Nonlinear Least-squares Regression Research Articles

Mathematical Modeling of Public Opinions: Parameter Estimation, Sensitivity Analysis, and Model Uncertainty Using an Agree-Disagree Opinion Model

In this paper, we present a mathematical model that describes agree-disagree opinions during polls. We first present the different compartments of the model. Then, using the next-generation matrix method, we derive thresholds of the stability of equilibria. We consider two sets of data from the Reuters polling system regarding the approval rating of the U.S presidential in two terms. These two weekly polls data track the percentage of Americans who approve and disapprove of the way the President manages his work. To validate the reality of the underlying model, we use nonlinear least-squares regression to fit the model to actual data. In the first poll, we consider only 31 weeks to estimate the parameters of the model, and then, we compare the rest of the data with the outcome of the model over the remaining 21 weeks. We show that our model fits correctly the real data. The second poll data is collected for 115 weeks. We estimate again the parameters of the model, and we show that our model can predict the poll outcome in the next weeks, thus, whether the need for some control strategies or not. Finally, we also perform several computational and statistical experiments to validate the proposed model in this paper. To study the influence of various parameters on these thresholds and to identify the most influential parameters, sensitivity analysis is carried out to investigate the effect of the small perturbation near a parameter value on the value of the threshold. An uncertainty analysis is performed to evaluate the forecast inaccuracy in the outcome variable due to uncertainty in the estimation of the parameters.

Weather-related thresholds for wildfire danger in a Mediterranean region: The case of Greece

The objective of the following paper is to identify weather-related thresholds for wildfire danger, i.e., the potential extent of fire, based on local weather conditions. The target area is Greece, a wildfire prone Mediterranean country which experienced on average 2000 wildfires annually over the last two decades. Initially, the Fire Weather Index (FWI) component of the Canadian Fire Weather Index (FWI) System (FWI System) adopted by the European Forest Fire Information System (EFFIS), is evaluated with respect to its wildfire danger predictive ability. Hence, weather and wildfire data at municipality level and on a daily basis, for the period 2000–2016 are exploited. The analysis showed that the FWI thresholds proposed by EFFIS for assessing the level of fire danger in Europe are too low for the case of Greece and, therefore, are not representative of the country's fire weather conditions. Two statistical approaches, cluster analysis and non-linear least-squares regression, are subsequently applied to determine the most appropriate FWI thresholds for discrete levels of wildfire danger. The results are presented in 4 sets of FWI thresholds and they are further evaluated on the basis of verification measures. All sets of FWI thresholds were found to significantly improve the predictability of wildfire danger compared to the EFFIS fire danger class thresholds. In particular, two of them were found to meet selected performance requirements for a balanced predictive performance, namely a reduced overestimation of wildfire danger and increased reliability in danger classification. The results are expected to have significant practical implications for wildfire prevention and risk mitigation strategies implemented by the forest fire control agencies of the country.

Developing group contribution models for the estimation of Atmospheric Lifetime and Minimum Ignition Energy

The Atmospheric Lifetime (ALT) of a compound represents the potential for the atmospheric accumulation of chemicals. Chemicals with a long lifetime are more resistant to natural decomposition and remain in the environment for a longer period. Minimum Ignition Energy (MIE) is one of the most important properties when evaluating hazardous chemicals. Despite the significance of these environment and safety-related properties, currently, there are no group contribution (GC) models that enable their predictive modeling. The present research aims at filling this gap. To this end, experimental data were collected from literature and the GC model parameters were estimated using the weighted nonlinear least-squares regression. Two approaches were applied; in the step-wise approach the parameters of the first, second and third order GC models were estimated sequentially. By comparison, all these parameters were optimized simultaneously in the second approach. The estimated average relative error and correlation coefficient for ALT model were 45.28% and 0.9999 for the step-wise approach, and 26.16% and 0.9999 for the simultaneous approach, respectively. In the case of MIE, the average relative error and correlation coefficient were 16.70% and 0.9964 for the step-wise approach and 11.48% and 0.9999 for the simultaneous approach, respectively. The proposed models not only provide novel tools for the environmental/safety analysis of the common chemicals when experimental values are unavailable, but they could also be applied to computer-aided product design problems; thus contributing towards the development of improved and more sustainable industrial processes.

Pharmacokinetic-Pharmacodynamic Characterization of Omadacycline against Haemophilus influenzae Using a One-Compartment In Vitro Infection Model.

Omadacycline is a novel aminomethylcycline with activity against Gram-positive and -negative organisms, including Haemophilus influenzae, which is one of the leading causes of community-acquired bacterial pneumonia (CABP). The evaluation of antimicrobial agents against H. influenzae using standard murine infection models is challenging due to the low pathogenicity of this species in mice. Therefore, 24-h dose-ranging studies using a one-compartment in vitro infection model were undertaken with the goal of characterizing the magnitude of the ratio of the area under the concentration-time curve (AUC) to the MIC (AUC/MIC ratio) associated with efficacy for a panel of five H. influenzae isolates. These five isolates, for which MIC values were 1 or 2 mg/liter, were exposed to omadacycline total-drug epithelial lining fluid (ELF) concentration-time profiles based on those observed in healthy volunteers following intravenous omadacycline administration. Relationships between change in log10 CFU/ml from baseline at 24 h and the total-drug ELF AUC/MIC ratios for each isolate and for the isolates pooled were evaluated using Hill-type models and nonlinear least-squares regression. As evidenced by the high coefficients of determination (r2) of 0.88 to 0.98, total-drug ELF AUC/MIC ratio described the data well for each isolate and the isolates pooled. The median total-drug ELF AUC/MIC ratios associated with net bacterial stasis and 1- and 2-log10 CFU/ml reductions from baseline at 24 h were 6.91, 8.91, and 11.1, respectively. These data were useful to support the omadacycline dosing regimens selected for the treatment of patients with CABP, as well as susceptibility breakpoints for H. influenzae.

Ratcheting assessment in the tubesheets of heat exchangers using the nonlinear isotropic/kinematic hardening model

In this paper, the ratcheting phenomena in the tubesheet of a heat exchanger, which made of modified 9Cr–1Mo steel, has been investigated. The nonlinear isotropic/kinematic hardening model (combined model) is used to investigate the progressive strains due to the cyclic pressure and temperature loading. Therefore, three series of tests were carried out at different temperatures (room temperature, 300 C∘, 520 C∘) to gain stable hysteresis cycles and to obtain the hardening parameters of the desired material. Via least-squares nonlinear regression, the constitutive coefficients are obtained. In addition the effect of tube number on the progressive strains has been investigated. Therefore, three models of tubesheets with different tube numbers are considered. The results show that the progressive strains initially are significant at each cycle and gradually decrease from their initial amount, they reach a stable state, as the number of the tubes increases, and the more progressive strain accumulates.

Quickstart for SIRD Modeling of the COVID-19 Outbreak

Overview: There are a number of different methodologies that one can employ in order to model the outbreak of an infectious disease, in this case the novel 2019 coronavirus (COVID-19). Some, like generalized logistic models or Richards models rely on the expectation of a logistic pattern of growth in cumulative cases and clasically do not incorporate such complex dynamics as isolation of infected individuals, shelter-in-place orders for the general population (as instituted in New York City), or other change in public health policy over time. Here we present an implementation of a Susceptible-Infected-Recovered-Deceased (SIRD) model, with parameter fitting to real-world data, which can assist in projecting the overall trajectory of an outbreak in response to such complex changes in the environment. Our methodology is contained in a freely available IPython notebook, with the goal of providing a good starting point for other citizen scientists interested in exploring and forecasting the COVID-19 outbreak. Methodology: While a great deal can be learned from the simpler style of models mentioned above, the SIRD model allows for a great deal of nuance in forecasting because it attempts to approximate real-world dynamics, namely the flux of individuals between compartments in the outbreak; for example, susceptible people become infected at a specific rate, and those infected people then recover or die at specific rates. Our implementation of this model utilizes a system of ordinary differential equations (ODEs) inspired by the work of Diego Caccavo [1]. Typically we model the rate of infection as a constant β multiplied by the overall proportion of infected people and by the # of susceptible people. In our methodology, we have instead modeled this β value as a function of time β(t). In this way, we can account for changes in infection rate, for example a decrease due to a lockdown at timepoint t_lockdown (with shelter-in-place, for example) or an increase due to the lifting of such a lockdown at timepoint t_lift (Fig C). After establishing the equations which will dictate the dynamics of the model, we fit the parameters (β, 𝜏_𝛽, 𝛾, 𝛿) using non-linear least-squares regression via a function provided by the SciPy package. Results: We demonstrate a functional IPython Notebook which allows for fitting of SIRD model parameters to real-world datasets. Additionally, we can form rudimentary projections of potential outbreak trajectories in response to real-world changes in the environment in which an outbreak is occuring by modifying the system of ODEs. For example, we show the effect of changing the date on which shelter-in-place measures are lifted on a simulated New York City (NYC). We first fit the parameters of the SIRD model (Fig C) using real-world outbreak data from NYC provided by the NY Times. We then run the model, demonstrating that lifting shelter-in-place public health measures after only a month causes a rebound and second peak in cases in the simulated New York City (Fig A). On the other hand, lifting the shelter-in-place orders after two months allows the outbreak in the simulated city to die down without a second spike in cases (Fig B). Conclusions: Overall, we believe that there is a great deal of predictive and explanatory power provided by SIRD-type models. We hope that other researchers in the field can use our work as a basis for further customization and tailoring of the system of ODEs, allowing these models to be fit to a variety of different cities, states, or other regions. That said, we also want to urge caution to those hoping to utilize these models to exactly predict the course of an outbreak or develop specific timing of public policies. These models are simply projections, and are highly limited by the overall limited availability and quality of data at this point in the COVID-19 outbreak.

Comparison of three different statistical approaches (non-linear least-squares regression, survival analysis and Bayesian inference) in their usefulness for estimating hydrothermal time models of seed germination

AbstractHydrothermal time (HTT) models describe the time course of seed germination for a population of seeds under specific temperature and water potential conditions. The parameters of the HTT model are usually estimated using either a linear regression, non-linear least squares estimation or a generalized linear regression model. There are problems with these approaches, including loss of information, and censoring and lack of independence in the germination data. Model estimation may require optimization, and this can have a heavy computational burden. Here, we compare non-linear regression with survival and Bayesian methods, to estimate HTT models for germination of two clover species. All three methods estimated similar HTT model parameters with similar root mean squared errors. However, the Bayesian approach allowed (1) efficient estimation of model parameters without the need for computation-intensive methods and (2) easy comparison of HTT parameters for the two clover species. HTT models that accounted for a species effect were superior to those that did not. Inspection of credibility intervals and estimated posterior distributions for the Bayesian HTT model shows that it is credible that most HTT model parameters were different for the two clover species, and these differences were consistent with known biological differences between species in their germination behaviour.

Government Size, the Composition of Public Spending and Economic Growth in Netherland

The performance of the fiscal policy is influenced significantly by the relationships and associations among the governmental size, the composition public and private spending and the economic growth of a country. The primary goal of this research study is to evaluate the impact of these factors and to evaluate the significance of these factors in the economic growth of the Netherlands. The economy of Netherlands is characterized as the 17th largest in the world and it presents stable and sustainable growth. In this altercation the researcher aimed to evaluate the significance of the governmental spending and size. For this purpose, the researcher used the data from 2004-2014 from the 12 provinces of Netherlands. The data was subjected to a unit root analysis so that the stationarity properties of the panel data can be evaluated. The unit root test results showed that the variables were stationary at I(0). In order to abstain from the endogeneity issues that can be present in such types of datasets the researcher used level and per capita variables as a robustness evaluation. The empirical framework was based upon the Cobb-Douglas production function and used the modern CES substitution elasticities to compute as the inputs of private capital and government spending in the production function. The nonlinear least-squares regression estimation method was used to evaluate the impact of the variables upon one another. The results indicate that the public investments and current governmental disbursements are conjoined in order to account for the inflexibility of the communal budget. Moreover, the governmental spending was found to be greater than 85 percent indicating that the provincial sectors are focused upon the stimulation of the economy.

Dissecting the statistical properties of the linear extrapolation method of determining protein stability.

The linear extrapolation method to determine protein stability from denaturant-induced unfolding experiments is based on the observation that the free energy of unfolding is often a linear function of the denaturant concentration. The value in the absence of denaturant is then estimated by extrapolation from this linear relationship. Parameters and their confidence intervals are typically estimated by nonlinear least-squares regression. We have compared different methods for calculating confidence intervals and found that a simple method based on linear theory gives accurate results. We have also compared three different parameterizations of the linear extrapolation method and show that the most commonly used form is problematic since the stability and m-value are correlated in the nonlinear least-squares analysis. Parameter correlation can in some cases causes problems in the estimation of confidence intervals and regions and should be avoided when possible. Two alternative parameterizations show much less correlation between parameters.

A spectral weighting function for abiotic photodegradation based on photochemical emission of CO2 from leaf litter in sunlight

Photodegradation can be a significant driver of leaf litter decomposition although the spectral effectiveness of sunlight in driving this process is not well characterized. We developed spectral weighting functions (WFs) for the photochemical emission of CO2 from three leaf litter types using 10 cutoff filters that provided contrasting polychromatic sunlight under clear skies in Tempe, AZ, USA. An iterative nonlinear least-squares regression fitting procedure was used to estimate how effective sunlight at a given wavelength was in eliciting CO2 emission. Although absolute CO2 emission rates varied appreciably among litter types, their WFs were very similar. Using the average WF of all litter types, the effectiveness of sunlight declined from 300 nm by one and two orders of magnitude at 399 and 498 nm, respectively. The slope of the WF was most similar to WFs for CO emission from terrestrial leaf litter and photobleaching of dissolved organic matter in lakes, and was much more gradual than WFs addressing UV damage to biotic processes. Peak effectiveness of clear-sky noon sunlight with our WF occurred at 330 nm, with UV-B (280–320 nm), UV-A (320–400 nm) and visible (400–550 nm) wavebands responsible for 9, 61 and 30% of CO2 emission, respectively. Results from past field studies suggest that solar UV is typically less effective in driving litter mass loss than our WF predicts; we discuss possible reasons for this discrepancy. The gradual slope of our WF implies that differences in UV-B irradiance associated with stratospheric ozone thickness or latitude are unlikely to significantly influence photochemical litter emission.

Patient asynchrony modelling during controlled mechanical ventilation therapy

Background and objectiveMechanical ventilation therapy of respiratory failure patients can be guided by monitoring patient-specific respiratory mechanics. However, the patient's spontaneous breathing effort during controlled ventilation changes airway pressure waveform and thus affects the model-based identification of patient-specific respiratory mechanics parameters. This study develops a model to estimate respiratory mechanics in the presence of patient effort. MethodsGaussian effort model (GEM) is a derivative of the single-compartment model with basis function. GEM model uses a linear combination of basis functions to model the nonlinear pressure waveform of spontaneous breathing patients. The GEM model estimates respiratory mechanics such as Elastance and Resistance along with the magnitudes of basis functions, which accounts for patient inspiratory effort. Results and discussionThe GEM model was tested using both simulated data and a retrospective observational clinical trial patient data. GEM model fitting to the original airway pressure waveform is better than any existing models when reverse triggering asynchrony is present. The fitting error of GEM model was less than 10% for both simulated data and clinical trial patient data. ConclusionGEM can capture the respiratory mechanics in the presence of patient effect in volume control ventilation mode and also can be used to assess patient-ventilator interaction. This model determines basis functions magnitudes, which can be used to simulate any waveform of patient effort pressure for future studies. The estimation of parameter identification GEM model can further be improved by constraining the parameters within a physiologically plausible range during least-square nonlinear regression.

Особливості моделювання твірної поверхні стовбурів дуба звичайного

Узагальнено досвід дослідження форми стовбурів дерев, який дав змогу зробити висновок про переваги математичного моделювання твірної поверхні для аналізу збігу стовбурів. На основі дослідного матеріалу, зібраного в дубових насадженнях Придніпровського правобережного Лісостепу на 17 тимчасових пробних площах, проаналізовано залежність форми стовбурів дуба звичайного (Quercus robur L.) від висоти та діаметра на висоті 1,3 м. За допомогою графічного аналізу та t-тесту середніх значень коефіцієнтів форми Шиффеля на 5 %-му рівні значущості виявлено відмінність у формі стовбурів дуба різних груп діаметрів. За розрядами висот статистично значущої різниці, за характером збігу не встановлено. Виконаний аналіз дав змогу обґрунтувати доцільність моделювання збігу стовбурів дуба звичайного незалежно від висоти, але в межах 3-х груп діаметрів: 20-28 см, 32-40 см та 44-64 см. Як моделі твірної поверхні стовбурів апробовано показниково-степеневі математичні рівняння A. Kozak (1988) і R. Newnham (1992). Підбір параметрів рівнянь виконано для вибірки з 171 модельного дерева в середовищі R за допомогою функції nls − нелінійна мінімізація суми квадратів відхилень. Систематична помилка обох рівнянь виявилася близькою до нуля (0,9-1,7 %), що дало змогу прийняти їх для моделювання твірної поверхні стовбурів різної форми для встановлених груп діаметрів. Розроблені моделі дають змогу прогнозувати діаметри стовбурів дуба на будь-якій висоті зі стандартною помилкою 1,5-3,2 см. Все ж аналіз розподілу залишків математичних моделей засвідчив переваги моделі A. Kozak (1988), яку рекомендовано використовувати надалі для моделювання розмірно-якісної структури стовбурів дуба звичайного.

Nonlinear Estimation of Variables for Heat Release Calculation Using a Gradient Method

Advanced combustion such as the partially premixed combustion (PPC) is characterized by high energy efficiency. However, they are sensitive to the inlet condition and injection of a combustion engine. Therefore, it is essential to use combustion feedback. The accuracy of the feedback variables, derived from the cylinder pressure signal, is crucial for effective combustion feedback control. This paper proposes a nonlinear least-squares regression method to estimate the pressure offsets and variable polytropic exponent in heat release calculation automatically. The combustion feedback variables derived from the auto-tuned heat-release rate were applied to a heavy-duty compression ignition (CI) engine burning with gasoline fuel.

Determination of Desorption Isotherms of Potato Using Gravimetric Method and Fast Isotherm Method

The desorption isotherms of potato (Solanum tuberosum) were determined for a range of temperature 30–60 °C using gravimetric and fast isotherm method over the range of relative humidity 5–85%. The objective of this work is to investigate and document the best practice to perform experiments using both these two methods. The desorption isotherms obtained from the gravimetric method were fitted using three models: GAB, BET, and Oswin. A nonlinear least-square regression analysis was used to evaluate the constants of the three isotherm models. The goodness of the fit was determined by two statistical parameters: standard error and correlation coefficient. GAB model was found to be competent to describe desorption isotherms of potato followed by BET and Oswin model. Also, the sorption behavior of potato obtained from the fast isotherm method was validated to the standard gravimetric method.

Duloxetine plasma level and antidepressant response

BackgroundMajor Depressive Disorder (MDD) is associated with a high rate of inadequate treatment response, which is mainly due to the large inter-individual genetic variability in pharmacokinetic and pharmacodynamic targets of antidepressant drugs. Little is still known about the exact association between plasma level of first-line antidepressants and clinical response. This is particularly true for duloxetine, a dual serotonin and norepinephrine reuptake inhibitor recommended as first-line treatment for MDD. The aim of this study was to investigate the association between serum concentration of duloxetine (SCD) and antidepressant response (AR). Methods66 MDD patients treated with duloxetine 60 mg/day monotherapy were recruited in an outpatient setting and followed for three months. Hamilton Depression Rating Scale - 21 (HAMD-21) was administrated at baseline, at month 1, and at month 3 to assess AR. SCD was measured at steady state. Linear regression analysis and nonlinear least-squares regression were used to estimate association between SCD and AR. ResultsSCD showed a high inter-individual variability in our sample, despite the duloxetine fixed oral dosage. We found a strong association between SCD and AR following a bell-shaped function at month 1 and at month 3. Nonetheless, within the recommended SCD range of 30–120 ng/mL a more linear correlation between SCD and AR was observed. DiscussionOur results suggest that for duloxetine the association between SCD and AR likely follows a bell-shaped quadratic function with poor AR at subtherapeutic SCD and progressive decrease of AR at higher SCD. The maximum antidepressant efficacy seems to require SCD values next to the highest recommended SCD (30–120 ng/mL), probably because of the optimal saturation of both serotonin and norepinephrine transporters. Thus, taking into account the observed high interindividual variability of SCD, our findings suggest that for MDD patients treated with duloxetine, SCD could be a useful tool to guide the treatment by optimizing the oral dosage in order to increase the AR rate.

Modeling viscosity of moderate and light dead oils in the presence of complex aromatic structure

Crude oil viscosity measurements are very crucial in the field of petroleum industries. Difficulties associated with obtaining accurate measured viscosity values for reservoir oils have turned the light to estimate viscosity through empirical correlations to alleviate these laboratory difficulties. This work is a supplementary study for a previous research work, done on Egyptian heavy crude oil samples, to cover all types of reservoir oils. The proposed work started with evaluating the previously published viscosity correlations that considered as a useful method to provide preliminary values for viscous oil reservoirs characterization. The obtained viscosity values showed poor performance of applying these correlations, as these correlations depend only on oil specific gravity and operating temperature. Therefore, there is a need for correlating a new effective viscosity model using asphaltene content as one of the main representative parameters. Asphaltene is considered as a complex aromatic structure which causes problems in reservoir oils. In this work, laboratory measurements have been made on five-hundred database points of Egyptian moderate and light dead oil samples obtained from different locations to build accurate viscosity correlation model. The best fit accurate empirical correlation has been found using multiple least-square nonlinear regression analysis for ranges of viscosity measurements from 23.06 to 43.18 OAPI. Testing of the new proposed viscosity model, with another set of laboratory measured viscosity data, shows high performance and accuracy in predicting Egyptian moderate and light dead crude oils viscosity as compared with literature viscosity correlations.

A kinetic study for the Fenton and photo-Fenton paracetamol degradation in an annular photoreactor

A kinetic model describing Fenton and photo-Fenton degradation of paracetamol (PCT) and consumption of hydrogen peroxide (H2O2) was proposed. A set of Fenton and photo-Fenton experiments (18 runs in total) was performed by fixing the initial concentration of PCT to 40 mg L−1 and varying the initial concentrations of H2O2 and ferrous ion, Fe2+. The experimental set-up was a well-stirred annular photoreactor equipped with an actinic BL TL-DK 36 W/10 1SL lamp. Experimental results highlighted that PCT is no more detected by HPLC analysis within a minimum reaction time of 2.5 and a maximum reaction time of 15.0 min. Besides, a maximum conversion of total organic carbon (TOC) of 68.5% was observed after 75 min of reaction in case of using UV radiation and the highest concentrations of the Fenton reagents. The experimental data were used to fit the kinetic model. The radiation field inside the reactor was taken into account through the local volumetric rate of photon absorption, evaluated by assuming a line source model with spherical and isotropic emission. The kinetic parameters were estimated by using a non-linear least-squares regression procedure and root mean square errors (RMSE) were calculated in order to validate the feasibility of the proposed model. A good agreement between experimental and predicted data was observed and the lowest values of RMSE resulted in 5.84 and 9.59% for PCT and H2O2 normalized concentrations, respectively.

Spectroscopic studies of inclusion complexation between ortho derivatives of p-methylaminobenzoate and α- and γ-cyclodextrins

Using the steady-state and time-resolved spectroscopic techniques and quantum-chemical calculations, photophysical and photochemical properties of the two ortho derivatives of p-methylaminobenzoate (methyl o-methoxy p-methylaminobenzoate (I) and methyl o-hydroxy p-methylaminobenzoate (II)) have been studied in binary mixture THF-H2O and aqueous solutions containing different concentrations of α- and γ-CD. Nonlinear solvatochromic shifts of the absorption and fluorescence bands were observed for both fluorophores in a mixture of polar aprotic (THF) and polar protic (H2O) solvents. This nonlinearity has been explained in terms of the non-specific (dielectric enrichment of the solvent around the polar solute) and specific (hydrogen bond) solute-solvent interactions. Spectroscopic measurements were used to investigate the role of H-bonding solute-solvent interactions, and the excited-state intramolecular proton transfer process in the formation of inclusion complexes between fluorophore and cyclodextrins. The obtained results were used to calculate, according to Benesi–Hildebrand's plot and nonlinear least-squares regression analysis, equilibrium constants of the fluorophore-cyclodextrin inclusion complexes. Performed analysis indicates also that both 1:1 and 1:2 inclusion complexes were formed between studied compounds and α- and γ-cyclodextrins.

Life assessment and health monitoring of rolling element bearings: an experimental study

Rolling element bearings are the key elements of almost all rotating machineries and play a major role in efficient performance of such machines. Industries are facing difficulties to develop a reliable methodology that can help to predict the remaining useful life of such machine elements, so that these can be replaced before catastrophic failure. This study proposes a data-driven framework for predicting the remnant life of bearings, based on nonlinear dimensionality reduction and least-square support vector regression. Experiments are conducted to assess the life of bearing. Vibration signals are extracted from the test bearing and various time and frequency domain features are used to form a health index. This health index is then used for learning and training the regression model which helps in assessment of remaining useful life. Vibration parameters monitoring and wear mechanisms observations have been carried out to identify the various degradation stages of the bearing. Results show the potential of proposed methodology for predicting the remaining useful life of the bearing.

Stepwise regression modeling for compressive strength assessment of mortar containing metakaolin

A stepwise regression (SR) model is developed as a reliable modeling method for simulating and predicting the compressive strength of mortars containing metakaolin at the age of 3, 7, 28, 60, and 90 days. The required data in training and testing state obtained from a reliable data base. A new formulation based on the model have been proposed to predict the compressive strength of mortars containing metakaolin. Besides, to model verification a nonlinear least squares regression (NLSR) has been also developed. Then, a comparison has been made between the proposed SR formulae and NLSR to have an idea about the predictive power of the SR method.