Model Uncertainty Representation for a Convection-Allowing Ensemble Prediction System Based on CNOP-P

Formulating model uncertainties for a convection-allowing ensemble prediction system(CAEPS)is a much more challenging problem compared to well-utilized approaches in synoptic weather forecasting.A new approach is proposed and tested through assuming that the model uncertainty should reasonably describe the fast nonlinear error growth of the convection-allowing model,due to the fast developing character and strong nonlinearity of convective events.The Conditional Nonlinear Optimal Perturbation related to Parameters(CNOP-P)is applied in this study.Also,an ensemble approach is adopted to solve the CNOP-P problem.By using five locally developed strong convective events that occurred in pre-rainy season of South China,the most sensitive parameters were detected based on CNOP-P,which resulted in the maximum variations in precipitation.A formulation of model uncertainty is designed by adding stochastic perturbations into these sensitive parameters.Through comparison ensemble experiments by using all the 13 heavy rainfall cases that occurred in the flood season of South China in 2017,the advantages of the CNOP-P-based method are examined and verified by comparing with the well-utilized stochastically perturbed physics tendencies(SPPT)scheme.The results indicate that the CNOP-P-based method has potential in improving the under-dispersive problem of the current CAEPS.

Cost-Benefit Assessment of Inspection and Repair Planning for Ship Structures Considering Corrosion Model Uncertainty

Owing to high costs and unnecessary inspections necessitated by the traditional inspection planning for ship structures, the risk-based inspection and repair planning should be investigated for the most cost-effective inspection. This paper aims to propose a cost-benefit assessment model of risk-based inspection and repair planning for ship structures subjected to corrosion deterioration. Then, the benefit-cost ratio is taken to be an index for the selection of the optimal inspection and repair strategy. The planning problem is formulated as an optimization problem where the benefit-cost ratio for the expected lifetime is maximized with a constraint on the minimum acceptalbe reliability index. To account for the effect of corrosion model uncertainty on the cost-benefit assessment, two corrosion models, namgly, Paik＇ s model and Guedes Soares＇ model, are adopted for analysis. A numerical example is presented to illustrate the proposed method. Sensitivity studies are also providet. The results indicate that the proposed method of risk-based cost-benefit analysis can effectively integrate the economy with reliability of the inspection and repair planning. A balance can be achieved between the risk cost and total expected inspection and repair costs with the proposed method, which is very. effective in selecting the optimal inspection and repair strategy. It is pointed out that the corrosion model uncertainty and parametric uncertaintg have a significant impact on the cost-benefit assessment of inspection and repair planning.

A Nonlinear Representation of Model Uncertainty in a Convective-Scale Ensemble Prediction System

How to accurately address model uncertainties with consideration of the rapid nonlinear error growth characteristics in a convection-allowing system is a crucial issue for performing convection-scale ensemble forecasts.In this study,a new nonlinear model perturbation technique for convective-scale ensemble forecasts is developed to consider a nonlinear representation of model errors in the Global and Regional Assimilation and Prediction Enhanced System(GRAPES)Convection-Allowing Ensemble Prediction System(CAEPS).The nonlinear forcing singular vector(NFSV)approach,that is,conditional nonlinear optimal perturbation-forcing(CNOP-F),is applied in this study,to construct a nonlinear model perturbation method for GRAPES-CAEPS.Three experiments are performed:One of them is the CTL experiment,without adding any model perturbation;the other two are NFSV-perturbed experiments,which are perturbed by NFSV with two different groups of constraint radii to test the sensitivity of the perturbation magnitude constraint.Verification results show that the NFSV-perturbed experiments achieve an overall improvement and produce more skillful forecasts compared to the CTL experiment,which indicates that the nonlinear NFSV-perturbed method can be used as an effective model perturbation method for convection-scale ensemble forecasts.Additionally,the NFSV-L experiment with large perturbation constraints generally performs better than the NFSV-S experiment with small perturbation constraints in the verification for upper-air and surface weather variables.But for precipitation verification,the NFSV-S experiment performs better in forecasts for light precipitation,and the NFSV-L experiment performs better in forecasts for heavier precipitation,indicating that for different precipitation events,the perturbation magnitude constraint must be carefully selected.All the findings above lay a foundation for the design of nonlinear model perturbation methods for future CAEPSs.

Optimal Reinsurance and Dividend Under Model Uncertainty

In this paper,the authors analyze the optimal reinsurance and dividend problem with model uncertainty for an insurer.Here the model uncertainty represents possible deviations between the real market and the assumed model.In addition to the incorporation of model uncertainty into the traditional diffusion surplus process,the authors include a penalty function in the objective function.The proposed goal is to find the optimal reinsurance and dividend strategy that maximizes the expected discounted dividend before ruin in the worst case of all possible scenarios,namely,the worst market.Using a dynamic programming approach,the problem is reduced to solving a Hamilton-Jacob-Bellman-Isaac(HJBI)equation with singular control.This problem is more difficult than the traditional robust control or singular control problem.Here,the authors prove that the value function is the unique solution to this HJBI equation with singular control.Moreover,the authors present a verification theorem when a smooth solution can be found,and derive closed-form solution when the function in the objective function is specified.

Sliding mode-based adaptive tube model predictive control for robotic manipulators with model uncertainty and state constraints

In this paper,the optimal tracking control for robotic manipulators with state constraints and uncertain dynamics is investigated,and a sliding mode-based adaptive tube model predictive control method is proposed.First,utilizing the high-order fully actuated system approach,the nominal model of the robotic manipulator is constructed as the predictive model.Based on the nominal model,a nominal model predictive controller with the sliding mode is designed,which relaxes the terminal constraints,and realizes the accurate and stable tracking of the desired trajectory by the nominal system.Then,an auxiliary controller based on the node-adaptive neural networks is constructed to dynamically compensate nonlinear uncertain dynamics of the robotic manipulator.Furthermore,the estimation deviation between the nominal and actual states is limited to the tube invariant sets.At the same time,the recursive feasibility of nominal model predictive control is verified,and the ultimately uniformly boundedness of all variables is proved according to the Lyapunov theorem.Finally,experiments show that the robotic manipulator can achieve fast and efficient trajectory tracking under the action of the proposed method.

Characterizing model uncertainty of upper-bound limit analysis on slopes using 3D rotational failure mechanism

The slope stability assessment is a classical problem in geotechnical engineering.This topic have attracted many researcher’s attention and various theoretical models for predicting critical slope heights or safety factors in the light of the limit equilibrium(LE)method and the kinematical approach of limit analysis(LA)method.Meanwhile,a large number of experimental studies have been conducted to check the slope stability.Using centrifuge testing results,this paper aims to employ Bayesian method to characterize the model uncertainties of the classical three-dimensional rotational failure mechanism proposed by Michalowski and Drescher(2009)to predict critical slope heights in frictional soils,by incorporating the test uncertainties and parameter uncertainties.The obtained results show that the LA three-dimensional rotational failure mechanism overestimates the critical slope height compared with the LE method,and the experimental observational uncertainty has negligible influences on the posterior statistics of model uncertainty.

Robust design of sliding mode control for airship trajectory tracking with uncertainty and disturbance estimation

The robotic airship can provide a promising aerostatic platform for many potential applications.These applications require a precise autonomous trajectory tracking control for airship.Airship has a nonlinear and uncertain dynamics.It is prone to wind disturbances that offer a challenge for a trajectory tracking control design.This paper addresses the airship trajectory tracking problem having time varying reference path.A lumped parameter estimation approach under model uncertainties and wind disturbances is opted against distributed parameters.It uses extended Kalman filter(EKF)for uncertainty and disturbance estimation.The estimated parameters are used by sliding mode controller(SMC)for ultimate control of airship trajectory tracking.This comprehensive algorithm,EKF based SMC(ESMC),is used as a robust solution to track airship trajectory.The proposed estimator provides the estimates of wind disturbances as well as model uncertainty due to the mass matrix variations and aerodynamic model inaccuracies.The stability and convergence of the proposed method are investigated using the Lyapunov stability analysis.The simulation results show that the proposed method efficiently tracks the desired trajectory.The method solves the stability,convergence,and chattering problem of SMC under model uncertainties and wind disturbances.

An Improved CREAM Model Based on DS Evidence Theory and DEMATEL

Cognitive Reliability and Error Analysis Method(CREAM)is widely used in human reliability analysis(HRA).It defines nine common performance conditions(CPCs),which represent the factors thatmay affect human reliability and are used to modify the cognitive failure probability(CFP).However,the levels of CPCs are usually determined by domain experts,whichmay be subjective and uncertain.What’smore,the classicCREAMassumes that the CPCs are independent,which is unrealistic.Ignoring the dependence among CPCs will result in repeated calculations of the influence of the CPCs on CFP and lead to unreasonable reliability evaluation.To address the issue of uncertain information modeling and processing,this paper introduces evidence theory to evaluate the CPC levels in specific scenarios.To address the issue of dependence modeling,the Decision-Making Trial and Evaluation Laboratory(DEMATEL)method is used to process the dependence among CPCs and calculate the relative weights of each CPC,thus modifying the multiplier of the CPCs.The detailed process of the proposed method is illustrated in this paper and the CFP estimated by the proposed method is more reasonable.

Reliability estimation of mechanical seals based on bivariate dependence analysis and considering model uncertainty

The reliability estimation of mechanical seals is of crucial importance due to their wide applications in pumps in various mechanical systems.Failure of mechanical seals might cause leakage,and might lead to system failure and other relevant consequences.In this study,the reliability estimation for mechanical seals based on bivariate dependence analysis and considering model uncertainty is proposed.The friction torque and leakage rate are two degradation performance indicators of mechanical seals that can be described by the Wiener process,Gamma process,and inverse Gaussian process.The dependence between the two indicators can be described by different copula functions.Then the model uncertainty is considered in the reliability estimation using the Bayesian Model Average(BMA)method,while the unknown parameters in the model are estimated by Bayesian Markov Chain Monte Carlo(MCMC)method.A numerical simulation study and fatigue crack study are conducted to demonstrate the effectiveness of the BMA method to capture model uncertainty.A degradation test of mechanical seals is conducted to verify the proposed model.The optimal stochastic process models for two performance indicators and copula function are determined based on the degradation data.The results show the necessity of using the BMA method in degradation modeling.

The Risk Transfer of Non-tradable Risks under Model Uncertainty

In the context of model uncertainty, we study the optimal design and the pricing of financial instruments aiming to hedge some of non-tradable risks. For the existence of model uncertainty, the preference can be represented by the robust expected utility （also called maxmin expected utility） which can be put in the framework of sublinear expectation. The problem of maximizing the issuer＇s robust expected utility under the constraint imposed by the buyer can be transformed to the problem of minimizing the issuer＇s convex measure under the corresponding constraint. And here the convex measure measures not only the risks but also the model uncertainties.

Financial asset price bubbles under model uncertainty

We study the concept of financial bubbles in a market model endowed with a set P of probability measures,typically mutually singular to each other.In this setting,we investigate a dynamic version of robust superreplication,which we use to introduce the notions of bubble and robust fundamental value in a way consistent with the existing literature in the classical case P={P}.Finally,we provide concrete examples illustrating our results.

Uncertainty analysis for the calculation of marine environmental design parameters in the South China Sea

The calculation results of marine environmental design parameters obtained from different data sampling methods,model distributions,and parameter estimation methods often vary greatly.To better analyze the uncertainties in the calculation of marine environmental design parameters,a general model uncertainty assessment method is necessary.We proposed a new multivariate model uncertainty assessment method for the calculation of marine environmental design parameters.The method divides the overall model uncertainty into two categories:aleatory uncertainty and epistemic uncertainty.The aleatory uncertainty of the model is obtained by analyzing the influence of the number and the dispersion degree of samples on the information entropy of the model.The epistemic uncertainty of the model is calculated using the information entropy of the model itself and the prediction error.The advantages of this method are that it does not require many-year-observation data for the marine environmental elements,and the method can be used to analyze any specific factors that cause model uncertainty.Results show that by applying the method to the South China Sea,the aleatory uncertainty of the model increases with the number of samples and then stabilizes.A positive correlation was revealed between the dispersion of the samples and the aleatory uncertainty of the model.Both the distribution of the model and the parameter estimation results of the model have significant effects on the epistemic uncertainty of the model.When the goodness-of-fit of the model is relatively close,the best model can be selected according to the criterion of the lowest overall uncertainty of the models,which can both ensure a better model fit and avoid too much uncertainty in the model calculation results.The presented multivariate model uncertainty assessment method provides a criterion to measure the advantages and disadvantages of the marine environmental design parameter calculation model from the aspect of uncertainty,which is of great significance to analyze the uncertainties in the calculation of marine environmental design parameters and improve the accuracy of the calculation results.

Opinion: the use of natural hazard modeling for decision making under uncertainty

Decision making to mitigate the effects of natural hazards is a complex undertaking fraught with uncertainty. Models to describe risks associated with natural hazards have proliferated in recent years. Concurrently, there is a growing body of work focused on developing best practices for natural hazard modeling and to create structured evaluation criteria for complex environmental models. However, to our knowledge there has been less focus on the conditions where decision makers can confidently rely on results from these models. In this review we propose a preliminary set of conditions necessary for the appropriate application of modeled results to natural hazard decision making and provide relevant examples within US wildfire management programs.

Introduction to the Special Issue on Advances in Neutrosophic and Plithogenic Sets for Engineering and Sciences:Theory,Models,and Applications

Recently,research on uncertainty modeling has been progressing rapidly,and many essential and breakthrough studies have already been done.There are various ways to handle these uncertainties,such as fuzzy and intuitionistic fuzzy sets.Although these concepts can take incomplete information in various real-world issues,they cannot address all types of uncertainty,such as indeterminate and inconsistent information.The neutrosophic theory founded by Florentin Smarandache in 1998 constitutes a further generalization of fuzzy set,intuitionistic fuzzy set,picture fuzzy set,Pythagorean fuzzy set,spherical fuzzy set,etc.Since then,this logic has been applied in various science and engineering domains.

A review of uncertain factors and analytic methods in long-term energy system optimization models

A larger number of uncertain factors in energy systems influence their evolution.Owing to the complexity of energy system modeling,incorporating uncertainty analysis to energy system modeling is essential for future energy system planning and resource allocation.This study focusses on long-term energy system optimization model.The important uncertain parameters in the model are analyzed and divided into policy,economic,and technical factors.This study specifically addresses the challenges related to carbon emission reduction and energy transition.It involves collecting and organizing relevant research on uncertainty analysis of long-term energy systems.Various energy system uncertainty modeling methods and their applications from the literature are summarized in this review.Finally,important uncertainty factors and uncertainty modeling methods for long-term energy system modeling are discussed,and future research directions are proposed.

Effects of Bayesian Model Selection on Frequentist Performances: An Alternative Approach

It is quite common in statistical modeling to select a model and make inference as if the model had been known in advance;i.e. ignoring model selection uncertainty. The resulted estimator is called post-model selection estimator (PMSE) whose properties are hard to derive. Conditioning on data at hand (as it is usually the case), Bayesian model selection is free of this phenomenon. This paper is concerned with the properties of Bayesian estimator obtained after model selection when the frequentist (long run) performances of the resulted Bayesian estimator are of interest. The proposed method, using Bayesian decision theory, is based on the well known Bayesian model averaging (BMA)’s machinery;and outperforms PMSE and BMA. It is shown that if the unconditional model selection probability is equal to model prior, then the proposed approach reduces BMA. The method is illustrated using Bernoulli trials.

Modeling and Robust Backstepping Sliding Mode Control with Adaptive RBFNN for a Novel Coaxial Eight-rotor UAV

This paper focuses on the robust attitude control of a novel coaxial eight-rotor unmanned aerial vehicles(UAV) which has higher drive capability as well as greater robustness against disturbances than quad-rotor UAV. The dynamical and kinematical model for the coaxial eight-rotor UAV is developed, which has never been proposed before. A robust backstepping sliding mode controller(BSMC) with adaptive radial basis function neural network(RBFNN) is proposed to control the attitude of the eightrotor UAV in the presence of model uncertainties and external disturbances. The combinative method of backstepping control and sliding mode control has improved robustness and simplified design procedure benefiting from the advantages of both controllers. The adaptive RBFNN as the uncertainty observer can effectively estimate the lumped uncertainties without the knowledge of their bounds for the eight-rotor UAV. Additionally, the adaptive learning algorithm, which can learn the parameters of RBFNN online and compensate the approximation error, is derived using Lyapunov stability theorem. And then the uniformly ultimate stability of the eight-rotor system is proved. Finally, simulation results demonstrate the validity of the proposed robust control method adopted in the novel coaxial eight-rotor UAV in the case of model uncertainties and external disturbances.

A review of progress in coupled ocean-atmosphere model developments for ENSO studies in China

El Nino-Southern Oscillation(ENSO) is the strongest interannual signal that is producedby basinscale processes in the tropical Pacific,with significant effects on weather and climate worldwide.In the past,extensive and intensive international efforts have been devoted to coupled model developments for ENSO studies.A hierarchy of coupled ocean-atmo sphere models has been formulated;in terms of their complexity,they can be categorized into intermediate coupled models(ICMs),hybrid coupled models(HCMs),and fully coupled general circulation models(CGCMs).ENSO modeling has made significant progress over the past decades,reaching a stage where coupled models can now be used to successfully predict ENSO events 6 months to one year in advance.Meanwhile,ENSO exhibits great diversity and complexity as observed in nature,which still cannot be adequately captured by current state-of-the-art coupled models,presenting a challenge to ENSO modeling.We primarily reviewed the long-term efforts in ENSO modeling continually and steadily made at different institutions in China;some selected representative examples are presented here to review the current status of ENSO model developments and applications,which have been actively pursued with noticeable progress being made recently.As ENSO simulations are very sensitive to model formulations and process representations etc.,dedicated efforts have been devoted to ENSO model developments and improvements.Now,different ocean-atmosphere coupled models have been available in China,which exhibit good model performances and have already had a variety of applications to climate modeling,including the Coupled Model Intercomparison Project Phase 6(CMIP6).Nevertheless,large biases and uncertainties still exist in ENSO simulations and predictions,and there are clear rooms for their improvements,which are still an active area of researches and applications.Here,model performances of ENSO simulations are assessed in terms of advantages and disadvantages with these differently formulated coupled models,pinpointing to the areas where they need to be further improved for ENSO studies.These analyses provide valuable guidance for future improvements in ENSO simulations and predictions.

Uncertainty analysis of seawater intrusion forecasting

In order to describe the importance of uncertainty analysis in seawater intrusion forecasting and identify the main factors that might cause great differences in prediction results, we analyzed the influence of sea level rise, tidal effect, the seasonal variance of influx, and the annual variance of the pumping rate, as well as combinations of different parameters. The results show that the most important factors that might cause great differences in seawater intrusion distance are the variance of pumping rate and combinations of different parameters. The influence of sea level rise can be neglected in a short-time simulation （ten years, for instance）. Retardation of seawater intrusion caused by tidal effects is obviously important in aquifers near the coastline, but the influence decreases with distance away from the coastline and depth away from the seabed. The intrusion distance can reach a dynamic equilibrium with the application of the sine function for seasonal effects of influx. As a conclusion, we suggest that uncertainty analysis should be considered in seawater intrusion forecasting, if possible.