear regression models for blood glucose estimation based on near-infrared facial images from 760 to 1650 nm wavelength

Seismic vulnerability analysis of hospitals and school buildings considering the Gaussian regression algorithm

This study combines the Gaussian regression algorithm to propose a nonlinear regression model that can be used to evaluate the seismic vulnerability of regional hospitals and school buildings. The failure features and disaster mechanisms of hospital and school buildings affected by the Jishishan (JSS) earthquake on December 18, 2023, and the Wenchuan (WC) earthquake on May 12, 2008, were reported. The samples of 252 damaged buildings (37 hospitals and 215 schools) in Dujiangyan city affected by the Wenchuan earthquake for which the author participated in the survey were collected and counted. Hospitals and school buildings were classified according to the types of reinforced concrete (RC) and masonry structures, and earthquake vulnerability probability matrices for hospital and school building clusters were established considering the actual failure probabilities. A total of 2103,213 acceleration records (from the Wenchuan earthquake) monitored by 12 real stations were selected. Using dynamic time history and response spectrum analysis methods, time history and spectrum curves were generated, considering the influence of different seismic directions. Using the developed Gaussian regression model, vulnerability comparison curves and parameter matrices considering multiple regression algorithms were generated. This paper considers the effects of the construction year and number of floors on the seismic vulnerability of hospital and school buildings. Seismic vulnerability curves and failure probability matrices were generated and established on the basis of actual structural failure probabilities. According to regression and vulnerability surface analysis, the evaluation results of the proposed model are highly consistent with actual field observations.

A Multi-Mechanism Fusion Method for Robust State of Charge Estimation via Bidirectional Long Short-Term Memory Model with Mixture Kernel Mean p-Power Error Loss Optimized by Golden Jackal Optimization Algorithm

Abstract Accurate state of charge (SOC) estimation is crucial for effective battery management in various applications. The bidirectional long short-term memory (BiLSTM) as an outstanding nonlinear regression model can be used for SOC estimation. This work develops a novel multi-mechanism fusion method based on BiLSTM to further enhance its estimation performance for SOC, in which the convolutional neural network (CNN), attention mechanism, and mixture kernel mean p-power error (MKMPE) loss are introduced into the BiLSTM framework for addressing different issues. First, the introduction of CNN components aims to extract essential features from battery data, enhancing the model's comprehension of complex information. Then, the attention mechanism is used to further refine the model's perceptual ability and a robust MKMPE loss is introduced into the BiLSTM framework to replace its original mean squared error loss, and a novel robust model is developed to suppress non-Gaussian noise interference. Finally, some key hyperparameters of the proposed model are fine-tuned using the golden jackal optimization algorithm, resulting in improved estimation performance. Comparative numerical experiments are meticulously conducted in various cases to evaluate the performance of the proposed method, and the experiment results demonstrate that it can perform outstanding effectiveness in handling non-Gaussian noise scenarios.

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.

A statistical modelling approach to feedforward neural network model selection

Feedforward neural networks (FNNs) can be viewed as non-linear regression models, where covariates enter the model through a combination of weighted summations and non-linear functions. Although these models have some similarities to the approaches used within statistical modelling, the majority of neural network research has been conducted outside of the field of statistics. This has resulted in a lack of statistically based methodology, and, in particular, there has been little emphasis on model parsimony. Determining the input layer structure is analogous to variable selection, while the structure for the hidden layer relates to model complexity. In practice, neural network model selection is often carried out by comparing models using out-of-sample performance. However, in contrast, the construction of an associated likelihood function opens the door to information-criteria-based variable and architecture selection. A novel model selection method, which performs both input- and hidden-node selection, is proposed using the Bayesian information criterion (BIC) for FNNs. The choice of BIC over out-of-sample performance as the model selection objective function leads to an increased probability of recovering the true model, while parsimoniously achieving favourable out-of-sample performance. Simulation studies are used to evaluate and justify the proposed method, and applications on real data are investigated.

Optimizing the polar phase transformation in PVDF-HFP/BaTiO3-activated carbon composite films with the mixture design of experiments

ABSTRACT A salient bottleneck to driving the wider use of polyvinylidene fluoride (PVDF) and its copolymers in smart applications is the requirement for a high-voltage poling process required to activate their β -phase crystal structure before the realisation of the piezoelectricity response. In pursuit of enhancing the β-phase content of PVDF-based films, various approaches have been employed in recent years. Yet, a perfect solution to the challenge remains elusive. Here, we report a preliminary investigation into the production of unpoled poly(vinylidene fluoride-hexafluoropropylene) (PVDF-HFP) films reinforced with barium titanate (BaTiO3) and activated carbon (AC) to improve the piezoelectric property. Employing the mixture design of experiments (MDOE) method, various formulations of the composite’s constituents weight fractions were determined. Afterwards, series of composite films were produced via a toxic-free solution casting method and characterised by Fourier Transform Infrared Spectrum (FTIR) to determine the β-phase content. A non-linear polynomial regression model was established from the experimental FTIR data, and the adequacy of the model was confirmed using ANOVA. Subsequently, an MDOE-enabled optimisation was undertaken, generating a formulation of the composite to obtain the highest β-phase content to be 15 wt.% BaTiO3 and 0.74 wt.% AC. This combination produces a theoretically predicted β-phase content of 72.7 %. A further experimental test employing the optimal formulation produced a β-phase content of 71.90 %, achieved with neither mechanical stretching, thermal annealing, nor electrical poling.

Regression Models for Tree Volume Prediction in Pinus Wallichiana Stands of South Western Himalayan Region of Kashmir

This study focuses on assessing tree species diversity and evaluating the efficacy of both linear and non-linear regression models for predicting tree volume. The research was conducted in the slopes of the Pir Panjal range within the Shopian Forest Division, situated in the South-Western Himalayan Region of Kashmir. Data on Pinus wallichiana stands, including diameter at breast height (D) and tree height (H), were meticulously collected using appropriate measurement instruments. Employing a multi-stage sampling technique, ten plots of uniform size (10m x 10m) were selected across 20 blocks, and subsequently, 25 trees were randomly chosen from each plot. Six different linear and non-linear regression equations were fitted to the data, and the most suitable equation was identified for volume estimation. To evaluate the performance of the fitted regression models, metrics such as R-squared (R²), adjusted R², root-mean-square error (RMSE), and Theil’s U statistic were employed. Additionally, validation procedures involved using the half-split approach and the Chow test. Upon analysis, it was determined that when employing diameter (D) and considering the joint effectof diameter and height (D2H (I)) as independent variables, the linear model (V=-1.41+15.12D) and power model (V=2.301 I0.502), quadratic model (V=1.8726+0.663 I- 0.011 I²) with highest R², lowest RMSE and Theil’s U statistic respectively, emerged as the most suitable for volume estimation, demonstrating superior accuracy compared to alternative models. Consequently, our findings extend beyond academic inquiry, offering practical implications for sustainable forest management and planning in the Western Himalayan Regions of Kashmir. By providing robust volume estimation models tailored to Pinus wallichiana stands, our study equips forest managers and policymakers with essential tools for informed decision-making.

Virtual active power sensor for eolic self-consumption installations based on wind-related variables

Abstract Green energy production is expanding in individual and large-scale electricity grids, driven by the imperative to reduce greenhouse gas emissions. This research performs a comparative analysis of several linear and non-linear regression models, intending to identify the most effective method to estimate the active power produced for a mini wind turbine using meteorological variables, looking for a reliable virtual sensor. The modeling process followed a feature selection step before applying eight machine learning techniques whose results were statistically analysed to determine the best performance. The implemented virtual sensor accurately estimated the active power, being an interesting tool for anomaly detection, maintenance management or decision-making.

Sustainable Concreting: Optimization Modelling of the Strength Properties of Bio-Self Compacting Concrete Incorporating Sporosarcina Pasteurii, Calcined Clay and Limestone Powder

Sustainable concreting is prerequisite for infrastructural development in developing countries so as to meet up with the sustainable development goal of adequate mass housing and other critical infrastructure. Thus, research is ever ongoing aimed at developing cheaper and more durable concrete via the incorporation of bio-based by-products in concrete to improve its properties, as well as optimizing the quantities of these secondary materials for maximum and optimal concrete production. One such revolutionary concrete that is yet to find full application in the developing world is self-compacting concrete, because of the cost and attendant environmental effects. There is thus a need to arrive at optimal materials quantities that can maximize concrete properties without recourse to many trial and error experimentations that are both time and resources consuming. The application of modelling tools in concrete technology aids in the optimization of concrete constituents for optimal self-compacting concrete performance. This research uses optimization techniques to optimize the bacteria dosage as well as model the Compressive and Tensile strength properties of a calcined clay and Limestone powder blended ternary self-compacting concrete using sporosarcina pasteurii as Microbial induced calcite precipitation agent and calcium lactate as nutrient source. The Bacteria was incorporated into the concrete at a bacterial content of 1.5x108cfu/ml, 1.2x10 cfu/ml and 2.4x109cfu/ml corresponding to the McFarland turbidity scale of 0.5, 4 and 8 while the nutrient (calcium lactate) content was 0.5, 1.0 and 2.0% by weight of cement for each bacterial content. The Compressive strength and tensile strengths at 28 days were determined and the results used for both the model development, strength optimization and model validation, with the strengths as the dependent variable (y) and the bacterial content corresponding to a McFarland scale of and calcium lactate content as the independent variables, X1 and X2 respectively. The results show an improvement in the compressive strength from 32N/mm2 to 45.2N/mm2 at the optimal bacterial and nutrient content of 1.2x10 cfu/ml and 0.5% respectively, and tensile strength from 4.01N/mm2 to 5.0N/mm2. Also, the non-linear regression models proved adequate for optimizing the bacterial content for optimal self-compacting concrete performance. Journal of Engineering Science 15(1), 2024, 11-19

Computational fluid dynamics modeling of gas bubble separation efficiency in downhole separators and vertical / inclined annulus: An experimental validation and analysis

This study presents a comprehensive investigation into gas bubble separation efficiency in a vertical downhole separator using computational fluid dynamics (CFD) modeling, which is validated with experimental data. The research aims to provide detailed insights into the separation mechanisms and the factors affecting them, such as liquid velocity, gas bubble sizes, and positions. Using an Euler-Lagrange multiphase model, the behavior of individual gas bubbles within the liquid-gas mixture was simulated. The results demonstrate that separation efficiency decreases as the liquid flow rate increases. This reduction in efficiency occurs because the increased liquid flow rate drags more bubbles within the stream, making it harder for them to separate. The separation process is primarily driven by the buoyancy force acting on the bubbles and the velocity profile of the liquid flow. Smaller bubbles, which tend to be near the casing wall, separate more efficiently, while larger bubbles are predominantly located between the second and third quarters of the annulus space. The "quarters" refer to radial divisions from the casing wall to the tubing wall, with the first quarter closest to the casing wall and the fourth quarter closest to the tubing wall. The study introduces a nonlinear regression model based on the numerical results to predict liquid slug separation efficiency. This model, validated against experimental data, accurately predicts separation efficiency and offers a robust methodology for estimating the efficiency of gravity-driven gas-liquid separators. This methodology is crucial for refining separator design and improving the operational efficiency of downhole separation systems, which are vital for enhancing the performance of pumping systems in oil and gas wells. The contributions of this study include a deeper understanding of the downhole separation process, the development of a simplified model for assessing bubble separation efficiency, and the potential application of the proposed methodology to different gas-liquid separator designs and inclination angles, thereby informing the design and operation of downhole separation systems.

Nonparametric Bayesian optimal designs for Unit Exponential regression model with respect to prior processes(with the truncated normal as the base measure)

Nonlinear regression models are extensively applied across various scientific disciplines. It is vital to accurately fit the optimal nonlinear model while considering the biases of the Bayesian optimal design. We present a Bayesian optimal design by utilising the Dirichlet process as a prior. The Dirichlet process serves as a fundamental tool in the exploration of Nonparametric Bayesian inference, offering multiple representations that are well-suited for application. This research paper introduces a novel one-parameter model, referred to as the ’Unit-Exponential distribution’, specifically designed for the unit interval. Additionally, we employ a stick-breaking representation to approximate the D-optimality criterion considering the Dirichlet process as a functional tool. Through this approach, we aim to identify a Nonparametric Bayesian optimal design.

Accuracy of goodness-of-fit criteria for nonlinear regression: a study via Monte Carlo simulation

Nonlinear regression models are widespread in the literature, and one of their main applications is in the study of sigmoidal growth curves. There are several models for this purpose, and the most used are the logistic, Gompertz, von Bertalanffy, and Brody models. Each one of them has its own characteristics and is more suitable for a given curve shape. There are several criteria in the literature for selecting the most appropriate model, but there is no consensus on the best criteria. Thus, the present study aims to evaluate the accuracy of the main selection criteria via Monte Carlo simulation, considering the logistic, Gompertz, von Bertalanffy, and Brody nonlinear regression models. Four simulation scenarios are used, each simulated with ideal curves of the logistic, Gompertz, von Bertalanffy and Brody models. Next, the 4 models are adjusted for each of the scenarios, and the main quality criteria found in the literature are calculated to assess the ability of the criteria to identify the most appropriate model for each scenario. The results show that the criteria asymptotic index, mean absolute error and coefficient of determination choose the correct model more often than the other criteria studied. Although the measures of the Battes and Watts curvature and box bias are important for the evaluation of the goodness-of-fit of the models, they are not indicated for the selection of the best model.

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.

Predictive value of neutrophil to lymphocyte ratio, platelet to lymphocyte ratio, and systemic inflammatory index for detection of recurrence of pleomorphic adenoma of the major salivary glands: a multicenter study

BackgroundThe aim of this study was to investigate the correlation between inflammatory biomarkers such as the systemic immune-inflammation index (SII), the neutrophil-to-lymphocyte ratio (NLR) and the platelet-to-lymphocyte ratio (PLR) and the recurrence of pleomorphic adenomas (PAs). MethodsRetrospective multicenter study. 608 patients diagnosed with PA and treated by tumor enucleation were included in the analyses. The patients. were extracted from a twenty-year database of two referral centers (January 2000 to January 2020). Data about age, sex, voluntary habits, tumor characteristics, tumor treatment and values of NLR, PLR and SII were collected. A receiver operating characteristic (ROC) curve was used to calculate the optimal cut-off values for SII, PLR and NLR. A linear regression model (LRM) and a non-linear logistic regression model (NLRM) were implemented for NLR, PLR and SII. ResultsAll three inflammatory parameters were statistically significant correlated to the recurrence of the tumor. The best performance was achieved by NLR (cut-off 2.960) with AUC = 0.91, accuracy of 96.1%, sensitivity of 78.4% and specificity of 97.2%, PPV = 64.4% and NPV = 98.6%. LRM and NLRM including all hematological parameters did not improve performance in terms of recurrence detection. ConclusionThe use of three inflammatory biomarkers could be a useful tool to predict recurrence of tumor in case of PA ≤ 3 cm. NLR in particular could be sensitive with a cut-off of 2.960. The use of NLR, PLR and SII could be a good reference point for surgical decision making and follow-up in clinical practice.

Optimization of aerodynamic drag reduction for truck trailer model via machine learning

From advanced fairing designs and spoilers to novel airflow management systems, the quest for drag reduction (DR) in truck trailers is critical for cleaner and more sustainable transport. In this study, a particle swarm optimization (PSO) integrated machine learning approach is developed to optimize the DR performance of a bare truck trailer (BTT) with and without half airfoils and roof fairings. The study aims to reach the optimal truck trailer design with fewer experiments by searching the entire solution space with machine learning methods thanks to the developed approach. For this purpose, the experimental setup was initially designed and the experimental results were obtained. The experimental inputs are Airfoil thickness, Roof Fairing (RF) positions, and Reynolds number, while the experimental output is the drag coefficient. These inputs and outputs were arranged via data preprocessing and then modeled using machine learning methods. Modeling was performed with Artificial Neural Network (ANN) and multiple regression models. In addition to the ANN model setup with appropriate topology, linear and non-linear multiple regression models were established. Comparisons were performed using statistical metrics and it was determined that ANN was the superior model. Using the ANN’s prediction model, the drag coefficients were derived from the whole parameter values of both airfoil thickness and RF positions in the solution space for all Reynolds number and an optimization process was performed by PSO. As a result of the analysis, optimal parameter values were determined as 0.10 and 5.0 mm for the airfoil thickness and RF position. As a result of the experimental validation, it is seen that the BTT_NACA 0010_RF-0.5 model, designed with the optimum parameter values, demonstrated a DR performance of 34.7 %, which is the highest value compared to others. Thus, the heuristic process was experimentally validated and optimized by saving time and cost.

Process Parameters Optimization and Numerical Simulation of AlCoCrFeNi High-Entropy Alloy Coating via Laser Cladding.

The use of laser cladding technology to prepare coatings of AlCoCrFeNi high-entropy alloy holds enormous potential for application. However, the cladding quality will have a considerable effect on the properties of the coatings. In this study, considering the complex coupling relationship between cladding quality and the process parameters, an orthogonal experimental design was employed, with laser power, scanning speed, and powder feed rate as correlation factor variables, and microhardness, dilution rate, and aspect ratio as characteristic variables. The experimental data underwent gray correlation analysis to determine the effect of various process parameters on the quality of cladding. Then, the NSGA-II algorithm was used to establish a multi-objective optimization model of process parameters. Finally, the ANSYS Workbench simulation model was employed to conduct numerical simulations on a group of optimized process parameters and analyze the change rule of the temperature field. The results demonstrate that the laser cladding coating of AlCoCrFeNi high-entropy alloy with the single pass is of high quality within the determined orthogonal experimental parameters. The powder feed rate exerts the most significant influence on microhardness, while laser power has the greatest impact on dilution rate, and scanning speed predominantly affects aspect ratio. The designed third-order polynomial nonlinear regression model exhibits a high fitting accuracy, and the NSGA-II algorithm can be used for multi-objective optimization to obtain the Pareto front solution set. The numerical simulation results demonstrate that the temperature field of AlCoCrFeNi high-entropy alloy laser cladding exhibits a "comet tail" phenomenon, where the highest temperature of the molten pool is close to 3000 °C. The temperature variations in the molten pool align with the features of laser cladding technology. This study lays the groundwork for the widespread application of laser cladding AlCoCrFeNi high-entropy alloy in surface engineering, additive manufacturing, and remanufacturing. Researchers and engineering practitioners can utilize the findings from this research to judiciously manage processing parameters based on the results of gray correlation analysis. Furthermore, the outcomes of multi-objective optimization can assist in the selection of appropriate process parameters aligned with specific application requirements. Additionally, the methodological approach adopted in this study offers valuable insights applicable to the exploration of various materials and diverse additive manufacturing techniques.

Biomethane production modelling from third-generation biomass

Third-generation biomass constitutes a renewable energy source that could substitute fossil fuels. This study evaluated the biomethane potential (BMP) of Ulva sp., Codium sp. and Undaria pinnatifida through anaerobic digestion. The daily production of biomethane was evaluated using different models, including Modified Gompertz, Chen and Hashimoto, First-order, Transfer and Cone models, as well as an Artificial Neural Network (ANN) model. The experimental BMP was 0.17, 0.26, and 0.32 Nm³/kg VS for Ulva sp., Codium sp., and U pinnatifida, respectively. Among the non-linear regression models, the Transfer model (R2 > 0.9915) and the First-order model (R2 > 0.9889) are the ones that best fit the experimental data. However, the ANN shows a better fit (R2 > 0.999 and RMSE<4.537) to the data compared to the non-linear regression models. Furthermore, ANN can capture the complexity of biological systems, allowing for more accurate and detailed modelling of the processes involved. The identification and optimization of the biomethane potential of macroalgae contribute to developing sustainable energy alternatives, offering a renewable energy source that could mitigate the environmental stress associated with traditional fossil fuels.

Machine learning method predicting thermal performance of conformal cooling systems

The incorporation of conformal cooling systems has significantly enhanced the efficiency and quality of injection molding process. While several automated methods have been developed for creating conformal cooling channels in injection molds, the current optimization process for conformal cooling design parameters is hindered by labor-intensive iterative thermal simulation processes and the substantial reliance on empirical human knowledge. This paper presents an innovative machine learning method to assess the thermal performance of conformal cooling systems by employing a combination of a non-linear regression model and a neural network. By employing a logarithmic regression model describing the temperature graph and a neural network predicting the coefficients of the logarithmic regression model, the thermal performance of specified conformal cooling systems can be assessed and predicted precisely. This methodology empowers designers to evaluate the thermal efficiency of conformal cooling systems efficiently and effectively to further optimize the conformal cooling design parameters without relying on tedious manual thermal and fluid simulation processes.

Simultaneous Inference Using Multiple Marginal Models.

This tutorial describes single-step low-dimensional simultaneous inference with a focus on the availability of adjusted p values and compatible confidence intervals for more than just the usual mean value comparisons. The basic idea is, first, to use the influence of correlation on the quantile of the multivariate t-distribution: the higher the less conservative. In addition, second, the estimability of the correlation matrix using the multiple marginal models approach (mmm) using multiple models in the class of linear up to generalized linear mixed models. The underlying maxT-test using mmm is discussed by means of several real data scenarios using selected R packages. Surprisingly, different features are highlighted, among them: (i) analyzing different-scaled, correlated, multiple endpoints, (ii) analyzing multiple correlated binary endpoints, (iii) modeling dose as qualitative factor and/or quantitative covariate, (iv) joint consideration of several tuning parameters within the poly-k trend test, (v) joint testing of dose and time, (vi) considering several effect sizes, (vii) joint testing of subgroups and overall population in multiarm randomized clinical trials with correlated primary endpoints, (viii) multiple linear mixed effect models, (ix) generalized estimating equations, and (x) nonlinear regression models.

Modeling of Growth in Turkeys by Nonlinear Regression Models

Nonlinear regression models are commonly used in many areas, such as physics, chemistry, biology, and engineering. In these models, the solution of normal equations is more difficult than normal equations of linear regression models. Iterative algorithms are used to solve these equations. It is highly important to choose an appropriate initial value while using these algorithms. The values obtained during the study or from previous studies can be used as an initial value. With an inappropriately chosen initial value, the number of iterations will increase, and convergence may also not occur. In this study, the nonlinear Gompertz, Richards, and Weibull models of turkey growth were considered by taking the data on female turkey weight, and it was investigated which of these models was the most appropriate model for turkey growth using the R program