Values Of Unknown Parameters Research Articles

Uncertain parameter estimation for a class of nonlinear systems using a polynomial representation of outputs

A novel approach to estimation of structured uncertainties is proposed for a class of nonlinear systems based on algebraic geometry tools. The notion of Polynomial Partition of Unity (PPU) is introduced and it constitutes a key feature of the proposed estimation technique, whose main advantage is the potentiality of being executed offline. Provided that the system dynamics satisfy some PPU and gradient properties, and collecting a sufficient number of measurements at different time steps, the values of unknown parameters are proved to be included in the finite set of common solutions to a family of polynomial equations. An optimization method based on multiple-models is then proposed to further refine the estimation. The case-study of sensorless permanent magnet synchronous motors is presented as a support to theoretical developments.

Dynamically Substructured System Testing for Railway Vehicle Pantographs

]The overall objective of this paper is to establish a dynamically substructured system (DSS) testing approach for railway vehicle pantographs. In this approach a pilot study quasi-pantograph (QP) is tested within a laboratory environment, where the catenary wire, contact wire and catenary support (abbreviated as ‘catenary’ in this paper) are modelled as a numerical substructure. This is simulated in real time and in parallel with the operation of the physical substructure, i.e. the QP rig itself. The entire DSS is driven by parametric excitation within the catenary model, whilst the numerical and physical substructures are synchronised at their interface via the DSS control technique of [1]. Simulation and physical experimental investigations of the pilot QP rig, constructed within the Advanced Control and Test Laboratory at the University of Bristol, UK, demonstrate the efficacy of the method when subjected to parametric variations, unknown parameter values and parametric excitation.

Comparison of two PV array models for the simulation of PV systems using five different algorithms for the parameters identification

Simulation is of primal importance in the prediction of the produced power and automatic fault detection in PV grid-connected systems (PVGCS). The accuracy of simulation results depends on the models used for main components of the PV system, especially for the PV module. The present paper compares two PV array models, the five-parameter model (5PM) and the Sandia Array Performance Model (SAPM). Five different algorithms are used for estimating the unknown parameters of both PV models in order to see how they affect the accuracy of simulations in reproducing the outdoor behavior of three PVGCS. The arrays of the PVGCS are of three different PV module technologies: Crystalline silicon (c-Si), amorphous silicon (a-Si:H) and micromorph silicon (a-Si:H/μc-Si:H).The accuracy of PV module models based on the five algorithms is evaluated by means of the Route Mean Square Error (RMSE) and the Normalized Mean Absolute Error (NMAE), calculated for different weather conditions (clear sky, semi-cloudy and cloudy days). For both models considered in this study, the best accuracy is obtained from simulations using the estimated values of unknown parameters delivered by the ABC algorithm. Where, the maximum error values of RMSE and NMAE stay below 6.61% and 2.66% respectively.

Human judgment vs. quantitative models for the management of ecological resources.

Despite major advances in quantitative approaches to natural resource management, there has been resistance to using these tools in the actual practice of managing ecological populations. Given a managed system and a set of assumptions, translated into a model, optimization methods can be used to solve for the most cost-effective management actions. However, when the underlying assumptions are not met, such methods can potentially lead to decisions that harm the environment and economy. Managers who develop decisions based on past experience and judgment, without the aid of mathematical models, can potentially learn about the system and develop flexible management strategies. However, these strategies are often based on subjective criteria and equally invalid and often unstated assumptions. Given the drawbacks of both methods, it is unclear whether simple quantitative models improve environmental decision making over expert opinion. In this study, we explore how well students, using their experience and judgment, manage simulated fishery populations in an online computer game and compare their management outcomes to the performance of model-based decisions. We consider harvest decisions generated using four different quantitative models: (1) the model used to produce the simulated population dynamics observed in the game, with the values of all parameters known (as a control), (2) the same model, but with unknown parameter values that must be estimated during the game from observed data, (3) models that are structurally different from those used to simulate the population dynamics, and (4) a model that ignores age structure. Humans on average performed much worse than the models in cases 1-3, but in a small minority of scenarios, models produced worse outcomes than those resulting from students making decisions based on experience and judgment. When the models ignored age structure, they generated poorly performing management decisions, but still outperformed students using experience and judgment 66% of the time.

Nonlinear Adaptive Controller Design for Power Systems with STATCOM via Immersion and Invariance

In this paper, a nonlinear adaptive control of generator excitation and Static Synchronous Compensator (STATCOM) is proposed to enhance the transient stability and voltage regulation of an electrical power system. The proposed controller is designed via an adaptive immersion and invariance (I&I) methodology. In particular, a nonlinear model of the power system including two unknown constant parameters, namely an unknown damping coefficient and an unknown perturbation in mechanical power, is considered. It will be shown that the adapive I\&I control law and the parameter adaptation law proposed can accomplish the convergence of the system states to the real value of unknown parameters. Additionally, they can achieve transient stabilization along with voltage regulations. The adaptive I&I controller is validated using a simulation study on a single-machine infinite bus (SMIB) power system and compared with the standard I&I controller and an adaptive backstepping controller. Simulation results are given to indicate the effectiveness of the proposed controller for the transient stabilization and voltage regulation.

Bias correction of the Akaike information criterion in factor analysis

The higher-order asymptotic bias for the Akaike information criterion (AIC) in factor analysis or covariance structure analysis is obtained when the parameter estimators are given by the Wishart maximum likelihood. Since the formula of the exact higher-order bias is complicated, simple approximations which do not include unknown parameter values are obtained. Numerical examples with simulations show that the approximations are reasonably similar to their corresponding exact asymptotic values and simulated values. Simulations for model selection give consistently improved results by the approximate correction of the higher-order bias for the AIC over the usual AIC.

Integration of industrial videogrammetry and artificial neural networks for monitoring and modeling the deformation or displacement of structures

The need to monitor structures permanently and the necessity of performing measurements in a continuous space are of the most important factors which cause some restrictions, such as the rising cost, the dependence on the environment conditions and requirement for high-tech tools for permanent control of displacement and deformation of structures. Videogrammetry, which is used in different fields of industry and manufacturing as a precise and low-cost measurement method, can be utilized in this field. But the use of videogrammetry to control a structure deformation or displacement has four problems including synchronization of cameras in a permanent and long-term monitoring, the need for approximate values of unknown parameters, the necessity for automating the prediction of structure deformation or displacement and the need for high-speed computing. The evaluation of the system designed and implemented in this research shows that using videogrammetry based on the method presented in the research and the integration of videogrammetry and artificial neural networks can solve these problems. The system can be applied to produce the data which are needed for decision support systems to control displacement or deformation of structures intelligently.

Bayesian Analysis of a Threshold Stochastic Volatility Model

This paper proposes a parsimonious threshold stochastic volatility (SV) model for financial asset returns. Instead of imposing a threshold value on the dynamics of the latent volatility process of the SV model, we assume that the innovation of the mean equation follows a threshold distribution in which the mean innovation switches between two regimes. In our model, the threshold is treated as an unknown parameter. We show that the proposed threshold SV model can not only capture the time‐varying volatility of returns, but can also accommodate the asymmetric shape of conditional distribution of the returns. Parameter estimation is carried out by using Markov chain Monte Carlo methods. For model selection and volatility forecast, an auxiliary particle filter technique is employed to approximate the filter and prediction distributions of the returns. Several experiments are conducted to assess the robustness of the proposed model and estimation methods. In the empirical study, we apply our threshold SV model to three return time series. The empirical analysis results show that the threshold parameter has a non‐zero value and the mean innovations belong to two separately distinct regimes. We also find that the model with an unknown threshold parameter value consistently outperforms the model with a known threshold parameter value. Copyright © 2016 John Wiley & Sons, Ltd.

Testing composite parametrical hypotheses without applying the reduction

Usually when the parametrical hypotheses are being tested the Wald reduction from composite hypothesis to the simple one is used. However, in order to apply the reduction method it is needed to know the distribution law of unknown parameter. Practically such a law cannot be determined precisely using the experimental data. First of all, it requires long supervision over the controlled stationary process to provide an inalterability of probability characteristics of the process. In practice the modifications in technological process could be made, and therefore the probability characteristics of the process can also change. Using the example of exponential distribution the algorithm of testing composite parametrical hypothesis about the distribution parameter which does not exceed the declared threshold value without use of reduction is considered in article. Such approach is based on the fact that the partition boundary of the sample space depends monotonously on unknown value of the interest parameter.

Shock capturing data assimilation algorithm for 1D shallow water equations

We propose a new data assimilation algorithm for shallow water equations in one dimension. The algorithm is based upon Discontinuous Galerkin spatial discretization of shallow water equations (DG-SW model) and the continuous formulation of the minimax filter. The latter allows for construction of a robust estimation of the state of the DG-SW model and computes worst-case bounds for the estimation error, provided the uncertain parameters belong to a given bounding set. Numerical studies show that, given sparse observations from numerical or physical experiments, the proposed algorithm quickly reconstructs the true solution even in the presence of shocks, rarefaction waves and unknown values of model parameters. The minimax filter is compared against the ensemble Kalman filter (EnKF) for a benchmark dam-break problem and the results show that the minimax filter converges faster to the true solution for sparse observations.

Populating parameters of web services by automatic composition using search precision and WSDL weight matrix

Web service composition is meant for connecting different web services according to the requirement. This research implements a system for invoking the web services according to the users' requirement and composing the services if required. The unknown values of input parameters are populated by composing available web services automatically and dynamically. The methodology used here is searching the requested services according to the functional word using Bing search engine, processing the search results which have high precision, computation of WSDL weight matrix to select suitable web services for user satisfaction, and populating unknown input parameters' values by composing the web services. Composable web services are found by intra-cluster search and inter-cluster search among different operations of community web services. Composition rule is framed for the services involved in resolving unknown values, pre-condition and effect elements are tested before composition, and web services are invoked according to the composition rule.

Estimating data stream tendencies to adapt clustering parameters

A wide-range of applications based on processing of data streams have emerged in the last decade. They require specialised techniques to obtain representative models and extract information. Traditional data clustering algorithms have been adapted to include continuously arriving data by updating the current model. Most of data stream clustering algorithms aggregate new data into models according to parameters usually set by users. Problems arise when choosing the values of given parameters. When the phenomenon under study is stable, an analysis of a sample of the data stream or a priori knowledge can be used. However, when the behaviour changes over collection, parameters become obsolete and, consequently, the performance is degraded. In this paper, we study the problem of how to automatically adapt control parameters of data stream clustering algorithms. In this sense, we introduce a novel approach to estimate and use data tendencies in order to automatically modify control parameters. We present a proof of the convergence of our approach towards an ideal and unknown value of the control parameter. Experimental results confirm the estimation of data tendency improves learning control parameterisation.

Fast Determination of Vehicle Suspension Parameters via Continuous Time System Identification

Having accurate estimates for the parameter values of different vehicle components is crucial when it comes to the level of virtual testing of vehicle dynamics. Since these values are often not directly available, they need to be obtained from measurements. The most straightforward, but also most expensive way to obtain unknown values is by disassembling the car and by performing tests on the separate vehicle components. A solution that is often much cheaper is to infer estimates of the parameter values from measurements obtained by performing different driving maneuvers with the car. In this paper we show how methods from direct continuous time system identification (CT SysId) can be used to obtain accurate estimates for parameter values of the vehicle suspension system. The dynamic tests consist in exciting the suspension system by driving over one or several small obstacles and by recording the dynamic response of the car. CT Sysld is used to adapt the unknown parameter values of a tentative car model in order to best match the measured data. Evaluation of the approach using a multi-body simulation tool showed that the identified parameter values match well with the ones of the simulated vehicle suspension system.

Inverse problems for delay differential equations using the Collage Theorem

We present a theoretical framework to solve inverse problems for systems of delayed ordinary differential equations (delay ODEs) that allows us to estimate the values of unknown parameters, such as coefficients and time delays, using available time series data. This work builds on similar results for non-delayed ODEs, inspired by the Collage Theorem. We discuss technical details related to the implementation of the method, including the use of non-convex optimization to recover unknown delay values. The performance of the method is demonstrated using simulated and noised datasets to recover parameters in models applied to human health. These include an additive delay model for the population dynamics of malaria transmission, and a distributed delay model for the homeostasis of glucose and insulin in the bloodstream.

Identification of tire force characteristics using a Hybrid method

The present study applies a Hybrid method for identification of unknown parameters in a semi-empirical tire model, the so-called Magic Formula. Firstly, the Hybrid method used a Genetic Algorithm (GA) as a global search methodology with high exploration power. Secondly, the results of the Genetic Algorithm were used as starting values for the Levenberg–Marquardt (LM) algorithm as a gradient-based method with high exploitation power. In this way the beneficial aspects of both methods are simultaneously exploited and their shortcomings are avoided. In order to establish the effectiveness of the proposed method, performance of the Hybrid method has been compared with other methods available in the literature. In addition, the use of GA as a Heuristic method for tire parameters identification has been discussed. Moreover, the extrapolation power of Magic Formula identified with Hybrid method has been properly investigated. Finally, the performance of the Hybrid method has been examined through tire parameter identification with priori known model. The results indicated that the Hybrid method has outstanding benefits such as high convergence speed, high accuracy, and null-sensitivity to the starting values of unknown parameters.

Abstract B2-33: Computational model of chimeric antigen receptor-engineered T cells

Abstract Introduction. The purpose of this study is to create a predictive model that can be used to test hypotheses about chimeric antigen receptor (CAR) activation of T cells in order to optimize the development of these engineered proteins used for cancer immunotherapy. CARs are engineered proteins that contain an extracellular antibody-like region linked to a selection of intracellular signaling domains involved in T cell activation. CAR-engineered T cells have shown promise in treating B cell lymphoma, but they have not been successfully applied to other types of cancers. Additionally, there have been serious side effects when T cell activation goes awry. The specific mechanisms of the signaling and co-stimulatory domains on the CAR are not well understood, and therefore they are hard to control. Developing a computational model capable of comprehensively and quantitatively describing the biochemical reactions involved the CAR-mediated T cell signaling network will help guide the development and optimization of CAR-based cancer immunotherapy. Methods. We have constructed a model of T cell signaling mediated by CARs. Due to the complexity of the multiprotein interactions in this pathway, a rule-based model was written in BioNetGen and implemented in MatLab. The model consists of coupled, nonlinear differential equations, which can be solved to predict the concentrations of molecular species in CAR-mediated T cell signaling. In parallel, we have obtained signaling data using flow cytometry measurements to quantify the time required for ERK phosphorylation, indicating signaling through the MAPK pathway. These data are used to calibrate the model and estimate unknown parameter values. Results. Our computational model is comprised of 181 rules, encoding 1,989 reactions between 20 species. The initial parameter estimates are based on experimentally measured values and a model of T cell receptor signaling (Altan-Bonnet, et al., 2005). Importantly, our model expands upon previous works by modeling separate pathways for specific signaling domains that can be incorporated into the CAR and incorporating more detail into the large multi-protein complexes downstream of the CAR. Extending the model to these multi-protein complexes allows us to predict the levels of downstream proteins that correlate to specific responses of T cell activation, including cell proliferation and survival. We constructed two CAR proteins with different signaling domains (CD3ζ-only and CD3ζ+CD28), and stably expressed them in the Jurkat T cell line. We similarly expressed CD19 in the K562 cell line to be used as target cells. The CAR cells were stimulated with target cells and stained for intracellular flow cytometry analysis of doubly phosphorylated ERK. We performed a local sensitivity analysis to identify the effect of individual parameters on the model predictions. This analysis identified six parameters that most significantly influenced the model. These parameters were fit to ERK phosphorylation data, and we estimated the optimal parameter values required to match the experimental measurements using a nonlinear optimization procedure. Interestingly, the fitted model predicts that the time required for phosphorylation of ERK differs in CD3ζ-only and CD3ζ-CD28 CARs, matching our experimental measurements. The fitting procedure identified multiple parameter sets that fit the data equally well, indicating model robustness. We are currently collecting additional flow cytometry measurements to validate the model predictions. Conclusions. The model is able to accurately represent the effects of CAR signaling to provide insight into how different signaling domains control the strength and persistence of activated T cells. This understanding can be used to optimize CAR engineered T cells to target cancer cells in a manner that is both sensitive and specific. Citation Format: Jennifer Rohrs, Pin Wang, Stacey D. Finley. Computational model of chimeric antigen receptor-engineered T cells. [abstract]. In: Proceedings of the AACR Special Conference on Computational and Systems Biology of Cancer; Feb 8-11 2015; San Francisco, CA. Philadelphia (PA): AACR; Cancer Res 2015;75(22 Suppl 2):Abstract nr B2-33.

Markov chain Monte Carlo simulation using the DREAM software package: Theory, concepts, and MATLAB implementation

Bayesian inference has found widespread application and use in science and engineering to reconcile Earth system models with data, including prediction in space (interpolation), prediction in time (forecasting), assimilation of observations and deterministic/stochastic model output, and inference of the model parameters. Bayes theorem states that the posterior probability, p(H|Y˜) of a hypothesis, H is proportional to the product of the prior probability, p(H) of this hypothesis and the likelihood, L(H|Y˜) of the same hypothesis given the new observations, Y˜, or p(H|Y˜)∝p(H)L(H|Y˜). In science and engineering, H often constitutes some numerical model, ℱ(x) which summarizes, in algebraic and differential equations, state variables and fluxes, all knowledge of the system of interest, and the unknown parameter values, x are subject to inference using the data Y˜. Unfortunately, for complex system models the posterior distribution is often high dimensional and analytically intractable, and sampling methods are required to approximate the target. In this paper I review the basic theory of Markov chain Monte Carlo (MCMC) simulation and introduce a MATLAB toolbox of the DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm developed by Vrugt et al. (2008a, 2009a) and used for Bayesian inference in fields ranging from physics, chemistry and engineering, to ecology, hydrology, and geophysics. This MATLAB toolbox provides scientists and engineers with an arsenal of options and utilities to solve posterior sampling problems involving (among others) bimodality, high-dimensionality, summary statistics, bounded parameter spaces, dynamic simulation models, formal/informal likelihood functions (GLUE), diagnostic model evaluation, data assimilation, Bayesian model averaging, distributed computation, and informative/noninformative prior distributions. The DREAM toolbox supports parallel computing and includes tools for convergence analysis of the sampled chain trajectories and post-processing of the results. Seven different case studies illustrate the main capabilities and functionalities of the MATLAB toolbox.

Effects of hydrologic conditions on SWAT model performance and parameter sensitivity for a small, mixed land use catchment in New Zealand

Abstract. The Soil Water Assessment Tool (SWAT) was configured for the Puarenga Stream catchment (77 km2), Rotorua, New Zealand. The catchment land use is mostly plantation forest, some of which is spray-irrigated with treated wastewater. A Sequential Uncertainty Fitting (SUFI-2) procedure was used to auto-calibrate unknown parameter values in the SWAT model. Model validation was performed using two data sets: (1) monthly instantaneous measurements of suspended sediment (SS), total phosphorus (TP) and total nitrogen (TN) concentrations; and (2) high-frequency (1–2 h) data measured during rainfall events. Monthly instantaneous TP and TN concentrations were generally not reproduced well (24 % bias for TP, 27 % bias for TN, and R2 < 0.1, NSE < 0 for both TP and TN), in contrast to SS concentrations (< 1 % bias; R2 and NSE both > 0.75) during model validation. Comparison of simulated daily mean SS, TP and TN concentrations with daily mean discharge-weighted high-frequency measurements during storm events indicated that model predictions during the high rainfall period considerably underestimated concentrations of SS (44 % bias) and TP (70 % bias), while TN concentrations were comparable (< 1 % bias; R2 and NSE both ~ 0.5). This comparison highlighted the potential for model error associated with quick flow fluxes in flashy lower-order streams to be underestimated compared with low-frequency (e.g. monthly) measurements derived predominantly from base flow measurements. To address this, we recommend that high-frequency, event-based monitoring data are used to support calibration and validation. Simulated discharge, SS, TP and TN loads were partitioned into two components (base flow and quick flow) based on hydrograph separation. A manual procedure (one-at-a-time sensitivity analysis) was used to quantify parameter sensitivity for the two hydrologically separated regimes. Several SWAT parameters were found to have different sensitivities between base flow and quick flow. Parameters relating to main channel processes were more sensitive for the base flow estimates, while those relating to overland processes were more sensitive for the quick flow estimates. This study has important implications for identifying uncertainties in parameter sensitivity and performance of hydrological models applied to catchments with large fluctuations in stream flow and in cases where models are used to examine scenarios that involve substantial changes to the existing flow regime.

Metamodeling and robust minimization approach for the identification of elastic properties of composites by vibration method

This paper describes a method for determination of elastic parameters (elastic moduli and Poisson's ratio) of orthotropic composite plate‐type structural elements using the results of natural frequency measurements. The identification of parameter values is provided by minimization of weighted squared difference (discrepancy) between physically measured frequencies and natural frequencies calculated by Finite Element Method. The metamodels for the frequency dependence on the elastic parameters and other geometrical and physical parameters of test specimens, including parameters with uncertainty (“noisy constants”) are built using experimental designs optimized according to the Mean Squared Error space filling criterion and third‐order polynomial approximations. The minimum of weighted squared difference between measured and calculated frequencies is found using the multistart random search method. The expressions for standard deviations of identified parameters depending on deviations of “noisy constants” are derived using linearized metamodels. The expressions for identification errors allow the statement of the identification task as a robust minimization problem by simultaneous minimization of the discrepancy function and standard deviations of the identified values by varying the values of unknown elastic parameters and weighting coefficients for different frequencies. The partial scaling of natural frequencies is used for the reduction of the uncertainty impact on the identification error. This allows reducing the identification error of elastic moduli about two times and Poisson's ratio about 20 times in comparison with the results obtained by using dimensioned frequencies.

A three domain covariance framework for EEG/MEG data

In this paper we introduce a covariance framework for the analysis of single subject EEG and MEG data that takes into account observed temporal stationarity on small time scales and trial-to-trial variations. We formulate a model for the covariance matrix, which is a Kronecker product of three components that correspond to space, time and epochs/trials, and consider maximum likelihood estimation of the unknown parameter values. An iterative algorithm that finds approximations of the maximum likelihood estimates is proposed. Our covariance model is applicable in a variety of cases where spontaneous EEG or MEG acts as source of noise and realistic noise covariance estimates are needed, such as in evoked activity studies, or where the properties of spontaneous EEG or MEG are themselves the topic of interest, like in combined EEG–fMRI experiments in which the correlation between EEG and fMRI signals is investigated.We use a simulation study to assess the performance of the estimator and investigate the influence of different assumptions about the covariance factors on the estimated covariance matrix and on its components. We apply our method to real EEG and MEG data sets.