Page 286 - Mechanical Engineers' Handbook (Volume 2)

4 Systems Engineering Methodology and Methods 277

• Microeconomic models represent an application of economic theories of firms and
consumers who desire to maximize the profit and utility of their production and con-
sumption alternatives.
Parameter estimation is a very important subject with respect to model construction and
validation. Observation of basic data and estimation or identification of parameters within
an assumed structure, often denoted as system identification, are essential steps in the con-
struction and validation of system models. The simplest estimation procedure, in both con-
cept and implementation, appears to be the least-squares error estimator. Many estimation
algorithms to accomplish this are available and are in actual use. The subjects of parameter
estimation and system identification are being actively explored in both economics and sys-
tems engineering. There are numerous contemporary results, including algorithms for system
identification and parameter estimation in very-large-scale systems representative of actual
physical processes and organizations.
Verification of a model is necessary to ensure that the model behaves in a fashion
intended by the model builder. If we can determine that the structure of the model corre-
sponds to the structure of the elements obtained in the problem definition, value system
design, and system synthesis steps, then the model is verified with respect to behaving in a
gross, or structural, fashion, as the model builder intends.
Even if a model is verified in a structural as well as parametric sense, there is still no
assurance that the model is valid in the sense that predictions made from the model will
occur. We can determine validity only with respect to the past. That is all that we can possibly
have available at the present. Forecasts and predictions inherently involve the future. Since
there may be structural and parametric changes as the future evolves, and since knowledge
concerning results of policies not implemented may never be available, there is usually no
way to validate a model completely. Nevertheless, there are several steps that can be used
to validate a model. These include a reasonableness test in which we determine that the
overall model, as well as model subsystems, responds to inputs in a reasonable way, as
determined by ‘‘knowledgeable’’ people. The model should also be valid according to sta-
tistical time series used to determine parameters within the model. Finally, the model should
be epistemologically valid, in that the policy interpretations of the various model parameters,
structure, and recommendations are consistent with ethical, professional, and moral standards
of the group affected by the model.
Once a model has been constructed, it is often desirable to determine, in some best
fashion, various policy parameters or controls that are subject to negotiation. The optimi-
zation or refinement-of-alternatives step is concerned with choosing parameters or controls
to maximize or minimize a given performance index or criterion. Invariably, there are con-
straints that must be respected in seeking this extremum. As previously noted, the analysis
step of systems engineering consists of systems analysis and modeling and optimization or
refinement of alternatives and related methods that are appropriate in aiding effective judg-
ment and choice.
There exist a number of methods for fine tuning, refinement, or optimization of indi-
vidual specific alternative policies or systems. These are useful in determining the best (in
terms of needs satisfaction) control settings or rules of operation in a well-defined, quanti-
tatively describable system. A single scalar indicator of performance or desirability is typi-
cally needed. There are, however, approaches to multiple objective optimization that are
based on welfare-type optimization concepts. It is these individually optimized policies or
systems that are an input to the evaluation and decision-making effort in the interpretation
step of systems engineering.
Among the many methods for optimization and refinement of alternatives are: