Progressive Reliability Method and Its Application to Offshore Mooring Systems

Assessing the reliability of complex systems (e.g. structures) is essential for a reliability-based optimal design that balances safety and costs of such systems. This paper proposes the Progressive Reliability Method (PRM) for the quantification of the reliability of complex systems. The proposed method is a closed-form solution for calculating the probability of failure. The new method is flexible to the definition of “failure” (i.e., can consider serviceability and ultimate-strength failures) and uses the rules of probability theory to estimate the failure probability of the system or its components. The method is first discussed in general and then illustrated in two examples, including a case study to find the safest configuration and orientation of a 12-line offshore mooring system. The PRM results are compared with results of a similar assessment based on the Monte Carlo simulations. It is shown in the example of two-component that using PRM, the importance of system components to system safety can be quantified and compared as input information for maintenance planning

Assessing capability instead of achieved functionings in risk analysis

A capability approach has been proposed to risk analysis, where risk is conceptualized as the probability that capabilities are reduced. Capabilities refer to the genuine opportunities of individuals to achieve valuable doings and beings, such as being adequately nourished. Such doings and beings are called functionings. A current debate in risk analysis and other fields where a capability approach has been developed concerns whether capabilities or actual achieved functionings should be used. This paper argues that in risk analysis the consequences of hazardous scenarios should be conceptualized in terms of capabilities, not achieved functionings. Furthermore, the paper proposes a method for assessing capabilities, which considers the levels of achieved functionings of other individuals with similar boundary conditions. The capability of an individual can then be captured statistically based on the variability of the achieved functionings over the considered population

Stochastic Life-cycle Sustainability Analysis

During their life-cycle, engineering systems typically suffer from deterioration due to regular operation and exposure to extreme events and harsh environmental conditions. As a result, regular or exceptional recovery strategies are often required to restore the system to a target safety and functionality level. There is a need to evaluate the associated impact of such strategies on the life-cycle sustainability of engineering systems. This paper proposes a novel stochastic formulation, named Stochastic Life-cycle Sustainability Analysis (SLCSA), for evaluating the sustainability of engineering systems throughout a time horizon of interest. In the SLCSA, the sustainability of the system is evaluated in terms of its environmental impact, which includes the impact of the construction, operation processes and recovery strategies that are associated with the various components of the system. The formulation proposes state-dependent stochastic models that capture the effects of gradual and shock deteriorations in the evaluation of the environmental impact of the system as well as the resilience of the system described by the recovery strategies. Moreover, the formulation accounts for the relevant uncertainties, such as those in the external conditions (e.g., environmental exposure and potential hazards), and those in the environmental emissions, associated with the materials and energy used throughout the system life-cycle. As an illustration, the proposed analysis is used to evaluate the life-cycle sustainability of a typical reinforced concrete (RC) bridge

Stochastic Differential Equations for the Deterioration Processes of Engineering Systems

A critical part of Life-Cycle Analysis of engineering systems is the modeling of their deterioration over time. A system might be subject to different deterioration processes that might impair its ability to sustain the future levels of demand. The attainment of a given level of deterioration might also prompt maintenance operations that may disrupt its ability to provide a regular service. Recently proposed formulations model the time-varying reliability of a system by looking at the evolution of state-variables that define the characteristics of the system. These state-dependent formulations rely heavily on the chosen models for the evolution of the state-variables over time. However, most models available in literature rely on simplifying assumptions that disregard the true nature of the processes, either by discretizing the time domain or by assuming independence among different processes acting on the system at the same time. This paper proposes to use a system of Stochastic Differential Equations to model the evolution of the state variables over time. The proposed formulation captures the continuous nature of the processes and takes into account the possible interactions among them. In addition, results from stochastic calculus could be used to facilitate the simulation of the processes and to obtain closed-form solutions for the distribution of the state variables over time. Moreover, the proposed models can be calibrated based on periodical monitoring of the state variables, should that be performed via Non-Destructive Evaluation or Structural Health Monitoring. A procedure for calibration is introduced and a brief explanatory example is provided.This work was supported in part by the MAE Center at the University of Illinois at Urbana-Champaign and the National Institute of Standards and Technology (NIST) through the Center for Risk-Based Community Resilience Planning under Award No 70NANB15H044. Opinions and findings presented are those of the authors and do not necessarily reflect the views of the sponsors

Resilience assessment of dynamic engineering systems

Resilience indicators are a convenient tool to assess the resilience of engineering systems. They are often used in preliminary designs or in the assessment of complex systems. This paper introduces a novel approach to assess the time-dependent resilience of engineering systems using resilience indicators. The temporal dimension is tackled in this work using the Dynamic Bayesian Network (DBN). DBN extends the classical BN by adding the time dimension. It permits the interaction among variables at different time steps. It can be used to track the evolution of a system’s performance given an evidence recorded at a previous time step. This allows predicting the resilience state of a system given its initial condition. A mathematical probabilistic framework based on the DBN is developed to model the resilience of dynamic engineering systems. A case study is presented in the paper to demonstrate the applicability of the introduced framework

probability models to assess the seismic safety of rigid block like structures and the effectiveness of two safety devices

Abstract When subject to earthquakes, some objects and structures, such as statues, obelisks, storage systems, and transformers, show a dynamic behavior that can be modeled considering the object/structure as a rigid block. Several papers have studied the dynamic behavior of both stand-alone rigid blocks and systems where rigid blocks have been paired with safety devices to prevent or delay the overturning of the blocks. Although the safety devices have generally been proven to be effective, their effectiveness changes substantially varying the parameters that characterize the system and the seismic input. This paper compares the seismic responses of stand along rigid blocks with those of blocks coupled with two candidate safety devices: an isolating base and a pendulum mass damper. To account for the relevant uncertainties, probabilistic seismic demand models are developed using a Bayesian approach. The probabilistic models are then used along with the overturning capacities of the blocks to construct fragility curves that give a prediction of the probability of overturning occurrence as a function of some characteristics of the blocks, of the safety devices, as well as of the seismic excitation, i.e. the slenderness of the body and the peak ground acceleration. The data needed to develop the probabilistic model are obtained integrating the nonlinear equations of motion of the two systems subject to selected ground motions. In the end, some numerical examples are proposed

Recovery Optimization of Interdependent Infrastructure: A Multi-Scale Approach

2) modeling the associated service recoveryand 3) developing a computationally manageable approach for the recovery modeling and optimization. This paper presents a novel multi-scale approach for the post-disaster recovery modeling and optimization of interdependent infrastructure. The multi-scale approach facilitates the recovery modeling and enables developing recovery strategies that are feasible to implement and easy to communicate. To enhance regional resilience, the paper integrates the recovery modeling into a multi-objective optimization problem. The optimization problem aims to schedule the required recovery activities such that disrupted services are restored as fast as possible, while minimizing the incurred cost. In the optimization problem, resilience metrics are introduced to monitor and quantify service recovery. The optimization problem is subject to recovery scheduling and network flow constraints, where each is formulated as a nested optimization. The multi-scale approach to the recovery optimization highlights the role of infrastructure at multiple scales to achieve selected recovery objective(s). As an illustration, the proposed approach is used to optimize the post-disaster recovery of interdependent infrastructure in a virtual community testbed.Rapid post-disaster recovery of infrastructure is necessary for prompt societal recovery. Regional resilience analysis can promote mitigation and recovery strategies that reduce the spatial extent and duration of infrastructure disruptions. Three significant challenges in regional resilience analysis are 1) modeling the physical recovery of infrastructureThis work was supported in part by the National Institute of Standards and Technology (NIST) through the Center for Risk-based Community Resilience Planning under Award No. 70NANB15H044 and by the National Science Foundation (NSF) under Award No. 1638346. Opinions and findings presented are those of the authors and do not necessarily reflect the views of the sponsors

Analysis of the Joint Effects of Thermal Stresses and Corrosion on Integral Abutment Bridges

The corrosion of reinforced concrete structures in coastal areas turns out to be very severe and can extend significantly in windy zones. Additionally, frequent temperature changes and, above all, exposure to extreme temperatures might induce wider cracks and micro‐cracks in concrete structures which, in turn, might accelerate the diffusion of corrosive agents. Motivated by this evidence, the present study aims at verifying the sensitivity of integral abutment bridges to the combined effect of thermal stresses and corrosion. Preliminary results show that a high thermal stress may amplify the negative effects of corrosion but also that the bridge used for the case study is more sensitive to thermal stresses than to corrosion

Modeling the Joint Probability Distribution of Main Shock and Aftershock Spectral Accelerations

Seismic risk analysis of deteriorating structures and infrastructure often requires predicting the intensity measures of earthquake ground motions in main shock-aftershock sequences. The uncertainty in the intensity measures of ground motions is typically a dominant contributor to the total uncertainty of the seismic risk analysis. A model for the joint probability distribution of main shock and aftershock intensity measures is thus required to accurately quantify the uncertainty in the seismic risk analysis. The spectral accelerations of ground motions have been identified as significant intensity measures for the seismic risk analysis of structures and infrastructure. The values of spectral accelerations can be affected by many factors representing the characteristics of the seismic source, travel path of seismic waves, and local site conditions. These factors can also introduce statistical dependence among main shock and aftershock spectral accelerations. This paper develops a novel formulation for the joint probability distribution of main shock and aftershock spectral accelerations at multiple periods. We select existing predictive models for the spectral accelerations of main shocks and develop a separate model for the spectral accelerations of aftershocks. The proposed formulation also estimates the correlations between the relevant pairs of model error terms in the two probabilistic predictive models for a wide range of periods. This allows us to separately capture the similarity in source and site and thus present the physical meanings. The increased vulnerability of structures and infrastructure in the aftermath of a damaging mainshock can further highlight the significance of capturing such correlations in the seismic risk analysis