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1.
Parameter uncertainty, sensitivity analysis and prediction error in a water-balance hydrological model 总被引:2,自引:0,他引:2
Kurt K. Benke Kim E. Lowell Andrew J. Hamilton 《Mathematical and Computer Modelling》2008,47(11-12):1134-1149
Analysis of uncertainty is often neglected in the evaluation of complex systems models, such as computational models used in hydrology or ecology. Prediction uncertainty arises from a variety of sources, such as input error, calibration accuracy, parameter sensitivity and parameter uncertainty. In this study, various computational approaches were investigated for analysing the impact of parameter uncertainty on predictions of streamflow for a water-balance hydrological model used in eastern Australia. The parameters and associated equations which had greatest impact on model output were determined by combining differential error analysis and Monte Carlo simulation with stochastic and deterministic sensitivity analysis. This integrated approach aids in the identification of insignificant or redundant parameters and provides support for further simplifications in the mathematical structure underlying the model. Parameter uncertainty was represented by a probability distribution and simulation experiments revealed that the shape (skewness) of the distribution had a significant effect on model output uncertainty. More specifically, increasing negative skewness of the parameter distribution correlated with decreasing width of the model output confidence interval (i.e. resulting in less uncertainty). For skewed distributions, characterisation of uncertainty is more accurate using the confidence interval from the cumulative distribution rather than using variance. The analytic approach also identified the key parameters and the non-linear flux equation most influential in affecting model output uncertainty. 相似文献
2.
《Applied Mathematical Modelling》2014,38(19-20):4885-4896
The moment independent importance measure is a popular global sensitivity analysis technique, and aims at evaluating contributions of the inputs to the whole output distribution. In this work, moment independent sensitivity analysis is performed for models with correlated inputs, by decomposing the importance measure into the uncorrelated part and correlated part. The correlated input variables are first orthogonalized, then the moment independent sensitivity analysis of the newly generated independent variables is performed. Discussions indicate that the moment independent importance measures, so obtained, can be interpreted as the full, correlated and uncorrelated contributions of the original inputs to the whole output distribution. Procedure of the proposed approach has been generalized. By the decomposition, the information provided by the moment independent importance analysis is enriched, which has been demonstrated by the application to several examples. 相似文献
3.
Y. Zhang 《Journal of Optimization Theory and Applications》2007,132(1):111-124
Most research in robust optimization has been focused so far on inequality-only, convex conic programming with simple linear
models for the uncertain parameters. Many practical optimization problems, however, are nonlinear and nonconvex. Even in linear
programming, the coefficients may still be nonlinear functions of the uncertain parameters. In this paper, we propose robust
formulations that extend the robust-optimization approach to a general nonlinear programming setting with parameter uncertainty
involving both equality and inequality constraints. The proposed robust formulations are valid in a neighborhood of a given
nominal parameter value and are robust to the first-order, thus suitable for applications where reasonable parameter estimations
are available and uncertain variations are moderate.
This work was supported in part by NSF Grant DMS-0405831 相似文献
4.
Knowledge-based models are ubiquitous in pure and applied sciences. They often involve unknown parameters to be estimated from experimental data. This is usually much more difficult than for black-box models, only intended to mimic a given input–output behavior. The output of knowledge-based models is almost always nonlinear in their parameters, so that linear least squares cannot be used, and analytical solutions for the model equations are seldom available. Moreover, since the parameters have some physical meaning, it is not enough to find some numerical values of these quantities that are such that the model fits the data reasonably well. One would like, for instance, to make sure that the parameters to be estimated are identifiable. If this is not the case, all equivalent solutions should be provided. The uncertainty in the parameters resulting from the measurement noise and approximate nature of the model should also be characterized. This paper describes how guaranteed methods based on interval analysis may contribute to these tasks. Examples in linear and nonlinear compartmental modeling, widely used in biology, are provided. 相似文献
5.
This work proposes a methodology of identifying linear parameter varying (LPV) models for nonlinear systems. First, linear local models in some operating points, by applying standard identifications procedures for linear systems in time domain, are obtained. Next, a LPV model with linear fractional dependence (LFR) with respect to measured variables is fitted with the condition of containing all the linear models identified in previous step (differential inclusion). The fit is carried out using nonlinear least squares algorithms. Finally, this identification methodology will then be applied to a nonlinear turbocharged diesel engine. 相似文献
6.
Developing suitable dynamic models of bioprocess is a difficult issue in bioscience. In this paper, considering the microbial metabolism mechanism, i.e., the production of new biomass is delayed by the amount of time it takes to metabolize the nutrients, in glycerol bioconversion to 1,3-propanediol, we propose a nonlinear time-delay system to formulate the fed-batch fermentation process. Some important properties are also discussed. Then, in view of the effect of time-delay and the high number of kinetic parameters in the system, the parametric sensitivity analysis is used to determine the key parameters. Finally, a parameter identification model is presented and a global optimization method is developed to seek the optimal key parameters. Numerical results show that the nonlinear time-delay system can describe the fed-batch fermentation process reasonably. 相似文献
7.
To accurately model software failure process with software reliability growth models, incorporating testing effort has shown to be important. In fact, testing effort allocation is also a difficult issue, and it directly affects the software release time when a reliability criteria has to be met. However, with an increasing number of parameters involved in these models, the uncertainty of parameters estimated from the failure data could greatly affect the decision. Hence, it is of importance to study the impact of these model parameters. In this paper, sensitivity of the software release time is investigated through various methods, including one-factor-at-a-time approach, design of experiments and global sensitivity analysis. It is shown that the results from the first two methods may not be accurate enough for the case of complex nonlinear model. Global sensitivity analysis performs better due to the consideration of the global parameter space. The limitations of different approaches are also discussed. Finally, to avoid further excessive adjustment of software release time, interval estimation is recommended for use and it can be obtained based on the results from global sensitivity analysis. 相似文献
8.
A huge body of empirical and theoretical literature has emerged on the relationship between foreign exchange (FX) uncertainty and international trade. Empirical findings about the impact of FX uncertainty on trade figures are at best weak and often ambiguous with respect to its direction. Almost all empirical contributions assume and estimate a linear relationship. Possible nonlinearity or state dependence of causal links between FX uncertainty and trade has been mostly ignored yet. In addition, widely used regression models have not been evaluated in terms of ex‐ante forecasting. In this paper we analyse the impact of FX uncertainty on sectoral categories of multilateral exports and imports for 15 industrialized economies. We particularly provide a comparison of linear and non‐linear models with respect to ex‐ante forecasting. In terms of average ranks of absolute forecast errors non‐linear models outperform both, a common linear model and some specification building on the assumption that FX uncertainty and trade growth are uncorrelated. Our results support the view that the relationship of interest might be non‐linear and, moreover, lacks of homogeneity across countries, economic sectors and when contrasting imports vs exports. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
9.
A. Balbás E. Galperin P. Jiménez. Guerra 《Journal of Optimization Theory and Applications》2005,126(2):247-264
The paper presents a sensitivity analysis of Pareto solutions on the basis of the Karush-Kuhn-Tucker (KKT) necessary conditions applied to nonlinear multiobjective programs (MOP) continuously depending on a parameter. Since the KKT conditions are of the first order, the sensitivity properties are considered in the first approximation. An analogue of the shadow prices, well known for scalar linear programs, is obtained for nonlinear MOPs. Two types of sensitivity are investigated: sensitivity in the state space (on the Pareto set) and sensitivity in the cost function space (on the balance set) for a vector cost function. The results obtained can be used in applications for sensitivity computation under small variations of parameters. Illustrative examples are presented.Research of this author was partially supported by Grant BEC2003-09067-C04-03.Research of this author was partially supported by NSERC Grant RGPIN-3492-00.Research of this author was partially supported by Grant BEC2003-09067-C04-02. 相似文献
10.
已知的线性模型的更新方程是在对模型加了不相关误差结构的约束, 或只对带有固定参数的一元线性模型考虑的. 本文考虑具有相关误差的多元线性模型下的更新方程, 给出了在补充参数, 数据或指标时, 未知参数阵的最佳线性无偏估计及残积阵的更新方程. 公式适用于固定参数与随机参数两种情形. 相似文献
11.
C. COLLARD 《数学年刊B辑(英文版)》2001,22(3):307-324
This paper gives all the two-dimensional membrane models obtained from formal asymptotic analysis of the three-dimensional geometrically exact nonlinear model of a thin elastic shell made with a Saint Venant-Kirchhoff material. Therefore, the other models can be quoted as flexural nonlinear ones. The author also gives the formal equations solved by the associated stress tensor and points out that only one of those models leads, by linearization, to the “classical“ linear limiting membrane model, whose justification has already been established by a convergence theorem. 相似文献
12.
《Applied Mathematical Modelling》2005,29(7):673-689
In this study a new insight into least squares regression is identified and immediately applied to estimating the parameters of nonlinear rational models. From the beginning the ordinary explicit expression for linear in the parameters model is expanded into an implicit expression. Then a generic algorithm in terms of least squares error is developed for the model parameter estimation. It has been proved that a nonlinear rational model can be expressed as an implicit linear in the parameters model, therefore, the developed algorithm can be comfortably revised for estimating the parameters of the rational models. The major advancement of the generic algorithm is its conciseness and efficiency in dealing with the parameter estimation problems associated with nonlinear in the parameters models. Further, the algorithm can be used to deal with those regression terms which are subject to noise. The algorithm is reduced to an ordinary least square algorithm in the case of linear or linear in the parameters models. Three simulated examples plus a realistic case study are used to test and illustrate the performance of the algorithm. 相似文献
13.
14.
Instability of models used in long term planning of large scale industrial projects is demonstrated. The uncertainty band around the balance set is introduced to account for unpredictable variations of important parameters or utilities created by instability in multi-objective optimization of large scale projects. Then, instability of dynamic models of growth is considered including population dynamics with saturation and long term optimal planning in social and economic spheres. A method of successive refinement in a synthetic multi-model system is proposed, and application of the sequence of refined models is illustrated on a real-life example of construction of a dam with yearly refinements of the initial model, based on past history of project realization. 相似文献
15.
This paper studies coupled heat equations with multi-nonlinearities of six nonlinear parameters. The critical blow-up exponent is established via a complete classification for all the six nonlinear parameters, where a precise analysis on the geometry of Ω and the absorption coefficients is given for the balanced interaction situation among the multi-nonlinearities. The main attention is contributed to non-simultaneous phenomena in the model to determine the necessary and sufficient conditions of non-simultaneous blow-up with suitable initial data, as well as the conditions under which any blow-up must be non-simultaneous. Finally, the model of the paper is characterized by a comparison with the known results for other models. 相似文献
16.
The common difficulty in solving a Binary Linear Programming (BLP) problem is uncertainties in the parameters and the model structure. The previous studies of BLP problems normally focus on parameter uncertainty or model structure uncertainty, but not on both types of uncertainties. This paper develops an interval-coefficient Fuzzy Binary Linear Programming (IFBLP) and its solution for BLP problems under uncertainties both on parameters and model structure. In the IFBLP, the parameter uncertainty is represented by the interval coefficients, and the model structure uncertainty is reflected by the fuzzy constraints and a fuzzy goal. A novel and efficient methodology is used to solve the IFLBP into two extreme crisp-coefficient BLPs, which are called the ‘best optimum model’ and the ‘worst optimum model’. The results of these two crisp-coefficient extreme models can bound all outcomes of the IFBLP. One of the contributions in this paper is that it provides a mathematical sound approach (based on some mathematical developments) to find the boundaries of optimal alpha values, so that the linearity of model can be maintained during the conversions. The proposed approach is applied to a traffic noise control plan to demonstrate its capability of dealing with uncertainties. 相似文献
17.
Jun Y. Kim Vivek Natarajan Scott D. Kelly Joseph Bentsman 《Nonlinear Analysis: Hybrid Systems》2010,4(3):513-523
In a recent work, the authors presented an extension of robust model reference adaptive control (MRAC) laws for spatially varying partial differential equations (PDEs) proposed by them earlier for the decentralized adaptive control of heterogeneous multiagent networks with agent parameter uncertainty using the partial difference equations (PdEs) on graphs framework. The examples provided demonstrated the capabilities of this approach under the assumption that individual vehicles executing coordinated maneuvers were fully actuated and characterized by linear dynamics. However, detailed models for autonomous vehicles–whether terrestrial, aerial, or aquatic–are often underactuated and strongly nonlinear. Using this approach, but assuming the plant parameters to be known, this work presents the model reference (MR) control laws without adaptation for the coordination of underactuated aquatic vehicles modeled individually in terms of strongly nonlinear dynamic equations arising from ideal planar hydrodynamics. The case of unknown plant parameters for this class of underactuated agents with complex dynamics is an open problem. The paper is based on an invited talk on adaptive control presented at the 2008 World Congress of Nonlinear Analysts. 相似文献
18.
《European Journal of Operational Research》1997,100(1):142-169
Mixed-integer optimization models for chemical process planning typically assume that model parameters can be accurately predicted. As precise forecasts are difficult to obtain, process planning usually involves uncertainty and ambiguity in the data. This paper presents an application of fuzzy programming to process planning. The forecast parameters are assumed to be fuzzy with a linear or triangular membership function. The process planning problem is then formulated in terms of decision making in a fuzzy environment with fuzzy constraints and fuzzy net present value goals. The model is transformed to a deterministic mixed-integer linear program or mixed-integer nonlinear program depending on the type of uncertainty involved in the problem. For the nonlinear case, a global optimization algorithm is developed for its solution. This algorithm is applicable to general possibilistic programs and can be used as an alternative to the commonly used bisection method. Illustrative examples and computational results for a petrochemical complex with 38 processes and 24 products illustrate the applicability of the developed models and algorithms. 相似文献
19.
This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results,, such as [1] and [2] are extended to AR(q)nonlinear regression models. 相似文献
20.
M. A. Eyler 《Journal of Optimization Theory and Applications》1985,45(1):159-163
The effect of small changes in parameter values on the sample values is investigated further. The concept of linearity with respect to parameters is introduced, and the linear and the nonlinear cases are treated separately. The relation with the sample-path analysis is discussed. 相似文献