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This paper discusses the pitfalls of using response surface methods when solving inverse problems and presents an adaptive artificial neural network-based inverse response surface method. The procedure is based on a coupling of the adaptive response surface method and artificial neural network-based inverse reliability analysis. The validity and accuracy of the method are tested on several examples. The first is a problem with a theoretical explicit nonlinear limit state function and one design parameter. Here, the accuracy of surrogate models for design parameter identification was tested for cases with the target values of the identified parameter both inside and outside of the initial range of values. The absolute percentage errors were 11.79 % and 0.19 % after the first and the last iteration of the identification process, respectively. The other two examples represent practical applications of the reliability design of structures with multiple design parameters and multiple reliability constraints. In the former, the limit state functions are defined explicitly, while in the latter, they are defined implicitly in the form of a structural analysis using the nonlinear finite element method. When assessing the reliability index values, very low absolute percentage error values were obtained in both examples. For the explicit form of the limit state function, the values were up to 0.50 % in all iterations. In the case of the implicitly defined limit state function, the absolute percentage error was equal to 6.45 % after the fist iteration and 0.79 % after the second iteration. [ABSTRACT FROM AUTHOR]

Advanced experimental evaluation of the mechanical fracture properties of quasi‐brittle materials is an important part of the design, assessment, and computational modeling of structures made of these materials. The aim is to determine parameters independent of the test configuration or the size of the test specimens. This paper presents the results of an extensive experimental program which is part of the development of a comprehensive multilevel approach for experimental–computational determination of the mechanical fracture parameters of concrete. Three‐point bending and wedge‐splitting tests were performed simultaneously using three different geometrically similar specimen sizes and two well‐separated depths of initial notches. Before the start of the main testing program, the pilot tests that were performed were aimed at the design of the most appropriate concrete mixture. Special attention was paid to the selection of a maximum aggregate grain size. In order to study the process of concrete aging and the development of its mechanical properties, the accompanying destructive and non‐destructive tests were carried out at different ages of hardening. Fracture parameters were evaluated using the effective crack‐length formulation and work‐of‐fracture method. Finally, the size‐independent specific fracture energy was back‐calculated from the measured specific fracture energy. [ABSTRACT FROM AUTHOR]

The paper describes the reliability‐based optimization of a TT‐shaped precast roof girder produced in Austria. An extensive experimental programme was performed using laboratory specimens to gain information on the mechanical fracture parameters of the utilized concrete. Subsequently, destructive shear tests were performed on scaled‐down and full‐scale girders under laboratory conditions. The experiments helped in the development of an accurate numerical model of the girder. The developed model was consequently used for the advanced stochastic analysis of structural response, followed by reliability‐based optimization, which was used to maximize the shear and bending capacities of the girder and minimize production cost under defined reliability constraints. The enormous computational requirements of the double‐loop optimization approach were significantly reduced by the utilization of an artificial neural network‐based surrogate model instead of the original nonlinear finite element model of the optimized structure. [ABSTRACT FROM AUTHOR]

Three sensitivity analysis methods are employed to achieve the optimum selection of the dominant random variables of selected concrete structures. The first of these methods uses the nonparametric rank‐order statistical correlation between the basic random input variables and the structural response output variable. The second is neural network ensemble‐based sensitivity analysis and the last of them is sensitivity analysis in terms of coefficient of variation. All of the methods were utilized and compared for two selected concrete structures: a prestressed concrete bridge made of MPD girders, and T‐shaped prestressed concrete roof girder. The obtained information was used to set up a stochastic model and response surfaces in an optimum manner and was employed in the subsequent determination of selected uncertain design parameters followed by load‐bearing capacity and reliability assessment. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with an adaptive artificial neural network‐based inverse response surface method utilized when performing reliability‐based design optimization of complex structural systems. Since calculating their reliability indicators (failure probabilities or reliability indices) is usually a time‐consuming task, the utilization of approximation methods with a view to reducing the computational effort to an acceptable level is an appropriate solution. A popular approximation method is the response surface method, where the limit state function is approximated using a suitable surrogate model. In this case, an artificial neural network is utilized. Construction of a response surface requires all variables of stochastic model to be known in advance. However, during the structural design, which is an inverse task, there are design parameters which are subject of reliability‐based design optimization procedure and thus not known at the start of the process. For such cases, an adaptive inverse response surface procedure is proposed. The procedure is based on a coupling of the adaptive response surface method and the artificial neural network‐based inverse reliability method. The validity and accuracy of the method is tested using example with explicit nonlinear limit state function. Obtained results as well as important aspects of the method are discussed. [ABSTRACT FROM AUTHOR]

An important step when designing and assessing the reliability of existing structures and/or structural elements is to calculate the reliability level described by failure probability or reliability index. Since calculating the structural response of complex systems such as bridges is usually a time-consuming task, the utilization of approximation methods with a view to reducing the computational effort to an acceptable level is an appropriate solution. The paper introduces a small-sample artificial neural network-based response surface method. An artificial neural network is used as an approximation (a so-called response surface) of the original limit state function. In order to be as effective as possible with respect to computational effort, a stratified Latin hypercube sampling simulation method is utilized to properly select training set elements. Subsequently, the artificial neural network-based response surface is utilized to calculate failure probability. To increase the accuracy of the determined failure probability, the response surface can be updated close to the failure region. This is performed by finding a new anchor point, which lies close to the design point of the limit state function. The new anchor point is then used to prepare the updated training set. The efficiency of the proposed method is tested for different training set sizes using a nonlinear limit state function taken from the literature, and the reliability assessment of three concrete bridges, one with explicit and two with implicit limit state functions in the form of finite element method models. [ABSTRACT FROM AUTHOR]

The correlations among selected parameters of concrete were investigated for concrete mixes of the strength classes C20/25, C25/30, C30/37, C40/50 and C50/60. The focus was laid on correlations between basic mechanical parameters such as compressive strength, tensile strength and modulus of elasticity as well as parameters related to concrete fracture, represented here by specific fracture energy. Laboratory tests examining the fracture behaviour and mechanical properties were carried out in order to determine the fundamental concrete parameters. In particular, standard compression tests on test cubes and three-point bending tests on beams with central edge notch were performed. Additional material parameters were identified using the inverse analysis technique. Finally, correlation factors between different parameters of concrete were identified using the rank-order correlation method. [ABSTRACT FROM AUTHOR]

A large number of old bridges are to be found on highways and roads all around the world. Considering their age and deterioration level, many of them need to be reconstructed. However, in the majority of cases, the load-bearing capacity of such bridges is just reduced to take account of their current state in spite of the fact that these structures continue to deteriorate. Their detailed reliability and lifetime assessment should therefore be a primary goal. Advanced methods of reliability analysis in combination with nonlinear finite element method-based analysis represent effective tools for the assessment of existing bridges. Data regarding the current level of load-bearing capacity and its expected development in the coming years (and whether or not the required level of reliability will be met) may help in the systematic scheduling of bridge maintenance and/or facilitate decision making about the effective reconstruction of the structure. This paper introduces a method for the probabilistic determination of the load-bearing capacity of bridges with respect to the progression of ongoing degradation processes over time. The method is used to determine the current load-bearing capacity of a 60-year-old reinforced concrete bridge, and for its estimation in the coming years until the end of the theoretical service life of the structure. [ABSTRACT FROM AUTHOR]

The use of stochastic non-linear computational mechanics in real-world applications faces a fundamental obstacle: the lack of knowledge regarding the stochastic properties of material parameters involved in the problem. The paper describes the results of an experimental program which was focused on the determination of fracture-mechanical parameters and their stochastic models of different concrete types after different hardening durations. The investigated types of concrete, C40/50 and C50/60, are used industrially for the production of pre-fabricated concrete elements (e.g. double T-shaped beam elements for roofing). The fracture-mechanical parameters were determined by wedge splitting tests on cubic specimens with notch. Moreover, numerical simulations were carried out for the identification of material parameters by using artificial neural networks. All results obtained from the individual tests will here be presented, compared and discussed. Finally, recommendations for stochastic models of selected parameters of the analysed concrete will be given. [ABSTRACT FROM AUTHOR]

Abstract: Knowledge regarding the values of fracture-mechanical parameters is critical for the virtual failure modeling of elements and structures made of concrete. A key parameter in nonlinear fracture mechanics modeling is the specific fracture energy of concrete, and its variability. Three-point bending tests on notched-beam specimens are fundamental experiments for the determination of fracture-mechanical parameters. In the present paper, two basic approaches are applied to determine fracture-mechanical parameter values from these tests: (i) the effective crack model/work-of-fracture method, and (ii) inverse analysis using artificial neural networks and stochastic simulations. First, the paper describes suitable methods for the determination of fracture-mechanical parameters. Second, the FraMePID-3PB software tool, which has been developed in order to automate the whole time consuming process of inverse analysis, is described. Finally, the verification of methodology and software is presented using two illustrative examples. [Copyright &y& Elsevier]

A new general inverse reliability analysis approach based on artificial neural networks is proposed. An inverse reliability analysis is a problem of obtaining design parameters corresponding to a specified reliability (reliability index or theoretical failure probability). Design parameters can be deterministic or they can be associated with random variables. The aim is to generally solve not only single design parameter cases but also multiple parameter problems with given multiple reliability constraints. Inverse analysis is based on the coupling of a stochastic simulation of the Monte Carlo type (the small-sample simulation method Latin hypercube sampling) and an artificial neural network. The validity and efficiency of this approach is shown using numerical examples with single as well as multiple reliability constraints and with single as well as multiple design parameters, and with independent basic random variables as well as random variables with prescribed statistical correlations. [ABSTRACT FROM AUTHOR]

Abstract: A new approach of inverse analysis is proposed to obtain parameters of a computational model in order to achieve the best agreement with experimental data. The inverse analysis is based on the coupling of a stochastic simulation and an artificial neural network (ANN). The identification parameters play the role of basic random variables with a scatter reflecting the physical range of potential values. A novelty of the approach is the utilization of the efficient small-sample simulation method Latin Hypercube Sampling (LHS) used for the stochastic preparation of the training set utilized in training the artificial neural network. Once the network has been trained, it represents an approximation consequently utilized to solve the key task: To provide the best possible set of model parameters for the given experimental data. The efficiency of the approach is shown using numerical examples from civil engineering computational mechanics. [Copyright &y& Elsevier]

Continuous welded rail is of high interest to operators of railway infrastructure facilities because of the reduced maintenance work and better train driving dynamics it offers. However, the application of continuous welded rail, in particular associated with its interaction with the superstructures of e.g. bridges, requires special caution with regard to the rail stresses in the transition area between the structure and the free field. These stresses are not only influenced by thermal deformations of the bridges but also by the clamp systems between the rails and e.g. the bridge. In general, these connectors are represented by spring elements during modelling, which: (a) causes singularities in the stress distributions in the rails, and (b) cannot capture all the mechanical system changes occurring due to loading, thermal effects, etc. The target of this paper is to present an alternative way of modelling the connection between rails and bridge superstructure based on composite materials which can overcome the disadvantages of the spring model. In particular, a nonlinear model of the whole system was developed for ballasted and non-ballasted track. Special attention was paid to the calibration of rail--bridge interaction and boundary conditions using measured data and code specifications. The aim of this study was to use the results of in-situ measurements to analyse the admissible stress in rails due to their interaction with a bridge caused by temperature loading. [ABSTRACT FROM AUTHOR]

The experimental results for quasi-brittle materials such as concrete and fibre-reinforced concrete exhibit high variability due to the heterogeneity of their aggregates, additives and general composition. An accurate assessment of the fracture-mechanical parameters of such materials (e.g. compressive strength fc and specific fracture energy Gf) turns out to be much more difficult and problematic than for other engineering materials. The practical design of quasi-brittle material-based structures requires virtual statistical approaches, simulations and probabilistic assessment procedures in order to be able to characterize the variability of these materials. A key parameter of non-linear fracture mechanics modelling is the specific fracture energy Gf and its variability, which has been a research subject for numerous authors although we will mention only [, ] at this point. The aim of this contribution is the characterization of stochastic fracture-mechanical properties of four specific, frequently used classes of concrete on the basis of a comprehensive experimental testing programme. [ABSTRACT FROM AUTHOR]

• The NNE is testified a superior surrogate model for parameter sensitivity analysis. • Properties of typical methods of parameter sensitivity analysis are fully clarified. • Strategy for sensitivity analysis of correlated variables are elaborated. • Mechanism of local and global methods for sensitivity analysis is revealed. • Robustness & accuracy of NNE in sensitivity analysis are demonstrated. Surrogate model-based sensitivity analysis, especially framed by neural network ensemble (NNE), is an attractive but unresolved issue in structural reliability assessment. In this paper, differing from existing studies, an overview and assessment of typical methods for surrogate model-based parameter sensitivity analysis, namely the input perturbation method, the local analysis of variance, the connection weight method, the non-parametric Spearman rank-order correlation method, and the Sobol indices method, are performed and demonstrated on three illustrative cases of increasing complexity: a simple theoretical instance, an engineering case of midspan deflection of a simply-supported beam, and a real-world practical application of shear failing in a precast concrete girder. Through comprehensive comparisons, several findings are obtained as follows: (i) the NNE is testified a superior surrogate model for sensitivity analysis to a single artificial neural network; (ii) robustness and accuracy of an NNE in sensitivity analysis are demonstrated; (iii) the properties of these parameter sensitivity analysis methods are fully clarified with distinguished merits and limitations; (iv) mechanism of local- and global- sensitivity analysis methods is revealed; and (v) the strategy for sensitivity analysis of correlated descriptive variables are elaborated to address the impact of correlation among random variables in engineering systems. [ABSTRACT FROM AUTHOR]

The investigation of longitudinal loads and their influence on stresses and internal forces in continuous welded rails (CWR) connected to bridge deck has been discussed intensively in the last 20 years. These discussions originated from the 1995 UIC-recommendation 774-3R, and led to the introduction of the Eurocode 1. These standards are very conservative. For instance, the code used a bi-linear stiffness–displacement law for the validation of the rail–bridge structure interaction and its effects on the rail stresses lead for short bridge spans to rail interruptions. The objective of this paper is to formulate the capacities and boundary conditions of the rail–structure interaction by means of extended numerical linear and nonlinear analyses, which are not fully comprehended in the standard specifications and therefore result in conservative interaction laws. The analyses have been carried out by means of monitoring-based nonlinear finite element modeling using advanced beam–spring interaction laws and specified thermomechanical considerations for capturing the real thermal expansion of bridge structures. [ABSTRACT FROM AUTHOR]