Effect Of Uncertainty In Model Parameters Research Articles

Formation Control of Multiple Underactuated Surface Vessels with a Disturbance Observer

To maintain the formation of underactuated surface vessels (USVs), this study designs a formation controller based on a virtual structure strategy. The problem of formation control is transformed into the problems of tracking the USV position and the virtual structure point position. Meanwhile, to eliminate the effects of model parameter uncertainties and external environment disturbances on USV tracking control, a compensation control algorithm based on disturbance estimation is proposed. The Lyapunov theorem is introduced to ensure that the trajectory tracking error of the proposed control algorithm eventually converges to any small region, which confirms global stability of the designed tracking error. The simulation results demonstrate that the proposed controller can eliminate the effect of external uncertain interference and maintain the formation of multiple USVs.

Uncertainty quantification: data assimilation, propagation and validation of the numerical model of the Arade river cable-stayed bridge

This paper aims at quantifying the uncertainties and their propagation effects in the numerical modelling of a cable-stayed bridge. To this purpose, the uncertainty quantification approach is implemented in a probabilistic finite element geometrically nonlinear elastic analysis performed in ANSYS®. The objective of this paper is to evaluate the impact of statistical treatment of significant parameters on the results and validate a predictive model. Given the uncertainties associated with the input parameters, the propagation of uncertainties of output parameters is evaluated by sampling-based approaches using Monte Carlo method. Finally, the probability density function of outputs is compared with experimental data to extract a measure of confidence in the numerical results. The methodology provides a tool to evaluate the effects of model parameter uncertainty on the modal response of the bridge. Although the results presented in this study are limited to a numerical model of a cable-stayed bridge, this methodology can be readily applied to the different bridges and structural typologies.

A Robust Traffic Control Model Considering Uncertainties in Turning Ratios

The effects of model parameter uncertainty on traffic flow control problems have recently drawn research attention. While the uncertainty in fundamental diagram related parameters has been investigated in the past, few articles have focused on network parameters uncertainty, including turning ratio uncertainty. To fill this gap, this article proposes a robust control model to deal with the uncertainties in the turning ratio by using distributionally robust chance constraints. The model allows one to compute the optimal control action that maximizes some objective, under all possible distributions of network parameters. We then apply this robust control framework to both a freeway network and an urban network, and evaluate the impact of uncertainty on optimal control inputs, over the test networks. The case studies show that compared to non-robust control, the proposed robust model can reduce congestion brought by the uncertainties and improve the overall throughput.

Uncertainty quantification and global sensitivity analysis of continuous distillation considering the interaction of parameter uncertainty with feed variability

In this work, uncertainty and sensitivity analyses were applied to study the joint effects of model parameter uncertainty and feed variability on the response of a computational code for methanol–water continuous distillation. First, model parameter uncertainty (liquid–vapour equilibrium (VLE), enthalpy and tray efficiency) was characterised using existing experimental data. Afterwards, three tower configurations working at two operational modes (fixed product composition and fixed operation conditions) were studied at three feed variability levels. Morris analysis revealed the high importance of the VLE and efficiency-related factors. Sobol sensitivity analysis determined with more precision the sensitivity of the response to the parameters and detected non-linear effects and interactions. The Monte Carlo propagation method allowed obtaining the uncertainty margins as a function of feed variability. The results showed high impact of the model parameter uncertainty and encourage the use of the methods shown to obtain robust designs and quantify simulation accuracy.

Sensitivity of process design to phase equilibrium uncertainty: Study of the isopropanol + DIPE + 2-methoxyethanol system

Process simulators depend on models for estimating basic thermodynamic properties. The parameters of these models are subject to uncertainties due to measurement errors in the experimental data and the uncertainties are typically assumed to be insignificant in process simulation. This work shows the effect of model parameter uncertainty in the process simulation of extractive distillation for the separation of a diisopropyl ether – isopropyl alcohol minimum boiling azeotrope with entrainer 2-methoxyethanol. This is achieved by extending the application of the uncertainty quantification framework used by Hajipour and Satyro to an extractive distillation process. The approach used was to obtain the best fit of experimentally available literature data and then perform uncertainty quantification based on the combined experimental and model uncertainties using a Monte Carlo simulation for the uncertainty propagation and Aspen Plus® for process simulation. This systematic analysis of model uncertainty provides quantitative insight into the propagation of thermodynamic model errors to the various unit operations. It was found that while the propagated model parameters are able to predict the phase behaviour with a 95% certainty, significant deviations may occur for the process simulation. The approach can be used to improve the confidence with which appropriate safe design margins are assigned to columns and identify the risk areas in the design.

The Second-Order Adjoint Sensitivity Analysis Methodology for Nonlinear Systems—II: Illustrative Application to a Nonlinear Heat Conduction Problem

This work presents an illustrative application of the second-order adjoint sensitivity analysis methodology (2nd-ASAM) to a paradigm nonlinear heat conduction benchmark, which models a conceptual experimental test section containing heated rods immersed in liquid lead—bismuth eutectic (LBE). This benchmark admits an exact solution, thereby making transparent the underlying mathematical derivations. The general theory underlying 2nd-ASAM indicates that for a physical system comprising Nα parameters, the computation of all of the first- and second-order response sensitivities requires (per response) at most Nα large-scale computations using the first-level adjoint sensitivity system (1st-LASS) and second-level adjoint sensitivity system (2nd-LASS), respectively. For this illustrative problem, six large-scale adjoint computations sufficed to compute exactly all 5 first-order and 15 distinct second-order derivatives of the temperature response to the five model parameters. The construction and solution of the 2nd-LASS require very little additional effort beyond the construction of the adjoint sensitivity system needed for computing the first-order sensitivities. Very significantly, only the sources on the right sides of the heat conduction differential operator needed to be modified; the left side of the differential equations (and hence the solver in large-scale practical applications) remains unchanged.The second-order sensitivities play the following roles: (1) They cause the expected value of the response to differ from the computed nominal value of the response; for the nonlinear heat conduction benchmark, however, these differences were insignificant over the range of temperatures (400 to 900 K) considered. (2) They contribute to increasing the response variances and modifying the response covariances, but for the nonlinear heat conduction benchmark, their contribution was smaller than that stemming from the first-order response sensitivities, over the range of temperatures (400 to 900 K) considered. (3) They provide the leading contributions to causing asymmetries in the response distribution. For the benchmark test section considered in this work, the heat source, the boundary heat flux, and the temperature at the bottom boundary of the test section would cause the temperature distribution in the test section to be skewed significantly toward values lower than the mean temperature. On the other hand, the model parameters entering the nonlinear, temperature-dependent expression of the LBE conductivity would cause the temperature distribution in the test section to be skewed significantly toward values higher than the mean temperature. These opposite effects partially cancel each other. Consequently, the cumulative effects of model parameter uncertainties on the skewness of the temperature distribution in the test section are such that the temperature distribution in the LBE is skewed slightly toward higher temperatures in the cooler part of the test section but becomes increasingly skewed toward temperatures lower than the mean temperature in the hotter part of the test section. Notably, the influence of the model parameter that controls the strength of the nonlinearity in the heat conduction coefficient for this LBE test section benchmark would be strong if it were the only uncertain model parameter. However, if all of the other model parameters are also uncertain, all having equal relative standard deviations, the uncertainties in the heat source and boundary heat flux diminish the impact of uncertainties in the nonlinear heat conduction coefficient for the range of temperatures (400 to 900 K) considered for this LBE test section benchmark.Ongoing work aims at generalizing the 2nd-ASAM to enable the exact and efficient computation of higher-order response sensitivities. The availability of such higher-order sensitivities is expected to affect significantly the fields of optimization and predictive modeling, including uncertainty quantification, data assimilation, model calibration, and extrapolation.

Signal extraction goodness-of-fit diagnostic tests under model parameter uncertainty: Formulations and empirical evaluation

ABSTRACTWe present a time-domain goodness-of-fit (gof) diagnostic test that is based on signal-extraction variances for nonstationary time series. This diagnostic test extends the time-domain gof statistic of Maravall (2003) by taking into account the effects of model parameter uncertainty, utilizing theoretical results of McElroy and Holan (2009). We demonstrate that omitting this correction results in a severely undersized statistic. Adequate size and power are obtained in Monte Carlo studies for fairly short time series (10 to 15 years of monthly data). Our Monte Carlo studies of finite sample size and power consider different combinations of both signal and noise components using seasonal, trend, and irregular component models obtained via canonical decomposition. Details of the implementation appropriate for SARIMA models are given. We apply the gof diagnostic test statistics to several U.S. Census Bureau time series. The results generally corroborate the output of the automatic model selection procedure of the X-12-ARIMA software, which in contrast to our diagnostic test statistic does not involve hypothesis testing. We conclude that these diagnostic test statistics are a useful supplementary model-checking tool for practitioners engaged in the task of model-based seasonal adjustment.

Parameter-Dependent Lyapunov Functions in the Robust Control of Discrete Linear Repetitive Processes Using Previous Pass-Windowed Information

Abstract The variables in multidimensional systems are functions of more than one indeterminate, and such systems cannot be controlled by standard systems theory. This paper considers a subclass of these systems that operate over a subset of the upper-right quadrant of the two-dimensional (2D) plane in the discrete domain with a specified recursive structure known as repetitive processes. Physical examples of such processes are known and also their representations can be used in the analysis of other classes of systems, such as iterative learning control. This paper gives new results on the use of the parameter-dependent Lyapunov functions for stability analysis and controls law design of a subclass of repetitive processes that arise in application areas. These results aim to eliminate or reduce the effects of model parameter uncertainty.

Predictive sliding mode based cascade control for parametric uncertainty

In this paper, a predictive sliding mode control based cascade control strategy is proposed for improving system performance and to reduce the effect of uncertainty in model parameters such as varying time-delay and varying time constant of the system. The proposed structure has two controllers in the primary loop and one controller in the secondary loop. The disturbance rejection and delay compensation strategies are incorporated in the primary loop. The primary controller is designed with Smith predictor based sliding mode control to eliminate the effects of model parameter uncertainty, which occur due to modeling inaccuracies in identification of overall primary process model into first order plus dead-time model. The disturbance rejection control law is designed to reduce the effect of disturbances in steady state operating condition. The secondary controller is designed based on conventional sliding mode approach with first order sliding surface. A new control scheme has been proposed looking for superior performance and robustness improvement. Simulation example is given to illustrate the use of the proposed method and its superiority over some existing design methods.

基于SWAT模型参数不确定性的黑河流域流量预测

水文模拟不确定性研究是当今水文科学研究中的热点问题。本文以流域水文模型SWAT为例，以黑河流域作为研究区，基于贝叶斯理论和方法，探讨SWAT模型参数不确定性对流量模拟和预测结果的影响。结果表明，在黑河流域，降水的变化幅度越大，模型参数不确定性对流量模拟和预测的影响越小；在降水变化相同条件下，温度增加会使模型参数不确定性对流量预测值的影响增大；在模型参数不确定性影响下，预测流量的不确定性区间夏季(尤其是6、7月份)最大；随着降水的减少预测流量值趋于减少，但预测流量值的不确定性区间变化不大；随着气温的升高，春季流量预测值有所增加，且春季流量预测值的不确定性区间也趋于增大；降水增加条件下，随着气温的降低，预测流量过程线越来越尖耸；降水减少条件下，随着气温的降低，预测流量过程线形状变化不大。 Uncertainty issue in hydrological modeling is a hot topic in recent hydrological research. Taking Heihe river basin as the study area, we mainly focused on the uncertainty in runoff prediction resulted from SWAT model parameter uncertainty. Bayesian method was employed for nine sensitive parameter estimations. We used 95% CI of runoff prediction to illustrate the uncertainty in runoff prediction caused by model parameter uncertainties. Results showed that: the larger the range of changing in precipitation, the narrower the 95% CIs of runoff prediction, the less effects of model parameter uncertainties to runoff prediction. With the increasing of temperature, the 95% CIs of runoff prediction were stretched if the precipitation kept stable, which means that the increases in temperature would lead to larger effects of model parameter uncertainty to runoff prediction. The 95% CIs of summer runoff prediction were the largest, followed by those of autumn and winter runoff predictions. With the decreasing of precipitation, the runoff prediction showed decreasing, while the corresponding 95% CI was little changed. With the increasing of temperature, both the spring runoff prediction and its 95% CI showed increasing.

Influence of Model Parameter Uncertainty on Seismic Transverse Response and Vulnerability of Steel–Concrete Composite Bridges with Dual Load Path

This paper uses a fully probabilistic approach to investigate the seismic response of multispan continuous bridges with dissipative piers and a steel–concrete composite (SCC) deck, the motion of which is transversally restrained at the abutments. This bridge typology is characterized by complex dual load path behavior in the transverse direction, with multiple failure modes involving both the deck and the piers. Proper assessment of the seismic vulnerability of these structural systems must rigorously take into account all pertinent sources of uncertainty, including uncertainties in both the seismic input (record-to-record variability) and the properties defining the structural model (model parameters). Model parameter uncertainty affects not only the structural capacity, but also the seismic response of a structural system. However, most of the procedures for seismic vulnerability assessment focus on the variability of the response resulting solely from seismic input uncertainty. These procedures either neglect model parameter uncertainty effects or incorporate these effects only in a simplified way. A computationally expensive but rigorous procedure is introduced in this work to include the effects of model parameter uncertainty on the seismic response and vulnerability assessment of SCC bridges with dual load path. Monte Carlo simulation with Latin hypercube sampling, in conjunction with probabilistic moment–curvature analysis, is used to build probabilistic finite-element models of the bridges under study. Extended incremental dynamic analysis is used to propagate all pertinent sources of uncertainty to the seismic demand. The proposed procedure is then applied to the assessment of three benchmark bridges exhibiting different seismic behavior and dominant failure modes. Comparison of the response variability induced by seismic input uncertainty and the response variability induced by model parameter uncertainty highlights the importance of accounting for the latter when evaluating the safety of the typology of bridges considered in this study.

Regionalisation of hydrological model parameters under parameter uncertainty: A case study involving TOPMODEL and basins across the globe

In this paper, we present a method to account for modeling uncertainties while regionalising model parameters. Linking model parameters to physical catchment attributes is a popular approach that enables the application of a conceptual model to an ungauged site. The functional relationship can be derived either from the calibrated model parameters (direct calibration method) or by calibrating the functional function (regional calibration method). Both of these approaches are explored through a case study involving TOPMODEL and a number of small- to medium-sized humid basins located in various geographic and climatic regions around the globe. The predictive performance of the functional relationship derived using the direct calibration method (e.g., multiple regression, artificial neural network and partial least square regression) varied among the different schemes. However, the average of the model parameters estimated from regionalisation schemes based on direct calibration is found to be a better surrogate. Even with the use of a parsimonious hydrological model and with posing model calibration as a multi-objective problem, the model parameter uncertainty and its effect on model prediction were observed to be high and varied among the basins. Therefore, to avoid the effect of model parameter uncertainty on regionalization results, a regional calibration method that skips direct calibration of the hydrological model was implemented. This method was improved in order to take into account multiple objective criteria while calibrating regional parameters. The predictive performance of the improved regional calibration method was found to be superior to the direct calibration method, indicating that the identifiability of model parameters has an apparent effect on deriving predictive models for regionalisation. However, the regional calibration method was unable to uniquely identify the regional relationship, and the modeling uncertainties quantified using Pareto optimal regional relationships were considerable. Regionalisation schemes that are based on direct calibration do not explicitly account for the modeling uncertainties. Therefore, to account for these uncertainties in model parameters and regionalisation schemes, methods based on regionalisation of vectors of model parameters (i.e. regionalizing the vectors of equally likely values of model parameters) and posterior probability distribution of model parameters (i.e. estimating the posterior probability distribution of model parameters at ungauged sites by linking the entries of model parameters’ covariance matrix and the posterior mean of model parameter to the catchment attributes) are introduced. The uncertainties in model prediction as quantified from both methods closely followed the prediction uncertainties quantified from calibrated posterior probability distributions of model parameters. Moreover, though the prediction uncertainties associated with the regional calibration method as quantified from the Pareto optimal regional relationship were comparatively higher than those obtained from the direct calibration schemes, they were in close agreement with the prediction uncertainties quantified from the calibrated posterior probability distribution. The ensemble of simulated flows realized from the model parameters sampled from regionalized posterior probability distributions for five ungauged basins are also presented as validation of the proposed methodology.

REGIONALISATION OF POSTERIOR PROBABILITY DISTRIBUTION OF MODEL PARAMETERS : PREDECTION ON UNGAGUED BASIN

In the case study presented here, the calibrated parameters of a Conceptual Rainfall-Runoff (CRR) model could not be uniquely identified. Moreover, the Posterior Probability distribution (PPD) of Model Parameters varied among basin depending upon the basin attributes and data aspects. So the assessment of parameter uncertainty of CRR models should become the integral part of regionalisation. For that reason, we proposed a regionalisation scheme which instead of regionalizing the single best value of model parameters, regionalizes the PPD of model parameters. Subsequently the number of model parameters are sampled from the estimated distribution and fed into the model. Regionalisation of PPD addresses the effect of model parameter uncertainty in the result of regionalisation. The uncertainties in model prediction quantified from proposed methods closely followed the prediction uncertainties quantified from PPD of model parameters conditioned on observation in the presented case study.

Multivariate approach to the thermal challenge problem

This paper presents an engineering approach to the thermal challenge problem defined by Dowding et al. (this issue). This approach to model validation is based on a multivariate validation metric that accounts for model parameter uncertainty and correlation between multiple measurement/prediction differences. The effect of model parameter uncertainty is accounted for through first-order sensitivity analysis for the ensemble/validation tests, and first-order sensitivity analysis and Monte-Carlo analysis for the regulatory prediction. While sensitivity based approaches are less computational expensive than Monte-Carlo approaches, they are less likely to capture the far tail behavior of even mildly nonlinear models. The application of the sensitivity based validation metric provided strong evidence that the tested model was not consistent with the experimental data. The use of a temperature dependent effective conductivity with the linear model resulted in model predictions that were consistent with the data. The correlation structure of the model was used to pool the prediction/measurement differences to evaluate the corresponding cumulative density function (CDF). Both the experimental CDF and the predicted CDFs indicated that the regulatory criterion was not met.

Optimal City-Center Takeoff Operation of Tiltrotor Aircraft in One Engine Failure

This paper investigates optimal tiltrotor flight trajectories and performance in vertical takeoff operations from a city-center heliport considering the possibility of one engine failure. A two-dimensional longitudinal rigid body model of a tiltrotor aircraft is used. Tiltrotor flights after engine failure in both continued takeoff and rejected takeoff are formulated as nonlinear optimal control problems that minimize the heliport size, subject to various constraints from safety considerations and tiltrotor performance limitations. These problems are parametrized via collocation into parameter optimization for numerical solutions. Extensive numerical solutions are obtained, and sensitivity analyses are conducted to examine effects of model parameter uncertainties. Optimization results indicate that the maximum gross weight capability of a tiltrotor in a vertical operation is determined by the need for safe landing in the event of a single engine failure. The height at which the decision for either continuing or rejecting the takeoff is made depends on the need to maintain sufficient height during the continued takeoff flight after an engine failure.