Identification and Visualization of Potential Performance Problems based on Performance

5.2 Identification and Visualization of Potential Performance Problems based on Performance Deviations

Given generated EPAR models, the next goal is to create and validate a new model-based method that (1) can automatically calculate performance deviations and (2) infer and visualize potential energy problems with the associated digital and thermal images in 3D. Figure 5.3 shows an overview of the proposed method.

Figure 5.3 Overview of the Data and Process in the Performance Deviation Analysis Method

The proposed method for EPARv2.0 builds on the EPAR modeling method (Section 5.1) and leverages two new algorithms:

 EPAR (Section 5.1): using an unordered collection of thermal and digital images captured from the buildings under inspection, 3D building geometrical and thermal point cloud models are automatically generated and integrated to form an actual 3D spatio-thermal model. Then, the building energy performance is simulated through the numerical analysis based on as-designed building information, generating expected 3D spatio-thermal models.

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Finally, the two models are superimposed in a common 3D environment, forming EPAR models along with 3D-registered images;

 EPARv2.0: Two new algorithms for 3D thermal mesh modeling based on k-d tree structures and the nearest neighbor searching method are developed for automated calculation of performance deviations. Based on the temperature deviations and a threshold, potential building performance problems are inferred and visualized based on a metaphor of traffic light colors in EPAR models. The following sections describe each step in detail (Golparvar-Fard and Ham 2014).

5.2.1 3D mesh modeling of building thermal profiles

In order to calculate deviations between actual and expected thermal performance in EPAR models, the measured and simulated indoor surface temperatures are compared at the level of 3D point. To that end, the following data sets are defined:

 (𝑃_𝐴¹, 𝑃_𝐴², . . . , 𝑃_𝐴^𝑗) denote a set of actual 3D thermal points. These points are the outcomes of the image-based 3D thermal modeling method. 𝑃_𝐴^𝑖 =< 𝑋_𝐴^𝑖, 𝑅𝐺𝐵_𝐴^𝑖 > encapsulates the 3D location (𝑋_𝐴^𝑖) and color value (𝑅𝐺𝐵_𝐴^𝑖) of each 3D point, and j is the number of points in the actual 3D thermal point cloud model. Each RGB color value corresponds to a normalized temperature scale, and in turn represents an absolute thermal value.

 (𝑃_𝑆¹, 𝑃_𝑆², … , 𝑃_𝑆^𝐾) denote a set of simulated 3D thermal points resulted from the numerical analysis. 𝑃_𝑆^𝑖 =< 𝑋_𝑆^𝑖, 𝑅𝐺𝐵_𝑆^𝑖 > encapsulates 3D location (𝑋_𝑆^𝑖) and color values (𝑅𝐺𝐵_𝑆^𝑖) of each 3D point, and k is the number of vertex in the VRML-based CFD model. Here, each RGB color value corresponds to an absolute thermal value.

In EPAR models in form of point clouds, the user need to manually find the closest pairs between the actual and expected 3D thermal points for performance comparison. Through experimental observations, it was found that the manual extraction and comparison between the two 3D point cloud models is not trivial and prone to error. In particular, the actual 3D thermal point cloud resulted from the image-based 3D reconstruction typically includes large numbers of points that do not belong to the building geometry, which further makes the comparison challenging. To overcome the challenge in direct application of point cloud-based EPAR models

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for performance comparison, a new method for generating 3D mesh models of the actual thermal performance is proposed to improve the model completeness by leveraging the VRML-based CFD models as a geometrical baseline. The proposed approach for 3D mesh modeling of the actual thermal performance is to first find the closest point 𝑃_𝐴^𝑖 for each 𝑃_𝑆^𝑖 according to the distance between two points, and then convert the RGB color values of 𝑃_𝑆^𝑖 (𝑅𝐺𝐵_𝑆^𝑖 ) into the RGB color values of the corresponding 𝑃_𝐴^𝑖 (𝑅𝐺𝐵_𝐴^𝑖). Ultimately, a new 3D point data set <𝑃_𝑀¹, 𝑃_𝑀², . . . , 𝑃_𝑀^𝑘> is generated which will be used for 3D thermal mesh modeling. Here, k is the number of points in the simulated 3D thermal model, and 𝑃_𝑀^𝑖 =< 𝑋_𝑀^𝑖 , 𝑅𝐺𝐵_𝑀^𝑖 > encapsulates the 3D location (𝑋_𝑀^𝑖 ) and color value (𝑅𝐺𝐵_𝑀^𝑖 ) of each 3D point. These points are subsequently used to generate the polygons that are required for the mesh modeling process. Figure 5.4 summarizes the proposed 3D thermal mesh modeling algorithm.

Figure 5.4 Algorithm for 3D Mesh Modeling of Actual Thermal Performance

To find the closest points for pairing, the brute-force method was first used to calculate the distance from the query point to every other point in the corresponding dataset. Next, all the distances are sorted in an ascending order, and the pair which yields the shortest distance among all neighboring points is selected. Given a significant number of points in the generated point cloud, such naïve method requires high computational cost since it calculates the distance for every

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possible configuration. Instead, to minimize computational time required for finding the nearest neighbor to each query point 𝑃_𝑆^𝑖 , the simulated thermal points 𝑃_𝑆^𝑖 are mapped into a k-d tree structure. The k-d tree algorithm is a computational approach for space-partitioning of data structure to organize points in a k-dimensional space (de Berg et al. 2008). The binary trees are used to store spatial data in a multi-dimensional space. The k-d trees recursively divide the set of points into subsets with half of the points of the parent node by a line perpendicular to one of the dimensions. The resulting point sets are partitioned into equal halves using the hyperplane of a different dimension. Partitioning process stops once each point locates its own leaf cell. Ultimately, the k-d trees hierarchically decompose overall space into a series of cells so that no cell contains too many points. The nearest neighbor search with the k-d tree algorithm can be done efficiently by using the decomposing properties of the tree. This eliminates a large portion of the overall search space, allowing significant improvement in the computational time. First, each tree including the root node and the sub-domains are examined. A multi-dimensional query is composed of several 1-dimensional sub-queries. Starting from the root node, the query algorithm is recursively performed to the entire branch. Once the query algorithm reaches a leaf node, the distance to the node point is stored as the current best nearest distance. Then, the query algorithm looks into each parent node, identifying the possibility of other domain including a closer point than the current best. To do that, the query algorithm identifies whether the splitting hyperplane intersects with a hypersphere around the search point. As the hyperplanes are axis-aligned, the distance between the splitting coordinate of the search point and the current node is compared with the distance from the search point to the current best. If the hyperplane intersects the hypersphere, the query algorithm is implemented to find the closer points in the other branch of the tree, following the same recursive process. If the hypersphere does not cross the splitting plane, the entire branch is eliminated. All these processes are repeatedly done until all domains are either searched or discarded. Once the algorithm fails to find a closer point 𝑃_𝐴^𝑖 given a query point 𝑃_𝑆^𝑖, the searching process is terminated and yields the nearest neighbor 𝑃_𝐴^𝑖. Lastly, the RGB color value of the resulting nearest neighbor 𝑃_𝐴^𝑖 is fed into the proposed mesh modeling algorithm.

5.2.2 Calculating actual and simulated temperature values and visualizing performance deviations

The actual and simulated temperature values (𝑇_𝐴^𝑖 and 𝑇_𝑆^𝑖 respectively) are calculated from the RGB

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color values of each vertex in EPAR models. First, the normalized temperature scales of both thermal images and CFD models (𝑇𝑆 and 𝐶𝑆 respectively) are converted into a fixed range of RGB color values (𝑅𝐺𝐵_𝑇𝑆 and 𝑅𝐺𝐵_𝐶𝑆 respectively). As long as a consistent color spectrum is used for visualization, this process does not need to be repeated for different data collections. Then, given 𝑅𝐺𝐵_𝐴^𝑖 and 𝑅𝐺𝐵_𝑆^𝑖, the matching RGB color values in 𝑅𝐺𝐵_𝑇𝑆 and 𝑅𝐺𝐵_𝐶𝑆 are searched, and then 𝑇_𝐴^𝑖 and 𝑇_𝑆^𝑖 for point 𝑖 are calculated by using Equations 9 and 10 respectively:

𝑇_𝐴^𝑖 = 𝑇𝑆_𝑚𝑖𝑛+ (𝑅𝐺𝐵_𝑇𝑆^𝑖 − 1) ×𝑇𝑆_𝑚𝑎𝑥− 𝑇𝑆_𝑚𝑖𝑛

𝐿𝑒𝑣𝑒𝑙_𝑇𝑆− 1 (9)

𝑇_𝑆^𝑖 = 𝐶𝑆_𝑚𝑖𝑛+ (𝑅𝐺𝐵_𝐶𝑆^𝑖 − 1) ×𝐶𝑆_𝑚𝑎𝑥 − 𝐶𝑆_𝑚𝑖𝑛

𝐿𝑒𝑣𝑒𝑙_𝐶𝑆− 1 (10)

Here, 𝑇𝑆_𝑚𝑎𝑥 and 𝑇𝑆_𝑚𝑖𝑛 are the maximum and minimum values of temperature scale used in building thermography, and similarly 𝐶𝑆_𝑚𝑎𝑥 and 𝐶𝑆_𝑚𝑖𝑛 are the maximum and minimum values of temperature scale used in the VRML-based CFD model. 𝐿𝑒𝑣𝑒𝑙_𝑇𝑆 and 𝐿𝑒𝑣𝑒𝑙_𝐶𝑆 indicate the range of each RGB color value chart converted from temperature scales used for building thermography and VRML-based CFD model respectively.

The final step is to compute the deviations of two models and visualize them in EPAR models using a metaphor based on traffic light colors. Since the geometry of VRML-based CFD models was used for 3D mesh modeling of actual thermal performances as a geometrical baseline, 3D actual and expected thermal mesh models share the same coordinate system. Thus, by computing the difference between 𝑇_𝐴^𝑖 and 𝑇_𝑆^𝑖 for each 3D vertex in EPAR models, indoor surface thermal performance deviations can be simply calculated. Small deviations between actual measurements and simulation results are typically related to the inherent uncertainty in measurement accuracy of a thermal camera and the numerical analysis, and thus can be expected.

Thus, the user needs to set a threshold for inferring the presence of potential performance problems in building environments. Based on the threshold, the areas with or without potential performance problems are color-coded with red and green colors respectively in EPAR models.

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CHAPTER 6. MEASURING ACTUAL THERMAL RESISTANCE AND DETECTING