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Adjoint-based optimization approach
TMG Correlation uses gradient-based optimization algorithms, which rely on computing the gradient of the objective function. The gradient is the variation of the objective function with respect to the design variables. TMG Correlation uses the adjoint method to compute the gradient.

User help
- Introduction to TMG Correlation
- TMG Correlation workflow
- TMG Correlation interface
  The TMG Correlation user interface is integrated in Simcenter 3D using NX Open and contains unique features to conduct a thermal correlation analysis, in addition to standard tools and commands described in the Simcenter 3D Online help and the NX Online help.
- Thermal correlation analysis preparation
  Before conducting a thermal correlation analysis, it is important to properly prepare your simulation model and the reference data.
- Understanding thermal correlation analysis
  The thermal correlation is a calibration process that helps you find the best thermal solution that minimizes the error between the computed and target temperatures at different locations and times.
- Managing the reference data
  In TMG Correlation, reference data refers to the temperature and time data that come from experimental tests or from prior and validated simulation models. They are named sensors and are used as targets for the optimization of the correlated solution.
- Understanding design variables
  A design variable is a simulation entity of your model that the TMG Correlation solver varies within a specific range during the optimization to reduce the gap between the reference data and the simulation results.
- Setting up the optimization
  In optimization, the goal is to find values for the design variables that minimize the difference between the reference data and the correlated solution results.
- Monitoring the optimization
  Use the Solution Monitor and Solution Control Monitor to track the analysis during the solve. The monitors provide solver-specific information for the TMG thermal solver and the thermal correlation analysis.
- Analyzing the optimization results
  After you solve a thermal correlation analysis, you can analyze the results of the optimization process in the TMG Correlation dialog box.
- Updating the simulation model
  After you verified the optimization results, you must update the simulation model to reflect any changes that were made during the thermal correlation analysis so that you can continue your modeling in Simcenter 3D.
- Theory
  - Governing equation
    TMG Correlation optimizes the temperatures computed by the TMG thermal solver that solves for the heat conduction in a solid domain.
  - Objective function
    The TMG Correlation optimizer minimizes the objective function, F, that represents the error between the computed and target temperatures at different locations and times.
  - Adjoint-based optimization approach
    TMG Correlation uses gradient-based optimization algorithms, which rely on computing the gradient of the objective function. The gradient is the variation of the objective function with respect to the design variables. TMG Correlation uses the adjoint method to compute the gradient.
  - Optimization algorithms
    TMG Correlation computes the step length, α, when updating the design variable vector using the specified optimization algorithm method. All methods are local gradient-based optimization algorithms.
  - References
- Legal notice
- License agreement

Adjoint-based optimization approach

TMG Correlation uses gradient-based optimization algorithms, which rely on computing the gradient of the objective function. The gradient is the variation of the objective function with respect to the design variables. TMG Correlation uses the adjoint method to compute the gradient.

With the adjoint method [1], the gradient is obtained by the summation of the derivative of the objective function with the product of the adjoint vector and the derivative of the residuals.

Where:

is the vector of the design variables.
is the derivative of the objective function with respect to the design variables.
is the transposed of the adjoint vector corresponding to the temperature that is computed from the adjoint equation.
is the derivative of the residuals of the governing equation with respect to the design variable, which is approximated by design variable perturbation.

Adjoint equation

The adjoint vector is computed based on the Jacobian matrix of the conduction equation and the derivative of objective function:

Where:

is the derivative of the residual with respect to the temperature.
is the derivative of objective function with respect to temperature.

Update of the design variable vector

The new design variable vector is computed as follows:

α is the step length, which is computed via the specified optimization algorithms.