Nonlinear Processes (nonlinear + process)

Distribution by Scientific Domains

Selected Abstracts

A Dependence Metric for Possibly Nonlinear Processes

C. W. Granger
Abstract., A transformed metric entropy measure of dependence is studied which satisfies many desirable properties, including being a proper measure of distance. It is capable of good performance in identifying dependence even in possibly nonlinear time series, and is applicable for both continuous and discrete variables. A nonparametric kernel density implementation is considered here for many stylized models including linear and nonlinear MA, AR, GARCH, integrated series and chaotic dynamics. A related permutation test of independence is proposed and compared with several alternatives. [source]

Disparate Scale Nonlinear Interactions in Edge Turbulence

M. Yagi
Abstract In this topical review, we explain the recent achievement in the study of nonlinear interactions, putting an emphasis on the relevance to edge turbulence. First, we start from the survey of the essence in the nonlinear theory of drift wave -zonal flows systems, and visit the experimental observations of the nonlinear interactions of tokamak edge turbulence. Secondly, the universality of intermittent convective transport in the SOL of different magnetic devices are shown. Then, we discuss evolution of collisional drift wave instability in the linear plasma configuration, which is bounded by end plates having analogy to SOL plasmas. By introducing the Numerical Linear Device, the intermittent evolution of large-amplitude instabilities, generation mechanism of the poloidal flow and other nonlinear process are examined. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

Projection and partitioned solution for two-phase flow problems

Andrea Comerlati
Abstract Multiphase flow through porous media is a highly nonlinear process that can be solved numerically with the aid of finite elements (FE) in space and finite differences (FD) in time. For an accurate solution much refined FE grids are generally required with the major computational effort consisting of the resolution to the nonlinearity frequently obtained with the classical Picard linearization approach. The efficiency of the repeated solution to the linear systems within each individual time step represents the key to improve the performance of a multiphase flow simulator. The present paper discusses the performance of the projection solvers (GMRES with restart, TFQMR, and BiCGSTAB) for two global schemes based on a different nodal ordering of the unknowns (ORD1 and ORD2) and a scheme (SPLIT) based on the straightforward inversion of the lumped mass matrix which allows for the preliminary elimination and substitution of the unknown saturations. It is shown that SPLIT is between two and three time faster than ORD1 and ORD2, irrespective of the solver used. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Adaptive transfer function-based control of nonlinear process.

Case study: Control of temperature in industrial methane tank
Abstract The state model-based transfer function models are applied for adaptation of linear controller and disturbance compensator in a feedback/feed-forward control system of nonlinear process. An advantage of the presented adaptation method is the avoidance of artificial disturbances or iterative identification procedures for on-line estimation of process dynamic parameters. The adaptation is based on linearization of the process model at each sampling time about the current state point, independent of the process being at steady-state or transient conditions. The linear time-varying dynamics model is updated on-line using measured values of process variables and reduced to the first-order plus time delay transfer function models in order to directly apply well-developed controller tuning rules. Computational aspects of the adaptation method are discussed and computation algorithms are presented. The adaptive feedback/feed-forward control system was applied for controlling temperature in industrial methane tank, dynamic parameters of which vary in a wide range due to variations of methane-tank process load and external conditions. The heat balance-based process state model is developed and validated using observation data of real plant. Computer simulation of the proposed control system performance under extreme operating conditions demonstrates fast adaptation of controller parameters, robust behaviour and significant improvement in the controllers' performance compared to that of fixed-gain controllers. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A robustness approach to linear control of mildly nonlinear processes

T. Schweickhardt
Abstract We present a novel approach toward linear control of nonlinear systems. Combining robust control theory and nonlinearity measures, we derive a method to (i) assess the nonlinearity of a given control system, (ii) derive a suitable linear model (not necessarily equivalent to the local linearization), and (iii) design a linear controller that guarantees stability of the closed loop containing the nonlinear process. A distinctive feature of the approach is that the nonlinearity analysis, linear model derivation and linear controller synthesis can be done on an operating regime specified by the designer. Examples are given to illustrate the approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

CARS microscopy of lipid stores in yeast: the impact of nutritional state and genetic background

Christian Brackmann
Abstract We have developed a protocol for sub-micrometer resolved and chemically specific imaging of lipid storage in vivo employing coherent anti-Stokes Raman scattering (CARS) microscopy of one of the most important model organisms Saccharomyces cerevisiae,the yeast cell. By probing the carbon,hydrogen vibration using the nonlinear process of CARS, lipid droplets in the yeast cells clearly appear, as confirmed by comparative studies on relevant labeled organelles using two-photon fluorescence microscopy. From the images, unique quantitative data can be deduced with high three-dimensional resolution, such as the volume, shape, number, and intracellular location of the neutral lipid stores. We exemplify the strength and usability of the method for two cases: the impact on lipid storage of the nutritional condition (starvation and type of carbon source available) as well as of genetic modification of two fundamental metabolic regulation pathways involving carbohydrate and lipid storage (BCY1 and DGA1, LRO1, ARE1/2 deletions), respectively. While the impact of carbon source on the total cellular lipid volume was minimal, long-term starvation induces a significant accumulation of lipid droplets. We also confirm that the lipid-storage-deficient mutant is indeed unable to synthesize lipid droplets, and that the inability of the bcy1 -mutant to store carbohydrates is compensated by a two-fold increase in stored neutral lipids. We note that there is a significant cell-to-cell variability in neutral lipid storage in general, i.e. that there is a correspondence to the noise found for gene expression also in lipidomics. Copyright © 2009 John Wiley & Sons, Ltd. [source]

The funnel experiment: The Markov-based SPC approach

Gonen Singer
Abstract The classical funnel experiment was used by Deming to promote the idea of statistical process control (SPC). The popular example illustrates that the implementation of simple feedback rules to stationary processes violates the independence assumption and prevents the implementation of conventional SPC. However, Deming did not indicate how to implement SPC in the presence of such feedback rules. This pedagogical gap is addressed here by introducing a simple feedback rule to the funnel example that results in a nonlinear process to which the traditional SPC methods cannot be applied. The proposed method of Markov-based SPC, which is a simplified version of the context-based SPC method, is shown to monitor the modified process well. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Optimizing Service Attributes: The Seller's Utility Problem,

Fred F. Easton
Abstract Service designers predict market share and sales for their new designs by estimating consumer utilities. The service's technical features (for example, overnight parcel delivery), its price, and the nature of consumer interactions with the service delivery system influence those utilities. Price and the service's technical features are usually quite objective and readily ascertained by the consumer. However, consumer perceptions about their interactions with the service delivery system are usually far more subjective. Furthermore, service designers can only hope to influence those perceptions indirectly through their decisions about nonlinear processes such as employee recruiting, training, and scheduling policies. Like the service's technical features, these process choices affect quality perceptions, market share, revenues, costs, and profits. We propose a heuristic for the NP-hard service design problem that integrates realistic service delivery cost models with conjoint analysis. The resulting seller's utility function links expected profits to the intensity of a service's influential attributes and also reveals an ideal setting or level for each service attribute. In tests with simulated service design problems, our proposed configurations compare quite favorably with the designs suggested by other normative service design heuristics. [source]

The real exchange rate and real interest differentials: the role of nonlinearities

Nelson C. Mark
Abstract Recent empirical work has shown the importance of nonlinear adjustment in the dynamics of real exchange rates and real interest differentials. This work suggests that the tenuous empirical linkage between the real exchange rate and the real interest differential might be strengthened by explicitly accounting for these nonlinearities. We pursue this strategy by pricing the real exchange rate by real interest parity. The resulting first-order stochastic difference equation gives the real exchange rate as the expected present value of future real interest differentials which we compute numerically for three candidate nonlinear processes. Regressions of the log real US dollar prices of the Canadian dollar, deutschemark, yen and pound on the fundamental values implied by these nonlinear models are used to evaluate the linkage. The evidence for linkage is stronger when these present values are computed over shorter horizons than for longer horizons. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Fast implementations and rigorous models: Can both be accommodated in NMPC?

Victor M. Zavala
Abstract In less than two decades, nonlinear model predictive control has evolved from a conceptual framework to an attractive, general approach for the control of constrained nonlinear processes. These advances were realized both through better understanding of stability and robustness properties as well as improved algorithms for dynamic optimization. This study focuses on recent advances in optimization formulations and algorithms, particularly for the simultaneous collocation-based approach. Here, we contrast this approach with competing approaches for online application and discuss further advances to deal with applications of increasing size and complexity. To address these challenges, we adapt the real-time iteration concept, developed in the context of multiple shooting (Real-Time PDE-Constrained Optimization. SIAM: Philadelphia, PA, 2007; 25,52, 3,24), to a collocation-based approach with a full-space nonlinear programming solver. We show that straightforward sensitivity calculations from the Karush,Kuhn,Tucker system also lead to a real-time iteration strategy, with both direct and shifted variants. This approach is demonstrated on a large-scale polymer process, where online calculation effort is reduced by over two orders of magnitude. Copyright © 2007 John Wiley & Sons, Ltd. [source]

A robustness approach to linear control of mildly nonlinear processes

T. Schweickhardt
Abstract We present a novel approach toward linear control of nonlinear systems. Combining robust control theory and nonlinearity measures, we derive a method to (i) assess the nonlinearity of a given control system, (ii) derive a suitable linear model (not necessarily equivalent to the local linearization), and (iii) design a linear controller that guarantees stability of the closed loop containing the nonlinear process. A distinctive feature of the approach is that the nonlinearity analysis, linear model derivation and linear controller synthesis can be done on an operating regime specified by the designer. Examples are given to illustrate the approach. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Fault-tolerant control of nonlinear processes: performance-based reconfiguration and robustness

Prashant Mhaskar
Abstract This work considers the problem of control system/actuator failures in nonlinear processes subject to input constraints and presents two approaches for fault-tolerant control that focus on incorporating performance and robustness considerations, respectively. In both approaches, first a family of candidate control configurations, characterized by different manipulated inputs, is identified for the process under consideration. Performance considerations are first incorporated via the design of a Lyapunov-based predictive controller that enforces closed-loop stability from an explicitly characterized set of initial conditions (computed using an auxiliary Lyapunov-based nonlinear controller). A hierarchical switching policy is derived, that uses stability considerations (evaluated via the presence of the state in the stability region of a control configuration) to ascertain the suitability of a candidate backup configuration and then performance considerations are again considered in choosing between the suitable backup configurations. Next, we consider the problem of implementing fault-tolerant control to nonlinear processes subject to input constraints and uncertainty. To this end, we first design a robust hybrid predictive controller for each candidate control configuration that guarantees stability from an explicitly characterized set of initial conditions, subject to uncertainty and constraints. A switching policy is then derived to orchestrate the activation/deactivation of the constituent control configurations. Finally, simulation studies are presented to demonstrate the implementation and evaluate the effectiveness of the proposed fault-tolerant control method. Copyright © 2005 John Wiley & Sons, Ltd. [source]

Nonlinear experimental design using Bayesian regularized neural networks

AICHE JOURNAL, Issue 6 2007
Matthew C Coleman
Abstract Novel criteria for designing experiments for nonlinear processes are presented. These criteria improve on a previous methodology in that they can be used to suggest a batch of new experiments to perform (as opposed to a single new experiment) and are also optimized for discovering improved optima of the system response. This is accomplished by using information theoretic criterion, which also heuristically penalize experiments that are likely to result in low (nonoptimal) results. While the methods may be applied to any type of nonlinear-nonparametric model (radial basis functions and generalized linear regression), they are here exclusively considered in conjunction with Bayesian regularized feedforward neural networks. A focus on the application of rapid process development, and how to use repeated experiments to optimize the training procedures of Bayesian regularized neural networks is shown. The presented methods are applied to three case studies. The first two case studies involve simulations of one and two-dimensional (2-D) nonlinear regression problems. The third case study involves real historical data from bench-scale fermentations generated in our laboratory. It is shown that using the presented criteria to design new experiments can greatly increase a feedforward neural network's ability to predict global optima. © 2007 American Institute of Chemical Engineers AIChE J, 2007 [source]

Step and pulse response methods for identification of wiener processes

AICHE JOURNAL, Issue 2 2006
Ho Cheol Park
Abstract Lack of simple identification methods for nonlinear processes hinders field applications of nonlinear control systems. For identification methods that are as simple as those for the first order plus time delay models of linear dynamical processes, graphical and least squares methods to identify Wiener-type nonlinear processes from standard responses, such as step, pulse, and square-wave responses, are proposed. Static nonlinear functions are identified independently in Wiener-type nonlinear processes. Graphical methods extract discrete points of the nonlinear static function or a continuous non-parametric model of the nonlinear static function iteratively. The least squares method provides a parametric model of the nonlinear static function. The identified static nonlinear function can be used to design a simple linearizing control system. To illustrate the proposed identification methods, simulation and experimental results are given. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source]

Game theoretic approach to multiobjective designs: Focus on inherent safety

AICHE JOURNAL, Issue 1 2006
Anjana Meel
Abstract A method for designing processes that are inherently safer,with the primary focus on disturbances having the potential for unbounded hazardous responses,is introduced. In cases where safety is not threatened (as in isothermal fermentation reactors), but product quality can rapidly degrade, this method provides designs that ensure high product quality (as in pharmaceutical processes). Using game theory, the method accounts for the trade-offs in profitability, controllability, safety and/or product quality, and flexibility. For nonlinear processes that are hard to control; that is, have an unstable and/or nonminimum-phase steady state, over a wide range of operating conditions, extended bifurcation diagrams are introduced. When a steady state is nonminimum phase, the process may exhibit inverse response. The steady states of processes are classified on the basis of instability and nonminimum-phase behavior to segregate the operating regimes into distinct zones. Locally optimal designs, one corresponding to each zone, are obtained first. These are compared with other locally optimal designs at alternate operating conditions, and/or process reconfigurations, to obtain the globally optimal design using game theory. Four indices,profitability, controllability, safety and/or product quality, and flexibility,characterize the optimality of a design. A novel index for safe operation and/or product quality at a steady state is formulated as a function of the eigenvalues of the Jacobian of the process model and the Jacobian of the process zero dynamics, providing a quantitative measure of instability and nonminimum-phase behavior. The application of the proposed method to an isothermal, continuous stirred-tank reactor (CSTR) with van der Vusse reactions, an exothermic CSTR, and an anaerobic fermentor with substrate and product inhibition is presented. © 2005 American Institute of Chemical Engineers AIChE J, 2006 [source]

Constrained process monitoring: Moving-horizon approach

AICHE JOURNAL, Issue 1 2002
Christopher V. Rao
Moving-horizon estimation (MHE) is an optimization-based strategy for process monitoring and state estimation. One may view MHE as an extension for Kalman filtering for constrained and nonlinear processes. MHE, therefore, subsumes both Kalman and extended Kalman filtering. In addition, MHE allows one to include constraints in the estimation problem. One can significantly improve the quality of state estimates for certain problems by incorporating prior knowledge in the form of inequality constraints. Inequality constraints provide a flexible tool for complementing process knowledge. One also may use inequality constraints as a strategy for model simplification. The ability to include constraints and nonlinear dynamics is what distinguishes MHE from other estimation strategies. Both the practical and theoretical issues related to MHE are discussed. Using a series of example monitoring problems, the practical advantages of MHE are illustrated by demonstrating how the addition of constraints can improve and simplify the process monitoring problem. [source]

A symbolic test for testing independence between time series

Mariano Matilla-García
In this article we introduce a test for independence between two processes {Xt} and {Yt}. To this end we rely on symbolic dynamics and permutation entropy as a measure of dependence. As a result, a nonparametric (model-free) test for either linear or nonlinear processes is presented. The test is consistent for a broad range of dependent alternatives. Empirical simulations indicate and highlight the general utility of the test for time-series analysts. [source]

Further Evidence on PPP Adjustment Speeds: the Case of Effective Real Exchange Rates and the EMS,

Ivan Paya
Abstract Two different approaches intend to resolve the ,puzzling' slow convergence to purchasing power parity (PPP) reported in the literature [see Rogoff (1996), Journal of Economic Literature, Vol. 34.] On the one hand, there are models that consider a non-linear adjustment of real exchange rate to PPP induced by transaction costs. Such costs imply the presence of a certain transaction band where adjustment is too costly to be undertaken. On the other hand, there are models that relax the ,classical' PPP assumption of constant equilibrium real exchange rates. A prominent theory put together by Balassa (1964, Journal of Political Economy, Vol. 72) and Samuelson (1964 Review of Economics and Statistics, Vol. 46), the BS effect, suggests that a non-constant real exchange rate equilibrium is induced by different productivity growth rates between countries. This paper reconciles those two approaches by considering an exponential smooth transition-in-deviation non-linear adjustment mechanism towards non-constant equilibrium real exchange rates within the EMS (European Monetary System) and effective rates. The equilibrium is proxied, in a theoretically appealing manner, using deterministic trends and the relative price of non-tradables to proxy for BS effects. The empirical results provide further support for the hypothesis that real exchange rates are well described by symmetric, nonlinear processes. Furthermore, the half-life of shocks in such models is found to be dramatically shorter than that obtained in linear models. [source]

Thermo-optic nonlinear response of silver nanoparticle colloids under a low power laser irradiation at 532,nm

Rouhollah Karimzadeh
Abstract The thermo-optical properties of silver nanoparticles (AgNPs) in the water are investigated under irradiation of a continuous wave (CW) laser at 532,nm. Thermal conductivity of the AgNP colloids is estimated using the Maxwell model. The closed Z-scan measurements reveal thermal contribution for the nonlinear refractive index of the AgNPs. The Z-scan behavior is investigated based on nonlocal thermo-optic process. It is shown that the aberrant thermal lens model is in excellent agreement with the Z-scan experimental results of the sample. A fit allows extracting the values of nonlinear refractive index and thermo-optic coefficient to be ,1.0,×,10,8,cm2/W and ,0.99,×,10,4,W/mK, respectively. Our results suggest that thermal nonlinear effects play an important role in the development of photonic application involving metal nanoparticle colloids and in the investigation of nonlocal nonlinear processes. [source]

Application of support vector regression for developing soft sensors for nonlinear processes,

Saneej B. Chitralekha
Abstract The field of soft sensor development has gained significant importance in the recent past with the development of efficient and easily employable computational tools for this purpose. The basic idea is to convert the information contained in the input,output data collected from the process into a mathematical model. Such a mathematical model can be used as a cost efficient substitute for hardware sensors. The Support Vector Regression (SVR) tool is one such computational tool that has recently received much attention in the system identification literature, especially because of its successes in building nonlinear blackbox models. The main feature of the algorithm is the use of a nonlinear kernel transformation to map the input variables into a feature space so that their relationship with the output variable becomes linear in the transformed space. This method has excellent generalisation capabilities to high-dimensional nonlinear problems due to the use of functions such as the radial basis functions which have good approximation capabilities as kernels. Another attractive feature of the method is its convex optimization formulation which eradicates the problem of local minima while identifying the nonlinear models. In this work, we demonstrate the application of SVR as an efficient and easy-to-use tool for developing soft sensors for nonlinear processes. In an industrial case study, we illustrate the development of a steady-state Melt Index soft sensor for an industrial scale ethylene vinyl acetate (EVA) polymer extrusion process using SVR. The SVR-based soft sensor, valid over a wide range of melt indices, outperformed the existing nonlinear least-square-based soft sensor in terms of lower prediction errors. In the remaining two other case studies, we demonstrate the application of SVR for developing soft sensors in the form of dynamic models for two nonlinear processes: a simulated pH neutralisation process and a laboratory scale twin screw polymer extrusion process. A heuristic procedure is proposed for developing a dynamic nonlinear-ARX model-based soft sensor using SVR, in which the optimal delay and orders are automatically arrived at using the input,output data. Le domaine du développement des capteurs logiciels a récemment gagné en importance avec la création d'outils de calcul efficaces et facilement utilisables à cette fin. L'idée de base est de convertir l'information obtenue dans les données d'entrée et de sortie recueillies à partir du processus dans un modèle mathématique. Un tel modèle mathématique peut servir de solution de rechange économique pour les capteurs matériels. L'outil de régression par machine à vecteur de support (RMVS) constitue un outil de calcul qui a récemment été l'objet de beaucoup d'attention dans la littérature des systèmes d'identification, surtout en raison de ses succès dans la création de modèles de boîte noire non linéaires. Dans ce travail, nous démontrons l'application de la RMVS comme outil efficace et facile à utiliser pour la création de capteurs logiciels pour les procédés non linéaires. Dans une étude de cas industrielle, nous illustrons le développement d'un capteur logiciel à indice de fluidité à état permanent pour un processus d'extrusion du polymère d'acétate de vinyle-éthylène à l'échelle industrielle en utilisant la RMVS. Le capteur logiciel fondé sur la RMVS, valide sur une vaste gamme d'indices de fluidité, a surclassé le capteur logiciel fondé sur les moindres carrés non linéaires existant en matière d'erreurs de prédiction plus faibles. Dans les deux autres études de cas, nous démontrons l'application de la RMVS pour la création de capteurs logiciels sous la forme de modèles dynamiques pour deux procédés non linéaires: un processus de neutralisation du pH simulé et un processus d'extrusion de polymère à deux vis à l'échelle laboratoire. Une procédure heuristique est proposée pour la création d'un capteur logiciel fondé sur un modèle ARX non linéaire dynamique en utilisant la RMVS, dans lequel on atteint automatiquement le délai optimal et les ordres en utilisant les données d'entrée et de sortie. [source]

The dynamics of NAO teleconnection pattern growth and decay

Steven B. Feldstein
Abstract This investigation performs both diagnostic analyses with NCEP/NCAR re-analysis data and forced, barotropic model calculations to examine the dynamical mechanisms associated with the growth and decay of the North Atlantic Oscillation (NAO) teleconnection pattern. The diagnostic calculations include projection and composite analyses of each term in the stream-function-tendency equation. The results of the analyses reveal a complete life cycle of growth and decay within approximately two weeks. The positive NAO phase is found to develop after anomalous wavetrain propagation across the North Pacific to the east coast of North America. This contrasts with the negative NAO phase which appeared to develop in situ. Both high-frequency (period <10 days) and low-frequency (period >10 days) transient eddy fluxes drive the NAO growth. After the NAO anomaly attains its maximum amplitude, the high-frequency transient eddy fluxes continue to drive the NAO anomaly in a manner that is consistent with a positive feedback process. The decay of the NAO occurs through both the divergence term and the low-frequency transient eddy fluxes. The temporal and spatial properties of the divergence term are found to be consistent with Ekman pumping. These results illustrate many important differences between the NAO and Pacific/North American (PNA) teleconnection patterns, perhaps most striking being that the NAO life cycle is dominated by nonlinear processes, whereas the PNA evolution is primarily linear, In addition, the relation between the NAO and the zonal index is discussed. Copyright © 2003 Royal Meteorological Society [source]

Using ARX and NARX approaches for modeling and prediction of the process behavior: application to a reactor-exchanger

Yahya Chetouani
Abstract Chemical industries are characterized often by nonlinear processes. Therefore, it is often difficult to obtain nonlinear models that accurately describe a plant in all regimes. The main contribution of this work is to establish a reliable model of a process behavior. The use of this model should reflect the normal behavior of the process and allow distinguishing it from an abnormal one. Consequently, the black-box identification based on the neural network (NN) approach by means of a nonlinear autoregressive with exogenous input (NARX) model has been chosen in this study. A comparison with an autoregressive with exogenous input (ARX) model based on the least squares criterion is carried out. This study also shows the choice and the performance of ARX and NARX models in the training and test phases. Statistical criteria are used for the validation of the experimental data of these approaches. The identified neural model is implemented by training a multilayer perceptron artificial neural network (MLP-ANN) with input,output experimental data. An analysis of the inputs number, hidden neurons and their influence on the behavior of the neural predictor is carried out. In order to illustrate the proposed ideas, a reactor-exchanger is used. Satisfactory agreement between identified and experimental data is found and results show that the neural model predicts the evolution of the process dynamics in a better way. Copyright © 2008 Curtin University of Technology and John Wiley & Sons, Ltd. [source]

Models for Bounded Systems with Continuous Dynamics

BIOMETRICS, Issue 3 2009
Amanda R. Cangelosi
Summary Models for natural nonlinear processes, such as population dynamics, have been given much attention in applied mathematics. For example, species competition has been extensively modeled by differential equations. Often, the scientist has preferred to model the underlying dynamical processes (i.e., theoretical mechanisms) in continuous time. It is of both scientific and mathematical interest to implement such models in a statistical framework to quantify uncertainty associated with the models in the presence of observations. That is, given discrete observations arising from the underlying continuous process, the unobserved process can be formally described while accounting for multiple sources of uncertainty (e.g., measurement error, model choice, and inherent stochasticity of process parameters). In addition to continuity, natural processes are often bounded; specifically, they tend to have nonnegative support. Various techniques have been implemented to accommodate nonnegative processes, but such techniques are often limited or overly compromising. This article offers an alternative to common differential modeling practices by using a bias-corrected truncated normal distribution to model the observations and latent process, both having bounded support. Parameters of an underlying continuous process are characterized in a Bayesian hierarchical context, utilizing a fourth-order Runge,Kutta approximation. [source]