Multiple Model Parameters Research Articles

Multiple parametric mathematical model of the process of consolidation of inhomogeneous soils

Multiple parametric mathematical model of the process of consolidation of inhomogeneous soils

Mechanical-Chemical-Mineralogical Controls on Permeability Evolution of Shale Fractures

We report experimental observations of permeation of CO2-rich aqueous fluids of varied acidic potential (pH) on three different shales to investigate mechanical, chemical, and mineralogical effects on fracture permeability evolution. Surface profilometry and SEM-EDS (scanning electron microscopy with energy-dispersive X-ray spectroscopy) methods are employed to quantify the evolution in both roughness on and chemical constituents within the fracture surface. Results indicate that, after 12 hours of fluid flow, fracture effective hydraulic apertures evolve distinctly under different combinations of shale mineralogy, effective stress, and fluid acidity. The evolution of roughness and transformation of chemical elements on the fracture surface are in accordance with the evolution of permeability. The experimental observations imply that (1) CO2-rich aqueous fluids have significant impact on the evolution of fracture permeability and may influence (and increase) shale gas production; (2) shale mineralogy, especially calcite mineral, decides the chemical reaction and permeability increasing when CO2-rich aqueous fluids flow through fractures by free-face dissolution effect; (3) clay mineral swelling reduces fracture aperture and additively calcite pressure solution removes the bridging asperities, which are the main reasons for fracture permeability decrease; (4) competition roles among clay mineral swelling, mineral pressure solution, and free-face dissolution determine how fracture permeability changes. Furthermore, a multiple parameter model is built to analyze effective hydraulic aperture evolution in considering above three mechanisms, which provide a reference to forecast fracture permeability evolution in shale formations.

Improving multiple model parameters of a complex fluid-loaded structure from acoustic measurements

A method for correcting multiple mechanical and acoustical properties in a finite element model using the Neumann series is presented and demonstrated with numerical examples. In previous work, the authors developed a method for estimating a model parameter in a complex structure using a Neumann series as an approximation to system response. The method computed the sensitivity of the system response due to changes in the parameter and subsequently determined the change needed in the parameter to bring model response into agreement with vibration measurements. This previous work demonstrated the accuracy and computational efficiency of the method when correcting one model parameter. In the present work, the authors extend the analysis to compute sensitivities for multiple parameters of a system, allowing for the correction of more than one parameter. The limits and accuracies of the method are explored for a canonical acoustic system in which a complex structure interacts with an acoustic medium. Two uncertain model parameters of the system are corrected by bringing model response into agreement with acoustic measurements. Results of these examples will be reviewed and presented to illustrate the accuracy and robustness of the method. A method for correcting multiple mechanical and acoustical properties in a finite element model using the Neumann series is presented and demonstrated with numerical examples. In previous work, the authors developed a method for estimating a model parameter in a complex structure using a Neumann series as an approximation to system response. The method computed the sensitivity of the system response due to changes in the parameter and subsequently determined the change needed in the parameter to bring model response into agreement with vibration measurements. This previous work demonstrated the accuracy and computational efficiency of the method when correcting one model parameter. In the present work, the authors extend the analysis to compute sensitivities for multiple parameters of a system, allowing for the correction of more than one parameter. The limits and accuracies of the method are explored for a canonical acoustic system in which a complex structure interacts with an acoustic medium. Two uncer...

Fitting jump models

Abstract We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of model parameters is active at each data point. The framework is quite general and encompasses popular classes of models, such as hidden Markov models and piecewise affine models. The shape of the chosen loss functions to minimize determines the shape of the resulting jump model.

Co-existing feedback loops generate tissue-specific circadian rhythms.

Gene regulatory feedback loops generate autonomous circadian rhythms in mammalian tissues. The well-studied core clock network contains many negative and positive regulations. Multiple feedback loops have been discussed as primary rhythm generators but the design principles of the core clock and differences between tissues are still under debate. Here we use global optimization techniques to fit mathematical models to circadian gene expression profiles for different mammalian tissues. It turns out that for every investigated tissue multiple model parameter sets reproduce the experimental data. We extract for all model versions the most essential feedback loops and find auto-inhibitions of period and cryptochrome genes, Bmal1-Rev-erb-α loops, and repressilator motifs as possible rhythm generators. Interestingly, the essential feedback loops differ between tissues, pointing to specific design principles within the hierarchy of mammalian tissue clocks. Self-inhibitions of Per and Cry genes are characteristic for models of suprachiasmatic nucleus clocks, whereas in liver models many loops act in synergy and are connected by a repressilator motif. Tissue-specific use of a network of co-existing synergistic feedback loops could account for functional differences between organs.

2412 Cost effectiveness analysis of operative Versus antibiotic management for uncomplicated appendicitis

2412 Cost effectiveness analysis of operative Versus antibiotic management for uncomplicated appendicitis

On the effect of model parameters on forecast objects

Abstract. Many physics-based numerical models produce a gridded, spatial field of forecasts, e.g., a temperature map. The field for some quantities generally consists of spatially coherent and disconnected objects. Such objects arise in many problems, including precipitation forecasts in atmospheric models, eddy currents in ocean models, and models of forest fires. Certain features of these objects (e.g., location, size, intensity, and shape) are generally of interest. Here, a methodology is developed for assessing the impact of model parameters on the features of forecast objects. The main ingredients of the methodology include the use of (1) Latin hypercube sampling for varying the values of the model parameters, (2) statistical clustering algorithms for identifying objects, (3) multivariate multiple regression for assessing the impact of multiple model parameters on the distribution (across the forecast domain) of object features, and (4) methods for reducing the number of hypothesis tests and controlling the resulting errors. The final output of the methodology is a series of box plots and confidence intervals that visually display the sensitivities. The methodology is demonstrated on precipitation forecasts from a mesoscale numerical weather prediction model.

Vibration-based damage detection for a population of nominally identical structures: Unsupervised Multiple Model (MM) statistical time series type methods

The problem of vibration-based damage detection for a population of nominally identical structures is considered via unsupervised statistical time series type methods. For this purpose a population sample comprising 31 nominally identical composite beams with significant beam-to-beam variability in the dynamics is employed, with impact-induced damage at various positions and two distinct energy levels. Two Multiple Model, MM, based statistical time series type methods are postulated, assessed, and compared with two ‘conventional’ methods. The assessment is based on a comprehensive and systematic procedure, making use of thousands of test cases via a ‘rotation’ procedure, with the results presented in the form of Receiver Operating Characteristic, ROC, curves. These indicate that ‘conventional’ methods are mostly ineffective, especially with low impact energy damages. On the other hand, the postulated Multiple Model parameter based methods achieve significantly improved performance, characterized as very good and providing overall correct damage detection rates approaching 100% for false alarm rates at or above 5%.

Numerically accurate computational techniques for optimal estimator analyses of multi-parameter models

Modelling unclosed terms in partial differential equations typically involves two steps: First, a set of known quantities needs to be specified as input parameters for a model, and second, a specific functional form needs to be defined to model the unclosed terms by the input parameters. Both steps involve a certain modelling error, with the former known as the irreducible error and the latter referred to as the functional error. Typically, only the total modelling error, which is the sum of functional and irreducible error, is assessed, but the concept of the optimal estimator enables the separate analysis of the total and the irreducible errors, yielding a systematic modelling error decomposition. In this work, attention is paid to the techniques themselves required for the practical computation of irreducible errors. Typically, histograms are used for optimal estimator analyses, but this technique is found to add a non-negligible spurious contribution to the irreducible error if models with multiple input parameters are assessed. Thus, the error decomposition of an optimal estimator analysis becomes inaccurate, and misleading conclusions concerning modelling errors may be drawn. In this work, numerically accurate techniques for optimal estimator analyses are identified and a suitable evaluation of irreducible errors is presented. Four different computational techniques are considered: a histogram technique, artificial neural networks, multivariate adaptive regression splines, and an additive model based on a kernel method. For multiple input parameter models, only artificial neural networks and multivariate adaptive regression splines are found to yield satisfactorily accurate results. Beyond a certain number of input parameters, the assessment of models in an optimal estimator analysis even becomes practically infeasible if histograms are used. The optimal estimator analysis in this paper is applied to modelling the filtered soot intermittency in large eddy simulations using a dataset of a direct numerical simulation of a non-premixed sooting turbulent flame.

Multivariate Alarm Systems for Time-Varying Processes Using Bayesian Filters With Applications to Electrical Pumps

Alarm systems are critically important for safety and efficiency of industrial plants. However, many alarm variables in contemporary alarm systems are generated in a way being isolated from related process variables, resulting in false and missing alarms. This paper is motivated by abnormality detection for condensate-water electrical pumps in thermal power plants and proposes a method to design multivariate alarm systems for time-varying processes. A novel feature to distinguish normal and abnormal conditions is observed on the variation rates of multiple linear regression model parameters. A model estimator based on Bayesian filters is formulated to track the variations of model parameters in normal conditions, and not to do so in abnormal conditions so that absolute cumulative modeling errors are large enough to raise alarms. The effectiveness of the proposed method is validated by industrial case studies.

Analysis of Algorithms for Stable Estimation of Coefficients of Multiple Linear Regression Models

Computational experiments on model data were performed in order to study the effectiveness of the algorithms for realization of the least absolute deviations (LAD) method and the generalized method of the least absolute deviations (GLAD) when estimating the parameters of multiple linear regression models based on descent through the nodal straight lines. In addition, a comparative analysis of the algorithms of descent through nodal straight lines for LAD and GLAD with known exact and approximate methods to solve tasks (2) and (3) was carried out.

Determination of Quark-Gluon-Plasma Parameters from a Global Bayesian Analysis

The quality of data taken at RHIC and LHC as well as the success and sophistication of computational models for the description of ultra-relativistic heavy-ion collisions have advanced to a level that allows for the quantitative extraction of the transport properties of the Quark-Gluon-Plasma. However, the complexity of this task as well as the computational effort associated with it can only be overcome by developing novel methodologies: in this paper we outline such an analysis based on Bayesian Statistics and systematically compare an event-by-event heavy-ion collision model to data from the Large Hadron Collider. We simultaneously probe multiple model parameters including fundamental quark-gluon plasma properties such as the temperature-dependence of the specific shear viscosity η/s, calibrate the model to optimally reproduce experimental data, and extract quantitative constraints for all parameters simultaneously. The method is universal and easily extensible to other data and collision models.

The critical role of uncertainty in projections of hydrological extremes

Abstract. This paper aims to quantify the uncertainty in projections of future hydrological extremes in the Biala Tarnowska River at Koszyce gauging station, south Poland. The approach followed is based on several climate projections obtained from the EURO-CORDEX initiative, raw and bias-corrected realizations of catchment precipitation, and flow simulations derived using multiple hydrological model parameter sets. The projections cover the 21st century. Three sources of uncertainty are considered: one related to climate projection ensemble spread, the second related to the uncertainty in hydrological model parameters and the third related to the error in fitting theoretical distribution models to annual extreme flow series. The uncertainty of projected extreme indices related to hydrological model parameters was conditioned on flow observations from the reference period using the generalized likelihood uncertainty estimation (GLUE) approach, with separate criteria for high- and low-flow extremes. Extreme (low and high) flow quantiles were estimated using the generalized extreme value (GEV) distribution at different return periods and were based on two different lengths of the flow time series. A sensitivity analysis based on the analysis of variance (ANOVA) shows that the uncertainty introduced by the hydrological model parameters can be larger than the climate model variability and the distribution fit uncertainty for the low-flow extremes whilst for the high-flow extremes higher uncertainty is observed from climate models than from hydrological parameter and distribution fit uncertainties. This implies that ignoring one of the three uncertainty sources may cause great risk to future hydrological extreme adaptations and water resource planning and management.

2D data-space cross-gradient joint inversion of MT, gravity and magnetic data

We have developed a data-space multiple cross-gradient joint inversion algorithm, and validated it through synthetic tests and applied it to magnetotelluric (MT), gravity and magnetic datasets acquired along a 95km profile in Benxi-Ji'an area of northeastern China. To begin, we discuss a generalized cross-gradient joint inversion for multiple datasets and model parameters sets, and formulate it in data space. The Lagrange multiplier required for the structural coupling in the data-space method is determined using an iterative solver to avoid calculation of the inverse matrix in solving the large system of equations. Next, using model-space and data-space methods, we inverted the synthetic data and field data. Based on our result, the joint inversion in data-space not only delineates geological bodies more clearly than the separate inversion, but also yields nearly equal results with the one in model-space while consuming much less memory.

Quantifying uncertainty in auto-compensating laser-induced incandescence parameters due to multiple nuisance parameters

Auto-compensating laser-induced incandescence (AC-LII) can be used to infer the particle volume fraction of a soot-laden aerosol. This estimate requires detailed knowledge of multiple model parameters (nuisance parameters), such as the absorption function of soot, calibration coefficients, and laser sheet thickness, which are imperfectly known. This work considers how uncertainties in the nuisance parameters propagate into uncertainties present in soot volume fraction (SVF) and peak particle temperature estimates derived from LII data. The uncertainty of the nuisance parameters is examined and modeled using maximum entropy prior distributions. This uncertainty is then incorporated into the estimates of SVF and peak temperature through a rigorous marginalization technique. Marginalization is carried out using a Gaussian approximation, which is a fast alternative to techniques previously employed to compute uncertainties of AC-LII-derived quantities.

Uncertainty in complex three-dimensional sediment transport models: equifinality in a model application of the Ems Estuary, the Netherlands

Estuarine suspended sediment transport models are typically calibrated against suspended sediment concentration data. These data typically cover a limited range of the actual suspended sediment concentration dynamics, constrained in either time or space. As a result of these data limitations, the available data can be reproduced with complex 3D transport models through multiple sets of model calibration parameters. These various model parameter sets influence the relative importance of transport processes such as settling, deposition, erosion, or mixing. As a result, multiple model parameter sets may reproduce sediment dynamics in tidal channels (where most data is typically collected) with the same degree of accuracy but simulate notably different sediment concentration patterns elsewhere (e.g. on the tidal flats). Different combinations of model input parameters leading to the same result are known as equifinality. The effect of equifinality on predictive model capabilities is investigated with a complex three-dimensional sediment transport model of a turbid estuary which is subject to several human interventions. The effect of two human interventions (offshore disposal of dredged sediment and restoration of the tidal channel profile) was numerically examined with several equifinal model settings. The computed effect of these two human interventions was relatively weakly influenced by the model settings, strengthening confidence in the numerical model predictions.

Adaptive control for robot manipulators using multiple parameter models

In this paper, we propose multiple parameter models based adaptive switching control system for robot manipulators. We first uniformly distribute the parameter set into a finite number of smaller compact subsets. Then, distributed candidate controllers are designed for each of these smaller compact subsets. Using Lyapunov inequality, a candidate controller is identified from the finite set of distributed candidate controllers that best estimates the plant at each instant of time. The design reduced the observer-controller gains by reducing modeling errors and uncertainties via identifying an appropriate control/model via choosing largest guaranteed decrease in the value of the Lyapunov function energy function. Compared with CE based CAC design, the proposed design requires smaller observer-controller gains to ensure stability and tracking performance in the presence of large-scale modeling errors and disturbance uncertainties. In contrast with existing adaptive method, multiple model based distributed hybrid design can be used to reduce the energy consumption of the industrial robotic manipulator for large scale industrial automation by reducing actuator input energy. Finally, the proposed hybrid adaptive control design is experimentally tested on a 3-DOF PhantomTM robot manipulator to demonstrate the theoretical development for real-time applications.

Partitioning of Dichloro-diphenyl-trichloroethane and Its Metabolites Between Artificial Solid Media and Air

Soil–air partitioning is an important diffusive process affecting the environmental fate of organic compounds. In this study, the soil–air partition coefficients (KSA) for dichloro-diphenyl-trichloroethane and its metabolites (designated as DDTs, the sum of p, p′- and o, p′-isomers of DDT, DDD, and DDE) over a temperature range from 5 to 50 °C in artificial solid media were determined by a solid–fugacity meter. The results showed that log KSA gradually increased with soil organic carbon content (fOC). A reversed relationship was observed between log KSA values and the environmental temperatures (T). The enthalpy changes (ΔHSA) indicated that o, p′-isomers required more energy to release from artificial solid media to the gas phase. Moreover, with increasing temperature, the slope of the regression line of log KSA vs. log KOA (octanol–air partition coefficient) was approaching to 1. Based on factors influencing soil–air partitioning and the experimental data, a multiple parameter (T, fOC, and KOA) model was used to predict the KSA values for DDTs.

PeTTSy: a computational tool for perturbation analysis of complex systems biology models.

BackgroundOver the last decade sensitivity analysis techniques have been shown to be very useful to analyse complex and high dimensional Systems Biology models. However, many of the currently available toolboxes have either used parameter sampling, been focused on a restricted set of model observables of interest, studied optimisation of a objective function, or have not dealt with multiple simultaneous model parameter changes where the changes can be permanent or temporary.ResultsHere we introduce our new, freely downloadable toolbox, PeTTSy (Perturbation Theory Toolbox for Systems). PeTTSy is a package for MATLAB which implements a wide array of techniques for the perturbation theory and sensitivity analysis of large and complex ordinary differential equation (ODE) based models. PeTTSy is a comprehensive modelling framework that introduces a number of new approaches and that fully addresses analysis of oscillatory systems. It examines sensitivity analysis of the models to perturbations of parameters, where the perturbation timing, strength, length and overall shape can be controlled by the user. This can be done in a system-global setting, namely, the user can determine how many parameters to perturb, by how much and for how long. PeTTSy also offers the user the ability to explore the effect of the parameter perturbations on many different types of outputs: period, phase (timing of peak) and model solutions. PeTTSy can be employed on a wide range of mathematical models including free-running and forced oscillators and signalling systems.To enable experimental optimisation using the Fisher Information Matrix it efficiently allows one to combine multiple variants of a model (i.e. a model with multiple experimental conditions) in order to determine the value of new experiments. It is especially useful in the analysis of large and complex models involving many variables and parameters.ConclusionsPeTTSy is a comprehensive tool for analysing large and complex models of regulatory and signalling systems. It allows for simulation and analysis of models under a variety of environmental conditions and for experimental optimisation of complex combined experiments. With its unique set of tools it makes a valuable addition to the current library of sensitivity analysis toolboxes. We believe that this software will be of great use to the wider biological, systems biology and modelling communities.Electronic supplementary materialThe online version of this article (doi:10.1186/s12859-016-0972-2) contains supplementary material, which is available to authorized users.

Rapid Computation of Thermodynamic Properties over Multidimensional Nonbonded Parameter Spaces Using Adaptive Multistate Reweighting.

We show how thermodynamic properties of molecular models can be computed over a large, multidimensional parameter space by combining multistate reweighting analysis with a linear basis function approach. This approach reduces the computational cost to estimate thermodynamic properties from molecular simulations for over 130,000 tested parameter combinations from over 1000 CPU years to tens of CPU days. This speed increase is achieved primarily by computing the potential energy as a linear combination of basis functions, computed from either modified simulation code or as the difference of energy between two reference states, which can be done without any simulation code modification. The thermodynamic properties are then estimated with the Multistate Bennett Acceptance Ratio (MBAR) as a function of multiple model parameters without the need to define a priori how the states are connected by a pathway. Instead, we adaptively sample a set of points in parameter space to create mutual configuration space overlap. The existence of regions of poor configuration space overlap are detected by analyzing the eigenvalues of the sampled states' overlap matrix. The configuration space overlap to sampled states is monitored alongside the mean and maximum uncertainty to determine convergence, as neither the uncertainty or the configuration space overlap alone is a sufficient metric of convergence. This adaptive sampling scheme is demonstrated by estimating with high precision the solvation free energies of charged particles of Lennard-Jones plus Coulomb functional form with charges between -2 and +2 and generally physical values of σij and ϵij in TIP3P water. We also compute entropy, enthalpy, and radial distribution functions of arbitrary unsampled parameter combinations using only the data from these sampled states and use the estimates of free energies over the entire space to examine the deviation of atomistic simulations from the Born approximation to the solvation free energy.