3.9 Multidisciplinary Design Optimization

Coupled analyses create a system problem¶

Multidisciplinary design optimization coordinates design decisions across interacting engineering disciplines. A discipline analysis may be written

y_i=A_i(z_i,z_s,y_{j\ne i}),

where $z_i$ is local to discipline $i$ , $z_s$ is shared, and $y_j$ are coupling variables received from other analyses. A multidisciplinary analysis (MDA) solves the coupled consistency equations before system objectives and constraints are evaluated.

For an electromechanical actuator, electromagnetic design determines torque and losses; structural design determines mass and compliance; thermal analysis determines temperature; control determines the requested operating history. Current affects heat, heat changes resistance, resistance changes available torque, and actuator size changes plant dynamics.

Monolithic and distributed organization¶

A monolithic formulation exposes all relevant variables and consistency constraints to one optimizer. Distributed MDO architectures partition variables or disciplines and coordinate subproblems. The best organization depends on model ownership, derivative availability, parallelism, intellectual-property boundaries, and coupling strength—not only equation count.

Dependency graphs guide formulation¶

A design-structure matrix or directed graph records which variables enter each analysis, objective, and constraint. It helps identify shared variables, feedback loops, removable redundancies, and opportunities for parallel evaluation. The graph in this chapter’s overview shows that actuator rating affects mass, force limits, energy, and closed-loop response; treating it as a control-only parameter would miss several couplings.

What MDO contributes to CCD¶

CCD inherits MDO principles: system-level objectives, explicit coupling variables, consistency constraints, decomposition, sensitivity propagation, and architecture selection. CCD then adds a special discipline—the controlled evolution of a dynamic system—whose variables and constraints may be functions of time.

Activity 3.9: draw an MDO graph¶

Activity 3.9: draw an MDO graph

For an electric vehicle, connect battery capacity, vehicle mass, thermal-system size, motor efficiency, supervisory control, range, acceleration, and cost. Identify local variables, shared variables, and at least one feedback loop.

Quantitative audit for Multidisciplinary Design Optimization: compare the following two feasible-design candidates.

Candidate	Plant loss $J_p$	Control loss $J_c$	$g_{\max}$	Evaluations
A	1.17	0.72	0.96	210
B	0.96	0.84	0.91	395

Use $J=0.6J_p+0.4J_c$ and require $g_{\max}\leq1$ .

Calculate objective values, feasibility margins, and percentage improvement.
Increase B plant loss by 8% for independent validation and repeat the ranking.
Compute objective improvement per 100 additional evaluations and state which result you would retain.