Bayesian Calibration Techniques Research Articles

Improving the Predictivity of a Steam Generator Clogging Numerical Model by Global Sensitivity Analysis and Bayesian Calibration Techniques

In pressurized nuclear reactors, steam generators are massive tubular heat exchangers transferring heat from the primary to the secondary fluid to produce the steam needed by the turbines. After several years of operation, because of deposit, their tube support plates (TSPs) can undergo clogging that may cause important economic and safety issues in case of nonpreventive actions. To understand and predict this phenomenon, several nondestructive examinations can generally be gathered at various times during the heat exchanger operation. A numerical mechanistic model has been recently developed and implemented in a dedicated computer code. The objective of this work is to improve the modeling of the clogging phenomenon to increase the predictive capability of the computer code. A global sensitivity analysis, based on Sobol’ indices, is first performed by the use of a metamodel that is learned on several runs of the computer code. Such an analysis, cast under a physical perspective, helps the identification of the most influential physical parameters and paves the way to a better understanding of TSP clogging. A Bayesian calibration of an epistemic calibration model parameter is then applied to fit the simulation results to experimental data. The additional information coming from the experimental data is then transferred to the calibration parameter with a mathematical model (artificial neural network). The resulting hybrid model thus compensates some lacks of the initial physical model on the considered data set.

Reduced scale stripline platform to extend accessible pressures on the Z machine: Shockless compression of platinum to 650 GPa

Reaching astrophysically relevant high energy density (HED) material states in the laboratory is an ongoing effort at multiple experimental facilities. We have developed a new dynamic compression platform for the Z Pulsed Power Facility that allows for sample sizes 100s of μm in thickness that accommodate multiple grains in order to fully capture bulk properties, such as material strength. A pair of experiments compressed platinum (Pt) to HED conditions and conventional inverse Lagrangian analysis as well as a recent Bayesian calibration technique were used to determine the principal isentrope to 650 GPa with density uncertainties of <2%. These low uncertainties are calculated for single sample experiments, presenting the possibility of even smaller experimental uncertainties with multiple samples the platform allows. Our new platform extends the accessible Pt ramp pressures achievable on the Z machine to over 80% of the pressure recently achieved using the National Ignition Facility planar Hohlraum platform. This new capability, the next generation evolution of the stripline platform, was made possible by advancements in both our understanding of the Z pulsed power driver and our overall magnetohydrodynamic modeling capabilities.

Archetype Modeling Uncertainty and Bayesian Calibration for Campus-scale Analysis of Seoul National University Buildings Energy Use

Purpose: Considering the gap in research on uncertainties in urban building energy modeling, with specific regard to archetype building development, this study seeks to first throw light on archetype modeling’ sources of uncertainty, and second, solve these issues with the Bayesian calibration method. Method: By using a case area of Seoul National University, this paper models five 3D archetype buildings and estimates their monthly energy use intensities on EnergyPlus. The simulation results are modified with the Bayesian calibration technique, compared against existing, observational data before and after the Bayesian calibration, and further validated by computing the coefficient of the variation of the root mean square error. Result: Findings show that the Bayesian calibration may be considered to address uncertainty as it improves the simulation results; however, it is not a one-size-fits-all solution to uncertainties, caused by the lack of some parameters, not added to the model, which are crucial to the archetype characterization. Overall, this paper contributes to the research on urban building energy modeling-related uncertainties, hoping for urban planners to consider sources of uncertainty during the archetype characterization stage and make the adequate modeling decisions in the name of sustainable urban growth.

Bayesian calibration of building energy models for uncertainty analysis through test cells monitoring

Improving the energy efficiency of existing buildings is a priority for meeting energy consumption and CO2 emission targets in buildings. Building simulation tools play a crucial role in evaluating the performance of energy retrofit options. In this paper, a Bayesian calibration approach is applied to reduce the discrepancies between measured and simulated temperature data. Through its application to a test cell case study, the incorporation of sensitivity analysis and Bayesian calibration techniques are proven to improve the level of agreement between on-site measurements and simulated outputs, whilst accounting for both experimental and simulation uncertainties. The accuracy of a building simulation model developed using EnergyPlus was evaluated before and after calibration. Uncalibrated models were within the uncertainty ranges specified by the ASHARE Guidelines, with hourly simulation data over-predicting measurements by 3.2 °C on average. After Bayesian calibration, the average maximum temperature difference was reduced to around 0.68 °C, an improvement of almost 80%.

A generalized Bayesian approach to model calibration

In model development, model calibration and validation play complementary roles toward learning reliable models. In this article, we expand the Bayesian Validation Metric framework to a general calibration and validation framework by inverting the validation mathematics into a generalized Bayesian method for model calibration and regression. We perform Bayesian regression based on a user’s definition of model-data agreement. This allows for model selection on any type of data distribution, unlike Bayesian and standard regression techniques, that “fail” in some cases. We show that our tool is capable of representing and combining least squares, likelihood-based, and Bayesian calibration techniques in a single framework while being able to generalize aspects of these methods. This tool also offers new insights into the interpretation of the predictive envelopes (also known as confidence bands) while giving the analyst more control over these envelopes. We demonstrate the validity of our method by providing three numerical examples to calibrate different models, including a model for energy dissipation in lap joints under impact loading. By calibrating models with respect to the validation metrics one desires a model to ultimately pass, reliability and safety metrics may be integrated into and automatically adopted by the model in the calibration phase.

Bayesian calibration of underwater propagation models under uncertainty

Propagation models are notorious for the uncertainty of important parameters such as source strength, speed of sound profiles, and reflecting surface profiles. In many cases, one calibrates a model to measured data (e.g., sound levels or transmission loss) for the purposes of estimating these model parameters, i.e., for inverse modeling. Bayesian calibration methods have been developed that are extremely useful for calibration of models where parameters have high levels of uncertainty and problems may be under or over determined. The Kennedy and O’Hagen framework which uses a Gaussian process surrogate model to replace the model under calibration is especially useful when the underlying model is computationally expensive, and so, it may be difficult to apply many optimization based calibration methods. In this talk, we describe the application of the Kennedy and O’Hagen Bayesian Calibration framework to the calibration of an underwater ray tracing propagation model. The source strength and parameters for the sound speed profile are considered as highly uncertain. The Bayesian calibration technique is shown to improve model prediction and reduce the uncertainty of the unknown propagation parameters.

Improving accuracy of vehicle-terrain interface algorithms for wheeled vehicles on fine-grained soils through Bayesian calibration

The Vehicle-Terrain Interface (VTI) model for off-road vehicle performance is often used in virtual prototyping to support preliminary vehicle design. Five VTI algorithms for wheeled vehicles on fine-grained soils are calibrated in this study using a Bayesian calibration technique and the Database Records for Off-road Vehicle Environments (DROVE): powered and unpowered sinkage, drawbar pull, motion resistance, and gross traction. These algorithms are improved through a two-stage Bayesian calibration technique utilizing the Metropolis algorithm with three separate calibration strategies. The VTI and proposed algorithms are compared for performance in coefficient of determination and root-mean square error. The results from each algorithm were validated through k-fold cross validation with five folds. The final algorithms from the best performing strategy after accounting for increased complexity for each of the five performance parameters are reported as calibrated algorithms. Validated improvements in coefficient of determination are recorded for all five parameters: 7.8% for powered sinkage, 1.4% for unpowered sinkage, 6.4% for drawbar pull, 0.9% for motion resistance, and 12.5% for gross traction. Improvements are also seen in the normalized root-mean square error performance: 13.4% for powered sinkage, 1.9% for unpowered sinkage, 7.6% for drawbar pull, 17.5% for motion resistance, and 23.2% for gross traction.

Comprehensive evaluation of the influence of meta-models on Bayesian calibration

Many efforts are used to eliminate the gaps between physical measurements and simulation results. The Bayesian calibration technique is one of the popular automatic calibration methods Allowing for all sources of uncertainty, the method attempts to correct inadequate models and parameters that produce discrepancies between prediction and observed data. Bayesian calibration requires numerous iterations of simulation. To reduce the computational cost, a meta-model is often used to replace the original detailed model. This paper evaluates and analyzes the influence of meta-model accuracy on the outcomes of the Bayesian calibration for building energy simulation model. The following five meta-models: multiple linear regression model, neural network, support vector machine, multivariate adaptive regression splines, and Gaussian process emulator are investigated and compared. The study varies the ranges of input parameters to explore the associated accuracy of the built meta-models. The calibration results are evaluated and compared using three criteria: simulation time, the coefficient of variation with root mean square error (CVRMSE) to true input parameter values, and CVRMSE to observed outputs (monthly and annual energy use intensity). The paper confirms that there are significant differences in simulation time and accuracy for different types of meta-models. The most accurate meta-model tested is the Gaussian process emulator (GPE), while it requires the longest computing time. The multiple linear regression model is the fastest but shows the worst performance in the calibration for the true input parameters. All the calibrated models, however, can predict well the outputs against the observations.

Comparison of Traditional and Bayesian Calibration Techniques for Gray-Box Modeling

Bayesian and nonlinear least-squares methods of calibration were evaluated and compared for gray-box modeling of a retail building. Gray-box model calibration is one form of system identification and is examined here with perturbations to the simple yet popular European Committee for Standardization (CEN)-ISO thermal network model. The primary objective was to understand whether the computational expense of probabilistic Bayesian techniques is required to provide robustness to signal noise, specifically with regard to lower dimensional problems (physical or semiphysical), where model calibration is preferred over uncertainty quantification. The Bayesian approach allows parameter interactions and trade-offs to be revealed, one form of sensitivity analysis, but its full power for uncertainty quantification cannot be harnessed with gray-box or other simplified models. Surrogate data from a detailed building energy simulation program were used to ensure command over latent variables, whereas a range of signal-to-noise and noise colors were considered in the experimental study. The fidelity to the building zone temperature and thermal load was the basis for comparing results. Utilization of uniform priors showed that both methods performed similarly well. Bayesian calibration outperformed traditional methods on noisy data sets; however, traditional methods were adequate up to an approximately 25% noise level. The thermal gray-box model calibration has the intended application of embedded model predictive control, where speed, accuracy, and robustness are crucial. Traditional methods required approximately 100 times less CPU time and are recommended given the model simplicity, application, and expected system noise levels.

Systems approaches in global change and biogeochemistry research.

Systems approaches have great potential for application in predictive ecology. In this paper, we present a range of examples, where systems approaches are being developed and applied at a range of scales in the field of global change and biogeochemical cycling. Systems approaches range from Bayesian calibration techniques at plot scale, through data assimilation methods at regional to continental scales, to multi-disciplinary numerical model applications at country to global scales. We provide examples from a range of studies and show how these approaches are being used to address current topics in global change and biogeochemical research, such as the interaction between carbon and nitrogen cycles, terrestrial carbon feedbacks to climate change and the attribution of observed global changes to various drivers of change. We examine how transferable the methods and techniques might be to other areas of ecosystem science and ecology.

Bayesian calibration method used to elucidate carbon turnover in forest on drained organic soil

Depending on the balance between sink and source processes for C, drained organic forest soil ecosystems can be in balance or act as net sinks or sources of CO2 to the atmosphere. In order to study the effect of groundwater level and soil temperature on C-flux, the CoupModel was calibrated (climate data, groundwater levels, soil CO2 flux, net ecosystem fluxes of CO2-exchange, sensible heat flux and latent heat flux, forest production etc.) for a drained forest in Sweden. Bayesian calibration techniques were used to elucidate how different parameters and variables were interlinked in C-circulation. The calibrated model reproduced abiotic and biotic variables reasonably well except for root respiration, which was largely underestimated. Bayesian calibration reduced the uncertainties in the model and highlighted the fact that calibrations should be performed with a high number of parameters instead of specific parameter values.

Bayesian Calibration of Computer Models

Summary We consider prediction and uncertainty analysis for systems which are approximated using complex mathematical models. Such models, implemented as computer codes, are often generic in the sense that by a suitable choice of some of the model's input parameters the code can be used to predict the behaviour of the system in a variety of specific applications. However, in any specific application the values of necessary parameters may be unknown. In this case, physical observations of the system in the specific context are used to learn about the unknown parameters. The process of fitting the model to the observed data by adjusting the parameters is known as calibration. Calibration is typically effected by ad hoc fitting, and after calibration the model is used, with the fitted input values, to predict the future behaviour of the system. We present a Bayesian calibration technique which improves on this traditional approach in two respects. First, the predictions allow for all sources of uncertainty, including the remaining uncertainty over the fitted parameters. Second, they attempt to correct for any inadequacy of the model which is revealed by a discrepancy between the observed data and the model predictions from even the best-fitting parameter values. The method is illustrated by using data from a nuclear radiation release at Tomsk, and from a more complex simulated nuclear accident exercise.