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This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

The accurate measurement of diverse displacements of structures is an important index for the evaluation of a structure’s safety. In this study, a comparative analysis was conducted to determine the integrated RTK-GPS/accelerometer method that can provide the most precise structure displacement measurements. For this purpose, three methods of calculating the dynamic displacements from the acceleration data were comparatively analyzed. In addition, two methods of determining dynamic, static, and quasi-static displacements by integrating the displacements measured from the RTK-GPS system and the accelerometer were also comparatively analyzed. To ensure precise comparison results, a cantilever beam was manufactured onto which diverse types of displacements were generated to evaluate the measurement accuracy by method. Linear variable differential transformer (LVDT) measurements were used as references for the evaluation to ensure accuracy. The study results showed that the most suitable method of measuring the dynamic displacement with the accelerometer was to calculate the displacement by filtering and double-integrating the acceleration data using the FIR band-pass filter. The integration method that uses frequency-based displacement extraction was most appropriate for the integrated RTK-GPS/accelerometer method of comprehensively measuring the dynamic, static, and quasi-static displacements.

With the development of design technology, civil structures are increasingly being designed with thinner, lighter, and more flexible designs. The volume of construction materials is also decreasing, and structures are gaining economic and aesthetic advantages. Most civil structures, however, are constantly exposed to diverse natural and environmental conditions, including strong winds, earthquakes, and tsunamis, and therefore, to abnormal ultimate loads. Abnormal ultimate loading may even cause structures to collapse. An example is the Tacoma Narrows Bridge, which was opened in 1940. This bridge was the third longest suspension bridge in the US, and it collapsed within months of opening due to unexpected strong winds, which were not considered in the design stage. Therefore, it is important to monitor and evaluate the structural integrity of the main infrastructure. The structural integrity of many items can be evaluated, but displacement is generally used. This is because short-term and long-term displacements are indicators of structural behavior, and structural integrity can be evaluated in diverse ways using these displacement values. Accordingly, precise displacement measurement is required to ensure the reliable evaluation of a structure’s condition [

The accelerometer is a widely used instrument for measuring structural displacements [

The real-time kinematic global positioning system (RTK-GPS) is recognized as efficient for measuring static and quasi-static displacements, due to its high accuracy (about 1 cm error for temporary measurement and about 1 mm error for long-term measurement) and its ability to measure the 3D absolute coordinates based on the terrestrial reference frame [

This study was conducted to determine the most accurate of the present structure displacement measurement methods that are based on integrated RTK-GPS/accelerometer calculations. The displacement measurement method that is based on integrated RTK-GPS/accelerometer calculation integrates the RTK-GPS and accelerometer displacement measurement methods. Accordingly, the integrated method is influenced by the appropriateness of the two displacement measurement methods and by the method of integrated calculation. RTK-GPS displacement measurements are less affected by their data processing method than are accelerometer displacement measurements. Three methods were used to compare the effects of different acceleration data processing methods: first, the noise within the noise bandwidth is removed by using the same digital filter as that used for the most widely used finite impulse response (FIR) and then double-integration is applied [

Two methods of calculating the displacements from the measured acceleration are possible: removing the noise from the acceleration measurement data with a band-pass filter and applying double integration, or using the central differencing scheme and the Tikhonov regularization scheme without additional filtering. In this study, the former method was classified into two methods according to the type of band-pass filter: the case of using the FIR filter (Method A1) and that using the EMD filter (Method A2). We compared these two methods and compared the method of using central differencing and that of Tikhonov regularization (Method A3). The degrees of accuracy of the methods were then analyzed.

The displacements were calculated by removing the noise from the acceleration data using a band-pass filter, and then applying double integration _{0} is the initial position, and _{0} is the initial velocity.

The initial position (_{0}) and the initial velocity (_{0}) cannot be measured using the accelerometer, and must be calculated using a separate method. This initial value problem can be solved by applying two conditions. The first condition is that the only displacement that can be measured using the accelerometer is dynamic displacement. According to this condition, static or quasi-static displacement can be measured using other methods, including RTK-GPS. A certain value can be used as the initial position value in processing the accelerometer data. The initial position problem can be addressed by calculating the relative displacement based on a specific value and adjusting it based on the static or quasi-static displacement that is measured using another method. The second condition is that an incorrect initial velocity generates a linear positional error in the calculated displacement. Therefore, the initial velocity value problem can be addressed by calculating the displacement using a specific initial velocity and estimating and removing the linear tendency of the calculated displacement.

Digital filters, which are used as band-pass filters for noise filtering, are largely divided into FIR and infinite impulse response (IIR) filters. For choosing the band-pass filter, Method A1 uses the discrete-Fourier-transform (DFT)-based FIR filter, which has a simple structure and ensures stability. The IIR filter is more difficult to design and apply than the FIR filter, but requires a shorter time for calculation. Considering the performance of the recent high-speed processor, however, its advantage cannot justify its replacement of the FIR filter [

In order to select the band-pass filter, Method A2 uses an EMD filter. EMD is a new time-frequency analysis method that adaptively and efficiently decomposes the signal, and was introduced by Huang _{n}_{n}

The EMD filter is represented by

In Method A2, the EMD filter was used in the band-pass filtering stage, among the acceleration data processing processes as shown in

Hong [

The matrix _{w}

The methods of measuring the overall displacement by integrating the accelerometer displacement measurement (for dynamic structure displacement) and the RTK-GPS displacement measurement (for static and quasi-static displacement) include the RTK-GPS-based simple integration method and the integration that uses frequency-based displacement extraction.

The simple integrated calculation visually and precisely synchronizes the measurements from RTK-GPS and the accelerometer, and fits the displacements measured from the accelerometer into the RTK-GPS measurements [

The integration procedure is as follows. As shown in (1) in _{1} and _{2} that is measured from the accelerometer is shifted based on the RTK-GPS measurements. At _{2}, however, a deviation between the RTK-GPS and accelerometer measurements (Δ

The integrated calculation method based on frequency-based displacement extraction was proposed by Li

The core part of this integrated calculation is the extraction of the low-frequency bandwidth from the RTK-GPS measurements. Li

As shown in

A commercial square-shaped steel pipe was used as the beam in the test. The steel pipe had an ultimate tensile strength of 410 MPa, a yield tensile strength of 240 MPa, and a modulus of elasticity of 200 GPa. A cantilever beam specimen consisting of concrete blocks and a steel pipe beam was manufactured to compare the accuracies of the diverse data processing methods. In addition, LVDT, RTK-GPS, and a low-cost triaxial accelerometer were installed on the beam for the measurement. The test results were stored in a laptop PC after visual time synchronization.

The data for the RTK-GPS measurement were processed on a laptop PC. The time on the laptop PC was constantly updated according to the GPS time to synchronize the time data for the acceleration and LVDT measurements with the GPS time data. The distance between the GPS on the cantilever beam and the base station GPS was maintained at up to 15 m to ensure accurate RTK-GPS measurements. To analyze the accuracy of the three aforementioned acceleration data processing methods and the two integrated RTK-GPS/accelerometer calculation methods, three displacements were given to the cantilever beams, and whether or not the displacements could be accurately calculated was determined using the accelerometer or the integrated RTK-GPS/accelerometer.

To ensure accurate evaluation, three displacements were generated on the cantilever beam. Among the three displacements shown in

Three acceleration data processing methods were used to measure the dynamic displacement of the structure, as described in Section 2. The dynamic displacements in

Prior to the integrated RTK-GPS/accelerometer calculation, the displacement measurement accuracy of RTK-GPS was analyzed. The static and quasi-static displacements of the structure were measured using RTK-GPS, and the accuracy of the RTK-GPS measurement method directly affected the accuracy of the integrated calculation results. The quasi-static displacement that was similar to that in

As shown in

The two methods that were described in Section 3 were used for the integrated calculation of the RTK-GPS and accelerometer measurements. To comparatively evaluate the degrees of accuracy of these two methods, quasi-static and dynamic displacements were simultaneously generated at the end of the cantilever beam, and their degrees of accuracy were evaluated by comparing the results with the LVDT measurements, as shown in

In the integrated calculation using Method I2, the low-frequency displacements were extracted from the RTK-GPS measurements, and were then integrated with the high-frequency displacements that were measured using an accelerometer. First, the RTK-GPS measurements were decomposed by frequency using the EMD method, as shown in

EMD was the only method used to extract the high-frequency displacements from the acceleration data. After the acceleration data were decomposed into IMF functions and residuals in the EMD method, the IMF functions, except for one low-frequency IMF and residual, were summarized to extract the high-frequency displacements.

In this study, diverse acceleration data processing methods and integrated calculation methods were evaluated to determine an optimal integrated RTK-GPS/accelerometer calculation method for structure displacement measurement. A cantilever beam bending test was conducted to evaluate the accuracy and usefulness of acceleration data processing methods and integrated calculation methods. For the evaluation, the LVDT measurements were directly compared with the results of the displacement estimation methods.

The accuracies of the three displacement calculation methods that used acceleration data processing were comparatively analyzed. The accuracy was highest when an FIR band-pass filter and double integration were used for the calculation, and it was also high when central differencing and Tikhonov regularization were used. This indicates that the displacement calculation methods can be used to measure the dynamic displacement with an accelerometer. The method with the EMD filter and double integration can also be used, but its accuracy was inferior to that of the aforementioned two methods.

The quasi-static displacement in the structure was measured using the RTK-GPS method. The displacements were measured with 5 mm deviations on average at a maximum error of 30 mm.

Among the integrated RTK-GPS/accelerometer calculation methods, the RTK-GPS-based simple integrated calculation and the frequency-based displacement extraction measured both the dynamic and quasi-static displacements. The test results showed that the latter was more accurate, with 4 mm deviations on average at a maximum error of 20 mm.

Referencing the results of the test conducted in this study, it was found that precise and overall measurement of the multiple structural displacements was possible using the optimal RTK-GPS/accelerometer integration method, which was used in this study.

For further study, an experiment involving the application of the optimal method to a real structure will be conducted to verify the benefits of the method.

The accuracy-related values in the conclusion of this study are experimental values, and cannot be considered absolutely accurate due to the characteristics of the RTK-GPS method that are affected by the GPS satellite signal reception environment. Further studies and tests are required to present more general and stricter standards.

This work was supported by the Postdoctoral Research Program of Sungkyunkwan University (2011).

Calculation of the dynamic displacement using the acceleration data.

Filtering of the acceleration data using an EMD filter.

Time windowing technique [

RTK-GPS-based simple integrated calculation process.

Concept of the integrated calculation according to frequency-based displacement extraction.

Specimen and devices.

Three types of displacement measurement.

Displacement measurements from the LVDT and the accelerometer (Method A1).

Displacement measurements from the LVDT and the accelerometer (Method A2).

Displacement measurements from the LVDT and the accelerometer (Method A3).

Displacements measured from the accelerometer using the processing method.

Histogram of the displacement measurement errors using the acceleration data processing method.

Example of the experiment result for assessing the accuracy of the vertical displacements measured from RTK-GPS, with the distribution of the RTK-GPS measurements with the LVDT values as reference. The dashed rectangles indicate excessive errors.

LVDT measurements, RTK-GPS/accelerometer integrated calculation results (Method I1), and long-frequency displacements from the RTK-GPS measurements.

LVDT measurements and integrated RTK-GPS/accelerometer calculation results for the enlarged dashed rectangle area in

RTK-GPS measurements decomposed by frequency using the EMD method. The intrinsic mode functions (IMFs) 1–5 and one residual were generated.

LVDT and RTK-GPS measurements and low-frequency displacements extracted from the RTK-GPS measurements.

LVDT measurements, RTK-GPS/accelerometer integrated calculation results (Method I2), and low-frequency displacements from the RTK-GPS measurements.

LVDT measurements and integrated RTK-GPS/accelerometer calculation results for the enlarged dashed rectangle area in

Histogram of the integrated RTK-GPS/accelerometer calculation error by method.

Key informations of LVDT transducer and RTK-GPS surveying.

Items | Specification | Items | Specification |
---|---|---|---|

Type | CDP-100 (tokyo sokki kenkujo) | Used software | RTKNavTM (Novatel Inc.) |

Capacity | 100 mm | GPS receiver/antenna | GX1200 with PPS/Event option (Leica Geosystems Inc.)/LEIAX1202GG (Leica Geosystems Inc.) |

Rated output | 5 mV/V ± 0.1% (10,000 × 10^{−6} strain ± 0.1%) |
GPS antenna calibration | Antenna calibration information from national geodetic survey of USA was used |

Sensitivity | 100 × 10^{−6} strain/mm |
GPS base station position | Previously determined by static GPS surveying method referred to national GPS station |

Nonlinearity | 0.1% RO | Reference frame (ellipsoid)/Positioning method | ITRF 2000 (GRS 1980)/Real time kinematic positioning (using RTCM 2.3 correction message) |

Temperature range | −10∼+60 °C | Ephemeris/Positioning frequency | Broadcasting ephemeris/1 Hz |

Accuracy using the acceleration data processing method.

Maximum deviation (m) | 0.0119 | 0.0423 | 0.0226 |

Mean deviation (m) | 0.0011 | 0.0041 | 0.0018 |

Standard deviation (m) | 0.0023 | 0.0085 | 0.0037 |

Ratio of less than 5 mm deviation (%) | 94.4 | 81.9 | 93.4 |

Accuracy of the vertical displacements measured with RTK-GPS.

Maximum deviation (m) | 0.0253 |

Mean deviation (m) | 0.0057 |

Standard deviation (m) | 0.0076 |

Ratio of less than 20 mm deviation (%) | 96.5 |

Accuracy of the integrated RTK-GPS/accelerometer calculation according to method.

Maximum deviation (m) | 0.0273 | 0.0153 |

Mean deviation (m) | 0.0037 | 0.0037 |

Standard deviation (m) | 0.0053 | 0.0050 |

Ratio of less than 5 mm deviation (%) | 89.2 | 91.2 |