Euro-SiBRAM’2002 Prague, June 24 to 26, 2002, Czech Republic
Session 1
Basic Simulation Concepts Applicable in Codified Design
Abstract
The engineering profession has accepted the risk-based design concept and most of the current design guidelines and codes have either been modified or are being modified to implement the concept. Due to the significant advancement in computer technology and computational power, simulation is a viable alternative to the codified approach. It is expected that this world body of distinguished scholars on reliability-based design will help to formulate the future direction in simulation-based design. In keeping with the spirit of this colloquium, some broad questions need to be addressed to help guide the discussion. Some of the questions are: (1) Is the simulation-based design concept mature enough to be considered as an alternative to the currently available codified approach? (2) At present, should designers have the option to use either the simulation-based approach or the codified approach? (3) What should be the mechanism to convey designers’ preferences to a governing body responsible for maintaining the overall safety of structures? (4) If simulation-based design is accepted as an alternative approach to satisfy the current requirements, which organization(s) should provide leadership in distributing information on uncertainty in parameters, software, and technical support? Should this support be available at the local, national, or international level? (5) What is the future of simulation-based design considering the advancement in computer and information technology?
Key Words: Codified design, simulation, explicit and implicit performance functions, structural system, reference value, strength, serviceability, and durability limit states
In general, engineering design consists of proportioning the elements of a system to satisfy various criteria of performance, safety, serviceability, and durability under various demands. The presence of uncertainty cannot be avoided in every phase of engineering analysis and design, but it is not simple to satisfy design requirements in the presence of uncertainty. After three decades of extensive work in different engineering disciplines, several reliability evaluation procedures of various degrees of complexity are now available. First-generation design guidelines and codes are being developed and promoted worldwide using some of these procedures.
These reliability-based design codes are very similar to the earlier deterministic codes. The advanced reliability concepts used in developing these codes generally remain unknown to designers. Furthermore, it may be difficult for an experienced design engineer to consider the presence of levels of uncertainty different than those used to develop the reliability-based design guidelines for a particular design application. In most cases, these guidelines were developed to consider the behavior of elements of complex structural systems satisfying an explicit performance criterion. The evaluation of system reliability using information on element level reliabilities may not be simple. In some cases, the behavior of complex structural systems may need to be estimated using many simplifying assumptions including the support and connection conditions and various sources of nonlinearity. In general, performance functions are implicit for complex structural systems. For a given performance function, the reference value to define it properly may not have been developed or accepted by the profession.
Simulation is an alternative for implementing the risk-based design concept in practical design. Lewis and Orav (1989) wrote, “Simulation is essentially a controlled statistical sampling technique that, with a model, is used to obtain approximate answer for questions about complex, multi-factor probabilistic problems.” They added, “It is this interaction of experience, applied mathematics, statistics, and computing science that makes simulation such a stimulating subject, but at the same time a subject that is difficult to teach and write about.” Theoretical simulation is usually performed numerically with the help of computers, allowing a more elaborate representation of a complicated engineering system than can be achieved by physical experiments, and it is often cheaper than physical models. It allows a designer to know the uncertainty characteristics being considered in a particular design, to use judgment to quantify randomness beyond what is considered in a typical codified design, to evaluate the nature of implicit or explicit performance functions, and to have control of the deterministic algorithm used to study the realistic structural behavior at the system level.
The method commonly used for this purpose is called the Monte Carlo simulation technique. In the simplest form of the basic simulation, each random variable in a problem is sampled several times to represent the underlying probabilistic characteristics. Solving the problem deterministically for each realization is known as a simulation cycle, trial, or run. Using many simulation cycles will give the probabilistic characteristics of the problem, particularly when the number of cycles tends to infinity. Using computer simulation to study the presence of uncertainty in the problem is an inexpensive experiment compared to laboratory testing. It also helps evaluate different design alternatives in the presence of uncertainty, with the goal of identifying the optimal solution. The use of simulation in engineering design was strongly advocated by Marek et al. (1995), Schueller in his keynote address, and others. Elishakoff (2001) wrote an interesting essay on Monte Carlo simulation.
This gathering of distinguished scholars on risk-based design is a significant development and is expected help to implement the simulation-based engineering design as an alternative to the classical codified approach. However, there are still many challenges that need to be addressed first. In all fairness, similar challenges may exist in the current codified approach, and the discussions in this colloquium may also help improve the codified approach.
The Monte Carlo simulation technique has six essential elements: (1) defining the problem in terms of all the random variables; (2) quantifying the probabilistic characteristics of all the random variables in terms of their probability density functions and the corresponding parameters; (3) generating values of these random variables; (4) evaluating the problem deterministically for each set of realizations of all the random variables, or simply numerical experimentation of the problem; (5) extracting probabilistic information from N such realizations; and (6) determining the accuracy and efficiency of the simulation. The success of implementing the Monte Carlo simulation in design will depend on how accurately each element is addressed. All these elements will be discussed in detail in the following sessions.
The introduction of the load and resistance factor design (LRFD) approach for the design of steel structures by the American Institute of Steel Construction (AISC) was an important development in civil engineering (AISC, 2001). The preliminary attempts in this effort assumed that load effects and the resistance were lognormally distributed, and the first-order second moment (FOSM) method (Haldar and Mahadevan, 2000a) was used to estimate the reliability and derive the load and resistance factors. Later, the advanced first-order second-moment (AFOSM or FORM) approach was used to accommodate more complex design situations and include probability distributions other than the lognormal distribution. Although some of the major advantages of this approach have been well publicized and accepted in the profession, it is appropriate to reevaluate it in the context of simulation-based design.
The LRFD method was based on reliability analysis of isolated simple structural elements and was calibrated to achieve levels of reliability similar to conventional allowable stress-based design guidelines. The use of isolated simple structures to derive the safety factors is related to the basic design philosophy common to all codified design procedures. There are several advantages to isolated member approach (Bjorhovde et al., 1978): (1) in deterministic design methods that use factors of safety, it is not practical to prepare detailed requirements for each structural configuration; (2) the characteristics of the individual members and connections themselves are independent of the framework; and (3) most research has been devoted to the study of such elements, and theoretical and experimental verification of their performance is readily available. Nevertheless, the performance of a member is directly dependent on its location in a structural configuration and on its relationship or connection with other members in the framework (Mahadevan and Haldar, 1991). An important objective of reliability-based design methods is to reduce the scatter of non-uniform risk levels produced under various load combinations, but Mahadevan and Haldar observed that in many cases it fails to do so. The codified approach also fails to consider the statistical correlations among the design variables.
Popper (1982) wrote, “The fundamental idea underlying scientific determinism is that the structure of the world is such that every future event can in principle be rationally calculated in advance, if only we know the laws of the nature and the present state of the world.” The nonlinear state of the structure needs to be considered appropriately in estimating the probability of failure. But since the code does not address the minimum analytical requirement for deterministic evaluation, this area has been overlooked. Haldar and Mahadevan (2000b) advocated the use of nonlinear stochastic finite element approach for this purpose.
In the current codified approach, the reference or permissible or allowable value is required for the reliability evaluation, but in many situations the reference values are unknown. In defining the serviceability requirement, the latest LRFD code (AISC, 2001) states “Deformation in structural members and structural systems due to service loads shall not impair the serviceability of the structures.” The reference value for the fatigue-related problem has yet to be. The information on critical crack size or the damage accumulation function has yet to be developed (Zhao et al., 1994). Time-dependent reliability has been generally overlooked.
Simulation will enable estimation of the system reliability or the system’s limit state, nonlinear behavior, the location of a structural element in a complicated structural system, correlation characteristics of random variables, etc. However, it is unable to estimate reliability if the reference values are known. The outcome of the simulation could be different depending on the number of simulation cycles and the characteristics of computer-generated random numbers. One fundamental drawback is the time or cost of simulation. Huh and Haldar (2001) reported that simulating 100,000 cycles in a supercomputer (SGI Origin 2000) to estimate the reliability of a one-bay two-story steel frame subjected to only 5 second of an earthquake loading may take more than 23 hours. The efficiency of simulation can be improved by using variance reduction techniques (VRTs), which can be grouped in several ways (Haldar and Mahadevan, 2000a). One approach is to consider whether the variance reduction method alters the experiment by altering the input scheme, by altering the model, or by special analysis of the output. The VRTs can also be grouped according to description or purpose (i.e., sampling method, correlation methods, and special methods). Haldar and Mahadevan (2000a) noted that VRTs increase the computational difficulty for each simulation, and a considerable amount of expertise may be necessary to implement them. The most desirable feature of simulation, its basic simplicity, is thus lost.
Based on the above discussions, it is clear that the simulation approach provides a very reasonable alternative to the commonly used codified approach. However, there are still some issues need to be addressed before it can be adopted. Issues related to the efficiency and accuracy of the deterministic algorithm to be used in simulations, the appropriate way to quantify the randomness, information to be used to define the statistical characteristics, defining appropriate performance functions and the selection of reference values, evaluating correlation characteristics of random variables present in complex systems, simulation of random variables versus random field, simulation of multi-variate random variables, system reliability, the effect of load combinations, time dependent reliability, available software to implement the simulation-based concept, etc., need further evaluation. Documentation of case studies will also help in this endeavor. It is expected that this world body of distinguished scholars on reliability-based design will help to formulate the future direction in simulation-based design.
It is appropriate to address some difficult but important questions on simulation-based reliability evaluation and engineering design. Some of representative questions and the author’s opinion are listed below.
5.1 Is the simulation-based design concept mature enough to be considered as an alternative to the currently available codified approach?
In this author’s opinion, yes. Simulation-based design has not been fully developed at this stage, but this provides more flexibility in implementing the concept.
5.2 At present, should engineers have the option to use either the simulation-based approach or the codified approach?
Theoretically, designers should have the option to use either approach. In the Czech Republic, the simulation-based design option is now available (CSN 73 1401-1998 - Appendix A). However, the non-uniqueness of the design outcomes will be a problem for a regulatory agency responsible for approving the design.
5.3 What should be the mechanism to convey designers’ preferences to a governing body responsible for maintaining the overall safety of structures?
During the transition period, designers should submit designs using both the codified and simulation-based approaches. As the time passes and the governing body becomes familiar with the simulation-based approach, the codified design may not be required. This learning process could take several years.
5.4 If simulation-based design is accepted as an alternative approach to satisfy current requirements, which organization(s) should provide leadership in distributing information on uncertainty in parameters, software, and technical support? Should this support be available at the local, national, or international Level?
In the current applications of the codified approach, each country has its own design code. Extending the idea to simulation-based design, each country should have its own guidelines. Software and technical support could be provided at the national level, but this approach may be more appropriate for smaller countries than for larger ones.
5.5 What is the future of simulation-based design considering the advancement in computer and information technology?
Extensive use of information technology is necessary to implement the simulation-based design concept. It can be used in the following way. The characteristics of a random variable should be stored at the national level, and any designer should have access to that information at any time. To assure the success of simulation-based design, some benchmark case studies should be archived at the national level for use in testing the skill of designers.
Simulation is an attractive option in engineering design that needs to be explored. But a transition period will be necessary before it can become the only alternative to implement the risk-based engineering design concept. Active involvement of scholars from all over the world is necessary to implement it.
[1] American Institute of Steel Construction, Manual of Steel Construction, Load and Resistance Factor Design, 3rd Edition, Chicago, IL, 2001.
[2] Bjorhovde, R., Galambos, T.V., and Ravindra, M.K., “LRFD Criteria for Steel Beam-Columns,” Journal of the Structural Engineering, ASCE, 104(9), 1371-1388, 1978.
[3] Czech Institute of Standards, CSN 73 1401-1998 Design of Steel Structures, Prague, Czech Republic.
[4] Elishakoff, I., “Essay on the Role of the Monte Carlo Method in Stochastic Mechanics,” Monte Carlo Simulation, Schueller & Spanos (Editors), Balkema, Rotterdam, 619-627, 2001.
[5] Haldar, A., and Mahadevan, S., Probability, Reliability And Statistical Methods In Engineering Design, John Wiley & Sons, New York, NY, 2000a.
[6] Haldar, A., and Mahadevan, S., Reliability Assessment Using Stochastic Finite Element Analysis, John Wiley & Sons, New York, NY, 2000b.
[7] Huh, J., and Haldar, A., “Stochastic Finite Element-Based Seismic Risk Evaluation for Nonlinear Structures,” Journal of the Structural Engineering, ASCE, 127(3), 323-329, 2001.
[8] Marek, P., Guštar, M., and Anagnos T. Simulation-Based Reliability Assessment for Structural Engineers. CRC Press, Inc. Boca Raton, Florida, 1995.
[9] Lewis, P.A.W., and Orav, E.J., Simulation Methodology for Statisticians, Operations Analysts, and Engineers, Vol. 1, Wadsworth & Brooks/Cole Advanced Books & Software, Pacific Grove, California, 1989.
[10] Mahadevan, S., and Haldar, A., “Stochastic FEM-Based Validation of LRFD”, Journal of Structural Engineering, ASCE, 117(5), 1393-1412, 1991.
[11] Popper, K.R., The Open Universe, Hutchinson, London, 1982.
[12] Zhao, Z., Haldar, A., and Breen, F.L., "Fatigue Reliability Evaluation of Steel Bridges," Journal of the Structural Division, ASCE, 120(5), 1608-1623, 1994.