An approximate epistemic uncertainty analysis approach in the presence of epistemic and aleatory uncertainties

Epistemic uncertainty analysis is an essential feature of any model application subject to ‘state of knowledge’ uncertainties. Such analysis is usually carried out on the basis of a Monte Carlo simulation sampling the epistemic variables and performing the corresponding model runs.In situations, however, where aleatory uncertainties are also present in the model, an adequate treatment of both types of uncertainties would require a two-stage nested Monte Carlo simulation, i.e. sampling the epistemic variables (‘outer loop’) and nested sampling of the aleatory variables (‘inner loop’). It is clear that for complex and long running codes the computational effort to perform all the resulting model runs may be prohibitive.Therefore, an approach of an approximate epistemic uncertainty analysis is suggested which is based solely on two simple Monte Carlo samples: (a) joint sampling of both, epistemic and aleatory variables simultaneously, (b) sampling of aleatory variables alone with the epistemic variables held fixed at their reference values.The applications of this approach to dynamic reliability analyses presented in this paper look quite promising and suggest that performing such an approximate epistemic uncertainty analysis is preferable to the alternative of not performing any.     

Effects of thaumasite on bond strength of reinforcement in concrete

The conditions necessary for the formation of thaumasite are well known and much work is in progress to identify concrete mixes resistant to thaumasite form of sulfate attack (TSA). However, there have been no data to indicate how TSA affects the nature and strength of the bond between reinforcement steel and concrete and hence the load capacity of reinforced concrete elements.

During works to repair and strengthen the thaumasite-affected Tredington–Ashchurch Overbridge in Gloucestershire, sections of column were removed and placed in storage. These column sections presented an opportunity to perform pullout tests on full size TSA-affected structural elements and unaffected control specimens from the same structure. In total 63 pullout tests were performed on plain round reinforcement bars embedded in two unaffected and four TSA-affected reinforced concrete elements. The sections were also characterised in terms of estimated in situ cube strength and depth of softened zone.

A statistical analysis of the experimental results indicates that the bond of the plain round reinforcement bars in the unaffected concrete exceeded that of the plain round reinforcement bars in the TSA-affected concrete. TSA reduced the mean experimental bond coefficient by 24% for corner bars and 10% for other bars, representing an average reduction in mean experimental bond coefficient of 15% for all bars.     

Robust optimization of concrete strength estimation using response surface methodology and Monte Carlo simulation

A new approach is proposed for the robust optimization of concrete strength estimation using response surface methodology and Monte Carlo simulation. The essence of the suggested procedure lies in the reliable prediction of concrete strength as a simple function of unit mass, water/cement ratio, age and superplasticizer content. The derived model provides sufficiently accurate results for the calibration and verification phases, the latter of which is conducted using data that were not used for model development. The results of additional analysis indicate that residuals in the calibration and verification stages have a normal distribution. Is its also shown that the uncertainty of estimated coefficient values has a statistically insignificant effect on concrete strength, confirming the reliability of the proposed model. Moreover, analysis of the effect of laboratory measurement errors indicates the robustness of concrete compressive strength against the variation in measured parameter values.     

Latin hypercube sampling and the propagation of uncertainty in analyses of complex systems

The following techniques for uncertainty and sensitivity analysis are briefly summarized: Monte Carlo analysis, differential analysis, response surface methodology, Fourier amplitude sensitivity test, Sobol' variance decomposition, and fast probability integration. Desirable features of Monte Carlo analysis in conjunction with Latin hypercube sampling are described in discussions of the following topics: (i) properties of random, stratified and Latin hypercube sampling, (ii) comparisons of random and Latin hypercube sampling, (iii) operations involving Latin hypercube sampling (i.e. correlation control, reweighting of samples to incorporate changed distributions, replicated sampling to test reproducibility of results), (iv) uncertainty analysis (i.e. cumulative distribution functions, complementary cumulative distribution functions, box plots), (v) sensitivity analysis (i.e. scatterplots, regression analysis, correlation analysis, rank transformations, searches for nonrandom patterns), and (vi) analyses involving stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty.     

A Bayesian model averaging method for software reliability modeling and assessment

The software reliability modeling is of great significance in improving software quality and managing the software development process. However, the existing methods are not able to accurately model software reliability improvement behavior because existing single model methods rely on restrictive assumptions and combination models cannot well deal with model uncertainties. In this article, we propose a Bayesian model averaging (BMA) method to model software reliability. First, the existing reliability modeling methods are selected as the candidate models, and the Bayesian theory is used to obtain the posterior probabilities of each reliability model. Then, the posterior probabilities are used as weights to average the candidate models. Both Markov Chain Monte Carlo (MCMC) algorithm and the Expectation–Maximization (EM) algorithm are used to evaluate a candidate model's posterior probability and for comparison purpose. The results show that the BMA method has superior performance in software reliability modeling, and the MCMC algorithm performs better than EM algorithm when they are used to estimate the parameters of BMA method.     

Temporary bond strength of partly cured epoxy adhesive for anchoring prestressed CFRP strips on concrete

Externally bonded Carbon Fiber Reinforced Polymer (CFRP) strips have been used for strengthening reinforced concrete structures. This paper presents an experimental study on the debonding of externally bonded CFRP strips anchored to a concrete substrate by a commercial epoxy adhesive. The study represents the basis for the characterization of an innovative ‘gradient method’, giving the possibility to anchor prestressed CFRP strips to concrete without the use any mechanical anchorage systems such as plates and bolts. Bond between the two components is achieved by an epoxy adhesive able to carry loads after an accelerated curing process under elevated temperatures. The effect of heating configuration/duration, strip thickness and bond length on the temporary bond resistance have been investigated using prestressed and non-prestressed CFRP-strips. Besides the optimization of the heating elements necessary for the curing process, curing parameters for an optimal temporary bond strength could be determined. Twenty-five minutes of heating and curing at 90 °C was found to be an optimum heating configuration, resulting in better short-term mechanical performances than after conventional curing at room temperature for several days. The main reason is a temporarily softer adhesive which allows the use of the full bond length by reducing shear force peaks.     

Finite element model updating using Hamiltonian Monte Carlo techniques

Bayesian techniques have been widely used in finite element model (FEM) updating. The attraction of these techniques is their ability to quantify and characterize the uncertainties associated with dynamic systems. In order to update an FEM, the Bayesian formulation requires the evaluation of the posterior distribution function. For large systems, this function is difficult to solve analytically. In such cases, the use of sampling techniques often provides a good approximation of this posterior distribution function. The hybrid Monte Carlo (HMC) method is a classic sampling method used to approximate high-dimensional complex problems. However, the acceptance rate of HMC is sensitive to the system size, as well as to the time step used to evaluate the molecular dynamics trajectory. The shadow HMC technique (SHMC), which is a modified version of the HMC method, was developed to improve sampling for large system sizes by drawing from a modified shadow Hamiltonian function. However, the SHMC algorithm performance is limited by the use of a non-separable modified Hamiltonian function. Moreover, two additional parameters are required for the sampling procedure, which could be computationally expensive. To overcome these weaknesses, the separable shadow HMC (S2HMC) method has been introduced. This method uses a transformation to a different parameter space to generate samples. In this paper, we analyse the application and performance of these algorithms, including the parameters used in each algorithm, their limitations and the effects on model updating. The accuracy and the efficiency of the algorithms are demonstrated by updating the finite element models of two real mechanical structures. It is observed that the S2HMC algorithm has a number of advantages over the other algorithms; for example, the S2HMC algorithm is able to efficiently sample at larger time steps while using fewer parameters than the other algorithms.     

Numerical assessment for impact strength measurements in concrete materials

Measurement of dynamic strength of concrete at impact relevant strain rates and pressures is the purpose of the described study. Therefore, an experimental design of direct planar impact experiments with longitudinal and transverse strain gauges is analyzed in predictive hydrocode simulations using an elastic–plastic damage model for concrete. The calculations and first experimental results on mortar show decreasing phase velocities of stress waves both in longitudinal and lateral gauges. The model clearly associates it with the onset of damage, possibly interpreted as a failure wave. Numerical analysis is furthermore used to compare a monolithic target block to a thoroughly assembled concrete sample in order to include flat gauges in the material. The planned experimental procedure to derive wave speeds, particle velocities and strain rates from stress measurements is anticipated and validated on the basis of simulated gauge signals. The most important finding is the prediction and first experimental confirmation that concrete ultimate strength and damaged yield stress can be derived at strain rates in the order of 10⁴/s from the proposed type of experiments. This technique promises new insight into the strength and failure processes of concrete in the challenging loading region around the characteristic minimum of the shock particle velocity relationship.     

Modelling of fracture process in concrete using a novel lattice model

Papers deals with simulations of fracture process in quasi-brittle materials like concrete with a novel lattice model. Concrete was described mainly as a three-phase material composed of aggregate, cement matrix and interfacial transition zones. The calculations were carried out for concrete specimens subject to uniaxial extension, shear and extension and three-point bending. Two-dimensional and three-dimensional simulations were performed. The advantages and disadvantages of the proposed model were outlined.     

A modified pull-out test for bond of near-surface mounted FRP rods in concrete

Among the strengthening techniques based on fiber-reinforced polymer (FRP) composites, the use of near-surface mounted (NSM) FRP rods is emerging as a promising technology for increasing flexural and shear strength of deficient concrete, masonry and timber members. In order for this technique to perform effectively, bond between the NSM reinforcement and the substrate material is a critical issue. Aim of this project was to investigate the mechanics of bond between NSM FRP rods and concrete, and to analyze the influence of the most critical parameters on the bond performance. Following up to previous investigations, a different type of specimen was designed in order to obtain a test procedure as efficient and reliable as possible. Among the investigated variables were: type of FRP rod (material and surface pattern), groove-filling material, bonded length, and groove size. Results of the first phase of the project are presented and discussed in this paper.     

考虑力学机制和不确定性影响的钢筋混凝土柱概率抗剪承载力模型

为了克服传统确定性抗剪承载力模型无法合理考虑不确定性因素影响所存在的缺陷,研究建立了一种能够综合考虑力学机制和不确定性影响的钢筋混凝土（RC）柱概率抗剪承载力模型。首先基于桁架-拱模型,综合考虑混凝土、箍筋和拱作用的抗剪承载力贡献以及不确定性的影响,建立了RC柱概率抗剪承载力模型的解析表达式;然后结合贝叶斯理论和马尔科夫链蒙特卡洛（MCMC）法,确定了概率模型参数的后验分布信息,并分析了概率模型参数的先验分布信息以及更新批次对概率模型参数后验分布的稳定性和收敛性的影响;最后利用试验数据验证了该概率模型的有效性。分析表明,随着试验数据的增加,概率模型参数的后验分布可以实现不断更新;概率抗剪承载力模型不仅可以合理描述抗剪承载力的概率分布特性,而且可以校准分析传统确定性抗剪承载力模型的计算精度。     

Optimization of normal and high strength recycled aggregate concrete mixtures by using packing model

This paper analyzes the possibility of applying the Compressible Packing Model (CPM) for the proportion of concrete mixtures produced with Recycled Concrete Aggregates (RCAs). As a matter of fact, the RCAs are composed of natural aggregates and attached mortar and, as a consequence, they generally present a higher porosity in comparison with ordinary natural aggregates. The higher porosity of RCAs can affect the resulting Recycled Aggregate Concretes (RACs) properties and, for this reason, the mix design procedure available in literature for ordinary concrete mixture cannot be applied as such in the case of RACs. In this context, the present work first presents a preliminary study in which the optimal mixing procedure for RACs is investigated and then, a possible extension of the CPM in the case of RACs is analyzed. Several structural RAC mixtures were designed for three strength classes (25, 45 and 65 MPa) by considering the variation of the aggregate replacement from 0 to 100%. Finally, the proposed procedure is experimentally validated by performing mechanical and durability tests on selected mixtures for the three strength classes with a RCAs content up to 60%. The results reported herein demonstrate the applicability of the CPM for recycled concrete mixtures and highlight as the rational use of RCAs lead to produce structural RAC without affecting its mechanical and the durability performance.     

A comprehensive Bayesian approach for model updating and quantification of modeling errors

This paper presents a comprehensive Bayesian approach for structural model updating which accounts for errors of different kinds, including measurement noise, nonlinear distortions stemming from the linearization of the model, and modeling errors due to the limited predictability of the latter. In particular, this allows the computation of any type of statistics on the updated parameters, such as joint or marginal probability density functions, or confidence intervals. The present work includes four main contributions that make the Bayesian updating approach feasible with general numerical models: (1) the proposal of a specific experimental protocol based on multisine excitations to accurately assess measurement errors in the frequency domain; (2) two possible strategies to represent the modeling error as additional random variables to be inferred jointly with the model parameters; (3) the introduction of a polynomial chaos expansion that provides a surrogate mapping between the probability spaces of the prior random variables and the model modal parameters; (4) the use of an evolutionary Monte Carlo Markov Chain which, in conjunction with the polynomial chaos expansion, can sample the posterior probability density function of the updated parameters at a very reasonable cost. The proposed approach is validated by numerical and experimental examples.     

浅海环境不确定性对声场扰动的影响

探索海洋环境各水声参数的不确定性所引发的声场扰动,对提高水声场预报的准确性与科学性至关重要,极具理论意义与应用价值。基于Workshop’97浅海环境基准模型,以扰动声场与实际声场的相关性函数作为量化指标,通过Kraken波动理论数值模型与马尔科夫链蒙特卡罗随机统计思想,基于单因子变量原则模拟分析了浅海水平不变环境中各水声参数声场扰动敏感性大小及其相关性,结果表明:沉积层声速C_1、水深D_1敏感性最强,沉积层衰减系数αs、沉积层密度ρs、沉积层声速C_2、沉积层厚度D_2、基底声速C_3次之,基底衰减系数αb、基底密度ρb几乎无影响;αs、ρs、C_1、D_1敏感性随距离增加逐渐增强,C_2、D_2、C_3敏感性随距离增加逐渐减弱;D_2、C_2,D_2、C_3,C_1、C_3,C_2、C_3之间存在较强的正相关性,D_2、C_1,C_1、C_2之间为显著的负相关性。     

Bond strength prediction for deformed steel rebar embedded in recycled coarse aggregate concrete

This paper summarizes the results of an experimental investigation into the bond behavior between recycled aggregate concrete (RAC) and deformed steel rebars, with the main variables being the recycled coarse aggregate replacement ratio (RCAr) and water-to-cement ratio of the concrete mixture. The investigation into splitting cracking strength indicates that the degradation of the bond splitting tensile stress of the cover concrete was affected by not only the roundness of the coarse aggregate particles but also the weak interfacial transition zone (ITZ) between the cement paste and the RCA that has a more porous structure in the ITZ than normal concrete. In this study, a linear relationship between the bond strength and the density of the RCA was found, but the high compressive strength reduced the effects of the parameters. To predict the bond strength of RAC using the main parameters, a multivariable model was developed using nonlinear regression analysis. It can be inferred from this study that the degradation characteristic of the bond strength of RAC can be predicted well, whereas other empirical equations and code provisions are very conservative.     

Computer arithmetic for probability distribution variables

The uncertainty in the variables and functions in computer simulations can be quantified by probability distributions and the correlations between the variables. We augment the standard computer arithmetic operations and the interval arithmetic approach to include probability distribution variable (PDV) as a basic data type. Probability distribution variable is a random variable that is usually characterized by generalized probabilistic discretization. The correlations or dependencies between PDVs that arise in a computation are automatically calculated and tracked. These correlations are used by the computer arithmetic rules to achieve the convergent approximation of the probability distribution function of a PDV and to guarantee that the derived bounds include the true solution. In many calculations, the calculated uncertainty bounds for PDVs are much tighter than they would have been had the dependencies been ignored. We describe the new PDV Arithmetic and verify the effectiveness of the approach to account for the creation and propagation of uncertainties in a computer program due to uncertainties in the initial data.     

A semiparametric model for compositional data analysis in presence of covariates on the simplex

Compositional data occur as natural realizations of multivariate observations comprising element proportions of some whole quantity. Such observations predominate in disciplines like geology, biology, ecology, economics and chemistry. Due to unit sum constraint on compositional data, specialized statistical methods are required for analyzing these data. Dirichlet distributions were originally used to study compositional data even though this family of distribution is not appropriate (see Aitchison, 1986) because of their extreme independence properties. Aitchison (1982) endeavored to provide a viable alternative to existing methods by employing Logistic Normal distribution to analyze such constrained data. However this family does not include the Dirichlet class and is therefore unable to address the issue of extreme independence. In this paper generalized Liouville family is investigated to model compositional data which includes covariates. This class permits distributions that admit negative or mixed correlation and also contains non-Dirichlet distributions with non-positive correlation and overcomes deficits in the Dirichlet class. Semiparametric Bayesian methods are proposed to estimate the probability density. Predictive distributions are used to assess performance of the model. The methods are illustrated on a real data set.     

Determination of the kink point in the bilinear softening model for concrete

The characterization of the softening curve from experimental results is essential for predicting the fracture behavior of quasi-brittle materials like concrete. Among various shapes (e.g. linear, exponential) to describe the softening behavior of concrete, the bilinear softening relationship has been extensively used and is the model of choice in this work. Currently, there is no consensus about the location of the kink point in the bilinear softening curve. In this study, the location of the kink point is proposed to be the stress at the critical crack tip opening displacement. Experimentally, the fracture parameters required to describe the bilinear softening curve can be determined with the “two-parameter fracture model” and the total work of fracture method based on a single concrete fracture test. The proposed location of the kink point compares well with the range of kink point locations reported in the literature, and is verified by plotting stress profiles along the expected fracture line obtained from numerical simulations with the cohesive zone model. Finally, prediction of experimental load versus crack mouth opening displacement curves validate the proposed location of the kink point for different concrete mixtures and also for geometrically similar specimens with the same concrete mixture. The experiments were performed on three-point bending specimens with concrete mixtures containing virgin coarse aggregate, recycled concrete coarse aggregate (RCA), and a 50-50 blend of RCA and virgin coarse aggregate. The verification and validation studies support the hypothesis of the kink point occurring at the critical crack tip opening displacement.