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Running the Numbers

SwRI-developed software helps simplify reliability predictions of complex systems

By David S. Riha, Ben H. Thacker, Ph.D. and Jason B. Pleming

SwRI NESSUS developers are (from left) Research Engineer Jason B. Pleming, Manager Dr. Ben H.Thacker and Principal Engineer David S. Riha, all from SwRI’s Mechanical and Materials Engineering Division. Their work experience and interests are concentrated in computational mechanics with an emphasis in probabilistic analysis methods, structural reliability, model validation and computer methods development. Recent applications include aerospace, automotive, biomechanics, geomechanics and weapons systems.

Numerical simulation, or the use of numerical methods to quantitatively represent a physical system, is increasingly becoming the method of choice for reliability studies involving complex, large-scale systems such as the space shuttle. The same methods can be applied for simulating complicated events such as an automobile collision. 

Probabilistic analysis accounts for such uncertainties as the physical environment, manufacturing conditions and material quality that have a direct impact on the variation of a system’s performance. The approach allows analysts to predict the reliability of engineered systems and identify important design and manufacturing variables for unique or expensive systems that are impractical or impossible to test. It also is used for predicting the reliability of products manufactured in large numbers, where warranty costs are prohibitive or unacceptable for high failure rates, or where small changes in the manufacturing process while maintaining a quality standard can lead to substantial cost savings.

Southwest Research Institute (SwRI) has been addressing the need for efficient probabilistic analysis methods for nearly 20 years, beginning with the development of the NESSUS® (Numerical Evaluation of Stochastic Structures Under Stress) probabilistic analysis computer program. Recently, SwRI has focused on improving the NESSUS software to reduce the learning curve required for defining probabilistic problems, improving support for large-scale numerical models and increasing the robustness of the underlying algorithms. NESSUS can simulate uncertainties in loads, geometry, material behavior, and other user-defined random variables to predict the response, reliability and sensitivity measures of systems.

Analysts are developing higher-fidelity models that more closely represent the actual behavior of a system. Finite element models with millions of elements are not uncommon and often involve multiple coupled physics such as solid mechanics, structural dynamics, hydrodynamics, heat conduction, fluid flow, transport, chemistry and acoustics. Even with the remarkable advances in  computer speeds, simulations performed with these  high-fidelity models can take hours or days to complete a single deterministic analysis. Because probabilistic analysis methods require repeated deterministic solutions, efficient methods are needed.

NESSUS is being used to quantify the risk of cervical spine injury to aviators during ejection and other high-g maneuvers. A computational approach is required because experiments of many scenarios of interest are impossible on human subjects. The project is being sponsored by the Office of Naval Research.

NESSUS Probabilistic Analysis Software

NESSUS is a general-purpose tool for computing the probabilistic response or reliability of engineered systems. SwRI researchers initially developed the software to help NASA assess uncertainties in critical space shuttle main engine components. The NESSUS framework allows the user to link traditional and advanced probabilistic algorithms with analytical equations, external computer programs including commercial finite element codes, and general combinations of the two. Eleven probabilistic algorithms are available including traditional methods such as Monte Carlo simulation and the first-order reliability method (FORM) and advanced methods such as the advanced mean value (AMV) and adaptive importance sampling (AIS). In addition, NESSUS provides a hierarchical modeling capability that can link different analysis packages and analytical functions. Once the probabilistic response is quantified, the results can be used to support risk-informed decisions regarding system reliability. 

Most engineering structures fail according to a complex pattern in which the nonperformance of one component, or a combination of events, leads to a system failure. System reliability assessment, which considers failure of multiple components or multiple failure modes of a single component, is available in NESSUS via a probabilistic fault tree analysis method. The failure of the system is defined through the fault tree by defining failure events and their combination with “AND” and “OR” gates. Each failure event considers a single failure event (component reliability), which can be defined by a finite element model or analytical function. 

In the NESSUS graphical user interface, an outline structure is used to define the elements required for the problem setup and execution. The user navigates through the nodes of the outline to set up the problem, define the analysis and view the results.

One of the most powerful features of NESSUS is its ability to link models together in a hierarchical fashion. In the problem statement window, each model is defined in terms of input/output variables and mathematical operators. This canonical description improves readability, conveys the essential flow of the analysis and allows complex reliability assessments to be defined when more than one model is required to define system performance. This hierarchical capability provides a general equation form to define performance by linking results from numerical analysis programs and analytical equations. 

Random variable statistics are defined in the random variable definition window in NESSUS. Tabular input is provided for distributions requiring parameters other than the mean and standard deviation, such as upper and lower bounds for truncated distributions. The probability density and cumulative distribution function plots provide a visual check of the defined random variable. 

Any function defined in the problem statement is assigned in the response model definition. The available definitions include regression, numerical and predefined models. The numerical model definition allows the use of finite element solvers, such as ABAQUS®, ANSYS®, NASTRAN® or a user-defined analysis program. The regression model definition allows input of function coefficients or datasets that can be fit using linear regression to standard functions. For example, the regression model allows for the use of experimental data to define a part of the system response. Finally, the predefined model definition allows the user to link user-programmed subroutines with NESSUS.

NESSUS was used to evaluate the reliability of a blast containment vessel. The probability of failure contours (right) indicate regions of critical importance in the design not identified by the worst-case deterministic plastic strain contours (left). The study was conducted in conjunction with the Los Alamos National Laboratory.


In 1999, Los Alamos National Laboratory contracted with SwRI to adapt NESSUS for application to extremely large and complex weapon reliability problems. In 2002, SwRI was contracted by the NASA Glenn Research Center to further enhance NESSUS for application to large-scale, aero-propulsion system problems. These two large programs resulted in the release of NESSUS Version 8.2, which earned a 2005 R&D 100 Award from R&D Magazine. This retooled version now includes a sophisticated, Java-based graphical user interface, three-dimensional probability contouring and results visualization, capabilities for performing advanced design of experiments and sensitivity analysis, a probabilistic input database and state-of-the-art interfaces to many new third-party codes including ABAQUS, ANSYS, LS-DYNA®, MSC.NASTRAN® and ParaDyn.

One of the distinguishing capabilities of NESSUS 8.2 is the large number of predefined interfaces to external analysis programs that allow organizations to exploit the investment and expertise in using their chosen deterministic analysis packages to evaluate reliability. NESSUS is also tailored to include customized interfaces to organization-proprietary packages. These interfaces allow the appropriate analysis program to be used to predict model response, utilize existing models for reliability quantification, and exploit corporate expertise and investment in using a specific analysis program.

NESSUS 8.2 is now easier to use and more robust with the recent addition of the graphical user interface to assist with problem definition, error checking and results visualization. With the addition of efficient probabilistic analysis methods and capabilities for interfacing to large-scale performance models, NESSUS provides a practical tool for predicting reliability to support decisions involving cost- or safety-critical problems for a wide range of engineered structures. 

The NESSUS software is particularly useful for large, complex calculations, such as simulating a small car colliding with a larger vehicle. Using a model that can predict the reliability of vehicle safety based on multiple failure modes can reduce expensive crash testing, quantify reliability and provide manufacturing and material cost versus crashworthiness metric tradeoffs.

In Use Worldwide

Government agencies, industry and universities are currently using the NESSUS software. Some current applications of NESSUS include aerospace structures, automotive structures, biomechanics, gas turbine engines, geomechanics, nuclear waste disposal and packaging, offshore structures, pipelines and rotordynamics. 

The software has been used to determine the risk of turbine rotor fracture in jet engines; to assess the long-term safety of the nation’s first underground, high-level radioactive waste repository; to reduce the time and cost required to certify gas turbine engine designs; and to quantify reliability of engine components and the thermal protection system of the space shuttle. NESSUS has also been used to quantify the risk of cervical spine injury to aviators during ejection, to develop a mathematical model that provides realistic simulations of vehicle crashes, and to quantify the reliability and identify important design parameters of an internal combustion engine crankshaft.

More than 1,500 copies of the NESSUS software have been distributed to organizations in more than 30 countries. In addition to some of the government and industry applications listed previously, NESSUS is used extensively by universities for both research and teaching. Several SwRI technical divisions also use the NESSUS software and technology in support of their programs. Information about licensing the NESSUS software, probabilistic technology support and additional application examples can be found on the NESSUS website,

Every year since 1990, SwRI researchers have offered a four-and-a-half- day short course on probabilistic analysis and design based on the technology and the application of the NESSUS software. To date, more than 500 engineers, scientists and technical managers have participated.


NESSUS Version 8.2 is already having a significant positive impact for users in government, industry and academia. In addition to application to nuclear weapon certification for three U.S. Department of Energy laboratories, NESSUS Version 8.2 was recently used to address a space shuttle return-to-flight issue for the NASA Engineering and Safety Center (see article on Page 2). The software is also being used to solve engine design issues for the automotive industry and to assist in the design of safety systems for U.S. Navy aviators. Since the launch of the NESSUS website in 2002, there have been hundreds of free downloads of the demonstration version, some of them by students performing research in probabilistic mechanics. NESSUS is also being used in formal university courses throughout the world to teach probabilistic design. 

Comments about this article? Contact Riha at (210) 522-5221 or; Thacker at (210) 522-3896 or

NESSUS earns 2005 R&D 100 award

On October 20, a team of researchers from SwRI, NASA Glenn Research Center, Mustard Seed Software and Los Alamos National Laboratory will receive a 2005 R&D 100 award for NESSUS 8.2, a commercial version of the NESSUS software code. Each year, R&D Magazine selects 100 significant technological achievements of the past year to receive the awards. SwRI has won 29 R&D 100 awards since 1971.

“NESSUS 8.2 is a practical tool for assessing uncertainties and predicting reliability to support decisions involving cost- or safety-critical problems,” said Dr. Ben Thacker, manager of SwRI’s Reliability and Materials Integrity Section. “It is particularly useful for extremely large and complex problems and for one-of-a-kind systems, where testing is impractical or impossible. The development of NESSUS has been a team effort involving many very talented people. We’re very proud of this award.”

NESSUS 8.2 was used recently in the space shuttle return-to-flight program for the NASA Engineering and Safety Center to develop probabilistic and deterministic fracture mechanics models to quantify the reliability of a flowliner in the space shuttle main engine. NESSUS also was used to investigate the influence of uncertainties on the transport and impact of debris on the thermal protection system during shuttle ascent.

Thacker said the name NESSUS stands for “Numerical Evaluation of Stochastic Structures Under Stress.” However, the name may have other origins as well. Dr. Joao Diaz, an early NESSUS team member, is thought to have influenced the name. His doctoral dissertation refers to a character in the novel Ringworld named Nessus: “[He] is an alien spacecraft pilot with an almost obsessive preoccupation for anything that might hinder his own safety and well being.”

Published in the Summer 2005 issue of Technology Today®, published by Southwest Research Institute. For more information, contact Joe Fohn.

Summer 2005 Technology Today
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