4142003 - Computational Reliability Tools for Design

Project Title/ID Number	Computational Reliability Tools for Design—4142003
Start/End Dates	10/1/03—9/30/04
Project Leader	Armen Der Kiureghian (UCB/F)
Team Members	Kazuya Fujimura (UCB/GS), Junho Song (UCB/GS)

F=faculty; GS=graduate student; US=undergraduate student; PD=post-doc; I=industrial collaborator; O=other

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1. Project Goals/Objectives:

Develop, implement, document and apply reliability and sensitivity methods in the OpenSees computational simulation framework.
Identify and track the propagation of uncertainties through the probabilistic performance-based earthquake engineering assessment procedure.
Develop parameter importance and sensitivity measures.
Investigate performance criteria (limit-state functions) applicable to non-linear degrading reinforced concrete structures under static and dynamic effects.
Apply reliability methods to the I880 test bed.

Specific goals for Year 7 include:

Implement efficient and robust methods for reliability analysis of inelastic structures under stochastic loading, including importance-sampling methods.
Enhance reliability models and computational tools to solve “systems” problems characterized by multiple limit-state functions (multi-criteria performance).
Develop and implement random field models.
Further develop the application to the I-880 test bed.

2. Role of this project in supporting PEER’s mission (vision):

This project supports the PEER strategic plan by providing an advanced tool for uncertainty and reliability analysis in OpenSees. These tools are essential for performance-based earthquake engineering analysis and design. Analysis options include propagation of uncertainties, sensitivity analysis, reliability and fragility assessment, and parameter importance measures.

3. Methodology Employed:

Use is made of the following methodologies:

Response sensitivity analysis by the direct differentiation method (DDM),
The first-order second-moment (FOSM) method for analysis of uncertainty propagation,
The first-order reliability method (FORM) for reliability and fragility analysis,
Importance sampling and Monte Carlo simulation methods for uncertainty propagation and reliability analysis,
Stochastic representation of ground motion in the form of a filtered train of random pulses,
The FORM for reliability sensitivity and parameter importance measures, and
For stochastic dynamic problems, FORM and importance sampling methods are used to compute out-crossing rates and first-excursion probabilities. These methods are all implemented in the open-source, object-oriented platform OpenSees and are readily available for download from the web.

4. Brief Description of past year’s accomplishments (Year 6) & more detail on expected Year 7 accomplishments:

Terje Haukaas posted a fully functioning version of the sensitivity and reliability modules of OpenSees last year with the completion of his Ph.D. thesis in August 2003. The thesis by Haukaas documents the theory and formulation of sensitivity, uncertainty and reliability methods and their implementation in OpenSees. Guides for users and developers are also presented. A slightly modified version of this thesis has been submitted for publication as a PEER report. An important part of this study is a comprehensive application of sensitivity, uncertainty and reliability analysis to the I880 test bed viaduct. This application demonstrates the use of the reliability tools in OpenSees for a “real-world” problem with thousands of degrees of freedom and hundreds of random variables. Also investigated is the relative importance of various sources of uncertainty on the performance of the viaduct. Selected results from this application are presented below.

Figure 1 shows uncertainty propagation in probabilistic pushover analysis of the viaduct. The results show that the uncertainty in the displacement for a given load rapidly increases with loss of stiffness. A similar but less dramatic increase is observed in the uncertainty of the load for a given displacement. Figure 2 shows the cumulative distribution and probability density functions of the displacement and load when the lateral stiffness reaches 20% of the initial stiffness.

(a) (b)
Figure 1. Mean and mean ± standard deviation of (a) displacement for given load,
(b) load for given displacement.

(a) (b)
Figure 2. CDF and PDF of displacement (a) and load (b) at 20% of elastic tangent.

The application to I880 test bed also helped us identify areas where further development is needed. Specifically, our experience showed that for stochastic dynamic problems there is need for more robust and efficient reliability algorithms for application to “real-world” structures. One of the main goals of Year 7 is focused on this development. We are currently developing and implementing efficient algorithms for application to “real-world” structures.

5. Other Similar Work Being Conducted Within and Outside PEER and How This Project Differs:

Finite element reliability codes have been developed and used by NASA, Boeing, Southwest Research Institute, Los Alamos and a few other entities. General-purpose reliability codes have been developed at the Technical University of Munich (STRUREL), Det Norske Veritas (PROBAN), the University of California, Berkeley (CalREL) among others. The on-going development in OpenSees is unique in several aspects. This is the first general-purpose finite element reliability code developed in the open-source, object-oriented programming paradigm and it is the first code to handle nonlinear structures. Other researchers within PEER (G. Fenves at UCB, J. Conte at UCSD) are also working on DDM sensitivities in OpenSees. These groups are using the framework developed by our prior research. Their work is complementary, as each group addresses a particular element or material within OpenSees. We are also aware of theoretical work in this area by researchers in MCEER and are following it with interest.

6. Plans for Year 8 if project is expected to be continued:

A long-term goal of this project is to develop and implement tools for random field reliability analysis allowing the modeling of uncertain media, such as soils. A framework and initial implementation of this method is targeted for completion by September 2004. In Year 8, we would like to start implementation of this methodology in OpenSees.
Another objective is to incorporate tools for model uncertainty analysis in OpenSees. It is intended to use Bayesian uncertainty analysis methods to assess the model error based on laboratory and field observations, and incorporate it in reliability assessment.
We would like to expand the library of stochastic ground motion models and corresponding simulation algorithms in OpenSees.
We believe there is need for promoting use of advanced reliability methods in practical performance-based engineering by demonstrating the use of probabilistic tools available in OpenSees to comprehensive real-world problems. We intend to develop such demonstrative examples in Year 8 for increasingly more elaborate applications.

7. Describe any actual instances where you are aware your results have been used in industry:

We are communicating with a diverse group of approximately 30 researchers within and outside PEER, who have reported interest in performing reliability and response sensitivity analysis with OpenSees. This number is expected to grow, as OpenSees becomes a simulation tool for NEES. The reliability modules in OpenSees are also used in graduate courses at UC Berkeley. The PI will be teaching a course this summer in Italy, where this software will also be used.

8. Expected Milestones & Deliverables:

Development and implementation methods for reliability analysis under dynamic loads. March 31, 2004.
Implement new algorithms for reliability analysis with multiple performance criteria. July 2004.
Implement improved importance sampling and other simulation methods. July 2004.
Carry out reliability analysis of I-880 test bed using the improved algorithms. These improvements will allow reliability analysis for dynamic loads, accounting for nonlinear behavior of the bridge. September 2004.
Develop and implement tools for random field reliability analysis allowing the modeling of uncertain media, such as soils. This is a long-term objective. A framework and initial implementation is targeted for completion by September 2004.