Photogrammetry article

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The Photogrammetric Record28(142): 211226 (June 2013)

DOI: 10.1111/phor.12024

VALIDATING THE SUPPORTING STRUCTURE OF A

PARABOLIC SOLAR COLLECTOR USING CLOSE

RANGE PHOTOGRAMMETRY

Javier ROCA-PARDI ~NAS ([email protected])

University of Vigo, Spain

Celestino ORDO~NEZ ([email protected])

Silverio GARCIA-CORTES ([email protected])

Antonio BELLO ([email protected])

University of Oviedo, Spain

Abstract

The optical efciency of parabolic trough collectors depends on their

geometric agreement with the parabolic prole design which, in turn, largelydepends on the structure supporting the collector. A method for assessing the

degree of agreement between the measured geometry and the theoretical design

surface is described, which takes into account uncertainty in the point coordinatesand is based on kernel smoothing and bootstrapping methods. The technique was

applied to a 12 m long parabolic trough collector module with a newly designed

supporting structure. The analysis revealed that there were signicant differences

between the estimated and theoretical surfaces in several parts of the collector.

Keywords:bootstrap, close range photogrammetry, condence interval, kernelsmoothing

Introduction

IN MANY ENGINEERING APPLICATIONS, mathematical equations of greater or lesser complexity arerequired to t point clouds to surfaces with predened shapes. In most industrial settings,

85% of objects can be approximated by computer-aided design (CAD) primitives such asplanes, spheres, cones and cylinders (Rabbani and van den Heuvel, 2005). A commonapproach is to generate a point cloud for the object of interest using photogrammetry(Luhmann et al., 2006) or another measurement system such as laser scanning (Roca-Pardi~naset al., 2008; Sansoni et al., 2009). The resulting cloud is then tted to a surface dened by aseries of explicit parameters (Lukacs et al., 1998; Marshall et al., 2001) using least squares orother methods. Each t is analysed to test that it corresponds to the design parameters and todetermine whether a better t could be achieved with alternative parameters. The randomsample consensus (RANSAC) (Fischler and Bolles, 1981) and the Hough transform (Hough,1962; Sarti and Tubaro, 2002; Rabbani and van den Heuvel, 2005) are two of the mostcommon methods used to select explicit parameter values that bestt the point cloud, as they

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reduce error and improve robustness. Both of these methods are based on the hypothesis thatthe point cloud actually ts a specic surface model design; sometimes, however, it isinteresting to check whether this is in fact true for the entire surface area.

In this paper a method for testing whether a point cloud ts a specic parameter-basedsurface shape without presupposing an initial surface model is described. Using the well-known bootstrapping resampling technique (Efron and Tibshirani, 1994), tests for signicantdifferences, for a specied condence level, were undertaken between the estimated surfaceand the theoretical surface for any part of the object. Using this methodology, the interceptfactor for a solar collector system was calculated. Small discrepancies between the actualand theoretical shape of the parabolic surface could cause some of the solar radiationreected by the collector mirrors to miss the absorber tube, thus considerably reducingenergy production. Garca-Cortes et al. (2012) provide a description of this process but thepresent paper explains, in more detail, the photogrammetric analysis performed, with a more

detailed assessment using alternative computational techniques.The data required to calculate the geometry of a solar collector system are typically

determined using close range photogrammetry (Pottler et al., 2005; Lupfert et al., 2007) or

deectometry in the case of solar power tower heliostats (Ulmer et al., 2011) and dishpanels (Ulmer et al., 2008). These two methods are conceptually different. While closerange photogrammetry consists of measuring coordinates corresponding to points along the

surface of the receptors, deectometry consists of measuring the slopes of small areas of thesurface. In both cases, however, the direction of the vectors normal to the surface of thereectors is calculated at multiple points. In the case of parabolic trough collectors,calculating normal vectors enables the path of the reected rays to be calculated so as tocheck that they strike the receiver tube located at the focal line of the collector.

Solar collectors, like the one discussed in this paper, should be designed andconstructed so that at least 95% of the reected sunlight reaches the receiver tube. For thisreason, they are inspected by companies accredited by ofcial bodies. Normally theseinspections are made using photogrammetry, but uncertainty in the t of the surface is nottaken into account. Given the importance of such estimates for the marketing of solarcollectors, the method in this paper aims to improve on these results.

The method proposed is also useful for other problems where it is important todetermine whether the surface of an object estimated from a point cloud, obtained usingphotogrammetry, laser scanning or another method, adapts to a certain theoretical shape fora specic condence level. Such problems include reverse engineering (Sienz et al., 2000;Son et al., 2002) and dimensional control (Martnez et al., 2010) issues in elds such ascivil engineering (Wissler and Froehlich, 1994), shipbuilding (Menna et al., 2009) and thechemical industry (Jones et al., 1996).

This paper is structured as follows. The next section describes the method used toestimate whether the estimated surface of an object, calculated from a point cloud, matchesthe theoretical surface. The following section briey describes the characteristics of the solarcollector system analysed and summarises the method used to generate the point cloud. Theresults are then presented and analysed and, nally, conclusions are drawn.

Statistical Methods

Surface Estimation

In this paper a non-parametric method for estimating a surface represented by a point

cloud was used (Roca-Pardi~nas et al., 2008; Armesto et al., 2010). Unlike classical least

Roca-Pardi~nas et al. Validating a parabolic solar collector using close range photogrammetry

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squares tting, this estimation method does not consider an a priori parameter-based surfacemodel. The algorithm employed is based on local bivariate kernel smoothers (Sarda andVieu, 1999), which enable any 25D surface to be estimated without previously assuming aparameter-based shape.

Consider (X, Y, Z) as the spatial coordinates for each point on the object surface andassume that coordinate Z can be obtained from a special unknown function, m(X, Y), whichrepresents a smooth, but unknown, surface so that Z = m(X, Y). Each pointfXi; Yi;Zigni1, where n is the sample size obtained by photogrammetry or anothermeasurement method, can be considered as a measure of the point (Xi, Yi, Zi) on the surfaceof the object, such that:

Xi; Yi;Zi Xi; Yi;Zi eXi ; eYi; eZi 1

where eXi ; eYi; eZi represents the measurement error of the ith point. Using a Taylorexpansion, the function m(X, Y) can be approximated at points (X, Y) in the neighbourhoodof any given point (X0, Y0) by

mX; Y abXX0 cYY0 2

where b and c are the slopes of the plane m(X, Y) in the directions of the X and Y axes,respectively.

The calculation ofmX; Y as the estimate of m(X, Y) at any given point was achievedusing a non-parametric regression method (Hardle, 1990) based on local polynomial kernelsmoothers.

The following function / was minimised for each xed value over the n points:

/Xni1

WhXix0;Yiy0ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXix02 Yiy02 Zi a bXix0 cYiy02

q3

where

WhXix0; Yiy0 1ffiffiffiffiffiffi

2pp exp X

ix02 Yiy02

2h

( ) 4

is a weighting function that depends on the Euclidean distance between (X, Y) and (X0, Y0).

The bandwidth h is a trade-off between the bias and the variance of the resulting estimates.In this work, cross-validation was used to automatically select the bandwidth (Hastie andTibshirani, 1990).

Condence Testing for Surface Parameters

One of the goals of this research was to determine if m(X, Y) follows a specicparametric form, that is, ifm(X, Y) = mh(X, Y), where h is a parameter (or parameters) thatdetermines the form of m. The interest was in testing the null hypothesis H0: m(X, Y) =mh(X, Y) or, equally, ifd = m(X, Y) mh(X, Y) = 0, for all values of (X, Y).

In practice, d(X, Y) is not known, meaning that its estimate d

m

X; Y

mh

X; Y

must be used. Of course, since dX; Y is only an estimate of the theoretical d(X, Y), the

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sampling uncertainty for these estimates should be taken into account. A condence intervalaround d(X, Y) is thus derived for a (1 a)100% condence level (for example, a = 005).The null hypothesis is accepted if 0 lies within this interval. To obtain the samplingdistribution of the target statistic, a large number of random samples were obtained usingbootstrapping (Hall, 1992; Efron and Tibshirani, 1994).

Given (X, Y), the steps for constructing the condence interval for the theoreticald(X, Y) are as follows:

Step 1. Obtain an estimate ofd(X, Y) from the sample dataXi; Yi;Zi i1; . . .; n asexplained above.

Step 2. For b = 1 to B (for example, B = 1000), simulate a random sampleXb1 ; Yb1 ;Zb1; . . .; Xbn ; Ybn ;Zbn by randomly sampling n items from the original datasetXi; Yi;Zi i1; . . .; n with replacement (each individual value Xi; Yi;Zi has aprobability 1/(n 1) of occurring) and calculating the bootstrapped estimate dbx;y.

Step 3. Finally, a two-tailed statistical test was applied by calculating the (1 a)100%limits for the condence interval ofd(X, Y):

da=2X; Y; d1a=2X; Y 5

wheredp(X, Y) represents thep percentile of the bootstrapped estimates d1x;y; . . .; dBx;y.Bootstrap resampling techniques are time-consuming processes because it is necessary to

estimate the model many times. Moreover, the use of cross-validation to choose thebandwidths used in the non-parametric estimates implies a high computational cost, since it isnecessary to repeat the estimation operations several times to select the optimal bandwidths.

Consequently, recourse to some computational acceleration technique is fundamental toensure that the problem can be addressed adequately in practical situations. To speed up this

process, binning techniques were used (Roca-Pardi~nas et al., 2008).

Application

Parabolic Solar Collector Systems

Parabolic trough collectors (PTCs Fig. 1) are a common type of solar collectorsystem used in concentrating solar plants. They are more widely used than other

Fig. 1. Solar parabolic trough collector assembled in the vertical position (the receiver tube is not shown). Theimages show the support structure at the back (left) and the mirrors on the front (right).


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technologies such as solar power towers or parabolic dish systems. PTCs concentrate thesuns rays at the focal line of the parabolic reector, which is tted with a tube, known as areceiver or absorber tube, containing a liquid (generally oil) whose temperature graduallyincreases. This thermal energy is transferred to water stored in heat exchangers, producinghigh-pressure superheated steam that feeds an electricity-producing turbine-generator system.

A PTC consists of a support structure, parabolic reectors (or mirrors) and a sun-trackingsystem. Several collector models exist, such as EuroTrough (Geyer et al., 2002), SCX,SGX-1 (Solargenix Energys Technologies, 2011), LS-3 and LS-2 (Luz Energy Corporation,2011), each with different characteristics in terms of aperture, concentration ratio and opticalefciency. Optical efciency is a function of the transmissivity of the glass covering thereceiver tube, the absorptivity of the steel of which the tube is made, the reectivity of themirrors and the geometry of the collector (Kreith and Goswami, 2007). Microscopic andmacroscopic imperfections in the surface shape mean that not all incident solar radiation

reaches the receiver tube. Most macroscopic imperfections occur during the assembly of thestructure with the reectors. The whole efciency of the collector is quantied by an interceptfactor, typically 095 for a correctly installed system (Kreith, 2007). The intercept factor canbe dened as the ratio of the energy intercepted to the energy reected by the parabola(Kalogirou, 1996). Errors affecting the intercept factor include misalignment of mirrors andabsorber tube, tracking errors (for collectors which operate in a solar eld), geometric errors

(departure of PTC shape from the parabolic cylinder design) and the assumed energydistribution of the suns rays, called sunshape (Schubnell, 1992).

Geometric errors (prole errors) are responsible for most efciency losses in a PTC.Quantifying this error is the objective of this research as it is important when validating anew design for a supporting structure.

Data Collection

The collector studied was installed in isolation to investigate the behaviour of a newdesign for the supporting structure and its inuence on the geometric component of theintercept factor. A receiver tube was not installed although, for intercept factor calculationpurposes, it was assumed that it would be perfectly aligned. Given that the purpose was toquantify assembly errors and deviations in the supporting structure due to a lack of rigidity,and to estimate uncertainty in the geometric component of the intercept factor, a number ofother simplications were made in the study. Thus in calculating the intercept factor, thefollowing three factors were not considered: (a) sunshape (solar energy distribution over theapparent diameter); (b) tracking mechanism error; and (c) mirror small-surface deformations.Sunshape (Buie et al., 2003) could signicantly affect the estimated intercept factor, with adecrease of 10% to be expected in some high-rate concentrators like parabolic dishes(Schubnell, 1992). Since sunshape does not depend on the collector geometry, and given thatthe measured collector is a non-homologated prototype, this factor was not taken into account

Table I. Design specications of the parabolic collector.

Length 12 mAperture 577 mNumber of mirrors 28Size of mirrors:

Interior 1501 mm 9 1701 mmExterior 1644 mm 9 1701 mm

Focal distance, f(Z= Y2

/4f) 171 m


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in this study. The reason for not analysing mirror defects is that these are in the range ofmicrons (Shortis et al., 2008) and thus far beyond the precision required in this study.

The solar trough collector studied in this work can be seen in Fig. 1. Its technicalspecications are summarised in Table I.

To reconstruct the surface shape of a PTC (Lupfert et al., 2001; Geyer et al., 2002),whose theoretical shape is given by the equation Z = Y

2/4f, with f = 171 m in this instance,close range photogrammetry was used. Although the collector was measured in both ahorizontal and a vertical position, in this paper only the horizontal position is studied.

Photogrammetric Work

Due to the lack of natural target points on the surface of the solar collector and because ofthe reective nature of the mirrors, special targets were used to capture the coordinates. Theusual procedure is to attach a sheet of adhesive vinyl with a printed array of targets, of anappropriate size and shape, to the surface. In this case a mesh consisting of circular black targets(4 cm diameter) was used. The targets were printed on vinyl at intervals of 10 cm vertically and5cm horizontally (Fig. 2) against a white background and were detected automatically duringthe photogrammetric processing with Eos Systems PhotoModeler 2012. The thickness of the

vinyl was 75 nm. The centres of these targets were determined by the software using leastsquares matching (LSM) (Forstner, 1982; Ackermann, 1984; Grun, 1985). The PhotoModelersoftware has two different sub-pixel extraction methods (centroid and LSM) and automatically

decides which one to use based on the diameter of the target in pixels. In this case LSM, themore precise method, was used for all the targets by selecting a very large diameter threshold.About 7000 target points were measured on the surface of the mirrors for each position; 97%ofthese points appeared in four or more photographs, providing good image redundancy.

Images were captured using a previously calibrated CANON EOS 1000D SLR camerawith an 18 to 55 mm lens (principal distance 18 mm; physical pixel size 57lm; sensorresolution 101 Mpixel). This consumer-grade DSLR camera had a basic zoom lens, whichis well known to be a cause of instability (Shortis et al., 2006) but no other suitable camerawas available at that time. All the work was done using the wide-angle (18 mm) position.The photographs were taken from convergent stations around the collector from a crane,

Fig. 2. Front view of the collector with the vinyl targets attached. A few codedtargets can be observed and also some gaps left after installation.


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oor or monopod (5 m long), depending on collector position and the space availablearound the structure.

Several tens of images were taken for each collector position with the purpose ofimproving the geometry and precision (Fraser et al., 2005) by increasing the number ofobservations and favouring the decoupling of the internal and external camera parametersduring the bundle adjustment with self-calibration. However, at this point a practicallimitation was encountered, imposed by the software: the large number of object points, thelarge number of images and the camera/lens instability forced a reduction in the number ofimages in the project. In the end only 12 images could be included in the adjustment. Someauthors (Remondino and El-Hakim, 2006) claim, however, that non-signicant improvementmust be expected from measuring points in more than four images. For this reason theimage redundancy was maintained at that level for most of the object points in the project.

With no external control points available, a free network adjustment was made, based

on a pseudo-inverse calculation of the design matrix for the global equation system(Granshaw, 1980; Cooper and Cross, 1988). This procedure allows the inner accuracy to bestudied in isolation from any external error. During the bundle adjustment processing in

PhotoModeler 2012, the internal camera parameters were allowed to change slightly foreach photo (Fraser et al., 1995). In this way the bundle adjustment process could absorbpart of the instability that could be expected from the camera lens in a self-calibration

procedure. In order to compare the collector geometry with the theoretical one, a post-processing scaling of the results was made using a single distance, located in the centralpart of the collector. This distance was between two very well dened targets to minimisethe chance of introducing any systematic error. The geometric precision of professional

Table II. Results from the 7000-point photogrammetric network for the collector in the horizontal positionwith two adjustment variants: free network and constraint adjustment for six distances.

Network characteristics Adjustment type

Free network adjustment Constrained adjustment

Number of images 12Mean image scale 1/497Number of points 7102Average point angle 87Points marked in fewer than four images < 3%

x y ra x y ra

RMS image coordinate residuals (pixels) 0067 0055 0087 0068 0055 0087Maximum residual 078 077 084 078 0075 092Object point standard errors (mm) X Y Z X Y Z Mean 0096 0084 0094 0187 0123 0097Minimum 0067 0056 0067 0067 0057 0068Maximum 0249 0438 0486 0413 0619 0488Mean object point standard error 0091 0136Mean relative precision 1/145 609 1/98 235

RMS check distance precision (mm) 121 101Maximum 257 227Minimum 002 001Mean relative precision (external) 1/11 000 1/13 179Long distance discrepancy RMS (mm)between the two adjustment types

0799

a r ffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffix2 y2p :


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printer hardware, together with the very low deformation capacity of vinyl, were assumed todeliver a precision below 1 mm for this distance in the object space. Another 50 additionaldistances between targets were also measured and compared with their theoretical values toestimate the external precision achieved. The results for this free network adjustment can beseen in the corresponding column in Table II.

A constrained variant of the adjustment was also performed. In this case, six distancesbetween targets (distributed around the edges of the collector) were used to constrain the bundleadjustment procedure. All these distances were considered as xed constraints in the adjustment.

The quality of these adjustments can be assessed from the estimators shown in Table II.The root mean square (RMS) for image residuals is about 1/10 of a pixel, indicating goodinner precision for the model. Values for this estimator are also within the recommendedrange (1/10 to 1/40 of a pixel) (Pottler et al., 2005), thereby ensuring the projects to be free ofgross errors. The object point precision values were also found to be below 1 mm (1 sigma).

The RMS check distance values in Table II quantify the external precision. The constrainedadjustment appears to produce a slight increase in external precision without degrading theinner precision. The internal precision obtained from the inner constraints was slightly better

than the precision from the distance-constrained adjustment. Nonetheless, the contrarybehaviour can be observed for the external precision, probably due to the poor performancethat can be expected from a zoom lens (Shortis et al., 2006). This is hardly surprising as, by

denition, a free network has to derive the minimum mean variance for point coordinates(Fraser et al., 2005). The coordinates obtained for the points were exported to text les forfurther processing; the resulting point clouds were translated and rotated to be compared withthe estimated and theoretical shape of the collector. Garca-Cortes et al. (2012) provide adescription of this process but the present study explains, in more detail, the photogrammetricanalysis performed. Thus the results for the free and constrained network adjustments areshown in Table II and a more robust method for verifying the external precision has also beenused. Five distances (between 12 and 55 m) have been used for a comparison between the

Fig. 3. Distribution of check distances. All distances measure 1 m. Scaling was performed after the free networkadjustment with only a single scaling distance located in the centre of the collector. In the constrained

adjustment, only the six distances indicated by rectangles were included in the adjustment.


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external precisions of the constrained and free network adjustments, resulting in an RMSdiscrepancy of 0799 mm (Fig. 3).

Fig. 4 represents the error ellipsoids for each of the measured points. The maximumvalue of the major axes for all the ellipsoids is 0

873 mm.

Results

Using the point cloud obtained by photogrammetry, a non-parametric surface wascreated using the method described in the Surface Estimation section (Fig. 5).

Fig. 6 depicts dX; Y and the corresponding 95% condence interval for two crosssections of the collector. It can be observed that there are some Yintercept intervals for whichthe interval between the upper and lower 95% condence limits (pecked lines) is entirelyabove or below zero, indicating that the estimated and theoretical surfaces of the PTC did notmatch. These areas corresponded to the edges of the reectors and were associated with agreater distance between these areas and the support structures, and also with the exure ofthe support caused by both the weight and deviations that occur, which should be correctedduring the assembly of the system. The method proposed in this paper can also be used todetermine whether the deviation from the theoretical surface shape is higher than a xedvalue simply by moving the horizontal line (at zero in Fig. 6) towards this value.

Fig. 7 depicts, for a cross section of the parabolic trough, the theoretical values and theestimated b and c values from equation (2) for the plane calculated from the point cloud,

together with the 95% condence intervals. Parameter b (Fig. 7, top) could be considered tobe zero across the section as the corresponding condence intervals include zero. Incontrast, there are several areas where parameter c (Fig. 7, bottom) (partial derivative withrespect to Y) was signicantly different from the theoretical value.

Fig. 4. 3D view of the point cloud with error ellipsoids for each point. The size of the error ellipsoids ismagnied 500 times for viewing purposes.


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Fig. 5. Surface tted to the point cloud using non-parametric regression.

Fig. 6. Functiond(95% condence interval indicated by the pecked lines) used to test for signicant differencesbetween the theoretical and estimated surface shapes corresponding to two cross sections (left and right graphs)

of the collector. Units are in millimetres.


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The vector normal to the surface at each point is N = (b,c, 1). Using the estimatedcoefcient c, the angle / = arctan(

1/c), which denes the direction of the normal vector

N for a cross section (normal to the X axis) of the reector surface, was calculated. Taking

Fig. 7. Theoretical and estimated values (95% condence interval) for coefcients b (top) and c (bottom) (seeequation (2)) for the plane tted to the collector surface and corresponding to a cross section of the surface.The rectangle in the lower graph shows an interval in which the theoretical value of c is outside the

condence interval, indicating that it is signicantly different from the estimated value.


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into account the standard practice, the longitudinal component of the normal vector has notbeen considered, since, although it can cause deections across the receiver, they are notconsidered relevant because its effect is mainly to deect the suns rays in the direction ofthe cylinder axis; thus, the reected rays also reach the focal line where the absorber islocated but a cross section located a little further away. Fig. 8 (top) shows the normalvector N at a point on the surface, together with the angle a (equal to 2/ p/2), whichdenes the direction of the reected ray at this point. The angle / and the corresponding95% condence interval for a cross section of the reector surface are depicted in Fig. 8(bottom). Each point on the surface was analysed to assess whether a was inside theinterval (b Db, b + Db), which meant that a solar ray reected at this point would reachthe tube. This process was repeated for all the surfaces estimated using bootstrapping(B = 1000 in this case). The 95% condence interval for the intercept factor was (8715%,8987%). Consequently, collector efciency was under the 95% recommended value for theintercept factor. It should be taken into account that, as already mentioned, the sunshapeeffect has not been considered in the calculation of the intercept factor.

Fig. 8. Cross section of the collector showing incident ray (Z), surface normal vector (N) and reected ray (r).Top: the vector t and angle Db dene the valid angular range for a reected ray to hit the absorber pipe.

Bottom: angle / and the corresponding 95% condence interval for a cross section of the reector surface.


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The areas of the collector where the reected rays missed the absorber are depicted inFig. 9, where it can be observed that the missed rays (dark areas) emanate from the edgesof the collector.

In the researchers view, providing a condence interval for the intercept factor is moreappropriate than the single value that is typically quoted, as the single value is based on asingle sample, whereas the condence interval expresses the effect that the uncertainty

associated with the original point cloud has on the intercept factor.Garca-Cortes et al. (2012) estimated that the intercept factor for the studied trough

collector was 9070%, which is a little above the upper limit (8987%) of the condenceinterval calculated in this paper. Given that the initial point cloud is nearly identical in bothstudies, this discrepancy is mainly explained by the fact that different methods were used tocalculate the normal vectors: a bivariate kernel smoother in this study and a Delaunaytriangulation in the earlier study. In the current work, a bivariate kernel smoother technique

was used for several reasons: (a) it is easy to implement; (b) it reduces the effect of noise inthe data; and (c) it is computationally less expensive than triangulation, which becomesimportant when the bootstrapping technique is applied. Nonetheless, for a signicance levelof 95%, 5 in every 100 measurements will yield an intercept value outside this range. Theresults for both studies indicate that the greatest discrepancies between the theoretical and

actual shapes occur at the collector edges.

Conclusions

A method for determining whether the shape of a surface computed from a point cloudts that of a surface dened by an explicit parameter-based equation has been described.The proposed method, based on non-parametric regression and bootstrapping, uses a statisticthat reveals differences between the tted surface and the theoretical surface, withcondence intervals set for a predetermined level of condence. The algorithm can be usedto calculate differences in a very short space of time, even for massive point clouds. Unlikethe method used in previous work by the authors (Garca-Cortes et al., 2012), the

methodology proposed in this paper provides a condence interval for the intercept factor,

1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 11000

2500

2000

1500

1000

500

0

500

1000

1500

2000

2500

Spatial distribution of reflected rays on the solar collector

Collector length (mm)

Collectoraperture(mm)

missed rayshit rays

Fig. 9. Top view of the solar collector. Black squares represent surface patches where the reected rays did nothit the absorber pipe.


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rather than a single value. This expresses the uncertainty in the point cloud which can betransferred to the intercept factor.

The application of the method to a PTC showed that the actual surface shape did notmatch the theoretical shape in parts, mainly at the edges. According to the uncertaintyanalysis performed, it could be concluded that, at the 95% condence level, the collectorsefciency was below the recommended value for the intercept factor. The differences aremainly attributed to mirror assembly misalignments and support structure deviations and,consequently, a review of the design and the mirror assembly procedure is recommended.

Further improvements could be carried out in future research. The photogrammetricwork could be strengthened if a better camera, especially with an improved lens, wasused. A xed focus lens with aspherical elements and better camera resolution valuescould increase the image point precision. In addition, the estimation of the interceptfactor could be improved using photogrammetric software that calculates the surface

normal vectors from the target extraction algorithm. External precision assessment couldalso benet from the use of reference length bars; this is also the recommendedprocedure to scale the photogrammetric model. Finally, greater redundancy in the image

network would be desirable.

references

Ackermann, F., 1984. High precision digital image correlation. 39th Photogrammetric Week, 1983,Universitat Stuttgart. Germany. Schriftenreihe 9: 231243.

Armesto, J., Roca-Pardi~nas, J., Lorenzo, H. and Arias, P., 2010. Modelling masonry arches shape usingterrestrial laser scanning data and nonparametric methods. Engineering Structures, 32(2): 607615.

Buie, D., Monger, A. G. and Dey, C. J., 2003. Sunshape distributions for terrestrial solar simulations. SolarEnergy, 74(2): 113122.

Cooper, M. A. R. and Cross, P. A., 1988. Statistical concepts and their application in photogramemtry and

surveying. Photogrammetric Record, 12(71): 637

663.Efron, B. and Tibshirani, R. J., 1994. An Introduction to the Bootstrap. Chapman and Hall/CRC, Boca

Raton, Florida, USA. 436 pages.Fischler, M. A. and Bolles, R. C., 1981. Random sample consensus: a paradigm for model tting with

applications to image analysis and automated cartography. Communications of the ACM, 24(6): 381395.Forstner, W., 1982. On the geometric precision of digital correlation. International Archives of

Photogrammetry and Remote Sensing, 24(3): 176189.Fraser, C. S., Shortis, M. R. and Ganci, G., 1995. Multi-sensor system self-calibration. Videometrics IV.

SPIE, 2598: 215.Fraser, C. S., Woods, A. and Brizzi, D., 2005. Hyper redundancy for accuracy enhancement in automated

close range photogrammetry. Photogrammetric Record, 20(111): 205217.GarcIa-Cortes, S., Bello-GarcIa, A. and Ordo~nez, C., 2012. Estimating intercept factor of a parabolic

solar trough collector with new supporting structure using off-the-shelf photogrammetric equipment.

Applied Energy, 92: 815

821.Geyer, M., Lupfert, E., Osuna, R., Esteban, A., Schiel, W., Schweitzer, A., Zarza, E., Nava, P.,Langenkamp, J. andMandelberg, E., 2002. EuroTrough parabolic trough collector developed for costefcient solar power generation. 11th International Symposium on Concentrating Solar Power andChemical Energy Technologies, Zurich, Switzerland. 7 pages.

Granshaw, S. I., 1980. Bundle adjustment methods in engineering photogrammetry. Photogrammetric Record,10(56): 181207.

Grun, A., 1985. Adaptive least squares correlation: a powerful image matching technique. South AfricanJournal of Photogrammetry, Remote Sensing and Cartography, 14(3): 175187.

Hall, P., 1992. On bootstrap condence intervals in nonparametric regression. Annals of Statistics, 20(2): 695711.

Hardle, W., 1990. Applied Nonparametric Regression. Cambridge University Press, Cambridge, UK. 333pages.

Hastie, T. J. and Tibshirani, R. J., 1990. Generalized Additive Models. Chapman and Hall, London, UK. 335

pages.


2013 The Authors



15/16

Hough, P. V. C., 1962. Method and means for recognizing complex patterns. US Patent Ofce. Patent No.3069654.

Jones, M. A., Chapman, D. P., Hamid, A. A. and Deacon, A. T. D., 1996. Close range photogrammetryusing geometric primitives for efcient CAD modelling of industrial plant. International Archives of

Photogrammetry and Remote Sensing, 31(B5): 284

289.Kalogirou, S., 1996. Parabolic trough collector system for low temperature steam generation: design andperformance characteristics. Applied Energy, 55(1): 119.

Kreith, F. and Goswami, D.Y. (Eds.), 2007. Handbook of Energy Efciency and Renewable Energy. CRCPress, Boca Raton, Florida, USA. 1113 pages.

Luhmann, T., Robson, S., Kyle, S. and Harley, I. A., 2006. Close Range Photogrammetry: Principles,Techniques and Applications. Whittles, Caithness, Scotland. 510 pages.

Lukacs, G., Martin, R. and Marshall, D., 1998. Faithful least-squares tting of spheres, cylinders, conesand tori for reliable segmentation. Proceedings of Fifth European Conference on Computer Vision,Freiburg, Germany. 671686.

Lupfert, E., Geyer, M., Schiel, W., Esteban, A., Osuna, R., Zarza, E. and Nava, P., 2001.EuroTrough design issues and prototype testing at PSA. Proceedings of Solar Forum 2001. Solar Energy:The Power to Choose, Washington, DC, USA. 389393.

Lupfert, E., Pottler, K., Ulmer, S., Riffelmann, K.-J., Neumann, A. and Schiricke, B., 2007.

Parabolic trough optical performance analysis techniques. Journal of Solar Energy Engineering, 129(2):147152.

LUZ ENERGY CORPORATION. http://www.luzenergy.com/ [Accessed: 18th July 2011].Marshall, D., Lukacs, G. and Martin, R., 2001. Robust segmentation of primitives from range data in the

presence of geometric degeneracy. IEEE Transactions on Pattern Analysis and Machine Intelligence, 23(3):304314.

MartInez, S., Cuesta, E., Barreiro, J. and Alvarez, B., 2010. Methodology for comparison of laserdigitizing versus contact systems in dimensional control. Optics and Lasers in Engineering, 48(12): 12381246.

Menna, F., Ackermann, S., Scamardella, A., Troisi, S. and Nocerino, E., 2009. Digitalphotogrammetry: a useful tool for shipbuilding applications. Proceedings of 13th Congress of theInternational Maritime Association of the Mediterranean (IMAM), Istanbul, Turkey. 607614.

Pottler, K., Lupfert, E., Johnston, G. H. G. and Shortis, M. R., 2005. Photogrammetry: a powerful tool

for geometric analysis of solar concentrators and their components. Journal of Solar Energy Engineering,127(1): 94101.Rabbani, T. and van den Heuvel, F., 2005. Efcient Hough transform for automatic detection of cylinders in

point clouds. International Archives of Photogrammetry, Remote Sensing and Spatial Information Sciences ,36(3/W19): 6065.

Remondino, F. and El-Hakim, S., 2006. Image-based 3D modelling: a review. Photogrammetric Record,21(115): 269291.

Roca-Pardi~nas, J., Lorenzo, H., Arias, P. and Armesto, J., 2008. From laser point clouds to surfaces:statistical nonparametric methods for three-dimensional reconstruction. Computer-Aided Design, 40(5):646652.

Sansoni, G., Trebeschi, M. and Docchio, F., 2009. State-of-the-art and applications of 3D imaging sensorsin industry, cultural heritage, medicine, and criminal investigation. Sensors, 9(1): 568601.

Sarda, P. and Vieu, P., 1999. Smoothing kernel regressionIn Smoothing and Regression: Approaches,Computation, and Application (Ed. M. Schimek). Wiley, New York, USA. 607 pages.

Sarti, A. and Tubaro, S., 2002. Detection and characterization of planar fractures using a 3D Houghtransform.Signal Processing, 82(9): 12691282.

Schubnell, M., 1992. Sunshape and its inuence on the ux distribution in imaging solar concentrators.Journal of Solar Energy Engineering, 114(4): 260266.

Shortis, M. R., Bellman, C. J., Robson, S., Johnston, G. J. and Johnson, G. W., 2006. Stability ofzoom and xed lenses used with digital SLR cameras. International Archives of Photogrammetry, RemoteSensing and Spatial Information Sciences, 36(5): 285290.

Shortis, M. R., Johnston, G. H. G., Pottler, K. and Lupfert, E., 2008. Photogrammetric analysis ofsolar collectors. International Archives of Photogrammetry, Remote Sensing and Spatial InformationSciences, 37(5): 8187.

Sienz, J., Szarvasy, I., Hinton, E. and Andrade, M. L., 2000. Computational modelling of 3D objects byusing tting techniques and subsequent mesh generation. Computers & Structures, 78(13): 397413.

SOLARGENIX ENERGYS TECHNOLOGIES. http://www.solargenix.com/ [Accessed: 4th February 2011].


2013 The Authors



16/16

Son, S., Park, H. and Lee, K. H., 2002. Automated laser scanning system for reverse engineering andinspection. International Journal of Machine Tools & Manufacture, 42(8): 889897.

Ulmer, S., Heller, P. and Reinalter, W., 2008. Slope measurements of parabolic dish concentrators usingcolor-coded targets. Journal of Solar Energy Engineering, 130(1): 011015.1011015.5.

Ulmer, S., M

arz, T., Prahl, C., Reinalter, W. and Belhomme, B., 2011. Automated high resolutionmeasurement of heliostat slope errors. Solar Energy, 85(4): 681687.Wissler, R. and Froehlich, C., 1994. Three-dimensional imaging laser scanner for the inspection of tunnels.

SPIE, 2249: 96106.

Resume

Le rendement optique dun capteur solaire parabolique depend du degre dajustement de sa geometrie

avec la conception du prol parabolique, qui a son tour depend en grande partie de la structure qui supporte

le capteur. Cet article presente une methode pour evaluer le degre dadequation entre la mesure et la theorie

de la conception de surface geometrique, prenant en compte lincertitude des coordonnees des points et basee

sur des methodes de lissage du noyau et damorc

age. Ces techniques ontete appliquees a un capteur solaire de12 m de long avec une structure de soutien de conception nouvelle. Notre analyse a permis de mettre en

evidence des differences signicatives entre les surfaces theoriques et estimees dans plusieurs zones du capteur.

Zusammenfassung

Der optische Wirkungsgrad von Parabolrinnenkollektoren hangt von der geometrischen Ubereinstimmung

mit dem parabolischen Prol aus dem Design ab, welches wiederum von der Stutzkonstruktion des Kollektors

abhangt. Es wird eine Methode vorgestellt, die den Grad der Ubereinstimmung der gemessenen Oberache mit

der Geometrie der theoretischen Oberache aus dem Design ermittelt. Die Methode berucksichtigt die

Unsicherheit der Punktkoordinaten und basiert auf Glattungs- und Bootstrapping Methoden. Der Ansatz wurde

an einem 12 m langen Parabolrinnenkollektor mit neuartiger Stutzkonstruktion erprobt. Die Analyse ergab, dass

es in mehreren Bereichen des Kollektors signikante Unterschiede zwischen der geschatzten und der

theoretischen Oberache gibt.

Resumen

La eciencia optica de un colector solar parabolico depende del grado de ajuste de su geometra con el

perl parabolico de dise~no, que a su vez depende en gran medida de la estructura que soporta el colector. En

este trabajo se muestra un metodo para valorar el grado de ajuste entre la geometra medida y la supercie

teorica de dise~no que tiene en cuenta la incertidumbre en las coordenadas de los puntos y se basa en metodos

de suavizado de nucleo y bootstrap. Estas tecnicas se aplicaron a un PTC de 12 m de largo con una estructura

de soporte de nuevo dise~no. Nuestro analisis revelo que el colector mostraba diferencias signicativas entre las

supercies teorica y estimada en varias zonas.


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Photogrammetry article

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