First-order Linear Models Research Articles

Dynamic Bayesian hierarchical peak over threshold modeling for real-time crash-risk estimation from conflict extremes

Using traffic conflict-based extreme value theory (EVT) models to quantify real-time crash-risk of road facilities is a promising direction for developing proactive traffic safety management strategies. Existing EVT real-time crash-risk analysis studies have only focused on using block maxima models. This study proposes a dynamic Bayesian hierarchical peak over threshold modeling approach to estimate real-time crash-risk based on traffic conflicts. The proposed approach combines quantile regression, dynamic updating approach, Bayesian hierarchical structure, and the peak over threshold method to generate time-varying generalized Pareto distributions to derive real-time crash-risk measures (i.e., crash probability and return level). The derived real-time crash-risk measures are applied to estimate cycle-level crash-risk at three signalized intersections in Surrey, British Columbia. Five approaches are used to dynamically update the model parameters, including time trend model, generalized autoregressive conditional heteroskedasticity process approach, as well as the first-order, second-order, and third-order dynamic linear models. For comparison, static models are also developed. All the developed models are compared in terms of statistical fit and predictive performance. Based on the best fitted dynamic model, cycle-level crash probability and return level are calculated to measure signalized intersection safety at cycle level. The results show that dynamic models considerably outperform static models in terms of statistical fit and predictive performance. Further, the third-order dynamic model has the best performance, which is probably due to that the model incorporates two linear trends to respectively describe the variation of the coefficients as well as its change to better account for the variation in the effect of time-varying covariates. However, it should be noted that the third-order dynamic model development needs more computation time than other dynamic models, which may limit the application of the model.

Modeling and optimization of cutting process parameters in face milling of EN 31 alloy steel using nanoparticle fluids

ABSTRACT With the progression in technologies, conventional cutting of metal with flood cooling is superseded by some other means, viz. minimum quantity lubrication (MQL). Here, in this current work, we present that hexagonal boron nitride (hBN) nano-fluid particles are used in terms of percentage mixed in SAFCO lubricant oil. The factors, viz. cutting velocity, depth and percentage of nanoparticles are varied to obtain the mathematical models and optimisation of responses, viz. temperature and surface roughness. Desirability function analysis (DFA) approach is adopted for the optimisation process, and regression analysis is executed for the mathematical modelling. Also, criteria importance through inter criteria (CRITIC) approach was implemented to evaluate the weightage of responses first before the DFA application. The analysis of variance reveals that all the factors taken into the existent are significantly affecting the outcomes, and nanoparticles percentage being the most one. The percentage increase of nanoparticles in oil leads to better surface conditions, as depicted by the result. The ideal settings for the optimisation of responses undertaken may be expressed as follows: 600 rpm cutting speed, 0.1 mm of depth and 2% nanoparticle percentage in MQL. The mathematical modelling confirms that first-order linear models are sufficient for both the responses under the given set of design of experiments.

Solving discrete first-order matrix linear control problems with general parametric uncertainties: A probability-density-based approach

This paper deals with the probabilistic analysis of discrete first-order linear control models with uncertainties. For the sake of generality in our stochastic analysis, we assume that all model parameters (the initial and final states, the matrix containing the free dynamics part, and the control’s coefficient) are random variables with an arbitrary joint probability density function. We then combine some results from classical Control Theory with Probability Theory to obtain, under very general hypotheses, the first probability density function of the control and the solution, which are parametric stochastic processes. To illustrate our theoretical findings, we also show two numerical examples and a classical discrete macroeconomic model whose parameters are treated as random variables.

Experimental and Modelling Comparison of the Effects of UV Energy on Liquefaction Efficiency in Coal Liquefaction Mechanism

Coal liquefaction process gives very efficient results, especially for value-added chemicals production from low-quality coal. However, when the literature is examined, notably there is not enough scientific study for liquefaction mechanisms. Here, in this study, There are five different liquefaction mechanisms of Beypazarı coals. It includes four different UV light power and a catalyst environment using 180 watts of UV power. Created first-order linear discrete models were proposed and compared with the experimental results. Additionally, the reaction rate constants for each proposed kinetic model were calculated using the Kalman filter method. However, to evaluate the compatibility of the experimental results and the modeling results, the sum of the squared differences of the values calculated from the experimental data and the models was examined. Because of these studies, it has been observed that the rate constants of direct oil formation from coal at 120 and 180 watts of UV power are at least three times greater than the rate constants for the formation of asphaltene and pre-asphaltene from coal. Simultaneously, The results demonstrate that models with reversible and parallel steps are more compatible with experimental data. Experimental data and modeling results are much more compatible with the studies conducted on Beypazarı coals in a 180-watt UV-catalyzed environment compared to a 180-watt catalyst-free environment. In the presence of ZnO catalyst, the rate constants occurring in the conversion reaction from coal to oil were again three times faster than the conversion rate constants from coal to asphaltene and from coal to preasphaltene. In the modeling and experimental results conducted in the catalyst environment, the efficiency was higher than the catalyst-free environment. The best fit was obtained using model that has both reversible (between asphaltene: coal, asphaltene: oil, and asphaltene: preasphaltene) and irreversible (coal: oil, coal: preasphaltene and preasphaltene: oil) reaction steps. The model also evidenced that reversible reactions are critical on the liquefaction of Beypazarı coal.

Wind farms in AGC: Modelling, simulation and validation

Wind farms are increasingly interested in participating in the secondary frequency control, especially in power systems where AGC is organized by regulation zones comprising generation units of different technologies. In order to estimate the wind farms behaviour and overall impact on automatic generation control (AGC), a reasonably simple wind farm model is needed. First-order and second-order linear models of wind farms are proposed in the literature in AGC-related studies. However, these simple models neglect key dynamic features for AGC integration of wind farms, such as artificial ramp limitations, dead bands, communication delays and start-up delays caused by turbine orientation. This paper presents a still simple wind farm model, however representing all relevant dynamics and availability constraints at power system control level. Applying an illustrative case study, model parameters are tuned and validated by means of field measurements, recorded during a response trail run of a real wind farm of 30 MW installed power operating within the Spanish power system.

Permanent deformation prediction of asphalt concrete mixtures – A synthesis to explore a rational approach

Exploring a reliable laboratory test parameter to predict the rutting (permanent deformation) susceptibility of asphalt concrete (AC) mixtures remains a challenge to asphalt industry. Flow Number (FN) test as part of the HMA mix- and structural- design processes is used to characterize the AC mixtures rutting resistance and optimize field performance. Cognizant of the noise-characteristic of FN test data and need to apply post-processing techniques, this study explores a new parameter – FN Index as a ratio of traditional FN (cycles) and corresponding accumulated permanent strains. The FN and dynamic modulus (DM) tests are conducted on the Superpave gyratory compacted specimens. Twelve (six wearing course and six base course) mixtures were selected including Superpave, Asphalt Institute, British Standard dense bituminous macadam, and Pakistan’s National Highway Authority gradations. Under the hypothesis of axial compression applied on the cylindrical specimen, first-order multiple linear regression models are developed for FN and FN Index as a function of the binder, volumetric parameters, gradation, and DM to estimate permanent deformation. The results indicate that FN models are strongly correlated with DM values at 38°C and 54.4°C temperature, gradation, volumetric, and Superpave rutting parameter. The predictive capability of developed models is validated using data of 16 different AC mixtures acquired from published literature. The findings of this study provide guidance to asphalt mix designers for providing cost-effective designs within specified levels of rutting resistance.

Identification of ankle plantar-flexors dynamics in response to electrical stimulation

Modeling the muscle response to functional electrical stimulation (FES) is an essential step in the design of closed-loop controlled neuroprostheses. This study was aimed at identifying the dynamic response of ankle plantar-flexors to FES during quiet standing. Thirteen healthy subjects stood in a standing frame that locked the knee and hip joints. The ankle plantar-flexors were stimulated bilaterally through surface electrodes and the generated ankle torque was measured. The pulse amplitude was sinusoidally modulated at five different frequencies. The pulse amplitude and the measured ankle torque fitted by a sine function were considered as input and output, respectively. First-order and critically-damped second-order linear models were fitted to the experimental data. Both models fitted similarly well to the experimental data. The coefficient of variation of the time constant among subjects was smaller in the case of the second-order model compared to the first-order model (18.1%vs. 79.9%, p<0.001). We concluded that the critically-damped second-order model more consistently described the relationship between isometric ankle torque and surface FES pulse amplitude, which was applied to the ankle plantar-flexors during quiet standing.

Random First-Order Linear Discrete Models and Their Probabilistic Solution: A Comprehensive Study

This paper presents a complete stochastic solution represented by the first probability density function for random first-order linear difference equations. The study is based on Random Variable Transformation method. The obtained results are given in terms of the probability density functions of the data, namely, initial condition, forcing term, and diffusion coefficient. To conduct the study, all possible cases regarding statistical dependence of the random input parameters are considered. A complete collection of illustrative examples covering all the possible scenarios is provided.

Ozone exposure and flux-based response functions for photosynthetic traits in wheat, maize and poplar

Ozone exposure- and dose-response relationships based on photosynthetic leaf traits (CO2 assimilation, chlorophyll content, Rubisco and PEPc activities) were established for wheat, maize and poplar plants grown in identical controlled conditions, providing a comparison between crop and tree species, as well as between C3 and C4 plants. Intra-specific variability was addressed by comparing two wheat cultivars with contrasting ozone tolerance. Depending on plant models and ozone levels, first-order, second-order and segmented linear regression models were used to derive ozone response functions. Overall, flux-based functions appeared superior to exposure-based functions in describing the data, but the improvement remained modest. The best fit was obtained using the POD0.5 for maize and POD3 for poplar. The POD6 appeared relevant for wheat, although intervarietal differences were found. Our results suggest that taking into account the dynamics of leaf antioxidant capacity could improve current methods for ozone risk assessment for plants.

Cortical Thickness, Cortico-Amygdalar Networks, and Externalizing Behaviors in Healthy Children

Fronto-amygdalar networks are implicated in childhood psychiatric disorders characterized by high rates of externalizing (aggressive, noncompliant, oppositional) behavior. Although externalizing behaviors are distributed continuously across clinical and nonclinical samples, little is known about how brain variations may confer risk for problematic behavior. Here, we studied cortical thickness, amygdala volume, and cortico-amygdalar network correlates of externalizing behavior in a large sample of healthy children. Two hundred ninety-seven healthy children (6-18 years; mean = 12 ± 3 years), with 517 magnetic resonance imaging scans, from the National Institutes of Health Magnetic Resonance Imaging Study of Normal Brain Development, were studied. Relationships between externalizing behaviors (measured with the Child Behavior Checklist) and cortical thickness, amygdala volume, and cortico-amygdalar structural networks were examined using first-order linear mixed-effects models, after controlling for age, sex, scanner, and total brain volume. Results significant at p ≤ .05, following multiple comparison correction, are reported. Left orbitofrontal, right retrosplenial cingulate, and medial temporal cortex thickness were negatively correlated with externalizing behaviors. Although amygdala volume alone was not correlated with externalizing behaviors, an orbitofrontal cortex-amygdala network predicted rates of externalizing behavior. Children with lower levels of externalizing behaviors exhibited positive correlations between orbitofrontal cortex and amygdala structure, while these regions were not correlated in children with higher levels of externalizing behavior. Our findings identify key cortical nodes in frontal, cingulate, and temporal cortex associated with externalizing behaviors in children; and indicate that orbitofrontal-amygdala network properties may influence externalizing behaviors, along a continuum and across healthy and clinical samples.

System-Level Online Power Estimation Using an On-Chip Bus Performance Monitoring Unit

Quality power estimation is a basis of efficient power management of electronic systems. Indirect power measurement, such as power estimation using a CPU performance monitoring unit (PMU), is widely used for its low cost and area overheads. However, the existing CPU PMUs only monitor the core and cache activities, which result in a significant accuracy limitation in the system-wide power estimation including off-chip memory devices. In this paper, we propose an on-chip bus (OCB) PMU that directly captures on-chip and off-chip component activities by snooping the OCB. The OCB PMU stores the activity information in separate counters, and online software converts counter values into actual power values with simple first-order linear power models. We also introduce an optimization algorithm that minimizes the energy model to reduce the number of counters in the OCB PMU. We compare the accuracy of the power estimation using the proposed OCB PMU with real hardware measurement and cycle-accurate system-level power estimation, and demonstrate high estimation accuracy compared with CPU PMU-based estimation method.

FSR methods for second-order regression models

Most variable selection techniques focus on first-order linear regression models. Often, interaction and quadratic terms are also of interest, but the number of candidate predictors grows very fast with the number of original predictors, making variable selection more difficult. Forward selection algorithms are thus developed that enforce natural hierarchies in second-order models to control the entry rate of uninformative effects and to equalize the false selection rates from first-order and second-order terms. Method performance is compared through Monte Carlo simulation and illustrated with data from a Cox regression and from a response surface experiment.

A First-Order Linear Model for the Estimation of Detonation Velocity

A linear multivariable model has been derived for the estimation of detonation velocity. Then, its two simplified forms, first-order linear models, have been proposed as estimators of detonation velocities of a large population of explosives having different skeletal structures. Then, the models are analyzed mathematically and regression equations are obtained and discussed. The first model possesses two independent variables E/M and density, whereas the second one is based on E/M only. The total energy (E) is obtained at the level of UB3LYP/6-31G(d) and M is the molecular weight of the explosive considered.

Spatial autoregressive structure of meander evolution revisited

Meandering rivers are intrinsically dynamic geomorphic systems that exhibit progressive change in their planforms as they migrate across their floodplains. Recent research in river meandering has focused on the development of linear mathematical models of meander migration. These models, which are based on momentum and mass conservation principles, aim to capture the basic physical mechanisms governing flow-sediment interactions in meandering rivers. A common attribute of the models is that bank erosion is represented as a linear function of near-bank velocity and near-bank velocity is expressed as a spatial convolution of channel curvature. Thus, in all of these process-based models, planform curvature, as mediated through its influence on near-bank velocity, has a strong effect on channel migration. Mathematical details of the curvature–migration relation depend on the number of curvature related convolution terms in the model; the number of such terms increases with increasing model order. Although first- through fourth-order linear models have been developed, few studies have examined rigorously the relation between planform curvature and migration in natural rivers to determine if even the simplest model-based curvature–migration relations correspond to relations derived from empirical data. This paper evaluates empirically the spatial structure of the relation between upstream planform curvature and local channel migration for bends along the Beatton River, British Columbia, Canada. In particular, we compare empirically derived curvature–migration relations to the exponential-decay form of this relation embodied in first-order linear mathematical models of meander migration. For this purpose, we use a refined empirical methodology and recently developed analytical techniques that overcome limitations of a similar analysis of the Beatton River bends conducted by Furbish (1991). The refined methodology examines the influence of upstream lags of planform curvature on migration rates. The new analytical techniques provide data on channel curvature and migration rate at a much finer spatial interval than in the analysis of Furbish (1991). The validity of the approach for revealing the exponential-decay structure of the curvature–migration relation is confirmed by applying it to a synthetic data set generated using a first-order mathematical model. In contrast to the findings of Furbish (1991), our results for the Beatton River bends show that the structure of the spatially distributed upstream curvature effect is more complex than pure exponential decay. The findings suggest that oscillatory components of the relation between curvature and migration rate are important in the planform dynamics of individual complex bends. These findings are consistent with results of recent empirical analysis of the curvature–migration relation based on discrete signal processing and with the structure of the curvature–migration relation in high-order mathematical models of meander migration.

Identification of gene interactions in fungal–plant symbiosis through discrete dynamical system modelling

Fungal-plant root associations involve nutrient exchanges, between the partners and the soil, particularly phosphate, that benefit both organisms. Discrete dynamical system (DDS) models are reconstructed to capture gene regulation in the arbuscular mycorrhizae Glomus versiforme-Medicago trunculata root symbiosis. Previously published time-course gene expression data derived from various days post-inoculation were clustered to identify genes co-regulated in mycorrhizal roots. Uncolonised roots grown with high phosphate provide a key nutritional control condition. First-order linear DDS models were created using a data-driven method to fit to the observed gene expression data. The result of the modelling constitutes active gene interactions in the regulatory network of the plant root at 8, 15, 22, 31 and 36 days post-inoculation. These genes are involved in basic metabolism, development, oxidative stress and defense pathways, and show consistent dynamic behaviours in the model. The functions of previously unannotated genes were further elucidated from the developed system maps.

RCA models with GARCH innovations

Rapid developments of time series models and methods addressing volatility in computational finance and econometrics have been recently reported in the financial literature. The non-linear volatility theory either extends and complements existing time series methodology by introducing more general structures or provides an alternative framework (see Abraham and Thavaneswaran [B. Abraham, A. Thavaneswaran, A nonlinear time series model and estimation of missing observations, Ann. Inst. Statist. Math. 43 (1991) 493–504] and Granger [C.W.J. Granger, Overview of non-linear time series specification in Economics, Berkeley NSF-Symposia, 1998]). In this work, we consider Gaussian first-order linear autoregressive models with time varying volatility. General properties for process mean, variance and kurtosis are derived; examples illustrate the wide range of properties that can appear under the autoregressive assumptions. The results can be used in identifying some volatility models. The kurtosis of the classical RCA model of Nicholls and Quinn [D.F. Nicholls, B.G. Quinn, Random Coefficient Autoregressive Models: An Introduction, in: Lecture Notes in Statistics, vol. 11, Springer, New York, 1982] is shown to be a special case.

Identification of an Electric Resistance Furnace

In this paper, the identification of an electric resistance furnace is described. Physical modeling is applied to obtain a mathematical description that captures the static and dynamic behavior of the furnace. Experimental data are collected and used for estimating the parameters of the furnace, which is found to be a dominantly first-order system. First-order linear, bilinear, and direction-dependent models are employed to describe the characteristics of the furnace. A comparison between the quality of these models is made. It was found that the bilinear model provides the best fitting among the three models considered for this particular application.

A Tunable Family of Nonlinear Models

First-order linear dynamic models are extremely popular in a wide variety of applications, but significant nonlinearities are often present, making it desirable to have a simple nonilnear extension of this basic model. This paper considers a particular extension that permits continuous tuning of qualitative model behavior over an enormous range. A number of special cases are discussed and various qualitative characterizations are considered, including steady-state behavior, stability, responses to periodic inputs, and inverse models.

Comparison of non-linear and linear models for estimating haemoglobin adduct stability

According to the kinetic theory for the build-up and elimination of haemoglobin (Hb) adducts, unstable Hb adducts are simultaneously eliminated by zero-order Hb turnover and first-order chemical instability. Thus, the elimination of unstable Hb adducts is non-linear with respect to time. Nonetheless, many studies of Hb adduct stability have characterized the elimination of Hb adducts using linear zero-order or linear first-order models. This paper demonstrates the use of non-linear regression to estimate the first-order rate constant of Hb adduct instability (k) using data on the elimination of Hb adducts in rats dosed with benzene or ortho -toluidine. Results obtained using non-linear regression models are compared with results from the more commonly employed zero- and first-order linear models. It is shown that exposure estimates based on measured levels of unstable Hb adducts can be severely biased if zero-order turnover is assumed. Furthermore, based on published data, estimates of k are subject to estimated relative biases in the range of -4% to 96% when first-order linear models are used to characterize Hb adduct instability.

Multilevel Multifactor Designs for MultivariateCalibration

Multilevel experiments are common in chemistry, especially in calibration and mixture problems. This paper presents designs for l = 2–5 different concentration levels and l2 corresponding experiments. The importance of orthogonality between successive factors is discussed. It is shown that up to 12 mutually orthogonal factors can be generated for a five-level design. Methods of generating designs are generalised. The designs are restricted to first-order (linear) models, typical of most instrumental calibration experiments.