Uncertainty Propagation Analysis Research Articles

Developing a probabilistic compaction model for the Northern Carnarvon Basin using Bayesian inference

AbstractExhumation affects sedimentary basin evolution by influencing structural, pressure and temperature dynamics, thereby impacting energy resource formation. Compaction‐based methods are widely used to quantify exhumation, utilising sonic and porosity data to track sediment uplift from its maximum burial depths. However, uncertainties arise from applying empirical compaction models developed for specific geological regions, highlighting the need for region‐specific models. Even such region‐specific models contain uncertainties, which can compromise exhumation estimates. We, therefore, develop a probabilistic compaction model for the Northwest Shelf Basins using sonic data from normally compacted and unexhumed shales from the Northern Carnarvon Basin (NCB). The model's robustness is estimated using MCMC, and uncertainty propagation analysis is employed to assess the impact of model uncertainty on the model's predictive applications. The model shows exponential porosity reduction with depth, demonstrating rapid compaction from the surface to ca. 2 km and slower compaction thereafter. The model is then applied to interpret new datasets from the Canning, Gippsland and NCB regions. The results reveal that while some parts of the NCB exhibit normal compaction without exhumation, others were significantly exhumed. Conversely, Canning and Gippsland Basin data indicate signs of significant exhumation, as suggested by previous studies, thereby confirming the model's effectiveness outside the Northwest Shelf. Since the model could not explain data from exhumed regions, we inferred new models incorporating “exhumation” parameters to interpret the complex compaction histories of these areas, and the best‐fitting models were selected using the Bayes Factor method. Uncertainty analysis revealed that the impacts of model uncertainty on exhumation estimates are consistent across wide depth ranges. Our findings highlight the need to refine compaction models for better predictive reliability and informed resource exploration in sedimentary basins.

State uncertainty propagation and sensitivity analysis of the post-impact binary asteroid system

State uncertainty propagation and sensitivity analysis of the post-impact binary asteroid system

Uncertainty sensitivity analysis for vibration properties of composite doubly-curved shallow shells using Kriging method

This paper presents a Kriging based global sensitivity analysis (GSA) method for the frequency response of displacements of composite doubly-curved shallow shells. A unified solution is utilized to develop the dynamic vibration formulation using the First-order Shear Deformation Theory (FSDT) and the Rayleigh-Ritz method. Kriging surrogate model is employed to substitute the frequency response function (FRF) of displacements. Ten parameters including materials and geometrical dimension are considered as input uncertain variables. A variance-based GSA method for dynamic model is employed to quantify the influence of each uncertain parameter. In addition, to avoid the computational burden of Monte Carlo simulation method (MCS), the presented sensitivity indices are computed analytically based on the Kriging mode, which further improves computational efficiency. Based on the convergence studies and comparison with traditional methods, the accuracy and efficiency of the present method are validated. The results shows that the frequency response of displacements exhibits greater sensitivity to changes in width, and thickness is more influential than others in the example from this article. Finally, the presented numerical results demonstrate vibration characteristics of different types of shells and observation points, which can also serve as a reference for further study on uncertainty-propagation analysis.

Uncertainty propagation analysis for an aviation accelerometer using an improved saddlepoint approximation method

Uncertainty propagation analysis for an aviation accelerometer using an improved saddlepoint approximation method

Activation cross section for 85Rb(n,2n)84mRb and 85Rb(n,p)85mKr reactions with uncertainty propagation and covariance analysis

The cross section of 85Rb(n,2n)84mRb and 85Rb(n,p)85mKr reactions were measured at neutron energy range 12–20 MeV using activation analysis followed by off-line γ-ray spectroscopic technique. The quasi mono-energetic neutrons were produced through 7Li(p,n)7Be reaction. The measurements were done relative to 27Al(n,α)24Na reference monitor reaction cross section. The detailed uncertainty propagation from the attributes present in measurements was performed using covariance analysis. The γ-ray self-attenuation and background low neutron energy corrections were performed in the measurement studies. Theoretical calculations were performed by TALYS-1.96 nuclear code. The comparison of measured values with the available data in EXFOR database and evaluated data from JENDL-5 and EAF-2010 shows the measured cross section values of 85Rb(n,p)85mKr reaction were slightly higher than the published values, evaluated data and theoretical data while for 85Rb(n,2n)84mRb, the measured values were consistent with the published data.

Dynamic uncertainty propagation analysis framework for nonlinear control problem based on manifold learning and optimal polynomial method and its application on active suspension system

A novel uncertainty propagation method based on manifold learning and optimal polynomial model is proposed to quantify and analyze the dynamic uncertainties of the nonlinear feedback control system. To deal with the multiple objectives and constraints of the nonlinear control problem, a barrier Lyapunov-function-based nonlinear filtered backstepping controller is developed and applied to active suspension system to obtain superior ride comfort performance under limited structural constraints. Considering the errors in the production, manufacturing, and assembly, the probability density function is employed to quantify the structural parameter uncertainties in the nonlinear control system. Moreover, to reveal the dynamic propagation mechanism of uncertainties in the system with nonlinearity, the manifold learning method is proposed to reduce the dimensionality of the dynamic system to avoid the complexity of uncertainty propagation. Simultaneously, data-driven optimal polynomial model is utilized to accurately approximate the internal mechanism of nonlinear filtered backstepping control system. Based on that, the response uncertainties of the nonlinear control system are accurately and quickly quantified through dynamic moment information and uncertain fluctuation space. Finally, an active suspension system with nonlinearities and uncertainties is developed to verify the effectiveness of the controller with improved ride comfort and better handling safety and the superiority of the framework in terms of efficiency and accuracy of the dynamic uncertainty propagation analysis for nonlinear control problem.

Propagation of hybrid uncertainty by synthesizing B-spline chaos and augmented change of probability measure

Acquiring engineering data is frequently expensive, resulting in sparse data that may lead to a lack of knowledge for design and analysis. Thus, it is not always feasible to precisely determine the probability density functions (PDFs) of uncertain model parameters. Under such circumstances that involve simultaneous aleatory and epistemic uncertainties, repeated uncertainty propagation (UP) analysis is generally required. In this paper, a novel approach for hybrid UP is proposed by integrating B-spline chaos and augmented change of probability measure (aCOM) for meeting different goals. The B-spline chaos is adopted to represent the complicated computational model as a function of an arbitrary input random variable, while the aCOM is employed to reconstruct the PDF of the model output when the input PDF is changed due to epistemic uncertainty. In the case of small epistemic uncertainty, hybrid UP can be achieved directly by changing the assigned probabilities of existing sample results. While in the case of large epistemic uncertainty, additional samples from an augmenting PDF are generated. The proposed method is compatible with both cases. The numerical algorithm of the proposed method is presented and illustrated by four benchmark problems. Further, the accuracy and efficiency of the proposed method are substantiated by four numerical examples compared with analytical solutions or Monte Carlo simulations. An attempt to enhance the proposed method with the aid of active subspace methods to handle high-dimensional problems is also discussed in this work. The limitations and potential improvements of the proposed approach are outlined as well.

Inter-laboratory reproduction and sensitivity study of a finite element model to quantify human femur failure load: Case of metastases

IntroductionMetastases increase the risk of fracture when affecting the femur. Consequently, clinicians need to know if the patient's femur can withstand the stress of daily activities. The current tools used in clinics are not sufficiently precise. A new method, the CT-scan-based finite element analysis, gives good predictive results. However, none of the existing models were tested for reproducibility. This is a critical issue to address in order to apply the technique on a large cohort around the world to help evaluate bone metastatic fracture risk in patients. The aim of this study is then to evaluate 1) the reproducibility 2) the transposition of the reproduced model to another dataset and 3) the global sensitivity of one of the most promising models of the literature (original model). MethodsThe model was reproduced based on the paper describing it and discussion with authors to avoid reproduction errors. The reproducibility was evaluated by comparing the results given in the original model by the original first team (Leuven, Belgium) and the reproduced model made by another team (Lyon, France) on the same dataset of CT-scans of ex vivo femurs. The transposition of the model was evaluated by comparing the results of the reproduced model on two different datasets. The global sensitivity analysis was done by using the Morris method and evaluates the influence of the density calibration coefficient, the segmentation, the orientations and the length of the femur. ResultsThe original and reproduced models are highly correlated (r2 = 0.95), even though the reproduced model gives systematically higher failure loads. When using the reproduced model on another dataset, predictions are less accurate (r2 with the experimental failure load decreases, errors increase). The global sensitivity analysis showed high influence of the density calibration coefficient (mean variation of failure load of 84 %) and non-negligible influence of the segmentation, orientation and length of the femur (mean variation of failure load between 7 and 10 %). ConclusionThis study showed that, although being validated, the reproduced model underperformed when using another dataset. The difference in performance depending on the dataset is commonly the cause of overfitting when creating the model. However, the dataset used in the original paper (Sas et al., 2020a) and the Leuven's dataset gave similar performance, which indicates a lesser probability for the overfitting cause. Also, the model is highly sensitive to density parameters and automation of measurement may minimize the uncertainty on failure load. An uncertainty propagation analysis would give the actual precision of such model and improve our understanding of its behavior and is part of future work.

Stochastic mesoscale characterization of ablative materials for atmospheric entry

This study addresses the estimation of material properties at a mesoscopic level using the PuMA software from an uncertainty quantification perspective. Stochastic simulation with PuMA is primarily related to the random distribution of fibers, which is an intrinsic source of uncertainty. Additionally, the selection of certain physical parameters, such as the fiber's thermal conductivity, introduces further uncertainties. The first contribution of this study is to propose a low-cost surrogate-based methodology with an unequal allocation scheme, applied for the first time to the stochastic mesoscale characterization of ablative materials. The second contribution is a study on uncertainty propagation and sensitivity analysis of material properties, providing a systematic assessment of the choice of voxel resolution for both the fibers and the domain. Specifically, the convergence of quantities of interest can be monitored, thus identifying the minimal reference elementary volume.

Multimodal uncertainty propagation analysis for the morphing wings of cross-domain variant aircraft

Multimodal uncertainty propagation analysis for the morphing wings of cross-domain variant aircraft

Hybrid uncertainty propagation analysis of nonlinear systems in the frequency domain based on multi-scale random interval moment method

To quantify the impact of hybrid uncertainty (random and interval parameters) on the frequency-domain nonlinear dynamic response, the multi-scale method (MSM) and the random interval moment method (RIMM) are combined to establish a new uncertainty propagation analysis method, called the multi-scale random interval moment method (MS-RIMM). RIMM is used to describe the hybrid uncertainty, while MSM is used to determine the frequency-domain nonlinear dynamic response. The statistical characteristics (i.e., the expectation value and variance) of the amplitude-frequency response of the nonlinear system with hybrid uncertainties are derived. Furthermore, the accuracy and effectiveness of the proposed method are verified by comparing the results with those obtained using the multi-scale Monte Carlo simulation method (MS-MCSM). Overall, the results of this study can serve as a useful reference for the hybrid uncertainty propagation analysis of nonlinear systems and for predicting the frequency-domain nonlinear dynamic response.

A dimension reduction-based Kriging modeling method for high-dimensional time-variant uncertainty propagation and global sensitivity analysis

Surrogate models have been widely used in the uncertainty propagation and global sensitivity analysis of complex evaluation-expensive engineering problems. However, the construction of high-accuracy surrogate models for time-variant problems with high-dimensional inputs and outputs using a small number of training samples remains a challenge. To address this challenge, we propose a dimension reduction-based Kriging modeling (KMDR) method for high-dimensional time-variant uncertainty propagation and global sensitivity analysis. Singular value decomposition is performed on the original time-variant response to extract principal components from high-dimensional outputs. And the improved sufficient dimension reduction (ISDR) is performed on high-dimensional inputs to identify the latent input space with respect to each principal component of outputs. A ladle estimator with a rigorous mathematical definition is then employed to determine the number of principal components of the outputs and the dimensionalities of the latent input spaces. The ladle estimator considers variabilities in both eigenvalues and eigenvectors of a matrix and can determine the latent dimensionality more accurately and efficiently than existing approaches. Subsequently, Kriging models between high-dimensional inputs and each principal component of the outputs are constructed based on a newly devised Kriging kernel, which embeds the information of the ISDR into the kernel function and can achieve higher accuracy than directly constructing Kriging models between latent inputs and outputs. In addition, a generalized variance-based sensitivity index, which can quantify the effects of the inputs on the overall time-variant response, is defined and computed directly from Sobol’ sensitivity indices of the inputs at each time node. Finally, the surrogate model of the time-variant system constructed by the KMDR is directly adopted for efficient time-variant uncertainty propagation and global sensitivity analysis. Several examples demonstrate that the proposed approach can construct more accurate surrogate models and obtain more accurate time-variant uncertainty propagation and global sensitivity analysis results than existing methods with a small training set.

Reliability Analysis for RV Reducer by Combining PCE and Saddlepoint Approximation Considering Multi-Failure Modes

Abstract RV (Rotate Vector) reducer is an essential mechanical transmission device extensively used in industrial machinery, robotics, aerospace and other fields. The dynamic transmission characteristics and strength of the cycloidal pin gear, turning arm bearing of RV reducer significantly affect the motion accuracy and reliability of the whole equipment. Uncertainties from manufacturing and assembly error, working loads add complexity to these effects. Developing effective methods for uncertainty propagation and reliability analysis for the RV reducer is crucial. In this work, the mail failure modes of RV reducer are studied, and an effective reliability analysis method for RV reducer considering the correlation between multi-failure modes by combining polynomial chaos expansions (PCE) and saddlepoint approximation method (SPA) is proposed. This paper develops an uncertainty propagation strategy for RV reducer based on dynamic simulation and PCE method with high accuracy. On this basis, a surrogated cumulant generating function (CGF) and SPA are combined to analyze the stochastic characteristic for the failure behavior. Based on the probability density function (PDF) and cumulative distribution function (CDF) calculated by SPA, copula function is employed to quantify the correlations between the multi-failure modes. Then, the system reliability with multi-failure modes is estimated by SPA and optimal copula function. The proposed method provides an effective reliability assessment technology with high-accuracy for complex system under unknown physical model and distribution characteristics. The validity of the proposed approach is illustrated RV-320E reducer reliability estimation, offering a basis to improve the performance of complex dynamic system. .

Levelized cost of electricity in renewable energy communities: Uncertainty propagation analysis

Renewable Energy Communities (RECs) are being deployed all around the World as a technically feasible solution to decreasing users' dependence on fossil fuels. Several demonstration facilities have shown their potential to provide final consumers with clean energy and all associated environmental benefits. However, the economic evaluation of these systems as a whole set is more complex than evaluating generation technologies individually, which can be considered a barrier, and it may be more complicated to calculate its uncertainty with precision. This paper deals with this challenge and adapts a model for the evaluation of the global Levelized Cost of Electricity (LCOE) of a polygeneration microgrid to the characteristics of a typical REC, allowing the assessment of the distribution of the LCOE depending on the uncertainty of the input parameters. Thanks to its simple analytical formulation, the proposed model, that can be used for any combination of technologies (both renewable and conventional), provides relevant information on uncertainty propagation in a symbolic way that avoids the need to run numerical simulations or make assumptions on the distribution of the random input parameters. A case study has been presented, considering a typical small electrical REC with photovoltaic plants and micro wind turbines. Although the model can be defined to any market, as a representative example, it has been evaluated according to the current Spanish and Italian regulations, which are analyzed in depth with reference to the scientific literature. Results show that uncertainties in parameter estimates give rise to a very large scatter in the LCOE, pointing out a set of quantities whose role is crucial for a reliable estimate, among which electricity purchase and selling prices, yearly power load, and self-consumption / virtually-shared energy rates stand out.

Uncertainty propagation analysis for distributed hydrological forecasting using a neural network

AbstractThe last few decades have presented a significant increase in hydrological disasters, such as floods. In some countries, most of the environmental, socioeconomic, and biodiversity losses are caused by floods. Thus, flood forecasting is crucial to support an efficient disaster warning system. This work proposes a model for hydrological forecasting based on a neural network with a geographically aligned input named GeoNN. It employs weather radar data to obtain accumulated rainfall in each grid cell of the watershed and make 15‐ and 120‐min predictions of the outlet river level. An uncertainty propagation analysis was performed for GeoNN from a collection of test cases obtained by either using different schemes of the dataset partitioning or introducing different additive‐noise rates to the input data to provide a probability of flood occurrence and also an ensemble prediction. Both this probability and the ensemble were able to detect occurrences of river levels exceeding a given flood threshold.

Multi-source uncertainty propagation and sensitivity analysis of turbine blades with underplatform dampers

Underplatform dampers (UPDs) mitigate turbine blade vibrations in aeroengines through friction dissipation generated by the contact interface. However, in UPD design, uncertainties are often overlooked, including manufacturing discrepancies, excitation forces, and wear factors, leading to suboptimal predictions of structural dynamic responses. This study presents a dynamic model for the blade-UPD system with cyclic symmetric attributes, which simulates uncertainties using statistical methods. An efficient algorithm using adaptive techniques is proposed to construct polynomial chaos expansions (PCE) for precise and efficient uncertainty quantification (UQ) in turbine blades with UPDs. Further, the influence of single/multiple parameter uncertainties on the dynamic characteristics of the blade-UPD is explored. Sobol' indices are then employed to assess the sensitivity of uncertain factors to the vibration reduction properties of UPDs. The findings suggest that the new approach, which offers precise UQ at minimal computational cost, outperforms traditional methods like Ordinary Least Squares (OLS) and Sparse Least Angle Regression (LARS). Observations reveal a significant impact of parameter uncertainties on blade-UPD dynamic responses, which manifest as "resonance bands" and "frequency shifts" in some cases. Sensitivity analysis indicates noticeable variations in Sobol' indices for each uncertainty parameter as the excitation frequency changes. Specifically, the uncertainty in the friction coefficient demonstrates pronounced sensitivity to amplitude when slip occurs at the contact interface. Furthermore, the observed "drop" phenomenon in Sobol' indices is explained.

Measurement of the 12C(p,n)12N reaction cross section below 150 MeV

Objective. Proton therapy currently faces challenges from clinical complications on organs-at-risk due to range uncertainties. To address this issue, positron emission tomography (PET) of the proton-induced 11C and 15O activity has been used to provide feedback on the proton range. However, this approach is not instantaneous due to the relatively long half-lives of these nuclides. An alternative nuclide, 12N (half-life 11 ms), shows promise for real-time in vivo proton range verification. Development of 12N imaging requires better knowledge of its production reaction cross section. Approach. The 12C(p,n)12N reaction cross section was measured by detecting positron activity of graphite targets irradiated with 66.5, 120, and 150 MeV protons. A pulsed beam delivery with 0.7–2 × 108 protons per pulse was used. The positron activity was measured during the beam-off periods using a dual-head Siemens Biograph mCT PET scanner. The 12N production was determined from activity time histograms. Main results. The cross section was calculated for 11 energies, ranging from 23.5 to 147 MeV, using information on the experimental setup and beam delivery. Through a comprehensive uncertainty propagation analysis, a statistical uncertainty of 2.6%–5.8% and a systematic uncertainty of 3.3%–4.6% were achieved. Additionally, a comparison between measured and simulated scanner sensitivity showed a scaling factor of 1.25 (±3%). Despite this, there was an improvement in the precision of the cross section measurement compared to values reported by the only previous study. Significance. Short-lived 12N imaging is promising for real-time in vivo verification of the proton range to reduce clinical complications in proton therapy. The verification procedure requires experimental knowledge of the 12N production cross section for proton energies of clinical importance, to be incorporated in a Monte Carlo framework for 12N imaging prediction. This study is the first to achieve a precise measurement of the 12C(p,n)12N nuclear cross section for such proton energies.

Realistic estimation framework of radioactive release distributions into the environment during nuclear power plant accidents

Since the level 2 PSA of OPR-1000 was the requirement for regulatory purposes, Cs-137 release estimation was contained as the Nuclear Safety Act of ROK in which the Cs-137 release frequency exceeding 100 TBq was determined to happen less than 1.0E-6 per year after the Fukushima Daiichi Accident. However, Cs-137 release estimation from the conventional level 2 PSA of OPR-1000 provided uncertainty due to dominant accident sequence consideration. Thus, this study aimed to develop systematic methods through the overall framework to quantify realistic uncertainty concerns of radioactive material release using sensitivity and uncertainty analysis methods and apply them to OPR-1000. This framework helped to quantify confidential value for the Cs-137 release under the BEPU approach using both parametric and non-parametric methods to cover both realistic and conservative points. Uncertainty propagation analysis showed the unexpected uncertainty increase of Cs-137 release exceeding 100 TBq. The non-parametric uncertainty analysis provided higher conservative concerns for safety than the realistic concerns in terms of economics when compared with the parametric uncertainty analysis. Wilks’ uncertainty analysis showed the importance to consider conservative Cs-137 release in order to reach the higher safety need. Sensitivity analysis showed reasonable relationships between engineering safety parameters with the Cs-137 release.

Hybrid uncertainty propagation based on multi-fidelity surrogate model

There always exist multiple uncertainties including random uncertainty, interval uncertainty, and fuzzy uncertainty in engineering structures. In the presence of hybrid uncertainties, the hybrid uncertainty propagation analysis can be a challenging problem, which suffers from the computational burden of double-loop procedure when numerical simulation techniques are employed. In this work, a novel method for efficient hybrid uncertainty propagation analysis with the three types of uncertainties is proposed. Generally, multi-fidelity surrogate models, such as Co-Kriging, can greatly improve the computational efficiency by leveraging information from a low-fidelity model to build a high-fidelity approximate model. However, the traditional multi-fidelity surrogate model methods always calculate the hybrid uncertainty propagation result by combining with several numerical simulation techniques. This process can introduce post-processing errors unless unlimited number of samples are used, which is impossible in engineering application. In order to address this issue, the analytical solutions of the output mean and output variance are derived based on the Co-Kriging, and the resulting mean and variance are both random variables. Moreover, a new adaptive framework is established to strengthen the estimation accuracy of the hybrid uncertainty propagation result, by combining the augmented expected improvement function and the derived mean random variable. Several applications are introduced to demonstrate the effectiveness of the proposed method for solving hybrid uncertainty propagation problems.

Modeling rainfall-induced landslide using the concept of local factor of safety: Uncertainty propagation and sensitivity analysis

Rainfall-induced landslides (RILS) are commonly investigated using hydro-mechanical models with the concept of local factor of safety. The inputs of these models are usually prone to uncertainties. An uncertainty analysis is required to investigate how uncertainties propagate through the model and impact the predictions. An appropriate strategy for uncertainty propagation analysis is suggested in this work to deal with nonlinearity and high dimensionality of RILS problems. It proceeds by performing a sensitivity analysis in two steps. A screening technique is first applied to eliminate insignificant parameters. Then, a global sensitivity analysis is performed to rank the parameters by order of importance. The Sobol indices are used as sensitivity metrics. The polynomial chaos expansion is used to compute the Sobol indices. The proposed strategy is first applied to a hypothetical benchmark and then to a more realistic configuration where prior knowledge of parameters and type of soil are considered. The results show that, when prior knowledge of soil is available, the most important parameters are the coefficient of cohesion, friction angle and air entry pressure head, respectively. The results also show that 10% uncertainty on these parameters leads to about 20% uncertainty on the prediction of slope stability.