Model simplification by asymptotic order of magnitude reasoning

AbstractOne of the hardest problems in reasoning about a physical system is finding an approximate model that is mathematically tractable and yet captures the essence of the problem. This paper describes an implemented program AOM which automates a powerful simplification method. AOM is based on two domain-independent ideas: self-consistent approximations and asymptotic order of magnitude reasoning. The basic operation of AOM consists of five steps: (1) assign order of magnitude estimates to terms in the equations, (2) find maximal terms of each equation, i.e., terms that are not dominated by any other terms in the same equation, (3) consider all possible n-term dominant balance assumptions, (4) propagate the effects of the balance assumptions, and (5) remove partial models based on inconsistent balance assumptions. AOM also exploits constraints among equations and submodels. We demonstrate its power by showing how the program simplifies difficult fluid models described by coupled nonlinear partial differential equations with several parameters. We believe the derivation given by AOM is more systematic and easily understandable than those given in published papers

Knowledge composition methodology for effective analysis problem formulation in simulation-based design

In simulation-based design, a key challenge is to formulate and solve analysis problems efficiently to evaluate a large variety of design alternatives. The solution of analysis problems has benefited from advancements in commercial off-the-shelf math solvers and computational capabilities. However, the formulation of analysis problems is often a costly and laborious process. Traditional simulation templates used for representing analysis problems are typically brittle with respect to variations in artifact topology and the idealization decisions taken by analysts. These templates often require manual updates and "re-wiring" of the analysis knowledge embodied in them. This makes the use of traditional simulation templates ineffective for multi-disciplinary design and optimization problems. Based on these issues, this dissertation defines a special class of problems known as variable topology multi-body (VTMB) problems that characterizes the types of variations seen in design-analysis interoperability. This research thus primarily answers the following question: How can we improve the effectiveness of the analysis problem formulation process for VTMB problems? The knowledge composition methodology (KCM) presented in this dissertation answers this question by addressing the following research gaps: (1) the lack of formalization of the knowledge used by analysts in formulating simulation templates, and (2) the inability to leverage this knowledge to define model composition methods for formulating simulation templates. KCM overcomes these gaps by providing: (1) formal representation of analysis knowledge as modular, reusable, analyst-intelligible building blocks, (2) graph transformation-based methods to automatically compose simulation templates from these building blocks based on analyst idealization decisions, and (3) meta-models for representing advanced simulation templates VTMB design models, analysis models, and the idealization relationships between them. Applications of the KCM to thermo-mechanical analysis of multi-stratum printed wiring boards and multi-component chip packages demonstrate its effectiveness handling VTMB and idealization variations with significantly enhanced formulation efficiency (from several hours in existing methods to few minutes). In addition to enhancing the effectiveness of analysis problem formulation, KCM is envisioned to provide a foundational approach to model formulation for generalized variable topology problems.Ph.D.Committee Co-Chair: Dr. Christiaan J. J. Paredis; Committee Co-Chair: Dr. Russell S. Peak; Committee Member: Dr. Charles Eastman; Committee Member: Dr. David McDowell; Committee Member: Dr. David Rosen; Committee Member: Dr. Steven J. Fenve

System Concepts and Formal Modelling Methods for Business Processes

The major quality breakthrough of the 1980s was the realisation by management that business and manufacturing processes are the key to customer service and organisational performance. This thesis is concerned with the overall problem of modelling of business processes. Of special interest is the study of business processes through an interdisciplinary approach that cuts across the boundaries of management and information technology. The overall effort is placed on being able to move from a purely conceptual level of describing a business process to a more formal one, enabling decision making, and driving the analysis away from experience, intuition, and informal debate. The extended review and presentation of the various modelling methodologies given here, serve as a guide to their basic concepts and capabilities. A particular case study - the management of the human resources in a consulting company - has been used in this thesis to enable the evaluation of the modelling techniques. Hence, models have been produced, as well as simulation results to indicate the limitations, the advantages and the information gained. Through this application, the understanding of requirements for modelling analysis and decision making of business processes was acquired. Particularly, two very important techniques were investigated. System Dynamics and Petri nets provide the answers when process models are geared to deliver not only qualitative but also quantitative results. However, Petri nets provide the mathematical notation and the plethora of analysis tools needed for the validation, verification, and performance analysis of the model. Additionally, two different simulation software packages were used, based on these methodologies; Ithink®, which is based on System Dynamics, and Alpha/Sim®, based on Petri nets theory. The model produced in the case study depicts perfectly the capabilities of the two techniques. Petri nets is not the total business modelling solution, it can be complemented by other methods, such as System Dynamics and discrete-time modelling as shown in Chapter 6. The feasibility of all these modelling techniques lies entirely on the analyst, who should use them alternately to satisfy the requirements of the problem