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УДК 528.482
КОНТРОЛЬ КАЧЕСТВА И АНАЛИЗ ДЕФОРМАЦИЙ ДЕРЕВЯННЫХ СООРУЖЕНИЙ
Фолькер Швигер
Университет Штутгарта, Geschwister-Scholl-Str. 24D, D-70174, Stuttgart, Германия, доктор наук, профессор, директор Института инженерной геодезии, тел. +49-(0711)-6858-4044, факс: +49-(0711)-6858-4044, e-mail: volker.schwieger@ingeo.uni-stuttgart.de
Аннетте Шмитт
Университет Штутгарта, Институт инженерной геодезии, Geschwister-Scholl-Str. 24D,
D-70174, Stuttgart, Германия, тел. +49-(0711)-6858-4065, факс: +49-(0711)-6858-4065, e-mail: an-nette.scheider@ingeo.uni-stuttgart.de
Рассматривается применение геодезии в роботизированном строительстве деревянных сооружений, включая контроль качества индивидуально изготовленных пластин из дерева и анализ деформации полностью построенного павильона для двух эпох. Сравнивались нормальные вектора решетчатых поверхностей для двух эпох, и они показали отсутствие деформаций. Одной из главных причин является невысокая точная регистрация определение положения с точностью 7 мм. Выявлено, что изготовленные пластины незначительно отличались данной модели. Погрешность измерений была в пределах 0, 11 мм, и это подтвердило, что на пластины изготовлены с точностью 0,42 мм. Кроме того доказано, что в течение шести недель форма деревянные пластины изменилась незначительно.
Ключевые слова: лазерный сканер, лазерный трекер, контроль качества, анализ деформаций.
QUALITY CONTROL AND DEFORMATION ANALYSIS FOR A TIMBER CONSTRUCTION
Volker Schwieger
University of Stuttgart, Geschwister-Scholl.-Str. 24D, 70174 Stuttgart, Germany, Dr.-Ing., Professor, Director of the Institute of Engineering Geodesy, tel. +49-(0711)-6858-4044, fax: +49-(0711)-6858-4044, e-mail: volker.schwieger@ingeo.uni-stuttgart.de
Annette Schmitt
University of Stuttgart, Institute of Engineering Geodesy, Geschwister-Scholl.-Str. 24D, 70174 Stuttgart, Germany, tel. +49-(0711)-6858-4044, fax: +49-(0711)-6858-4044, e-mail: annette.schmitt@ingeo.uni-stuttgart.de
The contribution deals with geodetic contributions to robotic timber construction. It covers the quality control of individually fabricated timber plates and the deformation analysis of the completely constructed pavilion scanned in two epochs. The latter shows no deformations if the normal vectors of the meshed surfaces are compared between the epochs. One of the main reasons is the low accurate registration and geo-referencing reaching values up to 7 mm. For the first task it could be shown that the fabricated plates do not differ significantly from the given model. The measurement uncertainty of around 0.11 mm assures a plate fabrication uncertainty of around 0.42 mm. Additionally, it could be proven that the plates do not significantly change their shape within 6 weeks.
Key words: Laser Scanner, Laser Tracker, Quality Control, Deformation Analysis.
1. INTRODUCTION, PROJECT AND OBJECTIVES
New developments in computational design offer new individual fabrication processes in timber construction. Industrial robots can be used in timber construction to develop new design approaches. But no statements about the accuracy which can be reached in these cases are available. However, quality control for a timber prototype building fabricated by robots has to be realized.
The investigations described in this paper, are part of the project Robotic fabrication in Timber Construction. It is a project driven by architects, structural and geodetic engineers of the University of Stuttgart together with industrial partners like timber fabricators and the federal state Baden-Württemberg. The goal was to develop a lightweight timber construction system which combines robotic fabrication with computational design and simulation processes (Krieg et al., 2014).
A prototype is built at the horticultural show Landesgartenschau 2014 in Schwäbisch Gmünd, Baden-Württemberg, Germany. The prototype is made of 243 timber plates made of beech plywood. These 50 millimeter thin plates are manufactured by an industrial robot with seven degrees of freedom. The plate structure of this prototype recalls the skeletal shell of a sand dollar, a species of sea urchins. The sand dollar has a skeletal shell of polygonal plates of calcium carbonate which "are joint by interlocking calcite protrusions that are the biological equivalent to man-made finger joints" (Krieg et al., 2014). Each plate has an individual shape and position. The shape and position is calculated by an optimization and simulation process (Krieg et al., 2014). The structure of the plates will be visible after setting up the prototype. Factors like statics and extension of the robot are considered. At the end, 7600 finger joints are produced. The pavilion shown in Figure 1 has got a floor space of 125 m2 and the surface envelope of 245 m2, but there are only 12 m3 of timber used (ICD, 2015).
Figure 1 : Left: Exterior view of the pavilion; Right: Plate structure ©ICD/ITKE/IIGS, University of Stuttgart
One role of the geodetic engineer is to determine the fabrication accuracy of the individual timber plates. In this way the automated robotic construction process is
controlled using the Laser Tracker API Radian and a valid uncertainty value with respect to the fabrication is delivered. Further on it was controlled if the geometry of the plates changes over time under different meteorological conditions.
The second role is the analysis of the deformations after construction of the pavilion which is also called prototype by the architectural partners. For this task the whole prototype has been scanned three times using a Leica HDS 7000 Scanner.
2. QUALITY CONTROL OF TIMBER PLATES
2.1 Measurement Instrument and Process
Since the timber plates should be fabricated with an uncertainty below 1 mm, a laser trackers is the right choice to control the quality of the fabrication. In this paper, the laser tracker API Radian from Automated Precision Inc. (API) is used together with the probing tool IntelliProbe360™. With the probing tool, shown in Fig. 3 it is possible to measure, for example, hidden points. The software Spatial Analyzer from New River Kinematics is used to operate the laser tracker and to realize the analysis. The specialty of the laser tracker is the fact that it works with two kinds of distance measuring principles. On one hand, it can be used with the interferometric distance measuring method, which is based on the Michelson-Interferometer and delivers distance differences only. This method offers an accuracy of 5 ^m on 10 m. On the other hand the tracker offers an absolute distance measuring method. This mode is the one which has to used together with the IntelliProbe360™, since the so called birdbath, a known point signalled by an adapter at the laser tracker (Fig.2), cannot be used for the IntelliProbe360™, which means that there is no known absolute distance for the interferometric measuring method. The producer specifies an uncertainty in 3D points of ±126 ^m for two sigma in a distance of 7 m using the absolute distance measuring method (API, 2014).
Figure 2: Laser tracker with the reflector in the birdbath
For this project a special tip for the IntelliProbe360™ is needed to measure the edges of the timber elements. The tip, shown in Fig. 3, is designed by the Institute of
Engineering Geodesy Stuttgart (IIGS), because there are no comparable tips available on the market. This tip offers the possibility to measure the point of the edges directly, whereupon the tip cannot slip down from the edge. Before the measuring task was started, the tip is tested measuring a precise metal work piece, which is produced with a fabrication standard deviation sF of better than 0.1 mm in the workshop of IIGS. One of the edges of the work piece is measured ten times. From the deviations between the measurement values and the CAD model the can be calculated. In this case the s FM stands for the combined standard deviation of measurement and fabrication. However, since the fabrication standard deviation is known, the measurement standard deviation can be calculated as followed:
SM — V SFM ^F . (1)
The measurement standard deviation in X-direction reaches 0.086 mm, and in Y-direction 0.063 mm. However, the 2D-accuracy is 0.106 mm. The Z-direction is not important for the context of the project because the this direction is superposed by external effects and should not to be considered
To get an overview about the fabrication uncertainty of the plates, 24 plates of the 243 plates were quality controlled. The industry specification for timber fabrication is e.g. 4 mm tolerance for lengths of 1 m (DIN18203-3). According to a rule of thumb (Witte and Schmidt, 2006) this yields to a standard deviation of 1 mm for fabrication. These specifications are not of importance for this project, since the fabrication of the plates cannot be restricted to length or cross section. A clear tolerance specification was not given.
Figure 3: IntelliProbe360™ with the special designed tip
First of all, the laser tracker has to be aligned to the plate. For that reason, the CAD model of the plate is integrated into Spatial Analyzer. The software offers a tool to align the laser tracker to the CAD model. This tool first uses the so called 3-2-1-Transformation to find a common coordinate system between measurements and CAD model (New River Kinematics, 2013). Afterwards, a 6 ParameterTransformation, which is called Best-Fit-Transformation, is realized. The 3-2-1-Transformation calculates an approximated solution for stationing. This means a common coordinate system for CAD and the instrument is created. The first point measured is the origin; with the second point the x-axis is created and with the third point the xy-plane is defined. The z-axis is orthogonal to the xy-plane (New River Kinematics, 2013). For this alignment, a spherically mounted retroreflector (SMR) is used. In this case the laser tracker operates in the interferometric mode.
After the alignment, the edge points are measured. At each finger joint ten points are measured with the special designed tip for the IntelliProbe360™. At the outside section of the plates between three and six points are measured. An example for the measured points is shown in Fig. 4. All these points are measured discretely.
Figure 4: Laser tracker measurements of the finger joints
2.2 Analysis Method
After finishing the measurements, the deviations between the measurements and the CAD model are calculated by the Spatial Analyzer function Relationship. Deviations are visible that are effects caused by the alignment. To minimize these effects, a function named Minimizing Relationship is used. This calculates the optimal parameters of a 6 parameter transformation by adjustment theory (New River Kinematics, 2013). An iterative algorithm minimizes the standard deviation sFM over all measured points of one plate. The standard deviation is calculated as follows:
where I is the deviation between the measurements and the CAD model and n is the number of the deviations. Global systematic deviations are assumed to be eliminated, because of the before mentioned function Minimizing Relationship. Local systematic effects are randomized by this function.
For the quality control it is interesting to know if the deviations between the CAD model and the measurement are significant. For the test, the deviation dx between the CAD model and the measurement in each direction is divided through the sFM. The test statistic is given by:
y = 7- . (3)
SFM
The quantile for the null hypothesis is y1_« = 1, 9 6, with a significance level of
2
5%. This double-sided test assumes the Gaussian distribution. If y < yx_a, the null
2
hypothesis is accepted, which means that the deviations between the measurements and CAD model are not significant. If the test is not accepted, the deviations are significant.
To analyze the deformation between two epochs, one has to consider that it is not possible to measure the same point in both epochs. This is because the measured points could not be marked and Spatial Analyzer constructs lines and surfaces from the measured points. However, it is not possible to compare point measurements directly. In this case, the average deviation d of the measurements from each inner and each outer side of the individual finger joint is calculated for both epochs. This average deviation is subtracted from each other and divided through the root square sum of the sFMfrom both epochs. This test induces to a general statement about global deformation of a plate. The test statistic is given by
I^epoch i ~ depochj I sA\
y = i p p == , (4)
FMgpochi FM epOChj
where i and j are different epoch numbers. Again the test takes the Gaussian distribution as a basis with a significant level of 5%. The quantile is the same like for
equation (3). If y < y1_£, the null hypothesis is accepted; this means that there are no
2
deformations between the two epochs. Otherwise, if the null hypothesis is not accepted, deformations at the tested edge are significant.
2.3 Results
In Fig. 5 an example of the deviations in 2D is shown. The color bar on the right side shows the absolute values of the deviations. Most of the deviations are between 0.001 mm and 0.352 mm. All deviations of the plate shown in Fig. 5, are pointing to the middle of the plate. In comparison to the CAD the plate is smaller than it should be.
auto vectors: soll-ljt-vergleich B01 4
Figure 5: Example of deviations in 2D
After minimization, an average sFM for all plates in X- and Y-direction is calculated. In X-direction the average sFM is 0.292 mm and in X-direction it is 0.332 mm. This resulting sF for the 24 measured plates in X-direction is 0.28 mm and in Y-direction 0.32 mm. This leads to a 2D fabrication accuracy of 0.42 mm. For the Z-direction the accuracy is not calculated because plywood has the tendency to buckle and dish (Krieg, et al., 2014). So the values in Z-direction are showing an effect, that is not fabrication induced.
On the base of the standard deviation for the fabrication the significance of the deviations can be determined by using equation (3). In Table 1 the number of significant deviations in both coordinate directions and their percentage rates are given.
Table 1
Number of significant deviations and the percentage rates
X Y
number 192 167
percentage 3.6 % 3.1 %
Four of the 24 plates are measured three times, because the behavior of the timber after production, after a long term of storage and after the transport to the building site should be analyzed. The measurements on the building site where made in a carport which protects the laser tracker and the plates against solar radiation. The measuring and analysis process for these measurements is similar to the one for all 24 plates.
In Table 2 the sFM per epoch and element is shown. The sFM changes between the different epochs up to 0.19 mm. But the minimum and maximum cannot be assigned to one designated epoch.
Table 2
sFM in different epochs
plate 1 dx [mm] dy [mm] 2d [mm]
epoch 1 0.346 0.393 0.524
epoch 2 0.286 0.550 0.620
epoch 3 0.301 0.479 0.566
plate 2 dx [mm] dy [mm] 2d [mm]
epoch 1 0.505 0.508 0.716
epoch 2 0.532 0.470 0.710
epoch 3 0.408 0.281 0.495
plate 3 dx [mm] dy [mm] 2d [mm]
epoch 1 0.306 0.210 0.371
epoch 2 0.307 0.191 0.362
epoch 3 0.458 0.264 0.529
plate 4 dx [mm] dy [mm] 2d [mm]
epoch 1 0.277 0.439 0.519
epoch 2 0.316 0.531 0.618
epoch 3 0.296 0.564 0.637
For these measurements each plate is tested statistically as described in section 2.2. The count of significant deviations is almost equal for the first two epochs. In the third epoch, there are more significant deviations in X- and Y-direction. The reason for that is not caused by metrology and cannot be clarified in the current state of research.
By way of example, the significance of the deviations is controlled for one plate and one epoch comparison. The first epoch is measured directly after fabrication and the second epoch on the building site six weeks later. During these six weeks the plates were stored in a construction hall of the timber constructor. The tested plate is plate 1 and the null hypothesis is accepted for all 52 edges. This means that there are no significant deformations between the two epochs.
3. DEFORMATION ANALYSIS OF THE TIMBER PAVILION
3.1 Measurement Instrument and Process
After the pavilion was completely constructed, it should be controlled if the timber was ageing or deforming with respect to external influences like temperature. Therefore the pavilion was scanned in three epochs. For geo-referencing a geodetic network is set up around the pavilion. This network includes five points in a local coordinate system, shown in Fig. 6, and was measured with a tachymeter Leica TS30. The network was measured in each epoch to ensure that there are no movements in
the network. In addition to the five points around the pavilion same unmarked points inside the pavilion were measured.
After measuring the geodetic network the pavilion is scanned with the laser scanner HDS7000 from Leica Geosystems. This phase-shift-based laser scanner delivers a point uncertainty below a mm, but does not reach laser tracker accuracy. Nevertheless a laser scanner was used for the measurements, since it leads to a dense point cloud and the determination of surfaces and volumes. During the first and the second epoch an exhibition was implemented inside the pavilion, for that reason it was necessary to scan the pavilion from six positions. In the third epoch three positions were sufficient, because the exhibition was finished and disappeared. For registration and geo-referencing targets were used.
The registration and geo-referencing was carried through using Leica Cyclone. The registration was realized classically, which means first a rough registration was made, followed by a fine registration. For the first epoch the mean error for registration is 2 mm, for the second epoch it is 3 mm. In the third epoch the mean registration error is 6 mm. For geo-referencing the mean error in the first epoch is 2 mm and for the third epoch it is 7 mm.
After registration and geo-referencing, the point clouds were filtered and de-noised. However, all points which are not representing the pavilion were deleted. In Fig. 7 the original and the cleaned point clouds are presented. For the deformation analysis the floor of the pavilion is deleted, since it is oscillating due to kinematic louds e.g. pedestrians.
Figure 6: Location of the reference points
Figure 7: Left: original registered point cloud; Right: cleared point cloud
(Wilhelm, 2014)
3.2 Analysis Method
With the freeware JAG3D the adjustment of the geodetic network and the deformation analysis is realized. JAG3D uses the GauB-Markov-Model for the adjustment; free adjustments are programmed by inner constraint solution (Losler, 2014). Observations are directions, distances and vertical angles, as well as heights of the reflectors. The approximated coordinates are calculated by polar survey. The results from epoch 1 and epoch 3 could be used for the geo-referencing of the point clouds (Schmitt and Schwieger, 2015).
Based on this adjustment the deformation analysis is realized with JAG3D (Losler, 2014) too. The software package is based on the implicit hypothesis. Before starting the deformation analysis the networks of both epochs are adjusted to detect measurement errors and to develop the stochastic model. For the congruency analysis, a common adjustment for both epochs is calculated. First the reference points are checked for invariance before checking the object points. For this check, the deformation vector dk between the two epochs is calculated and tested for significance. The variance-covariance-matrix Qddk is calculated, too (Losler, 2014). The following tests were made:
j _i
T _ p (5)
1p n o , k 2 1 m,co , (5)
T 4 Q d dk rffc _ p (6)
1 p o st,k m^ p m,f- m , (6)
m c0
with m are the degrees of freedom of the coordinates, g Q is the a priori variance factor and gQ is the a posteriori variance factor. pm>00 or Pm>f-m are the quantiles of Fisher-distribution (Lösler, 2014). This method is described in detail in (Jäger et al., 2005).
For the deformation analysis of the complete point clouds the cleaned point clouds are modelled. In this case, a triangulation irregular network (TIN) is calculated with Geomagic Studio 2012. The advantage is the in a TIN outliers could be detected and eliminated. Small gaps are closed. With the cleaned TINs the deformation analysis is done using Geomagic Qualify 2012.
For the deformation analysis the first epoch is the reference model. For both models, the reference model and the test model, the lengths of the normal vectors were calculated and subtracted from each other to get . The normal vectors are always showing apart from the scanners. However, positive deformations are shrinkage and negative deformations are expansion (Wilhelm, 2014).
The significance is realized according to Heunecke et al. (2013). The test value is:
T = —, (7)
°Ax
with the standard deviation of the detected deviation, which is calculated as followed, in case of no correlations between the epochs:
gax = >i e x + Gi e з, (8)
GXEi is the standard deviation of the indicated epochs (i = 1,3). They are given by the law of error propagation:
G
XE , = Vg| + G2L , (9)
with gr as standard deviation of registration, which is 3 mm for the comparison of the first and second epoch and 6 mm for comparison between the first and the third epoch. is the standard deviation of single point determination of the laserscans with 1 mm (Wilhelm, 2014). By means of g^ a threshold value can be calculated, which identifies significant deviations between both epochs. The test value T is Gaussian distributed and the confidence probability should be 95%. This leads to a quantile of y^ _ a/2 = 1 , 9 6. The threshold value may be calculated for different probabilities a leading to different quantiles. However, the threshold is set to (Wilhelm, 2014):
I Ax | >yx _a-GAx . (10)
In the case of the comparison between the first and the third epochs, the tachym-eter network fot geo-referencing is used. Both TINs are in the same coordinate system, so no transformation is necessary and the TINs can be compared directly.
The comparison between the first two epochs is not described here. Some geo-referencing problems lead to two alternative approaches. The authors refer to Schmitt and Schwieger (2015) for further information.
3.3 Results
The first and third epochs are compared directly using the geo-referencing which was realized by the tachymeter network. The standard deviation between both epochs is aAx = 6 , 9 mm. However, the threshold value is calculated by using equation (10) to 13.4 mm. The comparison shows that 99.6% of the deviations are in the range between -2 mm and 2 mm. The deviations are shown in Fig. 8.
Figure 8: Overview of the results, epoch 3-epoch 1 - Geomagic 2012
4. CONCLUSION
Regarding quality control using the laser tracker the investigation shows that a fabrication accuracy of around 0.4 mm is reachable. This is proven by a 2D measurement accuracy of around 0.11 mm.
The first test regarding the individual measurements shows the percentage of significant deviations at the individual plates is up to 3.6 %. Nevertheless, the timber
constructor had no problems to set up the prototype. These percentage values may be occurred, where robotics did not work precisely enough or the plate dish or buckle, so that the robotics did not reach these edges.
Additionally one plate is tested for deformations during storage. The test shows that there are no significant deformations during six week bearing. The test dealt with global deformations. Local deformations at the plate could not be detected, since the measurements at different epochs are not taken at identical points.
For the future the quality control measurement process should be integrated into the fabrication and construction process to have the possibility to improve the geometry of the plates during the fabrication phase.
Regarding deformation analysis using tachymeter and laser scanner, the first and the third measurements epochs could be geo-referenced directly. For the point cloud comparison of the two epochs no significant deformations occur.
In the future one has to investigate, how the single plates of the pavilion behave over time, because the deformation of the single plates vary between the borders of the plates and the middle of the plates. The question is, if the meshes between the different plates are the reason for the phenomenon or it is the result of the dishing of the plates.
Additionally a measurement mode and configuration should be developed to improve the quality of the geo-referencing, because the mean error of the registration of 7 mm in the third epoch has a big influence on the significance tests.
5. NOTICE
This paper is based on Schmitt (2015) and Schmitt and Schwieger (2015). To a large extent this contribution follows the two mentioned references word-by-word.
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CONTACTS
Prof. Dr.-Ing. habil. Volker Schwieger
Institute of Engineering Geodesy, Universität Stuttgart Geschwister-Scholl-Str. 24D, D-70174 Stuttgart, Germany phone: +49 (0711) 6858-4041 fax: +49 (0711) 6858-4044 Email: volker.schwieger@ingeo.uni-stuttgart.de
Dipl.-Ing. Annette Schmitt
Institute of Engineering Geodesy, Universität Stuttgart Geschwister-Scholl-Str. 24D, D-70174 Stuttgart, Germany phone: +49 (0711) 6858-4065 fax: +49 (0711) 6858-4044 Email: annette.schmitt@ingeo.uni-stuttgart.de
© Volker Schwieger, Annette Schmitt, 2015
