Global Nonlinear Modelling of Gas Turbine Dynamics Using NARMAX Structures

Pharmacokinetic-Pharmacodynamic Modeling and Simulation

Spectral knowledge-based regression for laser-induced breakdown spectroscopy quantitative analysis

Estimation of high-spatial resolution clear-sky longwave downward and net radiation over land surfaces from MODIS data

Implied volatility is (almost) past-dependent: Linear vs non-linear models

The pharmacokinetic parameters were estimated and the pharmacokinetic models of aprindine were evaluated in patients. Two pharmacokinetic models were used, comprising a linear elimination model and a non-linear elimination model, both one-compartment models in which first-order absorption is assumed. Twenty-two serum levels of patients in terms of TDM were measured and the pharmacokinetic parameters were estimated using the simple pool method. The pharmacokinetic parameters estimated using a linear model were ka= 0.244 (hr-1), ke=0.020 (hr-1) and Vd=1.778 (1/kg), while those using a non-linear model were ka=0.666 (hr-1), Km=2.022 (μg/ml), Vmax=0.106 (mg/hr/kg) and Vd=2.754 (1/kg).The non-linear model was more suitable than the linear model for the AIC (linear model:-12.59, non-linear model:-19.61). The parameters estimated using the non-linear model were therefore more accurate and were found to have a smaller bias than those estimated using the linear model.

In this chapter we consider dependent data but move from the linear models of Chap.8 to general regression models. As in Chap.6, we consider generalized linear models (GLMs) and, more briefly, nonlinear models. We first give an outline of this chapter. In Sect.9.2 we describe three motivating datasets to which we return throughout the chapter. The GLMs discussed in Sect.6.3 can be extended to incorporate dependences in observations on the same unit; as with the linear model, an obvious way to carry out modeling in this case is to introduce unit-specific random effects. Within a GLM a natural approach is for these random effects to be included on the linear predictor scale. The resultant conditional models are known as generalized linear mixed models (GLMMs), and these are introduced in Sect.9.3. In Sects.9.4 and9.5 we describe likelihood and conditional likelihood methods of estimation, with Sect.9.6 devoted to a Bayesian treatment. Section9.7 illustrates some of the flexibility of GLMMs by describing and applying a particular model for spatial dependence. An alternative random effects specification, based on conjugacy, is described in Sect.9.8. An important approach to the modeling and analysis of dependent data that is philosophically different from the random effects formulation is via marginal models and generalized estimating equations (GEE), and these are the subject of Sect.9.9. In Sect.9.10, a second GEE approach is described in which the estimating equations for the mean are supplemented with a second set for the variances/covariances. For GLMMs, extra care must be taken with parameter interpretation, and Sect.9.11 discusses this issue, emphasizing how interpretation differs between conditional and marginal models. In PartII of the book, which focused on independent data, Chap.7 was devoted to models for binary data. For dependent data, models binary data are less well developed, and so we do not devote a complete chapter to their description. However, Sect.9.12 introduces the modeling of dependent binary data, and, subsequently, Sects.9.13 and 9.14 describe conditional (mixed) and marginal models for binary data. Section 9.15 considers how nonlinear models, as defined in Sect.6.10, can be extended to the dependent data case. For such models, many applications concentrate on inference for units, and so the introduction of random effects is again suggested. We refer to the resultant class of models as nonlinear mixed models (NLMMs). Section9.16 considers issues related to the parameterization of the nonlinear model. Inference for nonlinear mixed models via likelihood and Bayes approaches is covered in Sects.9.17 and9.18, while GEE is briefly considered in Sect.9.19. The assessment of assumptions for general regression models is described in Sect.9.20, with concluding comments contained in Sect.9.21. Additional references appear in Sect.9.22.

Extraction of battery parameters using a multi-objective genetic algorithm with a non-linear circuit model

Purpose: To assess the impact of using breathing adapted radiotherapy on contralateral breast (CB) dose, to relate the thorax shape with the dose to the organs at risk (OARs) and to predict the risk for induced malignancies in CB using linear and non-linear models, following tangential irradiation of breast. Material and methods. Sixteen patients with stage I-II breast cancer treatment planned with tangential fields using deep inspiration breath hold (DIBH) and free breathing (FB) techniques were included in this analysis. The dose results mainly based on DVH analysis were compared. Four parameters were defined to describe thoracic shape. Excess relative risk (ERR) for cancer induction in CB, employing linear and non-linear models was calculated. Results. Average CB volumes exposed to a dose of 1 Gy is 1.3 times higher in DIBH plans than in FB plans. No significant difference in average V3Gy and V5Gy for DIBH and FB plans is observed. The average mean CB dose for DIBH and FB plans is 0.33 and 0.28 Gy, respectively. No correlation between thorax shape parameters and mean OARs dose is observed. The estimated average mean ERR with linear model is lower in FB plans (0.12) than for the DIBH plans (0.14). The estimated ERR with non-linear model is 0.14 for DIBH plans and 0.15 for FB plans. Conclusion. No significant difference in CB dose between DIBH and FB plans is observed. The four thorax shape parameters defined in this study can not be related to the dose at OARs using DIBH and FB radiation techniques. The ERR estimates for secondary CB cancer are nearly the same for FB and DIBH planning when using a linear and non-linear risk prediction models.

Population pharmacokinetic study of tacrolimus in pediatric patients with primary nephrotic syndrome: A comparison of linear and nonlinear Michaelis–Menten pharmacokinetic model

In this work, a nonlinear model is developed to simulate the respiratory system of neonatal infants. The nonlinear model is based on a model proposed by other researchers, but with varying parameters based on the oxygen saturation output [1]. The nonlinear model response is compared to the response of a linearized model given small and large step inputs. For small step sizes, the nonlinear and linear models responses are nearly identical. For larger step sizes, the nonlinear model has a higher steady state response. The linear and nonlinear models are also compared to clinical data taken from a bedside monitor. An error model is also developed given known ranges for model parameter variations. Since the varying parameters change performance, a robust controller is designed using the error model and performance specifications using a μ-synthesis optimization. The controller is shown to have robust stability and performance.

Nonlinear modeling of regenerative cycle micro gas turbine

Information on particulate matter forecast is significant as it allows residents to manage its undesirable effects. For the purpose of predicting PM10 concentration in the air of Tehran, various models were used, including (i) a linear model (multiple liner regression, MLR), (ii) two hybrid models (Adaptive Neuro-Fuzzy Inference System, ANFIS as well as ensemble empirical mode decomposition and general regression neural network, EEMD-GRNN), and (iii) a nonlinear model (multi-layer perceptron, MLP). The output variable in these models was the measure of suspended particles of PM10 while the predictor variables were the information on air quality which consisted of CO, NO2, O3, PM10 of the previous day, PM2.5, and SO2 as well as meteorological data which included average atmospheric pressure (AP), average maximum temperature (Max T), average minimum temperature (Min T), daily relative humidity level of the air (RH), daily total precipitation (TP), and daily wind speed (WS) for the year 2016 in Tehran. Analysis of the data revealed that in comparison with the results of MLR and MLP, ANFIS obtained the most accurate output (R2 = 0.97, root mean square error (RMSE) = 1.0713, and mean absolute error (MAE) = 0.6111) for the training phase and (R2 = 0.89, RMSE = 3.6165, and MAE = 2.8993) the testing phase. However, the hybrid models which were used in the current study had almost similar prediction results. As it can be concluded, in comparison with linear and nonlinear models, hybrid models turn out to have higher accuracy in predicting PM10 concentration.

Temperature-dependent development of pale damsel bug, Nabis capsiformis Geramer (hemiptera: nabidae) using linear and non-linear models

In the previous chapters, we discussed autoregressive linear mixed effects models. In this section, we discuss the relationships between the autoregressive linear mixed effects models and nonlinear mixed effects models, growth curves, and differential equations. The autoregressive model shows a profile approaching an asymptote, where the change is proportional to the distance remaining to the asymptote. Autoregressive models in discrete time correspond to monomolecular curves in continuous time. Autoregressive linear mixed effects models correspond to monomolecular curves with random effects in the baseline and asymptote, and special error terms. The autoregressive coefficient is a nonlinear parameter, but all random effects parameters in the model are linear. Therefore, autoregressive linear mixed effects models are nonlinear mixed effects models without nonlinear random effects and have a closed form of likelihood. When there are time-dependent covariates, autoregressive linear mixed effects models are represented by a differential equation and random effects. The monomolecular curve is one of the popular growth curves. We introduce other growth curves, such as the logistic curves and von Bertalanffy curves, and generalizations of growth curves. Re-parameterization is often performed in nonlinear models, and various representations of re-parameterization in monomolecular and other curves are provided herein.

Accurate forecasting of runoff as an important hydrological variable is a key task for water resources planning and management. Given the importance of this variable, in the current study, a multivariate linear stochastic model (MLSM) is combined with a multilayer nonlinear machine learning model (MNMLM) to generate a hybrid model for the spatial and temporal simulation of runoff in the Quebec basin, Canada. Monthly hydrological data from 2001 to 2013, including precipitation and runoff data from nine stations and Normalized Difference Vegetation Index (NDVI) extraction of MODIS data, are applied as input to the proposed hybrid model. At the first step of the hybrid modeling, data normality and stationary were examined by performing various tests. In the second step, MLSM was developed by defining four different scenarios and as a result 15 sub-scenarios. The first and second scenarios were developed based on one exogenous variable (precipitation or NDVI). In contrast, the second and third scenarios were developed based on two additional variables. In the first and third scenarios, the data are modeled without preprocessing. In the second and fourth scenarios, a preprocessing step is performed on the data. Then, in the third step, various combinations based on different time delays from runoff data were applied for developing nonlinear model. The comparisons are made between observed and simulated time series at various stations and based on the root mean squared error (RMSE), mean absolute error (MAE), correlation coefficient (R) and Akaike information criterion (AIC). The efficiency of the proposed hybrid model is compared with a novel machine learning model that was introduced in 2021 by Sultani et al., and it was also compared with the results obtained from the linear and nonlinear models. In most stations, delays (t-1) and (t-24) are identified as the most effective delays in hybrid and nonlinear modeling of runoff. Also, in most stations, the use of climatic parameters and physiographic factors as exogenous variables along with runoff data improves the results compared to the use of one variable. Results showed that at all stations, proposed hybrid model generally leads to more accurate estimates of runoff compared with various linear and nonlinear models. More accurate estimates of peak runoff values at all stations were another excellence of proposed hybrid model than other models.