Determination of uncertainties of geomechanical parameters of metamorphic rocks using petrographic analyses

Geomechanical parameters of intact metamorphic rocks determined from laboratory testing remain highly uncertain because of the great intrinsic variability associated with the degrees of metamorphism.The aim of this paper is to develop a proper methodology to analyze the uncertainties of geomechanical characteristics by focusing on three domains,i.e.data treatment process,schistosity angle,and mineralogy.First,the variabilities of the geomechanical laboratory data of Westwood Mine(Quebec,Canada)were examined statistically by applying different data treatment techniques,through which the most suitable outlier methods were selected for each parameter using multiple decision-making criteria and engineering judgment.Results indicated that some methods exhibited better performance in identifying the possible outliers,although several others were unsuccessful because of their limitation in large sample size.The well-known boxplot method might not be the best outlier method for most geomechanical parameters because its calculated confidence range was not acceptable according to engineering judgment.However,several approaches,including adjusted boxplot,2MADe,and 2SD,worked very well in the detection of true outliers.Also,the statistical tests indicate that the best-fitting probability distribution function for geomechanical intact parameters might not be the normal distribution,unlike what is assumed in most geomechanical studies.Moreover,the negative effects of schistosity angle on the uniaxial compressive strength(UCS)variabilities were reduced by excluding the samples within a specific angle range where the UCS data present the highest variation.Finally,a petrographic analysis was conducted to assess the associated uncertainties such that a logical link was found between the dispersion and the variabilities of hard and soft minerals.

Time-varying parameters estimation with adaptive neural network EKF for missile-dual control system

In this paper, a filtering method is presented to estimate time-varying parameters of a missile dual control system with tail fins and reaction jets as control variables. In this method, the long-short-term memory(LSTM) neural network is nested into the extended Kalman filter(EKF) to modify the Kalman gain such that the filtering performance is improved in the presence of large model uncertainties. To avoid the unstable network output caused by the abrupt changes of system states,an adaptive correction factor is introduced to correct the network output online. In the process of training the network, a multi-gradient descent learning mode is proposed to better fit the internal state of the system, and a rolling training is used to implement an online prediction logic. Based on the Lyapunov second method, we discuss the stability of the system, the result shows that when the training error of neural network is sufficiently small, the system is asymptotically stable. With its application to the estimation of time-varying parameters of a missile dual control system, the LSTM-EKF shows better filtering performance than the EKF and adaptive EKF(AEKF) when there exist large uncertainties in the system model.

Adaptive Leader-Follower Consensus Control of Multiple Flexible Manipulators With Actuator Failures and Parameter Uncertainties

In this paper,the leader-follower consensus problem for a multiple flexible manipulator network with actuator failures,parameter uncertainties,and unknown time-varying boundary disturbances is addressed.The purpose of this study is to develop distributed controllers utilizing local interactive protocols that not only suppress the vibration of each flexible manipulator but also achieve consensus on joint angle position between actual followers and the virtual leader.Following the accomplishment of the reconstruction of the fault terms and parameter uncertainties,the adaptive neural network method and parameter estimation technique are employed to compensate for unknown items and bounded disturbances.Furthermore,the Lyapunov stability theory is used to demonstrate that followers’angle consensus errors and vibration deflections in closed-loop systems are uniformly ultimately bounded.Finally,the numerical simulation results confirm the efficacy of the proposed controllers.

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.

Impulsive control of permanent magnet synchronous motors with parameters uncertainties

The permanent magnet synchronous motors （PMSMs） may have chaotic behaviours for the uncertain values of parameters or under certain working conditions, which threatens the secure and stable operation of motor-driven. It is important to study methods of controlling or suppressing chaos in PMSMs. In this paper, robust stabilities of PMSM with parameter uncertainties are investigated. After the uncertain matrices which represent the variable system parameters are formulated through matrix analysis, a novel asymptotical stability criterion is established. Some illustrated examples are also given to show the effectiveness of the obtained results.

Optimal Parameter and Uncertainty Estimation of a Land Surface Model: Sensitivity to Parameter Ranges and Model Complexities

Most previous land-surface model calibration studies have defined globalranges for their parameters to search for optimal parameter sets. Little work has been conducted tostudy the impacts of realistic versus global ranges as well as model complexities on the calibrationand uncertainty estimates. The primary purpose of this paper is to investigate these impacts byemploying Bayesian Stochastic Inversion (BSI) to the Chameleon Surface Model (CHASM). The CHASM wasdesigned to explore the general aspects of land-surface energy balance representation within acommon modeling framework that can be run from a simple energy balance formulation to a complexmosaic type structure. The BSI is an uncertainty estimation technique based on Bayes theorem,importance sampling, and very fast simulated annealing. The model forcing data and surface flux datawere collected at seven sites representing a wide range of climate and vegetation conditions. Foreach site, four experiments were performed with simple and complex CHASM formulations as well asrealistic and global parameter ranges. Twenty eight experiments were conducted and 50 000 parametersets were used for each run. The results show that the use of global and realistic ranges givessimilar simulations for both modes for most sites, but the global ranges tend to produce someunreasonable optimal parameter values. Comparison of simple and complex modes shows that the simplemode has more parameters with unreasonable optimal values. Use of parameter ranges and modelcomplexities have significant impacts on frequency distribution of parameters, marginal posteriorprobability density functions, and estimates of uncertainty of simulated sensible and latent heatfluxes. Comparison between model complexity and parameter ranges shows that the former has moresignificant impacts on parameter and uncertainty estimations.

IDENTIFICATION OF TIME-VARYING MODAL PARAMETERS USING LINEAR TIME-FREQUENCY REPRESENTATION

A new method of parameter identification based on linear time-frequencyrepresentation and Hubert transform is proposed to identity modal parameters of linear time-varyingsystems from measured vibration responses. Using Gabor expansion and synthesis theory, measuredresponses are represented in the time-frequency domain and modal components are reconstructed bytime-frequency filtering. The Hilbert transform is applied to obtain time histories of the amplitudeand phase angle of each modal component, from which time-varying frequencies and damping ratios areidentified. The proposed method has been demonstrated with a numerical example in which a lineartime-varying system of two degrees of freedom is used to validate the identification scheme based ontime-frequency representation. Simulation results have indicated that time-frequency representationpresents an effective tool for modal parameter identification of time-varying systems.

Robust H_∞ control for aseismic structures with uncertainties in model parameters

This paper presents a robust H∞ output feedback control approach for structural systems with uncertainties in model parameters by using available acceleration measurements and proposes conditions for the existence of such a robust output feedback controller. The uncertainties of structural stiffness, damping and mass parameters are assumed to be norm-bounded. The proposed control approach is formulated within the framework of linear matrix inequalities, for which existing convex optimization techniques, such as the LM1 toolbox in MATLAB, can be used effectively and conveniently. To illustrate the effectiveness of the proposed robust H∞ strategy, a six-story building was subjected both to the 1940 E1 Centro earthquake record and to a suddenly applied Kanai-Tajimi filtered white noise random excitation. The results show that the proposed robust H∞ controller provides satisfactory results with or without variation of the structural stiffness, damping and mass parameters.

Robust model-reference control for descriptor linear systems subject to parameter uncertainties

Robust model-reference control for descriptor linear systems with structural parameter uncertainties is investigated. A sufficient condition for existing a model-reference zero-error asymptotic tracking controller is given. It is shown that the robust model reference control problem can be decomposed into two subproblems： a robust state feedback stabilization problem for descriptor systems subject to parameter uncertainties and a robust compensation problem. The latter aims to find three coefficient matrices which satisfy four matrix equations and simultaneously minimize the effect of the uncertainties to the tracking error. Based on a complete parametric solution to a class of generalized Sylvester matrix equations, the robust compensation problem is converted into a minimization problem with quadratic cost and linear constraints. A numerical example shows the effect of the proposed approach.

Impacts of parameter uncertainties on deep chlorophyll maximum simulation revealed by the CNOP-P approach

Parameter uncertainty is a primary source of uncertainty in ocean ecosystem simulations.The deep chlorophyll maximum(DCM)is a ubiquitous ecological phenomenon in the ocean.Using a theoretical nutrients-phytoplankton model and the conditional nonlinear optimal perturbation approach related to parameters,we investigated the eff ects of parameter uncertainties on DCM simulations.First,the sensitivity of single parameter was analyzed.The sensitivity ranking of 10 parameters was obtained by analyzing the top four specifi cally.The most sensitive parameter(background turbidity)aff ects the light supply for DCM formation,whereas the other three parameters(nutrient content of phytoplankton,nutrient recycling coeffi cient,and vertical turbulent diff usivity)control nutrient supply.To explore the interactions among diff erent parameters,the sensitivity of multiple parameters was further studied by examining combinations of four parameters.The results show that background turbidity is replaced by the phytoplankton loss rate in the optimal parameter combination.In addition,we found that interactions among these parameters are responsible for such diff erences.Finally,we found that reducing the uncertainties of sensitive parameters could improve DCM simulations remarkably.Compared with the sensitive parameters identifi ed in the single parameter analysis,reducing parameter uncertainties in the optimal combination produced better model performance.This study shows the importance of nonlinear interactions among various parameters in identifying sensitive parameters.In the future,the conditional nonlinear optimal perturbation approach related to parameters,especially optimal parameter combinations,is expected to greatly improve DCM simulations in complex ecosystem models.

Robust sliding mode control for fractional-order chaotic economical system with parameter uncertainty and external disturbance

This paper presents a modified sliding mode control for fractional-order chaotic economical systems with parameter uncertainty and external disturbance. By constructing the suitable sliding mode surface with fractional-order integral, the effective sliding mode controller is designed to realize the asymptotical stability of fractional-order chaotic economical systems. Comparing with the existing results, the main results in this paper are more practical and rigorous. Simulation results show the effectiveness and feasibility of the proposed sliding mode control method.

Parameter uncertainty modeling of safety instrumented systems

In this study,a novel safety integrity level(SIL)determination methodology of safety instrumented systems(SISs)with parameter uncertainty is proposed by combining multistage dynamic Bayesian networks(DBNs)and Monte Carlo simulation.A multistage DBN model for SIL determination with multiple redundant cells is established.The models of function inspection test interval and function inspection test stages are alternately connected to form the multistage DBNs.The redundant cells can have different M out of N voting system architectures.An automatic modeling of conditional probability between nodes is developed.The SIL determination of SISs with parameter uncertainty is constructed by using the multistage DBNs and Monte Carlo simulation.A high-pressure SIS in the export of oil wellplatform is adopted to demonstrate the application of the proposed approach.The SIL and availability of the SIS and its subsystems are obtained.The influence of single subsystem on the SIL and availability of the SIS is studied.The influence of single redundant element on the SIL and availability of the subsystem is analyzed.A user-friendly SIL determination software with parameter uncertainty is developed on MATLAB graphical user interface.

Influence of seismicity parameter uncertainty on seismic hazard estimation of cities and towns

The influence on seismic hazard estimation for 310 cities and towns in the whole nation are studied in particular,owing to uncertainty of seismicity parameters caused by non-uniqueness in selecting statistical time ranges. Andthe regional sketch maps of the average varying values of intensity and the average relative varying values of peakacceleration with different probability of exceedance in 50 years are drawn in the Chinese mainland.

Portfolio Choice under the Mean-Variance Model with Parameter Uncertainty

Assuming the investor is uncertainty-aversion,the multiprior approach is applied to studying the problem of portfolio choice under the uncertainty about the expected return of risky asset based on the mean-variance model. By introducing a set of constraint constants to measure uncertainty degree of the estimated expected return,it built the max-min model of multi-prior portfolio,and utilized the Lagrange method to obtain the closed-form solution of the model,which was compared with the mean-variance model and the minimum-variance model; then,an empirical study was done based on the monthly returns over the period June 2011 to May 2014 of eight kinds of stocks in Shanghai Exchange 50 Index. Results showed,the weight of multi-prior portfolio was a weighted average of the weight of mean-variance portfolio and that of minimumvariance portfolio; the steady of multi-prior portfolio was strengthened compared with the mean-variance portfolio; the performance of multi-prior portfolio was greater than that of minimum-variance portfolio. The study demonstrates that the investor can improve the steady of multi-prior portfolio as well as its performance for some appropriate constraint constants.

On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Nash Model Parameter Uncertainty Analysis by AM-MCMC Based on BFS and Probabilistic Flood Forecasting

A hydrologic model consists of several parameters which are usually calibrated based on observed hy-drologic processes. Due to the uncertainty of the hydrologic processes, model parameters are also uncertain, which further leads to the uncertainty of forecast results of a hydrologic model. Working with the Bayesian Forecasting System (BFS), Markov Chain Monte Carlo simulation based Adaptive Metropolis method (AM-MCMC) was used to study parameter uncertainty of Nash model, while the probabilistic flood forecasting was made with the simu-lated samples of parameters of Nash model. The results of a case study shows that the AM-MCMC based on BFS proposed in this paper is suitable to obtain the posterior distribution of the parameters of Nash model according to the known information of the parameters. The use of Nash model and AM-MCMC based on BFS was able to make the probabilistic flood forecast as well as to find the mean and variance of flood discharge, which may be useful to estimate the risk of flood control decision.

Saddle Point Solution for System with Parameter Uncertainties

In this paper, we consider dynamical system, in the presence of parameter uncertainties. We apply max-min principles to determine the saddle point solution for the class of differential game arising from the associated dynamical system. We also provide sufficient condition for the existence of this saddle point.

Adaptive Containment Control for Fractional-Order Nonlinear Multi-Agent Systems With Time-Varying Parameters

This paper investigates adaptive containment control for a class of fractional-order multi-agent systems(FOMASs)with time-varying parameters and disturbances.By using the bounded estimation method,the difficulty generated by the timevarying parameters and disturbances is overcome.The command filter is introduced to solve the complexity problem inherent in adaptive backstepping control.Meanwhile,in order to eliminate the effect of filter errors,a novel distributed error compensating scheme is constructed,in which only the local information from the neighbor agents is utilized.Then,a distributed adaptive containment control scheme for FOMASs is developed based on backstepping to guarantee that the outputs of all the followers are steered to the convex hull spanned by the leaders.Based on the extension of Barbalat's lemma to fractional-order integrals,it can be proven that the containment errors and the compensating signals have asymptotic convergence.Finally,three simulation examples are given to show the feasibility and effectiveness of the proposed control method.

Exponential synchronization of stochastic impulsive perturbed chaotic Lur'e systems with time-varying delay and parametric uncertainty

This paper is devoted to investigating the scheme of exponential synchronization for uncertain stochastic impulsive perturbed chaotic Lur＇e systems. The parametric uncertainty is assumed to be norm bounded. Based on the Lyapunov function method, time-varying delay feedback control technique and a modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical uncertain chaotic Lur＇e systems with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities （LMIs）, which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. It is worth pointing out that the approach developed in this paper can provide a more general framework for the synchronization of multi-perturbation chaotic Lur＇e systems, which reflects a more realistic dynamics. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.