This study is dedicated to acquiring an approximate analytical solution of the transient response probability density function (PDF) of a single-degree-of-freedom linear oscillator under a non-Gaussian colored noise. The non-Gaussian colored noise is characterized by a first-order PDF and a specified power spectral density (PSD) with a bandwidth parameter and is represented by a one-dimensional Itô stochastic differential equation. The transient response PDFs of the oscillator are sought by applying an approximate analytical method for stationary response PDFs recently developed by the authors in a time-dependent manner. First, the equivalent non-Gaussian excitation method is applied to calculate the transient response moments up to the fourth order. Then, using these moments, the transient response PDFs are determined resorting to the Hermite moment model. The present analytical technique can treat any excitation PDF and bandwidth parameter value, as long as the combination of response skewness and kurtosis is within the applicable range of the Hermite moment model. In numerical examples, the transient response PDFs of the oscillator driven by highly non-Gaussian noises possessing symmetric and asymmetric PDFs are analyzed. Widely different bandwidth ratios between the excitation PSD and the system frequency response function are also taken into account, since the response PDF characteristics vary significantly with the bandwidth ratio. The accuracy of analytical results is illustrated through comparisons with the corresponding Monte Carlo simulation (MCS) results. Furthermore, the time-varying characteristics of the non-Gaussianity of the transient response PDF are investigated based on the obtained PDF solutions.

In its most general formulation, the safety for ageing infrastructure is represented as a function of the capacity and load effect. However, for ageing infrastructure, the imbedded complexity of time dependent capacity functions and variety of load components that can be present introduce a high level of uncertainty. In addition, due to the strategic importance of most of the civil infrastructure site specific deterioration, maintenance and repairs need to be accounted for. In order to provide an uninterrupted service systematic and practical models for evaluation of the likelihood of failure are needed.

Monitoring techniques that are emerging are increasing availability of site-specific data, however, with variable accuracy. For ageing infrastructure, the substantial issue of benchmarking performance cannot be resolved deterministically and probabilistic methodology that can integrate diverse data from various monitoring sources would be very valuable for owners. In this paper the continuous gamma process is implemented as an effective probabilistic model for infrastructure ageing process characterization.

Using the example of the capacity of a steel structure subject to corrosion, this paper will address application of continuous gamma process to include information from site-specific sources. Time dependent gamma process parameters are obtained from prior data, Micic (2019). The outcomes will be considered and evaluated against Straub et al. (2020) and corresponding traditional reliability analysis methods. It will be demonstrated that the stochastic gamma process offers consistent account of prior data and thorough prediction of future capacity thus, providing a useful planning tool.

Furthermore, assuming gradual ageing, it will be demonstrated that the methodology enables inclusion of emerging environmental data such as climate projections. Thus, it will be demonstrated that the stochastic gamma process representation for capacity is a consistent and a rigorous estimate for infrastructure safety prediction that enables inclusion of environmental, maintenance, repair and monitoring data.

In reliability-based seismic design, it is crucial to consider not only the uncertainty in the input ground motions, but also the uncertainty in the material properties of the system of interest. To investigate the uncertainty in the nonlinear seismic response of reinforced concrete (RC) piers, Takahashi et al. (2016) conducted a 3D shake table test at E-Defence in Japan. In this test, 16 medium-scale pier specimens were simultaneously excited against the JR Takatori station record of the 1995 Kobe earthquake to ensure the same dynamic inputs. The results showed that the nonlinear seismic responses, including the maximum displacement response and the residual displacement, can vary significantly due to the uncertainty in the material properties.

In this study, the RC pier specimen used in the above shake table test is modelled as a finite element (FE) model using the 3D nonlinear FE analysis software called COM3. The material properties, such as the compressive strength of the concrete and the yield strength of the rebar, are characterised as random variables based on the material test results. An adaptive probabilistic integration approach is then used to efficiently yet accurately quantify the uncertainty in the nonlinear seismic responses of the FE model. This approach is based on the Bayesian active learning methods, which have recently attracted much attention in the field of structural reliability. The results of the uncertainty propagation are compared with the results of the shake table tests.

It is also planned in our future work to investigate Bayesian model updating using the shake table test results to inversely quantify the uncertainty in the FE model parameters. A comparison of the model updating results and the material test results can provide an insight into the effects of modelling error and hysteresis nonlinearity on the uncertainty in the seismic responses.

A novel stochastic dynamics methodology for performing reliability analysis concerning complex hysteretic structural systems initially at rest and subjected to fully nonstationary seismic excitation is proposed. The approach aligns consistently with contemporary aseismic codes provisions whereas the induced seismic excitation vector consists of stochastic processes characterized by evolving power spectra, matching, in a stochastic sense, with the code compliant elastic response acceleration spectra of specified modal damping ratio and scaled ground acceleration. By leveraging the potent nonlinear stochastic dynamics concepts of stochastic averaging and statistical linearization, the method allows for the efficient determination of the approximative time-varying response amplitude joint probability density function. The proposed methodology enables the efficient estimation of evolving survival probability surfaces for various intensity measures adhering to various damage-state rules. Notably, an incremental mechanization analogous to the one used in standard incremental dynamic analysis is proposed to ensure the necessary compatibility for applications in the fields of structural and earthquake engineering. Characteristic of the structural behavior is that, for higher barriers associated with severe damage-states under low levels of excitation intensity, the survival first-passage probability reaches a constant non-zero value. The method is accompanied by a low computational cost addressing complex nonlinear and hysteretic structural behaviors while complying with current aseismic code provisions. A numerical example for illustrating the reliability of the proposed methodology is presented. The accuracy of the proposed method is assessed in a Monte-Carlo based context conducting nonlinear response time-history analysis which involves a large ensemble of accelerograms compatible with Eurocode 8 response acceleration spectra.

Ground Motion Prediction Equations (GMPE) are an important input for the probabilistic estimation of Earthquake Hazards. These models predict intensity parameters (i.e., spectral acceleration or velocity) induced by an earthquake as a function of the magnitude and source-to-site distance. GMPEs are proposed for earthquake sources, and their parameters are determined through model updating after direct field earthquake records from seismic stations. There are many GMPEs proposed in the literature for the different tectonic environments found in places like Northern South America (Colombia, Ecuador, and Venezuela). Probabilistic seismic hazard estimation methodologies involve using the best GMPEs to reduce uncertainty when estimating the design of earthquakes. Therefore, selecting the best models in an uncertain environment is an important task commonly faced in this analysis. This work presents an application of Bayesian model updating and model selection for estimating the uncertainty and comparing GMPEs for Northern South America.