Decision-Based Design Position Paper

Richard Balling
balling@byu.edu

Dept. of Civil Engineering
Brigham Young University
Provo, UT 84602
Phone: 801-378-2648
Fax: 801-378-4449

Question 1: What are the key activities designers perform in the design process?

I have developed and taught a required undergraduate course to our civil engineering students over the past 5 years. The course is titled "Civil Engineering Systems" and covers economics, design methodology, optimization, and risk.

Drawing upon my own beliefs as well as upon several texts on systems engineering, I present to students the following four-step design methodology:

1. CONCEPTION
2. FORMULATION
3. MODELLING
4. SEARCH

Is this approach consistent with decision-based design (DBD)? After reading more about DBD over the past few days, I think the answer is yes. The key ingredients of DBD are options, expectations, and values. Paraphrasing Hazelriggâs paper, "the preferr ed design is the option whose expectation has the highest value". Let me now describe the above four steps in DBD terminology.

The CONCEPTION step is devoted to the identification of the set of options. Competitive configurations are developed, and the design variables for each are identified. In the FORMULATION step, the value function is agreed upon by stakeholders. This may be a very political step, and ultimately involves formulating the value function in terms of expected outcomes as specifically as possible. The MODELLING step involves developing the analysis model which computes the expected outcomes for a given option. Once such a model is developed, the SEARCH process can begin for the preferred design. Search may be accomplished through formal optimization techniques or by less formal "trial-and-error" methods.

Feedback can occur at any point in the above four-step process. For example, one may be in the middle of the MODELLING step when one realizes that the value function needs to be reformulated. Thus, one drops back to the FORMULATION step. In another exa mple, after looking at the results from the SEARCH step, one may become aware of additional configurations that were not considered. Thus, one drops back to the CONCEPTION step.

What about the order of the steps? I think it is clear that MODELLING must preceed SEARCH, that FORMULATION must preceed MODELLING, and CONCEPTION must preceed MODELLING. It may not be necessary for CONCEPTION to preceed FORMULATION, although it is certainly easier to speak specifically about value when a few configurations are out on the table.

Question 4: Do you think design can be modelled in equation form?

Let the vector x be the set of design variables. Different values for x represent different design options. Assume that different configurations are symbolically represented through different values of x. Let V(x) be the value function. It must include risk and uncertainty as well as economics. For example it could be the expected present worth over the life-cycle. It would include costs/benefits associated with failure/success modes multiplied by their respective probabilit ies of occurance. Here are my "equations" for analysis and design:

Analysis Design

Given: x

Find: x

Calculate: V(x)

Maximize: V(x)

I have become interested in multidisciplinary design optimization (MDO). MDO is useful for the design of systems which are large and complex enough to require the efforts of multiple teams of designers. Thus, the vector x is partitioned among N disciplinary teams. The ith disciplinary team is responsible for determining the values of design variables in the vector x_i. In addition to partitioning the responsibility for determination of the design variables, we can also partition the analysis task among the disciplinary teams. Let the ith disciplinary team perform its part of the analysis and return a vector V_i of value parameters to the system level. This vector contains all the information from the discipline needed to determine the value of the system. Thus, the value of the system is: V(V₁,V₂,V₃,...,V_N).

In MDO, it is important that each discipline has autonomy over the determination of its own design variables x_i and over its own portion of the analysis (calculation of V_i). Clearly, V_i is a functio n of x_i. The difficulty, however, is that most systems are coupled. This means that V_i is also a function of y_ji where y_ji is a vector of "coupling functions" determined in Discipline j and sent to Discipline i. Similarly, Discipline i computes coupling functions y_ij which are sent to other Disciplines which are needed in the determination of their respective V_j. The crowning complication is the fact that y_ij may be a function of y_ji and vice-versa. Thus we have:

Analysis For Discipline System Analysis

Given: x_i,y_ji

Given: V_ii=1,N

Calculate: V_i,y_ij

Calculate: V

Now we have a chicken-and-egg problem in determining which disciplinary analysis is executed first since each discipline must wait for coupling functions from the other disciplines. This problem can be rectified by introducing target values y_ij for each coupling function y_ij. Disciplinary analyses take the target values as input rather than the coupling functions. It will be up to the system level to make sure that the target values match their corresponding coupling functions in the end. Target values Vâ_i are also introduced for each of the value parameters V_i. With these target values, the disciplines (and system) may be analyzed in parallel.

Analysis For Discipline System Analysis

Given: x_i,y_ji

Given: V_i

Calculate: V_i,y_ij

Calculate: V

In the MDO approach known as "collaborative optimization", disciplines may also design in parallel. The design problems are:

Design For Discipline iSystem Design

Find: x_i

Find:V_i, y_ij

Maximize: V

Satisfy: d_i=0

Iteration occurs between the system level and the discipline level. The system sends target values down to the disciplines, and the disciplines return their respective discrepancy functions d_i. Disciplinary design variables and analyses are hidden from the system level and all other disciplines. Thus, disciplinary autonomy is maintained.