# Dynamic Line Scan Thermography Parameter Design via Gaussian Process Emulation
## 3 Results
### Parameter Design  
Generating a response surface is a technique used in the design of experiments (DOF) often with the idea of investigating the interference between several factors in a process. It is possible to determine which factors have an influence on the output effect and in what way the output responds to a change in one or a collection of input parameters. Afterwards, the insight in the process and the response surface itself can be used to optimize the parameters in order to minimize/maximize the output effect of the process. In industrial applications, one is generally not interested in the influence of the different input parameters on the output effect. There, focus lies on how to optimize the efficiency of the inspection process itself, or in other words, how to reduce its economical impact on the overall production process. Once a Gaussian process is trained to emulate the simulations up to an adequate level, we can query the model with real-world engineering design questions. Below, we give a few examples. We picked the threshold values in these examples in an arbitrary way. Here, they only serve demonstrating purposes. They are, of course, application specific. In a practical setup, they depend on the type of the camera used, the ambient temperature in the production facility, the material of the sample under inspection, etc. **Example 1**. : _From a practical and economical point of view, the most crucial input parameter is the heating power. The reduction in the energy needed to heat a sample under inspection results in a drastic reduction in the inspection cost. To accommodate this, we can ask the following question: what parameter combination should be used to be able to detect a predefined defect with a certain start depth and diameter, with a minimal of amount of heating energy needed? For instance, we want to be able to detect a defect with a diameter of 14 mm, which is situated 6 mm below the surface. We query the GP posterior prediction for all test and training points by filtering on the input variables' start depth and diameter. Then, we filter the temperature difference on a range from 5 to 10 \({}^{\circ}\)C. A temperature difference that is lower might make it hard to detect with a given camera. A temperature difference that is higher means the sample under inspection is heated to a value that is too high, resulting in a waste of energy of an even and undesirable effect on the material itself. From all the remaining possible inputs, we choose the ones with the lowest heat load. In our case this is 50 W. We end up with a range for the distance between the camera and the heat source of 335 to 420 mm. All these values yield a temperature difference between 5 and 10 \({}^{\circ}\)C for the given defect. On the other hand, when the distance between the heat source and the camera is below this range, we can observe that the heat load has to be increased to 75 W to still yield a temperature difference between 5 and 10 \({}^{\circ}\)C._  
**Example 2**. : _In some practical scenarios, it is possible that the distance between the heat source and the camera has to be a fixed value, for instance, due to constraints on the physical setup in the production environment. We can ask the trained model, what parameter combination should be used to be able to detect a range of defects with only adjusting the heating power? Again, we filter the temperature difference on a range from 5 to 10 \({}^{\circ}\)C. We fix the distance between the heat source and the camera to 100 mm. We observe that we need a minimum of 500 W to be able to detect all defects