Graduate student Tong Zou and Professor Sankaran Mahadevan work through reliablity concepts.

Vanderbilt engineers spend a lot of time thinking about how to keep the unthinkable from happening.
       The Concorde crash, for instance. Or the Aloha Airlines flight in 1988 that turned a jet airplane into a convertible as the roof ripped off, pulling a stewardess out with it to her death. Or the Tacoma Narrows Bridge in 1940, which twisted in the wind and crumbled to the river below.
       Making sure that the equipment and structures we rely on are themselves reliable and functional is the purpose of the work of Associate Professor of Civil and Environmental Engineering Sankaran Mahadevan and his collaborators. His multidisciplinary teams have developed a set of techniques to predict safety and reliability with a high degree of confidence and at a much lower cost than is typically associated with traditional methods. These techniques can be used to improve maintenance and repair schedules and can ultimately lead to safer, more reliable and cost-efficient designs.
       This comprehensive set of analytical and predictive tools is unique to Vanderbilt, and many different private and governmental organizations are interested in applying the techniques to their products and processes.

Devising elegant solutions for complex problems
Finding alternatives to traditional reliability tests has become a practical necessity as equipment and structures have become more and more complex.
       "The original methods for determining reliability were based on running various tests on the equipment or structure being evaluated, which of course involved damage or destruction of several of the units," Professor Mahadevan says. "It's not practical to run physical reliability tests on large, complicated systems like the space shuttle or a suspension bridge, so we have to use mathematical models that can stand in for the real thing."
The models are developed by analyzing the product's physical characteristics and the ways the different components behave under varying conditions of temperature, pressure, load and other variables.
       Combining analytical approaches incorporated from physics, probability theory, optimization methods, mechanical and structural engineering, computer simulation techniques and many other disciplines, Professor Mahadevan's team can describe a predicted range of performance and reliability characteristics with a high degree of confidence.
       "The cornerstone of our method is what we call 'sensitivity analysis,' which we use to determine what parts of a system are most crucial to successful performance," Professor Mahadevan says. "The most sensitive components of a system are the parts that will make or break the system's mission, so those are the components we study in depth to make the prediction of the system's reliability."

Offering broad applicability
The analytical tools developed by the Vanderbilt engineers are being studied for application to a wide variety of systems (see box, below left). "In addition to aerospace and aeronautics structures, these techniques can be applied to engine structures; electronics equipment; civil structures such as buildings, bridges and hydraulic facilities and even organic systems such as rivers," Professor Mahadevan says.
       The team is currently working on a project for General Motors Corp. to develop safety and performance assessment tools to help the auto company improve its designs for car doors and for overall body integrity.
       The team will begin with an in-depth study of the door, focusing on the properties of the sealing material. "The material has to have the right amount of stiffness for the door to stick, but if it is too stiff the door will bounce back. If the material is too soft, it will leak. The properties of the material vary at different locations around the opening and respond to changing conditions of temperature and humidity. Also, the material changes over time. These are just a handful of the uncertainties we need to take into consideration," he says.
       Once the team's assessment is in place, GM can use the information to optimize its designs, creating the most workable and reliable equipment at the lowest cost.
       A companion project, funded by Sandia National Laboratories, combines analytical and test-based methods for cost-effective product reliability development.
       The Vanderbilt reliability assessment methods have already been tested and proven effective with helicopter rotor components made of composite materials, Professor Mahadevan says. "In the helicopter project we just completed for the U.S. Army, we found that by using our mathematical techniques we can predict the same level of reliability that can be determined by testing, at a much lower cost."

Assuring reliability in flight
Aircraft safety is a particular interest of Professor Mahadevan and his students, who are working on a major National Science Foundation (NSF) project expected to lead to better reliability prediction, inspection and repair procedures.
       An important part of the NSF project is a study of how corrosion affects aging aircraft and other structures. "Corrosion that begins in small pitting of aluminum and other materials can deteriorate further into cracks that can combine to cause a structure to fail," Professor Mahadevan says. "This phenomenon was responsible for the Aloha Airlines disaster. By making better predictions about the risks associated with corrosion, we can not only institute better maintenance procedures to prevent catastrophic failure, but we can make safer aircraft designs."

Teaching reliability techniques
Because of the method's flexibility and adaptability to many engineering systems, the techniques are being disseminated through the Internet and two new textbooks.
       The RELY interactive software program, funded initially by the NSF, enables students as well as other engineers to learn the array of reliability evaluation techniques the Vanderbilt team has developed. "With this software, we can show students how to use these techniques and give them more direct experience working with the concepts much more quickly than we were able to teach them using traditional classroom methods alone," he says.
       Engineers from around the world can access the same material from a World Wide Web site established last year. "It gives us a great deal of satisfaction to know that engineers are studying the methods we have developed to solve problems, create better designs and make important equipment and structures more safe, dependable and effective," Professor Mahadevan says.

 

RELIABILITY PROJECTS
-A SAMPLING-

National Science Foundation: Reliability analysis of aging structures-including bridges, pipes and aerospace equipment under corrosion, fatigue, wear and creep.

NASA: Reliability models for robust design (broad application); reliability analysis of solid rocket booster skirt; reliability analysis of solar concentrator to be used in space; consequence analysis models for instantaneous and progressive failures.

Sandia National Laboratories: Modeling and simulation for design accounting for uncertainty (broad applications); cost-effective reliability testing methods; mechanical reliability of electronic components.

General Motors: Application of reliability methods to assess safety and performance of automobile structures.

U.S. Army: Reliability assessment of helicopter rotor hubs made of composite materials.

Oak Ridge National Laboratory: Clinch River environmental restoration study of risk of contaminated sediment transport.

U.S. Department of Energy: Corrosion damage risk evaluation of structures in DOE sites.

National Science Foundation and Provost's Initiative on Technological Innovation in the Classroom: Development of RELY, Internet-based teaching software for reliability analysis.