International Journal of Reliability and Safety (8 papers in press)
Special Issue on: IJRS REC2016 Computing with Polymorphic Uncertain Data
 Uncertainty assessment in the results of inverse problems: application to damage detection in masonry dams
by Long NguyenTuan, Carsten Koenke, Volker Bettzieche, Tom Lahmer Abstract: In this work, we study the uncertainties in the results of inverse problems. The inverse problems solve damage identification problems in multifieldmultiphase problems for fluidflow problems in deforming porous materials under nonisothermal boundary conditions. These analyses are important within the structural health monitoring of masonry dams. Results of the inverse problems show a scatter due to different sources of uncertainties in model parameters, measurement data, field of measurements, and in the solving algorithms of the inverse problem. In order to see and analyse the scatter, the inverse problem is solved repeatedly by a sampling process. The uncertainty in the inverse solutions can be quantified by their probability distributions according to the sampling results. Keywords: damage identification; masonry dams; optimisation; uncertainty quantification; random field.
 Numerical simulation of wooden structures with polymorphic uncertainty in material properties
by Ferenc Leichsenring, Christian Jenkel, Wolfgang Graf, Michael Kaliske Abstract: Uncertainties are inherently present in structural parameters such as loadings, boundary conditions or resistance of structural materials. Especially material properties and parameters of wood are strongly varying in consequence of growth and environmental conditions. The considered uncertainties can be classified into aleatoric and epistemic uncertainty. To include this variation in structural analysis, available data need to be modelled appropriately, e.g. by means of probability and, furthermore, fuzzy probability based random variables or fuzzy sets. Therefore, a limited empirical data basis for Norway spruce, obtained by experiments according to DIN EN 408, is stochastically analysed including correlation, sensitivityanalyses and statistical tests. In order to comprehend uncertainties induced by estimating the distribution parameters, the stochastic approach has been extended by fuzzy distribution parameters to fuzzy probability based random variables according to [1, 2]. To cope with epistemic uncertainties for e.g. geometric parameters of knotholes, fuzzy sets are used. The consequence for wooden structures is determined by fuzzy stochastic analysis [3] in combination with a Finite Element (FE) simulation using an model suitable for characteristics of a timber structure by [4]. The uncertain results (e.g. displacements, failure loads) constituted by the proposed holistic approach defining the material properties based on an empirical data basis and the attempt of representing the uncertainties in material parameters and methods itself will be discussed. Keywords: polymorphic uncertainty; fuzzy randomness; stochastic modelling;rnwood mechanics; structural analysis.
 Using statistical and intervalbased approaches to propagate snow measurement uncertainty to structural reliability
by Árpád Rózsás, Miroslav Sýkora Abstract: Observations are inevitably contaminated with measurement uncertainty, which is a predominant source of uncertainty in some cases. In present practice, probabilistic models are typically fitted to measurements without proper consideration of this uncertainty. Hence, this study explores the effect of this simplification on structural reliability and provides recommendations on its appropriate treatment. Statistical and intervalbased approaches are used to quantify and propagate measurement uncertainty in probabilistic reliability analysis. The two approaches are critically compared by analysing ground snow measurements that are often affected by large measurement uncertainty. The results indicate that measurement uncertainty may lead to significant (order of magnitude) underestimation of failure probability and should be taken into account in reliability analysis. Ranges of the key parameters are identified where measurement uncertainty should be considered. For practical applications, the lower interval bound and predictive reliability index are recommended as point estimates using interval and statistical analysis, respectively. The point estimates should be accompanied by uncertainty intervals, which convey valuable information about the credibility of results. Keywords: measurement uncertainty; snow; structural reliability; interval arithmetic; maximum likelihood; deconvolution; statistics.
 Extrapolation of extreme traffic load effects on a cablestayed bridge based on weighinmotion measurements
by Naiwei Lu, Yang Liu, Michael Beer Abstract: The steadily growing traffic loading may become a hazard for the bridge safety. Compared with short and medium span bridges, longspan bridges suffer from simultaneous presence of multiple vehicle loads. This study presents an approach for extrapolating probabilistic extreme effects on longspan bridges based on weighinmotion (WIM) measurements. Three types of stochastic traffic load model are simulated based on the WIM measurements of a highway in China. The levelcrossing rate of each stochastic traffic load is evaluated and integrated for extrapolating extreme traffic load effects. The probability of exceedance of a cablestayed bridge is evaluated considering a linear traffic growth model. The numerical results show that the superposition of crossing rates is effective and feasible to model the probabilistic extreme effects of longspan bridges under the actual traffic loads. The increase of dense traffic flows is sensitive to the maximum load effect extrapolation. The dense traffic flow governs the limit state of traffic load on longspan bridges. Keywords: longspan bridge; traffic load; extreme value; levelcrossing theory; weighinmotion; probability of exceedance.
 Solving the power allocation problem using methods with result verification
by Ekaterina Auer, Cesar BenaventePeces, Andreas Ahrens Abstract: Characterising how different types of uncertainty in the multipleinput multipleoutput (MIMO) systems influence their performance is an important research topic. In this paper, we focus on the task of power allocation in fixed rate MIMO systems with singular value decomposition based channel separation. The interval analysis is used to develop a verified solution to the problem, taking bounded uncertainty in parameters and rounding errors into account. We demonstrate that power allocation improves the bit error rate (BER) using an exemplary 4x4 MIMO channel for two distinct choices of the channel matrix, and verify the upper bound on the BER under realistic uncertainty conditions. Besides, we show that a combined analytical/numerical procedure produces better results than the purely numerical one, and identify the parameters that the mathematical model is most sensitive to. Keywords: interval analysis; result verification; MIMO systems; power allocation.
 Fatigue reliability evaluation of shortspan concrete bridges under dynamic impacts of stochastic truck loading
by Yuan Luo, Donghaung Yan, Ming Yuan Abstract: This study presents an approach for the fatigue stress spectrum simulation of shortspan bridges under the dynamic impacts of stochastic traffic loading. This approach is used to evaluate the fatigue reliability of existing bridges using weighinmotion measurements. Response functions defined by intervals were used to approximate the equivalent fatigue stress range of the bridge under individual truck loads. Probability models of the fatigue stress ranges are evaluated with Gaussian mixture models. The effectiveness of the proposed method and its application to fatigue reliability assessment are validated via a case study of a simply supported bridge. The numerical results indicate that the impact effect of vehicle loads on a shortspan bridge leads to an obvious increase in both the stress range and the number of stress cycles. For an 'average' road roughness condition, the equivalent dynamic stress range is 1.34 times that of the static values. Both the degradation of the road surface roughness condition and the traffic growth lead to a significant decrease in the fatigue reliability. A maintenance schedule and a traffic management scheme can be developed based on this evaluation to ensure the fatigue safety of existing bridges. Keywords: fatigue reliability; vehiclebridge coupled vibration; response surface method; stochastic traffic flow; road surface roughness; traffic volume.
 Solution of uncertain linear systems of equations with probabilitybox parameters
by Naijia Xiao, Robert Mullen, Rafi Muhanna Abstract: The solution of linear systems of equations is often a component of engineering simulation and modeling. Often, the parameters of such a system of equations are uncertain. One representation of this uncertainty is the use of probabilityboxes (or pboxes), which do not require complete information about the probability distribution underlying the random variables. Pboxes are the bounds on allowable continuous distribution function for the random variables. Arithmetic operations on pboxes yield guaranteed lower and upper bounds on the probability distribution of the solution, regardless of the dependency among those uncertain parameters. In this paper, the solutions of linear systems of equations is presented in the context of finite element analysis of structural systems. Both the loading and material uncertainties are described by pboxes. Earlier MonteCarlo pbox approach was limited to independent uncertainties. The governing linear equations are solved by an iterative approach that exploits a fixedpoint formulation of the system of linear equations and pbox arithmetic operations. In order to reduce overestimation and obtain the tightest bounds possible, a decomposition of the stiffness matrix of the structure is adopted. The resulting formulation gives guaranteed lower and upper bounds of the probability distribution of the structural responses, at a high computational efficiency and a low overestimation level. Keywords: uncertainty; probabilitybox; matrix decomposition; iterative enclosure method.
 Structural Dynamic Problems in Time Domain under Uncertainty  An Interval Finite Element Approach
by Naijia Xiao, Francesco Fedele, Rafi Muhanna Abstract: An analysis of the structural dynamic response under uncertainty is presented. Uncertainties in load and material are modelled as intervals exploiting the interval finite element method (IFEM). To reduce overestimation and increase the computational efficiency of the solution, we do not solve the dynamic problem by an explicit stepbystep time integration scheme. Instead, our approach solves for the structural variables in the whole time domain simultaneously by an implicit scheme using discrete Fourier transform and its inverse (DFT and IDFT). Nontrivial initial conditions are handled by modifying the righthand side of the governing equation. To further reduce overestimation, a new decomposition strategy is applied to the IFEM matrices, and both primary and derived quantities are solved simultaneously. The final solution is obtained using an iterative enclosure method, and in our numerical examples the exact solution is enclosed at minimal computational cost. Keywords: interval finite element method; dynamic response; discrete Fourier transform; matrix decomposition; iterative enclosure method.
