MaplePrimes - MapleSim 1 Posts and Questions

Good Vibrations

Samir Khan — Thu, 04 Dec 2008 14:19:19 Z

Over the last few years, I’ve been lucky enough to spend time in Taiwan. In my first visit to Taipei, I was astounded by the sheer scale of the Taipei 101 skyscraper. At over 500m tall it dwarfed everything else in the skyline.

Given the proximity of many active fault lines, tall buildings in Taipei have a degree of earthquake protection engineered into them with a tuned mass damper .

Tuned mass dampers consist of a parasitic sprung mass connected in some way to a larger body, and are used to attenuate undesired vibrations. They’re tuned so that the natural frequency of parasitic sprung mass and the body it is connected to are similar.

The tuned mass damper at the top of the Taipei 101 building consists of a 780kg pendulum that’s supported on hydraulic cylinders at the top of the building. Here’s a video of it in action in May 08 when Taipei experienced the effect of an earthquake in China.

And this is a screengrab of a simplified MapleSim model of the mass damper in Taipei 101.

Tuned mass dampers have applications wherever undesired vibrations threaten the integrity of an engineered system. Renault, for example, fitted a tuned mass damper to their F1 car for the 2005 season. It was a sprung 9kg mass that attenuated the vibration of the chassis and the variation of the tire load as it road over bumps, and hence improved grip (it was later deemed illegal because it changed the aerodynamics of the vehicle).

Here’s a screengrab of a quarter car model created with MapleSim, with a tuned mass damper attached to the chassis.

MapleSim made creating both of these models remarkably simple. Instead of having to spend time deriving the system equations by hand, I simply connected the appropriate physical components together as they would appear on a schematic.

Because I can now concentrate on higher-order effects, I’m now developing higher-fidelity versions of both these applications. I’ll keep readers of this blog updated.

Repaying Old Debts

Tom Lee — Wed, 01 Oct 2008 20:33:16 Z

This weekend was reunion weekend for me. On Saturday I made the return journey to my alma mater, the University of Waterloo (i.e. I walked 10 minutes to the campus from my house), for the 20^th reunion of my Engineering Class of 1988. Among the various events and activities, I had the pleasure of having a sitdown chat with Professor Peter H. O’N. Roe, retired professor of Systems Design Engineering (my undergrad department) at the University.

Among the handful of people whom I can say were truly influential in my life, Peter was definitely one of the big ones. Among his academic achievements, he was a pioneer in a then fairly obscure field called “physical systems modeling”. His research in the late 1950’s and into the 1960’s laid the foundation of a modeling school of thought centered at the department of Systems Design Engineering. The concept was based on linear graph theory and proposed a mathematical framework for formulating the differential equations for a wide range of lumped parameter systems. It was approached from day one as a universal formalism for developing models of any lumped parameter system domain with clearly defined constitutive relationships based on physics.

I recall Peter’s SD 252 course in my sophomore year. Because this concept was still miles away from mainstream among the scientific community, we had no textbook – just thick Cerlox®-bound course notes prepared by him. I have to be honest … not all of his lectures were the stuff of excitement and inspiration ;-) I passed the course though and moved on and took a whole range of courses that were based on more orthodox engineering modeling paradigms and the path eventually led to grad school and beyond.

Through it all though, I always maintained a soft spot in my heart for Peter’s work. There is always something very elegant and grand about any theory that attempted to provide a unified theoretical foundation for a complex area of study.

Fast forward to September 29, 2008. I am preparing for a series of presentations in Europe on MapleSim (MapleSim presentations constitute a large proportion of my time these days) and I reflect on what MapleSim is: a generalized modeling environment for physical systems. Due to its Maple-based computation architecture, it is able to deal efficiently with the common mathematical framework that transcends lumped parameter physical system domains. Its symbolic engine also automatically generates and optimizes the required model equations. Based on this simple description, any thinking person should sense the connection between MapleSim and pioneering works by people like Peter.

The connection is actually more explicit, however. One of MapleSim’s particular strengths is its abilities in multibody mechanics – i.e. robots, complex moving parts in cars, etc. MapleSim’s multibody engine, in my opinion, is truly at the head of the pack and produces models that outperform models developed by other systems. Not surprisingly MapleSim’s multibody engine is based on linear graph theory and its implementation can be traced directly back to the body of work generated by Peter and his colleagues in his department. Much of the fundamental work in MapleSim’s modern implementation of linear graph-theoretic modeling is based on the work of another accomplished alumnus of the department, Dr. John McPhee, whose research refined linear graph theory techniques for a wide range of mechanical and mechatronic systems and, just as importantly, figured out how the theory adapts to modern computational frameworks like Maple’s symbolic computing.

In 1963, Peter was the first student to receive a PhD from the then nascent University of Waterloo. Within a scant few decades, this university became a world-class university in engineering, computing, and mathematics. WATFOR, the first Internet search engines, the Blackberry, and of course, Maple were among the many direct spinoffs of this institution. The university consciously engineered and continued to refine its reputation as highly innovative, creative, and even maverick in its approach to research and education.

In 1987, I was having coffee in a lounge when Peter walked in. A few pleasantries and chit chatty moments later, he basically talked me into applying for grad school. This is a significant moment because on the surface (i.e. based on my transcript), I would not have been considered the ideal candidate for advanced degrees, but Peter saw that I had genuine interest and respect for the work of the department and gave me the benefit of the doubt that I had a few off-days during my undergrad years ;-) For that I am eternally grateful.

Today, through my job, I’m a direct beneficiary of Peter’s research, as we prepare to introduce to the global community of engineers, more effective approaches to modeling – made more effective through techniques that exploit both the computational and expressive power of mathematics and made feasible and practical through the farseeing work of leaders like Dr. Peter Roe and it thrills me to no end that our products are the ones that are taking his legacy to market.

Today, Peter keeps busy by serving as the elected Alderman in the local government, as an active member of the Board of Governors of Renison University College (on which I too have the pleasure of serving), and as the continuing director in the international student exchange programs for the University of Waterloo. Oh, I guess I forgot to mention that Peter was a pioneer in exchange education as well.This posting is my long-overdue statement of thanks to my friend Peter.

Two solitudes

Tom Lee — Fri, 12 Sep 2008 18:33:16 Z

Yesterday I watched a demonstration of Maple being applied to the modeling and simulation of the internal deformations of human bones. The researcher was a mathematician working primarily in the biomedical modeling fields. The actual technique was to utilize the symbolic mathematical power of Maple to formulate the necessary equation pieces for a finite element model (FEM) of the internals of the bone. The equations are then fed into the legendary FEM solver ABAQUS.

Due to the notoriously non-linear qualities of human flesh and bone, traditional formulation methods developed for modeling beams and metals simply do not work. So as in the case of so many impressive engineering applications, the power of Maple is being deployed in the formulation or the pre-solution phase of modeling and in doing so, previously infeasible models now become feasible.

In many ways, the MapleSim concept embodies strong parallels. By applying more ambitious mathematics at the front end, greater complexity and performance can be achieved. The similarities, however, end there.

Thomas Kuhn (arguably the greatest modern thinker on philosophy of science) observed the growing communication gap among the various modern factions of the physical sciences, social sciences, and the humanities. Short of cocktail party chit chat, it is virtually impossible for two practitioners from different disciplines to collaborate in any meaningful way without a major investment of effort to learn their colleague’s “language”.

Within engineering, one of the most troubling (IMHO) divides is that between the lumped parameter modeling world, and the continuum modeling world. The lumped parameter people (which currently includes those of us cheering for MapleSim) work with a reduced view of the system details to get a sense of overall behavior -- so a component’s mass would be lumped into one number and a stick figure and forces only apply at singular points. The continuum people (like our bone-modeling friend) are interested in the intimate details – internal stresses, flow patterns of fluids around objects, etc. Mathematically, lumped people use ordinary differential equations (ODEs), continuum people use partial differential equations (PDEs).

Computationally, both solitudes have their own favorite tools and over time, well-known companies became large and wealthy by supporting the respective worldview with more and more specialized features and techniques. We now have weapons of mass computation ready to deal with any problem that comes its way … as long as it’s posed in the precise way that these tools (and their inventors) understand.

As we continue to look forward at our own plans for Maplesoft modeling tools, this is one of the fundamental challenges that we want to address. How can we provide a richer modeling environment that properly integrates the respective advantages of the lumped and continuum worlds. Success in this would take the whole notion of virtual modeling or model-based design to a new level of efficiency and effectively. This is a daunting challenge and so far the few examples that exist are really “plumbing” examples – i.e. how do you get data flowing from one side to another but the necessary scientific formalisms for integrating the two perspectives still needs substantial refinement.

If the world’s problems were solved by optimism alone, I’d say we’re in pretty good shape. The good news is, we are not part of the traditional pool of players in either lumped parameter modeling or continuum modeling. So we’ve had the opportunity, indeed luxury, of fresher thinking on the needs of next generation modeling. More good news, our user base has all sorts of people so we tend to draw guidance from a very diverse and creative bunch. And still more good news – if it’s absolutely necessary for you to delve into some mathematical concepts from other fields, having a vast array of symbolic math tools is a godsend when you try to sort through unfamiliar techniques. So the optimism is not formed in a vacuum – I think we have some pretty solid raw material to work with.

Kuhn also got us talking about “Paradigms” and “Paradigm Shifts”. Everyone was so impressed by these words that we’re now numb from overuse. We’ll use the terms in light conversation for the silliest things. My cat has moved from canned food to dry food … what a paradigm shift that was! If we succeed in producing effective modeling tools that properly integrate lumped and continuum view points, I think it may be a candidate for the title of paradigm shift. It’s relatively easy for us to further categorize and further divide complex contexts but bringing seemingly disparate contexts together into a better whole is far more difficult. But I was always taught that bringing people and ideas together was a good thing to do and I’m proud that Maplesoft is making a real attempt at doing this.

Postcards from the road: Part 1 -- On rocket science

Tom Lee — Mon, 08 Sep 2008 15:38:29 Z

One of the greatest pleasures of my job is meeting users and learning first hand of their achievements (hopefully with our products). Last week was a particularly eventful week and a distinct highlight was a visit our friends at the Canadian Space Agency (CSA) in Montréal.

Every kid who dreams of becoming an engineer probably has thought romantically about space at one time or another. At least for me, growing up with Apollo lunar missions and Skylab, space exploration defined engineering. So any time I get a chance to meet with real rocket scientists about Maplesoft matters, I get a double thrill. First, it’s about space, and second it’s about how our technology has played a key role in modern space exploration. The most prominent examples are the various space robots designed by the CSA for both the Space Station and shuttle missions. The famed Candadarms I and II and more recently, DEXTRE, are some of the most complex robots the world has ever produced and the models required to simulate these systems were generated with Maple-driven software produced by the CSA (see [CSA User Story]).

By now, you’ve probably been suitably bathed in the first generation of product info on MapleSim – automatic model equation generation, high performance multidomain simulations, and advanced multibody dynamics applications, etc. Prior to the introduction of the MapleSim concept were various engineering groups exploring these advanced modeling concepts on their own and the CSA was arguably the most active users of Maple in this sense.

Long before the days of rich GUI environments and push button simulation of MapleSim, CSA engineers programmed an impressive set of custom tools in Maple to generate highly complex models of space arms that included dozens of degrees of freedom – a task that was basically impossible to do by hand or with whatever software was then available. But with some imagination and a solid command of the capabilities of the Maple system, they were able to get the job done and in the end delivered a critical component that ensured the success of so many manned space missions.

For me, the success of the CSA with Maple technology is more than an interesting user story though. It’s really about validation of new engineering and scientific ideas. About 15 years ago I had the pleasure of meeting one of the current senior managers within CSA at a meeting on applications of Maple in engineering. I recall the very spirited chats I had with him on these fancy notions of automatically deriving equations of motion for physical systems but at the time the thought of such techniques scaling beyond the idealized contexts of academic examples seemed like science fiction. But in this case, reality did catch up to art and our CSA colleagues literally went to heaven and back with these techniques.

Today, MapleSim represents the leading front of modeling science but it’s heartening to know that a lot of the more innovative elements have been built on a fairly long history of precedent applications and techniques pioneered for and by real engineers and scientists. A lot of our visit to the CSA centered on the modeling needs for very ambitious upcoming missions such as the return to the Moon or missions to Mars. This time though, it felt a lot better as we’re now working from a pretty solid foundation of dedicated modeling technology … so now it’s on to figuring out how to model warp drives, teleporters, and holodecks.

Coming of Age

Tom Lee — Wed, 03 Sep 2008 07:27:00 Z

Two very significant things happened last week. First, my son Eric turned 13. Second, I got a new car. These two milestones merged into a singularly great long weekend as Eric and did our very first father-son roadtrip to the great city of Cleveland. The car was the first new car my family had bought in about eight years, and as hard as I tried to maintain meaningful conversation with Eric through the many hours, I have to admit that my attention was frequently diverted to the car … thoughts of “hey … that’s a nice ride”, “so that’s what sport suspension feels like”, or “Yes Eric, that’s a very good question on the American election but … I wonder what that button does”.

Even in the scant eight years, it seems that cars have experienced major transformation. For essentially the same amount of money that I spent on my last car, my new scoot is a lot safer, handles like a dream, is packed with conveniences, and goes like a bullet :-D This machine seemed orders of magnitude better than my last car. As great as my new car is though, the engineers in Detroit, Tokyo, and Munich are starting to express some concerns about future directions. Cars today have to be more than great … they have to be great AND green AND affordable AND great looking AND deploy the absolute latest technology. Moore’s law predicted that computing power accelerates at exponential rates. With the sheer amount of electronics in the modern car I suspect that Moore is approaching in the rearview mirror at an alarming speed and all auto companies are beginning to assess their ability to innovate at 21^st century speeds.

I’ve tossed around the phrase “math matters” for many years now and in general, I’ve used it in context of the growing importance of mathematics in industry. As design challenges become more complex engineers are discovering the inherent limits of the current software toolchain deployed for the analysis and design of engineering systems. The automotive industry has historically been at the forefront of innovative application of software. CAD, PLM (product lifecycle management), MBD (model based design), are clear examples of this segment’s foresight in the past. Increasingly, auto industry leaders are looking to reboot the toolchain with fresh software thinking. And mathematics has emerged to be a major dimension in the emerging toolchain. Direct access and manipulation of the underlying model equations, advanced mathematical transformations and algorithms, are all becoming much more prevalent. The theory is, more clever and efficient management of foundational math will lead to solutions of more complex design problems and ultimately reduce the design time. And of course, shorter design time correlates directly to competitive advantage as amazing new features and functionality can roll out faster.

MapleSim, our newest offering fully embraces this movement towards a more sophisticated application of mathematics in engineering. By making the math more accessible and manageable, engineers can develop and optimize more advanced and higher-fidelity models in significantly less time. Since the announcement of MapleSim, I’ve had countless occasions to present the merits of our new approach to modeling to engineers and it has been nothing short of amazing to see the reaction. People just “get it”. With the traditional toolchain, the development of the required system model equations was a highly manual, or extremely abstract process. A survey that Maplesoft undertook with two thousand engineers, showed that the majority still wrestle with paper and pencil to deal with the underlying math for their simulations and models. MapleSim is a pretty straight forward concept: it automates the model derivation AND solution process. Through a combination of a graphical interface and new symbolic algorithms to manage the modeling math, it effectively reduces or eliminates the dependence on manual processes. This simple message seems to be resonating with industry.

As part of our roadtrip, we stopped by to meet a few magazine editors representing auto industry publications. Part of it was the demands of my job, of course, but secretly more of it was to show my son what his dad did for a living and what kind of exciting things the old man was involved in. I thought the meetings went very well with good dialog emerging. I asked Eric what he’d thought of the meetings and whether he had learned anything. He commented “that was a disaster! All the guy did was ask a million questions and you guys just ended up talking for over an hour.” Working engineers aside, the reaction of the press has been another source of pride for us. They have seen software come and go and they have a good sense of what’s truly new and what is spin and so far, they have been genuinely impressed and interested in following the evolution of these new techniques. So those “million” questions, to me, was the greatest expression of interest and the best I could hope for in a meeting with the press. All indications are that you’ll hear a lot more from them in the near future.

Perhaps it’s too much to expect a 13 year old to fully appreciate how the introduction of a non-linear term in a differential equation will leads to better stability control or acceleration in his car a decade from now. But it was very heartening to have some meaningful conversation about work issues with this young man. Perhaps if I had shifted the focus of my MapleSim examples away from suspension systems to signal processing innovations in car audio that will truly capture the transcendental heavy metal nuances of Metallica, I could have gotten a bit more of a positive reaction from my son.