Toward a unified and automated design methodology for multi-domain dynamic systems using bond graphs and genetic programming
Introduction
Multi-domain dynamic system design differs from conventional design of electronic circuits, mechanical systems, and fluid power systems in part because of the need to integrate several types of energy behavior as part of the basic design. Multi-domain design is difficult because such systems tend to be complex and most current simulation tools operate over only a single domain. In order to automate design of multi-domain systems, such as mechatronic systems, a new approach is required [1]. The goal of the work reported in this paper is to develop a unified and automated procedure capable of designing mechatronic systems to meet given performance specifications, subject to various constraints. The most difficult aspect of the research is to develop a method that can explore the design space in a topologically open-ended manner, yet can find appropriate configurations efficiently enough to be useful and can be applied to multiple domains using a single tool. Our approach combines bond graphs (BGs) for representing the mechatronic system models with genetic programming (GP) as a means of exploring the design space.
BGs [2], [3], [4], [5], [6] allow us to capture the energy behavior underlying the physical aspects (as opposed to the information aspects) of mechatronic systems in a uniformly effective way across domains. They enable the analysis of multi-energy-domain systems with a unified inter-domain tool. Being topological structures, they are also ideal for representing a structured design space for open-ended generation and exploration. Finally, BGs allow efficient and rapid evaluation of individual designs, using a two-stage procedure––causal analysis of the graph followed, only if needed, by appropriate detailed calculation using a derived state model.
Sharpe and Bracewell [7] present the use of BG reasoning for the design of interdisciplinary schemes. They describe how conceptual scheme synthesis may be assisted and structured by the use of functions-mean trees developed by the application of BG-inspired rules. Youcef-Toumi [8] introduces an algorithm which identifies automatically the physical components and/or subsystems that are responsible for zero dynamics. Redfield [9] demonstrates the value of using BGs as a conceptual or configurational design tool for dynamic systems, using as an example a continuously variable transmission. Tay et al. [10] use a genetic algorithm to vary BG models. This approach adopts a variational design method, which means they make a complete BG model first, then change the BG topologically using a GA, yielding new design alternatives. Their goal is to provide a wider range of possible designs, and is closely related to that presented here, but within a topologically more limited search space.
GP is an effective way to generate design candidates in an open-ended, but statistically structured, manner. A critical aspect of the procedure is a fitness (or performance) measure, which must guide the evolution of candidate designs toward a suitable result in a reasonable time. There have been a number of research efforts aimed at exploring the combination of GP with physical modeling to find good engineering designs. Perhaps most notable is the work of Koza et al. [11], [12], [13], [14]. He presents a single uniform approach using GP for the automatic synthesis of both the topology and sizing of a suite of various prototypical analog circuits, including low-pass filters, operational amplifiers and controllers. This system has already shown itself to be extremely promising, having produced a number of patentable designs for useful artifacts, and is the most closely related approach to that proposed here; however, it works in a single energy domain. That means his approach requires a different simulation code or tool for each application. Writing a simulation code for an application is a very time-consuming job. If the design applications or domains are different, one must write or link to a simulation code for each new application.
The approach described here includes the potential advantages of both BGs and GP, with a powerful synergistic effect for automated, multi-domain, and topologically open-ended design. We use a unified evaluation tool based on BGs, most of which can be used for every application, even if they are in different domains, with relatively minor supplemental codes to provide any additional functionality required.
In this paper, we have not attempted to duplicate the results of other researchers such as Koza et al. for a specific problem; rather, we have demonstrated the effectiveness of our design methodology for applications in each of several different domains. As our first class of design problems, we chose one in which the objective is to realize a design having a specified set of eigenvalues. Since the problem can be studied effectively using linear components with constant parameters, we only needed to introduce one-port (generalized) resistance, capacitance, and inductance elements in our designs. Section 2 discusses the inter-domain nature, efficient evaluation and graphical generation of BGs. Section 3 describes evolution of BGs by GP. 4 Case study 1––eigenvalue assignment, 5 Case study 2––analog filter design, 6 Case study 3––printer drive redesign presents some results for an eigenvalue design, electric filter design and printer drive redesign problem, and Section 7 concludes the paper.
Section snippets
Unified and automated methodology and multi-domain dynamic systems
Due to the complexity of the engineering design problem, the need for efficiency in the design methodology is greatly increased. The most critical issues are automation of the design process and use of a unified design tool. Most design tools or methodologies require user interaction, so users must make many decisions during the design process. This makes the design procedure more complex and often introduces the need for trial-and-error iterations. The other issue is the need for a unified
Bond graph construction
A typical GP system (like the one used here) evolves GP trees, rather than more general graphs. However, BGs can contain loops, so we do not represent the BGs directly as our GP “chromosomes”. Instead, a GP tree specifies a construction procedure for a BG. BGs are “grown” by executing the sequence of GP functions specified by the tree, using the BG embryo as the starting point.
Initial studies were reported in Seo et al. [17] and Fan et al. [18]. The following set of BG elements: {C, I, R; 0,
Case study 1––eigenvalue assignment
Although the final design of practical multi-domain systems still requires physical realization of the best generated BG model, it is sufficient to design a BG model with the desired performance in order to demonstrate the utility of our automated design methodology for multi-domain systems. In this work, the main design objective is to find BG models with minimal distance errors from the target sets of eigenvalues. The problem of eigenvalue assignment has received a great deal of attention in
Problem definition
A filter design problem was used as a test of our approach for evolving electrical circuits with BGs, as first reported in Fan et al. [18]. Three kinds of filters were chosen to verify our approach––high-pass, low-pass, and band-pass filters. The embryo electric circuit and corresponding embryo BG model used in our filter design are shown in Fig. 23. We used converted Matlab routines to evaluate frequency response of the filters created. As Matlab provides many powerful toolboxes for
Problem definition
This example involves a drive system for a printer. The original problem was presented to one of the investigators by Denny and Oates of IBM, Lexington, KY, in 1972. Fig. 3 (in Section 2) shows a closed-loop control system to position a rotational load (inertia) denoted as JL, and Fig. 31 shows the subsystem initially designed (manually). The detailed specification involved reducing the vibration of the load to an acceptable level, given certain command conditions for input position.
The fitness
Conclusion
This paper has suggested a new design methodology for automatically synthesizing designs for multi-domain, lumped parameter dynamic systems with a unified tool. A careful combination of BGs and GP, including a multi-step evaluation procedure that greatly increases the efficiency of fitness assessment, appears to be an appropriate approach to development of a method for synthesis of complex multi-domain systems, such as mechatronic systems.
As a proof of concept for this approach, evolution of
Acknowledgements
The authors gratefully acknowledge the support of the National Science Foundation through grant DMI 0084934.
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