Quantifying Model Uncertainties and Sensitivities in Parallel Compressor Models

2021 ◽  
Author(s):  
Jonas Voigt ◽  
Keith-Noah Jurke ◽  
Julius Schultz ◽  
Ulrich Römer ◽  
Jens Friedrichs
Keyword(s):  
Structural Model ◽  
Input Parameter ◽  
Nonlinear Effects ◽  
Computational Effort ◽  
Distribution Functions ◽  
Model Errors ◽  
Unknown Parameters ◽  
Time Modeling ◽  
Input Parameters ◽  
Probabilistic Setting

Abstract In this work, we consider a parallel compressor model (PCM), which decomposes a compressor encountering non-uniform inflow into a distorted and an undistorted subcompressor, respectively, to determine its overall operating point. The main advantage of PCM modeling is a significantly reduced computational workload. At the same time, modeling errors are introduced, which need to be quantified together with model input uncertainties. Therefore, we introduce a probabilistic setting where unknown parameters are modeled as random variables. We carry out a global sensitivity analysis, which allows to reduce the complexity of the probabilistic model, by setting unimportant input parameters to their nominal values. This analysis attributes portions of the model output variance (the fan efficiency for instance) to particular input parameters or input parameter combinations, through so-called Sobol coefficients. We further include a parameter describing the PCM inflow averaging process into the analysis, which allows to determine the influence of specific modeling choices onto the predicted efficiency. Efficient sampling methods are needed to estimate the sensitivity coefficients with a reasonable computational effort. A key advantage of the global approach is that nonlinear effects are fully taken into account, the necessity of which will be demonstrated by our numerical examples. The model is also compared to CFD reference simulations to quantify structural model errors. This comparison is based on area validation metrics comparing the stochastic distribution functions of the probabilistic PCM model and the reference data.

scholarly journals Correcting a bias in a climate model with an augmented emulator

2019 ◽  
Author(s):  
Doug McNeall ◽  
Jonny Williams ◽  
Richard Betts ◽  
Ben Booth ◽  
Peter Challenor ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Land Surface ◽  
Structural Model ◽  
Climate Model ◽  
Input Parameter ◽  
Amazon Region ◽  
Model Errors ◽  
Input Parameters ◽  
Parameter Values ◽  
Gaussian Process Emulator

Abstract. A key challenge in developing flagship climate model configurations is the process of setting uncertain input parameters at values that lead to credible climate simulations. Setting these parameters traditionally relies heavily on insights from those involved in parameterisation of the underlying climate processes. Given the many degrees of freedom and computational expense involved in evaluating such a selection, this can be imperfect leaving open questions about whether any subsequent simulated biases result from mis-set parameters or wider structural model errors (such as missing or partially parameterised processes). Here we present a complementary approach to identifying plausible climate model parameters, with a method of bias correcting subcomponents of a climate model using a Gaussian process emulator that allows credible values of model input parameters to be found even in the presence of a significant model bias. A previous study (McNeall et al., 2016) found that a climate model had to be run using land surface input parameter values from very different, almost non-overlapping parts of parameter space to satisfactorily simulate the Amazon and other forests respectively. As the forest fraction of modelled non-Amazon forests was broadly correct at the default parameter settings and the Amazon too low, that study suggested that the problem most likely lay in the model's treatment of non-plant processes in the Amazon region. This might be due to (1) modelling errors such as missing deep-rooting in the Amazon in the land surface component of the climate model, (2) a warm-dry bias in the Amazon climate of the model, or a combination of both. In this study we bias correct the climate of the Amazon in a climate model using an augmented Gaussian process emulator, where temperature and precipitation, variables usually regarded as model outputs, are treated as model inputs alongside regular land surface input parameters. A sensitivity analysis finds that the forest fraction is nearly as sensitive to climate variables as changes in its land surface parameter values. Bias correcting the climate in the Amazon region using the emulator corrects the forest fraction to tolerable levels in the Amazon at many candidates for land surface input parameter values, including the default ones, and increases the valid input space shared with the other forests. We need not invoke a structural model error in the land surface model, beyond having too dry and hot a climate in the Amazon region. The augmented emulator allows bias correction of an ensemble of climate model runs and reduces the risk of choosing poor parameter values because of an error in a subcomponent of the model. We discuss the potential of the augmented emulator to act as a translational layer between model subcomponents, simplifying the process of model tuning when there are compensating errors, and helping model developers discover and prioritise model errors to target.

scholarly journals Correcting a bias in a climate model with an augmented emulator

2020 ◽  
Vol 13 (5) ◽  
pp. 2487-2509
Author(s):  
Doug McNeall ◽  
Jonny Williams ◽  
Richard Betts ◽  
Ben Booth ◽  
Peter Challenor ◽  
...  
Keyword(s):  
Gaussian Process ◽  
Land Surface ◽  
Structural Model ◽  
Climate Model ◽  
Input Parameter ◽  
Amazon Region ◽  
Model Errors ◽  
Input Parameters ◽  
Parameter Values ◽  
Gaussian Process Emulator

Abstract. A key challenge in developing flagship climate model configurations is the process of setting uncertain input parameters at values that lead to credible climate simulations. Setting these parameters traditionally relies heavily on insights from those involved in parameterisation of the underlying climate processes. Given the many degrees of freedom and computational expense involved in evaluating such a selection, this can be imperfect leaving open questions about whether any subsequent simulated biases result from mis-set parameters or wider structural model errors (such as missing or partially parameterised processes). Here, we present a complementary approach to identifying plausible climate model parameters, with a method of bias correcting subcomponents of a climate model using a Gaussian process emulator that allows credible values of model input parameters to be found even in the presence of a significant model bias. A previous study (McNeall et al., 2016) found that a climate model had to be run using land surface input parameter values from very different, almost non-overlapping, parts of parameter space to satisfactorily simulate the Amazon and other forests respectively. As the forest fraction of modelled non-Amazon forests was broadly correct at the default parameter settings and the Amazon too low, that study suggested that the problem most likely lay in the model's treatment of non-plant processes in the Amazon region. This might be due to modelling errors such as missing deep rooting in the Amazon in the land surface component of the climate model, to a warm–dry bias in the Amazon climate of the model or a combination of both. In this study, we bias correct the climate of the Amazon in the climate model from McNeall et al. (2016) using an “augmented” Gaussian process emulator, where temperature and precipitation, variables usually regarded as model outputs, are treated as model inputs alongside land surface input parameters. A sensitivity analysis finds that the forest fraction is nearly as sensitive to climate variables as it is to changes in its land surface parameter values. Bias correcting the climate in the Amazon region using the emulator corrects the forest fraction to tolerable levels in the Amazon at many candidates for land surface input parameter values, including the default ones, and increases the valid input space shared with the other forests. We need not invoke a structural model error in the land surface model, beyond having too dry and hot a climate in the Amazon region. The augmented emulator allows bias correction of an ensemble of climate model runs and reduces the risk of choosing poor parameter values because of an error in a subcomponent of the model. We discuss the potential of the augmented emulator to act as a translational layer between model subcomponents, simplifying the process of model tuning when there are compensating errors and helping model developers discover and prioritise model errors to target.

Uncertainty Quantification in Support of Severe Accident Analysis Code User Confidence Using MELCOR-DAKOTA

2021 ◽  
Author(s):  
Emmanuel Boafo ◽  
Emmanuel Numapau Gyamfi
Keyword(s):  
Sensitivity Analysis ◽  
Uncertainty Quantification ◽  
Hydrogen Generation ◽  
Input Parameter ◽  
Distribution Functions ◽  
Physical Models ◽  
Severe Accident ◽  
Accident Analysis ◽  
Melt Flow Rate ◽  
Input Parameters

Abstract Uncertainty and Sensitivity analysis methods are often used in severe accident analysis for validating the complex physical models employed in the system codes that simulate such scenarios. This is necessitated by the large uncertainties associated with the physical models and boundary conditions employed to simulate severe accident scenarios. The input parameters are sampled within defined ranges based on assigned probability distribution functions (PDFs) for the required number of code runs/realizations using stochastic sampling techniques. Input parameter selection is based on their importance to the key FOM, which is determined by the parameter identification and ranking table (PIRT). Sensitivity analysis investigates the contribution of each uncertain input parameter to the uncertainty of the selected FOM. In this study, the integrated severe accident analysis code MELCOR was coupled with DAKOTA, an optimization and uncertainty quantification tool in order to investigate the effect of input parameter uncertainty on hydrogen generation. The methodology developed was applied to the Fukushima Daiichi unit 1 NPP accident scenario, which was modelled in another study. The results show that there is approximately 22.46% uncertainty in the amount of hydrogen generated as estimated by a single MELCOR run given uncertainty in selected input parameters. The sensitivity analysis results also reveal that MELCOR input parameters; COR_SC 1141(Melt flow rate per unit width at breakthrough candling) , COR_ZP (Porosity of fuel debris beds) and COR_EDR (Characteristic debris size in core region) contributed most significantly to the uncertainty in hydrogen generation.

Localization of test/analysis structural model errors

1989 ◽  
Author(s):  
CHAUR-MING CHOU ◽  
JOHN O'CALLAHAN ◽  
CHI-HSING WU
Keyword(s):  
Structural Model ◽  
Model Errors ◽  
Test Analysis

scholarly journals CONCEPT OF ECONOMICAL‐MATHEMATICAL MODEL OF LAND MARKET

2007 ◽  
Vol 13 (4) ◽  
pp. 333-340
Author(s):  
Gintautas Šatkauskas
Keyword(s):  
Mathematical Model ◽  
Input Parameter ◽  
Market Price ◽  
Research Process ◽  
Land Market ◽  
Market Prices ◽  
Noise Background ◽  
Input Parameters ◽  
Main Components ◽  
Sufficient Precision

Input parameters, ie factors defining the market price of agricultural‐purpose land, are interrelated very often by means of non‐linear ties. Strength of these ties is rather different and this limits usefulness of information in the research process of land market prices. Influence of input parameter changes to the input parameters in case when there are rather substantial changes may be determined in someone direction with a sufficient precision, whereas in other directions with comparatively small changes of input parameters this influence is difficult to be separated from the “noise” background. Taking into account the above‐listed circumstances, the concept of economical‐mathematical model of land market should be as follows: there is carried out re‐parameterisation of the process by means of introduction of new parameters in such a way that the new parameters are not interrelated, and the full process is evaluated at the minimal number of these parameters. These requirements are met by the main components of the input parameters. Then normalisation of the main components is carried out and dependencies on new parameters are determined. It is easier to interpret the dependencies obtained having reduced the number of input parameters and the higher the non‐linearity of interrelations of primary land market data, the greater effect of normalisation of input-parameter components. The results are compared with the valuations of experts.

Mechanical Testing and Reliability Analysis for 3D Printed Cubic Lattices

2020 ◽  
Author(s):  
Nitin Nagesh Kulkarni ◽  
Stephen Ekwaro-Osire ◽  
Paul F. Egan
Keyword(s):  
3D Printing ◽  
Average Length ◽  
Input Parameter ◽  
Chi Square ◽  
Reliability Method ◽  
Input Parameters ◽  
Chi Square Test ◽  
Length Width ◽  
3D Printed

Abstract 3D printing has enabled new avenues to design and fabricate diverse structures for engineering applications, such as mechanically efficient lattices. Lattices are useful as implants for biological applications for supporting in vivo loads. However, inconsistencies in 3D printing motivates a need to quantify uncertainties contributing to mechanical failure using probabilistic analysis. Here, 50 cubic unit cell lattice samples were printed and tested with designs of 50% porosity, 500-micron beam diameters, and 3.5mm length, width, and height dimensions. The average length, width, and height measurements ranged from 3.47mm to 3.48mm. The precision in printing with a 95% confidence level was greater than 99.8%. Lattice elastic moduli ranged from about 270 MPa to 345 MPa, with a mean of 305 MPa. Probabilistic analyses were conducted with NESSUS software. The distributions of input parameters were determined using a chi-square test. The first-order reliability method was used to calculate the probability of failure and sensitivity of each input parameter. The elastic modulus was the most sensitive among all input parameters, with 57% of the total sensitivity. The study quantified printing inconsistencies and sensitives using empirical evidence and is a significant step forward for designing 3D printed parts for mechanical applications.

Optimizing Dressing Conditions for Minimum Flatness Tolerance when Grinding SKD11 Tool Steel

2021 ◽  
Vol 1020 ◽  
pp. 83-90
Author(s):  
Thi Hong Tran ◽  
Tran Ngoc Giang ◽  
Ngoc Vu Ngo ◽  
Thanh Danh Bui ◽  
Thanh Tu Nguyen ◽  
...  
Keyword(s):  
Tool Steel ◽  
Feed Rate ◽  
Input Parameter ◽  
Experimental Results ◽  
Grinding Wheel ◽  
Input Parameters

This study is to determine effects of the dressing parameters to the flatness tolerance (Fl) when grinding SKD11 steel using HaiDuong grinding wheel and also propose the suitable dressing parameters to obtain the smallest flatness tolerance. In this paper, the effects of the six input parameters including feed rate (S), depth of rough dressing cut (ar), rough dressing times (nr), depth of finish dressing cut (af), finish dressing times (nf) and non-feeding dressing (nnon) to the flatness tolerance were investigated. To find out the influence of each input parameter on output results, the S/N ratio was analysized. Evaluated experimental results show that, the average flatness tolerance was 4.05μm and deviation of this value was 11.38% compared with the predicted value.

Seismic hazard sensitivity analysis: A multi-parameter approach

1991 ◽  
Vol 81 (3) ◽  
pp. 796-817
Author(s):  
Nitzan Rabinowitz ◽  
David M. Steinberg
Keyword(s):  
Sensitivity Analysis ◽  
Seismic Hazard ◽  
Subjective Probability ◽  
Probability Distributions ◽  
Input Parameter ◽  
The Other ◽  
Probabilistic Assessment ◽  
Input Parameters ◽  
Parameter Approach

Abstract We propose a novel multi-parameter approach for conducting seismic hazard sensitivity analysis. This approach allows one to assess the importance of each input parameter at a variety of settings of the other input parameters and thus provides a much richer picture than standard analyses, which assess each input parameter only at the default settings of the other parameters. We illustrate our method with a sensitivity analysis of seismic hazard for Jerusalem. In this example, we find several input parameters whose importance depends critically on the settings of other input parameters. This phenomenon, which cannot be detected by a standard sensitivity analysis, is easily diagnosed by our method. The multi-parameter approach can also be used in the context of a probabilistic assessment of seismic hazard that incorporates subjective probability distributions for the input parameters.

On the thinning variations in hydrostatic forming of sheet metal

2021 ◽  
Vol 15 (1) ◽  
pp. 7824-7836
Author(s):  
Thu Thi Nguyen ◽  
N.D. Trung
Keyword(s):  
Sheet Metal ◽  
Thickness Distribution ◽  
Input Parameter ◽  
Relative Depth ◽  
Technological Parameters ◽  
Forming Technology ◽  
Input Parameters ◽  
Forming Characteristics ◽  
Cylindrical Cup ◽  
Forming Methods

In sheet metal forming, thinning phenomenon is one of the most concerned topics to ameliorate the final quality of the manufactured parts. The thinning variations depend on many input parameters, such as technological parameters, geometric shape of die, workpiece’s materials, and forming methods. Hydrostatic forming technology is particularly suitable for forming thin-shell products with complex shapes. However, due to the forming characteristics, the thinning variations in this technology are much more intense than in other forming methods. Therefore, in this paper, an empirical study is developed to determine the thinning variations in hydrostatic forming for cylindrical cup. Measurement of thickness at various locations of deformed products are conducted to investigate the thickness distribution and determine the dependence of the largest thinning ratio on the input parameters (including the blank holder pressure, the relative depth of the die and the relative thickness of the workpiece). The results are expressed in charts and equation which allow determining the effect of each input parameter on the largest thinning ratio.

scholarly journals A Dynamic Flight Model for Slocum Gliders and Implications for Turbulence Microstructure Measurements

2019 ◽  
Vol 36 (2) ◽  
pp. 281-296 ◽  
Author(s):  
Lucas Merckelbach ◽  
Anja Berger ◽  
Gerd Krahmann ◽  
Marcus Dengler ◽  
Jeffrey R. Carpenter
Keyword(s):  
Dissipation Rate ◽  
Input Parameter ◽  
Weather Conditions ◽  
Water Velocity ◽  
Doppler Velocity ◽  
Electromagnetic Current ◽  
Model Errors ◽  
Turbulent Dissipation ◽  
Adverse Weather ◽  
Flight Model

Abstract The turbulent dissipation rate ε is a key parameter to many oceanographic processes. Recently, gliders have been increasingly used as a carrier for microstructure sensors. Compared to conventional ship-based methods, glider-based microstructure observations allow for long-duration measurements under adverse weather conditions and at lower costs. The incident water velocity U is an input parameter for the calculation of the dissipation rate. Since U cannot be measured using the standard glider sensor setup, the parameter is normally computed from a steady-state glider flight model. As ε scales with U2 or U4, depending on whether it is computed from temperature or shear microstructure, respectively, flight model errors can introduce a significant bias. This study is the first to use measurements of in situ glider flight, obtained with a profiling Doppler velocity log and an electromagnetic current meter, to test and calibrate a flight model, extended to include inertial terms. Compared to a previously suggested flight model, the calibrated model removes a bias of approximately 1 cm s−1 in the incident water velocity, which translates to roughly a factor of 1.2 in estimates of the dissipation rate. The results further indicate that 90% of the estimates of the dissipation rate from the calibrated model are within a factor of 1.1 and 1.2 for measurements derived from microstructure temperature sensors and shear probes, respectively. We further outline the range of applicability of the flight model.

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