Nonparametric Modeling Approach Research Articles

Modeling Magnetorheological Dampers with Application of Nonparametric Approach

This article studies the application of nonparametric modeling approach to model magnetorheological (MR) dampers. For comparison purposes, another typical parametric modeling method for electrorheological (ER) and MR dampers is reviewed. The existing parametric MR damper model includes a stiff Bouc-Wen model that is not friendly for simulation study and real time implementation of model-based advanced control algorithms. In order to avoid the difficulties by using the existing parametric model, the test data from a commercialized MR damper is employed to develop nonparametric models, which can consist of a series of numerically efficient mathematic functions. In addition, the selected functions are required to be continuous and differentiable for potential model-based control algorithms. The results of the nonparametric models show that such different models are comparable. Furthermore, one nonparametric model is selected to be compared with a parametric model and the test data to illustrate the accuracy of the model. The comparison shows that the proposed nonparametric models are able to accurately predict the damper force characteristics, damper bilinear behavior, hysteresis, and electromagnetic saturation. It is further shown that the nonparametric models can be numerically solved with an integration step size of the order of 10 2 s, much faster than the parametric models of the order of 10 5 s, which clearly shows that the proposed nonparametric models are feasible even for real time model-based control algorithms.

A case study on non-parametric design method in ODM collaborative product development

There are two distinct solid design methodologies - parametric and non-parametric approaches. In the past 20 years, most industrial CAD users have been upgrading their CAD design methods from the non-parametric approach to the parametric one. However, with the new trends of globalisation, outsourcing and collaboration, it is timely to ask whether the parametric design is still effective. In this paper, a case study based on the non-parametric CAD modelling approach with a distributed collaborative design system is presented. A real project for a typical mechatronic product is studied in depth. Based on the case study and field observations, we have found that non-parametric modelling methodology enables collaboration in several ways. Further, the non-parametric modelling methodology shows many advantages. A comparative analysis has also been carried out via matching ODM design activities to the strengths and weaknesses of the two approaches. Finally, suggestions for future research directions of collaborative design are given.

A comparison of a parametric and a non-parametric method to value a non-rejectable public good

Some public programs jointly provide a mix of public goods and bads. Consequently, some individuals would pay for the program, while others would not, and might instead need compensation. We provide a parametric and a non-parametric modeling approach to estimate a net willingness to pay (WTP of gainers minus WTA of losers) for a non-rejectable mixed public-good/public-bad. We illustrate the models using data on valuation of prescribed burning of underbrush in forests, which reduces the risk of catastrophic wildfires but produces smoke emissions (the public bad). We compare the two empirical approaches to estimate the net WTP for the program.

Green turtle somatic growth dynamics in a spatially disjunct Great Barrier Reef metapopulation

The growth dynamics of green sea turtles resident in four separate foraging grounds of the southern Great Barrier Reef genetic stock were assessed using a nonparametric regression modeling approach. Juveniles recruit to these grounds at the same size, but grow at foraging-ground-dependent rates that result in significant differences in expected size- or age-at-maturity. Mean age-at-maturity was estimated to vary from 25–50 years depending on the ground. This stock comprises mainly the same mtDNA haplotype, so geographic variability might be due to local environmental conditions rather than genetic factors, although the variability was not a function of latitudinal variation in environmental conditions or whether the food stock was seagrass or algae. Temporal variability in growth rates was evident in response to local environmental stochasticity, so geographic variability might be due to local food stock dynamics. Despite such variability, the expected size-specific growth rate function at all grounds displayed a similar nonmonotonic growth pattern with a juvenile growth spurt at 60–70 cm curved carapace length, (CCL) or 15–20 years of age. Sex-specific growth differences were also evident with females tending to grow faster than similar-sized males after the juvenile growth spurt. It is clear that slow sex-specific growth displaying both spatial and temporal variability and a juvenile growth spurt are distinct growth behaviors of green turtles from this stock.

Spatial and temporal variability in somatic growth of green sea turtles (Chelonia mydas) resident in the Hawaiian Archipelago

The somatic growth dynamics of green turtles (Chelonia mydas) resident in five separate foraging grounds within the Hawaiian Archipelago were assessed using a robust non-parametric regression modelling approach. The foraging grounds range from coral reef habitats at the north-western end of the archipelago, to coastal habitats around the main islands at the south-eastern end of the archipelago. Pelagic juveniles recruit to these neritic foraging grounds from ca. 35 cm SCL or 5 kg (~6 years of age), but grow at foraging-ground-specific rates, which results in quite different size- and age-specific growth rate functions. Growth rates were estimated for the five populations as change in straight carapace length (cm SCL year−1) and, for two of the populations, also as change in body mass (kg year−1). Expected growth rates varied from ca. 0–2.5 cm SCL year−1, depending on the foraging-ground population, which is indicative of slow growth and decades to sexual maturity, since expected size of first-time nesters is ≥80 cm SCL. The expected size-specific growth rate functions for four populations sampled in the south-eastern archipelago displayed a non-monotonic function, with an immature growth spurt at ca. 50–53 cm SCL (~18–23 kg) or ca. 13–19 years of age. The growth spurt for the Midway atoll population in the north-western archipelago occurs at a much larger size (ca. 65 cm SCL or 36 kg), because of slower immature growth rates that might be due to a limited food stock and cooler sea surface temperature. Expected age-at-maturity was estimated to be ca. 35–40 years for the four populations sampled at the south-eastern end of the archipelago, but it might well be >50 years for the Midway population. The Hawaiian stock comprises mainly the same mtDNA haplotype, with no differences in mtDNA stock composition between foraging-ground populations, so that the geographic variability in somatic growth rates within the archipelago is more likely due to local environmental factors rather than genetic factors. Significant temporal variability was also evident, with expected growth rates declining over the last 10–20 years, while green turtle abundance within the archipelago has increased significantly since the mid-1970s. This inverse relationship between somatic growth rates and population abundance suggests a density-dependent effect on somatic growth dynamics that has also been reported recently for a Caribbean green turtle stock. The Hawaiian green turtle stock is characterised by slow growth rates displaying significant spatial and temporal variation and an immature growth spurt. This is consistent with similar findings for a Great Barrier Reef green turtle stock that also comprises many foraging-ground populations spanning a wide geographic range.

Order Determination in Nonlinear Time Series by Penalized Least-Squares

The determination of the order of an autoregressive model is of central interest when using a nonparametric modeling approach. While theory for kernel estimates of the autoregression function is well developed, dimensionality issues may arise when the order of the process increases. In this respect, multivariate adaptive regression splines offer an alternative worth considering because of their ability to efficiently control both bias and model dimension. Here, we present a penalized least-squares approach to order selection using multivariate adaptive regression splines to approximate the unknown regression function. The performance of the method is investigated through numerical simulations of linear and nonlinear models of different orders. Results suggest that the proposed method has a high probability of correct order selection, provided the sample size is sufficiently large with respect to the true order of the series. An analysis of electroencephalogram data is presented as an illustration.

The application of population pharmacokinetic modeling to individualized antibiotic therapy

This paper describes applications of population pharmacokinetic modeling to the optimization of antibiotic dosing. Parametric and nonparametric pharmacokinetic modeling approaches are discussed. Population models can be important extensions of therapeutic drug monitoring (TDM) in infectious disease. The concept of population model-based individualized antimicrobial therapy is described. With the availability of population modeling for obtaining PK parameter estimates, the focus has shifted to quantifying the antimicrobial effect and linking kinetics to drug effects. Examples of integrated pharmacokinetic–pharmacodynamic (PK–PD) models to describe bacterial killing as a function of drug concentration are discussed. Application of PK–PD mathematical models that correlate with microbiological and clinical outcomes will provide us with a better rationale for the proper dose selection of anti-infective therapy in different patient populations.

Flexible modeling of the effects of serum cholesterol on coronary heart disease mortality.

Current understanding of the impact of lipids and other risk factors on coronary heart disease is largely based on the results of parametric multiple regression analyses of large prospective studies. To assess the potential impact of the a priori assumption of linearity of continuous risk factors on the results of parametric analyses, the authors completed a secondary analysis of the Lipid Research Clinics Prevalence and Follow-up Studies (1972-1987) data using an assumption-free nonparametric modeling approach. The effects of total serum cholesterol and the ratio of total serum cholesterol to high density lipoprotein cholesterol, adjusted for common risk factors, were estimated using a smoothing spline method available in the generalized additive model extension of the multiple logistic regression. The data set included 2,512 men in the random sample of the Lipid Research Clinics study who did not take lipid-lowering medications. During the median follow-up of 12.6 years, 94 coronary heart disease deaths occurred. The generalized additive model fits the effects of total serum cholesterol (p < 0.01) and the ratio of total serum cholesterol to high density lipoprotein cholesterol (p < 0.02) significantly better than the parametric logistic regression. Validation studies confirmed that, among new observations arising from the same population, generalized additive model estimates predicted outcomes better than the parametric estimates. Nonlinear effects of both lipid measures were robust and may be clinically important. The authors conclude that the linearity assumption inherent in parametric models may result in biased estimates of the effects of total serum cholesterol on coronary heart disease mortality and recommend that their findings be verified in a nonparametric analysis of data from another large prospective study.

Experimental designs and emission rate modeling for chamber experiments

Abstract This paper considers some of the statistical aspects of estimating specimen emission rate profiles from chamber concentration level measurements, which is a major step in assessing indoor pollution levels. Parametric and nonparametric modeling approaches are applied to the problem, and their relative advantages and disadvantages are discussed. The issue of experimental design is also addressed, and the choice of an optimal set of experimental conditions and sampling times is considered. Some simulation results are presented to contrast the efficiencies of various experimental designs.

Pharmacokinetic-pharmacodynamic modeling of the central nervous system effects of heptabarbital using aperiodic EEG analysis

The concentration EEG effect relationship of heptabarbital was modeled using effect parameters derived from aperiodic EEG analysis. Male Wistar rats (n = 10) received an intravenous infusion of heptabarbital at a rate of 6-9 mg/kg per min until burst suppression with isoelectric periods of 5 sec or longer. Arterial blood samples were obtained and EEG was measured continuously until recovery of baseline EEG and subjected to aperiodic analysis for quantification. Two EEG parameters, the amplitudes per second (AMP) and the total number of waves per second (TNW), in five discrete frequency ranges and for two EEG leads were used as descriptors of the drug effect on the brain. The EEG parameters responded both qualitatively and quantitatively different to increasing concentrations of heptabarbital. Monophasic concentration effect curves (decrease) were found for the frequency ranges greater than 2.5 Hz and successfully quantified with a sigmoidal Emax model after collapsing the hysteresis by a nonparametric modeling approach. For the parameter TNW in the 2.5-30 Hz frequency range the value of the pharmacodynamic parameters EC50, Emax, and n (means +/- SD) were 78 +/- 7 mg/L, 11.4 +/- 1.7 waves/sec and 5.0 +/- 1.5, respectively. For other discrete frequency ranges, differences in EC50 were observed, indicating differences in sensitivity to the effect of heptabarbital. In the 0.5 +/- 2.5 Hz frequency range biphasic concentration effect relationships (increase followed by decrease) were observed. To fully account for the hysteresis in these concentration effect relationships, postulation of two effect compartments was necessary. To characterize these biphasic effect curves two different pharmacodynamic models were evaluated. Model 1 characterized the biphasic concentration effect relationship as the summation of two sigmoidal Emax models, whereas Model 2 assumed the biphasic effect to be the result of only one inhibitory mechanism of action. With Model 1 however realistic parameter estimation was difficult because the maximal increase could not be measured, resulting in high correlations between parameter estimates. This seriously limits the value of Model 1. Model 2 involves besides estimation of the classical pharmacodynamic parameters Emax, EC50, and n also estimation of the maximal disinhibition Amax. This model is a new approach to characterize biphasic drug effects and allows, in principle, reliable estimation of all relevant pharmacodynamic parameters.