AT527372B1 - Method for determining the relative vertical deformation of an object to be examined - Google Patents

Abstract

Method for determining the relative vertical deformation L'idup of an object (Ob) to be examined, in particular a structure, preferably a bridge, within a time span between temporally successive recording times (t1, t2) based on interferometric synthetic aperture radar (InSAR) data measured from at least one flying object, wherein the at least one flying object moves on a flight path in a flight direction repeatedly at temporal intervals over the object (Ob) to be examined and during this time records InSAR data along a viewing direction (LOS), wherein interferograms are created based on the recorded InSAR data, and wherein at least two persistent scatterer (PS) points (P1, P2) on the object (Ob) to be examined are determined as pixels that remain coherent over a sequence of interferograms, comprising the following steps: - Calculating the relative vertical deformation L'idup of the object (Ob) to be examined between the recording times (t1, t2) using the previously determined relative differential deformation lidLong in the longitudinal direction and the differential deformation change lidLOs -

Description

Description

[0001] The invention relates to a method for determining the relative vertical deformation Adıp of an object to be examined, in particular a structure, preferably a bridge, within a time period between successive recording times based on Interferometric Synthetic Aperture Radar (InSAR) data measured from at least one flying object according to claim 1.

[0002] In the following, numbers in square brackets [ ] refer to the bibliography at the end of the description.

[0003] Various methods for assessing the condition of structures are known from the state of the art. To date, the condition of bridges has been recorded primarily periodically through visual inspections, with the procedure in Austria being RVS 13.03.11 [1]. Metrological investigations are generally performed as a supplement to the visual inspection. In special cases, "special inspections," continuous monitoring systems are used. The existing approaches can be summarized into four groups:

- Detection of abnormal behavior - System or damage detection

- Monitoring of impacts

- Threshold monitoring

[0004] Sensor-based measurement methods record mechanical structural responses such as deformation, inclination, strain, etc. over time. Changes in the behavior of these responses can be caused by material-related reasons (e.g., material creep, settlement), changes in loading, or even changes in stiffness behavior (e.g., stiffness reduction due to damage). Changes in the static system (e.g., support subsidence in statically indeterminate systems) can also occur. Reliable conclusions can be drawn from known input variables (e.g., recording the load). Otherwise, the responses must be compared with predictions from models for interpretation of the measured data and condition assessment.

[0005] The most common test for measuring deformation is tachymetric surveying (theodolite/total station) or leveling, e.g., bridge leveling. This determines the structural response of the structure under investigation to constant loads (dead loads) or changes in deflection caused, for example, by a trigger such as material behavior, settlement, or load changes. This occurs when bridge tests reveal anomalies or, in certain cases, when overloads occur (e.g., in the Altersberg Bridge A10-2006 in Austria [2]). The tachymetric survey is based either on existing fixed-point fields (e.g., national coordinate systems such as the Austrian Federal Surveying Network) for absolute coordinate determination, or refers to known reference points from previous surveying activities. For practical reasons, no permanent monitoring is carried out, or if it is carried out only in exceptional cases, it is carried out using prisms mounted on the structure and fully automatic total stations.

[0006] Measurements of other mechanical quantities such as inclination, strain, and crack width were initially performed primarily during test loading (new construction prior to opening or during special tests) with known loads [3, 4] and are currently also used using crack spies or, if necessary, for special tests for continuous monitoring. Requirements for measurement technology for continuous monitoring are currently being standardized throughout Europe for geotechnical applications [7]. For example, EN_ISO 18674-1 [8], currently under development, lists options for shifting measuring points, including special cases such as vertical displacement components (= settlement or heave) and derived parameters, e.g., tilting and strain. These include: total station (tachymeter), leveling instrument, electronic distance measuring device, laser scanner, GNSS (differential GPS), radar interferometry (interference measurement method using radar) (InSar, terrestrial, or satellite-based).

[0007] Continuous observation of the deformation state of structures is a potentially promising indicator, but difficult to implement for continuous monitoring. Methods have been developed that attempt to determine deformation from measurements taken by inclinometers [5] or accelerometers [6]. The most common permanent system for vertical displacements is a flexible digital hose scale. It directly measures the deformation differences and utilizes the principle of hydrostatic settlement measurement using sensors attached to the structures. The vertical settlement of the sensors is determined relative to a reference sensor. This method is suitable for the continuous monitoring of geotechnical or deformation problems, but requires constant maintenance of the sensors (e.g., changing fluids, etc.), as well as interconnected pipes between the sensors and sensor-related temperature compensation (thermal expansion of the measuring fluid).

[0008] The SIBS [9] research project - Safety Assessment of Retaining Walls tested various methods of deformation measurement and assessment on real retaining walls. The necessary distinction between thermal deformations and those caused by unknown damage was supported by specially conducted thermal tests.

STRUCTURE-RELATED TEMPERATURE COMPENSATION:

[0009] In order to derive reliable statements regarding structural safety, high deformation accuracies (usually at least in the mm range) are necessary. To detect abnormal structural behavior, the temperature deformation of the structure must be compensated. Due to the size of the structures and the different materials and components, the temperature varies on site on the structure and, in the case of larger structures, also along the object (temperature fields resulting from shading, river crossings, valley crossings, different materials or component thicknesses, etc.). Transient thermal effects of the materials or structures under consideration must be taken into account, or the direct structure temperature must be measured, in order to optimally create temperature compensation models for sensor-based monitoring [10].

[0010] Furthermore, satellite-based monitoring methods (persistent scatterer interferometry) are known. As already mentioned, the method of satellite-based radar interferometry, based on the latest approaches, is well suited for long-term monitoring of the condition of objects, particularly structures and bridges. The following provides an overview of previous approaches.

[0011] The following shows schematically:

[0012] Fig. 1 shows the basic principle of satellite-based radar interferometry, [0013] Fig. 2 shows the method of persistent scatterer interferometry PSI, [0014] Fig. 3 shows the coordinate transformation according to [30],

[0015] Fig. 4 shows the image recordings and angles and position designations when looking east-west according to [31],

[0016] Fig. 5 is a representation of the coordinate transformation of ground movement directions using measurement data from two different orbital directions.

[0017] The basic principle of the satellite-based radar interferometry method is shown in Fig. 1 and Fig. 2.

[0018] Fig. 1 shows the basic principle of satellite-based radar interferometry: A measurement is taken using one or more radar antennas mounted on satellites, suitable for Interferometric Synthetic Aperture Radar (InSAR). The antennas transmit signals, which are received again after being backscattered by the Earth's surface. The satellites fly over the Earth's surface along their trajectory (=orbit O). The measurement is usually taken looking right (normal to the direction of flight), the measurement direction (line of sight (LOS))

is in the line of sight of the satellite Sat. Satellite images of Earth observation using radar waves are therefore taken in an oblique viewing direction, looking right and normal to the direction of flight. The interference shift of the radar signal is determined as a fraction of the wavelength \. This theoretically allows a very high level of accuracy to be achieved. For example, the ESA Sentinel 1 satellites use signals (C-band frequency) with a wavelength ) = 5.5 cm; shifts of fractions of this wavelength can be recorded. The deformation measurement of the Earth's surface is recorded during overflight in so-called scenes Sz (one scene Sz per overflight).

[0019] Fig. 2 shows a schematic representation of the Persistent Scatterer Interferometry (PSI) method. Multiple images (=scene Sz or SAR images) are evaluated. The focus is on those pixels that remain coherent across multiple images and thus function as persistent scatterers (PS) with a constant reflection across a series of images (usually at least 20 scene Sz). These coherent retroreflectors are used as a reference, and the differential shifts are evaluated.

[0020] ESA [16], for example, uses research satellites - Sentinel 1 - which orbit at an altitude of 693 km above the Earth's surface. The Sentinel-1 satellites 1A and 1B overfly the Earth in a synchronous (approximate) polar orbit slightly inclined to the Earth's axis (inclination 98.18°) [16]. The points on the Earth's surface are overflown in two orbital directions, once from south to north (ascending orbit ASC) and once from north to south (descending orbit DSC). The Sentinel-1 satellites 1A and 1B overfly the Earth in a synchronous (approximate) polar orbit. The images on Earth are taken in an oblique view (looking right) with a return period of 6 days in the same orbit. Since December 2021, satellite 1B has been out of service due to a solar storm. This reduced the number of images taken per year to that of one satellite: 12 days in the same orbit or every 6 days in the opposite orbit.

[0021] The data are recorded at a C-band frequency with a wavelength of A = 5.5 cm. In addition, there are several commercial providers (COSMO-SkyMed, ICESat) and other research satellites (e.g., Terra SarX) that have InSAR-capable radar antennas.

[0022] Persistent Scatterer Interferometry (PSI) is a powerful analysis method that can determine deformations on the Earth's surface with potentially very high accuracy, without the need for surface-mounted sensors. Specifically, PSI is a differential InSAR (Interferometric Synthetic Aperture Radar) radar technique that uses the properties of wave interference to derive measured variables. Using PSI, distance differences in the range of a fraction of the wavelength can be derived by comparing the phase values of corresponding pixels from different recording times (scenes) [11].

[0023] Basically, the PSI method does not require an on-site reflector; instead, natural retroreflectors (persistent scatterers PS) are used. As shown in Fig. 2, those pixels are examined that remain coherent across multiple images or interferograms (indicated in Fig. 2 as white circles with a black border), and thus function as PSI points as a coherent reflection across a series of images (= scenes or SAR images). For this purpose, a large number of images (usually more than 20) are processed, allowing a time series of deformations and the average offset rate for the persistent scatterer (PS) to be calculated [10]. This analysis of time series is specifically referred to as "multi-temporal satellite-based differential interferometry" (MTINSAR) [17]. With additional reflectors attached to the object being observed (corner reflectors or CR), the accuracy can be increased and better information such as clear point assignment can be obtained.

[0024] Lange et al. [1] used data from the non-commercial high-resolution satellite TerraSAR-X (TSX), operated by the German Aerospace Center and Airbus DS, in explicit research work to test the methods on various structures and buildings

8 m above sea level

to test. A 2019 project monitored hydropower plants using the highest-resolution mode, the so-called "Staring Spot-Light," with very high spatial resolution. This demonstrated that sub-cm accuracy is possible [12]. Dams were also surveyed using Sentinel-1 data, determining displacement rates of sub-cm/a. Another example where Sentinel-1 data has proven applicable is landslide detection, which enables the updating of existing maps of landslide boundaries and activity [13].

[0025] Lazecky et al. [14] demonstrates the potential for monitoring deformations and movements in bridge structures, including thermal expansion, in three case studies (bridges in Bratislava, Ostrava, and Hong Kong). Using surface temperature measurements and simple correlations, accuracy could be significantly increased. With installed sensors, it was possible to decompose the SAR phase difference with respect to the reference point between the phase change due to height difference and thermal expansion. Based on the suitability of the investigated data set and the assumption of linearity of these parameters, a correlation between temperature changes and the linear deformation rate over time was evaluated using MTINSAR methods. In this case, multiple orbits must always be combined simultaneously to determine the position.

[0026] Selvakumaran et al [15] developed ideas on how unrecorded unknown quantities could be clarified through a suitable statistical combination of SAR and in situ measurements, so that the absolute movements of the bridge can also be used. The absolute displacement cannot be measured using displacement measuring devices on the structure. Due to the frequency of satellite measurements and the noise within the measurements, only seasonal trends can be tracked, thus complementing conventional inspection systems. The problem of evaluations combining multiple orbital directions is also explicitly pointed out here. Especially when the images are taken from different viewing angles on different days or at different times of day, the structure, e.g., the bridge, is exposed to a different temperature, which affects the thermal movement. One possible evaluation is to use only points with the same structural temperature. The measurements carried out on Waterloo Bridge in London as part of the aforementioned work proved to be comparable when the relative movement of the points along the bridge to one another was used. Various loading conditions such as tidal movements, thermal expansion, deformations due to traffic loads as well as shrinkage and creep of the concrete complicate the interpretation.

[0027] Nettis et al. [17] provides a very good overview of research and initial applications of MTInSAR methods related to compensation of thermal structural deformations, which is summarized below: A first category of studies aims to modify or extend conventional MTInSAR algorithms for analyzing seasonal thermal deformations in order to use them for near-continuous bridge-specific monitoring [18, 28]. These studies mainly deal with individual case studies of highly loaded bridges. Huang et al. [23, 24] and Jung et al. [25], for example, focus on the application of MTInSAR techniques for long-span bridges (steel truss and cable-stayed bridges, respectively) in China using C-band Sentinel1 and X-band COSMO-SkyMed radar datasets. The authors use these different SAR datasets for long-term monitoring of bridge condition by decomposing the signals to isolate vertical detections and temperature-induced deformations. Cusson et al. [26, 27] address the same topic. They investigate the potential of satellite-based interferometry for analyzing temperature-induced deformations at low speeds (so-called thermal sensitivity) for road bridges in Canada using RADARSAT-2 data. The authors demonstrate a relevant correlation between the time series of PS displacements on the bridges and the ambient temperature. Furthermore, they find that railings on a bridge are reliable reflectors, allowing for multiple coherent PS measurements. In [27], Cusson et al. demonstrate the accuracy (error less than 0.25 mm°C) over the thermal sensitivity determined with MTINSAR.

The sensitivity of displacements is assessed by comparing it with a FEM analysis for two case study bridges featuring different types of U-shaped superstructures. Furthermore, an early warning system is proposed that issues warnings when appropriate thresholds for thermal deformation are exceeded.

[0028] Markogiannaki et al. [28] investigate how MTINSAR can be used to support visual bridge inspections using a long case study bridge in Greece. They decouple displacements due to temperature-induced effects and vertical detections and detect an evolving deformation of 1.8 mm/year with an absolute value of 9.5 mm, which, according to the authors, can be linked to evolving degradation phenomena confirmed by on-site inspections. Giordano et al. [29] propose a method for structural damage detection based on PS time series, neglecting unwanted deformations due to environmental conditions (e.g., temperature-induced deformations). The effectiveness of the method is demonstrated using a steel truss bridge, the Palatino Bridge in Rome, subject to settlement-induced deformations.

[0029] However, previous calculation approaches generally use measurement data from both orbital directions, ASC and DSC. The slant distances LOS (Line of Sight) measured via MTINSAR are directly combined to enable transformation into vertical and horizontal directions. Thus, for the example north-south overflight direction, only objects with a predominantly east-west orientation can currently be considered. For applications on the Earth's surface, particularly slopes and ground surfaces, horizontal displacement due to thermal change is insignificant. However, if structures such as bridges are being examined, structure-specific temperature compensation is required to increase accuracy. For temperature compensation, the associated thermal displacements are calculated. The determination is usually carried out from models, loaded with the associated (measured) temperature changes.

[0030] Conversion of the coordinate transformation known from the state of the art:

The satellites orbit the Earth in two orbits with two orbital directions (South/North = ASCENDING ASC and North/South = DESCENDING DEC) and thus provide a measured change in the phase in the line of sight (LOS) of the satellite for each orbit, along with the corresponding angle. The data is based on interferometrically determined phase differences in the radar signals (Differential SAR Interferometry), which are used over time series. These are pre-processed separately for each orbit using remote sensing techniques. The images of the Earth's surface are taken at different times by several days, depending on the orbital direction ASC or DSC. Previous approaches use the slant distance dIOS ase, dLOS dsc, measured from both orbital directions ASC and DSC to calculate a horizontal and a vertical displacement component on the Earth's surface (see Fig. 3).

[0031] Fig. 5 shows a schematic representation of the coordinate transformation according to [30] known from the prior art, in which the difference deformations between the time series represent the temporal development of the deformation dıos in the viewing direction LOS as deformation to the east de and as vertical deformation dp.

[0032] Thus, the coordinate transformation is underdetermined because no third orbital direction is present. Thus, for the exemplary north-south overflight direction, only the east-west deformation and the resulting calculated vertical displacements can be determined. The practical application is therefore very limited; it cannot be used to measure (bridge) structures oriented in the satellite's north-south trajectory. A basic scheme of the previous coordinate transformation from dıos to de: and vertically du is shown in Fig. 4 and Fig. 5. The differences (indicated by the letter "d") always refer to different time series.

[0033] The conversion of the coordinate transformation is carried out according to the following basic scheme:

* Satellites fly in orbits around the Earth and carry out, among other things, radar deformation measurements on the Earth's surface.

* Images are staggered due to the satellite's trajectory. For example, with Sentinel, a satellite passes the same spot on the Earth's surface every 12 days in the same orbit. Depending on the position on the Earth's surface, the spot is passed over by at least two orbits, ideally up to four, resulting in 60-120 images per year.

* You can only measure in the direction of view LOS for each flight path/orbit.

» The time series images are pre-processed and corrected using remote sensing methods (e.g. ellipsoidal, topographic, deformation-dependent, atmospheric correction, etc.).

* Several images are taken from which a coherent reference point (persistent scatterer point) can be identified (usually 20 images). (Reference time point = time t+).

* A further recording will be made at a later time when the satellite is back in the same place after a few days (recording time tz)

+ The time differential change of the position coordinates is calculated.

[0034] Fig. 4 shows a representation of the images, angles and position designations when looking east-west according to [31].

[0035] In detail, the determination of the change in the position coordinates in the prior art is carried out as follows: Definitions of the data:

8; - angle of incidence (known)

AaLD - Azimuth AZ - Viewing direction ALD (known)

dup -temporal vertical movement (wanted)

dn - temporal movement to the north (searched)

de - temporal movement to the east (wanted)

dıos - measured temporal delta of the slant distance measured at different recording times in the direction of view LOS

[0036] The dios motion consists, as shown in the figures, of three components: due, dn, and de. The trigonometric relationship with respect to angle of incidence θ and azimuth AaLD is given by the following equation 1 according to []:

dios = dupscos(0) — (dy * COS(AaıD) + dx * sin(dm.p)) * sin(0;) Equation 1

[0037] Fig. 1 shows a representation of the coordinate transformation of ground movement directions when using two orbits or orbital directions.

[0038] Disadvantages of the known state of the art: Equation 1 is underdetermined,

- the amount and direction of an actual point movement is unknown,

- The derivation of the vertical bridge motion is only possible with simultaneous projection of both orbital directions ASC - DSC. This means that Equation 1 is formulated for the two existing orbital directions, which were recorded at different times. Equation 1 is therefore still simply underdetermined.

[0039] For this reason, the following approximation is carried out in the prior art: Current application of the method is only possible for objects in east-west orientation, i.e. normal to the north-south flight direction and in approximate alignment in the direction of view LOS of the satellite.

- When the object is oriented east-west, the influence of the temporal motion to the north dy is subordinate and is neglected. Only two quantities remain that can be calculated.

- Determination of absolute position shift in east direction E as the difference of the individual time series (d£) taking into account both orbital directions ASC, DSC, and calculation of dp from equation 1.

[0040] Since the measurement from the two orbital directions ASC and DSC leads to different

Ss N

time series, this is well suited for slow ground movements. Due to strong temperature-related changes in the daily cycle, as occurs, for example, in many long-span bridges, the use of this method for structures is only possible to a limited extent, since the thermal displacement at the different recording times must be taken into account (structure-specific temperature compensation). As shown in many studies [11-29], to date in remote sensing/MTInSAR at least the surface or air temperature at the time of recording has been used as a correction for the thermal displacement component. This temperature was calculated parallel to the time series recordings and included in the evaluation. The decisive factor, however, is the component displacement itself, and thus the component temperature, which is a transient process and not directly proportional to the air temperature due to the inertia effects of the materials used.

[0041] The object of the invention is therefore to remedy this situation and to provide a method for determining the relative vertical deformation Adı,p of an object to be examined, which overcomes the known disadvantages, is applicable to objects with any orientation or alignment to the line of sight of a satellite or flying object from which the InSAR data are recorded, has improved accuracy and enables the best possible use of the available database.

[0042] The invention solves this problem with a method for determining the relative vertical deformation Adı of an object to be examined, in particular a structure, preferably a bridge, within a time period between successive recording times based on Interferometric Synthetic Aperture Radar (InSAR) data measured by at least one flying object,

- wherein the at least one flying object moves repeatedly over the object to be examined on a flight path in a flight direction at a time interval and during this time records InSAR data along a line of sight (LOS),

- where interferograms are created based on the recorded InSAR data, and

- where at least two persistent scatterer (PS) points on the object to be examined are identified as pixels that remain coherent over a sequence of interferograms,

with the features of patent claim 1. According to the invention, the following steps are provided:

- Determining the change in phase in the viewing direction with the corresponding angle of incidence θ between the viewing direction and the nadir direction and the corresponding angle α between the viewing direction projected onto a horizontal surface and the geographical north direction for the at least two PS points on the object to be examined based on interferograms created at at least two recording times,

- Deriving the differential deformation change Adıos of the object to be examined in the viewing direction of the flying object between the recording times based on the determined change in phase, in particular after correction of errors caused by phase jumps,

- Carrying out a coordinate transformation of the differential deformation change Adı os in the direction of the object to be examined, whereby the horizontal movement components of the differential deformation change Adıos are projected onto the longitudinal and transverse directions of the object to be examined, in particular using the angle ao5 between the longitudinal axis of the object projected onto a horizontal surface and the geographical north direction,

- Determination of the temperature, in particular the temperature of the object to be examined, in particular as an estimate and/or by measurement,

- Determination of the relative differential deformation occurring between the recording times Adıong In the longitudinal direction of the object to be examined between the viewing points corresponding to the PS points on the object to be examined, taking into account the determined temperature

- Calculation of the relative vertical deformation Adıp of the object to be examined between the recording times using the previously determined relative differential deformation Adıong in the longitudinal direction and the differential deformation change Adı os.

[0043] In the context of the invention, a flying object is understood to be any object that moves or flies over the Earth's surface at a distance from it along a predetermined, particularly closed, trajectory and can thereby record InSAR data. Such a flying object can be, for example, an airplane, a helicopter, a drone, or other unmanned aerial vehicles, but primarily satellites. Such flying objects have special radar antennas suitable for radar interferometry (Interferometric Synthetic Aperture Radar - InSAR).

[0044] In the case of a satellite, for example, such a trajectory may be an orbit which extends circularly or elliptically around the Earth, in particular on one side of the Earth from a first pole to a second pole opposite it and then on the other side of the Earth from the second pole to the first pole. The direction of flight is understood to be the direction of travel of the flying object as it moves along its trajectory, for example the orbital direction. The viewing direction of the flying object is understood to be the direction in which the flying object records InSAR data from objects on the Earth's surface. The nadir is understood to be the base point opposite the zenith, and the azimuth is understood to be the horizontal angle relative to the north direction.

[0045] InSAR data refers to the measurement data, for example SAR images of the satellites according to the InSAR method, which are pre-processed preferably using remote sensing methods and, if necessary after correction(s), analyzed interferometrically.

[0046] In the context of the invention, PS points on the object to be examined or pixels that remain coherent over a sequence of interferograms are understood to mean points or pixels that remain radiating the same at different recording times.

[0047] With a method according to the invention, it is advantageously possible to determine the relative vertical deformation Adıp of an object to be examined from the measured values of only a single orbital direction and the associated specific horizontal positional displacements of the observation points. The horizontal relative position change or deformation component occurring between the recording times due to thermal effects is advantageously also taken into account.

[0048] In contrast to the prior art, the main focus of a method according to the invention is not on the absolute change in position, but rather a relative displacement between two persistent scatterer points or the observation points corresponding to these PS points on the object to be examined is determined.

[0049] For this purpose, according to the invention, a coordinate transformation of the differential deformation change Adıos is carried out in the direction of the object to be examined and the horizontal movement components, i.e. the north component Ade and east component Adyr of the differential deformation change Adıos of the object are projected in the direction of the object, i.e. onto the longitudinal and transverse directions of the object to be examined.

[0050] In contrast to the methods known from the prior art, it is possible in this way to examine objects with any orientation or alignment to the viewing direction LOS of the flying object or its flight path. A method according to the invention is not dependent on the fact that, for example, when using InSAR data from Sentinel satellites, the north component Ady of the differential deformation change Adı os plays only a subordinate role if the object under investigation extends in an east-west direction. This means that the application of the known methods is only possible for objects with an east-west orientation, and for this purpose, measured values from two different flight or orbital directions ASC, DSC are required.

SS N 8

[0051] The advantages of this approach are based on the fact that it is no longer necessary to intersect different orbits in order to convert from the time-varying slant distance dı_os to the vertical direction dup.

[0052] This results in the following advantages:

» Denser time series, since the InSAR measurement data from different orbital directions can be used individually and do not need to be merged.

* More possible viewing points on the object under investigation, since the individual possible viewing points do not have to be viewed from two orbits or orbital directions each, so that a method according to the invention can also be applied to smaller bridges and provides improved accuracy.

* Increased accuracy as there is no longer any blurring due to thermal effects that occurred between different capture times.

* No restriction on the target orientation, whereas current methods currently only allow objects approximately aligned with the LOS of the satellite from which the InSAR data are measured. When using Sentinel satellites, for example, current methods require an east-west orientation of the object to be examined.

[0053] A further improved accuracy in determining the relative vertical deformation Adıp of an object to be examined can be achieved

- if the relative differential deformation Adrrans in the transverse direction of the object to be examined between the recording times is determined between the viewing points on the object to be examined corresponding to the PS points, taking into account the determined temperature and

- if the relative difference deformation Adr;ans in the transverse direction is also used when calculating the relative vertical difference deformation Adıp of the object to be examined between the recording times.

In this way, it is advantageously possible to achieve a particularly high accuracy in the determined relative vertical deformation Adıp for objects that are not longitudinally extended.

[0054] A particularly precise determination of the temperature relevant for the relative differential deformation Adıona in the longitudinal direction of the object under investigation can be achieved if the internal temperature of the object under investigation is measured to determine the temperature. This is achieved, for example, by drilling the temperature sensors into the interior of the structure in the case of a solid structure (e.g., made of concrete) or by gluing them to the surface in the case of thin-walled structures, e.g., made of steel. The accuracy of this temperature determination increases with the number of temperature sensors used in the cross-section and over the length of the structure.

[0055] An alternative or additional variant for determining the temperature relevant for the relative differential deformation Adıong in the longitudinal direction of the object to be examined, which requires only a few, particularly simply designed temperature sensors in the area of the object or completely without such temperature sensors, can be provided if the air temperature in the area of the object to be examined is measured and/or derived from weather data.

[0056] A further alternative or additional variant for determining the temperature relevant for the relative differential deformation Adıong in the longitudinal direction of the object to be examined, which does not require any temperature sensors in the area of the object, can be provided if an empirical temperature model is used to derive the internal temperature of the object to be examined based on network weather data.

[0057] According to a particularly exact and at the same time computationally particularly simple variant of a method according to the invention, it can be provided that in order to determine the relative differential deformation Adıong in the longitudinal direction of the object to be examined, the thermal

Deformation between the observation points corresponding to the PS points on the object to be examined is calculated using a mechanical model, taking into account the temperature, in particular the internal temperature of the object to be examined.

[0058] In order to further improve the calculation accuracy in determining the relative vertical deformation Adıp of an object to be examined, it can be provided that in order to determine the relative differential deformation Adıona in the longitudinal direction of the object to be examined and/or to calibrate the mechanical model used in a method according to the invention, the positional displacement between the observation points corresponding to the PS points on the object to be examined is determined by measurement, in particular by laser distance measurement.

[0059] In order to particularly effectively avoid misinterpretations caused by phase jumps in the measurement data, it can be provided in a method according to the invention that, before deriving the differential deformation change Adı os of the object to be examined, a correction of the phase number in the viewing direction of the flying object is carried out to correct errors caused by phase jumps, in particular a correction using statistical methods, preferably phase unwrapping, for the at least two PS points on the object to be examined based on at least two InSAR data sets recorded at approximately the same recording time, in particular along the same viewing direction.

[0060] In the context of the invention, the phase number refers to the integer number of waves determined for distance measurement by measuring the time signal. Phase ambiguities or phase jumps are caused by a misinterpretation of the phase number due to measurement errors in the timing when measuring the change in the slant distance in the line of sight (LOS) of the satellite and can be corrected using statistical methods, in particular phase unwrapping.

[0061] In this context, for a particularly effective use of the available InSAR data,

that at least one further flying object moves repeatedly over the object to be examined on a further flight path in a further direction of flight opposite to the direction of flight of the flying object and during this time records InSAR data along a further viewing direction, and

that to correct the phase number in the direction of view of the flying object for the at least two PS points on the object to be examined, InSAR data recorded at approximately the same recording time are used from the further flying object moving on the further flight path in the further, opposite, flight direction along the further viewing direction.

[0062] In order to be able to calculate the relative vertical deformation Adı of an object to be examined independently of the orientation of the object to the flight path of the flying object and from the InSAR data of a single flying object with only one flight direction in a particularly simple manner, it can be provided that the horizontal movement components in the east direction Ade: and in the north direction Ady of the differential deformation change Adıos are projected onto the longitudinal and transverse directions of the object to be examined according to

Adı — op)

Adrrans = Ady”sin(daLD — Aop)

[0063] In order to be able to determine the relative vertical deformation Adıp of an object to be examined with any orientation to the flight path of the flying object, regardless of the absolute movement of the object in the north direction in the case of longitudinally extended objects, it can be provided that the relative vertical deformation Ad is calculated according to

__ Adıos+Adziong*cos(daLD-Aop)*Sin(8;)

Adip a cos(8;j)

[0064] In order to determine the relative vertical deformation Adıp of an object to be examined with any orientation to the flight path of the flying object, independent of the absolute movement of the object

Ss N

In order to be able to determine the north direction for objects of any shape, it can be provided that the relative vertical deformation Adıp is calculated according to

— Adıos+(Adiong*cos(aaLD -A0ob)+AdrTrans*Sin(dALD —a0p))+sin(9))

Adip a cos(8;)

[0065] In order to be able to advantageously exploit the fact that the relative differential deformation Adıong in the longitudinal direction of the object to be examined is dominated by the thermal expansion of the object when calculating the relative differential deformation Adıong in the longitudinal direction of the object to be examined, it can be provided that the relative differential deformation Adıong in the longitudinal direction of the object to be examined is calculated according to a simple bar model according to

Adı * ap* AT

where AL is the relative distance between the observation points corresponding to the PS points on the object to be examined, ay is the specific expansion coefficient of the object to be examined and AT is the change in the internal temperature of the object to be examined and/or the air temperature in the area of the object to be examined between the recording times.

[0066] According to a particularly exact variant of a method according to the invention which can be adapted particularly easily to a wide variety of varying parameters, it can be provided that in order to determine the relative differential deformation Adıong in the longitudinal direction and/or in order to determine the relative differential deformation Adrıans in the transverse direction, a model, in particular a finite element model, is created and the relative differential deformation Adıorng in the longitudinal direction and/or the relative differential deformation Adr-ans in the transverse direction are modeled taking into account the specific expansion coefficient ay of the object to be examined and the change in the internal temperature of the object to be examined and/or the air temperature in the area of the object to be examined between the recording times.

[0067] In order to further improve the accuracy in determining the relative vertical deformation Ad of an object to be examined, it can be provided that before the PS points are determined - a correction, in particular an ellipsoidal, topographical, deformation-dependent and/or atmospheric correction, is carried out on the recorded InSAR data and/or - further signal processing steps are applied to the interferograms created.

[0068] Further advantages and embodiments of the invention will become apparent from the description and the accompanying drawings.

[0069] The invention is schematically illustrated below with reference to particularly advantageous, but not restrictive, embodiments in the drawings and is described by way of example with reference to the drawings.

[0070] The following shows schematically:

[0071] Fig. 6a, Fig. 6b an embodiment for a correction of misinterpreted phase jumps,

[0072] Fig. 7a shows the position of two observation points P+ and P2 on a bridge as a structure to be examined,

[0073] Fig. 7b shows a representation of the temporal change of the position of two viewing points P+ and P2 between two different recordings at the times t1 and t,

[0074] Fig. 8a the differential deformation dıos in the viewing direction LOS of the flying object, the horizontal motion components de, Ady of the differential deformation dıos and the angle aaLD,

[0075] Fig. 8b shows a representation of a coordinate transformation in the object direction within the framework of a method according to the invention,

[0076] Fig. 9 geometric relationship of the displacement components of the measured oblique distance dıos in the viewing direction LOS into the vectorial decomposition of the desired vertical direction dup vertika and the resulting longitudinal direction dLong,

[0077] Fig. 10a shows a representation of the temporal deformation Adıp of two reference points Ref on an object under investigation, calculated by means of a digital hose level, and the relative vertical deformation calculated according to the invention based on data from a first orbit,

[0078] Fig. 10b is a representation of the temporal deformation Adıp of two reference points Ref on an object under investigation, calculated by means of a digital hose level, and the relative vertical deformation calculated according to the invention based on data from a second orbit,

[0079] Fig. 10c shows a representation of the temporal deformation Adıp of two reference points Ref on an object under investigation, calculated by means of a digital hose level, and the relative vertical deformation calculated according to the invention based on data from a third orbit,

[0080] Fig. 10d shows a representation of the temporal deformation Adıp of two reference points Ref on an examined object calculated by means of a digital hose level and the relative vertical deformation calculated according to the invention based on data from a fourth orbit,

[0081] Fig. 11a shows a first embodiment of a statistical correction of the phase jumps by phase unwrapping,

[0082] Fig. 11b shows a second embodiment of a statistical correction of the phase jumps by phase unwrapping,

[0083] Fig. 11c shows a third embodiment of a statistical correction of the phase jumps by phase unwrapping,

[0084] Fig. 11d shows a fourth embodiment of a statistical correction of the phase jumps by phase unwrapping.

[0085] In the following, a method according to the invention for determining the relative vertical deformation Adı of an object Ob to be examined, for example a structure such as a bridge, within a time period between successive recording times based on Interferometric Synthetic Aperture Radar (InSAR) data measured by a satellite is explained first in general terms and then using specific exemplary embodiments.

[0086] Although a method according to the invention is described below using satellite-measured InSAR data for determining the relative vertical deformation Ad of a bridge as the object to be examined Ob, a method according to the invention is by no means limited to this type of flying object for measuring the InSAR data. It is only essential that the flying object, be it a satellite, an aircraft, a helicopter, a drone, or the like, moves repeatedly over the object to be examined on a constant, predetermined flight path in a flight direction at time intervals and, during this time, records InSAR data along a viewing direction LOS. Furthermore, a method according to the invention is not limited to elongated objects Ob such as bridges. Quite the opposite, a method according to the invention can be used to determine the relative vertical deformation Ad of any object Ob, which, above all, can have any orientation relative to the flight path of the flying object measuring the InSAR data.

GENERAL DESCRIPTION

[0087] A method according to the invention transforms deformations measured with flying objects, e.g., satellites, in a viewing direction, i.e., a slant distance or line of sight (LOS), of at least two uniquely attributable persistent scatterer (PS) points or the viewing points P+, P2 corresponding to these PS points on the object under investigation. For this purpose, at least two PS points on the object under investigation are determined as pixels that remain coherent over a sequence of interferograms.

[0088] Two observation points P-+, P>,, e.g., corner reflectors CR fixedly mounted on the object, which serve as a reference and amplify the radar signal, are defined, whose relative movements to each other are to be examined at different times t+, tz (see Fig. 7a, 7b). The calculation of the relevant relative vertical deformation Ad, of the two observation points P+4, P2 on the object Ob is then carried out on the basis of at least two scenes Sz or interferograms of the object Ob recorded at the times t;, tz.

[0089] First, based on interferograms created at at least two recording times t;, t2, the change in the phase in the viewing direction LOS with the associated angle of incidence θ; between the viewing direction LOS and the nadir direction Nad and the associated angle aa.Dd between the viewing direction LOS projected onto a horizontal surface and the geographical north direction N is determined for the at least two PS points on the object Ob to be examined. The differential deformation change Adıos of the object Ob to be examined in the viewing direction LOS of the flying object between the recording times t+, t2 is derived based on the determined change in the phase - preferably after correcting errors caused by phase jumps, which will be discussed in more detail below.

[0090] After an initial recording at the reference time t1, the position of the observation points P+;, P2 changes within the observed time period Δt= t2-t1. The relative vertical displacement Δdp between P+ and P>; within Δt, which is important for structural monitoring, can be determined using equation 1 given above:

Adip — dupz - dupi

[0091] Fig. 2a shows the position of two observation points or PS points P+4, P2 on an examined, elongated object Ob, namely a bridge, at a first time t1. Fig. 7b shows the temporal change in the position of the observation points or PS points P+, P2 between the recording times t1 and t2. Due to cooling, the bridge shortens and the two observation points P+4, P2 lower.

[0092] To determine the relative vertical deformation Adıp, according to the invention, a coordinate transformation is carried out from InSAR measurement data, preferably pre-processed by remote sensing. However, only InSAR data from ONE overflight direction or orbital direction are required, as well as the associated determined horizontal position shifts or movement components of the observation points P+, P2 on the object Ob. Both components, namely the slant distance calculated from InSAR data and the horizontal position shifts or movement components, are used in the coordinate transformation, and the relative vertical deformation Adı between the recording times t+, t2 is determined.

[0093] Within the scope of a method according to the invention, a coordinate transformation of the differential deformation change Adıos of the object to be examined Ob in the viewing direction LOS of the flying object into the direction of the object to be examined Ob takes place, taking into account the relative horizontal position changes (Adıong, Adtrans) on the object Ob, i.e. the horizontal movement components Ade, Ady of the differential deformation change Adıos are projected onto the longitudinal and transverse directions of the object to be examined Ob.

[0094] Starting from equation 1, the horizontal movement component is projected onto the longitudinal direction Adrrans and transverse direction Adrrans of the object Ob, in the bridge embodiment, as follows:

Adı — XBrücke) AdTrans = Adry*sin(da.D XBrücke)

where ob = ABridge azimuth of the bridge ZA difference of the temporal recordings.

[0095] Fig. 8a schematically shows the differential deformation dıios of the object to be examined Ob in the viewing direction LOS of the flying object, as well as the horizontal movement components de, Ady of the differential deformation dıos in the east direction E and in the north direction N and the angle aa.Dd between the viewing direction LOS projected onto a horizontal surface and the geographical north direction N. Fig. 8b schematically shows the coordinate transformation in the object direction with the horizontal movement components Adıong and Adrt,ans projected onto the longitudinal and transverse directions of the bridge under investigation and the angle Agrüeke between the longitudinal axis of the bridge projected onto a horizontal surface and the geographical north direction N.

[0096] Thus, equation 1 takes the following form:

Ad _ Adıos+(AdıonG*cos(daLD7Aob) +Adrrans*Sin(dALD-Aob))+Sin(9;) Equation 2 up cos(8;) g

[0097] For elongated or elongated objects Ob such as bridges, usually only the dominant displacement component in the object's longitudinal direction, i.e. the relative differential deformation Adıong in the longitudinal direction of the object Ob to be examined, is decisive, so that the relative differential deformation Adr;ans in the transverse direction of the object Ob to be examined can be disregarded, whereby equation 2 is reduced to equation 3:

__ Adıos+Adiong*C0S(&4LD-Aob)+*SiN(9;)

Adıp = 089 Equation 3

[0098] For objects Ob with any shape, the relative differential deformation Adr,ans in the transverse direction of the object Ob to be examined that occurred between the recording times can also be used to calculate the relative vertical deformation Adıp and equation 2 can be used.

[0099] The horizontal relative position change or deformation component occurring between the recording times t+, t2 due to thermal effects is taken into account according to the invention when determining the relative differential deformation Adıong in the longitudinal direction of the object to be examined Ob between the observation points corresponding to the PS points.

[00100] For this purpose, for example, temperature measurements and a calculation of the thermal displacement can be carried out using physical or engineering models - e.g. the bar models described above or multidimensional finite element (FE) models.

[00101] In principle, the following possibilities for determining or taking into account the temperature exist in a method according to the invention:

- To calculate the thermal horizontal deformation between the observation points P+4, P2, the measured internal (structural) temperature (=building temperature) can be used and the associated deformations can be calculated using, for example, a mechanical model.

[00102] - Instead of or in addition to using temperature measurement data of the internal temperature of the object under investigation, an empirical temperature model can also be used to calculate the object temperature from data from meteorological reanalyses. Such meteorological reanalyses use weather data in grids of varying resolution (e.g., 1 km x 1 km) with a temporal resolution of at least 1 h. This model incorporates, for example, meteorological information on air temperature, solar radiation, sun position, precipitation, and wind, and the associated temporal variations.

The object temperature profiles are calculated using equations from [33]. The corresponding deformations can also be calculated using, for example, a mechanical/physical or engineering FE model.

[00103] - Furthermore, in addition or alternatively, the horizontal positional displacement or the relative differential deformation Adıong in the longitudinal direction and/or the relative differential deformation Adrıans in the transverse direction of the object to be examined that occurred between the recording times can also be measured directly using metrological methods, e.g. by laser distance sensors.

[00104] The unknown horizontal object movements Adıong and Adrtrans can be determined, for example, using the following methods a)-c):

[00105] a) Simple model relationship or mechanical model:

The relative movement between two observation points P+, P2 in the longitudinal direction, i.e., the relative differential deformation Adıona in the longitudinal direction of the object under investigation, is determined by the bridge extension for elongated objects such as bridges. In most cases, this can be determined using the following approach:

Adı * ap* AT where:

AL is the relative distance between the freely selected measurement points located on the object Ob under investigation. These measurement points can be clearly assigned to the object Ob when using InSAR analysis with the corner reflectors mentioned above. If only natural persistent scatterer PS points are used, the determination of the position coordinates and thus the relative distance is correspondingly less precise due to the pixel size of approximately 5x20m, which, however, still ensures a sufficiently high accuracy. Ob is the specific expansion coefficient of the respective material, known from material tables or material libraries.

AT Change in the structure temperature between the recording times t+, tz, or the air temperature between the recording times t;, t2. This is used either as a directly measured internal (structure) temperature or as an air temperature directly from the weather data. This can also be calculated from weather data, e.g., using an empirical model or a transient thermal calculation, e.g., FEM of the bridge, and knowledge of the temperature time series (e.g., hourly from network weather data).

[00106] As already mentioned, a movement or a relative differential deformation Adrtrans in the transverse direction of the object under investigation can generally be neglected for longitudinally extended or elongated structures. Thus, the simplification of equation 2 results in equation 3, as stated above, where ao in this case corresponds to the azimuth of the bridge, i.e., the angle Apricke between the longitudinal axis of the object projected onto a horizontal surface and the geographical north direction.

[00107] b) Finite element (FE) model

A calculation model is created, the temperature change ΔT is applied as an acting variable, and the thermal deformation is calculated. Material-specific parameters, such as the expansion coefficient αy, are used from material libraries, and the actual boundary conditions/bridge supports are modeled. This also allows for a better representation of motion patterns restricted by constraint points, e.g., by fixed supports in integral bridges. The required variables Adıong and/or Adıans between the observation points are taken directly from the model and inserted into Equation 2 or Equation 3.

[00108] c) By means of distance sensors, the desired thermal displacement quantity Ad,ong in the longitudinal direction of the object to be examined Ob or Ad-7,-ans in the transverse direction of the object to be examined Ob between the viewing points P+4, P2 is directly measured.

[00109] Optionally, an automated algorithm can be used upstream for possible phase correction of the measurement (see Fig. 6a, 6b) to correct misinterpretations of phase

jumps (phase unwrapping), which is particularly advantageous for objects with larger deformation changes between measurements. The basic principle is a multiple observation or mutual comparison of several orbital directions, assuming that the object deformations that occur will generally behave in an affine manner. This assumption applies especially if the measurement was taken under similar temperature conditions (e.g., at the same time of day).

[00110] Starting from at least two O orbits or orbital directions, a mutual correction of the phase number in the viewing direction LOS is carried out using statistical methods, e.g., by a threshold deviation from the moving average of the observed orbits O in the range of a fraction of a wavelength. Values outside the threshold range (usually M4) are phase-corrected—each by the value of one wavelength (either added or subtracted), and a moving average is then again calculated using the corrected data. This process is iterative until the best possible correction is found and all values lie within the threshold.

[00111] The adjusted phase number is used to reconstruct the original travel time. This algorithm can be applied with different or identical orbits ©—with multiple orbit measurements increasing accuracy. Ideally, images taken at the same time or with only small temporal differences are used. If the actual object movement in the satellite's line of sight is greater than the selected threshold (a defined fraction of the wavelength), the method is suitable for correction.

[00112] In this context, Fig. 6a, 6b show a basic scheme for the application of statistical correction of misinterpreted phase jumps. The phase shift is measured at two points in time, where the circle symbolizes time t; and the triangle time t2. The phase number is only approximately known in the InSAR method due to the inaccuracy in the timekeeping. For example, with a wavelength of \=5.5 cm at time tz, a misinterpreted phase number can result in deviations in the shift by an integer multiple of nx5.5 cm (see Fig. 6b). Therefore, a simplified correction is preferably carried out and an adjustment of the slant distance d_os (viewing direction LOS) of at least 2 orbital directions is carried out. For deviations above the threshold value (a fraction of the wavelength ) (e.g., % of the wavelength A), the distance is corrected either upwards or downwards by the value of the wavelength X. This is repeated iteratively in steps until sufficient agreement is achieved.

[00113] Conclusion:

* With a method according to the invention, local relative deformation/settlement differences, i.e. the relative vertical deformations Ad, can be determined, but no information about the absolute positional displacement.

* It is assumed that for the horizontal deformations there are generally no other changes in position apart from the temperature-related components.

» If a reliable calculation of the horizontal movement is not possible, which can happen with very complex, statically indeterminate structures, a determination of the horizontal displacement, e.g. by measurements, is necessary.

* The method is not purely data-based and requires engineering knowledge of physical relationships and, above all, knowledge of structural behavior.

* Differentiating the vertical deformation components into a thermal component (e.g., heating of the pier and upward expansion) and a settlement-specific component is additionally advantageous, such as a classic structure-specific temperature compensation. This can be achieved analogously using conventional measurement methods, such as digital hose scales that record settlement differences.

[00114] The advantages of a method according to the invention are based on the fact that it is no longer necessary to intersect several different orbital directions in order to convert from the time-varying oblique distance dıos to the vertical direction dup. Furthermore, the consideration of temperature, e.g. in the form of the building temperature, is an integral,

advantageous component of the methodology according to the invention or the coordinate transformation according to the invention.

[00115] This results in the following advantages:

» Denser time series, since the InSAR measurement data from different orbital directions can be used individually and do not need to be merged.

* More possible viewing points on the object under investigation, since the individual possible viewing points do not have to be viewed from two orbits or orbital directions each, so that a method according to the invention can also be applied to smaller bridges and provides improved accuracy.

* Increased accuracy as there is no longer any blurring due to thermal effects that occurred between different capture times.

* No restriction on the target orientation, whereas current methods only allow objects approximately aligned with the LOS of the satellite from which the InSAR data is being measured. When using Sentinel satellites, for example, current methods require an east-west orientation of the object to be examined.

EXAMPLE OF IMPLEMENTATION

[00116] In the following, an embodiment is given for the calculation of the relative vertical deformation Ad, of a bridge to be examined within a time period between successive recording times t;, t2 based on InSAR data measured by a satellite Sat, wherein the orbit has an inclination with respect to the Earth's axis of approximately 100° relative to the horizon.

[00117] In the exemplary embodiment presented below, the viewing direction of the satellite that acquires the InSAR data is aligned with the bridge axis or the longitudinal axis of the bridge. In the exemplary embodiment, this means that the bridge axis has an azimuth, i.e., angle ABridge between the longitudinal axis of the bridge object projected onto a horizontal surface and the geographic north direction, of 10°.

[00118] This simplifies the calculation because the transverse bridge movement, i.e., the relative differential deformation Adr-ans in the transverse direction of the bridge under investigation, has no influence on the coordinate transformation and can thus be neglected, which facilitates the graphical representation and makes the explanation more understandable. Two observation points P+ and P> are defined for an object, a bridge, and the relative vertical deformation between the recording times t+ and tz is sought.

In the example below, information about the measurement object or object to be examined (Ob), a bridge, is initially provided. This includes the alignment of the bridge (A), the expansion coefficient of the bridge material (concrete) (ac), and the measurement points (distance to reference point 1 (AL).

[00119] Subsequently, the parameters of the satellite from which the measurements are carried out are given: angle of incidence θ and azimuth aD, as well as the pre-processed evaluation from the InSAR analyses: the deformations dıos in the viewing direction LOS for the two points considered P+4, P2 at two times t; and t2.

[00120] Next, for each point P+, P2, the absolutely measured deformation dıos is converted into the differential displacement or the differential deformation change Adıos with respect to the selected time period (usually the return period of the satellite). The absolutely measured deformations dıos at the two times t+, tz are subtracted to determine the relative deformation change Adıos of the considered points P+4, P2 within the selected time period.

[00121] Fig. 9 shows the geometric relationship of the displacement components of the measured oblique distance d_os in the viewing direction LOS into the vectorial decomposition of the desired vertical direction dup vertikaa and the resulting longitudinal direction dıong.

SS N 8

N8

Qi -hes AT 527 372 B1 2025-03-15 Ad.up =? desired relative vertical settlement between two points data bridge

AL := 100m relative distance between considered points

Bridge = 70° azimuth of the bridge

"_ 1075 ac =—

Satellite information

Expansion coefficient for concrete (literature)

O:=38.1° angle of incidence of the satellite CaıD := 80.8 ° azimuth of the satellite djos time1_point1 = 0.001 m = 1 mm LOS for time 1, point 1

djos time_point1 = 0.0021m = 2.1mm LOS for time 2, point 1 djos time1_pointz := 0.0021m = 2.1mm LOS for time 1, point 2 djos time2_point2 = 0.0071m = 7.1mm LOS for time 2, point 2

Conversion

dios_p1 = Cios_zeit2_Point1 7 Aios_zeit1_Point1 5 1.1 mm point 1

dios_p2 = Cjos_time2_point2 7 Aios_time1_point2 5 5>Mm point 2

Adıos := djos_p2 — dws.p1 = 3.9 mm difference of LOS between two

Measurement days and two points influence of temperature

T, := 15.1 °C Ty:= 17.1 °C Building temperature for time 1 and 2 AT :=T,-T,=2K Temperature difference between two measurement days Adı AT AL = 2 mm Engineering determination of expansion

between two points

Adıyans := 0 mm Engineering determination of the transverse deformation of the bridge between two points

Conversion of LOS into vertical settlement taking into account horizontal bridge movement due to temperature

Adam 2 Adios + (Adios ) COS(darp - Strache) } Arrans ) sin(daLD - Aprücke)) . sin(0) = 6.4964 mm

[00122] The next step involves structure-specific temperature compensation. In this example, the change in the structure temperature ΔT within the considered time period serves to determine the longitudinal expansion of the bridge using a model—in this case, a simple linear engineering equation derived from the bar model. The relative movement in the transverse direction was neglected in the illustrated example. Thus, all the necessary information is available to determine a vertical differential deformation of the bridge from the absolute measured deformation Δαos according to Equation 3.

COMPARATIVE TESTS

[00123] A method according to the invention for determining the relative vertical deformation Adıp of an object under investigation based on InSAR data was applied to a long-span motorway bridge as part of a research project and compared with an existing measuring system, a digital hose level, one of the most accurate systems with which differential settlements can be measured directly on structures. The digital hose level operates according to the principle of hydrostatic compensation of communicable

nicating vessels. Two sensors are attached to the object and connected to the measuring fluid via a connecting tube, and the relative vertical deformation differences are continuously recorded digitally over the measurement period.

[00124] The results of the relative vertical deformation Ad. of the bridge to be examined, determined using a method according to the invention, are shown in Fig. 10a to Fig. 10d, where "Ref" marks the reference deformations, i.e. the measurement results of the digital hose level, and "InSAR..." the evaluations of the satellite measurement data measured at the observation points (in this case, corner reflectors).

[00125] These time series of the relative bridge deformations dp, which mainly result from changing temperature deformations of the bridge, were evaluated separately for four recorded orbits (in Fig. 10a - Fig. 10d, the information InSAR DSC022, DSC124, ASC146 and ASC073 refers to the four orbits). Likewise, the temporally associated differential settlements were determined using measurements with the digital hose level. A simple rod model served as the temperature compensation model for the InSAR data, from which the relative differential deformation Adıong in the longitudinal direction of the object under investigation Ob was calculated. The achieved accuracies are summarized in Table 1 as a function of the temperature compensation used with input data for the object temperature from a) on-site measured temperature, b) air temperature, and c) building temperature from the empirical model described above as a standard deviation from the reference in [mm].

[00126] Fig. 10a - Fig. 10d show the calculated relative vertical deformation of Adı between two reference points (corner reflectors) on the object. As a reference value, the result of the digital hose level is shown in the diagram as a dashed line (Ref.), and the relative vertical deformation of the InSAR data calculated using a method according to the invention is shown in a solid black line (InSAR). This evaluation was carried out for four different orbit data sets over a measurement period of one year and evaluated at the respective overflight times of the satellites. Table 1 compares the results of the three methods for determining the structure temperature for the relative vertical deformation of Adıp.

[00127] The accuracy of the InSAR evaluation using the method according to the invention, as shown in Fig. 10 and Table 1, compared to the reference data (hose level) is sufficient for engineering monitoring of the bridge.

[00128] Table 1: Summary of the standard deviation of the deviations between the Adıp reference measurement system (digital hose level) and Adıp from InSAR data based on all available measurement data, and using different building temperatures for temperature compensation on the bar model. Values in [mm]

Orbit a) Sensor on site b) Air temperature c) Recommended Model DSC022 2.4 2.8 2.1 DSC124 2.4 3.4 2.4 ASC073 2.5 3.1 3.0 ASC146 3.6 4.4 4.2 Average 2.7 3.5 2.9

[00129] Fig. 3 - Fig. 11d finally show an embodiment of a statistical correction of the phase jumps (phase unwrapping), according to the algorithm described above. Preprocessed LOS data for two descending orbits, DSC022 and DSC124, are considered, and a moving average is calculated for each. Values outside the threshold range 4 are phase-corrected—in each case by the value of one wavelength X (either added or subtracted), and a moving average is calculated again. This process is repeated several times until the best possible correction is found and all values are within the threshold (achieved in Fig. 11d).

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Claims (1)

Patent claims 1. Method for determining the relative vertical deformation Ad, of an object (Ob) to be examined, in particular a structure, preferably a bridge, within a time period between successive recording times (t+, tz) based on Interferometric Synthetic Aperture Radar (InSAR) data measured by at least one flying object, - wherein the at least one flying object moves repeatedly over the object to be examined (Ob) on a flight path in a flight direction at a time interval and during this time records InSAR data along a viewing direction (LOS), - where interferograms are created based on the recorded InSAR data, and - wherein at least two persistent scatterer (PS) points (P1, P2) on the object to be examined (Ob) are determined as pixels which remain coherent over a sequence of interferograms, comprising the following steps: - determining the change in the phase in the viewing direction (LOS) with the associated angle of incidence θ between the viewing direction (LOS) and the nadir direction (Nad) and the associated angle ao between the viewing direction (LOS) projected onto a horizontal surface and the geographical north direction (N) for the at least two PS points on the object to be examined (Ob) based on interferograms created at at least two recording times (t+, t2), - Deriving the differential deformation change Adıos of the object to be examined (Ob) in the line of sight (LOS) of the flying object between the recording times (t+, t2) based on the determined change in phase, especially after correction of Errors caused by phase jumps, - Performing a coordinate transformation of the differential deformation change Adıos in the direction of the object to be examined (Ob), whereby the horizontal movements components (Ade., Adry) of the differential deformation change Adıos on the Longitudinal and transverse directions of the object to be examined (Ob) are projected, in particular especially by using the angle ao between the projected onto a horizontal surface decorated longitudinal axis of the object and the geographical north direction, - Determination of the temperature, especially the temperature of the object to be examined (Whether), in particular as an estimate and/or by measurement, - Determination of the relative difference that occurred between the recording times (t, tz) deformation Adıong In the longitudinal direction of the object to be examined (Ob) between the, the PS points corresponding to observation points (P+, P2) on the object to be examined. ject (Ob) taking into account the determined temperature, and - Calculation of the relative vertical deformation Adıp of the object to be examined (Ob) between the recording times (t+, tz) using the previously determined relative ven differential deformation Adıong In the longitudinal direction and the differential deformation change Adıos. 2, Method according to claim 1, characterized in that - that the relative differential deformation Adrrans in the transverse direction of the object to be examined (Ob) occurring between the recording times (t;, tz) between the observation points (P+, P2) corresponding to the PS points on the object to be examined (Ob) is determined taking into account the determined temperature and - that when calculating the relative vertical differential deformation Ad. of the object to be examined (Ob) between the recording times (t+, tz), the relative differential deformation Adr,ans in the transverse direction is also used. 3. Method according to claim 1 or 2, characterized in that the internal temperature of the object to be examined (Ob) is measured to determine the temperature. 4. Method according to one of the preceding claims, characterized in that to determine the temperature the air temperature in the area of the object to be examined 10. 11. 12. AT 527 372 B1 2025-03-15 (Whether) measured and/or derived from weather data. Method according to one of the preceding claims, characterized in that an empirical temperature model is used to determine the temperature in order to derive the internal temperature of the object to be examined (Ob) based on network weather data. Method according to one of the preceding claims, characterized in that in order to determine the relative differential deformation Adı eng in the longitudinal direction of the object to be examined (Ob), the thermal deformation between the observation points (P+, P2) corresponding to the PS points on the object to be examined (Ob) is calculated using a mechanical model, taking into account the temperature, in particular the internal temperature of the object to be examined (Ob). Method according to one of the preceding claims, in particular according to claim 6, characterized in that in order to determine the relative differential deformation Adıong in the longitudinal direction of the object to be examined (Ob) and/or to calibrate the mechanical model used according to claim 6, the positional displacement between the viewing points (P+, P2) corresponding to the PS points on the object to be examined (Ob) is determined by measurement, in particular by laser distance measurement. Method according to one of the preceding claims, characterized in that before deriving the differential deformation change Adıos of the object to be examined, in order to correct errors caused by phase jumps, a correction of the phase number in the viewing direction (LOS) of the flying object, in particular a correction using statistical methods, preferably phase unwrapping, is carried out for the at least two PS points on the object to be examined (Ob) based on at least two InSAR data sets recorded at approximately the same recording time, in particular along the same viewing direction (LOS), wherein it is provided in particular, that at least one further flying object moves repeatedly over the object to be examined (Ob) on a further flight path in a further direction of flight opposite to the direction of flight of the flying object and during this time records InSAR data along a further viewing direction (LOS>), and that to correct the phase number in the line of sight (LOS) of the flying object for the at least two PS points on the object to be examined, InSAR data recorded at approximately the same recording time from the further flying object moving on the further flight path in the further, opposite, flight direction along the further line of sight (LOS) are used. Method according to one of the preceding claims, characterized in that the horizontal movement components (Ade, Ady) of the differential deformation change Adıos are projected onto the longitudinal and transverse directions of the object to be examined (Ob) according to Adı — op) Adrrans = Ady*sin(daLD — op) Method according to one of the preceding claims, characterized in that the relative vertical deformation Adı is calculated according to _ Adıos + Adıong * COS(Aa_D — Aop) * Sin(θ;) Adip = cos(8;) Method according to one of the preceding claims, characterized in that the relative vertical deformation Adı, is calculated according to Adıos + (Adıong * COS(AaLD — Xop) + Adtrans * SIN(AaLD — ao») * sin(0;) cos(8;) Method according to one of the preceding claims, characterized in that the relative differential deformation Adıong in the longitudinal direction of the object to be examined (Ob) Adıy = is calculated according to Adı * ap * AT where AL is the relative distance between the observation points (P+, P2) corresponding to the PS points on the object to be examined (Ob), av is the specific expansion coefficient of the object to be examined (Ob) and AT is the change in the internal temperature of the object to be examined and/or the air temperature in the area of the object to be examined (Ob) between the recording times (t, tz). 13. Method according to one of the preceding claims, characterized in that in order to determine the relative differential deformation Adı eng in the longitudinal direction and/or in order to determine the relative differential deformation Adr;ans in the transverse direction, a model, in particular a finite element model, is created and the relative differential deformation Adı eng in the longitudinal direction and/or the relative differential deformation Adtıans in the transverse direction are modeled taking into account the specific expansion coefficient ay of the object to be examined (Ob) and the change in the internal temperature of the object to be examined (Ob) and/or the air temperature in the region of the object to be examined (Ob) between the recording times (t+, t2). 14. Method according to one of the preceding claims, characterized in that before the determination of the PS points - a correction, in particular an ellipsoidal, topographical, deformation-dependent and/or atmospheric correction, of the recorded InSAR data is carried out and/or - further signal processing steps are applied to the interferograms created. 6 sheets of drawings 24 / 30