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David H. Parker

CMSC

Experimental Uncertainty Analysis for NDT on the CSX Wilbur Bridge

Electronic distance measurements utilized to measure 3D coordinates of cardinal points

Published: Tuesday, April 23, 2019 - 21:06

A 154-page report by Moreu and LaFave in 2012 explains unique problems railroad bridge engineers must contend with. The gross weight of cars went from 200,000 pounds to 263,000 pounds in the 1970s, and to 286,000 pounds in 1991. The ratio of live to dead loads are much greater for railroads than highways. Dynamic forces due to such things as wheel hunting, rock and roll, locomotive tractive forces, and braking make it very desirable to measure motions in all three directions (i.e., longitudinal, transverse, and vertical directions), which is why a survey of railroad bridge engineers ranked measuring 3D deflections under live loads as the top research interest.

This article will argue that electronic distance measurement (EDM) instruments are uniquely qualified to perform such measurements. This is a technology that is unfamiliar to the bridge industry, so a feasibility study is needed. The CSX Railroad Wilbur Bridge is a 270-ft span Parker through truss bridge, built in 1903, which is still in revenue service, and representative of U.S. railroad bridges. The age, design, size, and geography make it a good selection for the feasibility study. Plans are presented for nondestructive testing and structural health monitoring of the structure by electronic distance measurement instruments in a trilateration/multilateration architecture. Instrument benchmark locations and cardinal points on the structure are identified. Uncertainty analyses are conducted for least-squares adjustments using the pre-analysis feature of MicroSurvey® STAR*NET software, which calculates the uncertainty of a prescribed measurement plan, based on entered instrument performance specifications.

The study was conducted for various combinations of measured distances in trilateration/multilateration architectures for distance measurements between 84 m and 383 m. Results are presented for both laser tracker and total station-class electronic distance measurement instruments. Uncertainties are calculated for measured 3D coordinates in the absolute reference coordinate system (which are directly dependent on the group refractive index of air), for differential measurements between adjacent cardinal points on the bridge (which are less dependent on the group refractive index), and for differential dynamic and vibrational measurements of individual points (which are insensitive to the group refractive index). Results confirm that the resultant 3D coordinate uncertainties make the measurement architecture attractive to railway bridge engineers for conducting static and dynamic load testing, and structural health monitoring.

Introduction

This is the fourth in a series of articles on the use of EDM instruments for nondestructive testing (NDT) and structural health monitoring (SHM). The four articles are cumulative, with each covering a different aspect of a common theme, so those interested in the subject should also review the first three papers1-3 and a related family of US Patents.4-7

It is the thesis of this series that the use of EDM for NDT and SHM has largely been overlooked, or misapplied, outside of the aerospace, precision manufacturing, and shipbuilding industries. The technology transfer from these high-technology industries presents significant opportunities in the civil, structural, mechanical, and software engineering fields, as well as expanded markets for instrument manufacturers, software companies, and service providers—particularly for large-scale static and dynamic metrology applications, such as bridges. The third of these articles argues3 that there is a major disconnect between the bridge engineering, NDT, and the Coordinate Metrology Society (CMS) communities—which this article is intended to address by example of a railroad bridge application.

Measurements desired by railroad bridge engineers

Railroad bridge engineers must contend with even greater challenges than highway bridge engineers due to the high ratio of live to dead load, large dynamic forces, and increasing heavy axle loads (HAL) due to increasing gross vehicle weight (GVW), which has gone from 200,000 pounds in the 1970s to 286,000 pounds in 1991.8 Dynamic forces are due to such things as wheel hunting, wheel flat spots, high center of gravity loads which induce rock and roll, locomotive tractive forces, braking forces, and discontinuities in stiffness at approaches.9-13

Moreu and LaFave published an extensive 154-page report14 in 2012 in which they interviewed 16 experts on railway bridges and structural engineering, with a combined experience of more than 500 years, as to research priorities for railway bridges.

There are a number of findings in this report that are particularly relevant to the CMS community, which are worth mentioning in arguments establishing the need for high-accuracy 3D measurements, and Level-Two-certified laser tracker metrologist necessary to conduct these NDT measurements.

The present state-of-the-art for SHM of bridges is to instrument the bridge with accelerometers, inclinometers, strain gages, extensometers, and temperature sensors. The report from 2012 addresses the problems of using accelerometers, which must be integrated twice, to measure displacement. Item 8 of the report states (p. 82):

“Finally, railroad bridge structural engineers showed specific interest in developing sensors that could collect the actual displacement of railroad bridges in real-time. In their opinion, displacement data could be of significant assistance for railroad bridge managers. However, these structural engineers expressed their concern of sensors being able to integrate acceleration records due to the Rigid Body Motion (RBM) intrinsic effect to the sensor being accelerated. This group of railroad bridge structural engineering experts showed interest in developing sensing tools and methods that can accurately measure real-time displacements of bridges under train traffic, in the three directions (longitudinal, transverse, and vertical).”

Section 8.1 of that same report states (p. 123):

“This survey-based study ranked measuring deflections under live loads as the current top research interest. According to the majority of the engineers in the survey, measuring real-time deflections under live load can be beneficial both in terms of railroad bridge management and railroad bridge replacement prioritization, especially for timber bridges.”

It will be argued that the proposed EDM measurements will provide hard, static, and dynamic, dead and live load, high accuracy, measurement data; from the field, for a large number of cardinal points on actual bridges, under actual operating load conditions, in the vertical, longitudinal, and transverse directions; that are repeatable, traceable to NIST, intuitively understood, and economical; which will assist in a global structural assessment of the bridge. In other words, more than the engineers in the 2012 report wished for.

An overview of EDM capabilities

The first article in this series includes a section titled, “An Introduction to Electronic Distance Measurement,” which will not be duplicated here. For the immediate purposes of this article, attention will be drawn to the capabilities and possible applications. The first article also includes an extensive review of the literature on previous attempts to measure bridges using EDM—and explains why those attempts were misapplications of the instruments used.

The second article (which was presented at CMSC 2017) covers a review of commercially available EDM instruments and arguments as to why the radial measurement capabilities are understated in the instrument companies’ published specifications.

Commercially available laser tracker instruments measure extremely accurately in the radial direction, but much less accurately in the two angles. However, full 3D capabilities are available by using three instruments in a trilateration architecture, i.e., measuring the distances by EDM from three instruments attached to stable ground monuments. This is explained in detail in US Patent application publication 2016/0274001.7 One can think of the architecture as a network of virtual extensometers, or strain gauges, with one end attached to an accurately surveyed point on the ground, and the other end attached, with a clear line of sight, to a cardinal point on a bridge.

Table 1 is a summary of published laser tracker instrument specifications showing the accuracies for range only. The much less accurate angles are generally about the same as a theodolite, i.e., about one arc second, or approximately 5 parts per million (5 μm/m), in each axis.

Manufacturer

Model

Range

Accuracy

Data Rate

API Automated Precision

Radian

80 m

10 μm or 0.7 μm/m

?

FARO

Vantage

80 m

16 μm + 0.8 μm/m

1,000 points/sec

Kern (no longer available)

ME5000 Mekometer

4,000 m

200 μm + 0.2 μm/m

?

Leica

AT403

160 m

10 μm

?

Leica

AT960-LR

160 m

0.5 μm/m

1,000 points/sec

Nikon

MV351 HS

50 m

10 μm + 2.5 μm/m

2 sec/point

NRAO (no longer available)

PSH97

1,000 m

50 μm + 1 μm/m

1,000 points/sec

Table 1: Range and accuracy for laser trackers

High-end total stations, intended for general surveying and construction, are much less accurate in range measurements than laser trackers and the measurements are much slower. However, the published range specifications are much longer, and the accuracies have improved to the point that they may be adequate for some quasi static SHM applications. For comparison purposes, a summary of published specifications for representative high-end total stations is shown in table 2. This article is directed to high accuracy, so unless specifically stated otherwise, EDM instruments will be assumed to be laser tracker class instruments in the discussion.

Manufacturer

Model

Range

Accuracy

Data Rate

Leica

TS60

3,500 m

600 μm + 1 μm/m

2.4 sec/point

Topcon

MS05AX

3,500 m

800 μm + 1 μm/m

?

Trimble

S9HP

7,000 m

800 μm + 1 μm/m

?

Table 2: Range and accuracy for representative total stations

Note that the published specification ranges of the currently available commercial laser tracker instruments are, it has been argued,2 artificially limited to relatively short distances, i.e., 80 m to 160 m. The specification ranges are more than sufficient for present customer instrument applications, but need to be longer for most bridge applications. The artificial range limitation is due to the inherent limitations of angle measurements and the need to specify the maximum permissible error (MPE) of 3D coordinates, as per the ASME B89.4.19 standard15 traditionally used in the industry, and the fact that heretofore there has been little market demand for longer-range specifications. This is not a limitation of the accuracy of EDM, which the table shows has been used at 4,000 m by the Kern ME5000 Mekometer, and 1,000 m for the National Radio Astronomy Observatory (NRAO) PSH97. The need for instrument manufacturers to provide full specifications of instrument capabilities is a subject addressed in detail in the second article in this series.

Unfortunately, the literature is limited on published experimental data that properly uses EDM for SHM applications. The discontinued ME5000 Mekometer is manually pointed and has no angle measurement transducers. The NRAO Green Bank Telescope (GBT) is a 100 m radio telescope built in the 1990s. At that time, the best commercially available instruments were total stations with a radial accuracy of around 3 mm. As part of the GBT project, NRAO built 20 custom EDM instruments, which they called the model PSH97, as seen in table 1. Example measurement results are in the earlier articles and will not be reproduced here.

As explained in more detail in the third article, modern EDM instruments are far superior to the early PSH97 instruments in every respect—except on paper.

Based on the published specifications alone, an engineer would probably not attempt to make the measurements proposed in this article with any of the modern instruments, due to the apparent distance and measurement speed constraints. Yet, the PSH97 experimental data demonstrated the proof of principle more than 20 years ago.

An example bridge measurement architecture

An example will illustrate the measurement architecture and utility. Figure 1 shows a plan view of the CSX Wilbur Bridge over Rondout Creek in Kingston, NY. According to Bridgehunter.com,16 the 1,232-ft long railroad bridge, built in 1903, includes a 269.7-ft. long, Parker through truss bridge over the creek. Based on the U.S. Geological Survey (USGS) Quadrangle Topo maps for Kingston East, and Kingston West, NY, the rail is at an elevation of about 150 ft, and the creek is at an elevation of about 10 ft.

As explained in the first article, to fully exploit the high accuracy of EDM, it is necessary to measure by trilateration, i.e., three distances must be measured from accurately measured locations in the coordinate frame of reference, such as stable concrete ground monuments, or benchmarks. Ideally, the three distances are from orthogonal directions for the strongest 3D measurements. In practice, it is rare that three orthogonal measurements can be made, so it is important to optimize instrument and target locations to optimize the measurements for the desired parameters being measured. For added accuracy, more than three measurements are made in a multilateration architecture and a least-squares adjustment of the measurements is made.

For example, if the only interest is vertical deflections, a single instrument located under the bridge may be sufficient. However, for SHM applications, the objective is to detect anomalies that are unpredictable, i.e., in general, there are almost an infinite number of failure possibilities. The more unusual the deviation is from nominal, the more interesting the measurements are.

A good example is a fracture of the top cord of the Delaware River Bridge in 2017.17 Measurements of the 3D coordinates of a number of cardinal points on the bridge would have indicated an anomaly that would have prompted a closer visual inspection. Quite likely, changes in the coordinates and dynamic performance characteristics would have been significant enough to have raised awareness before the crack progressed to a full fracture. This is one reason why, in general, full 3D coordinate measurements are desirable.

As explained in the section above, railroad bridge engineers are not only interested in the vertical deflections, but are also particularly interested in the transverse and longitudinal motions of railroad bridges—for both static and dynamic motions.

Figure 1 shows a Google Earth plan view of the bridge with benchmark locations BM101-BM107 indicated, which have been chosen for evaluation as one of the best practical EDM instrument locations for measurements of cardinal points on the bridge, with an emphasis on measuring the transverse, longitudinal, and vertical motions.

Figure 1: Google Earth plan view of CSX Wilbur Bridge showing instrument locations

The coordinates, in NAD83, for BM101-BM107 and the center of the through truss span were estimated from the USGS maps. The height of the bridge, above the rail, was estimated from the photograph18 in figure 2 to be around 50 ft. Table 3 lists the coordinates of BM101-BM107 and the top and bottom of the center of the through truss span. It also includes the approximate slope distances between the benchmarks and the top and bottom of the center of the bridge, which vary between around 84 m to 383 m.

Figure 2: View of cardinal points on southwest side from near creek level (Photo taken by Joseph) 16, 18 

 

Identifier

Lat N

Long W

Z ft/m

Center top m

Center bottom m

BM101

41-54-47.5

73-59-45.9

150/45.720

383

383

BM102

41-54-42.4

73-59-53.1

15/4.572

165

160

BM103

41-54-39.2

73-59-48.1

15/4.572

230

227

BM104

41-54-28.4

73-59-57.1

240/73.152

321

322

BM105

41-54-40.3

74-00-00.3

15/4.572

92

84

BM106

41-54-40.3

74-00-12.9

220/67.056

351

351

BM107

41-54-45.3

74-00-07.9

240/73.152

307

307

center top

41-54-38.8

73-59-57.8

200/60.960

center bottom

41-54-38.8

73-59-57.8

150/45.720

Table 3: Estimated coordinates of instruments and center of bridge top and bridge bottom, with approximate slant distances to center of bridge top and bridge bottom

Note that BM101 is at approximately the same elevation as the bridge, and lines of sight to the northeast side of the bridge are somewhat perpendicular to the track, which makes distance measurements for transverse movements, along the lines of sight, very accurate; but insensitive to vertical and longitudinal movements.

BM102 and BM103 are near the creek level, with lines of sight looking up to the northeast side of the bridge. These measurements are very sensitive to vertical deflections, transverse movements, and longitudinal movements. By combining all three distance measurements, a high-accuracy 3D coordinate may be determined.

BM104 is high on a mountain with lines of sight overlooking the southwest side of the bridge. The geometry makes the measurements sensitive to transverse and longitudinal movements, but less sensitive to vertical movements. BM105 is near the creek level with lines of sight looking up to the underside of the bridge. The geometry makes the measurements sensitive to longitudinal and vertical movements, but less sensitive to transverse movements. BM106 is high on a mountain with lines of sight perpendicular to the track. Like BM101, measurements are sensitive to transverse movement, but less sensitive to vertical and longitudinal movements.

BM107 is above the tunnel and above the top of the bridge with lines of sight down the track. The geometry makes the measurements sensitive to longitudinal movement, but insensitive to transverse and vertical movements. For measurements of the top of the bridge, BM107 can be combined with BM101-BM103 on the northeast side, and BM104-BM106 on the southwest side.

Figure 2 shows a photo18 of the southwest side of the bridge from a location on the ground west of BM105, which is offset from the northwest tower, under BSW119. Bridge cardinal points of the joints on the southwest side are identified as BSW101-BSW119, with corresponding cardinal points BNE101-BNE119 symmetrically located on the northeast side.

Passive retroreflector targets are permanently attached to the cardinal points with references which provide for replacement over the years, such as stainless steel weld plates with dowel pin connections for the retroreflectors. Conventional survey retroreflectors have a limited angle of acceptance. In order to provide for wide angles of acceptance, special retroreflector assemblies are required19,20 which virtually reflect from a common point—thus eliminating any Abbe errors.

Figure 3 shows a Google Earth view of cardinal points on the southwest side from near BM106, and Figure 4 shows a Google Earth view of cardinal points on the northeast side of the bridge from behind BM101.

Figure 3: Google Earth view of cardinal points on southwest side from near BM106

Figure 4: Google Earth view of cardinal points on northeast side from behind BM101 

In a typical NDT scheme, the benchmarks would be permanently established by concrete columns with provisions to accurately position EDM instruments over the benchmarks. The benchmarks would be accurately surveyed to establish a fixed coordinate system that would exceed the life of the bridge. Auxiliary benchmarks may be desired to reference the instrument to them. In other words, by measuring the distances to three or more reference benchmarks, the instrument location is determined.

With the retroreflector targets already permanently in place, a survey crew, working under the direction of a Level-Two certified laser tracker metrologist (certified by the Coordinate Metrology Society), would mount and operate the portable EDM instruments.

A series of measurements would be conducted, via remote control, from a central control location, for various load conditions. The measurements would be adjusted, in near real time, to determine the 3D coordinates of all cardinal points. After the data is reviewed, the survey crew would remove the instruments and proceed to the next bridge to be tested.

Uncertainty analysis

In preparation for a measurement campaign, it is always recommended to conduct an uncertainty analysis21 during the planning stages. This will ensure an optimum selection of instruments, target locations, and measurement locations. EDM instrument manufacturers’ customers tend to be highly sophisticated metrologists working in high-technology industries and government laboratories, which would quickly detect and call them out for not actually meeting published specifications. Therefore, the published specifications tend to err on the side of being overly conservative, and the actual measurements are conducted by automated instruments. The net result is that measurement uncertainties are highly predictable with a bias toward the conservative side.

An uncertainty analysis was run for various measurements under various assumptions for instrument specifications using the pre-analysis feature of the Star*Net 9 software package, by MicroSurvey ® Inc.

Star*Net allows one to virtually conduct a survey, based on a measurement plan and assumptions of instrument locations, target locations, and instrument uncertainty parameters. Assumptions are weighted by selected values and a least-squares adjustment is made using the virtual measurements. A sample Star*Net output listing is included in Appendix A.

Most EDM instrument specifications are for MPE, instead of the standard deviation. In such cases, NIST Technical Note 1297, section 4.6 21 recommends dividing by to obtain the standard uncertainty. For the purpose of this article, the more conservative assumption will be made to use the MPE as the standard deviation. The results are summarized in table 4.

From

To

N μm

E μm

Z μm

10 μm + 1 ppm

BM101-BM103

BNE_T

428

391

1219

BM101-BM107

BNE_T

215

121

268

BM104-BM106

BSW_T

336

351

447

BM104-BM107

BSW_T

308

296

329

BM101-BM103

BNE_B

397

355

1417

BM101-BM103, BM105

BNE_B

372

150

569

BM104-BM106

BSW_B

353

326

581

10 μm + 0.1 ppm

BM101-BM103

BNE_T

58

55

172

BM101-BM107

BNE_T

29

17

41

BM104-BM106

BSW_T

44

45

63

BM104-BM107

BSW_T

40

38

48

BM101-BM103

BNE_B

55

51

206

BM101-BM103, BM105

BNE_B

54

22

86

BM104-BM106

BSW_B

47

42

83

Table 4: Standard deviation of measured points for laser trackers 

In this pre-analysis software run, the coordinates of the instrument locations BM101-BM107 were assumed to be absolute and held fixed in the adjustments. Although Star*Net can handle thousands of points, this article will only use two points as an example. The top and bottom of the center of the span were used as approximate coordinates for a representative pair of cardinal points on the span. For the pre-analysis, the top node was given names BNE_T and BSW_T using the same coordinates for the center top in table 3, and the bottom node was given names BNE_B and BSW_B using the same coordinates for the center bottom in table 3. By assigning two names to each node, Star*Net treats them as independent nodes, which allows for possible differences in visibility. For example, some instruments may have clear lines of sight to nodes on the northeast side, but not the southwest side, while others may have clear lines of sight to both.

Referring to table 4, the first group of simulations assume the EDM instruments point with an accuracy of 5 sec and a measure range with an accuracy of 10 μm + 1 part per million (ppm). For example, the error in distance for a measurement at 100 m would be 110 μm, and at 200 m would be 210 μm, etc. The pointing accuracy of 5 sec would be around 25 ppm, or 2,500 μm at 100 m and 5,000 μm at 200 m. For all practical purposes, the 5-sec accuracy makes the angles irrelevant in the trilateration adjustment. Changing it to 50 sec would not significantly alter the results of the adjustment.

The first case is for measuring from BM101, BM102, and BM103 to the northeast side of the top of the center of the span in a set of trilateration measurements, i.e., BNE_T. Note, as a point of reference, that 100 μm is the thickness of a sheet of standard printer paper.

The adjustment shows that one could expect the standard deviation of the coordinates calculated by those measurements, under the assumptions made, in the N, E and elevation directions would be (428, 391, 1219) μm. The next assumption is that BNE_T was measured from all instrument locations BM101-BM107 in a set of multilateration measurements. Note that the standard deviations of (215, 121, 268) are a significant improvement over simply measuring from BM101-BM103, particularly in elevation.

In contrast, measurements from BM104, BM105, and BM106 to the southwest side of the top of the center of the span in a set of trilateration measurements, i.e., BSW_T, is much stronger in elevation (336, 351, 447). This is primarily due to the strategic location of BM105 almost under the bridge, which is very sensitive to vertical movement of the bridge. Other combinations of measurements are included in table 4.

For absolute accuracy of the coordinates of cardinal points, traceable to NIST, these standard deviations are about what one could expect. However, for a better understanding, one must analyze the sources of the errors. The assumption of a fixed 10 μm instrument error is probably not of much concern. The 1 ppm error warrants more consideration.

It is well known that EDM measurements are dependent on the speed of light, which is dependent on the group refractive index (GRI) of the air. The GRI of air is most dependent on temperature (about 1 part per million/C o), and to a lesser amount on humidity and pressure. Recall that the thermal coefficient of expansion for steel is around 11 ppm/C o, which must be taken into consideration when analyzing the bridge performance.

The easiest way to correct for the group refractive index in the outdoors is to use reference distances as refractometers.22 For example, if measurements are made from the instruments to fixed points, through a representative environment, the apparent distances will change due to changes in the GRI and the ratio of the distances. In other words, the GRI can be modeled out of the errors.

It should be noted that care must be taken to ensure a uniform environment. As with all high-accuracy surveys, measurements should be made at night or under uniform cloud cover for best results.

Uncertainty in the GRI is the source of the typical 1 ppm error used for laser trackers. It is noteworthy that this is a systematic error, not a random error. If one is actually concerned with differential movements, such as the movements between two joints, or how the bridge moves under loading, such as those measurements shown in the earlier articles for vibrations, the uncertainties of differential motions are much less than 1 ppm.

The lower part of table 4 is for the same cases, except assuming a 0.1 ppm instrument uncertainty, which experience has shown is a more realistic assumption for differential movement between adjacent points. Note the dramatic reduction in the standard deviations. For example, for BNE_T measured by BM101-BM103, the uncertainties go from (428,391,1219) to (58, 55, 172); and for BNE_T from BM101-BM107 from (215, 121, 268) to (29, 17, 41). Deflections due to a high-rail vehicle crossing the bridge would be measurable.

Table 5 shows similar simulations for total stations with 600 μm and 800 μm errors. As with laser trackers, the 1 ppm error is systematic. However, the 600 μm and 800 μm fixed errors are not systematic, so they tend to dominate the adjustments. Depending on the objective, this may be acceptable for a particular study.


From

To

N μm

E μm

Z μm

600 μm + 1 ppm

BM101-BM103

BNE_T

1192

1010

2377

BM104-BM106

BSW_T

821

814

1279

BM101-BM103

BNE_B

1161

936

2513

BM104-BM106

BSW_B

827

765

1408

600 μm + 0.1 ppm

BM101-BM103

BNE_T

910

815

2046

BM104-BM106

BSW_T

606

590

1099

BM101-BM103

BNE_B

894

754

2228

BM104-BM106

BSW_B

621

561

1252

800 μm + 1 ppm

BM101-BM103

BNE_T

1404

1164

2544

BM104-BM106

BSW_T

946

937

1464

BM101-BM103

BNE_B

1375

1091

2644

BM104-BM106

BSW_B

945

889

1550

800 μm + 0.1 ppm

BM101-BM103

BNE_T

1155

997

2331

BM104-BM106

BSW_T

760

742

1335

BM101-BM103

BNE_B

1137

928

2473

BM104-BM106

BSW_B

769

709

1452

Table 5: Standard deviation of measured points for total stations 

Analysis of measurements in light of bridge engineers desires

We turn now to how such high-accuracy measurements may be used in a global structural assessment of the bridge. From table 4, the smallest standard deviations are for the case where BNE_T is measured by all instruments BM101-BM107; (215, 121, 268) for 1 ppm; and (29, 17, 41) for 0.1 ppm. Due to visibility constraints, this is probably not a realistic case. A more practical architecture is measuring BSW_T from BM104-BM107 and measuring BSW_B from BM104-BM106. Note that BM107, above the tunnel, has clear lines of sight to the top of the bridge, but not the bottom of the bridge. For the 1 ppm case, the standard deviations are (308, 296, 329) and (353, 326,581). For the 0.1 ppm case, the standard deviations are (40, 38, 48) and (47, 42, 83).

Referring to figure 2, these accuracies would be indicative of the standard deviations for cardinal points BSW108 and BSW109. The combined standard deviation for differential measurement of the length of the member connecting the two joints would typically be estimated by taking the root sum square (RSS) of the elevation components of 48 μm and 83 μm, which would be 96 μm. Assume the length between BSW108 and BSW109 is 15 m, the standard deviation in a strain measurement would be 6.4 micro strain.

It can be argued that the standard deviation in the length between any pair of joints would be comparable. This would include between the BSW and BNE sides, and the diagonals, e.g., between BSW108 and BNE108 and between BSW108 and BNE110. The strain in the members connecting the 36 joints could be determined from the coordinate measurements, i.e., it would virtually be like having wireless strain gauges installed on the 104 members of the structure.

One interesting experiment would be to measure the coordinates of the 36 cardinal points under no live load conditions and then with a locomotive parked in the center of the span. In addition to the vertical deflections, it would be interesting to measure the transverse and longitudinal motions. Asymmetries in motions would be particularly interesting. Hysteresis would also be interesting when the live load is removed.

Another interesting experiment would be to measure motions while a locomotive is pulling cars across the bridge, i.e., introducing longitudinal forces on the structure. For example, slowly move onto the bridge and stop with the locomotive in the middle of the span. Then, apply predetermined longitudinal forces to start the train moving. This would also need to be measured for the locomotive pushing the cars and the locomotive approaching from opposite ends of the bridge to see if the abutments are symmetric.

Yet another interesting experiment would be to measure the cardinal points under braking conditions—in both directions. One would expect the motions due to the distributed longitudinal forces exerted by rail cars to be different from the localized longitudinal force exerted by a locomotive.

Still another interesting experiment would be to measure the cardinal points for trains passing at various speeds to subject the bridge to wheel flat spots, wheel hunting, and rock and roll.10

Conclusion

It has been shown that proposed measurements of the CSX Wilbur Bridge by EDM meet all of the desired results of railroad bridge engineers in the 2012 report—and then some. Specifically, the measurements are quantified and repeatable; performed on the actual bridge in question; performed under static and dynamic conditions; performed under experimental and revenue conditions; performed under dead and live loads; produce results in the vertical, longitudinal, and transverse directions; intuitively understood; measure strain; and economical. More than they wished for!

References

1 Parker, D.H., “Nondestructive Testing and Monitoring of Stiff Large-Scale Structures by Measuring 3-D Coordinates of Cardinal Points Using Electronic Distance Measurements in a Trilateration Architecture,” Conference on Nondestructive Characterization and Monitoring of Advanced Materials, Aerospace, and Civil Infrastructure 2017, Portland, OR, Vol. 10169 of Proceedings of SPIE, SPIE, March 2017, paper 1016918.

2 Parker, D.H., “Using Electronic Distance Measurement Instruments in NDT and Structural Health-Monitoring Applications,” Quality Digest, August 2017, paper given at CMSC 2017, Snowbird, UT, original title “Opportunities for the Use of Electronic Distance Measurement Instruments in Nondestructive Testing and Structural Health Monitoring Applications and How Instrument Manufacturers can Facilitate Early Adopters in New Fields.”

3 Parker, D.H., “Opportunities for the Use of Electronic Distance Measurement Instruments in Nondestructive Testing and Structural Health Monitoring and Implications for ASNT,” Proceedings of 27th ASNT Research Symposium, Orlando, FL, American Society for Nondestructive Testing, March 2018.

4 Parker, D.H. and Payne, J.M., Method for Measuring the Structural Health of a Civil Structure, U.S. Patent 7,895,015, 2011.

5 Parker, D.H. and Payne, J.M., Methods for Modeling the Structural Health of a Civil Structure Based on Electronic Distance Measurements, U.S. Patent 8,209,134, 2012.

6 Parker, D.H. and Payne, J.M., Methods for Measuring and Modeling the Structural Health of Pressure Vessels Based on Electronic Distance Measurements, U.S. Patent 9,354,043, 2016.

7 Parker, D.H. and Payne, J.M., Methods for Measuring and Modeling the Process of Prestressing Concrete During Tensioning/Detensioning Based on Electronic Distance Measurements, U.S. Patent Application Publication, 2016/0274001, 2016.

8 Martland, C.D., “Introduction of Heavy Axle Loads By the North American Rail Industry,” Journal of the Transportation Research Forum, Vol. 52, No. 2, pp. 103–125, 2013.

9 Moreu, F., LaFave, J.M., and Spencer, B.F., “New Regulations on Railroad Bridge Safety: Opportunities and Challenges for Railroad Bridge Monitoring,” Proceedings of SPIE, Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2012, Vol. 8345, pp. 834540–1 through 11, 2012.

10 Moreu, F., Jo, H., Li, J., Kim, R.E., Cho, S., Kimmle, A., Scola, S., Le, H., Spencer, B.F. Jr., and LaFave, J.M., “Dynamic Assessment of Timber Railroad Bridges Using Displacements,” Journal of Bridge Engineering, p. 04014114, 2014.

11 Moreu, F., Li, J., Jo, H., Kim, R.E., Scola, S., Spencer, B.F. Jr., and LaFave, J.M., “Reference-Free Displacements for Condition Assessment of Timber Railroad Bridges,” Journal of Bridge Engineering, p. 04015052, 2015.

12 Hoag, A., Hoult, N.A., Take, W.A., Moreu, F., Le, H., and Tolikonda, V., “Measuring Displacements of a Railroad Bridge Using DIC and Accelerometers,” Smart Structures and Systems, Vol. 19, No. 2, pp. 225–236, 2017.

13 Moreu, F., Garg, P., and Ayorinde, E., “RailroaBridge Inspections for Maintenance and Replacement Prioritization Using Unmanned Aerial Systems (UAS) with Laser Capabilities,” TRB Annual Meeting, number paper 18-06761, TRB, January 2018.

14 Moreu, F. and LaFave, J.M., Current Research Topics: Railroad Bridges and Structural Engineering, NSEL Report Series, Report No. NSEL-032, Newmark Structural Engineering Laboratory, Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, October 2012.

15 ASME B89.4.19-2006 Performance Evaluation of Laser-Based Spherical Coordinate Measurement Systems, The American Society of Mechanical Engineers, 2006.

16 Hicks, F., Harden, L., Vance, C., Martin, I., King, D., and Finigan, C., CSX-Wilbur Bridge, Ulster County, NY, Online, April 2012, http://bridgehunter.com/ny/ulster/wilbur-railroad/.

17 Foden, A., Gentz, C., Van Brunt, Z., and Rue, D., “Structural Monitoring of the Delaware River Turnpike Bridge Emergency Repairs, 2017 ASNT Annual Conference October 30-November 2, 2017 Proceedings, pp, 68–76. American Society for Nondestructive Testing, October 2017.

18 Joseph, Photo taken by Joseph, June 2011 License: Creative Commons Attribution-Non Commercial-ShareAlike (CC BY-NC-SA), BH Photo #239216 https://www.flickr.com/photos/josepha/5907193656/.

19 Parker, D.H., “Multidirectional Retroreflector Assembly with a Common Virtual Reflection Point Using Four-Mirror Retroreflectors,” Precision Engineering, No. 29, pp. 361–366, 2005.

20 Parker, D.H., Multidirectional Retroreflectors, U.S. Patent RE41877, 2010

21 Taylor, B.N. and Kuyatt, C.E., “Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results,” NIST Technical Note 1297, National Institute of Standards and Technology, 1994.

22 Parker, D.H., “Methods for Correcting the Group Index of Refraction at the PPM Level for Outdoor Electronic Distance Measurement,” Proceedings ASPE 2001 Annual Meeting, pp. 86–87, American Society for Precision Engineering, 2001. (Full presentation is available from The National Radio Astronomy Observatory [NRAO] Library, GBT Archive L0680.)

Appendix A

                  MicroSurvey STAR*NET-PRO Version 9,0,3,6298

                           Licensed for Demo Use Only

                       Run Date: Sun Mar 04 2018 15:30:51

                   Summary of Files Used and Option Settings

                   =========================================

 

                         Project Folder and Data Files

 

      Project Name       CSX WILBUR BRIDGE

      Project Folder C:\USERS\DAVID\DOCUMENTS\MICROSURVEY\STARNET\EXAMPLES

      Data File List  1. CSX Wilbur Bridge.dat

 

                            Project Option Settings

 

      STAR*NET Run Mode                   : Preanalysis

      Type of Adjustment                  : 3D

      Project Units                       : Meters; DMS

      Coordinate System                   : UTM83-18

      Geoid Height                        : 0.0000 (Default, Meters)

      Longitude Sign Convention           : Positive West

      Input/Output Coordinate Order       : North-East

      Angle Data Station Order            : At-From-To

      Distance/Vertical Data Type         : Slope/Zenith

      Convergence Limit; Max Iterations   : 0.010000; 10

      Default Coefficient of Refraction   : 0.070000

      Create Coordinate File              : Yes

      Create Geodetic Position File       : Yes

      Create Ground Scale Coordinate File : Yes

      Create Dump File                    : Yes

 

                       Instrument Standard Error Settings

 

      Project Default Instrument

        Distances (Constant)              :    0.000010 Meters

        Distances (PPM)                   :    1.000000

        Angles                            :    5.000000 Seconds

        Directions                        :    5.000000 Seconds

        Azimuths & Bearings               :    5.000000 Seconds

        Zeniths                           :    5.000000 Seconds

        Elevation Differences (Constant)  :    0.015240 Meters

        Elevation Differences (PPM)       :    0.000000

        Differential Levels               :    0.002403 Meters / Km

        Centering Error Instrument        :    0.000000 Meters

        Centering Error Target            :    0.000000 Meters

        Centering Error Vertical          :    0.000000 Meters

 

                    Summary of Unadjusted Input Observations

                    ========================================

 

                    Number of Entered Stations (Meters) = 11

 

Fixed Stations          Latitude         Longitude       Elev   Description

BM101            41-54-47.500000   73-59-45.900000     45.7200

BM102            41-54-42.400000   73-59-53.100000      4.5720

BM103            41-54-39.200000   73-59-48.100000      4.5720

BM104            41-54-28.400000   73-59-57.100000     73.1520

BM105            41-54-40.300000   74-00-00.300000      4.5720

BM106            41-54-40.300000   74-00-12.900000     67.0560

BM107            41-54-45.300000   74-00-07.900000     73.1520

 

Free Stations           Latitude         Longitude       Elev   Description

BNE_T            41-54-38.800000   73-59-57.800000     60.9600

BNE_B            41-54-38.800000   73-59-57.800000     45.7200

BSW_T            41-54-38.800000   73-59-57.800000     60.9600

BSW_B            41-54-38.800000   73-59-57.800000     45.7200

 

             Number of Measured Distance Observations (Meters) = 18

 

From       To            Distance   StdErr      HI      HT  Comb Grid Type

BM101      BNE_T         383.9279   0.0004   0.000   0.000  0.9996767   S

BM101      BNE_B         383.6253   0.0004   0.000   0.000  0.9996778   S

BM102      BNE_T         165.0266   0.0002   0.000   0.000  0.9996797   S

BM102      BNE_B         160.4597   0.0002   0.000   0.000  0.9996809   S

BM103      BNE_T         230.8119   0.0002   0.000   0.000  0.9996798   S

BM103      BNE_B         227.5690   0.0002   0.000   0.000  0.9996810   S

BM104      BSW_T         321.4086   0.0003   0.000   0.000  0.9996742   S

BM104      BSW_B         322.3467   0.0003   0.000   0.000  0.9996754   S

BM105      BSW_T          92.9382   0.0001   0.000   0.000  0.9996795   S

BM105      BSW_B          84.5640   0.0001   0.000   0.000  0.9996807   S

BM106      BSW_T         351.0028   0.0004   0.000   0.000  0.9996744   S

BM106      BSW_B         351.5978   0.0004   0.000   0.000  0.9996756   S

BM104      BNE_T         321.4086   0.0003   0.000   0.000  0.9996742   S

BM106      BNE_T         351.0028   0.0004   0.000   0.000  0.9996744   S

BM105      BNE_B          84.5640   0.0001   0.000   0.000  0.9996807   S

BM105      BNE_T          92.9382   0.0001   0.000   0.000  0.9996795   S

BM107      BNE_T         307.3868   0.0003   0.000   0.000  0.9996740   S

BM107      BSW_T         307.3868   0.0003   0.000   0.000  0.9996740   S

 

                    Number of Zenith Observations (DMS) = 18

 

From       To              Zenith      StdErr      HI      HT

BM101      BNE_T        87-43-30.18      5.00   0.000   0.000

BM101      BNE_B        90-00-00.00      5.00   0.000   0.000

BM102      BNE_T        70-01-12.37      5.00   0.000   0.000

BM102      BNE_B        75-08-28.24      5.00   0.000   0.000

BM103      BNE_T        75-51-33.70      5.00   0.000   0.000

BM103      BNE_B        79-34-57.86      5.00   0.000   0.000

BM104      BSW_T        92-10-26.12      5.00   0.000   0.000

BM104      BSW_B        94-52-54.58      5.00   0.000   0.000

BM105      BSW_T        52-38-48.79      5.00   0.000   0.000

BM105      BSW_B        60-52-59.85      5.00   0.000   0.000

BM106      BSW_T        90-59-42.46      5.00   0.000   0.000

BM106      BSW_B        93-28-44.45      5.00   0.000   0.000

BM104      BNE_T        92-10-26.12      5.00   0.000   0.000

BM106      BNE_T        90-59-42.46      5.00   0.000   0.000

BM105      BNE_B        60-52-59.85      5.00   0.000   0.000

BM105      BNE_T        52-38-48.79      5.00   0.000   0.000

BM107      BNE_T        92-16-23.31      5.00   0.000   0.000

BM107      BSW_T        92-16-23.31      5.00   0.000   0.000

 

             Number of Grid Azimuth/Bearing Observations (DMS) = 18

 

From       To            Bearing       StdErr

BM101      BNE_T      S44-56-42.44W      5.00

BM101      BNE_B      S44-56-42.44W      5.00

BM102      BNE_T      S43-36-41.88W      5.00

BM102      BNE_B      S43-36-41.88W      5.00

BM103      BNE_T      S86-10-14.86W      5.00

BM103      BNE_B      S86-10-14.86W      5.00

BM104      BSW_T      N03-32-48.24W      5.00

BM104      BSW_B      N03-32-48.24W      5.00

BM105      BSW_T      S51-53-41.47E      5.00

BM105      BSW_B      S51-53-41.47E      5.00

BM106      BSW_T      S83-05-30.30E      5.00

BM106      BSW_B      S83-05-30.30E      5.00

BM104      BNE_T      N03-32-48.24W      5.00

BM106      BNE_T      S83-05-30.30E      5.00

BM105      BNE_B      S51-53-41.47E      5.00

BM105      BNE_T      S51-53-41.47E      5.00

BM107      BNE_T      S49-55-11.13E      5.00

BM107      BSW_T      S49-55-11.13E      5.00

 

           Adjusted Bearings (DMS) and Horizontal Distances (Meters)

           =========================================================

                 (Relative Confidence of Bearing is in Seconds)

 

From       To          Grid Bearing   Grid Dist       95% RelConfidence

                                                    Brg    Dist       PPM

BM101      BNE_B      S44-56-41.83W    383.5695    0.44   0.0006    1.4414

BM101      BNE_T      S44-56-47.79W    383.5954    0.24   0.0004    1.0507

BM102      BNE_B      S43-36-38.63W    155.0383    1.07   0.0006    3.6604

BM102      BNE_T      S43-36-54.17W    155.0639    0.59   0.0004    2.6344

BM103      BNE_B      S86-10-47.95W    223.7753    0.85   0.0003    1.5139

BM103      BNE_T      S86-10-39.93W    223.8021    0.49   0.0003    1.3107

BM104      BNE_T      N03-32-38.08W    321.2046    0.19   0.0005    1.6447

BM104      BSW_B      N03-34-10.85W    321.0794    0.52   0.0009    2.6686

BM104      BSW_T      N03-34-29.86W    321.1017    0.48   0.0007    2.2823

BM105      BNE_B      S51-56-15.69E     73.8855    1.75   0.0008   10.2299

BM105      BNE_T      S51-55-07.74E     73.8714    1.20   0.0004    5.7387

BM105      BSW_B      S51-46-18.35E     73.8468    2.52   0.0008   10.2187

BM105      BSW_T      S51-46-09.66E     73.8099    2.51   0.0005    7.2761

BM106      BNE_T      S83-05-47.76E    350.9605    0.31   0.0003    0.8805

BM106      BSW_B      S83-04-19.96E    350.8412    0.52   0.0008    2.2288

BM106      BSW_T      S83-04-29.68E    350.8080    0.47   0.0007    1.9414

BM107      BNE_T      S49-55-31.71E    307.1375    0.28   0.0004    1.4059

BM107      BSW_T      S49-53-21.02E    307.0826    0.60   0.0005    1.7426

 

                               Error Propagation

                               =================

 

                Station Coordinate Standard Deviations (Meters)

 

Station                     N             E             Elev

BM101                     0.000001      0.000001      0.000001

BM102                     0.000001      0.000001      0.000001

BM103                     0.000001      0.000001      0.000001

BM104                     0.000001      0.000001      0.000001

BM105                     0.000001      0.000001      0.000001

BM106                     0.000001      0.000001      0.000001

BM107                     0.000001      0.000001      0.000001

BNE_T                     0.000215      0.000121      0.000268

BNE_B                     0.000372      0.000150      0.000569

BSW_T                     0.000308      0.000296      0.000329

BSW_B                     0.000353      0.000326      0.000581

 

                   Station Coordinate Error Ellipses (Meters)

                            Confidence Region = 95%

 

Station                 Semi-Major    Semi-Minor   Azimuth of       Elev

                            Axis          Axis     Major Axis

BM101                     0.000000      0.000000       0-00       0.000000

BM102                     0.000000      0.000000       0-00       0.000000

BM103                     0.000000      0.000000       0-00       0.000000

BM104                     0.000000      0.000000       0-00       0.000000

BM105                     0.000000      0.000000       0-00       0.000000

BM106                     0.000000      0.000000       0-00       0.000000

BM107                     0.000000      0.000000       0-00       0.000000

BNE_T                     0.000529      0.000293     173-56       0.000526

BNE_B                     0.000934      0.000304     166-28       0.001115

BSW_T                     0.000900      0.000534      42-36       0.000645

BSW_B                     0.000905      0.000753      31-54       0.001138

 

                        Relative Error Ellipses (Meters)

                            Confidence Region = 95%

 

Stations                Semi-Major    Semi-Minor   Azimuth of     Vertical

From       To               Axis          Axis     Major Axis

BM101      BNE_B          0.000934      0.000304     166-28       0.001115

BM101      BNE_T          0.000529      0.000293     173-56       0.000526

BM102      BNE_B          0.000934      0.000304     166-28       0.001115

BM102      BNE_T          0.000529      0.000293     173-56       0.000526

BM103      BNE_B          0.000934      0.000304     166-28       0.001115

BM103      BNE_T          0.000529      0.000293     173-56       0.000526

BM104      BNE_T          0.000529      0.000293     173-56       0.000526

BM104      BSW_B          0.000905      0.000753      31-54       0.001138

BM104      BSW_T          0.000900      0.000534      42-36       0.000645

BM105      BNE_B          0.000934      0.000304     166-28       0.001115

BM105      BNE_T          0.000529      0.000293     173-56       0.000526

BM105      BSW_B          0.000905      0.000753      31-54       0.001138

BM105      BSW_T          0.000900      0.000534      42-36       0.000645

BM106      BNE_T          0.000529      0.000293     173-56       0.000526

BM106      BSW_B          0.000905      0.000753      31-54       0.001138

BM106      BSW_T          0.000900      0.000534      42-36       0.000645

BM107      BNE_T          0.000529      0.000293     173-56       0.000526

BM107      BSW_T          0.000900      0.000534      42-36       0.000645

 

 

                           Elapsed Time = 00:00:00

 

19

42

01 00000001 Top of File

01 00000006 Summary of Files Used and Option Settings

02 00000009 Project Folder and Data Files

02 00000015 Project Option Settings

02 00000033 Instrument Standard Error Settings

03 00000035 Project Default Instrument

01 00000049 Summary of Unadjusted Input Observations

02 00000052 Entered Stations

03 00000054 Fixed Positions

03 00000063 Free Positions

02 00000069 Measured Distance Observations

02 00000091 Zenith Observations

02 00000113 Grid Azimuth/Bearing Observations

01 00000135 Adjusted Bearings and Horizontal Distances

01 00000160 Error Propagation

02 00000163 Station Coordinate Standard Deviations

02 00000178 Station Coordinate Error Ellipses

02 00000195 Relative Error Ellipses

01 00000218 End of File

000030D0

STAR*NET

0000F398

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About The Author

David H. Parker’s picture

David H. Parker

David H. Parker is the president of Parker Intellectual Property Enterprises LLC. With an master’s degree in physics and a bachelor’s degree in electrical engineering from Auburn University, Parker has more than 40 years of engineering experience, more than 30 years of metrology experience, and more than 10 years of patent-prosecution experience. Parker is a registered patent agent, a registered professional engineer, and holds 13 U.S. patents, with two U.S. patents pending.