Design of Experiments (DOE) — CAE Glossary

Design of Experiments, or DOE for short. It was originally systematized by R.A. Fisher in the 1920s as a statistical method to improve agricultural experiment efficiency. In CAE, it is used as a method to systematically determine which combinations of design variables to execute in the analysis. For example, if you want to run a crash analysis on a car bumper by varying three factors—plate thickness, material, and rib placement—total enumeration would mean hundreds of cases. With DOE, you can efficiently capture main effects and interactions with just dozens of analyses.

Exactly. CAE analyses can take hours to days per case. For example, with 5 factors and 5 levels each in full factorial design, you get $5^5 = 3{,}125$ cases. At 2 hours per case, that's about 260 days of computation. With DOE, the same 5 factors can be understood with 50–100 cases, capturing main effects and major interactions efficiently.

Arbitrary variation is the most dangerous approach. In practice, engineers often run only a handful of cases based on intuition and conclude something like "increasing thickness improves strength." But in reality, there may be interactions between thickness and material—perhaps increasing thickness with a certain material actually reduces fatigue life. DOE is a statistical safeguard against such oversights.

No, it cannot. OFAT—"fix all but one factor and vary it"—is the most basic parametric study method. It cannot detect interactions and only covers a fraction of the design space. DOE varies multiple factors simultaneously in a systematic way, so it can separate and estimate both main effects and interactions. Statistically, the information efficiency is far superior.

It's the method where you run every combination of all factor levels. With $k$ factors at $n$ levels each, you need $n^k$ experiments. Two factors at 3 levels = $3^2 = 9$ cases, but 10 factors at 3 levels = $3^{10} = 59{,}049$ cases. Practically impossible in CAE, so it's limited to cases with 3–4 factors and few levels.

Roughly: "divide each factor's value range into $N$ equal intervals and sample exactly one point from each interval." For example, if you want 20 samples of sheet thickness between 1.0–5.0 mm, you create 20 intervals of 0.2 mm each and randomly pick one point from each. Do this independently for all factors. This ensures even coverage of the design space without clustering—a common problem with pure random sampling.

A typical flow is: "Generate initial samples with LHS → Run CAE analyses → Build a surrogate model (response surface) → Optimize on the surrogate." For example, in airfoil shape optimization, you sample 100 points from 10 wing parameters using LHS, run 100 CFD cases, build a kriging model, then run genetic algorithm on that model. This replaces 100,000 CFD runs with just 100.

Very much so. Japanese automotive and electronics manufacturers especially value quality engineering traditions. The heart of Taguchi is two things: orthogonal arrays and S/N ratio. Orthogonal arrays ($L_9$, $L_{18}$, $L_{27}$, etc.) distribute factor combinations uniformly with minimal experiments. The S/N ratio quantifies robustness against variability in three categories: nominal-is-best, smaller-is-better, and larger-is-better.

Good example. Suppose you want to prevent wrinkling and tearing in press forming. Control factors: blank holder force, punch speed, die radius, and lubrication (4 factors at 3 levels each). Using $L_9$ orthogonal array, you run only 9 forming simulations. Add noise factors—material lot variation (sheet thickness tolerance, r-value change)—in an outer orthogonal array. Evaluating results with S/N ratio immediately shows "blank holder force has the strongest effect, but punch speed doesn't matter for tearing."

If DOE answers "where to compute," RSM answers "build a continuous mathematical model from the results." The two are usually paired. Run CAE at sample points chosen by DOE, then approximate the response (stress, displacement, drag coefficient) as a function of input variables. This surrogate model (proxy model) enables fast exploration.

Three main types. Polynomial approximation (second-order response surface) is simplest: $y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + \beta_{11}x_1^2 + \beta_{22}x_2^2 + \beta_{12}x_1 x_2$. Coefficients are determined using Box-Behnken or CCD (central composite design). Kriging (Gaussian process regression) passes through sample points and gives high interpolation accuracy, good for highly nonlinear responses. Neural network surrogates are increasingly common too.

Exactly. Take 4 fin parameters—pitch, height, thickness, angle—sample 60 points with LHS, and run conjugate heat transfer CFD on 60 cases. Build kriging models for heat transfer (Nu) and pressure drop (Δp). Multi-objective optimize for a Pareto front. One CFD case takes 3 hours, so 60 cases = 180 hours, about a week. Total enumeration would take years.