International Journal of Reliability and Safety

Nguyen-Tuan, Long; Koenke, Carsten; Bettzieche, Volker; Lahmer, Tom

doi: 10.1504/IJRS.2018.092498pmid: N/A

In this work, we study the uncertainties in the results of inverse problems. The inverse problems solve damage identification problems in multifield-multiphase problems for fluid-flow problems in deforming porous materials under non-isothermal 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.

Leichsenring, Ferenc; Jenkel, Christian; Graf, Wolfgang; Kaliske, Michael

doi: 10.1504/IJRS.2018.092499pmid: N/A

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. To include this variation in structural analysis, available data needs to be modelled appropriately, e.g. by means of probability and, furthermore, fuzzy probability based random variables or fuzzy sets. 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 studies by Möller et al. 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 in combination with a Finite Element (FE) simulation using a model suitable for characteristics of a timber structure by Jenkel and Kaliske.

Rozsás, Árpád; Sýkora, Miroslav

doi: 10.1504/IJRS.2018.092503pmid: N/A

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 interval-based 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.

Lu, Naiwei; Liu, Yang; Beer, Michael

doi: 10.1504/IJRS.2018.092504pmid: N/A

The steadily growing traffic loading may become a hazard for the bridge safety. Compared to short and medium span bridges, long-span bridges suffer from simultaneous presence of multiple vehicle loads. This study presents an approach for extrapolating probabilistic extreme effects on long-span bridges based on weigh-in-motion (WIM) measurements. Three types of stochastic traffic load models are simulated based on the WIM measurements of a highway in China. The level-crossing rate of each stochastic traffic load is evaluated and integrated for extrapolating extreme traffic load effects. The probability of exceedance of a cable-stayed 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 long-span 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 long-span bridges.

Auer, Ekaterina; Benavente-Peces, César; Ahrens, Andreas

doi: 10.1504/IJRS.2018.092506pmid: N/A

Characterising how different types of uncertainty in the multiple-input multiple-output (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 4 × 4 MIMO channel for two distinct choices of the channel matrix and compute an 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 parameters the mathematical model is most sensitive to.

Luo, Yuan; Yan, Donghaung; Yuan, Ming

doi: 10.1504/IJRS.2018.092514pmid: N/A

This study presents an approach for the fatigue stress spectrum simulation of short-span bridges under the dynamic impacts of stochastic traffic loading. This approach is utilised to evaluate the fatigue reliability of existing bridges. Response functions defined by intervals are used to approximate the equivalent fatigue stress range of the bridge. Probability models of the fatigue stress ranges are evaluated with Gaussian mixture models. The effectiveness of the proposed method is validated via a case study of a simply supported bridge. The numerical results indicate that the impact effect of vehicle loads on short-span bridge leads to an obvious increase in both the stress range and the number of stress cycles. Both the degradation of the road surface roughness condition and the traffic growth lead to a significant decrease in the fatigue reliability.

Xiao, Naijia; Fedele, Francesco; Muhanna, Rafi L.

doi: 10.1504/IJRS.2018.092516pmid: N/A

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 step-by-step 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). Non-trivial initial conditions are handled by modifying the right-hand 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.

Xiao, Naijia; Mullen, Robert L.; Muhanna, Rafi L.

doi: 10.1504/IJRS.2018.092515pmid: N/A

The solution of linear systems of equations is often a component of engineering simulation and modelling. Often, the system parameters are uncertain. One representation of this uncertainty is the use of probability-boxes (or p-boxes), which do not require complete information about the probability distribution underlying the random variables. P-boxes are the bounds on allowable continuous distribution function for the random variables. Arithmetic operations on p-boxes yield guaranteed bounds on the probability distribution of the solution, regardless the nature of dependency. The solutions of p-box linear systems of equations are presented in the context of FEA of structural systems. Loading and material uncertainties are described by p-boxes. Earlier Monte-Carlo p-box approach was limited to independent uncertainties. The governing p-box linear equations are solved by an iterative approach using a fixed-point formulation. The resulting formulation gives guaranteed bounds of the probability distribution of the structural responses, at a high computational efficiency and a low overestimation level.

Ray, Shashwati; Ralhan, Shimpy

doi: 10.1504/IJRS.2018.092519pmid: N/A

This paper addresses the problem of uncertainties in the input parameters by specifying them as compact intervals, taking into consideration the errors in modelling and measurement of transmission line parameters and also the continuous influence of load measurement errors and fluctuations in the load demand. The power flow equations are modelled as a set of nonlinear algebraic equations which are first linearised using Taylor series expansion and the solution is obtained by the Krawczyk's method of interval arithmetic. For the short circuit analysis the prefault conditions are obtained from power flow analysis and the faulty network is then solved using Thevenin's equivalent network as seen from the fault point. The proposed method is applied to 3 bus, 14 bus and 30 bus IEEE test systems where load currents and fault currents for each relay are obtained in bounded form and thus well-defined relay coordination pairs are available.

Cao, Ba Trung; Freitag, Steffen; Meschke, Günther

doi: 10.1504/IJRS.2018.092521pmid: N/A

In mechanised tunnelling, it is important to perform reliability analyses with respect to the tunnel face collapse and the damage risks of the tunnel lining and existing structures on the ground surface due to the tunnelling induced settlements. The reliability assessment requires to deal with limited information describing the local geology and the soil parameters due to the availability of only a small number of borehole data. In this paper, it is focused on real-time reliability analyses in mechanised tunnelling considering different types of uncertain data, i.e. combining epistemic and aleatoric sources of uncertainty within polymorphic uncertainty models. The system output of interest in these analyses is time variant tunnelling induced surface settlement fields, which are computed by a finite element simulation model. However, for real-time predictions with uncertain data, efficient and reliable surrogate models are required. A new surrogate modelling strategy is developed to predict time variant high dimensional fuzzy settlement fields in real-time. The predicted results of the new surrogate model show similar accuracy compared to the results obtained by optimisation based fuzzy analyses. Meanwhile, the computation time is significantly reduced especially in case of high dimensional outputs and in combination with the p-box approach in the case of polymorphic uncertain data.