Inverse Deep Learning Ray Tracing for Heliostat Surface Prediction

TL;DR

The paper tackles predicting heliostat surfaces from calibration target images to improve CSP flux density distribution. It introduces inverse Deep Learning Ray Tracing (iDLR), combining an encoder–decoder network with a differentiable NURBS-based heliostat model to infer surface shapes from target images using a semi-artificial, ray-tracing–driven training dataset. The NURBS parameterization reduces a million-plus surface parameters to $4 \times 8 \times 8$ $\, z$-control points ($256$ DOF) and enables differentiable, memory-efficient surface representations, yielding a median flux-density prediction accuracy of $0.92$ compared to the ideal model's $0.67$, and a surface MAE per point of $0.14$ mm. The approach supports sim-to-real transfer via domain randomization and holds promise for real-time CSP plant optimization, potentially enhancing receiver flux density and overall energy output while avoiding costly direct surface measurements.

Abstract

Concentrating Solar Power (CSP) plants play a crucial role in the global transition towards sustainable energy. A key factor in ensuring the safe and efficient operation of CSP plants is the distribution of concentrated flux density on the receiver. However, the non-ideal flux density generated by individual heliostats can undermine the safety and efficiency of the power plant. The flux density from each heliostat is influenced by its precise surface profile, which includes factors such as canting and mirror errors. Accurately measuring these surface profiles for a large number of heliostats in operation is a formidable challenge. Consequently, control systems often rely on the assumption of ideal surface conditions, which compromises both safety and operational efficiency. In this study, we introduce inverse Deep Learning Ray Tracing (iDLR), an innovative method designed to predict heliostat surfaces based solely on target images obtained during heliostat calibration. Our simulation-based investigation demonstrates that sufficient information regarding the heliostat surface is retained in the flux density distribution of a single heliostat, enabling deep learning models to accurately predict the underlying surface with deflectometry-like precision for the majority of heliostats. Additionally, we assess the limitations of this method, particularly in relation to surface accuracy and resultant flux density predictions. Furthermore, we are presenting a new comprehensive heliostat model using Non-Uniform Rational B-Spline (NURBS) that has the potential to become the new State of the Art for heliostat surface parameterization. Our findings reveal that iDLR has significant potential to enhance CSP plant operations, potentially increasing the overall efficiency and energy output of the power plants.

Figures (8)

• Figure 1: Inverse Deep Learning Ray Tracing (iDLR) embedded in the regular power plant operation. The heliostats are sequentially and fully automatically focused on a Lambertian target and target images are taken for the calibration (Camera-Target Method). Those target images contain information about the heliostat surface. Leveraging a deep learning model, this information is extracted and utilized to predict the heliostat surface, without the necessity of introducing new hardware or executing measurement which are not done yet during regular power plant operation. Consequently, the existing power plant systems and software can now operate seamlessly with an improved heliostat digital twin. This enhancement enables the power plant to operate more efficiently by achieving a more optimal flux density distribution (FDD) on the receiver.
• Figure 2: The simulative heliostat field that was used for validating the model. The solar tower (ST) is placed at the origin. At each heliostat position (helpos) the same 32 real measured heliostats were placed.
• Figure 3: The employed model utilizes up to 8 flux densities, along with corresponding sun and heliostat positions, as inputs. These scalar inputs undergo an affine transformation A, followed by weight demodulation, to map them into the image data stream. Subsequently, convolutional neural layers process those. The resulting w+ latent space is then fed into the generator of the styleGAN2 architecture, generating the cartesian representation of the surface spline.
• Figure 4: Illustration of the NURBs fitting procedure for an individual heliostat. The left panel depicts the normal vectors resulting from the NURBS parameterization, while the right panel displays cartesian representations of the surface.
• Figure 5: (a): The presented surface predictions are randomly selected. The top row illustrates the ground truth obtained through deflectometry, while the bottom row depicts the predictions generated by iDLR. b: The provided flux density predictions correspond to the heliostats shown above. The top row presents the ground truth, derived through ray tracing deflectometry surfaces, while the middle row showcases predictions generated by ray tracing the iDLR predictions. As a point of reference, the bottom row displays flux density predictions derived from the ideal heliostat assumption. It is noteworthy that the flux density prediction for poor iDLR surface predictions (see third heliostat from the left) is just as good as for those with a very good surface prediction. This phenomenon can be attributed to the inherent underdetermination of the problem. The flux density predictions generated from iDLR surface predictions significantly surpass those based on the ideal heliostat assumption.