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Abstract Photosynthetic light response curves serve as powerful mathematical tools for quantitatively describing the rate of photosynthesis of plants in response to changes in irradiance. However, in practical applications, the daunting task of selecting an appropriate nonlinear model to accurately fit these curves persists as a significant challenge. Thus, there arises a need for a method to systematically evaluate the efficacy of such models. In the present study, four distinct nonlinear models, namely Exponential Model (EM), Rectangular Hyperbola Model (RHM), Nonrectangular Hyperbola Model (NHM), and Modified Rectangular Hyperbola Model (MRHM), were used to fit the relationship between light intensity and the rate of photosynthesis across 42 empirical datasets. The goodness of fit for each model was assessed using the root-mean-square error, and relative curvature measures of nonlinearity were employed to assess the nonlinear behavior of the models. In terms of goodness of fit, pairwise difference tests of the root-mean-square error revealed that there was little to choose among the four models, although RHM gave a marginally poorer fit. However, in terms of nonlinear behavior, EM not only provided the most favorable linear approximation performance at the global level, but also exhibited the best close-to-linear behavior at the individual parameter level among the four models across the 42 datasets. Consequently, the results strongly advocate for EM as the most suitable mathematical framework for fitting photosynthetic light response curves. These findings provide insights into the model assessment for nonlinear regression in describing the relationship between the photosynthetic rate and light intensity.

This paper discusses the application of nonlinear regression to forecast and optimize the operation of catalytic cracking units under conditions of fuzzy information. Catalytic cracking is a crucial process in oil refining that produces high-quality gasoline and other light hydrocarbon products. However, the complexity of the process and the uncertainty of initial data complicate the modeling and optimization of plant operations. To address this issue, a nonlinear regression method is proposed that accommodates the fuzziness of input and output parameters described by linguistic variables. The methodology includes the collection and formalization of expert knowledge, the construction of fuzzy models, and their integration into the process control system. Forecasting is performed by creating regression models that describe the relationships between operational parameters and product quality characteristics. The paper presents a procedure for developing and applying nonlinear regression models, describes algorithms for synthesizing linguistic models, and provides examples of their use to optimize the operation of catalytic cracking units. The modeling results demonstrate the high adequacy and accuracy of the proposed method, as well as its advantages over traditional approaches in conditions of uncertainty and data scarcity. The scientific novelty of the research lies in the development and testing of advanced nonlinear regression models adapted for analyzing and optimizing catalytic cracking processes based on fuzzy data. These methods take into account the specificity and uncertainty of process data, improving the accuracy and reliability of forecasts, which facilitates more effective management of production processes in the petrochemical industry. The main reason for conducting this study is the need to improve the control of oil refining processes, particularly catalytic cracking, which plays an important role in producing high-quality gasoline. The complexity of this process and the presence of fuzzy information caused by fuzzy initial data require the development of new modeling and optimization methods. Existing traditional models based on deterministic methods are often insufficient under uncertainty. This leads to a decrease in the accuracy of process control, which can negatively affect the quality of the final product and production efficiency. The use of nonlinear regression in combination with fuzzy logic is a more flexible and adaptive approach that allows you to take into account the fuzziness and uncertainty of data and use expert knowledge to build models that match the actual operating conditions of the units. Thus, this study aims to solve the key problems associated with data uncertainty and the complexity of the catalytic cracking process, which will improve the accuracy of forecasting and optimization of the units. The main contribution is creating a model that uses nonlinear regression methods in combination with fuzzy logic. This allows uncertainty in input data (such as reactor temperature or pressure) to be effectively considered and processed to improve gasoline and other product yield forecasts. It is shown that using nonlinear regression combined with fuzzy logic significantly improves the management of technological processes, increases the output and quality of products, and reduces production costs. The conclusion of the paper discusses the prospects for further development of the methodology and its application to solve similar tasks in other areas of chemical technology.

Machine learning algorithms have achieved great success due to their excellent predictive performance, but their applicability is limited in areas where there is a high demand for model interpretability. Aiming at the weakness of lacking interpretability of machine learning algorithms, a new interpretable machine learning algorithm called ensemble trees penalized logistic rule regression is proposed based on the idea of rules ensemble, which can achieve comparable predictive performance to the ensemble trees algorithm with less structural complexity and retains the interpretive effect of logistic regression. Firstly, it extracts branches from ensemble trees such as random forest and XGBoost, and converts them into logic rules. Then, the rule set is pruned and deduplicated to obtain a streamlined rule set. Finally, the rules are incorporated into logistic regression as variables and complexity control is performed with Lasso algorithm. Taking the enterprise risk warning as an example, it is compared with multiple machine learning algorithms. The results show that this algorithm not only inherits the default discrimination ability of the ensemble trees well and exceeds most of the machine learning algorithms in various classification indices, but also can give the thresholds of the enterprise risk indices through the rules, which is convenient for enterprises to carry out risk management. Further, the enterprise credit score is produced according to this algorithm, which verifies its wide applicability. The obtained score conforms to the objective law and is discriminative, and the robustness of the model’s prediction performance is verified by three public datasets.

Expansive soils, known for their significant volume change with variations in moisture content, are widely distributed around the globe. Due to their swelling properties, expansive soils pose significant engineering challenges, especially in rapidly developing countries like China. This study aims to investigate the swelling mechanisms of expansive soils, focusing on the influence of crack characteristics on swelling behavior. The research methodology includes field investigations, laboratory experiments, and theoretical modeling. By comprehensively considering crack rate, dry density, initial moisture content, and overburden load, a nonlinear regression swelling model is proposed in this research. The degree of crack development in expansive soils is quantitatively characterized by the content of filling materials, leading to the establishment of a crack rate model for expansive soils. Swelling tests on expansive soils with different crack contents were conducted. The results show that the swelling rate is negatively correlated with the initial moisture content and positively correlated with dry density and crack rate. Additionally, the larger the crack rate, the more significant the change in the swelling rate. Furthermore, model validation confirms that this nonlinear regression model accurately describes the relationship between swelling rate and influencing factors. It offers a more precise prediction tool for infrastructure design and maintenance in expansive soil areas, advancing geotechnical engineering practices.

The effects of altered streamflow types on selected water quality parameters provide useful knowledge and information for prompt water pollution management. This study assesses the impacts of inter- and intra-year seasonal variability in streamflow types on selected water quality parameters. The study uses percentiles, multivariance correlation, and agglomerative hierarchical clustering analysis (AHC) in XLSTAT statistics software to achieve the study aim. Historical dataset for streamflow, rainfall, and selected water quality parameters between 2012 and 2020 for the Mthatha River catchment (MRC), Eastern Cape, South Africa were used to characterize the different seasonal variability impacts with the selected water quality parameters at both the upper and lower reach of the river. The result of the inter and intra-year seasonal variability analyses show that the catchment's flow magnitude varies between 2.0 and 2.7 m3/s in summer while the results of the nonlinear polynomial relationship between the grouped streamflow regime show a coefficient of correlation (R2) values of 0.4264 and 0.5643, suggesting that a mild alteration occurs in the catchment. Decision-makers would find the study useful in controlling the pollutant effluent discharge into the river at different times and maintaining standard effluent requirements as mitigation strategies for sustaining the river ecosystem. HIGHLIGHTS Flow regime characterization impacts on selected water quality variables.; Minimization of hazardous health impacts and aesthetic offensive odour that could pose danger to the lives and health of the community if not properly managed and disposed of.; River water quality assessment in relation to hydrological signatures characteristic in a catchment.; Climate change variability and impact on change streamflow type.;

This investigation focuses on flow energy, a crucial parameter in the design of water structures such as channels. The research endeavors to explore the relative energy loss (ΔEAB/EA) in a constricted flow path of varying widths, employing Support Vector Machine (SVM), Artificial Neural Network (ANN), Gene Expression Programming (GEP), Multiple Adaptive Regression Splines (MARS), M5 and Random Forest (RF) models. Experiments span a Froude number range from 2.85 to 8.85. The experimental findings indicate that the ΔEAB/EA exceeds that observed in a classical hydraulic jump with constriction section. Within the SVM model, the linear kernel emerges as the best predictor of ΔEAB/EA, outperforming polynomial, radial basis function (RBF), and sigmoid kernels. In addition, in the ANN model, the MLP network was more accurate compared to the RBF network. The results indicate that the relationship proposed by the MARS model can play a significant role resulting in high accuracy compared to the non-linear regression relationship in predicting the target parameter. Upon comprehensive evaluation, the ANN method emerges as the most promising among the candidates, yielding superior performance compared to the other models. The testing phase results for the ANN-MLP are noteworthy, with R = 0.997, average RE% = 0.63%, RMSE = 0.0069, BIAS = −0.0004, DR = 0.999, SI = 0.0098 and KGE = 0.995. HIGHLIGHTS This research reinforces the important of investigating the effect of arc-shaped constrictions in the flow path (such as constrictions from bridge piers).; This investigation improves the design of hydraulic control structures.; The performance of the ANN, GEP, MARS, M5, RF, SVM, and regression models has been evaluated using quantitative and qualitative indices (KGE, R, RE%, RMSE, BIAS, DR, scatter index (SI)).;

Previous studies have validated a performance equation (PE) and its generalized version (GPE) in describing the rotated and right-shifted Lorenz curves of organ size (e.g., leaf area and fruit volume) distributions of herbaceous plants. Nevertheless, there are still two questions that have not been adequately addressed by prior work: (i) whether the PE and GPE apply to woody plant species and (ii) how do the PE and GPE perform in comparison with other Lorenz equations when fitting data. To address these deficiencies, we measured the lamina length and width of each leaf on 60 Alangium chinense saplings to compare the performance of the PE and GPE with three other Lorenz equations in quantifying the inequality of leaf area distributions across individual trees. Leaf area is shown to be the product of a proportionality coefficient (k) and leaf length and width. To determine the numerical value of k, we scanned 540 leaves to obtain the leaf area empirically. Using the estimated k, the leaf areas of 60 A. chinense saplings were calculated. Using these data, the two performance equations and three other Lorenz equations were then compared and assessed using the root-mean-square error (RMSE) and Akaike information criterion (AIC). The PE and GPE were found to be valid in describing the rotated and right-shifted Lorenz curves of the A. chinense leaf area distributions, and GPE has the lowest RMSE and AIC values. This work validates the GPE as the best model in gauging variations in leaf area of the woody species.

This article aims to integrate ${k}$ -NN regression, false-nearest neighborhood (FNN), and trustworthiness and continuity (T&C) neighborhood-based measures into an efficient and robust feature selection method to support the identification of nonlinear regression models. The proposed neighborhood ranking-based feature selection technique (NRFS) is validated in three problems, in a linear regression task, in the nonlinear Friedman database, and in the problem of determining the order of nonlinear dynamical models. A neural network is also identified to validate the resulting feature sets. The analysis of the distance correlation also confirms that the method is capable of exploring the nonlinear correlation structure of complex systems. The results illustrate that the proposed NRFS method can select relevant variables for nonlinear regression models.

This study aimed to assess the effect of straw-mulching and sowing time on spring-wheat growth and also evaluate the suitability of nonlinear models (Logistic, Gompertz, Richards and Weibull models) in forecasting crop growth. The experiment followed a factorial design with two factors: three planting times (early, normal and late sowing times) at two different straw-mulching rates (3.75 t/ha straw [mulch] and 0 t/ha straw [no-mulch]). The following treatments were established from these factors: (1) early sowing without straw-mulch (ESW-T), (2) early sowing with straw-mulch (ESW-TS), (3) normal sowing without straw-mulch (NSW-T), (4) normal sowing with straw-mulch (NSW-TS), (5) late sowing without straw-mulch (LSW-T) and (6) late sowing with straw-mulch (LSW-TS). The results showed that, generally mulching improved soil water storage and enhanced biomass growth while early sowing combined with mulching (ESW-TS) gave the greatest results in terms of biomass growth. Furthermore, the logistic model was the most suitable for crop forecasting with a coefficient of determination (r 2) of 0.887 and a change in Akaike information criterion (∆AIC) of 0. The Gompertz model was next with r 2 = 0.884 and ∆AIC = 0.53, followed by the Weibull model (r 2 = 0.883, ∆AIC = 2.83). The Richards model showed the least performance (r 2 = 0.882, ∆AIC = 3.42). These results implied that the adoption of early sowing and straw-mulching could enhance soil water storage, improve wheat yields and improve climate resilience of agroecosystems on the Loess Plateau and similar dryland ecosystems. Furthermore, the logistic regression model can be a useful decision tool for testing the effectiveness of climate adaptation strategies.

Focusing on the situation of the low helium content in natural gas resource in China and the high cost of helium extraction, the OPEX prediction model of helium extraction that based on the Response Surface Methodology (RSM) is proposed. This method applies ASPEN-HYSYS software to simulate the helium extraction process flow for a given product composition, pressure, and temperature; Applying the Design Expert module for Response Surface Methodology(RSM) parameter design, combined with OPEX of existing projects, determine the key influencing factors and upper and lower limits of OPEX, and obtaining the corresponding OPEX for different parameter values; Applying the Box Behnken Design (BBD) principle to optimize the helium extraction process parameters of RSM, based on fitting results and parameter significance verification of second-order regression function, the OPEX prediction model is built.This method is applied to a domestic helium extraction project, and the unit helium extraction cost is between 100 and 119.52 yuan/m3, IRR is 13.37%. The result shows the project has economic benefit, and the method presents a good perspective application.

ABSTRACT: This study assessed distributions associated with Bayesian nonlinear modeling error in the description of total plant dry matteraccumulation (TDMA) of Allium sativumas a function of days after planting (DAP). According to the DIC criterion, Logistic and Gompertzmodels that use student’s t distribution error exhibited the highest DIC with logistic error distribution. In general, the difference of DIC in all the scenarios was not more than 5.The Bayes factor (BF) criterion showed no difference in the Logistic and Gompertzmodel fit when four distributions are used for the errors, where BF values do not exceed 2. Posterior distributions and the usual estimators of Logistic and Gompertz model parameters were similar even forvaried error distribution. In summary, there was no difference in the use of 4 distributions associated with the modeling error of garlic plant growth by the Bayes factor, whereby the results showed that alternating between error distributions significantly changes the number of Markov Chain Monte Carlo (MCMC) iterations.

Using data from the World Value and Financial Access Surveys from 2010 to 2021 in 13 countries in the Middle East and North African (MENA) region, this study investigates the nonlinear impact of general trust (GT) and confidence in banks (CIB) on financial inclusion (FI). In addition, it investigates whether bank risk-taking reinforces the negative effect between trust and financial inclusion. We also estimate a generalized quantile regression, and its results indicate a nonlinear (U-shaped) relationship between GT and FI and a nonlinear (Inverted U-shaped) relationship between CIB and FI. In addition, bank risk-taking strengthens the negative relationship between GT and FI. This is one of the first studies to investigate the relationship between general trust and financial inclusion with a nonlinear regression. Because the MENA region differs from others in terms of culture and religion, our results vary from those in prior papers on non-MENA countries.

Abstract Background An important problem in toxicology in the context of gene expression data is the simultaneous inference of a large number of concentration–response relationships. The quality of the inference substantially depends on the choice of design of the experiments, in particular, on the set of different concentrations, at which observations are taken for the different genes under consideration. As this set has to be the same for all genes, the efficient planning of such experiments is very challenging. We address this problem by determining efficient designs for the simultaneous inference of a large number of concentration–response models. For that purpose, we both construct a D-optimality criterion for simultaneous inference and a K-means procedure which clusters the support points of the locally D-optimal designs of the individual models. Results We show that a planning of experiments that addresses the simultaneous inference of a large number of concentration–response relationships yields a substantially more accurate statistical analysis. In particular, we compare the performance of the constructed designs to the ones of other commonly used designs in terms of D-efficiencies and in terms of the quality of the resulting model fits using a real data example dealing with valproic acid. For the quality comparison we perform an extensive simulation study. Conclusions The design maximizing the D-optimality criterion for simultaneous inference improves the inference of the different concentration–response relationships substantially. The design based on the K-means procedure also performs well, whereas a log-equidistant design, which was also included in the analysis, performs poorly in terms of the quality of the simultaneous inference. Based on our findings, the D-optimal design for simultaneous inference should be used for upcoming analyses dealing with high-dimensional gene expression data.

Strawberry (Fragaria × ananassa Duch.) production can be evaluated as repeated measurements, since the same plant is harvested multiple times during the production season. The objectives were to evaluate the production of fresh mass and fruit number in successive harvests and compare three strawberry clones in two cultivation conditions. Two experiments were carried out in two environmental cultivations: the rural property and the experimental area of the Plant Science Department, Federal University of Santa Maria, Brazil. The parameters of the nonlinear logistic model and their critical points were estimated via bootstrap for each condition and clone for fresh mass and fruit number with accumulated values, depending on the thermal sum accumulated during the production season. For nonlinear regression analysis, the ordinary least squares method was used with the Gauss–Newton algorithm. Confidence intervals were obtained for each parameter and estimated critical points, and they did not cross; the treatments were considered different. There were significant differences between clones and cultivation conditions for fruit mass and number. The nonlinear logistic models, adjusted for mass and number of strawberry fruits, detailed the production season, highlighting the main differences between cultivation conditions and clones.

A nonlinear log-Birnbaum–Saunders regression model with additive errors is introduced. It is assumed that the error term follows a flexible sinh-normal distribution, and therefore it can be used to describe a variety of asymmetric, unimodal, and bimodal situations. This is a novelty since there are few papers dealing with nonlinear models with asymmetric errors and, even more, there are few able to fit a bimodal behavior. Influence diagnostics and martingale-type residuals are proposed to assess the effect of minor perturbations on the parameter estimates, check the fitted model, and detect possible outliers. A simulation study for the Michaelis–Menten model is carried out, covering a wide range of situations for the parameters. Two real applications are included, where the use of influence diagnostics and residual analysis is illustrated.

One technique that is widely used in various fields, including nonlinear target tracking, is the extended Kalman filter (EKF). The well-known minimum mean square error (MMSE) criterion, which performs magnificently under the assumption of Gaussian noise, is the optimization criterion that is frequently employed in EKF. Further, if the noises are loud (or heavy-tailed), its performance can drastically suffer. To overcome the problem, this paper suggests a new technique for maximum correntropy EKF with nonlinear regression (MCCEKF-NR) by using the maximum correntropy criterion (MCC) instead of the MMSE criterion to calculate the effectiveness and vitality. The preliminary estimates of the state and covariance matrix in MCKF are provided via the state mean vector and covariance matrix propagation equations, just like in the conventional Kalman filter. In addition, a newly designed fixed-point technique is used to update the posterior estimates of each filter in a regression model. To show the practicality of the proposed strategy, we propose an effective implementation for positioning enhancement in GPS navigation and radar measurement systems.

Two types of grounding systems are recommended for use in the international standard IEC 62305-3, Part 3: Physical damage to structures and life hazard. One of these is a radial-based grounding system (type-A), which is used in soil resistivities of up to 3000 Ωm and is considered in this paper. It is a well-known fact that during lightning strikes, only a part of the grounding wire contributes to dissipating the lightning current into the surrounding soil. This effective part of the grounding system depends on several features, such as soil resistivity, burial depth, and rise time of the dissipated lightning current. The effect of all of these features on the effective length of the type-A grounding system is explored in this paper. A suitable supervised machine learning regression model is developed, which will enable readers to accurately approximate the effective length of the type-A grounding system for realistic values of input features. The trained model in the paper yielded an R2 value of 0.99998 on the test set. In addition, two simple mathematical formulas are also provided, which produce similar but less accurate results (R2 values of 0.989883 and 0.998557, respectively).

Analysis of dose-response data is an important step in many scientific disciplines, including but not limited to pharmacology, toxicology, and epidemiology. The R package drda is designed to facilitate the analysis of dose-response data by implementing efficient and accurate functions with a familiar interface. With drda it is possible to fit models by the method of least squares, perform goodness-of-fit tests, and conduct model selection. Compared to other similar packages, drda provides in general more accurate estimates in the least-squares sense. This result is achieved by a smart choice of the starting point in the optimization algorithm and by implementing the Newton method with a trust region with analytical gradients and Hessian matrices. In this article, drda is presented through the description of its methodological components and examples of its user-friendly functions. Performance is evaluated using both synthetic data and a real, large-scale drug sensitivity screening dataset.

In many applications, it is important to recognise the distribution of empirical data in almost real time. One of the specific applications is the identification of statistical models for fading in wireless systems of the base station receivers. This is one of the most important problems in spatial diversity. In this paper, we describe the methodology and the results of a nonlinear regression approach for recognising the distribution of the input signal with the values of its parameters. Furthermore, the proposed approach could be used for the real-time recognition of the probability distributions without any prior knowledge about the input signal. To prove its performance, the LevenbergâMarquardt nonlinear least-squares algorithm is tested on a large set of randomly generated signals with the Gamma, Rayleigh, Rician, Nakagami-m, and Weibull distributions. The experimental results demonstrate that this approach is accurate in recognizing statistical distributions from the signal.

Smart wearable sensors are increasingly integrated into everyday life, interfacing with the human body to enable real-time monitoring of biological signals. This study focuses on creating high-sensitivity capacitive-type sensors by impregnating polyester-based 3D spacer fabric with a Carbon Nanotube (CNT) dispersion. The unique properties of conductive particles lead to nonlinear variations in the dielectric constant when pressure is applied, consequently affecting the gauge factor. The results reveal that while the fabric without CNT particles had a gauge factor of 1.967, the inclusion of 0.04 wt% CNT increased it significantly to 5.210. As sensor sensitivity requirements vary according to the application, identifying the necessary CNT wt% is crucial. Artificial intelligence, particularly the Multilayer Perception (MLP) model, enables nonlinear regression analysis for this purpose. The MLP model created and validated in this research showed a high correlation coefficient of 0.99564 between the model predictions and actual target values, indicating its effectiveness and reliability.

The Lorenz curve is used to describe the relationship between the cumulative proportion of household income and the number of households of an economy. The extent to which the Lorenz curve deviates from the line of equality (i.e., y = x) is quantified by the Gini coefficient. Prior models are based on the simulated and empirical data of income distributions. In biology, the Lorenz curves of cell or organ size distributions tend to have similar shapes. When the Lorenz curve is rotated by 135 degrees counterclockwise and shifted to the right by a distance of 2, a three-parameter performance equation (PE), and its generalized version with five parameters (GPE), accurately describe this rotated and right-shifted curve. However, in prior studies, PE and GPE were not compared with the other Lorenz equations, and little is known about whether the skewness of the distribution could influence the validity of these equations. To address these two issues, simulation data from the beta distributions with different skewness values and six empirical datasets of plant (organ) size distributions were used to compare PE and GPE with three other Lorenz equations in describing the rotated and right-shifted plant (organ) size distributions. The root-mean-square error and Akaike information criterion were used to assess the validity of the two performance equations and the three other Lorenz equations. PE and GPE were both validated in describing the rotated and right-shifted simulation and empirical data of plant (organ) distributions. Nevertheless, GPE worked better than PE and the three other Lorenz equations from the perspectives of the goodness of fit, and the trade-off between the goodness of fit and the model structural complexity. Analyses indicate that GPE provides a powerful tool for quantifying size distributions across a broad spectrum of organic entities and can be used in a variety of ecological and evolutionary applications. Even for the simulation data from hypothetical extreme skewed distribution curves, GPE still worked well.

The advection–dispersion equation has been widely used to analyze the intermediate field mixing of pollutants in natural streams. The dispersion coefficient, manipulating the dispersion term of the advection–dispersion equation, is a crucial parameter in predicting the transport distance and contaminated area in the water body. In this study, the transverse dispersion coefficient was estimated using machine learning regression methods applied to oversampled datasets. Previous research datasets used for this estimation were biased toward width-to-depth ratio (W/H) values ≤ 50, potentially leading to inaccuracies in estimating the transverse dispersion coefficient for datasets with W/H > 50. To address this issue, four oversampling techniques were employed to augment the dataset with W/H > 50, thereby mitigating the dataset’s imbalance. The estimation results obtained from data resampling with nonlinear regression method demonstrated improved prediction accuracy compared to the pre-oversampling results. Notably, the combination of adaptive synthetic sampling (ADASYN) and eXtreme Gradient Boosting regression (XGBoost) exhibited improved accuracy compared to other combinations of oversampling techniques and nonlinear regression methods. Through the combined ADASYN–XGBoost approach, it is possible to enhance the transverse dispersion coefficient estimation performance using only two variables, W/H and bed friction effects (U/U*), without adding channel sinuosity; this represents the effects of secondary currents.

Air quality directly affects the health of humans. The health implications of poor air quality are recognized by professionals and the public alike and these concerns have driven both the proliferation of formal sensor networks, but also low-cost sensors which can be used in the home. The advancement of technology in recent years has also led to the rapid development of low-cost sensors. Given that citizens are concerned about the air quality of the environment in which they live, they are turning to the supply of low-cost sensors, as they are affordable. The question of the reliability of measurements from low-cost sensors remains an area of research. In this research work, the optimization of ozone (O3) and nitrogen dioxide (NO2) measurements of low-cost electrochemical air quality sensors is investigated by applying nonlinear regression, using a second-order polynomial equation as a correction factor. The proposed correction method is implementable in IoT devices, as it does not require high computational resources. The results show that the measurements are susceptible to correction, with the effect that the corrected values are close to the actual values obtained by the reference instruments of the Department of Environmental Pollution Control Project of Athens (PERPA), a service of the Greek Ministry of the Environment and Energy.

We propose a novel diffusion process having a mean function equal to the Pareto probability density function up to a constant of proportionality. We examine the probabilistic properties of the proposed model. Then, referring to the problem of statistical inference, we describe the approach employed to tackle the issue of obtaining parameter estimates by maximizing the likelihood function based on discrete sampling. This estimation reduces to solving a set of complex equations, that is accomplished using the simulated annealing algorithm. A simulation study is also given to validate the methodology presented. Finally, using a real-world example of the Moroccan child mortality rate, we obtain the fits and forecasts by employing the suggested stochastic process and nonlinear regression model.

Great importance is had in understanding the current situation of maritime transport and making predictions about its future. Maritime transport is an essential part of transportation, and correctly predicting installed main engine power has great significance in maritime transport with regard to fuel consumption and the generation of emissions. Nonlinear regression is a method with great potential in making predictions, as it allows for more realistic models to be developed using multiple variables. Vessels' dimensions of carrying capacity, gross tonnage, length, and breadth significantly impact the required main engine power. This article will calculate and estimate the installed main engine power for bulk carriers through nonlinear regression using data for the as yet highest number of bulk carriers (n = 9,174 ships) and compare the results with the studies in the literature. The developed model has an accuracy of 93.2% for six different bulk carrier types (Small, Handysize, Handymax, Panamax, Capesize, and Large Capesize). In addition, the study calculates the emissions these ships produce (NOx, SO2, CO2, HC, PM), estimating and demonstrating a nonlinear linear regression model for these ships' emission amounts. The performed analyses have found the main engine power required per unit of load to decrease as ship size increases. However, these analyses also show the emissions generated per unit of load to decrease as size increases, with Large Capesize vessels being found to have the lowest fuel consumption and emission generation per unit of load.

In this study, we aim to estimate parameters of nonlinear model by using ordinary least square. This paper used a real data set on exchange rate, inflation, exports, imports, investments, and budget deficit. The appropriate models of the data are cubic and Johnson Schumacher Model. Both Results of application data and Simulation study appear that the Johnson Schumacher nonlinear regression model is outstanding performance This paper develops the reliable alternative approach of parameter estimation based on the PSO algorithm in the model of nonlinear regression. When the PSO method is used for estimating of nonlinear regression model parameters. Estimating (Forecasting) of the exchange rate using Johnson Schumacher nonlinear model This study presents the following variables: (X1: inflation), (X2: exports), (X3: imports), (X4: investments), (X5: budget deficit). These represent the main variables that affect (Y: exchange rate). The study introduced two nonlinear models cubic and Johnson Schumacher nonlinear model. The Johnson Schumacher nonlinear model shows outstanding performance. The results of the simulation

Despite the existence of computationally efficient tools, the effort for parametric investigations is currently high in industry. In this paper, within the context of Li-Ion batteries, an efficient meta-modelling approach based on the Proper Generalized Decomposition (PGD) is considered. From a suitable design of experiments, a parametric model is trained and then exploited to predict, in real time, the system response to a specific parameter combination. In particular, two different methods are considered, the sparse PGD (sPGD) and the anchored-ANOVA based one (ANOVA-PGD). As a use case for the method the dynamic indentation test of a commercial lithium-ion pouch cell with a cylindrical impactor is selected. The cell model considers a homogenised macroscopic structure suitably calibrated for explicit finite element simulations. Four parameters concerning the impactor are varied, both non-geometric (mass and initial velocity) and geometric (diameter and orientation). The study focuses on multi-dimensional outputs, such as curves and contour plots. Inspired by earlier studies, the sPGD is used to predict the force-displacement curves. As a further development, the impactor kinetic energy curve and the displacement contours are both predicted using its recently developed variant ANOVA-PGD. Moreover, a novel curve alignment technique based on the Gappy Proper Orthogonal Decomposition (Gappy-POD) is suggested here. The meta-model is compared to the results of an FE simulation and the resulting deviations are then discussed.

Abstract In order to adapt to the development of modern education and provide education practitioners with decision‐making suggestions, it is necessary to understand the relationship between the public's attention to basic chemistry education (BCE) and academic attention. However, many existing research is based on a single platform to study social hot information, such as Google Index, Baidu Index, Web of Science, and so on. But they ignore the relationship that exists between the Baidu Index and related academic platforms, and ignore the common information reflected between them. This paper takes advantage of the big data method, through the big data of Baidu Index and the big data obtained from China National Knowledge Internet (CNKI) database, to study the network attention and academic attention of BCE, and propose a CVS‐LSP‐GP framework. It first selects keywords through correlation analysis, secondly uses the data obtained from the first step to construct a nonlinear regression model, and finally combines the results of gray prediction to predict the academic attention of CNKI related to BCE. The research results show that the BCE is mainly affected by the micro‐lecture teaching mode, and relevant education practitioners should integrate the micro‐lecture mode into teaching for more further research and practice.

Nonlinear regression plays a significant role as a method of analysis in different fields like statistics and simulations. While many researches focus on improving technical issues in the processes of nonlinear fitting, the absence of preprocessing, model selection, and validation is causing technical problems in various fields, i.e., statistical analysis and simulation methods. This work introduces a Python package named Copatrec, which facilitates preprocessing of data (i.e., data cleaning, standardization, and outlier detection), nonlinear model selection (from a group of complex behaviors’ mathematical expressions), and validation (by returning a result object that contains validation metrics and visualization functions), as observed in diverse scientific fields, including human-related sciences (e.g., social, political, economics, psychology, and health), and engineering fields like computer science (e.g., computer vision), electrical engineering, as well as fundamental science like physics and chemistry, where a precise characterization of the nonlinear relationship is central to the analytical outcome.

We describe an update to our open-source Python package, PCAfold, designed to help researchers generate, analyze and improve low-dimensional data manifolds. In the current version, PCAfold 2.0, we introduce novel tools and algorithms for assessing and optimizing low-dimensional manifolds. This includes a method that generates a “map” of local feature sizes that can help pinpoint researchers to problematic regions on a manifold. We introduce a novel cost function that characterizes the quality of a manifold topology with a single number. We develop two algorithms for feature selection based on principal component analysis (PCA) that use the cost function as an objective function to minimize. We introduce a quantity of interest (QoI)-aware dimensionality reduction strategy where data projections are computed using an artificial neural network and are directly optimized towards representing various projection-independent and projection-dependent QoIs. We also introduce an implementation of partition of unity networks (POUnets) for efficient reconstruction of QoIs from low-dimensional manifolds based on combining neural network classification with localized polynomial regression. Our software can be broadly applicable in all domains of science and engineering that aim to reduce data dimensionality, as well as in the fundamental research on representation learning.

This paper considers the black-box approximation problem where the goal is to create a regression model using only empirical data without incorporating knowledge about the character of nonlinearity of the approximated function. This paper reports on ongoing work on a nonlinear regression methodology called IBHM which builds a model being a combination of weighted nonlinear components. The construction process is iterative and is based on correlation analysis. Due to its iterative nature, the methodology does not require a priori assumptions about the final model structure which greatly simplifies its usage. Correlation based learning becomes ineffective when the dynamics of the approximated function is too high. In this paper we introduce weighted correlation coefficients into the learning process. These coefficients work as a kind of a local filter and help overcome the problem. Proof of concept experiments are discussed to show

Small-scale photovoltaic (PV) systems are essential for the local energy supply. The most commonly known PV cell is configured as a large-area p–n junction made from silicon, but PV systems today include PV cells of various manufactures and origins. The dependence relationship between current and voltage is nonlinear, known as the current–voltage characteristic. The values of the characteristic equation’s parameters define the working regime of the PV cell. In the present work, the parameter values are iteratively obtained by nonlinear regression for an explicit model. The acceleration of the convergence of these values is studied for an approximation simplifying the iterative calculation in the case of perpendicular offsets. The new estimations of parameters allow for a much faster estimate of the maximum power point of the PV system.

This paper presents the measurement and evaluation of the surfaces of molds produced using additive technologies. This is an emerging trend in mold production. The surfaces of such molds must be treated, usually using laser-based alternative machining methods. Regular evaluation is necessary because of the gradually deteriorating quality of the mold surface. However, owing to the difficulty in scanning the original surface of the injection mold, it is necessary to perform surface replication. Therefore, this study aims to describe the production of surface replicas for in-house developed polymer molds together with the determination of suitable descriptive parameters, the method of comparing variances, and the mean values for the surface evaluation. Overall, this study presents a new summary of the evaluation process of replicas of the surfaces of polymer molds. The nonlinear regression methodology provides the corresponding functional dependencies between the relevant parameters. The statistical significance of a neural network with two hidden layers based on the principle of Rosenblatt’s perceptron has been proposed and verified. Additionally, machine learning was utilized to better compare the original surface and its replica.

Global change in the climate is affecting tree/forest growth. There have been many studies that analyzed climate effects on tree growth. Results presented in these studies showed that the climate had both positive and negative effects on tree growth. The nature (positive/negative) and magnitude of the effects and the climate variables affecting growth depended on tree species. Climate-sensitive diameter growth models are not available for white pine (Pinus strobus L.) and white spruce (Picea glauca (Moench) Voss) plantations. These models are needed to project forest growth and yield and develop forest management plans. Therefore, diameter growth models were developed for white pine and white spruce plantations by incorporating climate variables. Four hundred white pine and white spruce trees (200 per species) were sampled from 80 (40 per species) even-aged monospecific plantations (five trees per plantation) across Ontario, Canada. Diameter–age pairs were obtained from these trees using stem analysis. A nonlinear mixed-effects modeling approach was used to develop diameter growth models. To make the models climate sensitive, model parameters were expressed in term of climate variables. Inclusion of climate variables significantly improved model fit statistics and predictive accuracy. For evaluation, diameters (inside bark) at breast height were estimated for three geographic locations (east, west, and south) across Ontario for an 80-year growth period (2021–2100) under three climate change (emissions) scenarios (representative concentration pathway or RCP 2.6, 4.5, and 8.5 watts m−2). For both species, the overall climate effects were negative. For white spruce, the maximum pronounced difference in projected diameters after the 80-year growth period was in the west. At this location, compared to the no climate change scenario, projected spruce diameters under RCPs 2.6 and 8.5 were thinner by 4.64 (15.99%) and 3.72 (12.80%) cm, respectively. For white pine, the maximum difference was in the south. Compared to the no climate change scenario, projected pine diameters at age 80 under RCPs 2.6 and 8.5 at this location were narrower by 4.54 (13.99%) and 7.60 (23.43%) cm, respectively. For both species, climate effects on diameter growth were less evident at other locations. If the values of climate variables are unavailable, models fitted without climate variables can be used to estimate these diameters for both species.

Blind noise level estimation is a key issue in image processing applications that helps improve the visualization and perceptual quality of images. In this paper, we propose an improved block-based noise level estimation algorithm. The proposed algorithm first extracts homogenous patches from a single noisy image using local features, obtaining the covariance matrix eigenvalues of the patches, and constructs dynamic thresholds for outlier discrimination. By analyzing the correlations between scene complexity, noise strength, and other parameters, a nonlinear discriminant coefficient regression model is fitted to accurately predict the number of redundant dimensions and calculate the actual noise level according to the statistical properties of the elements in the redundancy dimension. The experimental results show that the accuracy and robustness of the proposed algorithm are better than those of the existing noise estimation algorithms in various scenes under different noise levels. It performs well overall in terms of performance and execution speed.

To avoid fabric deformations due to plastic deformations, it is vital to predict how the fabric will behave under load in advance. This was the starting idea for the conducted research. The basic physical and mechanical properties of plain-weave fabric samples with the same density of warp and weft and in various angles were investigated in this paper. A comparison of the experimental and computational modulus of elasticity was performed. Based on the experimental results, a mathematical model and the corresponding mathematical equations of the stress-strain curve for the examined fabric samples were set up. Finally, a statistical analysis of the models and an evaluation of the parameters and representative indicators of the mathematical models have been implemented. The experimental values of the stress-strain curves are well described by all three of the chosen models. Still, mathematical model number three M3 is best suited and can be used with great accuracy in the theoretical calculation of breaking force and elongation for the selected type of fabric.

In mixture with varying concentrations model (MVC) one deals with a nonhomogeneous sample which consists of subjects belonging to a fixed number of different populations (mixture components). The population which a subject belongs to is unknown, but the probabilities to belong to a given component are known and vary from observation to observation. The distribution of subjects’ observed features depends on the component which it belongs to. Generalized estimating equations (GEE) for Euclidean parameters in MVC models are considered. Under suitable assumptions the obtained estimators are asymptotically normal. A jackknife (JK) technique for the estimation of their asymptotic covariance matrices is described. Consistency of JK-estimators is demonstrated. An application to a model of mixture of nonlinear regressions and a real life example are presented.

This study is concerned with the development of an optimum method for identification of supercritical CO2 permeability in thermoplastic films with moderate to excellent barrier properties namely, High-Density Polyethylene (HDPE), Raised-Temperature Polyethylene (PE-RT), Polyvinylidene Fluoride (PVDF) and aliphatic Polyketone (PK) at elevated temperatures (40 °C−82 °C). A high-temperature/high-pressure permeation cell was designed based on the “closed-volume/variable pressure” standard test method. The identified gas transport properties using the time lag method yielded significant error particularly for PVDF and PK, which was ascribed to the sole reliance on the accumulated pressure-rate in steady-state. This error was minimized using the Non-Linear Regression (NLR) by utilizing the full range of measured data including the transient state. The coefficient of determination between the measured and modeled data using NLR was quantified above 0.99 for all the polymers at the entire examined temperature range. The 1.4 % higher degree of crystallinity and 28.5 % smaller spherulite size caused 13.3 % higher diffusivity and 8.6 % lower solubility in PE-RT when compared with HDPE at 82°C. As a result of this trade-off, PE-RT exhibited only 3.5 % higher permeability than HDPE. The developed generalized temperature-dependent model provided the essential data for design optimization of gas barrier performance in multilayer high-temperature pressure-vessels.

Abstract The continuous generation of waste resulting from the industrial activities of humans has significantly been on the rise, especially liquid wastes emanating from cassava processing mills, which is a major cause for concern in developing countries. This study focused on the preparation of H3PO4 activated periwinkle carbon (APSC) and use in the removal of cyanide in cassava wastewater. The influence of variables such as pH, adsorbent dosage, contact time, and different cyanide concentrations was investigated in batch procedures. Results from the batch studies reveal a strong pH-dependent adsorption process with optimum cyanide removal occurring at pH 8. An equilibrium time of 80 min and adsorbent dosage of 3.0 g gave the highest percentage of cyanide adsorbed at 83.93%. The Pseudo-first-order, Pseudo-second-order, and Elovich kinetic models were used for the analysis of experimental data while equilibrium data analysis using Langmuir, Freundlich, and Redlich–Peterson was carried out to determine the best-fit isotherm model. The Coefficient of determination (r 2), Sum of square error (SSE), and Chi-square ( $$\chi^{2}$$ χ 2 ) were used to estimate the error deviations between the predicted and the experimental models using nonlinear regression analysis to determine models that best explain the adsorption process. Kinetic data fitted well to the Elovich and Pseudo-second-order kinetic model which implies chemisorption as the dominant adsorption process. The Redlich–Peterson and Langmuir model best describes the adsorption process suggesting mono-layer adsorption with the monolayer adsorption capacity of APSC found to be 2.856 mg.g−1.

Generalized additive models provide a flexible and easily-interpretable method for uncovering a nonlinear relationship between response and covariates. In many situations, the effect of a continuous covariate on the response varies across groups defined by the levels of a categorical variable. When confronted with a considerable number of groups defined by the levels of the categorical variable and a factor‐by‐curve interaction is detected in the model, it then becomes important to compare these regression curves. When the null hypothesis of equality of curves is rejected, leading to the clear conclusion that at least one curve is different, we may assume that individuals can be grouped into a number of classes whose members all share the same regression function. We propose a method that allows determining such groups with an automatic selection of their number by means of bootstrapping. The validity and behavior of the proposed method were evaluated through simulation studies. The applicability of the proposed method is illustrated using real data from an experimental study in neurology.

In the paper, the stochastic method of global extremum search is discussed, modified and tested. The method is based on normal distribution modeling and provides covariance matrix adaptation. The method is iterative; a genetic algorithm has been developed on its basis. The coordinates of the trial points of each generation are determined using the ”best” points of the previous generation and the values of standard normal random variables. Thus, at each stage of the search, a normal distribution is simulated, and its parameters (the mean and the covariance matrix) are estimated through the positions of the ”best” points of the previous generation. In this case, there is no need to calculate, store and transform the covariance matrix, which is indisputable advantage of this method. Practice has shown that the dispersion ellipsoid of normal distribution shrinks rapidly with generation number increasing, which can lead to an excessive narrowing the scanning area and obtaining a local extremum instead of a global one. The proposed modification of the method avoids this situation. The trial points are divided into two groups, which are simulated using normal random variables with different standard deviations, at least one of which is greater than 1. Thus, a kind of mutation of the population is carried out, which makes it possible to provide a sufficient number of sample points both near the “best” one and at a distance from it. The modified genetic algorithm is applied to solving the problem of estimating the parameters of nonlinear parametric regression. A successful minimization of the multiextremal function is performed. The stochastic method is used in combination with directional. The numerical results presented confirm the effectiveness of the introduced modification of the genetic algorithm and make it possible to choose from two directed methods the more efficient one for the problem under consideration

The paper is devoted to the formal description of the running time of the user task on some virtual nodes in the computing network. Based on the probability theory framework, this time represents a random value with a finite mean and variance. For any class of user task, these moments are the functions of the node resources, task numerical characteristics, and the parameters of the current node state. These functions of the vector arguments can be treated as some surfaces in the multidimensional Euclidean spaces, so the proposed models are called the stochastic time complexity surfaces. The paper also presents a class of functions suitable for the description of both the mean and variance. They contain unknown parameters which should be estimated. The article includes the statement of the parameter identification problem given the statistical results of the node stress testing, recommendations concerning the test planning, and preprocessing of the raw experiment data. To illustrate the performance of the proposed model, the authors design it for an actual database application—the prototype of the passengers’ personal data anonymization system. Its application functions are classified into two user task classes: the data anonymization procedures and fulfillment of the statistical queries. The authors identify the stochastic time complexity surfaces for both task types. The additional testing experiments confirm the high performance of the suggested model and its applicability to the solution of the practical providers’ problems.

More and more electronic devices are integrated into the modern vehicles with the development of intelligent vehicles.There are various design flaws and vulnerabilities hidden in a large number of hardware, firmware and software.Therefore, the vulnerabilities of intelligent vehicles have become the most important factor affecting the vehicle safety.The safety of vehicles is seriously affected by the disclosure of a large number of vulnerabilities, and the wide application of smart cars is also restricted.Vulnerability management is an effective method to reduce the risk of vulnerabilities and improve vehicle security.And vulnerability scoring is one the important step in vulnerability management procedure.However, current method have no capability assessing automotive vulnerabilities reasonably.In order to handle this problem, a vulnerability scoring model for intelligent vehicles was proposed, which was based on CVSS.The attack vector and attack complexity were optimized, and property security, privacy security, functional safety and life safety were added to characterize the possible impact of the vulnerabilities according to the characteristics of intelligent vehicles.With the machine learning method, the parameters in CVSS scoring formula were optimized to describe the characteristics of intelligent vehicle vulnerabilities and adapt to the adjusted and new added weights.It is found in case study and statistics that the diversity and distribution of the model are better than CVSS, which means the model can better score different vulnerabilities.And then AHP is used to evaluate the vulnerability of the whole vehicle based on the vulnerability score of the model, a score is given representing the risk level of whole vehicle.The proposed model can be used to evaluate the severity of information security vulnerabilities in intelligent vehicles and assess the security risks of the entire vehicle or part of the system reasonably, which can provide an evidence for fixing the vulnerabilities or reinforcing the entire vehicle.

More and more electronic devices are integrated into the modern vehicles with the development of intelligent vehicles. There are various design flaws and vulnerabilities hidden in a large number of hardware, firmware and software. Therefore, the vulnerabilities of intelligent vehicles have become the most important factor affecting the vehicle safety. The safety of vehicles is seriously affected by the disclosure of a large number of vulnerabilities, and the wide application of smart cars is also restricted. Vulnerability management is an effective method to reduce the risk of vulnerabilities and improve vehicle security. And vulnerability scoring is one the important step in vulnerability management procedure. However, current method have no capability assessing automotive vulnerabilities reasonably. In order to handle this problem, a vulnerability scoring model for intelligent vehicles was proposed, which was based on CVSS. The attack vector and attack complexity were optimized, and property security, privacy security, functional safety and life safety were added to characterize the possible impact of the vulnerabilities according to the characteristics of intelligent vehicles. With the machine learning method, the parameters in CVSS scoring formula were optimized to describe the characteristics of intelligent vehicle vulnerabilities and adapt to the adjusted and new added weights. It is found in case study and statistics that the diversity and distribution of the model are better than CVSS, which means the model can better score different vulnerabilities. And then AHP is used to evaluate the vulnerability of the whole vehicle based on the vulnerability score of the model, a score is given representing the risk level of whole vehicle. The proposed model can be used to evaluate the severity of information security vulnerabilities in intelligent vehicles and assess the security risks of the entire vehicle or part of the system reasonably, which can provide an evidence for fixing the vulnerabilities or reinforcing the entire vehicle.

The diameter at breast height (DBH) is the most important independent variable in biomass allometry models based on metabolic scaling theory (MST) or geometric theory. However, the fixed position DBH can be misleading in its use of universal scaling laws and lead to some deviation for the biomass model. Therefore, it is still an urgent scientific problem to build a high-precision biomass model system. A dataset of 114 trees was destructively sampled to obtain dry biomass components, including stems, branches, and foliage, and taper measurements to explore the applicability of biomass components to allometric scaling laws and develop a new system of additive models with the diameter in relative height (DRH) for each component of a Larch (Larix principis-rupprechtii Mayr) plantation in northern China. The variable exponential taper equations were modelled using nonlinear regression. In addition, applying nonlinear regression and nonlinear seemingly unrelated regression (NSUR) enabled the development of biomass allometric models and the system of additive models with DRH for each component. The results showed that the Kozak’s (II) 2004 variable exponential taper equation could accurately describe the stem shape and diameter in any height of stem. When the diameters in relative height were D0.2, D0.5, and D0.5 for branches, stems, and foliage, respectively, the allometric exponent of the stems and branches was the closest to the scaling relations predicted by the MST, and the allometric exponent of foliage was the most closely related to the scaling relations predicted by geometry theory. Compared with the nonlinear regression, the parameters of biomass components estimated by NSUR were lower, and it was close to the theoretical value and the most precise at forecasting. In the study of biomass process modelling, utilizing the DRH by a variable exponential taper equation can confirm the general biological significance more than the DBH of a fixed position.

Perceiving the uncertainty of the measurement has been changing over the past centuries, reflecting the advancement in the experimental techniques, the urge for reliable and reproducible measurement methodology, and development of mathematical data processing and evaluating algorithms. From the historical perspective, the concepts of considering the measurement uncertainty were firstly introduced with geographic and cartographic measurements. In this context, the works of Tobias Mayer on lunar landscape measurements are widely highlighted which, at that time, presented innovative approaches in data processing with the method of averages and pioneeringly addressed the issue of measurement error. In this study, we analyze in details the Mayer’s set of 27 non-linear equations with 3 unknown parameters and discuss the effect of Mayer’s linearization and subsequent mathematical procedures on the accuracy of the parameter values in contrast with the results from rigorous treatment of non-linear regression model involving the least-square method. In particular, we compare the values of the unknown parameters and their uncertainties in several variants in the linearized and non-linearized model, providing monitoring of a small deviation of the Mayer’s linearization. The results, presented here, show that despite the conceptual and computational simplification of the Mayer’s method, such an approach to data processing can be exploited, with an acceptable level of accuracy, in several practical situations even today.

The paper considers the possibility of using thin films based on samarium sulfide, as well as composite systems of metal-oxide semiconductors doped with rare-earth elements, as radiation-resistant sensitive materials for monitoring leaks of rocket fuel components. The data of electrophysical studies of the obtained sensor layers were processed within the framework of the semiconductor Fourier spectroscopy constructed in relation to gas-analytical systems and the nonlinear regression algorithm of selective calibration. The latter solves really the problem of sensors’ selectivity including distinguishing the substances of the same homology such as methane, propane and n-hexane.

The capacitive voltage transformer (CVT) is a widely-used voltage measuring instrument directly related to the safety and security of the power system operation. As the CVT’s range of application scenarios is getting wider, its environmental adaptability requirements become more stringent. Therefore, the CVT measurement error generated from the atmospheric environment is becoming a matter. This paper proposes a CVT measurement error correction method by employing a double regression-based particle swarm optimization compensation algorithm (DR-PSO). In DR-PSO, the double regression algorithm is used to calculate the rough result, and the theoretical formula is used to calculate the multi-type disturbance. Finally, the particle swarm optimization is used to determine the optimal influence factor matrix and obtain accurate results. Based on the transformer’s multidimensional operating data, the DR-PSO can be trained by the empirical data, and then the algorithm shall be used to correct CVT errors based on the real-time data. The test by actual data of State Grid proved that the root mean squared error of the proposed algorithm’s phase error was only 0.13, and the mean absolute error of the amplitude error is only 0.0009. Compared with other algorithms such as the equal weight method, information entropy method, and multiple regression method, the proposed algorithm can calculate the measurement error with the highest accuracy.

In this study, one-dimensional gamma ray source positions are estimated using a plastic scintillating optical fiber, two photon counters and via data processing with a machine learning algorithm. A nonlinear regression algorithm is used to construct a machine learning model for the position estimation of radioactive sources. The position estimation results of radioactive sources using machine learning are compared with the theoretical position estimation results based on the same measured data. Various tests at the source positions are conducted to determine the improvement in the accuracy of source position estimation. In addition, an evaluation is performed to compare the change in accuracy when varying the number of training datasets. The proposed one-dimensional gamma ray source position estimation system with plastic scintillating fiber using machine learning algorithm can be used as radioactive leakage scanners at disposal sites.