Uncertainty Model Research Articles

Research on Quantification of Structural Natural Frequency Uncertainty and Finite Element Model Updating Based on Gaussian Processes

During bridge service, material degradation and aging occur, affecting bridge functionality. Bridge health monitoring, crucial for detecting structural damage, includes finite element model modification as a key aspect. Current finite element-based model updating techniques are computationally intensive and lack practicality. Additionally, changes in loading and material property deterioration lead to parameter uncertainty in engineering structures. To enhance computational efficiency and accommodate parameter uncertainty, this study proposes a Gaussian process model-based approach for predicting structural natural frequencies and correcting finite element models. Taking a simply supported beam structure as an example, the elastic modulus and mass density of the structure are sampled by the Sobol sequence. Then, we map the collected samples to the corresponding physical space, substitute them into the finite element model, and calculate the first three natural frequencies of the model. A Gaussian surrogate model was established for the natural frequency of the structure. By analyzing the first three natural frequencies of the simply supported beam, the elastic modulus and mass density of the structure are corrected. The error between the corrected values of elastic modulus and mass density and the calculated values of the finite element model is very small. This study demonstrates that Gaussian process models can improve calculation efficiency, fulfilling the dual objectives of predicting structural natural frequencies and adjusting model parameters.

Testing a theory of strategic multi-product choice

This paper tests a theory of strategic multi-product choice (SMPC) using empirical evidence from a large-scale choice experiment, two smaller longitudinal choice experiments, and multi-market panel data. Multi-product choice involves two stages. In the first stage, the consumer chooses a set of substitutable products, where “set” refers to both the variety of alternatives and the quantities of each. In the second stage, the set is consumed. Assuming consumers are strategic, their consumption decisions will consider both the utility of whichever product is selected for consumption and the expected utility (i.e., value) of the set that remains. SMPC therefore requires a dynamic model. We test two such dynamic models in this paper. These models are derived from a basic random utility framework with a stochastic error term for the utility of each product alternative at the moment of consumption. Despite maintaining state variables for the quantity of every alternative, these SMPC dynamic models offer both a value function and optimal consumption policy in closed form. These structures allow us to test for strategic consumption in the second stage and for optimality of the choice sets selected in the first stage. Data from the large-scale choice experiment and the smaller longitudinal choice experiments support strategic consumer decision-making, consistent with SMPC theory. SMPC theory further predicts that the amount of variety consumers select will be higher for lower consumption rates and lower for higher consumption rates. Evidence from panel data of yogurt purchases supports this prediction. While we find that consumption choices are consistent with SMPC theory, they are not consistent with alternative explanations such as variety seeking or diversification bias. Viewed in its entirety, the empirical evidence presented in this paper confirms that both the choice set selected and the way it is consumed are consistent with dynamic models of future preference uncertainty.

Robust Voltage Control of a Single-Phase UPS Inverter Utilizing LMI-Based Optimization with All-Pass Filter Under System Uncertainty

This paper proposes a systematic control design for a single-phase LC-filtered inverter considering uncertain system parameters. One major difficulty in controlling single-phase power converters is the lack of a direct conversion method for transforming single-phase signals into dq-frame signals. By employing an all-pass filter in this proposed approach, it is possible to control the output voltage in terms of DC quantity or the dq-rotating frame. Furthermore, voltage stability and harmonic distortion (THD) minimization of the uninterruptible power supply (UPS) are major concerns in inverter design. Therefore, this controller uses integral action to get rid of steady-state errors and stabilize the closed-loop system by the state feedback control. In order to enlarge and guarantee the stability range in the presence of potential parameter fluctuations, an uncertainty model is being considered. In this context, the uncertainty models refer to the potential model with variations in the filter's inductance and capacitance caused by operating temperature, aging, and various external factors. The efficacy of the control approach is assessed through simulations and experiments, with the objective of comparing its results with those of the PI control using a control board featuring a TMS320F28335 digital signal processor. Consequently, the proposed approach offers lower THD at every load step with lesser afford in performance tuning in comparison to the PI method.

Energy and reserve procurement in integrated electricity and heating system: A high-dimensional covariance matrix approach based on stochastic differential equations

The integration of stochastic renewable energy sources into energy systems presents challenges due to flexibility insufficiency and uncertainty modeling inaccuracy. To address these challenges, this paper explores a high-dimensional covariance matrix approach based on stochastic differential equations (SDEs) for energy and reserve co-dispatch in integrated electricity and heating systems. By capturing the long-term correlation of wind power forecast errors, the SDE model simultaneously models point forecasts and high-dimensional positive-definite covariance matrices, resulting in a compact uncertainty set. To ensure computational efficiency, we employ duality theory to transform the stochastic co-dispatch problem with the high-dimensional uncertainty set into deterministic convex programming. Additionally, a virtual heat storage model is introduced for the district heating network, leveraging the thermal inertia of the network to enhance reserve capacity. Simulations validate the calibration and sharpness of the proposed high-dimensional uncertainty set. The results demonstrate that co-dispatch using the SDE-based uncertainty set reduces operational costs by 4.9% compared to a set that does not consider the long-term correlation of wind power, under a 95% coverage rate. Moreover, the storage capabilities of district heating pipelines and smart buildings provide cost-free reserves, saving the operational costs of the two test systems by 2.8% and 1.3%, respectively.

An efficient multi-timescale regulation strategy for distribution networks based on active and passive resources combined

Introducing solar and wind power into distribution networks (DNs) is an important initiative to promote the cleanliness and low-carbonization operation of DNs. However, the source and load outputs are uncertain in DNs, which will lead to problems of inaccurate regulation and insufficient renewable energy utilization. Therefore, this study provides an efficient multi-timescale regulation strategy for DNs based on active and passive resources combined. First, the day-ahead regulation model is constructed to minimize the total operating cost in a day for DNs. It aims to determine the on-load tap changer (OLTC) and capacitor bank (CB) switching schemes and consider them as the constraints for intraday regulation by power flow unification. Then, an intraday source and load uncertainty model is considered, which aims to cope with the problems of inaccuracies in the day-ahead source and load prediction. Based on this, the objective function of the intraday regulation model is set. It aims to minimize the deviation from the total day-ahead cost and then ensure the optimal system economy and determine the intraday new energy and energy storage system (ESS) short-time action scheme. Finally, the example results show that the proposed scheme can achieve the maximum utilization of renewable energy and improve the low-carbon economic operation of the whole system.

Efficient minimum blind area model for system and interference uncertainty

AbstractIn the anti‐interference of broadband communication radio, interference cancellation performance is seriously affected by the uncertainty of the working frequency selection of the communication system and the direction of hostile interference. The closed‐form solution of the interference cancellation weight value and the signal‐to‐interference noise ratio after the cancellation are derived and simplified to clarify the factors affecting interference cancellation quality. Then, the efficient blind area criterion is established for the low computational complexity in view of cancellation quality, which combines the radio communication index and anti‐interference demand index. Based on this criterion, the minimum blind area model is proposed for robust performance. The experimental results in the auxiliary antenna spacing optimisation are consistent with the theoretical analysis, verifying the effectiveness of the proposed model in dealing with uncertain communication frequency and interference direction. It is very promising in communication interference cancellation.

A stochastic rainfall model for reliability analysis of rainfall-induced landslides

ABSTRACT Rainfall is an important trigger for a large number of landslides. Physics-based quantitative risk assessment of rainfall-induced landslides requires modelling of rainfall uncertainty in addition to soil parameters. Explicit modelling of rainfall uncertainty should consider the uncertainties in rainfall intensity, duration, as well as the occurrence of rainfall events. Towards this aspect, this study proposes a stochastic rainfall model, where the joint distribution of rainfall duration and intensity is constructed using copula theory and the occurrence of rainfall events is described using Poisson process. Based on the proposed stochastic rainfall model, a computationally efficient reliability method with a machine learning-based surrogate model is developed for assessing the failure probability of a slope subjected to rainfall infiltration within a given time period. An illustrative example with real rainfall data from Singapore is utilised to demonstrate the proposed approach. The results suggest that the slope failure probability is less sensitive to the uncertainty in rainfall occurrence, but highly sensitive to the adopted inter-event time definition for characterisation of the rainfall event. Overall, this study provides a useful stochastic rainfall model and some practical guidelines for quantitative risk assessment of rainfall-induced landslides.

Enhancing optimization accuracy in power systems: Investigating correlation effects on objective function values

This study addresses the critical yet often overlooked aspect of incorporating correlations among input stochastic variables in power system planning and scheduling optimization. While existing literature has extensively focused on uncertainty modelling, there remains a gap in fully assessing the consequences of disregarding correlations on objective function values across different power network sizes. To bridge this gap, we utilize Monte Carlo simulation with Cholesky decomposition, alongside Quasi-Monte Carlo sampling and Latin Hypercube Sampling, to effectively model uncertainty and capture correlation coefficients among input variables, including wind, solar photovoltaic, and load power. The most efficient technique is then integrated into our optimization model, which is applied to small, medium, and large power network models. Our proposed optimization model addresses conflicting objectives using a hybrid NSGAII-MOPSO, aiming to simultaneously minimize total operational cost, power loss, and voltage deviation. By implementing this model on selected power networks and comparing outcomes between cases with independent and correlated variables, we rigorously assess discrepancies in objective function values. We visualize and analyze these errors across systems of varying sizes, shedding light on the impact of neglecting variable correlations. Notably, the maximum discrepancies are observed at $3.26/h, $40.66/h, and $2754.04/h for the IEEE 30-bus, IEEE 57-bus, and IEEE 118-bus systems, respectively. Crucially, as the system size increases, so does the magnitude of these differences, underlining the escalating impact of neglecting variable correlations on optimization outcomes. We stress the importance of integrating such considerations into future planning and operational strategies to mitigate errors and enhance decision-making processes.

Adaptive Robust Control of Uncertain Euler-Lagrange Systems Using Gaussian Processes.

This article proposes a novel adaptive robust control approach based on Gaussian processes (GPs) for the high-precision tracking problem of uncertain Euler-Lagrange (EL) systems with time-varying external disturbances. Given a prior dynamic model, the GP regression (GPR) technique is employed to obtain a nonparametric data-based uncertainty model, including its probabilistic confidence intervals. Based on the adaptive sliding mode control (ASMC) framework, the posterior means of GPs are utilized for dynamic compensation, whereas the posterior variances are applied to adjust the feedback gains. This proposed control strategy is robust against significant system uncertainty with low feedback gains. A novel adaptive law for updating hyperparameters based on tracking error feedback is presented, thereby improving the performance of both tracking control and GP modeling simultaneously. Compared to existing likelihood-based optimization methods, this hyperparameter adaptive law enables data-efficient and fast uncertainty learning for control applications. The proposed control strategy guarantees the semiglobal asymptotic convergence to zero tracking error with a specified probability. Simulations using an underwater robot model demonstrate that the utilization of GPs and hyperparameter adaptive law significantly improves the performance of tracking control and uncertainty learning.

An FTwNB Shield: A Credit Risk Assessment Model for Data Uncertainty and Privacy Protection

Credit risk assessment is an important process in bank financial risk management. Traditional machine-learning methods cannot solve the problem of data islands and the high error rate of two-way decisions, which is not conducive to banks’ accurate credit risk assessment of users. To this end, this paper establishes a federated three-way decision incremental naive Bayes bank user credit risk assessment model (FTwNB) that supports asymmetric encryption, uses federated learning to break down data barriers between banks, and uses asymmetric encryption to protect data security for federated processes. At the same time, the model combines the three-way decision methods to realize the three-way classification of user credit (good, bad and delayed judgment), so as to avoid the loss of bank interests caused by the forced division of uncertain users. In addition, the model also incorporates incremental learning steps to eliminate training samples with poor data quality to further improve the model performance. This paper takes German Credit data and Default of Credit Card Clients data as examples to conduct simulation experiments. The result shows that the performance of the FTwNB model has been greatly improved, which verifies that it has good credit risk assessment capabilities.

Towards trustworthy cybersecurity operations using Bayesian Deep Learning to improve uncertainty quantification of anomaly detection

Uncertainty quantification of cybersecurity anomaly detection results provides critical guidance for decision makers on whether or not to accept the results. Improving the trustworthiness of anomaly predictions can reduce the amount of alert false positives that security teams have to process. In this work we investigate the use of Bayesian Autoencoder (BAE) models for uncertainty quantification in anomaly detection. A novel heteroscedastic aleatoric uncertainty modelling method is explored that jointly considers aleatoric and epistemic uncertainty. Heteroscedastic aleatoric uncertainty is modelled on the latent layer of the BAE and further explored through considering the variational lower bound. An uncertainty quantification framework for cybersecurity is designed and verified on UNSW-NB15 and CIC-IDS-2017 data sets. This research enhances the modelling of uncertainty in the BAE model and expands its application in cybersecurity.

Uncertainty-Aware First-Principles Exploration of Chemical Reaction Networks.

Exploring large chemical reaction networks with automated exploration approaches and accurate quantum chemical methods can require prohibitively large computational resources. Here, we present an automated exploration approach that focuses on the kinetically relevant part of the reaction network by interweaving (i) large-scale exploration of chemical reactions, (ii) identification of kinetically relevant parts of the reaction network through microkinetic modeling, (iii) quantification and propagation of uncertainties, and (iv) reaction network refinement. Such an uncertainty-aware exploration of kinetically relevant parts of a reaction network with automated accuracy improvement has not been demonstrated before in a fully quantum mechanical approach. Uncertainties are identified by local or global sensitivity analysis. The network is refined in a rolling fashion during the exploration. Moreover, the uncertainties are considered during kinetically steering of a rolling reaction network exploration. We demonstrate our approach for Eschenmoser-Claisen rearrangement reactions. The sensitivity analysis identifies that only a small number of reactions and compounds are essential for describing the kinetics reliably, resulting in efficient explorations without sacrificing accuracy and without requiring prior knowledge about the chemistry unfolding.

Empirical uncertainty evaluation for the pose of a kinematic LiDAR-based multi-sensor system

Abstract Kinematic multi-sensor systems (MSS) describe their movements through six-degree-of-freedom trajectories, which are often evaluated primarily for accuracy. However, understanding their self-reported uncertainty is crucial, especially when operating in diverse environments like urban, industrial, or natural settings. This is important, so the following algorithms can provide correct and safe decisions, i.e. for autonomous driving. In the context of localization, light detection and ranging sensors (LiDARs) are widely applied for tasks such as generating, updating, and integrating information from maps supporting other sensors to estimate trajectories. However, popular low-cost LiDARs deviate from other geodetic sensors in their uncertainty modeling. This paper therefore demonstrates the uncertainty evaluation of a LiDAR-based MSS localizing itself using an inertial measurement unit (IMU) and matching LiDAR observations to a known map. The necessary steps for accomplishing the sensor data fusion in a novel Error State Kalman filter (ESKF) will be presented considering the influences of the sensor uncertainties and their combination. The results provide new insights into the impact of random and systematic deviations resulting from parameters and their uncertainties established in prior calibrations. The evaluation is done using the Mahalanobis distance to consider the deviations of the trajectory from the ground truth weighted by the self-reported uncertainty, and to evaluate the consistency in hypothesis testing. The evaluation is performed using a real data set obtained from an MSS consisting of a tactical grade IMU and a Velodyne Puck in combination with reference data by a Laser Tracker in a laboratory environment. The data set consists of measurements for calibrations and multiple kinematic experiments. In the first step, the data set is simulated based on the Laser Tracker measurements to provide a baseline for the results under assumed perfect corrections. In comparison, the results using a more realistic simulated data set and the real IMU and LiDAR measurements provide deviations about a factor of five higher leading to an inconsistent estimation. The results offer insights into the open challenges related to the assumptions for integrating low-cost LiDARs in MSSs.

Least squares adaptive control for uncertain system based on modified predictive model

AbstractThis research addresses the tracking problem of least squares adaptive control for a class of nonlinear system with mismatched uncertainties. Different from most of existing solutions, modified predictive model is integrated into the proposed least squares adaptive control architecture. The significant role of modified predictive model in the adaptive control architecture is to achieve smooth transient by filtering out the high‐frequency oscillations, which cannot be canceled out by use of the hypothetical parameterized uncertainty models. Meanwhile, in order to guarantee tracking performance, a generalized restricted potential function (GRPF) is designed to constrain the weighted Euclidean norm of the predictive error of the modified predictive model to be less than a predefined scalar worst‐case bound. Finally, comparative simulations via the generic transport model (GTM) are conducted to examine the effectiveness of the proposed method. The results show that the transient performance and tracking performance of the controlled system can be improved simultaneously by the proposed method.

A novel modified artificial rabbit optimization for stochastic energy management of a grid-connected microgrid: A case study in China

The energy management (EM) solution of the microgrids (MGs) is a crucial task to attain most economic, reliable and sustainable operation state of the MGs. This paper aims to solve the optimal scheduling and stochastic EM problem of a smart MG without and with demand side response (DSR) including MT, FC, PV, WT, and a battery storage system (BSS). A study case in Wenzhou city of China is conducted to reduce the operation cost and maximize the utilization of renewable energy. The system uncertainties like loading, temperature, solar irradiance and wind speed are considered which were obtained from real meteorological data. The normal, lognormal, Weibull PDFs as well as Monte-Carlo and RBS methods are used for uncertainty modelling. A modified artificial rabbit optimization (MARO) is proposed for EM solution based on three strategies including fitness-distance balance, exploitation mechanism of PDO and quasi-opposite-based learning (QOBL) to boost exploration and exploitation phases of traditional ARO. The statistical and non-parametric tests are applied via benchmark functions to validate the performance of MARO. As per the obtained results, the MARO is superior for EM solution compared to other techniques and the operation cost is reduced from 252.0721€ct/day to 184.8435€ct/day with saving of 26.86 % considerably with application of DSR.

Improved typical scenario-based distributionally robust co-dispatch of energy and reserve for renewable power systems considering the demand response of fused magnesium load

In recent years, the penetration of solar and wind power has rapidly increased to construct renewable energy-dominated power systems (RPSs). On this basis, the forecasting errors of renewable generation power have negative effects on the operation of the power system. However, traditional scheduling methods are overly dependent on the generation-side dispatchable resources and lack uncertainty modeling strategies, so they are inadequate to tackle this problem. In this case, it is necessary to enhance the flexibility of the RPS by both mining the load-side dispatchable resources and improving the decision-making model under uncertainty during the energy and reserve co-dispatch. In this paper, due to the great potential in facilitating the RPS regulation, the demand response (DR) model of fused magnesium load (FML) is first established to enable the deeper interaction between the load side and the whole RPS. Then, based on the principal component analysis and clustering algorithm, an improved typical scenario set generation method is proposed to obtain a much less conservative model of the spatiotemporally correlated uncertainty. On this basis, a two-stage distributionally robust optimization model of the energy and reserve co-dispatch is developed for the RPS considering the DR of FML. Finally, the proposed method is validated by numerical tests. The results show that the costs of day-ahead dispatch and re-dispatch are significantly decreased by using the improved typical scenario set and considering the DR of FML in regulation, which enhances the operation economy while maintaining the high reliability and safety of the RPS.

Uncertain pedestrian load modeling for structural vibration assessment in footbridge design

The request of material savings in bridge constructions leads to the development towards slender and lightweight structures, which are more sensitive to human-induced vibrations caused by walking pedestrians. The resulting accelerations do not endanger the structural safety, but can be perceived as unpleasant for the user and must therefore be restricted within the limit state of serviceability. For this purpose, the guidelines define acceleration intervals, called as “comfort levels” (CL), which evaluate the comfort of the pedestrians, given the maximum acceleration of the bridge. The model for human-induced loads in the design guideline is based on conservative and deterministic simplifications. In particular, the uncertainties in the human gait parameters are neglected. The main objective of this paper is to develop an uncertain load model for walking pedestrians based on Fourier series. The aleatory and epistemic uncertainties in the human gait parameters are quantified with appropriate uncertainty models relying on available data. In a dynamical finite element analysis, the model is used to simulate groups of pedestrians randomly walking over a bridge to calculate the resulting acceleration amplitudes. The approach is applied to a single span beam and to a real world footbridge using a 3D finite element model. The results are then evaluated within the CLs, enabling new assessment methods.

USE OF QUANTUM MODELS IN THE STUDY OF RELATIONSHIPS BETWEEN INNOVATIONS AND ECONOMIC DEVELOPMENT

The article analyzes the main aspects of the application of quantum models for the analysis of relationships between innovations and economic growth, which are a promising direction in economic science. The influence of trends and challenges of globalization and accelerated technological innovations, which play a key role in realizing competitive advantages and increasing productivity, is determined; in promoting the sustainable development of the economy. The author defines the dynamics of innovation processes, which causes the need for new approaches, such as the principles of quantum modeling, defines the content of quantum models in global business. In particular, the principles that allow for more accurate modeling of uncertainty and non-linear processes characteristic of innovative activity are considered. The author pays special attention to the use of quantum models for accurate forecasting and planning of economic development, development of effective strategies for scientific research and state policy in the field of innovation. The recommendations are aimed at carrying out a comprehensive analysis and assessment of the impact of quantum technologies on economic indicators of employment, indicators of investment activity and international trade. In further scientific developments, it is expected to improve the comparative analysis of classical and quantum economic models for determining effective approaches to innovation management. A promising direction of scientific research is the development of a methodical tool for optimizing investments in research and R&D to improve the mechanisms of state support for innovative activities. Emphasis is placed on the fact that research results will contribute to the creation of a new generation of economic strategies based on the principles of quantum economics, and will open up new horizons for the growth and development of the world market.

Business strategies to counter climate change risks to long lived production assets

The business community is concerned about how to account for long-lived production assets in an era of climate change. Globally, accounting standards and guidance are emerging but these are yet to provide the level of clarity required by the business and accounting profession on the uncertainty of future climate and how this can compromise some long-lived assets. Very few organisations have the necessary expertise and data to integrate climate change scenarios into their long-lived production asset accounting. This poses an additional risk to business and society. We explore different approaches for including risk and uncertainty in business accounting and reporting. Seven desk-based case studies of emerging practice in the food sector demonstrate how these varied climate risk and uncertainty models for infrastructure are being deployed around the world. Through review of data from company annual reports, documents and websites from 2021 to 2023, we find that specific climate-impacted long-lived asset accounting is relatively rare, notwithstanding that risk and uncertainty models are in effective use in other emerging areas. We provide recommendations on the development of data and modelling frameworks for climate-related financial data and an improved accounting discipline for climate-related financial impacts.

Small sample uncertainty evaluation of industrial robot position accuracy measurement based on grey model

The measurement of position accuracy of industrial robots has high complexity, and its uncertainty assessment is one of the important research topics. This study analyses the principle of measuring the position accuracy of industrial robots by laser tracker, the evaluation model of the measurement uncertainty of the position accuracy of industrial robots is established, and various factors affecting the measurement results are analysed, including industrial robot itself, the measurement instrument, the measurement personnel, the measurement strategy and the data processing method. There is a very small sample problem in the uncertainty evaluation process of the position accuracy of industrial robots. The literature and experiments show that the reliability of The Guide to the Expression of Uncertainty in Measurement is low under the condition of very small sample. In this study, an improved grey method is proposed to evaluate the uncertainty. The principle of the improved grey method is discussed in detail, and the general steps of the improved grey method are summarized. The experimental data prove that the standard deviation of very small sample calculated by the improved grey method has higher accuracy. Taking the position accuracy of an industrial robot measured by a laser tracker as an example, the improved grey method is successfully applied to the measurement uncertainty evaluation of the position accuracy of industrial robots.