Univariate Nonlinear Regression Research Articles

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

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

An Investigation of Molecular Property Prediction and Classification Based on Machine Learning Algorithms

With the rapid advancement of science and technology, chemical and physical research has entered an era of complexity and high dimensionality, where traditional research paradigms struggle to optimize vast chemical parameter searches. The Machine Chemist platform was developed in this context, leveraging big data and intelligent models to automate chemical synthesis, characterization, and testing processes. This study aims to predict the y1, y2 and y3 properties and classes of 2,580 molecules based on their physicochemical properties and improve model accuracy through data analysis and modeling. Data preprocessing involved removing missing values, duplicates, and outliers using the quartile method, resulting in an analyzable dataset. A scatter plot of y2 and id suggested a univariate polynomial function relationship, leading to the construction of a univariate nonlinear regression model. The model achieved a high prediction accuracy, with a low root mean square error and a high coefficient of determination. Additionally, the relationship between class and y1~y3 , x1~x100 indicators was examined, revealing mostly nonlinear relationships. A random forest model was established to classify 2,580 molecules into 1 to 4 classes based on the properties of 200,000 chemical molecules. The model's performance was evaluated using decision trees, confusion matrices, precision, and recall metrics. Finally, the SHAP method assessed the impact of feature indicators on classification outcomes, contributing to the development of a reliable molecular category prediction model.

Mathematical prediction model construction of network packet loss rate and nonlinear mapping user experience under the Internet of Things

Abstract In order to further improve the prediction accuracy, the network packet loss rate (PLR) prediction mathematical model based on the Internet of Things (IoTs) was proposed. First, the network data transmission module was established, and the network PLR prediction process was developed based on IoTs; second, the prediction framework of PLR was designed to obtain more accurate prior information. The relationship between PLR and user experience quality QoE is univariate and nonlinear. The mapping between PLR and user experience quality QoE is established using univariate nonlinear regression analysis; finally, a mathematical model of network PLR prediction is constructed to further improve the prediction accuracy. Experimental results show that the delays of network nodes are all within 5 s, which can ensure the real-time nature of data transmission. When the total number of packets and the number of lost packets are the same, the PLR predicted by the mathematical model designed by the authors is consistent with the actual PLR. Conclusion: The prediction effect of the model is better and has higher promotion value.

Socio-economic development drives solid waste management performance in cities: A global analysis using machine learning

Mismanaged municipal solid waste (MSW), the major source of plastics pollution and a key contributor to climate forcing, in Global South cities poses public health and environmental problems. This study analyses the first consistent and quality assured dataset available for cities distributed worldwide, featuring a comprehensive set of solid waste management performance indicators (Wasteaware Cities Benchmark Indicators – WABI). Machine learning (multivariate random forest) and univariate non-linear regression are applied, identifying best-fit converging models for a broad range of explanatory socioeconomic variables. These proxies describe in a variety of ways generic levels of progress, such as Gross Domestic Product – Purchasing Power per capita, Social Progress Index (SPI) and Corruption Perceptions Index. Specifically, the research tests and quantitatively confirms a long-standing, yet unverified, hypothesis: that variability in cities' performance on MSW can be accounted for by socioeconomic development indices. The results provide a baseline for measuring progress as cities report MSW performance for the sustainable development goal SDG11.6.1 indicator: median rates of controlled recovery and disposal are approximately at 45 % for cities in low-income countries, 75 % in lower-middle, and 100 % for both upper-middle and high-income. Casting light on aspects beyond the SDG metric, on the quality of MSW-related services, show that improvements in service quality often lag improvements in service coverage. Overall, the findings suggest that progress in collection coverage, and controlled recovery and disposal has already taken place in low- and middle-income cities. However, if cities aspire to perform better on MSW management than would have been anticipated by the average socioeconomic development in their country, they should identify ways to overcome systemic underlying failures associated with that socioeconomic level. Most alarmingly, ‘business as usual’ development would substantially increase their waste generation per capita unless new policies are found to promote decoupling.

Analysis of Longitudinal Guided Wave Propagation in the Functionally Graded Hollow Cylinder Using State-Vector Formalism and Legendre Polynomial Hybrid Approach

A numerical approach for analyzing the guided wave propagation behavior in a functionally graded material (FGM) hollow cylinder is presented. Based on the three-dimensional linear elasticity theory, the state matrix form of displacement and stress component is introduced into the differential governing equation. Combining with boundary conditions, the dispersion characteristic equations can be constructed. Meanwhile, taking the orthogonal completeness of Legendre series into consideration, the exhausting root findings of transcendental equation can be avoided, and it transforms the redundant integral operators into analytical expressions by means of its recursive properties. Moreover, it is not only unnecessary to stratify FGMs, and introducing the univariate nonlinear regression to modelling the arbitrary gradient distribution, and transforming the redundant integral operator into an analytical expression by means of recursive property. It should be pointed out that the coefficient matrix consists only zero and constant terms, which are related to the elastic constants and normalized wave number. And it provides a fast and effectively approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Meanwhile, the proposed method can get rid of the exhausted root-finding algorithm, and accordingly distinguish the different modes and the dispersion curves simultaneously. Finally, the typical non-stratified computation of dispersion curves of longitudinal guided wave for FGM hollow cylinder is realized. The accuracy of the proposed method is further demonstrated through comparison with the available data from Legendre polynomial method. Several numerical cases about iron based alumina FGM cylinder are studied, and the convergence of the present polynomial approach is discussed. Then the effect of the circumferential wave number, gradient variation, diameter-thickness ratio on the dispersion characteristics are illustrated. Moreover, the distribution characteristics of displacement and stress profiles of F(1,1) mode at a given frequency are discussed in detail. It is shown that the state-vector formalism and Legendre polynomial hybrid approach is a powerful tool in solving wave motions in FGM elastic cylinder, which lays a theoretical foundation for the non-destructive evaluation and quantitative characterization of the gradient structure characteristics of functionally graded hollow cylinder.

A novel liquid metal sensor with three microchannels embedded in elastomer

In this paper, a new type of liquid metal sensor structure is designed and fabricated, in which three microchannels, including one upper channel and two lower channels, are symmetrically arranged in PDMS (polydimethylsiloxane) elastomer. With this structure, pressure can be sensed by detecting resistance, and strain and curvature can also be sensed by detecting capacitance and resistance. The cross-sectional deformational of microchannel 1 in the pressure sensor and the corresponding resistance variation are deduced. The initial capacitance of the strain sensor is increased through the series–parallel connection of three microchannels, which effectively enlarges the capacitance variation per unit strain. Regression analysis of the experimental data is performed, and the univariate nonlinear regression can be simplified to a multivariate linear regression. Moreover, tests on the different commonly employed temperature (0 °C–20 °C) are conducted, it is found from the experimental results that the effect of commonly employed temperature on sensors can be neglected. The experimental data from the pressure sensor are in good agreement with the theoretical curve, especially in the range of 0–4 MPa. Within the measurable strain range (0%–30%), the experimental values of the strain sensors are in good agreement with the theoretical values. In addition, the analytical theory is developed to explain the performance of the sensor, although it can not explain all the observed data well.

Modeling guided wave propagation in functionally graded plates by state-vector formalism and the Legendre polynomial method

A numerical method is presented for the investigation of the propagation characteristic of guided waves in functionally gradient material (FGM) plates. Based on the State-vector formalism and Legendre polynomial method, the typical non-stratified computing of dispersion curves of FGMs is realized, by introducing the univariate nonlinear regression to optimize the arbitrary gradient distribution of material component. Comparing with the conventional Matrix method, the proposed method avoids the exhausting root-locating algorithm of solving the transcendental equation by a single-variable scanning process. This method turns it into an algebraic eigenvalue problem, which mainly depends on the orthogonal completeness and strong recursive property of Legendre polynomial series. It provides a fast and flexible approach to extracting the dispersion curves, displacement distribution and stress profile, simultaneously. Results from chrome-ceramic FGM plate are compared with those from the previous articles to confirm the feasibility and accuracy of the proposed method. Then, this approach is further applied to iron based alumina FGM. The dispersion curves with different gradient function are calculated to illustrate the influence of the gradient variation. Moreover, the influence of the cut-off order of Legendre orthogonal polynomials on the convergence of dispersion curves is also revealed through numerical examples. Utilizing the mapping relationship between the gradient distribution and the propagation characteristics, it gives theoretical support for nondestructive evaluation and quantitative estimation of the structural characteristics of FGM plates.

Prediction of corn price fluctuation based on multiple linear regression analysis model under big data

This paper mainly analyzes the changing trend of corn price and the factors that affect the price of corn. Using the data and regression analysis, the univariate nonlinear and multivariate linear regression models are established to predict the corn price, respectively. First, this paper establishes a univariate nonlinear regression model with time as the independent variable, and corn price is used as the dependent variable through the analysis of the trend of big data related to Chinese corn price from 2005 to 2016 by MATLAB, which is the computer-based analysis and processing method. The variation of the maize price with time was fitted. To a certain extent, the price trend of corn is predicted. However, the estimated price of corn in 2017 with this model will deviate from the actual value. According to the changes of related policies in our country, we analyzed the deviation of the original model, and the relationship between supply and demand is the main underlying factor that affects the price of corn. This paper selects maize-related big data from 2005 to 2016, we set its production consumption, import and export volume as independent variables, and we still use maize price as the dependent variable to establish a multiple linear regression model. At this stage, the time series analysis of the independent variable has obtained the forecast value of each independent variable in 2017, and then the model is used to predict the corn in 2017 more accurately.

A New Equation for Predicting Evolution of Oral Pain in Orthodontic Treatment: A Longitudinal, Prospective Cohort Study.

To develop an equation capable of relating the evolution of oral pain to the time elapsed, measured from the moment of dental archwire fitting and identifying when pain begins, peaks, and ends; and secondly, to compare pain during orthodontic treatment in relation to archwire material (steel or nickel-titanium [Ni-Ti]) and position (maxillary or mandibular) and patient age (child, teenager, or adult) and gender (male or female). A longitudinal prospective cohort study was conducted of 112 patients who filled in a scale to evaluate pain, noting the times when the pain occurred. The total sample consisted of 60 males and 52 females with a mean (± standard deviation [SD]) age of 19.8 ± 6.2 years. The sample was divided into five groups depending on archwire material and position, and patient age and gender. A univariate four-way ANOVA model was performed to compare mean pain levels between groups. Bonferroni test was used for multiple comparisons. A univariate nonlinear regression model was carried out for pain level, 95% confidence intervals (95% CI) were calculated, and the statistic R² was used. An equation was developed based on pain levels in relation to time elapsed, measured from the moment when the archwire had been fitted in the mouth. The equation had three coefficients related to mean pain values: overall pain, peak pain, and how pain decreased. It fitted all study groups with a correlation coefficient > 0.9. The model showed that pain levels were influenced by archwire material and patient gender and age, but not archwire position. The equation reproduced the data registered and can be applied to studies of pain derived from archwires, and this methodology could be used for other external agents fitted in the mouth. Patients receiving dental treatment involving external agents can be made aware of the pain they can expect to experience. This will enable them to distinguish expected pain from other pain, which will help them identify other pathologies requiring medical attention and to approach treatment with better motivation since the pattern of pain evolution is known in advance.

Modelling of the Elasticity Modulus for Rock Using Genetic Expression Programming

In rock engineering projects, statically determined parameters are more reflective of actual load conditions than dynamic parameters. This study reports a new and efficient approach to the formulation of the static modulus of elasticityEsapplying gene expression programming (GEP) with nondestructive testing (NDT) methods. The results obtained using GEP are compared with the results of multivariable linear regression analysis (MRA), univariate nonlinear regression analysis (URA), and the dynamic elasticity modulus (Ed). The GEP model was found to produce the most accurate calculation ofEs. The proposed approach is a simple, nondestructive, and practical way to determineEsfor anisotropic and heterogeneous rocks.

Impaired GFR is the most important determinant for FGF-23 increase in chronic kidney disease

Objectives It is unclear whether fibroblast growth factor-23 (FGF-23) increases in response to phosphate accumulation or to decrease clearance in chronic kidney disease (CKD) as is the case with other low molecular weight proteins such as cystatin C (CysC). Design and methods This cross-sectional study measured serum FGF-23, CysC, and other serum markers of bone metabolism in 69 patients, aged 18 months–24 years, with various stages of CKD (eGFR = 11–214 mL/min). Results FGF-23 levels were significantly correlated with CysC and parathyroid hormone levels (PTH) on univariate non-linear regression analysis. In multivariate linear regression analysis, log (CysC) ( β = 0.660, p < 0.0001), log (PTH) ( β = 0.038, p = 0.37), and phosphate ( β = 0.222, p = 0.028) explained 69.1% of the variance of FGF-23. Conclusions CysC had the largest unique contribution to FGF-23 variance in this model, supporting the hypothesis that renal clearance may be the most responsible factor for elevated FGF-23 levels in early stages of CKD.

SYMMETRIC NONLINEAR REGRESSION

ABSTRACTAn estimation tool for symmetric univariate nonlinear regression is presented. The method is based on introducing a nontrivial set of affine coordinates for diffeomorphisms of the real line. The main ingredient making the computations possible is the Connes‐Moscovici Hopf algebra of these affine coordinates.

Designing experiments for single output multilayer perceptrons

Where should a researcher conduct experiments to provide training data for a multilayer perceptron This question is investigated and a statistical method for selecting optimal experimental design points for multilayer perceptrons is introduced. Two-class discrimination problems are examined in which the multilayer perceptron is viewed as a univariate nonlinear regression model. A selection criterion is developed based on the volume of the joint confidence ellipsoid for the weights in a multilayer perceptron. The criterion is minimized to find optimal design points. Minimization is accomplished using Powell's algorithm when the feature space is continuous and a discrete exchange algorithm when the feature space is discrete. An example is used to demonstrate the superiority of optimally selected design points over randomly chosen points and points chosen in a grid pattern. In addition, two measures are developed to rank the design points in terms of their relative importance.

Functional approach to the asymptotic normality of the non-linear least squares estimator

The derivation of the asymptotic normality LSE's under univariate non-linear regression models is presented based on the weak convergence of the natural random field generated by the sum of squared residuals. Some examples, showing that neglecting the condition of uniform convergence leads to serious errors are presented. This approach is analogous to that of Le Cam's for the case of a known smooth family of distributions.

Une nouvelle forme du test de la matrice d'information

We develop a new form of the information matrix test for a wide variety of statistical models, and present full details for the special case of univariate nonlinear regression models. Chesher (1984) showed that the implicit alternative of the information matrix test is a model with random parameter variation. We exploit this fact by constructing the test against an explicit alternative of this type. The new test is computed using a double-length artificial regression, instead of the more conventional outer product of the gradient regression, which although easy to use, is known to give test statistics with distributions very far from the asymptotic nominal distribution even in rather large samples. The new form on the other hand performs remarkably well, at least in the context of regressions models. Some approximate finite-sample distribution are calculated and lend sup port to the use of the new form of the test.

Nonlinear Statistical Models.

Univariate Nonlinear Regression. Univariate Nonlinear Regression: Special Situations. A Unified Asymptotic Theory for Nonlinear Models with Regression Structure. Univariate Nonlinear Regression: Asymptotic Theory. Multivariate Nonlinear Regression. Nonlinear Simultaneous Equations Models. A Unified Asymptotic Theory for Dynamic Nonlinear Models. References. Index.