Ronald C. Rosenberg

Toward a unified and automated design methodology for multi-domain dynamic systems using bond graphs and genetic programming

Abstract This paper suggests a unified and automated design methodology for synthesizing designs for multi-domain systems, such as mechatronic systems. A multi-domain dynamic system includes a mixture of electrical, mechanical, hydraulic, pneumatic, and/or thermal components, making it difficult use a single design tool to design a system to meet specified performance goals. The multi-domain design approach is not only efficient for mixed-domain problems, but is also useful for addressing separate single-domain design problems with a single tool. Bond graphs (BGs) are domain independent, allow free composition, and are efficient for classification and analysis of models, allowing rapid determination of various types of acceptability or feasibility of candidate designs. This can sharply reduce the time needed for analysis of designs that are infeasible or otherwise unattractive. Genetic programming is well recognized as a powerful tool for open-ended search. The combination of these two powerful methods is therefore an appropriate target for a better system for synthesis of complex multi-domain systems. The approach described here will evolve new designs (represented as BGs) with ever-improving performance, in an iterative loop of synthesis, analysis, and feedback to the synthesis process. The suggested design methodology has been applied here to three design examples. The first is a domain-independent eigenvalue placement design problem that is tested for some sample target sets of eigenvalues. The second is in the electrical domain––design of analog filters to achieve specified performance over a given frequency range. The third is in the electromechanical domain––redesign of a printer drive system to obtain desirable steady-state position of a rotational load.

A Novel Evolutionary Engineering Design Approach for Mixed-Domain Systems

This paper presents an approach to engineering design of mixed-domain dynamic systems. The approach aims at system-level design and has two key features: first, it generates engineering designs that satisfy predefined specifications in an automatic manner; second, it can design systems belonging to different or mixed physical domains, such as electrical, mechanical, hydraulic, pneumatic, thermal systems and/or a mixture of them. Two important tools are used in this approach, namely, bond graphs and genetic programming. Bond graphs are useful because they are domain independent, amenable to free structural composition, and are efficient for classification and analysis, allowing rapid determination of various types of acceptability or feasibility of candidate designs. Genetic programming, on the other hand, is a powerful tool for open-ended topological search. To prevent the premature convergence often encountered in evolutionary computation, a hierarchical fair competition model is adopted in this work. Examples of an analog filter design and an MEM filter design illustrate the application of the approach.

Essential gyrators and reciprocity in junction structures

Abstract This paper proposes an extended definition of reciprocity for a multiport junction structure based on the concept of essential gyrator coupling. Two theorems are given for junction structures containing gyrators and an algorithm is presented for identifying essential gyrators. The results are useful both theoretically and for designing efficient computation procedures for junction structures.

HEMO: a sustainable multi-objective evolutionary optimization framework

The capability of multi-objective evolutionary algorithms (MOEAs) to handle premature convergence is critically important when applied to real-world problems. Their highly multi-modal and discrete search space often makes the required performance out of reach to current MOEAs. Examining the fundamental cause of premature convergence in evolutionary search has led to proposing of a generic framework, named Hierarchical Fair Competition (HFC)[9], for robust and sustainable evolutionary search. Here an HFC-based Hierarchical Evolutionary Multi-objective Optimization framework (HEMO) is proposed, which is characterized by its simultaneous maintenance of individuals of all degrees of evolution in hierarchically organized repositories, by its continuous inflow of random individuals at the base repository, by its intrinsic hierarchical elitism and hyper-grid-based density estimation. Two experiments demonstrate its search robustness and its capability to provide sustainable evolutionary search for difficult multi-modal problems. HEMO makes it possible to do reliable multi-objective search without risk of premature convergence. The paradigmatic transition of HEMO to handle premature convergence is that instead of trying to escape local optima from converged high fitness populations, it tries to maintain the opportunity for new optima to emerge from the bottom up as enabled by its hierarchical organization of individuals of different fitnesses.

Hierarchical evolutionary synthesis of MEMS

We discuss the hierarchy that is involved in a typical MEMS design and how evolutionary approaches can be used to automate the hierarchical design and synthesis process for MEMS. At the system level, the approach combining bond graphs and genetic programming can lead to satisfactory design candidates of system level models that meet the predefined behavioral specifications for designers to tradeoff. At the physical layout synthesis level, the selection of geometric parameters for component devices is formulated as a constrained optimization problem and addressed using a constrained GA approach. A multiple-resonator microsystem design is used to illustrate the integrated design automation idea using evolutionary approaches.

Automated synthesis of mechanical vibration absorbers using genetic programming

Abstract Conceptual innovation in mechanical engineering design has been extremely challenging compared to the wide applications of automated design systems in digital circuits. This paper presents an automated methodology for open-ended synthesis of mechanical vibration absorbers based on genetic programming and bond graphs. It is shown that our automated design system can automatically evolve passive vibration absorbers that have performance equal to or better than the standard passive vibration absorbers invented in 1911. A variety of other vibration absorbers with competitive performance are also evolved automatically using a desktop PC in less than 10 h.

Estimating Eigenvalues for a class of Dynamic systems

Abstract In a previous work an approach was presented for extracting information about the eigenvalues of a linear, time-invariant dynamic system directly from a graphical model. In this paper a generalization is given of the results previously obtained. For some particular cases we can give the entire spectrum. For these cases the spectrum is shown as a function of the structure of an abstract form of the bond graph model. For more general cases, we give upper limits on the imaginery part, and upper and lower limits on the real parts, of the eigenvalues. In contrast to most existing methods, the information about the eigenvalues is generated prior to deriving the state equations. When suitably automated, the results obtained here can provide a considerable reduction in the computational effort required to get information about eigenvalues. This feature is particularly useful in an interactive design context.

Clarifying Energy Storage Field Structure in Dynamic Systems

The energy variables associated with a dynamic system can be considered as a set of candidate state variables. However, when algebraic coupling among the energy variables exists, then the associated state-space equations are implicit in form. Typically, such equations require implicit integration methods for their solution, unless the original model is modified suitably. Bond graph models, through the use of causality techniques, allow one to identify the existence of algebraic energy-variable coupling. Based on the detailed nature of the coupling, various options are available for solving such problems. In this paper a modification of and extension to the standard Sequential Causality Assignment Procedure is given that permits the detailed identification of the structure of energy fields.

Modeling and simulation of large-scale, linear, multiport systems

A large number of physical and engineering systems may be represented directly in terms of component energy characteristics and their power interactions. When the system elements are modeled as energetic multiports, and their interconnections by power bonds, then the bond graph language is a natural one for describing the entire system. Bond graphs may be written for dynamic systems involving various energy types, such as electrical, mechanical, fluid and thermal; all energy types may be coexistent. Useful modeling elements include multiport storages, dissipators, and junction elements and transducers, as well as sources. Bond graph models of linear multiport systems may be transformed to state-space form by a powerful algorithm based upon operational causality. From the state-space equations, dynamic responses may be obtained by the matrix exponential technique, thereby allowing the direct digital simulation of linear multiport models. The ENPORT program is a realization of the bond graph reduction algorithm. It is a principal purpose of this paper to describe the procedure upon which ENPORT is based, and to present some results. Important features of ENPORT are its choice of physically significant state variables, its use of operational causality to obtain an orderly formulation of system equations, and its ability to handle systems containing static storage subfields.

An algorithm for automatic identification of R-fields in bong graphs

Bond graphs may be used to model the power flow in dynamic systems. They are especially attractive for modeling systems which function in coupled energy domains, for example, electromechanical systems. For such systems, bond graphs can be used to provide a natural subdivision into power/energy fields: storage, sources, transformers, and dissipation. In the case of nonlinear dissipative fields, implicit, nonlinear, coupled systems of algebraic equations may arise. Causality assignment on the bond graph provides a basis for detecting implicit formulations. This paper presents an algorithm for detection and solution of these forms within a model, thereby providing an opportunity for efficient numerical solution, and includes a brief introduction to bond graphs via an electromechanical system example.