Model Uncertainty Research Articles

Integrating Factor Models Using Bayesian Model Averaging: Evidence from Korea

This study applies the Bayesian model averaging approach to the Korean stock market data to yield an integrated factor model that can address model uncertainty. During the period from 2004 to 2022, we choose 14 factors and 10 macro predictors and generate a total of 10,485,760 candidate factor models by considering all possible combinations of each variable and whether to allow for model mispricing. The integrated model estimates the expected return and covariance matrix by combining the predictions of all the candidate models using Bayesian posterior probabilities as weights. In the Korean stock market, there is no clear winner model with dominant posterior probabilities, implying that model uncertainty is substantial. The optimal portfolio of the integrated model has a higher out-of-sample Sharpe ratio and lower downside risk than benchmark factor models. Model uncertainty has a significant impact on the estimation of the covariance matrix of the integrated model, and model disagreement about expected returns is particularly acute during periods of sharp market declines. In the presence of model uncertainty, Bayesian investors perceive equities to be riskier than historical volatility.

Uncertainty-Aware Time Series Anomaly Detection

Traditional anomaly detection methods in time series data often struggle with inherent uncertainties like noise and missing values. Indeed, current approaches mostly focus on quantifying epistemic uncertainty and ignore data-dependent uncertainty. However, consideration of noise in data is important as it may have the potential to lead to more robust detection of anomalies and a better capability of distinguishing between real anomalies and anomalous patterns provoked by noise. In this paper, we propose LSTMAE-UQ (Long Short-Term Memory Autoencoder with Aleatoric and Epistemic Uncertainty Quantification), a novel approach that incorporates both aleatoric (data noise) and epistemic (model uncertainty) uncertainties for more robust anomaly detection. The model combines the strengths of LSTM networks for capturing complex time series relationships and autoencoders for unsupervised anomaly detection and quantifies uncertainties based on the Bayesian posterior approximation method Monte Carlo (MC) Dropout, enabling a deeper understanding of noise recognition. Our experimental results across different real-world datasets show that consideration of uncertainty effectively increases the robustness to noise and point outliers, making predictions more reliable for longer periodic sequential data.

Observer based finite-time adaptive fractional-order sliding mode control of DFIG wind turbines with unknown dynamic parameters

In this study, we investigate adaptive finite-time fractional-order sliding mode control (AFFSMC) of DFIG wind turbines (DWTs) under model uncertainty in finite time. A fractional-order sliding surface is first constructed to develop the concept. A robust terminal adaptive sliding mode controller is then designed for pitch angle control of wind turbine to achieve finite-time stability at high wind speeds to regulate the produced electric power in Zone III of the turbine’s working range. This is all with this assumption that there is no any information about the dynamics of the turbine due to the significant uncertainties. Through the use of a stable adaptive law, the vector of the wind turbine’s unknown dynamic parameters is approximated in this method. An observer is also proposed to estimate both turbine speed and external disturbances term. The closed-loop system’s finite-time stability study and the finite-time convergence of the turbine output were both carried out using the dynamic model of the system and the proposed Lyapunov theory. Some numerical examples are also presented together with a comparison to the standard integer sliding mode control to demonstrate the correctness of the control law.

Probabilistic geophysical inversion of complex resistivity measurements using the Hamiltonian Monte Carlo method

Summary In this work, we introduce the probabilistic inversion of tomographic complex resistivity (CR) measurements using the Hamiltonian Monte Carlo (HMC) method. The posterior model distribution on which our approach operates accounts for the underlying complex-valued nature of the CR imaging problem accurately by including the individual errors of the measured impedance magnitude and phase, allowing for the application of independent regularization on the inferred subsurface conductivity magnitude and phase, and incorporating the effects of cross-sensitivities. As the tomographic CR inverse problem is non-linear, of high dimension and features strong correlations between model parameters, efficiently sampling from the posterior model distribution is challenging. To meet this challenge we use HMC, a Markov-chain Monte Carlo method that incorporates gradient information to achieve efficient model updates. To maximize the benefit of a given number of forward calculations, we use the No-U-Turn sampler (NUTS) as a variant of HMC. We demonstrate the probabilistic inversion approach on a synthetic CR tomography measurement. The NUTS succeeds in creating a sample of the posterior model distribution that provides us with the ability to analyze correlations between model parameters and to calculate statistical estimators of interest, such as the mean model and the covariance matrix. Our results provide a strong basis for the characterization of the posterior model distribution and uncertainty quantification in the context of the tomographic CR inverse problem.

New Prediction Of Cracks Propagation In Repaired Steel Plate With Bonded Composite Patch At Cyclic Loading

Abstract This study presents a numerical prediction of the fatigue life of steel panels repaired by a composite patch. The effect of length cracks, the stress ratio R and properties of the patch is presented. The obtained results show that the bonded composite repair significantly reduces the stress intensity factors at the tip of repaired cracks. The results are in a good agreement with those in the literature. The Monte Carlo method is used to predict the distribution function governing crack propagation in fatigue analysis. In computing the failure probability of the structure, we consider the statistical uncertainty associated with key variables, along with the previously discussed model uncertainty. The results obtained highlight the considerable impact of variations in crack length and stress ratio on the distribution function. Notably, uncertainty in these parameters significantly amplifies the probability of structural failure in plates, thereby diminishing overall structural durability.

A Nonlinear Suspension Road Roughness Recognition Method Based on NARX-PASCKF

Road roughness significantly impacts vehicle safety and dynamic responses. For nonlinear suspension systems, the nonlinear characteristics often make it challenging for estimators to identify the actual road roughness accurately. This paper proposes a hybrid road roughness identification algorithm based on nonlinear auto-regressive with exogenous inputs (NARX) and a process noise adaptive square root cubature Kalman filter (PASCKF) to address this issue. Driven by vehicle acceleration data, an NARX-based road roughness identification system is constructed to mitigate the model uncertainties. Furthermore, a hybrid strategy is proposed. On the one hand, the accurate road roughness estimated by the NARX is converted into process noise covariance, enhancing the estimator’s accuracy and convergence rate. Another switching strategy is proposed to optimize the non-convergence issues of the PASCKF. Finally, simulation and actual vehicle experiment data demonstrate that this approach offers superior identification accuracy and adaptability compared to the standalone SCKF algorithm.

Reducing the Uncertainty in the Tropical Precipitation through a Multi‐Criteria Decision‐Making Approach

ABSTRACTThe inherent model uncertainty in precipitation projections is found to be more dominant over tropical regions thereby reducing the reliability of using them in climate change impact assessment studies. To address such issues, a subset of well performing global climate models (GCMs) can provide narrow range of possible future outcomes, which can be helpful in formulating mitigation and adaptation strategies that are more targeted and efficient. In this study, climate models are selected based on their performance in simulating relative humidity and vertical velocity since these variables play an important role in precipitation simulation and significantly contribute toward the intermodel spread. The models are evaluated by using various statistical performance measures and ranked using multi‐criteria decision‐making approaches. Finally, based on Jenks natural breaks optimization algorithm, subset of GCMs consisting of ACCESS1.0, ACCESS1.3 and INM‐CM4 models, are considered as the best possible subset for precipitation simulation over tropical land regions. Two observational precipitation datasets are further considered to investigate the effectiveness of the proposed framework. The proposed methodology is validated to be effective in identifying the best climate models since the resulting subset is capable of both capturing observed precipitation and minimizing the uncertainty in future projections. Hence, this methodology can be utilized further for performance evaluation of GCMs focusing different geography and climatic drivers.

Efficient Structural Damage Detection with Minimal Input Data: Leveraging Fewer Sensors and Addressing Model Uncertainties

In the field of structural damage detection through vibration measurements, most existing methods demand extensive data collection, including vibration readings at multiple levels, strain data, temperature measurements, and numerous vibration modes. These requirements result in high costs and complex instrumentation processes. Additionally, many approaches fail to account for model uncertainties, leading to significant discrepancies between the actual structure and its numerical reference model, thus compromising the accuracy of damage identification. This study introduces an innovative computational method aimed at minimizing data requirements, reducing instrumentation costs, and functioning with fewer vibration modes. By utilizing information from a single vibration sensor and at least three vibration modes, the method avoids the need for higher-mode excitation, which typically demands specialized equipment. The approach also incorporates model uncertainties related to geometry and mass distribution, improving the accuracy of damage detection. The computational method was validated on a steel frame structure under various damage conditions, categorized as single or multiple damage. The results indicate up to 100% accuracy in locating damage and up to 80% accuracy in estimating its severity. These findings demonstrate the method’s potential for detecting structural damage with limited data and at a significantly lower cost compared to conventional techniques.

Assessment of the Choked Flow Model of RELAP5 for Application of Inverse Quantification Methods

In the framework of deterministic safety analysis, best estimate plus uncertainty methodologies can provide a more informative detailed analysis of transients than conservative approaches. However, one important step in the application of such methodologies is derivation of uncertainty of the physical models. Probability density functions of the physical model parameters are obtained by applying inverse uncertainty quantification (IUQ) methods to experimental data. The present work deals with evaluation of the experimental database and assessment of the simulation model, which are required steps prior to the application of IUQ methods. The U.S. Nuclear Regulatory Commission system code RELAP5 has been applied for simulation of three experimental databases on choked/critical flow: Sozzi-Sutherland, Super MobyDick, and Marviken Critical Flow Tests. First, the adequacy of the experimental data to the specific target domain is carried out, to then proceed to calibration of the input model parameters by combining the use of Gaussian Process metamodels and optimization schemes. The assessment of the simulation models is performed by evaluating independently accuracy, precision, and consistency through four statistical indicators, including a novel indicator to evaluate the consistency of the results. The final results indicate that the model is capable of reproducing the selected experimental database and overall average accuracy, precision, and consistency below the 10% threshold and can be used for application of IUQ methods.

Improved FPTPPF-based predefined-time tracking control of a UVMS with actuator faults

In this paper, a new predefined-time control scheme is proposed for the trajectory tracking problem of an underwater vehicle-mechanic system (UVMS) with external disturbances, model uncertainties and actuator faults. First, a predefined-time controller is proposed to achieve convergence in a predefined time so that the convergence time does not depend on the initial value of the system. Second, considering the possible grasping and transportation tasks for the UVMS, an improved flexible predefined-time prescribed performance function (FPTPPF) with self-adjustment capability is proposed to avoid the vulnerabilities of the existing prescribed performance functions. A control framework is constructed for the integral barrier Lyapunov function and FPTPPF, which can achieve good tracking performance. Third, a predefined-time extended state observer (ESO) is constructed to address the problems caused by external disturbances, model uncertainties and actuator faults. For strong sudden disturbances, the H∞ control strategy is designed via the backstepping method, which effectively improves the robustness. Finally, the predefined-time stability of the system is proven via Lyapunov stability theory, where the tracking errors can converge to a small region of the null domain in a predefined time. The performance and superiority of the proposed predefined-time control method are verified via simulation comparisons.

Estimation of Tree Diameter at Breast Height from Aerial Photographs Using a Mask R-CNN and Bayesian Regression

A probabilistic estimation model for forest biomass using unmanned aerial vehicle (UAV) photography was developed. We utilized a machine-learning-based object detection algorithm, a mask region-based convolutional neural network (Mask R-CNN), to detect trees in aerial photographs. Subsequently, Bayesian regression was used to calibrate the model based on an allometric model using the estimated crown diameter (CD) obtained from aerial photographs and analyzed the diameter at breast height (DBH) data acquired through terrestrial laser scanning. The F1 score of the Mask R-CNN for individual tree detection was 0.927. Moreover, CD estimation using the Mask R-CNN was acceptable (rRMSE = 10.17%). Accordingly, the probabilistic DBH estimation model was successfully calibrated using Bayesian regression. A predictive distribution accurately predicted the validation data, with 98.6% and 56.7% of the data being within the 95% and 50% prediction intervals, respectively. Furthermore, the estimated uncertainty of the probabilistic model was more practical and reliable compared to traditional ordinary least squares (OLS). Our model can be applied to estimate forest biomass at the individual tree level. Particularly, the probabilistic approach of this study provides a benefit for risk assessments. Additionally, since the workflow is not interfered by the tree canopy, it can effectively estimate forest biomass in dense canopy conditions.

Soil landscapes of the United States (SOLUS): Developing predictive soil property maps of the conterminous United States using hybrid training sets

AbstractDetailed soil property maps are increasingly important for land management decisions and environmental modeling. The US Soil Survey is investing in production of the Soil Landscapes of the United States (SOLUS), a new set of national predictive soil property maps. This paper documents initial 100‐m resolution maps of 20 soil properties that include various textural fractions, physical parameters, chemical parameters, carbon, and depth to restrictions. Many of these properties have not been previously mapped at this resolution. A hybrid training strategy helped increase training data by roughly 10‐fold over previous similar studies by combining commonly used laboratory data with underutilized field descriptions tied to soil survey map unit component property estimates (to help represent within polygon variability) as well as randomly selected soil survey map unit weighted average property estimates. Relative prediction intervals were used to help select which training data sources improved model performance. Conventional and spatial cross‐validation strategies yielded generally strong coefficients of determination between 0.5 and 0.7, but with substantial variability and outliers among the various properties, types of training data, and depths. Internal review of the maps highlighted both strengths and weaknesses of the maps, but most of the critical comments were in areas with high model uncertainty that can be used to guide future improvements. Generally, previously glaciated areas and complex large alluvial basins were harder to model. The new SOLUS 100‐m maps will be updated in the future to address identified issues and feedback as users interact with the data.

Model uncertainty quantification of a degradation model of miter gates using normalizing flow-based likelihood-free inference

Degradation modeling is essential for failure prognostics of miter gates and subsequent risk-informed maintenance or operational decision-making. Typically, degradation models are formulated based on certain assumptions and simplifications and may not fully capture the complexity of underlying degradation mechanisms. Even minor errors in such models may lead to significant discrepancies in failure prognostics due to error accumulation over time. Aiming to improve the accuracy of the degradation model and ensure reliable failure prognostics, this article proposes a degradation model updating framework for miter gates using normalizing flow-based likelihood-free inference, accounting for both model parameter uncertainty and model form uncertainty (i.e., model bias). The proposed work consists of two phases: the offline training phase and the online updating phase. During the offline training phase, the unknown model bias term is modeled as a random noise with uncertain standard deviation. Synthetic data are then generated using a physical model based on prior knowledge of the uncertain model parameters and model bias. The synthetic data are utilized to train an inference model, which has a summary network for data compression and a conditional invertible neural network for parameter estimation. In the online updating phase, the trained inference model uses strain observations to obtain posterior samples. The Gaussian mixture model and dual particle filter techniques are utilized to recursively update posterior samples, thereby improving the estimation accuracy. Subsequently, model bias is inversely estimated using the degradation model, which uses the updated model parameters and the gap length from the inference model. Following that, a regression model is constructed to correct the biases inherent in the simplified degradation model. This process is implemented iteratively over time to perform continuous model updating and failure prognostics. Results of a case study demonstrate the efficacy of the proposed framework in reducing both model parameter uncertainty and recovering model biases and thereby improving the accuracy of failure prognostics of miter gates.

Best Practices in Developing a Workflow for Uncertainty Quantification for Modeling the Biodegradation of Mg-Based Implants.

Computational models of electrochemical biodegradation of magnesium (Mg)-based implants are uncertain. To quantify the model uncertainty, iterative evaluations are needed. This presents a challenge, especially for complex, multiscale models as is the case here. Approximating high-cost and complex models with easy-to-evaluate surrogate models can reduce the computational burden. However, the application of this approach to complex degradation models remains limited and understudied. This work provides a workflow to quantify different types of uncertainty within biodegradation models. Three surrogate models-Kriging, polynomial chaos expansion, and polynomial chaos Kriging-are compared based on the minimum number of samples required for surrogate model construction, surrogate model accuracy, and computational time. The surrogate models are tested for three computational models representing Mg-based implant biodegradation. Global sensitivity analysis and uncertainty propagation are used to analyze the uncertainties associated with the different models. The findings indicate that Kriging proves effective for calibrating diverse computational models with minimal computational time and cost, while polynomial chaos expansion and polynomial chaos Kriging exhibit greater capability in predicting propagated uncertainties within the computationalmodels.

Seismic risk estimates for reinforced concrete structures with incorporation of corrosion and aftershock

Numerous reinforced concrete (RC) structures are exposed to aggressive environments, such as chloride, mainshock and aftershock. These environmental and extreme loads have the potential to increase the seismic risks during structure's service life. This study introduces a practical probabilistic methodology to estimate the seismic risk of corroded RC frame subjected to mainshock-aftershock sequences. In this methodology, a time-variant modeling strategy is used to simulate the geometrical and mechanical properties of structural degraded materials. The Bayesian updating theorem is employed to calibrate the demand models, which are then used to estimate the fragilities and confidence intervals considering the model uncertainties. A Copula-based approach is conducted to generate joint probability of mainshock and aftershock intensities and the seismic hazard of the mainshock-aftershock scenario. Finally, the seismic risk and associated confidence intervals are estimated by integrating over all mainshock and aftershock intensities levels. A typical corroded RC frame structure is used to illustrate the proposed methodology. The results show that the contribution of corrosion and aftershock would lead a 10 times higher seismic risks compared to scenarios considering only mainshock damage. It is necessary to account for the influence of both corrosion and aftershock in seismic design.

Control Design and Implementation of Autonomous Robotic Lawnmower

This paper presents the trajectory tracking control design and implementation of feedback linearization (FL) and robust feedback linearization (RFL), applicable to a robotic lawnmower with four mecanum driving wheels. The RFL control design additionally includes a robust control law. These two nonlinear control laws are developed to enable the controlled robotic lawnmower to accurately follow any specified trajectory. The simulation outcomes illustrate that the suggested control law based on RFL displays superior trajectory tracking accuracy and resilience compared to the FL control method in the case of a robotic lawnmower operating under demanding conditions. These conditions encompass environmental disturbances and uncertainties in modeling. The RFL control method also exhibits lower energy consumption compared to the FL control method. Finally, using the RFL controller derived from this study, the error in trajectory tracking in computer simulations and the actual mowing performance have demonstrated outstanding results.

Retrospective validation of automatic sleep analysis with grey areas model for human-in-the-loop scoring approach.

State-of-the-art automatic sleep staging methods have demonstrated comparable reliability and superior time efficiency to manual sleep staging. However, fully automatic black-box solutions are difficult to adapt into clinical workflow due to the lack of transparency in decision-making processes. Transparency would be crucial for interaction between automatic methods and the work of sleep experts, i.e., in human-in-the-loop applications. To address these challenges, we propose an automatic sleep staging model (aSAGA) that effectively utilises both electroencephalography and electro-oculography channels while incorporating transparency of uncertainty in the decision-making process. We validated the model through extensive retrospective testing using a range of datasets, including open-access, clinical, and research-driven sources. Our channel-wise ensemble model, trained on both electroencephalography and electro-oculography signals, demonstrated robustness and the ability to generalise across various types of sleep recordings, including novel self-applied home polysomnography. Additionally, we compared model uncertainty with human uncertainty in sleep staging and studied various uncertainty mapping metrics to identify ambiguous regions, or "grey areas", that may require manual re-evaluation. The validation of this grey area concept revealed its potential to enhance sleep staging accuracy and to highlight regions in the recordings where sleep experts may struggle to reach a consensus. In conclusion, this study provides a technical basis and understanding of automatic sleep staging uncertainty. Our approach has the potential to improve the integration of automatic sleep staging into clinical practice; however, further studies are needed to test the model prospectively in real-world clinical settings and human-in-the-loop scoring applications.

Dual-Arm Space Robot On-Orbit Operation of Auxiliary Docking Prescribed Performance Impedance Control

The impedance control of a dual-arm space robot in orbit auxiliary docking operation is studied. First, for the closed-chain hybrid system formed by the dual-arm space robot after capture operation, the dynamic equation of position uncontrolled and attitude controlled is established. The second-order linear impedance model and second-order approximate environment model are established for the problem of simultaneous output force/pose control of the end of the manipulator. Then, aiming at the transient performance control requirements of the dual-arm space robot auxiliary docking operation in orbit, a sliding mode controller with equivalent replacement of tracking errors is designed by introducing Prescribed Performance Control (PPC) theory. Next, Radial Basis Function Neural Networks (RBFNN) are used to accurately compensate for the modeling uncertainties of the system. Finally, the stability of the system is verified by Lyapunov stability determination. The simulation results show that the attitude control accuracy is better than 0.5°, the position control accuracy is better than 10−3 m, and the output force control accuracy is better than 0.5 N when it reaches 30 N. It also indicated that the proposed control algorithm can limit the transient performance of the controlled system within the preset range and achieve high-precision force/pose control, which ensures a more stable on-orbit auxiliary docking operation of the dual-arm space robot.

AIGD-PFT: the first AI-driven global daily gap-free 4 km phytoplankton functional type data product from 1998 to 2023

Abstract. Long time series of spatiotemporally continuous phytoplankton functional type (PFT) data are essential for understanding marine ecosystems and global biogeochemical cycles as well as for effective marine management. In this study, we integrated artificial intelligence (AI) technology with multisource marine big data to develop a spatial–temporal–ecological ensemble model based on deep learning (STEE-DL). This model generated the first AI-driven global daily gap-free 4 km PFT chlorophyll a concentration product from 1998 to 2023 (AIGD-PFT). The AIGD-PFT significantly enhances the accuracy and spatiotemporal coverage of quantifying eight major PFTs: diatoms, dinoflagellates, haptophytes, pelagophytes, cryptophytes, green algae, prokaryotes, and Prochlorococcus. The model input encompasses (1) physical oceanographic, biogeochemical, and spatiotemporal information and (2) ocean colour data (OC-CCI v6.0) that have been gap-filled using a discrete cosine transform–penalized least squares (DCT-PLS) approach. The STEE-DL model utilizes an ensemble strategy with 100 residual neural network (ResNet) models, applying Monte Carlo and bootstrapping methods to estimate the optimal PFT chlorophyll a concentration and assess the model uncertainty through ensemble means and standard deviations. The model's performance was validated using multiple cross-validation strategies – random, spatial-block, and temporal-block methods – combined with in situ data, demonstrating STEE-DL's robustness and generalization capability. The daily updates and seamless nature of the AIGD-PFT data product capture the complex dynamics of coastal regions effectively. Finally, through a comparative analysis using a triple-collocation analysis (TCA) approach, the competitive advantages of the AIGD-PFT data product over existing products were validated. The complete product dataset (1998–2023) can be freely downloaded from https://doi.org/10.11888/RemoteSen.tpdc.301164 (Zhang and Shen, 2024a).

Uncertainty in dynamic econometric input-output models: a Norwegian case study

Input-output models used for macroeconomic impact and policy analysis are often characterised by large data sets and resource-heavy computing. However, the types of results they provide are sensitive to uncertainty in their core assumptions. Various approaches have been proposed to account for the uncertainty in one or more parts of the analysis assumptions. Although it is standard practice to include varied cases in policy analysis, the notion of stochasticity of parameters across periods of time is less widespread. Costly numerical computing and difficulty in interpreting the results complicate this approach. In this work, we adapt an environmentally-extended dynamic econometric input-output model to account for uncertainty of various kinds. We demonstrate the methodology in the case of building renovation. The results provide insight into situations where explicitly considering uncertainty as part of the analysis is useful, as well as others in which no additional information was gained from such treatment.