Overview

Attune™ is a program for test/analysis correlation and model updating. It uses design sensitivity and optimization methods to identify model changes that minimize the differences between test and analysis results. This approach has been shown to be highly effective for a variety of test/analysis correlation problems.

Attune has many advantages for performing test/analysis correlation:

  • The design sensitivity approach is very efficient. Linear perturbation methods provide sensitivity coefficients at a fraction of the cost of a normal modes analysis.

  • Design sensitivity coefficients clearly identify the important properties in the finite element model (FEM).

  • Attune can correlate multiple configurations of a model simultaneously, which facilitates the correlation of complex models.

  • The FEM is updated directly. No intermediate matrix updating is required.

  • Attune works with Nastran, Abaqus, and Salinas models.

  • Attune can define design variables and export them to a ready-to-run Nastran input file.

  • Attune updates Nastran input files without flattening INCLUDE files or round-tripping data. Only the necessary lines are changed, leaving the rest of the file(s) unmodified.

  • Attune can take closely spaced symmetric modes into account in the cross-orthogonality or cross-modal assurance criteria (MAC) correlation.

  • Few iterations are usually required to update the FEM, saving schedule and computer resources.

  • The updated FEM of the test configuration can easily be modified to represent flight configurations.

  • Attune is graphical user interface (GUI)-driven, which allows the engineer to drive the model-updating process.

  • Attune has a convenient interface with Microsoft Excel for documenting the model updating process.

  • Attune uses the Visualization Toolkit (VTK) for model and results viewing, allowing mode shapes to be viewed for large models.

Sensitivity Analysis

Attune uses design sensitivity analysis (DSA) to predict changes to important results (such as modal frequencies, static deflections, mode shapes, etc.) if specified items in the model (such as spring constants) are varied. The important results are called “state variables” since they measure critical states of the structure. They are also called “design constraints” in Nastran. The items that may be varied are called “design variables.”

Design sensitivity coefficients define the relationship between the state and design variables. A design sensitivity coefficient relates how much a state variable will change given a change in a design variable. Linear perturbation methods [ 5, 6 ] are used to calculate design sensitivity coefficients. This approach is very efficient; design sensitivity coefficients can be calculated at a small fraction (10% to 20%) of the cost of standard normal modes analysis.

The cost of calculating design sensitivities varies with the type of sensitivity calculated. Modal frequency sensitivities are typically calculated at a very low cost, while mode shape and cross-orthogonality sensitivities can be very computationally costly, depending on the retained number of degrees of freedom (DOF), the number of modes, and the number of design variables.

Optimization Techniques

Attune uses several optimization techniques in the correlation process. Each technique has advantages and disadvantages.

Monte Carlo

The Monte Carlo algorithm is “brute-force” technique. A user-defined number of designs is randomly generated. For each design, the stiffness matrix is updated based on modal matrix sensitivities. An eigensolution is computed with the updated stiffness matrix. The objective function is evaluated based on the revised modal parameters. The design with the minimum objective function value is chosen as optimal. The benefit of this method is that it cannot be trapped by local minima. On the other hand, because each design is chosen at random, there is no guarantee that the global minimum will be an element of the design population. Likewise, there is no guarantee that the solution will improve with iteration.

Gradient

The gradient algorithm uses the modal matrix sensitivities to compute approximate sensitivities of the modal parameters. The derivatives of the modal parameters are linearized approximations about the current design. An attempt to minimize the objective function, subject to constraints, is made based on these approximate sensitivities. The approximate modal parameter sensitivities are recomputed for the new design. Iteration continues until no further improvement can be made. Unlike the Monte Carlo algorithm, the gradient algorithm uses the current design and approximate derivatives of the modal parameters to find an improved solution. This implies incremental improvement with each iteration. However, the gradient algorithm can become trapped in local minima or can overshoot because of inaccuracies in the linear approximation of the derivatives.

Genetic Algorithm

For the genetic algorithm, the design variables can only take on discrete values within the permitted range. Like the Monte Carlo algorithm, a user-defined number of designs is generated randomly and evaluated using the objective value function. Unlike the Monte Carlo algorithm, the genetic algorithm iteratively improves the pool of design candidates. As a discrete (non-derivative–based) optimization method, the genetic algorithm is not susceptible to the same problems as the gradient algorithm. The disadvantage of the genetic algorithm is that an iteration is typically more computationally intensive than the other optimization methods. This is the default optimization method and tends to have the greatest success in finding model improvements.