AT527372A2 - Method for determining the relative vertical deformation of an object to be examined - Google Patents

Abstract

Method for determining the relative vertical deformation ∆dup of an object (Ob) to be examined, in particular a structure, preferably a bridge, within a time period between temporally successive recording times (t1, t2) based on interferometric synthetic aperture radar (InSAR) data measured by at least one flying object, - wherein the at least one flying object moves on a flight path in a flight direction repeatedly at a time interval 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: - determining the change in the phase in the viewing direction (LOS) with the associated angle of incidence θi between the viewing direction (LOS) and the nadir direction (Nad) and the associated angle αALD between the viewing direction (LOS) projected onto a horizontal surface and the geographic 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 (t1, t2), - deriving the differential deformation change ∆dLOS of the object to be examined (Ob) in the viewing direction (LOS) of the flying object between the recording times (t1, t2) based on the determined change in phase, in particular after correcting errors caused by phase jumps, - carrying out a coordinate transformation of the differential deformation change ∆dLOS in the direction of the object to be examined (Ob), wherein the horizontal movement components (∆dE, ∆dN) of the differential deformation change ∆dLOS are applied to the longitudinal and transverse directions of the object to be examined (Ob), in particular using the angle αOb between the longitudinal axis of the object projected onto a horizontal surface and the geographical north direction, - determining the temperature, in particular the temperature of the object to be examined (Ob), in particular as an estimate and/or by measurement, - determining the relative differential deformation ∆dLong in the longitudinal direction of the object to be examined (Ob) between the viewing points (P1, P2) corresponding to the PS points on the object to be examined (Ob) that occurred between the recording times (t1, t2), taking into account the determined temperature, and - calculating the relative vertical deformation ∆dup of the object to be examined (Ob) between the recording times (t1, t2) using the previously determined relative differential deformation ∆dLong in the longitudinal direction and the differential deformation change ∆dLOS.

Description

Interferometric Synthetic Aperture Radar (InSAR) data according to claim 1.

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

Various methods for determining the condition of structures are known from the state of the art. To date, the condition of bridges is mainly recorded periodically by visual inspections, whereby in Austria the procedure is according to RVS 13.03.11 [1]. Metrological investigations are usually carried out as a supplement to the visual inspection. In special cases, “special inspections”, permanent monitoring systems are used. The existing approaches for this can be found in

four groups:

- Detecting abnormal behavior - System or damage detection - Monitoring of effects

- threshold monitoring

Sensor-based measurement methods record the mechanical structural reaction such as deformation, inclination, strain, etc. over time. Changes in the behavior of these reactions can be caused by material-related reasons (e.g. material creep, settlement), changes in the load or even changes in the stiffness behavior (e.g. reduction in stiffness when damage occurs). 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 reactions must be compared with forecasts from models in order to interpret the measurement data and determine the condition.

The most common test for measuring deformation is tachymetric surveying (theodolites/total stations) or leveling, e.g. bridge leveling. This involves measuring the structural response of the structure under investigation to constant loads (dead loads) or changes in deflection, which may be caused by a trigger such as material behaviour,

mounted prisms and fully automatic total stations.

Measurements of other mechanical quantities such as inclination, strain and crack width were initially mainly carried out during test loading (new construction before 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], which is currently being drafted, lists options for shifting measuring points, including special cases such as vertical displacement components (= settlement or uplift) and derived parameters, e.g. tilting and strain. These are: total station (tachymeter), leveling instrument, electronic distance measuring device, laser scanner, GNSS (differential GPS), radar interferometry (interference measurement method with radar) (InSar, terrestrial or satellite-based).

Continuous observation of the deformation state of the structures is a potentially promising indicator, but not easy to implement for continuous monitoring. Methods have been developed that attempt to determine the deformation from measurements of inclination sensors [5] or from acceleration sensors [6]. The most common permanent system for vertical displacements is a flexible digital hose scale. It directly measures the deformation differences and uses the principle of a hydrostatic settlement measurement by sensors attached to the structures. It determines the vertical settlement of the sensors relative to a reference sensor. The method is suitable for continuous monitoring of geotechnical or deformation problems, but requires constant maintenance of the sensors (e.g. changing the fluids...), as well as connected pipes between the sensors and sensor-related temperature compensation (thermal expansion of the measuring fluid).

thermal tests.

Building-related temperature compensation: In order to be able to derive reliable statements for the structural safety, high

Deformation accuracies (usually at least in the mm range) are necessary. In order 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.). Unsteady 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 create the best possible temperature compensation models for sensor-based observation [10].

Furthermore, methods of satellite-based monitoring (Persistant Scatterer Interferometry) are known. As already mentioned, the method of satellite-based radar interferometry based on the latest approaches is well suited to implementing long-term monitoring of the status of objects, in particular buildings and bridges. An overview of previous approaches to this is given below.

The following shows schematically:

Fig. 1 a representation of the basic principle of satellite-based radar interferometry, Fig. 2 a representation of the method of Persistent Scatterer Interferometry PSI,

Fig. 3 a representation of the coordinate transformation according to [30],

Fig. 4 a representation of the images and angle and location designation when looking east-west according to [31],

Fig. 5 shows the coordinate transformation of ground motion directions at

Use of measurement data from two different orbital directions.

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

Fig. 2 shows a schematic representation of the Persistent Scatterer Interferometry (PSI) method. Several images (=scene Sz or SAR images) are evaluated. The focus is on those pixels that remain coherent across multiple images and thus act as persistent scatterers (PS) as a constant reflection over a series of images (usually at least 20 scene Sz). These coherent reflectors are used as a reference value and the difference shifts are evaluated.

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 fly over the Earth in a synchronous (approximate) polar orbit, which is slightly inclined to the Earth's axis (inclination 98.18°) [16]. The points on the Earth's surface are flown over in two orbital directions, once from south to north (ascending orbit ASCENDING) and once from north to south (descending orbit DSC). The Sentinel-1 satellites 1A and 1B fly over the Earth in a synchronous (approximate) polar orbit. The images on Earth are taken in an oblique viewing direction - 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.

have.

The Persistent Scatterer Interferometry (PSI) method is a powerful analysis method that can determine deformations on the earth's surface with potentially very high accuracy without sensors being mounted on the surface. In detail, PSI is a differential InSAR (Interfometic Synthetic Aperture Radar) radar method in which the properties of wave interference are used to derive measured variables. With the help of PSI, distance differences in the range of a fraction of the wavelength A can be derived by comparing the phase values of corresponding pixels from different recording times (scenes) [11].

Basically, the PSI method does not require a reflector on site, but uses natural reflectors (persistent scatterers PS). As can be seen in Fig. 2, those pixels that remain coherent across multiple images or interferograms (indicated in Fig. 2 as white circles with black borders) are examined and thus act 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, which allows a time series of the deformations and the average offset rate for the persistent scatterer (PS) to be calculated [10]. This evaluation of time series is specifically referred to as “multi-temporal satellite-based differential interferometry” (MTInSAR) [17]. The accuracy can be increased with additional reflectors attached to the object under observation (corner reflectors or CR).

and a better statement such as clear point allocation can be made.

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. A 2019 project observed hydroelectric power plants, recorded with the highest resolution mode, the so-called "Staring Spot-Light" with a very high spatial resolution. This showed that accuracy in the sub-cm range is possible [12]. Dams were also measured with Sentinel-1 data and displacement rates of sub-cm/a were determined. Another

An example where Sentinel-1 data has proven applicable is the detection

7747

Lazecky et al. [14] show in three case studies (bridges in Bratislava, Ostrava and Hong Kong) the potential for monitoring deformations and movements including thermal dilation in bridge structures. With surface temperature measurements and simple relationships, the accuracy could be increased significantly. With installed sensors, it was possible to decompose the SAR phase difference in relation to the reference point between the phase change due to height difference and thermal expansion. Based on the suitability of the data set examined and the assumption of the linearity of these parameters, a correlation of the temperature changes and the linear deformation rate in the time period was evaluated using MTINSAR methods, whereby several orbits were always used simultaneously to determine the position.

must be combined.

Selvakumaran et al [15] developed ideas on how to clarify unknown quantities that were not recorded using 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 either. Due to the frequency of satellite measurements and the noise within the measurements, only seasonal trends can be tracked, which complements conventional inspection systems. Here, the problem of evaluations using a combination of several orbit directions is also explicitly pointed out. In particular, if the images are taken from different 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 only use points at the same structure temperature. The measurements carried out as part of the aforementioned work on the Waterloo Bridge in London proved to be comparable when the relative movement of the points along the bridge to each other is used. Various loading cases such as tidal movements, temperature expansion, deformations due to traffic loads as well as shrinkage and creep of the concrete

make interpretation difficult. Nettis et al. [17] provides a very good overview of research and

first applications of MTInSAR methods in terms of compensation of

thermal structural deformations, which is reproduced below: A

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 the displacements due to temperature-related effects and vertical detections and find an evolving deformation of 1.8 mm/year with an absolute value of 9.5 mm, which the authors believe 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 undesirable deformations due to environmental conditions (e.g. temperature-related deformations). The effectiveness of the method is demonstrated using a steel truss bridge, the Palatino Bridge in Rome, which

is subject to deformations due to settlement.

with the associated (measured) temperature changes.

State-of-the-art coordinate transformation conversion:

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 viewing direction/measurement direction of the satellite Line of Sight (LOS), with the corresponding angle, for each orbit. The basis is 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 on the Earth's surface are taken several days apart depending on the orbital direction ASC, DSC. Previous approaches use the slant distance dios ase, dios ase, measured from both orbital directions ASC, DSC to calculate a horizontal and a vertical displacement component on the Earth's surface (see Fig. 3).

Fig. 5 shows a schematic representation of the coordinate transformation known from the state of the art according to [30], in which the difference deformations between the time series represent the temporal development of the deformation dıos in the direction of view LOS as deformation to the east dr: and as vertical deformation du,.

This means that the coordinate transformation is underdetermined, since there is no third orbital direction. For example, for a north-south overflight direction, only the east-west deformation and the resulting vertical position shifts can be determined. The practical application is therefore very limited, and no (bridge) structures oriented in the satellite's north-south flight path can be determined.

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

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

* The recordings are staggered due to the satellite's flight path. 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 point is flown over by at least 2 orbits, ideally up to 4 orbits, resulting in 60-120 recordings 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 = time t+).

* Another recording will be made at a later time when the satellite is back in the same place after a few days (recording time t2)

* The temporal differential change of the position coordinates is calculated.

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

In detail, the determination of the change in position coordinates in the state of the 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)

d\n- temporal movement to the north (wanted)

de — temporal movement to the east (wanted)

dios- measured temporal delta of the slant distance measured at different recording times in the viewing direction LOS

The dios motion consists of three components, as shown in the figures: dup, du and de. The trigonometric relationship in terms of angle of incidence 8; and azimuth aaLD is given by the following equation 1 according to []:

A AA AT Equation 1

Fig. 1 shows a representation of the coordinate transformation of ground motion directions when using two orbits or orbital directions.

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 set up for the two existing orbital directions, which, however, occur at different times

were included. Equation 1 is therefore still simply underdetermined.

For this reason, the following approximation is used in the state of the art:

- The method can currently only be applied to objects in an east-west orientation, i.e. normal to the north-south flight direction and approximately aligned with the LOS line of sight of the satellite.

- If the object is oriented in an east-west direction, the influence of the temporal movement to the north dy is subordinate and is neglected. There are only two quantities left that can be calculated.

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

Since the measurement from the two orbital directions ASC and DSC takes place at different times, 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 buildings 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 works [11-29], 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.

which was calculated parallel to the time series recordings and is included in the evaluation. However, the decisive factor is the component displacement itself, and thus the component temperature, which is a non-stationary process and not directly proportional to the air temperature due to the inertia effects of the materials used.

The object of the invention is therefore to remedy this situation and to provide a method for determining the relative vertical deformation Adıp 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 existing database.

The invention solves this problem with 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,

- wherein the at least one flying object moves repeatedly over the object to be examined on a flight path in a flight direction at intervals of time 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 determined as pixels that remain coherent over a sequence of interferograms,

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

- Determining the change in phase in the viewing direction with the associated angle of incidence θ between the viewing direction and the nadir direction and the associated angle daD between the viewing direction projected onto a horizontal surface and the geographic 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 Adıos 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 aos 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 observation 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 difference deformation Adıong in the longitudinal direction and the differential deformation change Adıos.

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, in particular closed, flight path and can record InSAR data in the process. Such a flying object can be, for example, an airplane, a helicopter, a drone or other unmanned flying objects, but primarily satellites. Such flying objects have special radar antennas that are suitable for radar interferometry (Interferometric Synthetic Aperture Radar - InSAR).

In the case of a satellite, for example, such a flight path can be an orbit that extends in a circle or elliptically around the earth, in particular on one side of the earth from a first pole to a second pole opposite this and then on the other side of the earth from the second pole to the first pole. The direction of flight is the direction of travel of the flying object as it moves along its flight path, for example the orbital direction. The direction of view of the flying object is the direction in which the flying object records InSAR data from objects on the earth's surface. The nadir is the foot point opposite the zenith, and the azimuth is the horizontal angle relative to the north direction.

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

become.

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.

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 position shifts 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.

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.

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 the east component Ady 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.

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 Adıos only plays a minor role if the object being examined extends in an east-west direction, which means that the known methods can only be applied to objects

with east-west orientation is possible and for which measured values from two different flight or orbital directions ASC, DSC are required.

The advantages of this approach are based on the fact that it is no longer necessary to intersect different orbits in order to access the time-varying obliquity distance

dıos to the vertical direction dup.

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 have 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 exposure times.

* No restriction on the orientation of the measurement object, whereas with known methods only objects with an approximate orientation in the line of sight LOS of the satellite from which the InSAR data is measured are possible. When using Sentinel satellites, for example, an east-west orientation of the object to be examined is necessary with known methods.

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 that occurred between the recording times is determined between the observation points on the object to be examined corresponding to the PS points, taking into account the determined temperature and

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

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

to achieve.

A particularly precise determination of the temperature relevant for the relative differential deformation Adıong in the longitudinal direction of the object to be examined can be achieved if the internal temperature of the object to be examined is measured to determine the temperature. This is done, 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.

An alternative or additional variant for determining the temperature relevant for the relative differential deformation Adıorng 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 does not require any such temperature sensors at all, can be provided if the air temperature in the area of the object to be examined is measured and/or derived from weather data.

Another alternative or additional variant for determining the temperature relevant for the relative differential deformation Adıorng 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.

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 Adıeong 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.

To further improve the calculation accuracy when 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 shift between the

PS points corresponding to viewing points on the object to be examined are determined by measurement, in particular by laser distance measurement.

In order to particularly effectively avoid misinterpretations caused by phase jumps in the measurement data, a method according to the invention can provide that, before deriving the differential deformation change Adıos 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 at approximately the same recording time, in particular along the same viewing direction.

recorded InSAR data sets.

In the context of the invention, the phase number is understood to mean the integer number of waves that are determined for the 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 timekeeping when measuring the change in the slant distance in the line of sight (LOS = Line of Sight) of the satellite and can be eliminated by statistical methods, in particular phase unwrapping.

be corrected.

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 opposite to the direction of flight of the flying object and during this time records InSAR data along a further viewing direction, and

that in order 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, images taken from the further flying object moving on the further flight path in the further, opposite, flight direction along the further direction of view at approximately the same recording time

InSAR data can be used.

In order to determine the relative vertical deformation Adıp of an object to be examined in a particularly simple way, regardless 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 order to be able to do this, it can be provided that the horizontal movement components in east

Direction Ade and in the north direction Ads 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 = Adn”sin(da1D — Aop)

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, independent 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 Adıp is calculated according to

Ad = Adıos + Adıong * COS(AaLD — Aop) * Sin(6i) Up cos(8;)

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, independent of the absolute movement of the object in the north direction for objects with any shape, it can be provided that the relative vertical deformation Adıp is calculated according to

Ad. — Adıos + (Adıong * COS(AXa_LD — Xop) + Adrrans * SIN(AaLD — op) * sin(9;) UP cos(6;)

In order to be able to take advantage of 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, av 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.

According to a particularly precise and particularly easy to adapt to a wide variety of varying parameters 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

and/or to determine the relative differential deformation Adr;ars In the transverse direction a

Model, in particular a finite element model, is created and the relative differential deformation Adıong in the longitudinal direction and/or the relative differential deformation Adrrans in the transverse direction are modelled taking into account the specific expansion coefficient ab 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.

To further improve the accuracy in determining the relative vertical deformation Adıp of an object to be examined, it can be provided that before determining the PS points - 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

become.

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

The invention is schematically illustrated below in the drawings using particularly advantageous but non-limiting embodiments and is described by way of example with reference to the drawings.

The following shows schematically:

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

Fig. 7a a representation of the position of two observation points P+ and P; on a bridge as the structure to be examined,

Fig. 7b shows a representation of the temporal change of the position of two observation points P+ and P2 between two different images at the times t+ and t,,

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 daLD,

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

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 dıong,.

Fig. 10a 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 first orbit,

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,

Fig. 10c 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 third orbit,

Fig. 10d 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 fourth orbit,

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

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

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

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

In the following, a method according to the invention for determining the relative vertical deformation Adıp 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 and then using concrete embodiments.

Although a method according to the invention is described below using satellite

measured InSAR data for the determination of the relative vertical deformation Adıp of a bridge as the object to be examined Ob is described. A method according to the invention

is, however, by no means limited to this type of flying object for measuring the InSAR data. All that is essential is that the flying object, be it a satellite, an airplane, a helicopter, a drone or the like, moves on a constant, predetermined flight path in a flight direction repeatedly at intervals of time over the object to be examined and, in the meantime, 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. On the contrary, a method according to the invention can be used to determine the relative vertical deformation Adıp of any objects Ob, which, above all, can also have any orientation to the flight path of the flying object measuring the InSAR data.

General Description

A method according to the invention is used to transform deformations measured with flying objects, e.g. satellites, in a viewing direction, i.e. an oblique distance or line of sight LOS, of at least two clearly assignable 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.

Two observation points P;, P2, e.g. corner reflectors CR fixed to the object, which serve as a reference and amplification of 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 Adı, of the two observation points P+, P2 on the object Ob is then carried out on the basis of at least two images recorded at the times t+, t2.

Scenes Sz or interferograms of the object Ob.

First, based on interferograms created at at least two recording times t;, tz, the change in the phase in the viewing direction LOS with the associated angle of incidence 8; 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 geographic 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 determined based on the determined change in the phase

derived — preferably after correction of errors caused by phase jumps,

which will be discussed in more detail below.

After an initial recording at the reference time t+, the position of the observation points P+4, P2 changes within the observed time period At= t2-t4. The consideration of the relative vertical displacement Adıp between P+ and P;2 within At, which is important for building monitoring, can be carried out using equation 1 given above.

be determined to:

3 + Alp = Qypz 7 Aus

Fig. 2a shows the position of two observation points or PS points P+, P2 on an examined, elongated object Ob, namely a bridge, at a first time t. Fig. 7b shows the temporal change in the position of the observation points or PS points P+1, P2 between the recording times t+ and t2. Due to cooling, the bridge shortens and the two observation points P+;, Po sink.

To determine the relative vertical deformation Adıp, a coordinate transformation is carried out according to the invention 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 specific horizontal position shifts or movement components of the observation points P+4, P2 on the object Ob. Both components, namely the oblique distance calculated from InSAR data and the horizontal position shifts or movement components are used in the coordinate transformation and the relative vertical deformation Adıp

between the recording times t+, tz.

In the context 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 is carried out in the direction of the object to be examined Ob, taking into account the relative horizontal position changes (Adıong, Adtrans) on the object Ob, i.e. the horizontal movement components Ade, Adyn of the differential deformation change Adıos are projected onto the longitudinal and transverse directions of the object to be examined Ob.

Based on equation 1, the horizontal motion component is projected onto the longitudinal Adıong and transverse direction Adrtrans of the object Ob, in the example of the bridge, as follows:

Adı — ABrücke)

Adrrans = Adn*sin(da1p — crutch)

where Cob = (Bridge Azimuth of the bridge

A Difference in the temporal recordings.

Fig. 8a shows schematically the differential deformation dıos of the object to be examined Ob in the viewing direction LOS of the flying object, as well as the horizontal motion components de, Ady of the differential deformation dıos in the east direction E and in the north direction N and the angle as.o between the viewing direction LOS projected onto a horizontal surface and the geographic north direction N. Fig. 8b shows schematically the coordinate transformation in the object direction with the horizontal motion components Adıong UNd AdTrans projected onto the longitudinal and transverse directions of the bridge under investigation and the angle Agrücke Zbetween the longitudinal axis of the bridge projected onto a horizontal surface and the geographic north direction N.

Thus, equation 1 takes the following form:

Ad = Adıns + {Ad $ COS Car — App) * Adzpans SPUR app — Cop)) + in(8;) GileichHE cos{8;) ung 2

Zen

For longitudinally extended or elongated objects such as bridges, usually only the dominant displacement component in the longitudinal direction of the object, i.e. the relative differential deformation Adıong in the longitudinal direction of the object to be examined Ob, is decisive, so that the relative differential deformation Adrrans in the transverse direction of the object to be examined Ob can be disregarded, which reduces equation 2 to equation 3:

Ad = Adıos * Adıong * COS(Maıp 7 Kopp) + SIn(8;)} ze =

i Equation 3 ME COS {RC

24147

For objects Ob with any shape, the relative differential deformation Adrtrans occurring between the recording times in the transverse direction of the object Ob to be examined can also be used to calculate the relative vertical deformation Adıp

and equation 2 is used.

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 difference deformation Adıong in the longitudinal direction of the object to be examined Ob between the observation points corresponding to the PS points.

For example, temperature measurements and a calculation of the thermal displacement using physical or engineering models — e.g. the bar models or multidimensional finite element (FE) models described above — can be used.

be made.

In principle, the following options 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+, P2, the measured internal (structure) temperature (=building temperature) can be used and the associated deformations can be

can be calculated using, for example, a mechanical model.

- Instead of or in addition to using temperature measurement data of the internal temperature of the object to be examined, 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 a grid of different resolutions (e.g. 1 kmx1 km) with a temporal resolution of at least 1 h. This model includes, for example, meteorological information on air temperature, solar radiation, position of the sun, precipitation and wind, and the corresponding temporal courses of the object temperature are calculated using equations from [33]. The corresponding deformations can also be calculated using, for example, a mechanical/physical or

engineering FE model.

- Furthermore, in addition or as an alternative, the horizontal position shift or the

relative difference deformation occurring between the recording times Adıong In

Longitudinal direction and/or the relative differential deformation AdrTrans IN transverse direction of the object to be examined also by measurement, e.g. by

Laser distance sensors can be measured directly.

The unknown horizontal object motion Adıong and Adtans can be determined using the following methods a)-c):

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 Adıong in the longitudinal direction of the object to be examined, is characterized by the bridge extension in elongated objects such as bridges. In most cases, this can be determined using the following approach:

Adı * Op? AT

where:

AL is the relative distance between the freely selected measurement points located on the object Ob to be examined. These measurement points can be clearly assigned to the object Ob when using InSAR evaluation 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 approx. 5x20m, but this still ensures a sufficiently high level of accuracy.

From 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;, t2, 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. from network weather data hourly).

As already mentioned, a movement or a relative differential deformation Adrtrans in the transverse direction of the object to be examined can usually be neglected in the case of longitudinally extended or elongated structures. Thus, the simplification of equation 2 follows equation 3, as stated above, where ao, in this case the azimuth of the

Bridge, i.e. the angle ABridge between the longitudinal axis of the object projected onto a horizontal surface and the geographical north direction.

b) Finite element (FE) model

A calculation model is created and the temperature change AT is applied as an effective variable and the thermal deformation is calculated. The material-specific parameters such as the expansion coefficient ay are used from material libraries, and the actual boundary conditions/bridge bearings are modeled. This also makes it possible to better depict movement patterns that are hindered by constraint points, e.g. by fixed bearings in integral bridges. The required variables Adıong and/or AdrTrans between the observation points are taken directly from the model and inserted into equation 2 or equation 3.

c) By means of distance sensors, the desired thermal displacement quantity Adıong IN the longitudinal direction of the object to be examined Ob or Adırans In the transverse direction of the object to be examined Ob is directly measured between the observation points P+;, P2.

Optionally, an automated algorithm can be used upstream to correct the phase of the measurement (see Fig. 6a, 6b) to correct misinterpretations of phase jumps (phase unwrapping), which is particularly advantageous for objects with larger changes in deformation between measurements. The basic principle is a multiple observation or a mutual comparison of several orbital directions, whereby it is assumed that object deformations that occur will generally behave in an affine manner to one another. This assumption applies in particular if the measurement was carried out under similar temperature conditions (e.g. at the same time of day).

A mutual correction of the phase number in the direction of view LOS is carried out from at least two O orbits or orbital directions using statistical methods, e.g. by a threshold deviation from the moving average of the orbits O under consideration in the range of a fraction of a wavelength. Values outside the threshold range (usually \/4) are phase-corrected - each by the value of a wavelength (either added or subtracted), and then a moving average is again formed with the corrected data. This process is run iteratively until the best possible correction is found and all values are within the threshold value.

27147

The adjusted phase number is used to reconstruct the original travel time. This algorithm can be used with different or the same orbits O - whereby multiple orbit measurements increase the accuracy. Ideally, images taken at the same time or with only small differences in time are used. If the actual object movement in the direction of view of the satellites is greater than the selected threshold value (defined fraction of the wavelength), the method is suitable for correction.

In this context, Fig. 6a, 6b show a basic scheme for the application of the statistical correction of misinterpreted phase jumps. The phase shift is measured at two points in time, with the circle symbolizing the time t+ and the triangle the 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 A\=5.5cm 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 oblique distance dıios (viewing direction LOS) of at least 2 orbital directions is carried out. In the case of deviations above the threshold value (a fraction of the wavelength ) (e.g. % of the wavelength A), the distance is either corrected up or down by the value of the wavelength \. This is repeated iteratively in steps until

there is sufficient agreement.

Conclusion:

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

* It is assumed that there are generally no changes in position for the horizontal deformations other than 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.

* A differentiation of the vertical deformation components into a thermal component (e.g. heating of pillars and expansion upwards) and a settlement-specific component is additionally advantageous, such as a classic structure-specific

Temperature compensation. This can be done analogously with conventional measuring methods, such as digital hose scales that record settlement differences.

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 the 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.

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 have 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 exposure times.

* No restriction on the orientation of the measurement object, whereas with known methods only objects with an approximate orientation in the line of sight LOS of the satellite from which the InSAR data is measured are possible. When using Sentinel satellites, for example, an east-west orientation of the object to be examined is necessary with known methods.

embodiment

In the following, an example of how to calculate the relative vertical deformation Adıp of a bridge to be examined within a time period between successive recording times t+, tz based on InSAR data measured by a satellite Sat is given, whereby the orbit has an inclination with respect to the Earth's axis of approximately 100° relative to the horizon.

In the embodiment shown below, the viewing direction of the satellite,

which records the InSAR data, is the same as the bridge axis or the longitudinal axis of the bridge. In the example, this means that the bridge axis has an azimuth, i.e.

Angle between the longitudinal axis of the bridge object projected onto a horizontal surface and the geographical north direction, of 10°.

This simplifies the calculation because the transverse bridge movement, i.e. Adrıan's relative differential deformation in the transverse direction of the bridge under investigation, has no influence on the coordinate transformation and can therefore be neglected, which facilitates the graphical representation and makes the explanation more understandable. Two observation points P+ and P>; are defined on an object, a bridge, and the relative vertical deformation between the recording times t+ and t2 is sought.

In the example below, information about the measuring object or object to be examined Ob, a bridge, is given at the beginning. This concerns the alignment of the bridge QABridge, the expansion coefficient of the bridge material

Concrete ae, and measuring points (distance to reference point 1 AL).

Subsequently, the parameters of the satellite from which the measurements are carried out are given: angle of incidence 8 and azimuth daLD, as well as the pre-processed evaluation from the InSAR analyses: the deformations dıos in the viewing direction LOS for the two considered points P+, P2 at two times t+ and t,.

This is followed by a conversion of the absolutely measured deformation dıos into the differential displacement or the differential deformation change Adıos for each point P+, P2 in relation to the selected time period (this is usually the return period of the satellite). The absolutely measured deformations dıos at the two times t+, t2 are subtracted in order to arrive at the relative deformation change Adıos of the points P-;, P2 considered within the selected time period.

Fig. 9 shows the geometric relationship of the displacement components of the

measured oblique distance dıios in the viewing direction LOS into the vectorial decomposition of the desired vertical direction dup vertikaı and resulting longitudinal direction dıong.

Acdıup = 7 sought relative vertical settlement between two points

details of the bridge

x 100 m relative distance between loaded points

azimuth of the bridge

Expansion coefficient for concrete (literature)

satellite information

Eis a Sun 38.1

angle of incidence of the satellite

LAKES Azimalh of Satefliian

LOS for time 1, point f LOS for time 2. point 3 LOS for time 1, point 2

LOS for time 2, point 2

== 1, 1 me point 1

= 5m Dunk 2

Difference of LOS between two measurement periods and two points

EN Bm 37.10 Building temperature for time 1 and 2 EN Temperature difference between two measurement days

engineering determination of the extent of the bridge between two points

Se AA ie Ce ALARM

engineering determination of the transverse deformation of the bridge between two points

Ay {3 dam AT A

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

ARE m

The next step is the structure-specific temperature compensation. In this example, the change in the structure temperature AT within the time period under consideration is used to calculate the expansion of the bridge in the longitudinal direction using a model — in this case a simple linear engineering equation determined from the

Rod model. The relative movement in the transverse direction was shown in the

This provides all the information needed to calculate a vertical differential deformation from the absolute measured deformation dıos according to

Equation 3 of the bridge.

comparative tests

An inventive method for determining the relative vertical deformation Adıp of an object to be examined 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 precise systems with which differential settlements can be measured directly on structures. The digital hose level works according to the principle of hydrostatic compensation of communicating vessels. Two sensors are attached to the object and connected to a connecting hose with measuring fluid and the relative vertical deformation differences are continuously measured over the measurement period.

recorded “digitally”.

The results of the relative vertical deformation Adıp 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 ...” marks the evaluations of the satellite measurement data measured at the observation points (in this case corner reflectors).

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). The temporally associated differential settlements were also determined using the digital hose level. A simple rod model was used as the temperature compensation model for the InSAR data, from which the relative differential deformation Adıorng in the longitudinal direction of the object Ob to be examined was calculated. The accuracies achieved are summarized in Table 1 as a function of the temperature compensation used with input data for the object temperature from a) temperature measured on site, b) air temperature, and c) building temperature from the empirical model described above as a standard deviation from the reference in [mm].

Fig. 10a - Fig. 10d show the calculated relative vertical deformation of Adıp 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 over the measurement period of one year, and evaluated at the respective overflight times of the satellites. Table 1 compares the results of the three methods of determining the building temperature for the relative

Vertical deformation of Adıp.

The accuracy of the InSAR evaluation using the method according to the invention shown in Fig. 10 and Table 1 in comparison to the reference data (hose scale) is sufficient for engineering monitoring of the bridge.

Table 1: Summary of the standard deviation of the deviations between Adıp reference measuring system (digital hose scale) and Adıp from InSAR data based on all available measurement data, and the deviations obtained 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

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 formed for each. Values outside the threshold range \/4 are phase-corrected - each by the value of a wavelength A (either added or subtracted), and a moving average is formed again. This process is run through several times until the best possible correction is found and all values are within the threshold value (achieved in Fig. 11d).

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Claims (1)

patent claims 1. Method for determining the relative vertical deformation Adı,p of an object to be examined (Ob), in particular a structure, preferably a bridge, within a time period between temporally successive recording times (tt, 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 time intervals over the object to be examined (Ob) 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, comprehensively the following steps: - Determine the change in the phase in the line of sight (LOS) with the corresponding Angle of incidence 8; between the line of sight (LOS) and the nadir direction (Nad) and the corresponding angle ao between the viewing direction projected onto a horizontal surface (LOS) and the geographic north direction (N) for at least two PS points on the object to be examined (Ob) based on at least two recording times (t, t2) created interferograms, - Deriving the differential deformation change Adıos of the object to be examined (Ob) in the viewing direction (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 Motion components (Ade, Ady) of the differential deformation change Adıos on the Longitudinal and transverse directions of the object to be examined (Ob) are projected, in particular by taking into account the angle ao between the plane projected longitudinal axis of the object and the geographic 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 differences between the recording times (t;, tz) Differential deformation Adıomg in the longitudinal direction of the object to be examined (Ob) between the observation points (P+4, P2) corresponding to the PS points on the object to be examined (Ob) taking into account the determined temperature, and - Calculation of the relative vertical deformation Adı of the object to be examined (Ob) between the recording times (t1, tz) using the previously determined relative differential deformation Adıona in the longitudinal direction and the differential Deformation change Adıos. 2, Method according to claim 1, characterized in - that the relative differential deformation Adr,ans occurring between the recording times (tt, tz) in the transverse direction of the object to be examined (Ob) 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 difference deformation Adıp of the object to be examined (Ob) between the recording times (t+, t2) additionally the relative differential deformation Adrrans in the transverse direction is used. 3. Method according to claim 1 or 2, characterized in that to determine the temperature, the internal temperature of the object to be examined (Ob) is measured becomes. 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 (Ob) is measured and/or derived from weather data. 5. Method according to one of the preceding claims, characterized in that to determine the temperature, an empirical temperature model is used to derive the internal temperature of the object to be examined (Ob) based on network weather data. 6. Method according to one of the preceding claims, characterized in that in order to determine the relative differential deformation Adıona 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). 7. 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 shift between the observation points (P+, P2) corresponding to the PS points on the object to be examined (Ob) is measured, in particular by laser distance measurement. 8. 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 on a further flight path in a further direction opposite to the flight direction of the flying object repeatedly moves over the object to be examined (Ob) at a time interval and during this time records InSAR data along a further viewing direction (LOS), and that in order to correct the phase number in the viewing direction (LOS) of the flying object for the at least two PS points on the object to be examined, from which on the further flight path in the further, InSAR data recorded at approximately the same time of recording from another flying object moving in the opposite direction of flight along the other line of sight (LOS) can be used. 9. 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 — Aob) AdrTrans = Adn”sin(da1p — Aop) 10. Method according to one of the preceding claims, characterized in that the relative vertical deformation Adıp is calculated according to Ad. — Ad‚ıos + Adıong * COS(AaiD — AXop) * SIn(G;) UP cos(0;) 11. Method according to one of the preceding claims, characterized in that the relative vertical deformation Adıp is calculated according to Ad = Adıos + (Adıong * COS(AarLD — Aop) + Adrrans * SIN(AaLD — op) * sin(9;) UP cos(0;) 12. 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) is calculated according to AdLong = AL * Op? AT where AL is the relative distance between the observation points (P1, 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 a model, in particular a finite element model, is created to determine the relative differential deformation Adıeng in the longitudinal direction and/or to determine the relative differential deformation AdrT.ars in the transverse direction and the relative differential deformation Adıona in the longitudinal direction and/or the relative differential deformation Adrtrans IN the transverse direction is modelled 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 area of the object to be examined (Ob) between the recording times (t;, tz). become. 14. Method according to one of the preceding claims, characterized in that before determining the PS points 40 / 47 a correction, in particular an ellipsoidal, topographical, deformation-dependent and/or atmospheric correction, is made to the recorded InSAR data and/or further signal processing steps are applied to the created interferograms become.