SCEM-UA Algorithm Research Articles

Experimental Validation of Optimal Parameter and Uncertainty Estimation for Structural Systems Using a Shuffled Complex Evolution Metropolis Algorithm

The uncertainty in parameter estimation arises from structural systems’ input and output measured errors and from structural model errors. An experimental verification of the shuffled complex evolution metropolis algorithm (SCEM-UA) for identifying the optimal parameters of structural systems and estimating their uncertainty is presented. First, the estimation framework is theoretically developed. The SCEM-UA algorithm is employed to search through feasible parameters’ space and to infer the posterior distribution of the parameters automatically. The resulting posterior parameter distribution then provides the most likely estimation of parameter sets that produces the best model performance. The algorithm is subsequently validated through both numerical simulation and shaking table experiment for estimating the parameters of structural systems considering the uncertainty of available information. Finally, the proposed algorithm is extended to identify the uncertain physical parameters of a nonlinear structural system with a particle mass tuned damper (PTMD). The results demonstrate that the proposed algorithm can effectively estimate parameters with uncertainty for nonlinear structural systems, and it has a stronger anti-noise capability. Notably, the SCEM-UA method not only shows better global optimization capability compared with other heuristic optimization methods, but it also has the ability to simultaneously estimate the uncertainties associated with the posterior distributions of the structural parameters within a single optimization run.

Quantifying multi-source uncertainties in multi-model predictions using the Bayesian model averaging scheme

Abstract This study focuses on a quantitative multi-source uncertainty analysis of multi-model predictions. Three widely used hydrological models, i.e., Xinanjiang (XAJ), hybrid rainfall–runoff (HYB), and HYMOD (HYM), were calibrated by two parameter optimization algorithms, namely, shuffled complex evolution (SCE-UA) method and shuffled complex evolution metropolis (SCEM-UA) method on the Mishui basin, south China. The input uncertainty was quantified by utilizing a normally distributed error multiplier. The ensemble simulation sets calculated from the three models were combined using the Bayesian model averaging (BMA) method. Results indicate the following. (1) Both SCE-UA and SCEM-UA resulted in good and comparable streamflow simulations. Specifically, the SCEM-UA implied parameter uncertainty and provided the posterior distribution of the parameters. (2) In terms of the precipitation input uncertainty, precision of streamflow simulations did not improve remarkably. (3) The BMA combination not only improved the precision of streamflow prediction, but also quantified the uncertainty bounds of the simulation. (4) The prediction interval calculated using the SCEM-UA-based BMA combination approach appears superior to that calculated using the SCE-UA-based BMA combination for both high flows and low flows. Results suggest that the comprehensive uncertainty analysis by using the SCEM-UA algorithm and BMA method is superior for streamflow predictions and flood forecasting.

Optimization of Power System Scheduling Based on Shuffled Complex Evolution Metropolis Algorithm

Due to the world’s increasingly serious energy crisis, shortage of resources, and environmental degradation, traditional power system analysis and scheduling optimization methods have faced new challenges. This article examines the features of optimal scheduling of power system containing cascade hydropower, and establishes a scheduling model based on the Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm. This model takes the cost of power generation, emission of gaseous pollutants, and the characteristics of the generators fully into account. Constraints on the changes in thermoelectric generator power output were added to the set of constraint conditions, reducing the impact of thermal power fluctuations on the power system. Here, the SCEM-UA algorithm was used to solve the problem of optimal power system scheduling and render the model capable of global optimization searches. Analyses of simulated cases have demonstrated that the SCEM-UA algorithm can resolve the conflict between convergence speed and global search capability, increasing the global search capability of the model.

Improvement of Multi-Satellite Real-Time Precipitation Products for Ensemble Streamflow Simulation in a Middle Latitude Basin in South China

The real-time availability of several satellite-based precipitation products has recently provided hydrologists with an unprecedented opportunity to improve current hydrologic prediction capability for vast river basins, particularly for ungauged regions. However, the accuracy of real-time satellite precipitation data remains uncertain. This study aims to use three widely used real-time satellite precipitation products, namely, TRMM Multi satellite Precipitation Analysis real-time precipitation product 3B42 (TMPA 3B42RT), Precipitation Estimation from Remote Sensing Information using Artificial Neural Network (PERSIAN), and NOAA/Climate Precipitation Center Morphing Technique (CMORPH), for ensemble stream flow simulation with the gridded xinanjiang (XAJ) model and shuffled complex evolution metropolis (SCEM-UA) algorithm in the middle-latitude Mishui basin in South China. To account the bias of the satellite precipitation data and consider the input uncertainty, two different methods, i.e. a precipitation error multiplier and a precipitation error model were introduced. For each precipitation input model, the posterior probability distribution of the parameters and their associated uncertainty were calibrated using the SCEM-UA algorithm, and 15,000 ensemble stream flow simulations were conducted. The simulations of the satellite precipitation data were then optimally merged using the Bayseian model averaging (BMA) method. The result shows that in Mishui basin, the three sets of real-time satellite precipitation data largely underestimated rainfall. Streamflow simulation performed poorly when the raw satellite precipitation data were taken as input and the model parameters were calibrated with gauged data. By implementing the precipitation error multiplier and the precipitation error model and then recalibrating the model, the behavior of the simulated stream flow and calculated uncertainty boundary were significantly improved. Furthermore, the BMA combination of the simulations from the three datasets resulted in a significantly better prediction with a remarkably reliable uncertainty boundary and was comparable with the simulation using the post-real-time bias-corrected research quality TMPA 3B42V7. The proposed methodology of bias adjustment, uncertainty analysis, and BMA combination collectively facilitates the application of the current three real-time satellite data to hydrological prediction and water resource management over many under-gauged basins. This research is also an investigation on the hydrological utility of multi-satellite precipitation data ensembles, which can potentially integrate additional more satellite products when the Global Precipitation Measuring mission with 9-satellite constellation is anticipated in 2014.

Probabilistic prediction of urban water consumption using the SCEM-UA algorithm

Prediction of urban water consumption can help to improve the performance of water distribution systems. Despite the obvious presence of uncertainty in measurements and in assumed model types/structures, most of the existing water consumption prediction models are developed and used in a deterministic context. Methods for more realistic assessment of parameter and model prediction uncertainties have begun to appear in literature only recently. A novel application of the Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) for the calibration of a water consumption prediction model is proposed here. The model is applied to a case study of the city of Catania (Italy) with the aim to predict daily water consumption. The SCEM-UA algorithm is used to calibrate the parameters of the artificial neural network based prediction model and in turn to determine the associated parameter and model prediction uncertainties. The results obtained using the SCEM-UA ANN approach were compared to the corresponding results obtained using other predictive models developed recently by the authors of the paper. When compared to the these models, the SCEM-UA ANN based water consumption prediction model shows similar predictive capability but also the ability to identify simultaneously the prediction uncertainty bounds associated with the posterior distribution of the parameter estimates.

Calibration of Water Distribution Hydraulic Models Using a Bayesian-Type Procedure

Estimating model parameters is a difficult, yet critical step in the use of water distribution system models. Most of the optimization-based approaches developed so far concentrate primarily on efficient and effective ways of obtaining optimal calibration parameter values. At the same time, very little effort has been made to determine the uncertainties (i.e., errors) associated with those values (and related model predictions). So far, this has typically been done using the first-order second moment (FOSM) method. Even though reasonably computationally efficient, the FOSM approach relies on several restrictive assumptions and requires computationally demanding calculation of derivatives. To overcome these limitations, the recently developed shuffled complex evolution metropolis (SCEM-UA) global optimization algorithm is linked to the Epanet2 hydraulic model and used to solve a least-squares-type calibration problem. The methodology is tested and verified on the Anytown literature case study. The main advantage of the SCEM-UA algorithm over existing approaches is that both calibration parameter values and associated uncertainties can be determined in a single optimization model run. In addition, no model linearity or parameter normality assumptions have to be made nor any derivatives calculated. The main drawback of the SCEM-UA methodology is that it could, potentially, be computationally demanding, although this is not envisaged as a major problem with current computers.

Parameter optimisation and uncertainty assessment for large-scale streamflow simulation with the LISFLOOD model

Summary This work addresses the calibration of the distributed rainfall-runoff model LISFLOOD and, in particular, the realistic quantification of parameter uncertainty and its effect on the prediction of river discharges for large European catchments. LISFLOOD is driven by meteorological input data and simulates river discharge in large drainage basins as a function of spatial information on topography, soils and land cover. Even though LISFLOOD is physically based to a certain extent, some processes are only represented in a lumped conceptual way. As a result, some parameters lack physical basis and cannot be directly inferred from quantities that can be measured. In the current LISFLOOD version five parameters need to be determined by calibration. We employ the Shuffled Complex Evolution Metropolis (SCEM-UA) global optimisation algorithm to automatically calibrate the model against daily discharge observations. The resulting posterior parameter distribution reflects the uncertainty about the model parameters after taking into account the discharge observations, and forms the basis for making probabilistic flow predictions. To overcome the computational burden the optimisation has been implemented using parallel computing. As an illustrative example, we demonstrate the methodology for the Meuse catchment upstream of Borgharen, covering approximately 21,000 km 2 . Results demonstrate the capabilities of the SCEM-UA algorithm to efficiently evolve to the target posterior distribution and to identify, except for the lower groundwater zone time constant, the LISFLOOD calibration parameters using daily discharge observations. It should be noted that the posterior parameter distributions are based on the assumption of independent errors. Analysis of the residuals revealed there is a strong evidence to reject this assumption. This will impact on the parameter posterior distributions and also lead to underestimation of the prediction limits.

Application of stochastic parameter optimization to the Sacramento Soil Moisture Accounting model

Hydrological models generally contain parameters that cannot be measured directly, but can only be meaningfully inferred by calibration against a historical record of input–output data. While considerable progress has been made in the development and application of automatic procedures for model calibration, such methods have received criticism for their lack of rigor in treating uncertainty in the parameter estimates. In this paper, we apply the recently developed Shuffled Complex Evolution Metropolis algorithm (SCEM-UA) to stochastic calibration of the parameters in the Sacramento Soil Moisture Accounting model (SAC-SMA) model using historical data from the Leaf River in Mississippi. The SCEM-UA algorithm is a Markov Chain Monte Carlo sampler that provides an estimate of the most likely parameter set and underlying posterior distribution within a single optimization run. In particular, we explore the relationship between the length and variability of the streamflow data and the Bayesian uncertainty associated with the SAC-SMA model parameters and compare SCEM-UA derived parameter values with those obtained using deterministic SCE-UA calibrations. Most significantly, for the Leaf River catchments under study our results demonstrate that most of the 13 SAC-SMA parameters are well identified by calibration to daily streamflow data suggesting that this data contains more information than has previously been reported in the literature.

Toward Improved Identifiability of Soil Hydraulic Parameters: On the Selection of a Suitable Parametric Model

We present a thorough identifiability analysis of the soil hydraulic parameters in the parametric models of Brooks and Corey (BC; Brooks and Corey, 1964), Mualem-van Genuchten (VG; van Genuchten, 1980), and Kosugi (KC; Kosugi, 1996, 1999) using the recently developed Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm (Vrugt et al., 2002b, and unpublished data). Because the SCEM-UA algorithm globally thoroughly exploits the parameter space and therefore explicitly accounts for parameter interdependence and nonlinearity of the employed parametric models, the algorithm is suited to generate a useful description of parameter uncertainty and its antithesis, parameter identifiability. A set of measured water retention characteristics of the UNSODA database (Leij et al., 1996) spanning a wide range of soil textures and three transient laboratory outflow experiments with decreasing flow rates were used to illustrate that a parameter identifiability analysis facilitates the selection of an adequate parametric model structure and provides useful information about the limitations of a model. Moreover, results suggest that one should be especially careful in establishing pedotransfer functions without knowledge of the underlying posterior uncertainty associated with the soil hydraulic parameters using direct estimation methods.

Toward Improved Identifiability of Soil Hydraulic Parameters

We present a thorough identifiability analysis of the soil hydraulic parameters in the parametric models of Brooks and Corey (BC; Brooks and Corey, 1964), Mualem–van Genuchten (VG; van Genuchten, 1980), and Kosugi (KC; Kosugi, 1996, 1999) using the recently developed Shuffled Complex Evolution Metropolis (SCEM-UA) algorithm (Vrugt et al., 2002b, and unpublished data). Because the SCEM-UA algorithm globally thoroughly exploits the parameter space and therefore explicitly accounts for parameter interdependence and nonlinearity of the employed parametric models, the algorithm is suited to generate a useful description of parameter uncertainty and its antithesis, parameter identifiability. A set of measured water retention characteristics of the UNSODA database (Leij et al., 1996) spanning a wide range of soil textures and three transient laboratory outflow experiments with decreasing flow rates were used to illustrate that a parameter identifiability analysis facilitates the selection of an adequate parametric model structure and provides useful information about the limitations of a model. Moreover, results suggest that one should be especially careful in establishing pedotransfer functions without knowledge of the underlying posterior uncertainty associated with the soil hydraulic parameters using direct estimation methods.