High cumulants of conserved charges and their statistical uncertainties

We study the influence of measured high cumulants of conserved charges on their associated statistical uncertainties in relativistic heavy-ion collisions. With a given number of events, the measured cumulants randomly fluctuate with an approximately normal distribution, while the estimated statistical uncertainties are found to be correlated with corresponding values of the obtained cumulants. Generally, with a given number of events, the larger the cumulants we measure, the larger the statistical uncertainties that are estimated. The error-weighted averaged cumulants are dependent on statistics. Despite this effect, however, it is found that the three sigma rule of thumb is still applicable when the statistics are above one million.

A Bayesian multi-model inference methodology for imprecise momentindependent global sensitivity analysis of rock structures

Traditional global sensitivity analysis(GSA)neglects the epistemic uncertainties associated with the probabilistic characteristics(i.e.type of distribution type and its parameters)of input rock properties emanating due to the small size of datasets while mapping the relative importance of properties to the model response.This paper proposes an augmented Bayesian multi-model inference(BMMI)coupled with GSA methodology(BMMI-GSA)to address this issue by estimating the imprecision in the momentindependent sensitivity indices of rock structures arising from the small size of input data.The methodology employs BMMI to quantify the epistemic uncertainties associated with model type and parameters of input properties.The estimated uncertainties are propagated in estimating imprecision in moment-independent Borgonovo’s indices by employing a reweighting approach on candidate probabilistic models.The proposed methodology is showcased for a rock slope prone to stress-controlled failure in the Himalayan region of India.The proposed methodology was superior to the conventional GSA(neglects all epistemic uncertainties)and Bayesian coupled GSA(B-GSA)(neglects model uncertainty)due to its capability to incorporate the uncertainties in both model type and parameters of properties.Imprecise Borgonovo’s indices estimated via proposed methodology provide the confidence intervals of the sensitivity indices instead of their fixed-point estimates,which makes the user more informed in the data collection efforts.Analyses performed with the varying sample sizes suggested that the uncertainties in sensitivity indices reduce significantly with the increasing sample sizes.The accurate importance ranking of properties was only possible via samples of large sizes.Further,the impact of the prior knowledge in terms of prior ranges and distributions was significant;hence,any related assumption should be made carefully.

DISTRIBUTED MONITORING SYSTEM RELIABILITY ESTIMATION WITH CONSIDERATION OF STATISTICAL UNCERTAINTY

Taking into account the whole system structure and the component reliability estimation uncertainty, a system reliability estimation method based on probability and statistical theory for distributed monitoring systems is presented. The variance and confidence intervals of the system reliability estimation are obtained by expressing system reliability as a linear sum of products of higher order moments of component reliability estimates when the number of component or system survivals obeys binomial distribution. The eigenfunction of binomial distribution is used to determine the moments of component reliability estimates, and a symbolic matrix which can facilitate the search of explicit system reliability estimates is proposed. Furthermore, a case of application is used to illustrate the procedure, and with the help of this example, various issues such as the applicability of this estimation model, and measures to improve system reliability of monitoring systems are discussed.

A reliability analysis framework coupled with statistical uncertainty characterization for geotechnical engineering

Reliability analysis plays an important role in the risk management of geotechnical engineering.For the random field-based method,it is expected that the uncertainty characterization of geo-material parameters and the realization of random field can be integrated effectively.Moreover,as the increase in measured data size is generally difficult in the field investigation of geotechnical engineering due to limitation of budget and time etc.,the statistical uncertainty resulting from sparse data should be paid great attention.Therefore,taking the determination of hyper-parameters for Bayesian-based conditional random field as the breakthrough,this study proposed a reliability analysis framework to achieve the expectation above.In this proposed reliability analysis framework,the present characterization method of statistical uncertainty is improved by setting the lognormal distribution as the prior distribution of scale of fluctuation(SOF).Subsequently,the performance of statistical uncertainty characterization method is tested by a set of unconfined compressive strength(UCS)database about rocks.Then,a case study about the stability analysis of slope is employed to demonstrate the beneficial effect of the proposed reliability analysis framework.It is found that the uncertainty in both the realization of random field and the reliability analysis results can be significantly mitigated by the proposed reliability analysis framework.

Jackknife based generalized resampling reliability approach for rock slopes and tunnels stability analyses with limited data:Theory and applications

An efficient resampling reliability approach was developed to consider the effect of statistical uncertainties in input properties arising due to insufficient data when estimating the reliability of rock slopes and tunnels.This approach considers the effect of uncertainties in both distribution parameters(mean and standard deviation)and types of input properties.Further,the approach was generalized to make it capable of analyzing complex problems with explicit/implicit performance functions(PFs),single/multiple PFs,and correlated/non-correlated input properties.It couples resampling statistical tool,i.e.jackknife,with advanced reliability tools like Latin hypercube sampling(LHS),Sobol’s global sensitivity,moving least square-response surface method(MLS-RSM),and Nataf’s transformation.The developed approach was demonstrated for four cases encompassing different types.Results were compared with a recently developed bootstrap-based resampling reliability approach.The results show that the approach is accurate and significantly efficient compared with the bootstrap-based approach.The proposed approach reflects the effect of statistical uncertainties of input properties by estimating distributions/confidence intervals of reliability index/probability of failure(s)instead of their fixed-point estimates.Further,sufficiently accurate results were obtained by considering uncertainties in distribution parameters only and ignoring those in distribution types.

Reliability-based robust geotechnical design of braced excavations considering multiple failure modes

Reliability design of braced excavation is still a challenge for geotechnical community.Optimization design is a normal method to control the safety and cost of braced excavations.This study presents an advanced reliability-based robust geotechnical design method,which can consider multiple failures and uncertainty of statistical information.A universal design sample was conducted to verify the necessity of considering the uncertainty of statistical information.Ultimate limit state and serviceability limit state of braced excavations were defined,and point estimating method was used to evaluate the standard deviation of failure probabilities.Two-objective and three-objective optimization models were developed to illustrate the application of proposed methods in detail.In addition,the performance of optimization algorithms and further application of multiple-objective models were discussed.The results from this study indicate that the proposed method has a good performance in determining the optimal design with reasonable robustness and cost.New algorithms have higher efficiency in solving nonlinear and multiple-objective optimization problems than the 2nd Non-dominated sorting genetic algo-rithm.This study can guide the design of retaining systems of braced excavations in clay.