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The stabilization potentials of NWPA and the CBR optimization were investigated on the treated olokoro lateritic soil. The soil was classified as an A-2-7 soil according to AASHTO classification method. From the stabilization procedure, it has been found that the admixture improved the strength characteristics of the stabilized lateritic soil for use as base material in pavement construction. With the laboratory results, a nonlinear regression relationship was formulated through the multiple regression algorithms for the California bearing ratio (R) as a dependent variable with optimum water content (w), maximum dry density (D), and percentage by weight additive of NWPA (SA) as the independent variables. The nonlinear relationship was linearized to enable the optimization operation with Simplex Linear Programming (Optimization) to be conducted. This iteration procedure was conducted and the results showed that the CBR (R) was optimized at Rmax=219.16% with x1= 48.103, x2=4.833, x3=13.45, and x4= 0.948 in the stabilization of lateritic soils with NWPA as an admixture applied in the percentages of 0, 3, 6, 9, 12, and 15%.

In the present study, a three-layer artificial neural network (ANN) and nonlinear regression models were developed to predict the performance of biogas production from the anaerobic hybrid reactor (AHR). Firstly, the performance of an AHR which is filled with perlite (2.38–4.36 mm) at fill rates of 1/3, 1/4 and 1/5 for the treatment of synthetic wastewater was investigated at a loading rate of 5, 7.5, 10, 12.5 and 15 kg COD m−3 day with 12, 24, 36 and 48 h of hydraulic retention time (HRT) under mesophilic conditions (37 ± 1 °C). In this study, experimental data were used to estimate the biogas production rate with models produced using both ANNs and nonlinear regression methods. Moreover, ten related variables, such as reactor fill ratio, influent pH, effluent pH, influent alkalinity, effluent alkalinity, organic loading rate, effluent chemical oxygen demand, effluent total suspended solids, effluent suspended solids and effluent volatile suspended solids, were selected as inputs of the model. Finally, ANN and nonlinear regression models describing the biogas production rate were developed. The R2, IA, FA2, RMSE, MB for ANNs and nonlinear regression models were found to be 0.9852 and 0.9878, 0.9956 and 0.9945, 0.9973 and 0.9254, 217.4 and 332, 36 and 222, respectively. The statistical quality of ANNs and nonlinear regression models were found to be significant due to its high correlation between experimental and simulated biogas values. The ANN model generally showed greater potential in determining the relationship between input data and the biogas production rate according to statistical parameters (except R2 and R). The results showed that the proposed ANNs and nonlinear regression models performed well in predicting the biogas production rate of AHR on behalf of avoiding economic and environmental sustainability problems.

Char produced from lignocellulosic biomass via slow pyrolysis have become one of the most feasible alternatives that can partially replace the utilisation of fossil fuels for energy production. In this study, the relationship between compositions of lignocellulosic biomass, operating conditions of slow pyrolysis, and characteristics of produced char have been analysed by using multiple nonlinear regression (MnLR) and artificial neural networks (ANN). Six input variables (temperature, solid residence time, production capacity, particle size, and fixed carbon and ash content) and five responses (char yield, and fixed carbon, volatile matter, ash content, HHV of produced char) were selected. A total of 57 literature references with 393–422 datasets were used to determine the correlation and coefficient of determination (R2) between the input variables and responses. High correlation results (>0.5) existed between pyrolysis temperature and char yield (-0.502) and volatile matter of produced char (-0.619), ash content of feedstock and fixed carbon (-0.685), ash content (0.871) and HHV (-0.571) of produced char. Whilst the quadratic model was selected for the regression model, then the model was further optimised by eliminating any terms with p-values greater than 0.05. The optimised MnLR model results showed a reasonable prediction ability of char yield (R2= 0.5579), fixed carbon (R2= 0.7763), volatile matter (R2= 0.5709), ash (R2= 0.8613), and HHV (R2= 0.5728). ANN model optimisation was carried out as the results showed “trainbr” training algorithm, 10 neurons in the hidden layer, and “tansig” and “purelin” transfer function in hidden and output layers, respectively. The optimised ANN models had higher accuracy than MnLR models with the R2greater than 0.75, including 0.785 for char yield, 0.855 for fixed carbon, 0.752 for volatile matter, 0.951 for ash and 0.784 for HHV, respectively. The trained models can be used to predict and optimise the char production from slow pyrolysis of biomass without expensive experiments.

We report results of experimental research into the process of acidic extraction of pectin-containing raw material (beet pulp) using the new model of the stirring element compared with the conventional grid stirrer. We have designed the experimental installation and devised a procedure for processing the results of studying the extraction process of pectin substances from pectin-containing raw materials (beet pulp), using the new combined stirring element. Mathematical models were constructed in the form of nonlinear regression equations based on the multifactor experiment planning method that employed input parameters of temperature, duration, and hydromodule. It was established that the principal influence on a change in the output parameters is exerted by the input variables of temperature and duration of the process. We show graphical dependences for quantitative and qualitative characteristics of pectin extracts (pectic substances concentration, molecular weight, complex- and gel-forming capability) depending on the input parameters of temperature and duration of the process for extraction of pectic substances. An analysis of these characteristics allowed us to determine the rational input parameters for the process of extraction of pectin substances. The rational working parameters of the process of acidic extraction of pectin substances from sugar beet pulp with the application of the new method for intensifying the process, are: temperature is 60...70 °C, duration is 1…1.1 hours, and hydromodule is 8...10. The purpose of this study was to intensify the extraction of pectic substances from pectin-containing raw materials, to improve technical level of the extraction process and to implement the developed method under industrial conditions. Based on the research results, the feasibility of the new method for intensification was established. Further implementation of these results in the food and processing industries would make it possible to produce a wide assortment of pectin-products (extracts, liquid and dry pectin concentrates).

Banana (Musa spp.) is one of the most nutritious and consumed fruits, especially in tropical countries. The drying of the fruit is an alternative against the injuries suffered, mainly during the post-harvest process. Thus, the knowledge of the physical properties of the product that is intended to be processed has a big importance for the dimensioning of equipment. Therefore, the objective of this work was to study the drying kinetics of the banana, transforming it into dried banana, besides evaluating the volumetric contraction suffered during drying. The bananas were dried in an oven at temperatures of 70, 60 and 50 ºC. The volumetric measurements were carried out before and after drying to determine the volumetric contraction during the process. After drying, the experimental data were modeled by nonlinear regression analysis by the Quase-Newton method, to adjust 4 mathematical models of moisture ratio and 5 mathematical models of volumetric contraction. Among the models tested, the best fit for the prediction of the Moisture Ratio was the exponential model, and for the Volumetric Contraction was the modified BALA and WOOD model.

I re-examined data for relative growth by the heart in four species of mammal to reconcile divergent reports that appear in the literature. Raw data for heart and body mass for Horro sheep, humans, gray kangaroos, and tammar wallabies were studied by linear and nonlinear regression, thereby enabling me to avoid the confounding effects of logarithmic transformation and to evaluate multiple statistical models for describing pattern in each set of observations. My analyses indicate that relative growth by the heart is monophasic in all four species and either isometric or near isometric on the arithmetic scale. The heart in these mammals consequently grows in mass in approximate proportion to growth in mass by the body. The appearance of biphasic allometric growth in prior studies was an artifact resulting from logarithmic transformation. Although parturition in sheep and humans is accompanied by a change in the distribution of blood out of the heart and into pulmonary and systemic circuits, the challenge is met without marked increases in absolute or relative size of the heart.

Heat treatment is renowned as the most environmentally friendly process of dimensional stabilization that can be applied to wood, in order to make it suitable for outdoor uses. It also darkens wood color and improves wood durability. The intensity of heat treatment can be appreciated by means of two parameters: the color change occured in wood due to the high temperature, and the mass loss, which is a measure of the degree of thermal degradation. In order to find a mathematical correlation between these two parameters, an experimental study was conducted with four European wood species, which were heat-treated at 180°C and 200ºC, for 1-3 hours, under atmosheric pressure.The paper presents the results concerning the color changes and mass losses recorded for the heat-treated wood samples compared to untreated wood. For all four species, the dependency between the color change and the mass loss was found to be best described by a logarithmic regression equation with R2 of 0.93 to 0.99 for the soft species (spruce, pine and lime), and R2 of 0.77 for beech. The results of this study envisage to simplify the assessment procedure of the heat treatment efficiency, by only measuring the color – a feature that is both convenient and cost-effective.

The present study investigates the influence of phase separated disintegration on waste activated sludge (WAS) biodegradability in a profitable manner. An effort has been taken in this study to disintegrate WAS in an economical way by deflocculating the WAS with 0.04 g/g SS of MgCl 2 . The bacterial cell disruption was proficient at 42 h, where floc disrupted-bacterially pretreated sludge showed prominent solubilization of about 21.4% than the bacterially pretreated sludge (10.5%). The kinetic analysis of disintegration (suspended solids (SS) reduction and particulate chemical oxygen demand (PCOD) reduction) for control, bacterially disintegrated, floc disrupted-bacterially disintegrated sludges was observed to be first order with rate constants 0.001, 0.003, 0.005 and 0.001, 0.002, 0.005 (h −1 ), respectively. The proposed method articulates the effectiveness of sludge disintegration in terms of VFA production of about 640 mg/L in anaerobic fermentation experiment. The model (exponential rise to maximum) explaining the Biochemical methane potential (BMP) assay was implemented in Matlab. 12v. The parameter estimation analysis affords an estimate of parameter uncertainty and correlation, and is obviously explains that floc disrupted-bacterially pretreated sludge showed higher biodegradability of about 0.22 (g COD/g COD) than the others. Cost estimation of the present study revealed net profit of about 27.3 USD in floc disrupted-bacterially pretreated sludge.

The extraction of polyphenols from wood chips into a wine model system was described using kinetics, over a period of 20 days. The wood chips tested were made from oak (Quercus alba), false acacia (Robinia pseudoacacia) and cherry (Prunus avium) wood. Kinetics were established using nonlinear regression and the leaching of polyphenols into the liquid model systems was found to obey a second-order model. The determination of basic kinetic parameters enabled the identification of leaching trends and comparison among the difference wood species used, as well as determination of the effect of the amount of chips added. Oak chips were found to enrich the model wine in polyphenolic substances significantly more compared with either acacia or cherry. Furthermore, the wine model treated with oak chips displayed a much higher reducing power on day 20 of the treatment. The correlation of the total polyphenol concentration at saturation with the amount of chips added, using nonlinear regression, revealed that in every case the maximum concentration of total polyphenols attained was linked with the amount of chips by a three-parameter exponential growth function. Possible differences pertaining to wood botanical species and polyphenolic load are discussed on the grounds of theoretical considerations for diffusion. Copyright © 2015 The Institute of Brewing & Distilling

A solar drying system was designed, constructed and tested for drying of seaweed. Seaweed is a potential source of renewable energy, and it can be converted into energy such as biofuel oil, biodiesel and gas. Red seaweed was dried to the final moisture content of 10% from 90% w.b in 15 h. Drying kinetics of red seaweed were investigated and obtained. The nonlinear regression procedure was used to fit three different drying models. The Page's model clearly showed a better fit to the experimental data between Newton's model and Henderson and Pabis model. The Page's model was resulted in the highest value of R2 and lowest values of MBE and RMSE. At average solar radiation of about 500 W/m2 and air flow rate 0.05 kg/s, the collector, drying system and pick-up efficiencies were found about 35, 27 and 95%, respectively. This study was performed with energy analysis and exergy analyses of the solar drying process of red seaweed. The specific energy consumption (SEC) of 2.62 kWh/kg was obtained. Moreover, the exergy efficiency of solar drying ranged from 1% to 93%, with an average of 30%. The values of improvement potential were found to be in the range of 0.3 and 630 W, with an average of 247 W.

Moisture content is an important feedstock quality in converting it into energy through biochemical or thermochemical platforms. Knowledge of moisture sorption relationship is useful in drying and storage to preserve the quality of feedstocks. Moisture sorption isotherms for potential feedstocks such as corn stover and big bluestem are missing. EMC values of corn stover and big bluestem were determined using static gravimetric technique with saturated salt solutions (ERH 0.12–0.89) at different temperatures (20, 30, and 40°C). Depending upon the ERH values, EMC values were ranged from 8.0 to 19.6 and 8.8 to 19.2% db for corn stover and big bluestem, respectively, and they followed typical type II isotherm found in food materials. Nonlinear regression was used to fit five commonly used three-parameter isotherm models (i.e., modified Oswin model, modified Halsey model, modified Chung-Pfost model, modified Henderson model, and the modified Guggenheim-Anderson-de Boer (GAB) model) to the experimental data. Modified Halsey emerged as the best model with highF-statistic andR2values with lowEmandEsand fairly random scattered residual plot for corn stover and big bluestem. These models can be used to predict the equilibrium moisture content of these feedstocks starting from harvesting, drying, preprocessing, transportation, storage, and conversion.

Density and viscosity are important physical properties since they are the properties most used in calculations involving fluid transport. The main objectives of the present study were to examine the rheological behaviour and determine the density of watermelon pulp at different temperatures (10, 20, 30, 40, 50 and 60 °C) and concentrations (8, 17, 26 and 35 °Brix) and to obtain models to describe the alterations in these physical properties as a function of temperature and concentration. A Searle concentric cylinder rheometer was used to study the rheological behaviour and the density was determined using pycnometers. The models used in this work were fitted by nonlinear regression. It was concluded that the watermelon pulp behaved as a pseudoplastic non-Newtonian fluid at all the temperatures and concentrations used and that the Ostwald-de-Waele model could be used to describe this behaviour. Models were found that described the simultaneous effect of temperature and concentration on the density and viscosity of watermelon pulp, and these could be very useful in the food industry.

The applicability of the model-independent method to pharmacokinetic analysis was statistically studied. For this purpose, two kinds of data were used, i.e., plasma disappearance data for warfarin (a typical example of a triple-exponential decay) and for amoxicillin (double-exponential decay). By using statistical analysis with least-squares fitting (SALS), a nonlinear regression analysis program, curve fittings were carried out with respect to those data sets. In the case of the warfarin data, the triple-exponential equation was superior to the model-independent one in terms of both the residual sum of squares and an information criterion (AIC). However, very little difference between the two could be seen by eye when the results were drawn on graph paper. In the case of the amoxicillin data, the model-independent equation was statistically superior to the double-exponential one. The applicability of this model-independent method to pharmacokinetic analysis was thus confirmed.

Correlation coecients a very broad range of statistical estimators that rivals least squares. The whole area could be called a \Correlation Estimation System." This paper outlines some of the numerous possibilities for using the system and gives some illustrative examples. Detailed explanations are developed in earlier papers. The formulae to make possible both the estimation and some of the computer coding to implement it are given. This approach has been taken in hopes that this condensed version of the work will make the ideas accessible, show their practicality, and promote further developments.

Regression analysis is a huge part of mathematical and applied statistics. Nonlinear regression analysis is a significant extension and complication of classical linear regression analysis, due to the use of nonlinear or partially nonlinear in parameters models that describe more adequately than linear model phenomena requiring statistical analysis. A large number of applied problems in the numerical scientific, technical, and humanitarian fields of knowledge give impetus to the development of nonlinear regression analysis. The task of estimation the vector signal parameter in the «signal + noise» observation models is a well-known problem of statistics of stochastic processes, and in the case of a nonlinear signal parameter is the problem of nonlinear regression analysis. Among the variety of nonlinear regression analysis problems the problem of estimating amplitudes and angular frequencies of the sum of harmonic oscillations that are observed against the background of a random noise, takes significant place due to its numerous applications. Statistical model of such a type is said to be trigonometric regression, and the problem of statistical estimation is called the problem of detecting hidden periodicities. The paper is devoted to the study of time continuous trigonometric regression model where the random noise is a linear L´evy driven stationary of the fourth order stochastic process with zero mean, integrable and square integrable impulse transmission function. This assumption leads to the integrability of the noise covariance function and cumulant function of the fourth order. To estimate unknown amplitudes and angular frequencies of such a trigonometric model we use the least squares estimators in the Walker sense, that is special parametric set are considered to distinguish properly different angular frequencies in the sum of harmonic oscillations. Theorem on strong consistency of the least squares estimators is proved in the paper under the assumption on the random noise described above. To obtain such a result a very important lemma was proved on the uniform tending to zero almost surely of the average value of L´evy-driven linear stochastic process Fourier transform. This Lemma is the main tool of the strong consistency Theorem proof. To prove the Theorem we, firstly, find some expressions for the least squares estimates of amplitudes via corresponding estimates of angular frequencies. Secondly, we substitute these formulas into the functional of the least squares method. The last step of the proof consists of the L2- norm transformation of the difference between empirical trigonometric regression function and true regression function such that this norm tends to zero almost surely if and on if the estimators are strongly consistent., Регресiйний аналiз є iстотною частиною математичної та прикладної статистики. Нелiнiйний регресiйний аналiз є значним розширенням та ускладненням класичного лiнiйного регресiйного аналiзу, завдяки використанню нелiнiйних або частково нелiнiйних за параметрами моделей, якi адекватнiше описують, нiж лiнiйнi моделi, явища, що потребують статистичного аналiзу. Велика кiлькiсть прикладних проблем у численних наукових, технiчних та гуманiтарних галузях знань дають поштовх розвитку нелiнiйного регресiйного аналiзу. Задача оцiнювання векторного параметра сигналу в моделях спостереження «сигнал + шум» є добре вiдомою проблемою статистики випадкових процесiв, та у випадку нелiнiйного параметра сигналу – задачею нелiнiйного регресiйного аналiзу. Серед рiзноманiтностi задач нелiнiйного регресiйного аналiзу оцiнювання амплiтуд та кутових частот суми гармонiчних коливань, що спостерiгається на фонi випадкового шуму, займає значне мiсце, завдяки її численним застосуванням. Статистичнi моделi такого типу називаються тригонометричними моделями регресiї, а проблема статистичного оцiнювання її параметрiв називається задачею виявлення прихованих перiодичностей. Статтю присвячено вивченню тригонометричної моделi регресiї, в якiй випадковий шум є лiнiйним Левi-керованим стацiонарним четвертого порядку випадковим процесом iз нульовим середнiм, iнтегровную та iнтегровную з квадратом iмпульсною перехiдною функцiєю. Це припущення призводить до iнтегровностi коварiацiйної функцiї та кумулянтної функцiї 4-го порядку. Для оцiнювання амплiтуд та кутових частот такої тригонометричної моделi ми використовуємо оцiнки найменших квадратiв у сенсi Уолкера, тобто розглянуто спецiальну множину параметрiв, щоб розрiзнити належним чином рiзнi кутовi частоти в сумi гармонiчних коливань. У статтi доведено теорему про сильну консистентнiсть оцiнки найменших квадратiв за описаними вище припущеннями щодо випадкового шуму. Для отримання такого результату було доведено дуже важливу лему про рiвномiрну збiжнiсть майже напевно середнього значення перетворення Фурьє лiнiйного Левi-керованого випадкового процеса. Ця лема є головним iнструментом доведення теореми про сильну консистентнiсть. Для доведення теореми, по-перше, знаходимо деякi представлення оцiнок найменших квадратiв амплiтуд через вiдповiднi оцiнки кутових частот. По-друге, ми пiдставляємо цi формули у функцiонал методу найменших квадратiв. Останнiй крок доведення полягає у перетвореннi L2-норми рiзницi мiж емпiричною тригонометричною функцiєю регресiї та iстиною функцiєю регресiї таким чином, що ця норма прямує до нуля майже напевно тодi i тiльки тодi, коли оцiнки є сильно консистентними.

Interval-valued data, a type of symbolic data, is given as an interval in which the observation object is not a single value. It can also occur frequently in the process of aggregating large databases into a form that is easy to manage. Various regression methods for interval-valued data have been proposed relatively recently. In this paper, we introduce a nonparametric regression model using the kernel function and a nonlinear regression model for the interval-valued data. We also propose applying the local linear regression model, one of the nonparametric methods, to the interval-valued data. Simulations based on several distributions of the center point and the range are conducted using each of the methods presented in this paper. Various conditions confirm that the performance of the proposed local linear estimator is better than the others.

One of the severe and prolonged disorder of the human brain which disturbs the behavioral characteristics of an individual completely such as interruption in the thinking process and speech is schizophrenia. It is a manifestation of many symptoms such as hallucinations, functional deterioration, disorganized speech and hearing sounds and speeches that are non-existent. In this paper, a computerized approach based on optimization and classification is done to analyze the classification of schizophrenia from Electroencephalography (EEG) signals. As EEG can analyze a lot of brain disorders and is used to study the diseases of the brain in an in-depth manner, it can be used to analyze the schizophrenia EEG signals. In this paper, three feature extraction techniques are employed such as Partial Least Squares (PLS) Non linear Regression technique, Expectation Maximization based Principal Component Analysis (EM-PCA) technique and Isometric Mapping (Isomap) technique. The extracted features are further optimized with four optimization algorithms such as Flower Pollination algorithm, Eagle strategy using different evolution algorithm, Backtracking search optimization algorithm and Group search optimization algorithm. The optimized values are then classified with varied versions of both Adaboost classifier and Naïve Bayesian Classifier. The individual results show that for normal cases, Isomap features when optimized with Backtracking search optimization algorithm and classified with Modest Adaboost classifier, a classification accuracy of 98.77% is obtained. The individual results show that for schizophrenia case, when Isomap features are optimized with Flower Pollination optimization algorithm and classified with Real Adaboost classifier, a classification accuracy of 98.77% is obtained.

Different anthropogenic influences and irresponsible actions pollute all the components of the environment and groundwater is no exception. Nitrates, which are one of the most common groundwater contaminants, come from different sources and they are not always easily detectable. The paper presents a study of a groundwater quality at the Varaždin wellfield in the north part of Croatia. The nitrate concentration at this location has been above the maximum allowed concentration for several decades, which has made the opening of new wellfields costly. Spatial distribution of the nitrate concentration at the wellfield is developed using Kriging interpolation method. An illegal dumpsite consisting of waste from a poultry farm has been identified as a nitrate pollution source. The paper shows that nitrate concentrations depend on the distance from the dumpsite. The results are shown in a scatter diagram and regression curves are fitted in the data based on modified Exponential, Logistic, Gompertz and Richards functions. Average contributions of point-source pollution to the groundwater nitrate concentration at the observed wellfield are assessed by using regression curves through the application of a theorem of the mean value for integrals, which are found to be in range 17.23-52.58 mg/L NO3- for the overall nitrate amount. This shows that the application of mineral fertilisers in agriculture is not always the only main cause of the increase in groundwater nitrate concentrations. Contributions from diffuse sources are assessed by the regression curves as well and they are found to be in range 30.52-53.10 mg/L NO3-. The sources of pollution are divided in an anthropogenic and non-anthropogenic group. The anthropogenic contributions are found to be 70.33 mg/L NO3-, whereas the non-anthropogenic sources contribute with 5.40 mg/L NO3- to the total nitrate concentration at the Varaždin wellfield.

Global horizontal irradiance (GHI) is a critical index to indicate the output power of the photovaltaic (PV). In traditional approaches, the local GHI can be measured with very expensive instruments, and the large-area GHI collection depends on complex satellite-based models, solargis algorithms, and the high-performance computers (HPC). In this paper, a novel approach is proposed to capture the GHI conveniently and accurately. Considering the nonstationary property of the GHI on cloudy days, the GHI capturing is cast as an image regression problem. In traditional approaches, the image regression problem is treated as two parts, feature extraction (for the images) and regression model (for the regression targets), which are optimized separately and blocked the interconnections. Considering the nonlinear regression capability, a convolutional neural network (CNN) based image regression approach is proposed to provide an End-to-End solution for the cloudy day GHI capturing problem in this paper. The multilayer CNN is based on the AlexNet and VGG. The L2 (least square errors) with regularization is used as the loss function in the regression layer. For data cleaning, the Gaussian mixture model with Bayesian inference is employed to detect and eliminate the anomaly data in a nonparametric manner. The purified data are used as input data for the proposed image regression approach. In the experiments, three-month sky images and GHI data (with 1-min resolution) are provided by the National Renewable Energy Laboratory (NREL) with the HPC system. The numerical results demonstrate the feasibility and effectiveness of the proposed approach.

In many scientific fields, the dynamics of the system are often known, and the main challenge is to estimate the parameters that model the behavior of the system. The question then arises whether one can use experimental measurements of the system response to derive the parameters? This problem has been addressed in many papers that focus mainly on data from a deterministic model, but few efforts have been made to use stochastic data instead. In this paper, we address this problem using the following procedure: first, we build the probabilistic stochastic differential models using a natural extension of the commonly used deterministic models. Then, we use the data from the stochastic models to estimate the model parameters by solving a nonlinear regression problem. Since the stochastic solutions are not differentiable, we use the well-known Nelder–Mead algorithm. Our numerical results show that the fitting procedure is able to obtain good estimates of the parameters requiring only a few sample data. This work was supported by Spanish Ministry of Sciences Innovation and Universities with the project PGC2018-094522-B-100 and by the Basque Government with the project IT1247-19.

This study aimed to investigate the prediction method of permeability and its anisotropy of tight oil reservoir via precise pore-throat tortuosity characterization and “umbrella deconstruction” method combining the approaches of the field emission SEM imaging, high resolution image processing, fine and large-scale mathematical statistics, nonlinear regression and other technical means. In this paper, the authors proposed the new calculation model of pore-throat tortuosity, the absolute permeability and the permeability anisotropy based on the improved deep understanding of reservoir. Results of the prediction on the tight oil reservoir of “YANCHANG” formation in Ordos Basin show that the errors of the new method in this paper are the smallest among the total five methods, respectively 0.023 × 10−3μm2 and 0.090 × 10−3μm2; the average values of other four methods were 0.090 × 10−3μm2 and 0.108 × 10−3μm2, respectively. The predicted results have higher accordance with the measured results, which proved the practicality of the new method. The samples has the highest permeability at the angle of 0°(180°/360°) and the permeability values are equal to 0.25 × 10−3μm2. Similarly, the sample has the lowest permeability at the angle of 22.5°(202.5°), 90°(270°), and 112.5°(292.5°), the permeability values are all equal to 0.06 × 10−3μm2. At the same time, the calculation of permeability anisotropy results shows that the anisotropy of tight oil reservoirs is very significant, and the permeability value in one direction is obviously higher than which in other directions. It is concluded that the precise description of pore throat geometry, especially the calculation of pore-throat tortuosity parameter, is one of the most important parameters affecting the prediction accuracy of permeability theoretically. Meanwhile, there are dominant seepage channels, which would play a very important guiding role in the prediction of hydrocarbon accumulation and seepage capacity. The conclusion will provide a more rigorous theoretical basis for the rapid and accurate evaluation of the physical properties of unconventional reservoirs.

Metalearning, an important part of artificial intelligence, represents a promising approach for the task of automatic selection of appropriate methods or algorithms. This paper is interested in recommending a suitable estimator for nonlinear regression modeling, particularly in recommending either the standard nonlinear least squares estimator or one of such available alternative estimators, which is highly robust with respect to the presence of outliers in the data. The authors hold the opinion that theoretical considerations will never be able to formulate such recommendations for the nonlinear regression context. Instead, metalearning is explored here as an original approach suitable for this task. In this paper, four different approaches for automatic method selection for nonlinear regression are proposed and computations over a training database of 643 real publicly available datasets are performed. Particularly, while the metalearning results may be harmed by the imbalanced number of groups, an effective approach yields much improved results, performing a novel combination of supervised feature selection by random forest and oversampling by synthetic minority oversampling technique (SMOTE). As a by-product, the computations bring arguments in favor of the very recent nonlinear least weighted squares estimator, which turns out to outperform other (and much more renowned) estimators in a quite large percentage of datasets.

The magnetic switchbacks observed recently by the Parker Solar Probe have raised the question about their nature and origin. One of the competing theories of their origin is the interchange reconnection in the solar corona. In this scenario, switchbacks are generated at the reconnection site between open and closed magnetic fields, and are either advected by an upflow or propagate as waves into the solar wind. In this paper we test the wave hypothesis, numerically modeling the propagation of a switchback, modeled as an embedded Alfvén wave packet of constant magnetic field magnitude, through the gravitationally stratified solar corona with different degrees of background magnetic field expansion. While switchbacks propagating in a uniform medium with no gravity are relatively stable, as reported previously, we find that gravitational stratification together with the expansion of the magnetic field act in multiple ways to deform the switchbacks. These include WKB effects, which depend on the degree of magnetic field expansion, and also finite-amplitude effects, such as the symmetry breaking between nonlinear advection and the Lorentz force. In a straight or radially expanding magnetic field the propagating switchbacks unfold into waves that cause minimal magnetic field deflections, while a super-radially expanding magnetic field aids in maintaining strong deflections. Other important effects are the mass uplift the propagating switchbacks induce and the reconnection and drainage of plasmoids contained within the switchbacks. In the Appendix, we examine a series of setups with different switchback configurations and parameters, which broaden the scope of our study. © 2021. The American Astronomical Society. All rights reserved., N.M. was supported by a Newton International Fellowship of the Royal Society. D.U. is thankful for the support received through FWF project P27800. This research has received financial support from the European Unions Horizon 2020 research and innovation program under grant agreement No. 824135 (SOLARNET) enabling D.U. a visit to Sheffield University. R.E. is grateful to Science and Technology Facilities Council (STFC, grant number ST/M000826/1) UK and the Royal Society for enabling this research. R.E. also acknowledges the support received by the CAS Presidents International Fellowship Initiative grant No. 2019VMA052 and the warm hospitality received at USTC of CAS, Hefei, where part of the contribution was made. V.M.N. acknowledges the STFC consolidated grant ST/T000252/1 and the BK21 plus program through the National Research Foundation funded by the Ministry of Education of Korea.In order to keep the main body of this paper more transparent, simulations with different switchback parameters and conditions are presented in this Appendix. These additional simulations are carried out in a nonexpanding uniform magnetic field. The results strengthen our conclusions on the property of switchbacks propagating through a gravitationally stratified corona, namely the significant deformations these undergo, and still display the other effects described in Section 3. With funding from the Spanish government through the Severo Ochoa Centre of Excellence accreditation SEV-2017-0709.

In this paper, the geometric design of a gravity-based separator is studied with a computational fluid dynamics method. ANSYS Fluent (18.2) is used to model the ratio of horizontal and vertical lengths with three dimensionless groups. A dimensional analysis method is used to develop a new correlation of separator geometric design. Corresponding plots were created and analyzed using nonlinear regression on the x–y Cartesian coordinate system. Also, manual iterations were performed to determine the coefficients in the general correlation relationship. The dimensional analysis results show that the Reynolds and Euler numbers have a direct correlation with separator design, which means increasing the Reynolds and Euler numbers require a separator with a larger length to height ratio to achieve the same separation efficiency. However, the Weber number has an inverse correlation with separator design, which means an increase in the Weber number requires a separator with a smaller length to height ratio. The new correlation developed in this paper can be used as a reference for separator geometry design to separate immiscible fluids with a wide range of fluid properties.

Hyper-parameter optimization is an essential task in the use of machine learning techniques. Such optimizations are typically done starting with an initial guess provided to hyper-parameter values followed by optimization (or minimization) of some cost function via gradient-based methods. The initial values become crucial since there is every chance for reaching local minimums in the cost functions being minimized, especially since gradient-based optimizing is done. Therefore, initializing hyper-parameters several times and repeating optimization to achieve the best solutions is usually attempted. Repetition of optimization can be computationally expensive when using techniques like Gaussian Process (GP) which has an $\mathcal{O}\left( {{n^3}} \right)$ complexity, and not having a formal strategy to initialize hyper-parameter values is an additional challenge. In general, re-initialization of hyper-parameter values in the contexts of many machine learning techniques including GP has been done at random over the years; some recent developments have proposed some initialization strategies based on the optimization of some meta loss cost functions. To simplify this challenge of hyper-parameter initialization, this paper introduces a data-dependent deterministic initialization technique. The specific case of the squared exponential kernel-based GP regression problem is focused on, and the proposed technique brings novelty by being deterministic as opposed to random initialization, and fast (due to the deterministic nature) as opposed to optimizing some form of meta cost function as done in some previous works. Although global suitability of this initialization technique is not proven in this paper, as a preliminary study the technique’s effectiveness is demonstrated via several synthetic as well as real data-based nonlinear regression examples, hinting that the technique may have the effectiveness for broader usage.

This article presents preliminary design formulas developed using a database of container ships built since 2015. Artificial neural networks and multiple nonlinear regressions with randomly searched functions were used to develop these formulas. The use of random search for nonlinear functions in a Multiple Nonlinear Regression model gave estimates which were just as precise as estimates created by the artificial neural network. All equations presented in this paper could have practical application for the estimation of dimensions, such as: length between perpendiculars, breadth, draught moulded and side depth. The equations were developed in relation to deadweight, TEU capacity and ship speed. These kinds of relationships have not been demonstrated before in ship theory. A statistical analysis showed that the main dimensions of the container ships can be estimated highly accurately by using the equations presented in the paper. The study showed that taking into account deadweight, TEU capacity and ship speed as three input parameters can improve the accuracy of an estimation by up to 44 percent, than when compared to the estimate accuracy of the design equations which are based on one input parameter.

The procedures to estimate the parameters are important in many scientific fields that are required to develop mathematical models. Thus, this paper is proposed as a Gravitational Search algorithm for estimating the parameters of nonlinear regression models. Also, a simulation study is conducted to investigate the performance of the proposed methods in this paper. The results show that GSA approach provides accurate estimates and is satisfactory for the parameter estimation of the nonlinear regression models.

One of the most versatile and powerful algorithms for the identification of nonlinear dynamical systems is the NARMAX (Nonlinear Auto-regressive Moving Average with eXogenous inputs) approach. The model represents the current output of a system by a nonlinear regression on past inputs and outputs and can also incorporate a nonlinear noise model in the most general case. In recent papers, one of the authors introduced a NARX (no noise model) formulation based on Gaussian Process (GP) regression and derived the corresponding expressions for Higher-order Frequency Response Functions (HFRFs). This paper extends the theory for the GP-NARX framework by providing a means of converting the GP prediction bounds in the time domain into bounds on the HFRFs. The approach is demonstrated on the Duffing oscillator.

The paper continues the authors’ work (Freise et al. The adaptive Wynn-algorithm in generalized linear models with univariate response. arXiv:1907.02708, 2019) on the adaptive Wynn algorithm in a nonlinear regression model. In the present paper the asymptotics of adaptive least squares estimators under the adaptive Wynn algorithm is studied. Strong consistency and asymptotic normality are derived for two classes of nonlinear models: firstly, for the class of models satisfying a condition of ‘saturated identifiability’, which was introduced by Pronzato (Metrika 71:219–238, 2010); secondly, a class of generalized linear models. Further essential assumptions are compactness of the experimental region and of the parameter space together with some natural continuity assumptions. For asymptotic normality some further smoothness assumptions and asymptotic homoscedasticity of random errors are needed and the true parameter point is required to be an interior point of the parameter space.

Stock market prediction is an activity to estimate the future value of a stock. The accurate prediction of particular share’s future price can lead to significant profit margins for an investor. The efficient market hypothesis states that prices of the stock depend on the available information and price changes, do not consider any hidden information. Therefore, prediction of stock plays a significant role to influence the investor’s decisions. It also acts a recommend system for investment related decision in stock market for short term investors and financial suffering system for long term shareholders. In this paper, we propose a stock market prediction system using machine learning algorithms. This paper first explores a few machine learning algorithms for estimating stock value and then proposes a solution that can predict the future stock value with higher accuracy. In this paper, we propose a deep learning based non-linear regression method to predict the stock price. The experiments are performed on two publically available datasets : Tesla Stock Price and New York Stock Exchange which consist of stock data from 2010 to 2020. The analysis of experimentation reveals that the proposed method performed better than existing machine learning based approaches.

The management of electricity consumption by household consumers requires multiple ways of consumer monitoring. One of these is the signature i(v) determined by monitoring the consumer voltage-current trajectory. The paper proposes a novel method for obtaining signatures of 2-multiple consumers, i.e., a pair of consumers connected in parallel. Signatures are obtained from samples of the voltage at the consumers&rsquo, terminals and of the total current absorbed by the consumers, measured at a frequency of only 20 Hz. Within the method, signatures are calculated using genetic algorithms (GA) and nonlinear regression, according to a procedure developed by the authors in a previous paper. The management of the data selected for the signature assignment represents the novelty. The method proposed in this paper is applied in two case studies, one concerning household consumers within the same power level, the other for household consumers of different power levels. The results confirm the possibility of obtaining signatures of i(v) type.

The constant elasticity of substitution production function describes the relationship between production results and production factors in the technological production process. The common production factors include capital and labor. In order to comprehensively reflect the input-output relationship, this paper generalizes the model and adds factors including energy, consumption, and import and export. With respect to estimating the parameters of the model, the paper proposes a high-precision and high-speed nonlinear regression method. The constant elasticity of substitution production function model is mainly used to calculate the contribution rates of economic growth factors, and this paper proposes a scientific and reliable calculating method. The final section of the paper proposes an empirical analysis of the contribution rates of Chinese economic growth factors.

This paper defines the waveform function and its corresponding concepts and axioms. The extreme value of stock price function is obtained from 24 known regression functions by using the method of seeking the extreme value, which is proven by the Shanghai stock index rising by 458.43%, 487.83% and 133.30% respectively in three different periods. This paper optimizes the expert RSI trading system with the method of mathematical extreme value, and writes the source code of the optimization formula, which provides a graphical and intuitive tool for investors. The average annual return, average winning rate and average net interest rate of waveform increasing function samples are 67.52%, 96.88% and 84.40%, respectively. The average annual return, average winning rate and average net interest rate of waveform decreasing function samples are 22.27%, 83.33% and 26.03%, respectively.

This paper presented a way of obtaining certain operating rules on time steps for the management of a large reservoir operation with a peak hydropower plant associated to it. The rules were allowed to have the form of non-linear regression equations which link a decision variable (here the water volume in the reservoir at the end of the time step) by several parameters influencing it. The rules were allowed to have the form of nonlinear regression equations which link a decision variable (here the water volume in the reservoir at the end of the time step) by several parameters influencing it. This paper considered the Dokan hydroelectric development, which operation data are available for. It was showing that both the monthly average inflows and the monthly power demands are random variables. A model of deterministic dynamic programming intending the minimization of the total amount of the squares differences between the demanded energy and the generated energy is run with a multitude of annual scenarios of inflows and monthly required energies. The operating rules achieved allow the efficient and safe management of the operation and it is quietly and accurately known the forecast of the inflow and of the energy demand on the next time step.

This paper addresses the problem of fitting nonlinear regression models in high-dimensional situations, where the number of predictors, p , is large relative to the number of observations, n . Most of the research in this area has been conducted under the assumption that the regression function has a simple additive structure. This paper focuses instead on single index models, which are becoming increasingly popular in many scientific fields including biostatistics, economics and financial econometrics. Novel methodology is presented for estimating high-dimensional single index models and simultaneously performing variable selection. A computationally efficient algorithm is provided for constructing a solution path. Asymptotic theory is developed for the proposed estimates of the regression function and the index coefficients in the high-dimensional setting. An investigation of the empirical performance on both simulated and real data demonstrates strong performance of the proposed approach.

This paper analyzes the Keqiao Textile Index of China, which reflects China Textile City, the leading wholesale textile market in China. China Textile City is a textile entrepot with the most extensive scale and the largest line of business in China, and it is the largest specialized market for light textile in Asia as well. Thus, it is worthwhile to analyze this index. In this paper, 10 variables that represent the factors that significantly influence the Textile Index are selected from the set of possible variables that are deemed to be valid to the index. 6 variables are identified as nonlinear and 4 as linear by the nonparametric method. Then, varying-coefficient partially linear models are established, dividing the index into five terms: one nonparametric term and four linear terms. Each of the five terms comprises approximately 20% of the index, with the linear terms accounting for nearly 80%. Among the six nonparametric variables, cotton index A plays the most important role. The empirical and simulated results consistently show that the percent of each of the five terms would not vary substantially during the sample period if cotton index A were not more than twice the sample mean. Thus, textile prices can be regulated by properly adjusting the cotton price.

The paper is devoted to establishing strong consistency of estimates of nonlinear characteristics of dynamic stochastic systems. To describe the shape of the nonlinearities, regression functions, i.e. conditional expectations of a random variable with respect to another one, are used. In turn, the nonlinear regression functions are estimated by using kernel-type algorithm approaches, which are suitable under fairly mild assumptions with respect to the system description. Within the approach, the key issue of the present paper is considering a case of mutually dependent observations. At the same time, conventional nonparametric approaches are based on regression estimates, which impose a number of conditions on sampled data, e.g. mutual independence, various mixing conditions, etc., while such assumptions are not always suitable for verifying within the practice of dynamic system considerations.

The aim of this paper is to develop nonlinear regression models with error distribution having the slash-elliptical family. A slash-elliptical random variable is defined as the quotient of two independent random variables, $Z$ and $U^{1/q}$, where $Z$ has an elliptical contoured distribution and $U$ has a uniform distribution. A key advantage of the slash-elliptical distribution is the simplicity by which the well-known elliptical contoured distribution can be modified to support increase in kurtosis. The main properties of the slash-elliptical distribution is symmetry, heavy tails and convergence to the elliptical contoured distribution as the limiting case of the shape parameter. One of the advantages of this distribution is to allow larger kurtosis than the elliptical contoured distribution. In this paper, we propose estimation method, residual analysis and generalized leverage for the new class of regression models. We also develop diagnostic measures under local influence approach and present a real data analysis.

This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects from observational data, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity". We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.

This paper deals with the problem of monitoring the freeze-drying process of thermo-labile products and particularly tracking the temperature and the position of the interface of sublimation. A novel and affordable way is proposed to estimate the vapor flow rate and, thus, retrieve the parameters of interest. This method is referred to as pressure decrease test (PDT) and is based on the shutoff of the controlled leakage valve and on the subsequent model-based analysis of the response of the process. In this paper, a detailed description of the PDT algorithm is given; furthermore, the method was tested upon two placebo formulations, that is, sucrose- and mannitol-based solutions, showing that the tool can give an accurate, complete, and noninvasive estimation of all the parameters of interest. These results also show that the method is a valid solution to various technical problems that arise when attempting to apply other techniques proposed in the literature, for example, the pressure rise test and the tunable diode laser absorption spectroscopy technology.

The paper presents a generalized regression technique centered on a superquantile (also called conditional value-at-risk) that is consistent with that coherent measure of risk and yields more conservatively fitted curves than classical least-squares and quantile regression. In contrast to other generalized regression techniques that approximate conditional superquantiles by various combinations of conditional quantiles, we directly and in perfect analog to classical regression obtain superquantile regression functions as optimal solutions of certain error minimization problems. We show the existence and possible uniqueness of regression functions, discuss the stability of regression functions under perturbations and approximation of the underlying data, and propose an extension of the coefficient of determination R-squared for assessing the goodness of fit. The paper presents two numerical methods for solving the error minimization problems and illustrates the methodology in several numerical examples in the areas of uncertainty quantification, reliability engineering, and financial risk management.

This paper proposes an improved global optimization technique, named Hybrid Coupled Local Minimizers (HCLM), which is inspired on the method of coupled local minimizers (CLM). The HCLM method uses a set of search points, called “particles”, initially spread over the search space, that are occasionally impulsively coupled, instead of permanently coupled. This approach leads to a much better optimization efficiency, because it combines the fast convergence (due to a Newton-based method that is used for each particle) with the capability of global optimization (resulting from the hybrid interaction which enables a parallel strategy). Such parallel and distributed computing process embedded with a trust region strategy relies on the hybrid interconnections of particles rather than individual particles, which is able to fully exploit the parallel nature of the computation and produce results which are more globally optimal. It is worth mentioning that the stability of each particle and the synchronization of all particles are also derived and proved by means of the contraction theory. The HCLM method is illustrated on several test functions with many local minima and applied to a problem of static nonlinear regression with multilayer perceptrons (MLPs) from given noisy measurement data.

In food quality monitoring, color is an important indicator factor of quality. The CIELab (L*a*b*) color space as a device independent color space is an appropriate means in this case. The commonly used colorimeter instruments can neither measure the L*a*b color in a wide area over the target surface nor in a contact-less mode. However, developing algorithms for conversion of food items images into L*a*b color space can solve both of these issues. This paper addresses the problem of L*a*b color prediction from multispectral images of different types of raw meat. The efficiency of using multispectral images instead of the standard RGB is investigated. In addition, it is demonstrated that due to the fiber structure and transparency of raw meat, the prediction models built on the standard color patches do not work for raw meat test samples. As a result, multispectral images of different types of meat samples (430-970nm) were used for training and testing of the L*a*b prediction models. Finding a sparse solution or the use of a minimum number of bands is of particular interest to make an industrial vision set-up simpler and cost effective. In this paper, a wide range of linear, non-linear, kernel-based regression and sparse regression methods are compared. In order to improve the prediction results of these models, we propose a supervised feature selection strategy which is compared with the Principal component analysis (PCA) as a pre-processing step. The results showed that the proposed feature selection method outperforms the PCA for both linear and non-linear methods. The highest performance was obtained by linear ridge regression applied on the selected features from the proposed Elastic net (EN) -based feature selection strategy. All the best models use a reduced number of wavelengths for each of the L*a*b components.

This paper deals with the issue of the likelihood inference for nonlinear models with a flexible skew-t-normal (FSTN) distribution, which is proposed within a general framework of flexible skew-symmetric (FSS) distributions by combining with skew-t-normal (STN) distribution. In comparison with the common skewed distributions such as skew normal (SN), and skew-t (ST) as well as scale mixtures of skew normal (SMSN), the FSTN distribution can accommodate more flexibility and robustness in the presence of skewed, heavy-tailed, especially multimodal outcomes. However, for this distribution, a usual approach of maximum likelihood estimates based on EM algorithm becomes unavailable and an alternative way is to return to the original Newton-Raphson type method. In order to improve the estimation as well as the way for confidence estimation and hypothesis test for the parameters of interest, a modified Newton-Raphson iterative algorithm is presented in this paper, based on profile likelihood for nonlinear regression models with FSTN distribution, and, then, the confidence interval and hypothesis test are also developed. Furthermore, a real example and simulation are conducted to demonstrate the usefulness and the superiority of our approach.

The global financial market has become extremely interconnected as it demonstrates strong nonlinear contagion in times of crisis. As a result, it is necessary to measure financial systemic risk in a comprehensive and nonlinear approach. By establishing a large set of risk factors as the main bones of the financial market network and applying nonlinear factor analysis in the form of so-called PolyModel, this paper proposes two systemic risk indicators that can prognosticate the advent and trace the development of financial crises. Through financial network analysis, theoretical simulation, empirical data analysis and final validation, we argue that the indicators suggested in this paper are proved to be very effective in forecasting and tracing the financial crises from 1998 to 2017. The economic benefit of the indicator is evidenced by the enhancement of a protective put/covered call strategy on major stock markets.

An attempt is made in this paper to develop an Enhanced Support Vector Regression (ESVR ) model with more un-interpretable kernel functions in the domain of forecasting the weather conditions. Every predicate model takes input data set parameters, processing with in specified levels of classification into variable sets and countered with a variable set reduction to reach the decision of prediction in a more confirm levels. This paper also provides a critical modeling design using the non linear regression namely support vector machines which is very non interpretable neural network designed as a two stage activity in prediction with more than three kernel functions for improving the performance of the SVMs experts in predicting the future weather happenings. Recording the input data set parameters of weather like temperature, water vapor, atmospheric pressure, dew point, wind speed, wind direction, rainfall, etc. compared with a MLP (Multi Layer preceptron) classification, SVM got much more esteemed performance in forecasting any one parameter with respect to others in a two stage procedure initial with self organizing maps and with best practice of more kernel functions investigation in weather forecasting.

Extended Abstract Membrane-based pressure driven processes have been widely studied and have been used in a myriad of applications. The objective of the characterization of membranes in which gas sorption obeys Henry’s law is to determine the solubility S and diffusivity D of the membrane. The time-lag method, developed by Daynes [1] and Barrer [2], is commonly used as the integral approach [3] in the characterization of membranes by measuring the cumulated amount of permeated gas after a sudden change of the upstream boundary condition [3]. One of the important assumptions of the time-lag method is that the amount of permeate gas accumulating in the downstream receiver is small enough to have a negligible effect on the driving force. To better satisfy this assumption, it was claimed that a capacity parameter (related to the receiver volume) should be small enough [4]. Nevertheless, due to the existence of measurement noise in experimental data, the accurate determination of the time lag is difficult and a small capacity parameter will intensify the effect of noise. The accuracy of the estimated time lag is also influenced by the noise level and the data analysis procedure. An alternative to obtain the membrane properties is to fit the variation of the pressure change in the downstream reservoir as a function of time using the nonlinear regression method [5]. By minimizing the sum of squares of the differences between the experimental data and the predictions from the numerical model, the best combinations of the membrane properties can be obtained. The latter method also allows using the real rather than ideal boundary conditions at the membrane interfaces. In this paper, the experimental results are obtained from the constant volume membrane system which consists of two fixed volumes separated by a membrane cell module [7]. The system is initially evacuated using a vacuum pump prior to each experiment. The permeation process is initiated by performing a step change of the gas pressure at the upstream side of the membrane. The progressive permeation of the gas within the membrane leads to a pressure increase at the downstream side of the membrane which is recorded by a high precision pressure transducer. The time lag can be determined from the time-axis intercept of the quasi steady-state portion of the pressure rise curve plotted versus time. To gain a better understanding of the gas permeation process, a numerical model was also used to simulate the real experimental process and to predict the behaviours of membranes and various boundary conditions [9, 10]. In this paper, practical suggestions for the determination of membrane properties are given based on the commonly used time-lag method and on the nonlinear regression method. For the time-lag method, the major sources of noise were analysed and the level of noise as well as the length of the evaluation window were evaluated to estimate the accuracy of time lag results. Suggestions are given based on how to reduce the noise by properly selecting the design parameters of the experiments, such as the downstream volume, and the data analysis. For the nonlinear regression method, results show that it is nearly impossible to recover the real values of the membrane permeation properties, i.e. S, D due to the very strong correlations that prevail between S and D. Instead of exploring the effect of individual values of the membrane properties, combinations of the property coefficients that lead to same accuracy were studied. Contour maps and suggestions on the relative weights of each section of the pressure rise versus time curve are provided in the paper to assist researchers to better use the characterization method of the membrane.

Nonlinear regression models have been widely used in practice for a variety of time series and cross-section datasets. For purposes of analyzing univariate and multivariate time series data, in particular, smooth transition regression (STR) models have been shown to be very useful for representing and capturing asymmetric behavior. Most STR models have been applied to univariate processes, and have made a variety of assumptions, including stationary or cointegrated processes, uncorrelated, homoskedastic or conditionally heteroskedastic errors, and weakly exogenous regressors. Under the assumption of exogeneity, the standard method of estimation is nonlinear least squares. The primary purpose of this paper is to relax the assumption of weakly exogenous regressors and to discuss moment-based methods for estimating STR models. The paper analyzes the properties of the STR model with endogenous variables by providing a diagnostic test of linearity of the underlying process under endogeneity, developing an estimation procedure and a misspecification test for the STR model, presenting the results of Monte Carlo simulations to show the usefulness of the model and estimation method, and providing an empirical application for inflation rate targeting in Brazil. We show that STR models with endogenous variables can be specified and estimated by a straightforward application of existing results in the literature.

The main objective of this article is to specify a nonlinear regression model, formulate the assumptions on them and aquire its linear pseudo model. A model may be considered a mathematical description of a physical, chemical or biological state or process. Many models used in applied mathematics and Mathematical statistics are nonlinear in nature one of the major topics in the literature of theoretical and applied mathematics is the estimation of parameters of nonlinear regression models. A perfect model may have to many parameters to be useful. Nonlinear regression models have been intensively studied in the last three decades. Junxiong Lin et.al [1] , in their paper, compared best –fit equations of linear and nonlinear forms of two widely used kinetic models, namely pseudo-first order and pseudo=second-order equations. K. Vasanth kumar [2], in his paper, proposed five distinct models of second order pseudo expression and examined a comparative study between method of least squares for linear regression models and a trial and error nonlinear regression procedures of deriving pseudo second order rare kinetic parameters. Michael G.B. Blum et.al [3] proposed a new method which fits a nonlinear conditional heteroscedastic regression of the parameter on the summary statistics and then adaptively improves estimation using importance sampling.