The geometry itself ( Gumbert et al., 2002) or the geometric parameters of the system, such as the area of cross section, moment of inertia, and length of the members, can be uncertain. Uncertainties in structural engineering problems can arise from various sources. In the first step, input uncertain parameters are identified and the sources of uncertainty for each input are properly characterized by probability measures such as probability density functions (PDFs). Three steps of a typical forward uncertainty quantification are described as (1) identification and characterization of the input parameters, (2) development of a suitable deterministic/stochastic model, and (3) forward propagation of the uncertainty. Each variable is called as a random variable in the stochastic analysis and the uncertainty associated with each random variable is represented by a probabilistic measure such as a probability density function (PDF).įig. 16.1 depicts a schematic representation for the forward propagation of uncertainty in the form of a flowchart. The stochastic model provides better understanding of the phenomena involved and is helpful in providing a reliable prediction with quantified uncertainties in such cases. Hence, a forward propagation of uncertainty is of prime importance in structural engineering problems. A brief introduction to the uncertainties in structural engineering design for practicing engineers can be found in the work reported by Bulleit (2008).Ī full-scale test is infeasible to conduct before construction, which compels engineers and researchers to rely more on computational modeling to acquire details on the structural behavior. In many cases of the structural engineering practice, the structure to be designed is mostly unique and no data are available about the QoI during the analysis and design in many cases, the situation continues even after construction of the structure. However, in case of the inverse problem, from some observations of the output QoI or other observable quantities, the corresponding uncertainties in the input parameters are decided, in such a way that, when these input parameters are fed through the system, those will produce the given output QoI ( Vogel, 2002).
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The known uncertainties in the inputs are propagated through the model to obtain the uncertainties in the output QoI ( Smith, 2014). In forward propagation of uncertainty (also known as push-forward problem), the uncertainties in the QoI are evaluated from the uncertainties in the inputs. Based on the set objectives, there are two types of uncertainty quantification problems, namely (1) forward propagation of uncertainty problem and (2) inverse problem.
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A computational model that quantifies the uncertainties from various sources can provide clear insight into the behavior of the structural system and make reliable predictions of the quantities of interest (QoI). Real-world structural engineering problems have, however, number of uncertainties associated with them and deterministic models alone are not sufficient for the prediction of these uncertainties.
![civil engineering structure civil engineering structure](https://www.en.aau.dk/digitalAssets/92/92340_risk-and-safety-management-aau-ses-650x350---05.jpg)
Similar to the most of the other engineering disciplines, civil engineering practice also follows deterministic analyses for structural analysis and design. Vasant Matsagar, in Handbook of Probabilistic Models, 2020 1.1 Introduction to stochastic analysis of structural systemsĬivil engineering structures are planned, analyzed, designed, and built in modern times using the predictions from computational models.