Best practices for TMG Correlation analyses

To determine the best settings for your thermal correlation analysis, it is recommended that you start with exploratory analyses before you run your final optimization analysis.

When you correlate and optimize a thermal model, a first exploratory thermal correlation analysis is useful to get more information about:

Sensor values that are the most difficult to reach.
Design variables that influence the most and the least the correlation.
Correlation times that you should specify for the final run.
Convergence criterion to use.

Use the results from the exploratory runs and the guidelines for TMG Correlation settings described in the following table to set up, optimize, and update your original thermal solution.


Settings	Exploratory analysis	Final optimization analysis
Targets	Do not use weights except if you already know which sensors are more important.	Add weights to your sensors to focus more on these weighted sensors when reducing the gap with the test data. For example, when a sensor is located near a critical component of the model, more weight on this sensor makes TMG Correlation focus more on reducing the gap with reference data at this sensor location.
Targets	Note: Adding weights to sensors can make your optimization problem stiffer.
Optimization design variables	Always specify minimum, maximum, and initial values for all optimization design variables. The minimum and maximum values define the design space for the variable. The wider the range between these values, the larger the design space becomes, allowing for more possible solutions. The initial value defines from where the optimizer starts minimizing the objective function. A different initial value may lead to a different solution.
Correlation times	By default, TMG Correlation lists all sensors time points and solution time steps. Considering all these correlation times is similar to optimizing the area between the sensor and solution curves. Note: When the optimizer has more correlation times, it has more targets to reach, thus, the optimization problem is more complex.
Correlation times	Use few correlation times as follows: Avoid using all sensor time points. Select times that have the highest differences between simulation and reference data. For quasi-steady state sections, use only one additional time within the section start and end times. For transient sections with steep slopes, use at least one additional time within the section start and end times.	Using the exploratory analysis results, you can identify the times where the temperature difference is still large and add one or two correlation times to improve the correlation.
Convergence criterion	Use a constant convergence criterion that satisfies your accuracy expectations for all correlation times.	If you have different accuracy expectation for different parts of your transient problems, use the time varying convergence criterion option to specify different convergence values for the different correlation times of your model, thus, satisfying your accuracy expectations for every correlation time separately.
Convergence criterion	In both runs, estimate the initial objective function value using the initial gap between simulation and reference data. Calculate the average absolute error for every correlation time of your problem. This gives you an idea how the objective function and average absolute errors are linked. Suggested values for convergence criteria: For a maximum error of 5 degrees with the reference data, define a convergence criterion of 1. For a maximum error of 0.5 degrees with the reference data, define a convergence criterion of 0.1.
Maximum design cycles	Fewer than 5 design cycles	10 to 20 design cycles are usually necessary to converge to an optimal solution for a well-defined correlation setup depending on the complexity of your correlation problem. If this is not enough, increase the value for your next correlation.
Optimization algorithm	If you have uncertainties about the ranges (min, max) of your design variables, use the default optimizer, which is MMA. If you are confident about the ranges (min, max) of your design variables, use the SLSQP optimizer.	When the min and max values of the optimization design variables are defined, SLSQP performs better and faster than the other algorithms.

Analyzing results from a thermal correlation analysis

When you analyze results from your thermal correlation analysis, especially the exploratory runs, you verify first the convergence results, then the design variable results, and finally the sensor results to update the settings for your next run.

Convergence results

Has the objective function decreased?

No—It means that your correlation setup is not well defined. TMG Correlation cannot improve the solution whatever the optimization design variable values are.
- Verify if the quantities you defined as design variables have an impact on the temperature computation at the sensor locations. If your design variables are located too far from the sensor locations in your model, they may not have any effect on the temperature computed at these locations.
- Verify your thermal model definition. Do you correctly model all heat transfer aspects as they exist in your reference data set? TMG Correlation uses the numerical representation (discretization) of your thermal problem through the energy equation to compute the adjoint equation, and then the gradient (sensitivities) of the design variables. If your thermal model does not represent with enough accuracy the reference data set, for example the test data, TMG Correlation is not able to converge toward a solution that matches the reference data. Your model may be missing a boundary condition (BC), such as a thermal coupling or convective BC, to model accurately the phenomenon.
Yes—It means that the correlation tool could reduce the gap with the test data. Check the profile of the objective function history plot to evaluate if it was converging toward a smaller value or not.

Design variables results

From the design variable values, evaluate the percentage each design variable varied after the exploratory run. This allows you to identify the most and least influential design variables.

Check whether some design variables reached their minimum or maximum bounds. TMG Correlation solves a mathematical problem: minimizing a temperature difference between two data sets. If the best way to solve this problem is to maximize or minimize a specific design variable, high chance to reach the min/max bound, TMG Correlation will do it. If a design variable reaches the min or max bound:

Does it make sense? For example, a heat transfer coefficient for natural convection should not reach very high value (>20), if a design variable defined on a heat transfer coefficient reaches a bound of 15 or 20, maybe there is something wrong in the model.
Do you have a sensor located close to the design variable?
- Yes—This sensor may have a large impact on the objective function. Use weights on other sensors to minimize the effect of this sensor, if it is relevant.
- No—Verify your thermal model definition around that part of your model. Maybe, there is a heat sink or heat load that controls the temperature difference at sensor locations.
Do you have enough sensors versus design variables?
- If you have more sensors than design variables, the problem is over constrained, which can lead to unfeasible or non converged solutions that minimize the objective function.
- If you have fewer sensors than design variables, the problem is under constrained, which can lead to unrealistic solutions that minimize the objective function.
- A reasonable ratio for sensors to design variables is generally within this range: 0.5 – 2, which means 1 for 2 or 2 for 1. Outside this range, depending on the locations of sensors versus design variables, you may face difficulties converging toward a solution.

Sensors results

Compare the sensor results before and after the correlation run and assess whether your correlation setup helped reduce the errors at sensor locations.