RAMDO Foundation

OPTION 1: RELIABILITY ANALYSIS

Sampling-based reliability analysis provides accurate reliability of performance measure using Monte Carlo simulation without requiring design sensitivity of performance measure. For efficiency, the performance measures are approximated by using local window surrogate models. Dynamic Kriging (DKG), which is an improved version of Kriging, is used for the surrogate modeling method. Input distributions can be represented using seven marginal distribution types (Normal, Lognormal, Weibull, Gumbel, Gamma, Extreme and Extreme type-II). Eight types of copulas are provided to depict statistical correlation of input random variables (Clayton, Frank, FGM, Gaussian, AMH, Gumbel, A12 and A14).

OPTION 2a: SAMPLING-BASED RBDO

Sampling-based reliability based design optimization (RBDO) provides an optimum design satisfying user-specified target reliability and minimizing the cost without requiring design sensitivity of performance measures. Instead, the method uses Monte Carlo simulation for reliability analysis and stochastic design sensitivity obtained from the score function method. The stochastic design sensitivity provides an accurate direction of design movement in the optimization process with a small additional computational cost. For efficiency, the performance measures are approximated by using local window surrogate models. Dynamic Kriging (DKG), which is an improved version of Kriging, is used for the surrogate modeling method. Input distributions can be represented using seven marginal distribution types (Normal, Lognormal, Weibull, Gumbel, Gamma, Extreme and Extreme type-II). Eight types of copulas are provided to depict statistical correlation of input random variables (Clayton, Frank, FGM, Gaussian, AMH, Gumbel, A12 and A14).

OPTION 2b: SENSITIVITY-BASED RBDO

Sensitivity-based reliability-based design optimization (RBDO) provides an optimum design satisfying user-specified target reliability using simulation solver (or user)-provided design sensitivity of performance measures. The sensitivity-based RBDO method approximates output variability using a linear approximation (FORM-based RBDO) or high-order approximation (DRM-based RBDO) of the limit state. The performance measure approach (PMA), which is robust, stable and accurate in the optimization process, has been used to provide accurate optimum design efficiently. While the target reliability is satisfied at the optimum design, the cost is minimized. The PMA also provides inverse reliability (decision whether current design satisfies target reliability or not). Input distributions can be represented using seven marginal distribution types (Normal, Lognormal, Weibull, Gumbel, Gamma, Extreme and Extreme type-II). Eight types of copulas are provided to depict statistical correlation of input random variables (Clayton, Frank, FGM, Gaussian, AMH, Gumbel, A12 and A14).

RAMDO Add-ons

INPUT MODELING AND VARIABLE SCREENING

Users may have only input data, and not the input joint probability distribution functions. In this case, the best fit distribution type and parameters are determined by RAMDO using the input data. The marginal distribution type and parameters are selected for each random variable first. Then the copula type and Kendall’s tau, which represents statistical correlation between random variables, is determined. Surrogate models may suffer from the curse of dimensionality in the sampling-based method. Therefore, an efficient and effective variable screening method has been developed for reduction of the dimension of the RBDO problem. In the variable screening method, important variables are selected according to their impact on the variance of the output distribution, which can be approximated using the univariate dimension reduction method (DRM).

OUTPUT DISTRIBUTION

It is often interesting to see how the distribution of performance measures changes as the current design changes due to the variability in the input variables. For efficiency, the performance measures are approximated by using local window surrogate models. Dynamic Kriging (DKG), which is an improved version of Kriging, is used for the surrogate modeling method. Input distributions can be represented using seven marginal distribution types (Normal, Lognormal, Weibull, Gumbel, Gamma, Extreme and Extreme type-II). Eight types of copulas are provided to depict statistical correlation of input random variables (Clayton, Frank, FGM, Gaussian, AMH, Gumbel, A12 and A14). RAMDO can generate the output distributions, which is the probability distributions of the performance measures, using Monte Carlo with the Dynamic Kriging surrogate models. The output distributions can used to calculate various statistics about the performance measures.

RELIABILITY-BASED ROBUST DESIGN OPTIMIZATION (RBRDO)

Robustness of performance measures may be desired by users in reliability problems. The robustness indicates consistency of performance measures under variability of input random variables. The robustness can be obtained by minimizing variance of output distribution using the sampling-based method. The stochastic sensitivity using score function can provide the direction of design for effective reduction of the variance of output distribution for robustness. Using the same sampling-based reliability analysis, users can mix robustness and reliability of performance measures in one design process. This is reliability-based robust design optimization (RBRDO).

CONFIDENCE-BASED RBDO FOR LIMITED INPUT DATA

In many engineering applications, only limited input data are available due to expensive testing cost and time. The limited input data could lead to an unreliable optimum design. To consider the uncertainty of input models due to the insufficient input data, confidence-based RBDO (C-RBDO) has been developed. In C-RBDO, all possible input distribution types and parameters are considered using the limited input data and Bayesian methods. Then, the probability of reliability output is obtained using the possible types and parameters. The probability indicates conservativeness-level of optimum design and users can specify the target conservativeness level. Hence, the users can have confidence in the RBDO optimum design that meets the target reliability. Moreover, design sensitivity for C-RBDO is developed as well for accurate and efficient optimization process.

RAMDO Plug-ins

HYPERSTUDY (Altair)

With the HyperStudy plug-in the user can import a HyperStudy model into RAMDO. Importing a model will load the random variables, random parameters, performance measures, and optimization problem definition into RAMDO. The HyperStudy plug-in allows RAMDO to carry out required DOE runs using the HyperStudy model which will carry out the DOE runs using the simulation solvers defined in the HyperStudy model.

ABAQUS (Dassault Systèmes)

Under development.

LS-OPT/LS-DYNA (LSTC)

Under development.

CUSTOM SIMULATION SOLVER

We can also work with users to create custom software plug-ins to interface RAMDO together with a commercial simulation solver, e.g., FEA, CFD, MBD, CEM, Casting Process Simulation, etc., or with an in-house simulation solver. Contact us for more details and a quote.

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Example Applications

  • Casting Process Design Optimization
  • Electromagnetic Device Designs
  • Superconducting Magnetic Energy Storage System Design
  • Fluid-Solid Interaction (FSI) Problems
  • Reduce Residual Deformation in Welding
  • Thermo-Elasto-Plastic Residual Deformation
  • Electro-Thermal Polysilicon Microactuator
  • High-Fidelity CFD Outputs
  • Fatigue Analysis and Durability
  • Explosion Analysis and Survivability
  • Vehicle and Machine Dynamics
  • Noise, Vibration, and Harshness (NVH)
  • Crashworthiness
  • Wind Turbine Blades Design
  • Wind Turbine Drivetrain Dynamics under Wind Load and Axial Misalignment Uncertainties

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