Speeding Up the Wheels of Change

New symbolic-based modeling technologies can help companies stay in the race

click to enlarge Figure 1: An example of a physical system model that was created using traditional signal-flow based simulation tools |

We have seen our share of bad economic news in recent weeks, as foreclosures, corporate bankruptcies and government bailouts have dominated the headlines. The automotive industry, one of today’s most competitive fields, is being similarly affected. As consumers deal with higher fuel costs and the effects of inflation and possible recession, they are beginning to scrutinize their buying decisions more and more carefully.

It’s just not enough anymore to build the fastest and most reliable car on the road; it also has to be the most fuel-efficient and cost-effective. Competition is fierce, and the buying public wants these new products now. The result is enormous pressure on the engineers tasked with producing new designs that will appeal to today’s consumers.

**Reducing time-to-market**

An industry expert with Toyota Motor Corporation, one of the world’s leading automobile companies, has confirmed that what limits the company’s growth is how quickly it can bring new products to market. Physical modeling and simulation techniques are key factors in reducing time-to-market. The concepts of physical modeling and model-based development are not new; sophisticated computer models are created to represent and simulate physical engineering systems. Testing and analysis of the model can be performed well before the physical prototyping phase, allowing designers to isolate problematic behavior and develop solutions in the early stages of the process. This translates into both time and cost savings, crucial ingredients to a company’s success.

click to enlarge Figure 2: A free body diagram for a simple spring-mass-damper system |

Many software tools are available to assist in generating virtual prototypes of systems. Based on a signal-flow concept, they address the challenges of numeric simulation. However, although these modeling tools were revolutionary when they were introduced, they do not adequately address today’s demands. The modeling environment they present to an engineer is not intuitive and is difficult to use. Signal-flow design works very well with control systems design but quickly reaches its limits when applied to physical modeling.

In order to use these traditional modeling tools, a user must first manipulate the physical system into a form that the software recognizes. This generally involves a great deal of time manually deriving mathematical equations to represent the system. Such derivations are time consuming, error prone and require advanced mathematical knowledge.

For example, even when working with something simple like a spring-mass-damper system, manually deriving the system equations is a lengthy process. A spring-mass-damper model is commonly used to represent components in mechanical systems, such as a vehicle suspension or connected bodies like train cars, allowing the systems to be modeled using basic second-order differential equations. However, before you get to the point of simulating this simple system and extracting valuable design information, you must first

• draw the free body diagram and extract from it mathematical relationships between the physical components

• derive the differential equations for the system

• convert these to integral form

• break these equations down to represent blocks.

click to enlarge Figure 3: Symbolic-based physical modeling tools, like the MapleSim graphical working environment, allow engineers to represent the system graphically. |

In addition, the resultant block diagram looks nothing like the original system representation. Several pages of derivation are required just to go from a free body diagram to the simple differential equation. If you consider applying this process to, for instance, the design of a hybrid vehicle steering system, the time spent and the resulting frustration become unacceptable in today’s fast-paced market.

**Faster, smarter designs**

The reality is that traditional signal-flow based simulation tools have not stood the test of time. As the complexity of today’s engineering models continues to advance in orders of magnitude, change is obviously required in order to stay competitive. History has shown us time and again how adversity and necessity are catalysts for innovation. The wheel, arguably the most famous invention of all time, no doubt came into being in response to early man’s need for transportation, not only of people but of goods. Similarly, today’s early adopters are looking into ways they can address their need for faster, smarter designs.

Mainstream engineers in Europe have begun to adopt next-generation modeling techniques, and engineers in North America also are beginning to consider how this new approach can help in their own physical modeling work. These techniques are based on a symbolic mathematical approach to physical modeling. Unlike purely numeric computation techniques, symbolic-based approaches automatically generate the equations representing the physical system, allowing users to extract meaning and insight about the model that would not be available otherwise. This can make all the difference and help to create better designs. In addition, symbolic simplification techniques are used to reduce the complexity of the resulting systems of equations in order to make even large systems tractable. Simulation speeds can increase by a factor of 10 as a result.

Symbolic-based physical modeling tools, like the multi-domain simulation software MapleSim from Maplesoft, allow engineers to represent the system graphically, using intuitive components such as gears, moving joints, pneumatic tires or electric circuit representation, making them easier to build and to understand. Engineering designs are described using components that represent their actual physical counterparts: electric circuits are built using resistors and inductors, and mechanical transmissions are built with gear sets and drive shafts.

A broad range of physical components across several physical domains is provided, including

• rotational and translational mechanics

• analog, digital, and multiphase electric circuits

• multibody mechanics

• thermodynamics

click to enlarge Figure 4: In a multibody system, engineering designs are described using components that represent their actual physical counterparts. |

These discrete physical components contain information about which physical laws they must obey, and two connected components exchange information about what physical quantities (such as energy, voltage, torque, and heat and mass flows) must be conserved. It is impossible to connect two components if it doesn’t make sense, since the application “knows” which domains and components make sense together. Traditional signal-flow blocks also can be incorporated and simulated, allowing users to build the model for both controller and physical system in the same environment.

The learning curve of such tools is much lower and faster than that of traditional modeling tools, and the design process is sped up considerably. Next-generation physical modeling tools handle the grunt work and allow the engineer to focus on what they do best — being creative, designing innovative products and solving challenging problems.

**The bottom line**

Finally, let’s consider how this affects the bottom line. How much time does a designer have to spend setting up his or her model before getting all the information needed for analysis and simulation? Because model equations are automatically generated from the graphical representation, the equations that define the components’ behavior do not have to be derived or entered manually. All of the necessary relational, physics and mathematical information for complex systems is automatically captured and managed, making it easier to develop efficient, high-fidelity models.

Since the system equations are generated symbolically, these complex models can be simplified automatically using sophisticated symbolic techniques such as automatic substitution, algebraic simplification and differential elimination before they are solved numerically, yielding concise models and high-speed simulations of sophisticated systems. All of this adds up to incredible time savings, which can range from a few days to many months, depending on the project.

Known for its innovative design philosophy and strong sales, Toyota is one company that is realizing the benefits of these new technologies: producing better products and dramatically shortening the product development cycle. It has entered into a multi-year partnership with Maplesoft to produce advanced physical modeling tools that are built on top of MapleSim modeling and simulation software. By describing the complex, acausal relationships of a physical model in a clear and efficient way, MapleSim and related tools enable simplification and optimization, taming the complexity of large models and reducing development and testing time.

These tools will help Toyota redesign its Model-Based Development process. The intent of this new process is to improve time-to-market and reduce cost, while maintaining high quality and reliability standards. Tools developed by Maplesoft will provide the fundamental mathematical framework for physical modeling within the new process. All areas of engineering development such as engines, transmissions, suspensions, braking systems, climate control systems and in-vehicle electronics stand to gain from the use of the new set of modeling tools. Similar benefits are to be realized in other industries.

This is merely the beginning of a sea change in the engineering world, which will become more and more evident in the coming months. Those who are taking advantage of the new symbolic-based modeling technologies are already realizing how much more efficient their work can become, with improvements in cycle times, cost optimization and smoother implementation of extremely complex systems. So far, engineers in all industries have been extremely successful in designing and building outstanding products. However, this does not guarantee future accomplishments in a fast-paced environment where system complexity continues to increase. By making sure that the ‘pit crew’s’ toolkit is fully equipped with the latest technology, companies stand a much better chance of staying in the race.

*Laurent Bernardin is Vice-President of Research and Development and Chief Scientist at Maplesoft. He may be reached at editor@ScientificComputing.com.*