sealPurdue News

November 4, 2002

Engineers create simple method for analyzing car designs

WEST LAFAYETTE, Ind. – Mechanical engineers at Purdue University have discovered a simple and speedy method for pinpointing and fixing design flaws in new cars.

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Douglas E. Adams, an assistant professor of mechanical engineering at Purdue, said he stumbled across a mathematical solution to a design bottleneck in automotive engineering. Engineers now have to rely on complex, time-consuming mathematical models to solve design problems in new cars that are soon to begin rolling off the assembly line.

Those mathematical models can take months to develop, yet they often miss essential details that are critical to accurately diagnose design problems.

"At the same time, companies usually don't have months to solve a problem," Adams said. "They need to find a solution within a few weeks."

There is, however, a simple alternative to these complex models, said Adams, who has conceived of a new experimental approach for analyzing design problems that avoids the time and expense now involved in conventional methods. The new technique drastically simplifies the mathematics used in conventional models, yet it can more accurately pinpoint design flaws.

Other researchers have developed similar techniques for relatively simple components. Adams and mechanical engineering graduate student Chulho Yang have expanded those earlier techniques, and they can apply their method to data from vehicle road tests performed by the automotive industry.

The new method developed by Adams, Yang and a team of engineers working for a company called ArvinMeritor Inc., in Columbus, Ind., takes a couple of days to set up in the lab and can then be used to test a car or one of its components within a matter of minutes.

The engineers demonstrated how their technique outperformed models in diagnosing a vibration problem in an economy car built by a major automotive manufacturer. Findings about the new method were detailed in a research paper presented Oct. 15 during the 39th Annual Technical Meeting of the Society of Engineering Science at Pennsylvania State University. The paper was written by Adams; Yang; Sung-Woo Yoo, a research engineer, and Han-Jun Kim, former director of systems engineering, both at ArvinMeritor, which manufactures automotive products.

The technique they have developed enables engineers to search for design flaws affecting a particular component even if the flaw originates in a different component.

"Sometimes the root cause for a problem with an exhaust system, for instance, originates outside of the exhaust system," Adams said.

The research team documented just such a scenario, in which a design change in a car's suspension system resulted in excess vibration in the exhaust system.

"The exhaust system hangs underneath the frame of an automobile and the suspension interacts with the exhaust system," Adams said. "If you change the suspension and you don't tell the exhaust system people about it, you are likely to introduce a problem in the exhaust system that looks like it was the exhaust system's fault but really is a suspension system issue."

An automaker faced with such a dilemma has to fix the problem quickly before the new car model begins rolling off the assembly line. Excess vibration can result in a noisier ride and eventually causes material fatigue and breakdowns.

"'Do no harm,' is the first rule of vibration control," Adams said. "You have to be able to make a change to one part of the system to mitigate the problem but not introduce other problems that we didn't have in the first place."

Engineers now use complicated models in which numerous car parts are represented by mathematical expressions that must take into consideration many precise mechanical details. The models have to include information such as the mass of components, their stiffness and dampening characteristics, and the exact forces involved. These models are themselves flawed, however, because they rely on approximations about the characteristics and interactions of automotive parts.

"If any of those approximations are incorrect, as they are for instance when mechanical joints or other complex components are involved, the model will fail to pinpoint the most efficient solution to the design problem by either missing a design alternative or proposing one that introduces other problems not predicted by the model," Adams said. "A major difference in our method is that we don't use approximations. We have found that you don't need to know all of those parameters. In fact, the only thing you need is a vibration measurement itself. We take measurements, and we use those raw measurements as a means to pinpoint the problem."

The engineers use sensors, called accelerometers, to record vibration. The sensors are placed at several key locations or on certain components on the car and the system is rocked back and forth with devices called "shakers," causing vibration. Sensors record the system's response to the vibration.

Data collected by the sensors are then used in a series of formulas in the models. Conventional models require a complex mathematical technique known as the "inverse approach." The approach makes it possible to incorporate vibration data into a mathematical model. Then, once a portion of the car – such as its exhaust system – is represented as a mathematical model, changes can be made to the model in attempts to predict how to fix problems.

"Think of it as sort of a middleman," Adams said. "You have a system and you have a model that you are trying to use to represent the system. You take data and then use the inverse approach to develop the experimental model.

"We are avoiding the inverse approach altogether, and that results in a big time savings," he said. "Of course, these complex models are often needed to do other kinds of important analyses in automotive-systems engineering, so we are not suggesting that the models should be discarded. However, in particular applications, a few measurements provided all the information needed to correct the problem."

The engineers used their technique to find the solution to a problem within an exhaust system for a new vehicle model that features a more sporty suspension than the standard model. The solution they found using their method proved to be better than the solution found with conventional models, which inadvertently introduced new design problems in the course of trying to correct the original problem.

"Testing is probably the most expensive part of the product research-and-development cycle," Adams said. "Our primary goal is to quicken the testing process by extracting very few measurements rather than an abundance of them."

The research has been funded by ArvinMeritor.

Writer: Emil Venere, (765) 494-4709,

Source: Douglas E. Adams, (765) 496-6033,

Related Web sites:
Society of Engineering Science Inc.

NOTE TO JOURNALISTS: An electronic or paper copy of the research paper is available from Emil Venere, (765) 494-4709,

Two sensors called accelerometers, seen attached in this photograph on the muffler and exhaust pipe, are used to record vibration. The sensors are placed at several key locations or on certain components on the car and the system is rocked back and forth with devices called "shakers," causing vibration. Sensors record the system's response to the vibration. Data collected by the sensors is then used in a series of formulas in models that require complex mathematics. Mechanical engineers at Purdue University, however, have developed a technique that uses the same vibration data without the complex mathematics to analyze problems in automotive designs. (Photo from Douglas Adams, Purdue School of Mechanical Engineering.)

A publication-quality graphic is available at


An Embedded Sensitivity Approach for Diagnosing System-Level Vibration Problems

Chulho Yang, Research Assistant,
and Douglas E. Adams, Assistant Professor
Purdue University School of Mechanical Engineering

Sung-Woo Yoo, Research Engineer,
and Han-Jun Kim, Director
ArvinMeritor, Systems Engineering

When diagnosing a system-level vibration problem, the goals are to identify which component or components are most responsible for the phenomenon and which changes to the system are most likely to mitigate the problem. The use of sensitivity analysis in diagnosing system-level vibration phenomena is examined in this work. A series of prototypical analytical examples including one, two, and larger degree-of-freedom linear system models are used to introduce the embedded sensitivity approach. It is shown that even if only one set of measured system input-output functions is available, an appropriate analytical parameterization of these functions leads to simple relationships between the measured functions and the desired embedded sensitivity functions. These relationships are a substantial finding because they suggest that although the inverse problem for source identification is ill-conditioned due to the correlation between the response characteristics of all the components at or near a mode of the system, there is nonetheless a means for identifying which components are more responsible for a given vibration phenomenon and the most effective design modifications for suppressing the problem. A simple five degree-of-freedom model is also used to explain seemingly contradictory test findings in an actual case study involving an automotive vehicle structure-borne noise problem, and the embedded sensitivity approach is used to examine design modifications for reducing that problem.

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