On the Role and Use of Mathematical Models in Engineering Design

Abstract

Mathematical models encompassing virtually all aspects of engineered products are in widespread use. Indeed, entire industries exist in support of some models: finite element models, computational fluid dynamics models, electric power grid load-flow models, process models, simulation models, and so on. Nonetheless, the purpose, construction, and use of models is not adequately understood. One major issue is that no model perfectly represents reality. Therefore models always diverge from reality somewhere, and they are always inaccurate by some amount. Estimation of model error and the use of model-generated results in support of engineering design decision making are key to the successful use of models.

The Cost of Jointness: Insights from Environmental Monitoring Systems in Low-Earth Orbit

“…Nadler & Tushman connected the abstract concept of information processing to decision making by defining it as "the gathering, interpreting, and synthesis of information in the context of organizational decision making" [121]. When an organization manages a complex technical system, its ability to process information and to make decisions is intimately connected to the system's development, since engineering itself is fundamentally a decision making process [123].…”

Detecting mistakes in engineering models: the effects of experimental design

“…This sufficiency criterion was proposed as an informal concept by Subrahmanian et al (1993). A similar, but more formal, conception was proposed based on decision theory so that a model may be considered valid to the extent that it supports a conclusion regarding preference between two design alternatives (Hazelrigg, 1999). In either of the preceding definitions, if a formal model contains a mistake as defined in section 1.1, the model should not continue to be used for design due to its insufficiency, invalidity, or both.…”

“…Engineers frequently view the processes of verification and validation of engineering models and the use of those models for design as separate. But engineering models are never fully validated for the full range of uses in engineering design (Hazelrigg, 1999). Mistakes in engineering models remain even when engineers feel confident enough to begin using them to make decisions.…”

Models as artefacts of a dual nature: a philosophical contribution to teaching about models designed and used in engineering practice

“…Models play an increasing role in the course of most engineering activities, and it is easy to observe how extensively various kinds of models are being used in different layers of today's engineering processes and in technological designs and developments (see, e.g., various discussions in this regard in Vincenti 1993;Veveris 1994;Hazelrigg 1999;Boon and Knuuttila 2009;Nersessain and Patton 2009;Pirtle 2010;Rossouw et al 2011;Schätz 2014;and particularly in Brockman 2008, where 'modelling' has been included in the title of the book, thereby giving a general introduction to this engineering activity). Therefore, the way to properly learn about these types of models has, accordingly, also received the attention of many educational approaches (e.g., Compton 2007 However, as acknowledged by scholars such as De Vries (2013), it seems that not much has yet been developed to educate about the content of models that are used in engineering practice, and '' [students] are not challenged to reflect on the nature and function of [models]' ' (De Vries 2013, p. 123).…”