For centuries, modelling was a task performed exclusively by humans assisted by no more than pencil and paper and very little existing literature or means of communication with peers. The situation changed after the introduction of mechanical devices and was further revolutionised by the introduction of computer systems. The latter enabled scientists to perform experiments in highly controlled virtual environments using no more than hardware and computer models. These models are typically referred to as simulators. This marked a complete paradigm shift, as the breadth and depth at which phenomena could be studied and predicted increased tremendously. Even when analytical solutions to problems were infeasible before, computer simulation offered suitable approximations.
A remarkable first success was already achieved as part of the Manhattan Project during World War II [3], however due to the complexity of running algorithms on the computer systems used as well as their limited processing power, too much expertise was required to justify commercialisation and widespread usage. It took years of development (both for hardware and software) for the merits of computer simulation to become more widely available. During the 1960s the General Purpose Systems Simulator (GPSS) [4] package and the Simula programming language marked the start of acceptance and strong interest in simulation. During this decade, the first Winter Simulation Conference1took place which still exists and celebrates
its 50th anniversary in 2017.
1.3.1
Computer modelling process
The process of developing computer models was discussed in detail by Kleijnen [5]. However, this section presents the simplified version by Sargent [6,7] as depicted in Figure1.1
The problem entity is the system or real-world problem phenomenon to be modelled. In a first step the problem must be captured in a conceptual model expressed by means of mathematical concepts, or verbal definitions resulting from an analysis and modelling phase. This is a task for the domain expert as he is familiar with the inner workings and specifics of the problem. The conceptual model is then translated into a computerised model which can be used for inference of the problem entity in the experimentation phase. For both these translation steps adequate validation and verification steps are required to assure that all assumptions and abstractions are reasonable, and that no mistakes are introduced by implementation. As a final step, the computer model must also be validated on the problem itself by assessing the
Data validity Problem entity Computerized model Conceptual model Conceptual model validity Operational validity Computerized model verification Experimentation Programming Implementation Analysis and modeling
Figure 1.1: The computer modelling process.
accuracy of the model over the problem domain. Finally, the data validity assures that throughout the process the data integrity is maintained and remains valid for model building, evaluation, testing, and performing experiments.
1.3.2
Computer models for engineering
Amongst the countless research domains and fields of research revolutionised by the merits of computer simulation, the field of engineering is a prime example as it continues to benefit greatly from the introduction of computer simulations. During product design, engineers are confronted with several complex systems which need to be designed and/or optimized. These systems are parametrised by several input parameters (or factors or variables) and emit a set of outputs (responses). Together, these input parameters form the input space (or design space), whereas outputs form the output space. Traditionally, several prototypes with varying settings of the input parameters were required to observe and learn the relationship with the output(s). This in order to assure quality criteria were met, to obtain optimal solutions for design choices and/or to evaluate the behaviour of products and components under varying conditions. Each of these prototypes can be regarded as a data point in the joint input/output space. Often a single prototype
was insufficient, and lessons learnt were used to improve the design. Therefore, the development process used to involve building several prototypes in order to gain more confidence in the solutions and understand the mapping from input to output space. A direct consequence of this approach is that the development process is both slow and not cost effective.
The introduction of computer simulations resulted in a speed up of development processes at a lower cost. By bundling implementations of material, mechanical and, physical properties into a software package which simulates the desired aspects of a system and performs the tests and experiments virtually, the number of required prototypes can be drastically reduced to only a few at the very end of the design process. These prototypes can be regarded purely as a validation of the simulations as part of the process outlined in Section 1.3.1. The simulation itself can be interpreted as a model and serves as an abstract layer between the engineer and the real world phenomena. Performing a virtual experiment is faster and less expensive. A direct consequence was an acceleration of development and system design, contributing to a shorter time-to-market and a more effective process in general. In addition, it was also possible to perform more virtual experiments providing a way to achieve better products and design optimality.