Validation

Throughout the implementation, many validations and testing steps are performed to verify and demonstrate the validity of the implemented algorithms. Validation is given high priority for several reasons. First, the implemented algorithms are complex and beyond the standard algebra usually applied. Therefore they require thorough verification. Apart from the extensive three-dimensional vector calculations, four-dimensional vectors and matrices are applied, and a large part of the calculation is based on complex-valued algebra. Beyond that, the main algorithms rely on the stochastic Monte Carlo approach, which also adds complexity to testing and validation. Finally, validation cases are essential to demonstrate the validity and suitability of the different modules and workflow in a comprehensive way. The field of physical optics is a rather special topic. Therefore, the availability of suitable validation data is limited. For this reason, published results of fields like astronomy and material science were used to demonstrate the functionality and validity of the implemented algorithms in the first step. The validation cases contained in section 4.9.3, are considered most important as they show the validity of the algorithms with high accuracy.

The more comprehensive and elaborate empirical validation covered in chapter 8 demonstrates the feasibility and effectiveness of the entire approach based on a typical object (tripled glazed shaded window). However, due to a lack of precise spectral optical measurements for the glazing and blind material, some generic assumptions are required. In the validation cases that replicate lab measurements on a singular surface (section 4.9.3), empirical data with high accuracy is available. In the case of full-system measurements, the calculation results must be compared with measured data containing a significantly higher error level. This must be taken into account, as full-system measurements under varying real-world conditions are challenging. Therefore, the validation of the physical optics modules (section 4.9.3) proves that the algorithm works accurately and precisely on the material surface level, while the system validation demonstrates that the method can handle complex objects consisting of many different materials and geometrical shapes. The latter also demonstrates how results with good accuracy can be achieved, even if the required spectrally resolved information is unavailable.
Further, the comparison of in-plane irradiance computed with the RadiCal/SIOP approach versus classical calculations performed in a dynamic building performance simulation represents an essential validation step (see section 6.2.6.). It proves that, although the RadiCal approach allows the consideration of complex optical scattering processes and complex geometries, it seamlessly and precisely transitions to the classical approach if a simple object is modelled.
No intermodal comparisons with the commonly applied calculation methods or tools are included in this work. The current state-of-the-art comprises different methods that can be performed at varying levels of detail (see chapter 3). The methods have different limitations and are often based on severe simplifications. Hence, a comprehensive intermodel comparison requires additional considerations and discussion beyond the scope of this work. Nonetheless, intermodel comparisons are considered essential and will be covered in subsequent publications.
Beyond these quantitative validations, the generation of rendered images using the RadiCal algorithms for backward raytracing is an additional conclusive validation step. Renderings are a powerful method to identify model shortcomings, potential singularities or numerical instabilities in the equations used. They do not allow precise quantitive analysis. However, the eye can identify model shortcomings, as it is very sensitive to singular errors that might occur. The rendered image is only able to provide a flawless, realistic appearance if billions of light scattering events – involving a multitude of configurations regarding surface orientations, wavelengths and light paths – are computed correctly.