•This paper proposes a new uncertain accelerated degradation model.•The model considers the epistemic uncertainties in time and unit dimensions.•This paper presents the uncertain statistical method ...for parameter estimations.•The model is suitable for limited data sizes in time and unit dimensions.
Accelerated degradation testing (ADT) has been widely used for the reliability and lifetime evaluations of highly reliable products. Generally speaking, the obtained ADT data are composed of two parts - the deterministic degradation trend and uncertainties. When only limited ADT data can be obtained, there will be a lack of knowledge on recognizing the population and lead to epistemic uncertainties. However, current accelerated degradation models fail to clearly distinguish and properly quantify the epistemic uncertainties in time and unit dimensions. Motivated by this problem, this paper constructs a new uncertain accelerated degradation model based on uncertainty theory and belief reliability theory, and presents the uncertain statistical method for parameter estimations. An application case is used to illustrate the proposed methodology and conduct discussions for the deterministic degradation trend and uncertainty analyses of the proposed methodology and the analyses of the proposed methodology to the data sizes in time and unit dimensions. Results show that under limited data sizes in time and unit dimensions, the proposed model can clearly distinguish and properly quantify the epistemic uncertainties in time and unit dimensions and is more suitable for the ADT modeling and analysis than the other two widely used accelerated degradation models.
This study describes a robust load‐frequency control (LFC) scheme in a two‐area interconnected power system with uncertain disturbances. A sector‐bounded H∞ control approach is used for compensating ...of the non‐linearities based on a minimum order dynamic LFC model to avoid the complexity of a high‐order model. The simulation in time domain from the use of the proposed controller has been compared with the use of a conventional proportional–integral (PI) type controller affected by the same load change. The simulated results have proved the significant improvement over the PI controller and have verified the effectiveness of the proposed robust H∞ controller which can minimise the frequency deviations significantly. This approach treats the tie‐line power exchanges in the presences of external disturbance, parameter uncertainties and accidental crashing of generating units as the structural or model uncertainties discussed in this study. Simulation results also show that the proposed H∞ controller guarantees robust performance and fast response under a wide range of operating conditions and system uncertainties.
In 2001, the National Nuclear Security Administration of the U.S. Department of Energy in conjunction with the national security laboratories (i.e., Los Alamos National Laboratory, Lawrence Livermore ...National Laboratory and Sandia National Laboratories) initiated development of a process designated Quantification of Margins and Uncertainties (QMU) for the use of risk assessment methodologies in the certification of the reliability and safety of the nation's nuclear weapons stockpile. A previous presentation, “Quantification of Margins and Uncertainties: Conceptual and Computational Basis,” describes the basic ideas that underlie QMU and illustrates these ideas with two notional examples that employ probability for the representation of aleatory and epistemic uncertainty. The current presentation introduces and illustrates the use of interval analysis, possibility theory and evidence theory as alternatives to the use of probability theory for the representation of epistemic uncertainty in QMU-type analyses. The following topics are considered: the mathematical structure of alternative representations of uncertainty, alternative representations of epistemic uncertainty in QMU analyses involving only epistemic uncertainty, and alternative representations of epistemic uncertainty in QMU analyses involving a separation of aleatory and epistemic uncertainty. Analyses involving interval analysis, possibility theory and evidence theory are illustrated with the same two notional examples used in the presentation indicated above to illustrate the use of probability to represent aleatory and epistemic uncertainty in QMU analyses.
High accuracy modeling of nanostructure is a crucial issue in nano electromechanical systems. This study investigates the effect of nanomaterial uncertainties on vibration and buckling behaviors of ...functionally graded (FG) nanobeams in thermal environment. The size-dependent governing differential equation is derived based on the nonlocal Euler–Bernoulli beam theory with the thermal effect and the analytical formulations of the natural frequencies are deduced. To avoid the shortcoming of probabilistic method in the case of inadequate data, a non-probabilistic uncertainty modeling for the FG nanobeams is developed by quantifying nanomaterial uncertainties as interval parameters. Meanwhile, a hull iterative algorithm (HIA) for solving this model is presented to evaluate the bounds of the natural frequencies. After validation of HIA by comparing with Monte Carlo simulation and sensitivity based interval analysis method, the detailed parametric study is performed to understand the combined influences of nanomaterial uncertainties and size-dependent parameter, power-law index as well as temperature change on the natural frequencies. Additionally, the lower bound of the critical buckling temperature is discussed under different size-dependent parameters and power-law indices. The bounds of the natural frequencies and the critical buckling temperature obtained here are helpful for the safety and optimal design of nano electromechanical systems.
In this paper, an adaptive output feedback prescribed performance controller is proposed for a hydraulic system with matched and mismatched uncertainties (including parametric uncertainties and ...uncertain nonlinearities), which always exist in physical hydraulic systems, and degrade the internal state stability and tracking response performance. By integrating the adaptive control and disturbance observer into the extended state observer, the matched and mismatched uncertainties can be feedforward compensated in the output feedback control. Then, based on the fusion of prescribed performance function and barrier Lyapunov function, the proposed practical method is designed via backstepping method for hydraulic systems, all states are maintained within a preset range by constraining the upper bound of the control errors and the output tracking error is kept within a predetermined boundary that decreases with time. Moreover, the stability of closed-loop system is analyzed by Lyapunov theory. Finally, comparative experimental results are obtained to verify the control performance of the proposed control strategy.
Thermodynamic uncertainty relations (TURs) represent one of the few broad-based and fundamental relations in our toolbox for tackling the thermodynamics of nonequilibrium systems. One form of TUR ...quantifies the minimal energetic cost of achieving a certain precision in determining a nonequilibrium current. In this initial stage of our research program, our goal is to provide the quantum theoretical basis of TURs using microphysics models of linear open quantum systems where it is possible to obtain exact solutions. In paper Dong et al., Entropy 2022, 24, 870, we show how TURs are rooted in the quantum uncertainty principles and the fluctuation–dissipation inequalities (FDI) under fully nonequilibrium conditions. In this paper, we shift our attention from the quantum basis to the thermal manifests. Using a microscopic model for the bath’s spectral density in quantum Brownian motion studies, we formulate a “thermal” FDI in the quantum nonequilibrium dynamics which is valid at high temperatures. This brings the quantum TURs we derive here to the classical domain and can thus be compared with some popular forms of TURs. In the thermal-energy-dominated regimes, our FDIs provide better estimates on the uncertainty of thermodynamic quantities. Our treatment includes full back-action from the environment onto the system. As a concrete example of the generalized current, we examine the energy flux or power entering the Brownian particle and find an exact expression of the corresponding current–current correlations. In so doing, we show that the statistical properties of the bath and the causality of the system+bath interaction both enter into the TURs obeyed by the thermodynamic quantities.
On the 23rd of June 2016, the United Kingdom voted to leave the EU, leading to months and years of economic policy uncertainties. Such uncertainties have not only characterized the UK but have become ...a center point for energy debate in recent times. Given the foregoing, this paper progresses to provide evidence on the role of Economic Policy Uncertainty in the Energy Consumption - Emission nexus in the UK. We use annual data spanning the period of 1985–2017 for the UK for CO2 emissions in tons per capita (CO2), real GDP (RGDP), energy use (EU), and economic policy uncertainty (EPU). The Autoregressive distributed lag model (ARDL) bound test is used to test the fitness of the model in the short and long term. Our model shows that EPU matters most in the short run, as it reduces the growth of CO2 emissions, while prolonged use of EPU in the UK, exhibit controversial influence, where CO2 emissions continue to rise. In addition, pairwise Granger causality shows a one-way causality running from energy use to CO2 emissions, CO2 emissions to economic policy uncertainty, and also from energy use to economic policy uncertainty. However, two-ways causality is found between real GDP and real GDP per capita. Overall, our results imply that EPU is likely to yield a positive effect on climate change for a short time, but continue dependent will, in the long run, create an unhealthy environment. We suggest that the UK government should consider implementing an additional long-run policy that will supplement the effort of EPU.
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•The role of EPU in the Energy Consumption - Emission nexus in the UK is assessed•A one-way causality runs from CO2 emissions to economic policy uncertainty•A uni-directional causality runs from energy use to economic policy uncertainty•EPU significantly moderates the impact of energy use on CO2 in the short and long run
Harmonic resonances exist inherently in power systems with varying affected areas and amplification levels. This paper presents a quantitative harmonic resonance assessment technique with sensitivity ...analysis under uncertainty to reveal the affected areas of a harmonic resonance and corresponding amplification severities at different buses. Resonance amplification conditions at the harmonic source bus (localized resonance) and non-harmonic-source bus (non-localized resonance) are distinguished, respectively, and then a novel index to quantify the harmonic propagation areas and corresponding amplification severities are established based on harmonic electrical distances. Apart from local sensitivity analysis (SA), a global SA method is further used to perform the SA of system uncertain parameters, and three types of sensitivity parameters are distinguished and defined. In addition, comparative analysis of the proposed method with existing harmonic resonance analysis methods shows that the proposed method can not only provide more information for harmonic resonance analysis and control but is also easy and practical.
•Overcome the problem of how to obtain the precise bounds of uncertain parameters in practical engineering.•A novel convex modelling method is proposed completely based on the sample data without ...empirical prediction in advance.•An optimization procedure is established to find the bounds of variations to cover all the given data with a small domain.•Strong prediction capability and good generalization ability of the method are revealed via evaluation criteria.•Accuracy and efficiency of the proposed method are illustrated by systematical comparisons.
In this paper, a novel method for non-probabilistic convex modelling with the bounds to precisely encircle all the data of uncertain parameters extracted from practical engineering is developed. The method is based on the traditional statistical method and the correlation analysis technique. Mean values and correlation coefficients of uncertain parameters are first calculated by utilizing the information of all the given data. Then, a simple yet effective optimization procedure is first introduced in the mathematical modelling process for uncertain parameters to obtain their precise bounds. This procedure works by optimizing the area of the convex model, at the same time, covering all the given data. Thus, the effective mathematical expression of the convex models are finally formulated. To test the prediction capability and generalization ability of the proposed convex modelling method, evaluation criteria, i.e. volume ratio, standard volume ratio, and prediction accuracy are established. The performance of the proposed method is systematically studied and compared with other existing competitive methods through test standards. The results demonstrate the effectiveness and efficiency of the present method.
New satellite missions (e.g., the European Space Agency's Sentinel‐1 constellation), advances in data downlinking, and rapid product generation now provide us with the ability to access ...space‐geodetic data within hours of their acquisition. To truly take advantage of this opportunity, we need to be able to interpret geodetic data in a prompt and robust manner. Here we present a Bayesian approach for the inversion of multiple geodetic data sets that allows a rapid characterization of posterior probability density functions (PDFs) of source model parameters. The inversion algorithm efficiently samples posterior PDFs through a Markov chain Monte Carlo method, incorporating the Metropolis‐Hastings algorithm, with automatic step size selection. We apply our approach to synthetic geodetic data simulating deformation of magmatic origin and demonstrate its ability to retrieve known source parameters. We also apply the inversion algorithm to interferometric synthetic aperture radar data measuring co‐seismic displacements for a thrust‐faulting earthquake (2015 Mw 6.4 Pishan earthquake, China) and retrieve optimal source parameters and associated uncertainties. Given its robustness and rapidity in estimating deformation source parameters and uncertainties, our Bayesian framework is capable of taking advantage of real‐time geodetic measurements. Thus, our approach can be applied to geodetic data to study magmatic, tectonic, and other geophysical processes, especially in rapid‐response operational settings (e.g., volcano observatories). Our algorithm is fully implemented in a MATLAB®‐based software package (Geodetic Bayesian Inversion Software) that we make freely available to the scientific community.
Key Points
We present a Bayesian approach for the inversion of geodetic data and demonstrate successful applications to synthetic and real data
Our approach allows rapid estimates of source parameters and uncertainties and is well suited for rapid‐response and operational settings
We have implemented our approach in a MATLAB®‐based software package (GBIS) that is made freely available to the scientific community
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