Publications

In most probabilistic risk assessments, there is a set of accident scenarios that involves the physical responses of a system to environmental challenges. Examples include the effects of earthquakes and fires on the operability of a nuclear reactor safety system, the effects of fires and impacts on the safety integrity of a nuclear weapon, and the effects of human intrusions on the transport of radionuclides from an underground waste facility. The physical responses of the system to these challenges can be quite complex, and their evaluation may require the use of detailed computer codes that are very time consuming to execute. Yet, to perform meaningful probabilistic analyses, it is necessary to evaluate the responses for a large number of variations in the input parameters that describe the initial state of the system, the environments to which it is exposed, and the effects of human interaction. Because the uncertainties of the system response may be very large, it may also be necessary to perform these evaluations for various values of modeling parameters that have high uncertainties, such as material stiffnesses, surface emissivities, and ground permeabilities. The authors have been exploring the use of artificial neural networks (ANNs) as a means for estimating the physical responses of complex systems to phenomenological events such as those cited above. These networks are designed as mathematical constructs with adjustable parameters that can be trained so that the results obtained from the networks will simulate the results obtained from the detailed computer codes. The intent is for the networks to provide an adequate simulation of the detailed codes over a significant range of variables while requiring only a small fraction of the computer processing time required by the detailed codes. This enables the authors to integrate the physical response analyses into the probabilistic models in order to estimate the probabilities of various responses.

In most probabilistic risk assessments, there is a subset of accident scenarios that involves physical challenges to the system, such as high heat rates and/or accelerations. The system`s responses to these challenges may be complicated, and their prediction may require the use of long-running computer codes. To deal with the many scenarios demanded by a risk assessment, the authors have been investigating the use of artificial neural networks (ANNs) as a fast-running estimation tool. They have developed a multivariate linear spline algorithm by extending previous ANN methods that use radial basis functions. They have applied the algorithm to problems involving fires, shocks, and vibrations. They have found that within the parameter range for which it is trained, the algorithm can simulate the nonlinear responses of complex systems with high accuracy. Running times per case are less than one second.

If there should be an accident involving drainage of all the water from a spent fuel pool, the fuel elements will heat up until the heat produced by radioactive decay is balanced by that removed by natural convection to air, thermal radiation, and other means. If the temperatures become high enough for the cladding or other materials to ignite due to rapid oxidation, then some of the fuel might melt, leading to an undesirable release of radioactive materials. The amount of melting is dependent upon the fuel loading configuration and its age, the oxidation and melting characteristics of the materials, and the potential effectiveness of recovery actions. The authors have developed methods for modeling the pertinent physical phenomena and integrating the results with a probabilistic treatment of the uncertainty distributions. The net result is a set of complementary cumulative distribution functions for the amount of fuel melted.

There are important differences between the safety principles for nuclear weapons and for nuclear reactors. For example, a principal concern for nuclear weapons is to prevent electrical energy from reaching the nuclear package during accidents produced by crashes, fires, and other hazards, whereas the foremost concern for nuclear reactors is to maintain coolant around the core in the event of certain system failures. Not surprisingly, new methods have had to be developed to assess the risk from nuclear weapons. These include fault tree transformations that accommodate time dependencies, thermal and structural analysis techniques that are fast and unconditionally stable, and parameter sampling methods that incorporate intelligent searching. This paper provides an overview of the new methods for nuclear weapons and compares them with existing methods for nuclear reactors. It also presents a new intelligent searching process for identifying potential nuclear detonation vulnerabilities. The new searching technique runs very rapidly on a workstation and shows promise for providing an accurate assessment of potential vulnerabilities with far fewer physical response calculations than would be required using a standard Monte Carlo sampling procedure.

Because many of the phenomenologically based codes used to support risk assessments require lone execution times, it is important to have a rationally based means for optimizing the choice of parameter values that are input to the code calculations. For this reason, we have developed a method for intelligently searching the space of parameter values to deduce, with as few computations as possible, the values that are most likely to lead to high risk. We have applied the method to a problem involving electrical initiation of an explosive due to the response of the system to fires. We have shown that our method can locate potential risk vulnerabilities with far fewer time-consuming physical response computations than would be necessary using standard sampling approaches.

Accurate finite-element simulation of 3-D nonlinear heat transfer in complex systems may require meshes composed of tens of thousands of finite elements and hours of CPU time on today`s fastest computers. To treat applications in which thousands of calculations may be necessary such as for risk assessment or design of high-temperature manufacturing processes, methods are needed which can solve these problems far more efficiently and maintain an acceptably high degree of accuracy. For this purpose, we developed the Thermal Evaluation and Matching Program for Risk Applications (TEMPRA). The primary differentiator between TEMPRA and comparable codes is its numerical formulation, which is designed to be unconditionally stable even with very large time steps, to afford good accuracy even with relatively coarse meshing, and to facilitate benchmarking/calibration through the use of adjustable parameters. Analysis for a sample problem shows that TEMPRA can obtain temperature response solutions with errors of less than 10% using approximately 1/1000 of the computer time required by a typical finite element code.

In today`s world, accurate finite-element simulations of large nonlinear systems may require meshes composed of hundreds of thousands of degrees of freedom. Even with today`s fast computers and the promise of ever-faster ones in the future, central processing unit (CPU) expenditures for such problems could be measured in days. Many contemporary engineering problems, such as those found in risk assessment, probabilistic structural analysis, and structural design optimization, cannot tolerate the cost or turnaround time for such CPU-intensive analyses, because these applications require a large number of cases to be run with different inputs. For many risk assessment applications, analysts would prefer running times to be measurable in minutes. There is therefore a need for approximation methods which can solve such problems far more efficiently than the very detailed methods and yet maintain an acceptable degree of accuracy. For this purpose, we have been working on two methods of approximation: neural networks and spring-mass models. This paper presents our work and results to date for spring-mass modeling and analysis, since we are further along in this area than in the neural network formulation. It describes the physical and numerical models contained in a code we developed called STRESS, which stands for ``Spring-mass Transient Response Evaluation for structural Systems``. The paper also presents results for a demonstration problem, and compares these with results obtained for the same problem using PRONTO3D, a state-of-the-art finite element code which was also developed at Sandia.

There are major differences between the safety principles for nuclear weapons and for nuclear reactors. For example, a principal concern for nuclear weapons is to prevent electrical energy from reaching the nuclear package during accidents produced by crashes, fires, and other hazards, whereas the foremost concern for nuclear reactors is to maintain coolant around the core in the event of certain system failures. Not surprisingly, new methods have had to be developed to assess the risk from nuclear weapons. These include fault tree transformations that accommodate time dependencies, thermal and structural analysis techniques that are fast and unconditionally stable, and Monte-Carlo-based sampling methods that incorporate intelligent searching. This paper provides an overview of the new methods for nuclear weapons, compares them with existing methods for nuclear reactors, identifies some of their dual-use characteristics, and discusses ongoing developmental activities.