Disclosure of Invention
The invention mainly aims to provide a sea-filling airport deformation evaluation method, a system, a terminal and a computer readable storage medium for combining InSAR and GNSS, and aims to solve the problems that in the prior art, targeted research on deformation monitoring is lacking or only a single deformation monitoring technology is adopted, so that the observation time and space sampling of deformation monitoring are limited, and the observation precision and reliability are not high.
In order to achieve the above purpose, the present invention provides a sea-filling airport deformation evaluation method combining InSAR and GNSS, the sea-filling airport deformation evaluation method combining InSAR and GNSS includes the following steps:
acquiring an image set and observation data of a target area, selecting a main image from the image set according to a preset rule, and preprocessing the observation data to obtain preprocessed data;
Extracting coherent points from the main image by adopting a dual-threshold strategy based on amplitude dispersion and a coherence coefficient, performing deformation inversion on the target area according to the coherent points to obtain a first deformation inversion result in a constructed three-dimensional coordinate system, and resolving the preprocessing data by a resolving algorithm to obtain first baseline vector data of an observation station in a geocentric coordinate system;
Transferring the first baseline vector data to a constructed station-core coordinate system to obtain second baseline vector data in the station-core coordinate system, and transferring the second baseline vector data to the three-dimensional coordinate system to obtain third baseline vector data in the three-dimensional coordinate system;
constructing a fitting estimation model, acquiring longitude and latitude information of any point in the target area, inputting the longitude and latitude information into the fitting estimation model, and outputting a deformation vector;
And constructing a data fusion model, inputting the third baseline vector data and the deformation vector into the data fusion model, outputting a deformation result, and generating a deformation monitoring result and a risk assessment report of the target area according to the deformation result.
Optionally, the sea-filling airport deformation evaluation method combining the InSAR and the GNSS, wherein the acquiring the image set and the observation data of the target area, selecting the main image from the image set according to a preset rule, and preprocessing the observation data to obtain preprocessed data specifically includes:
acquiring an SAR image set and observation data of a target area;
Randomly selecting a target image from the SAR image set, respectively performing interference calculation on the target image and other images in the SAR image set to obtain interferograms respectively corresponding to the target image and the other images in the SAR image set, and constructing an interference atlas by using all the interferograms;
continuing to select other images in the SAR image set as target images to perform interference calculation until all images in the SAR image set are completely calculated as target images, so as to obtain a plurality of interference atlas;
According to the time base line, the space base line and the Doppler frequency, calculating the overall coherence coefficient of each interference atlas, taking a target image corresponding to the interference atlas with the maximum overall coherence coefficient as a main image, and calculating the overall coherence coefficient as:
;
Wherein, Representing the overall coherence coefficient of the signal,The spatial coherence coefficient is represented by a spatial coherence coefficient,The coefficient of temporal coherence is represented as such,The doppler coherence coefficient is represented as such,Representing a thermal noise coherence coefficient;
and carrying out data calibration processing on the observed data, and carrying out format conversion processing on the calibrated observed data to obtain preprocessed data.
Optionally, the sea-filling airport deformation evaluation method combining InSAR and GNSS, wherein the method adopts a dual-threshold strategy based on amplitude dispersion and coherence coefficient, extracts coherent points in the main image, performs deformation inversion on the target area according to the coherent points to obtain a first deformation inversion result in a constructed three-dimensional coordinate system, and calculates the preprocessed data through a calculation algorithm to obtain first baseline vector data of the observation station in a geocentric coordinate system, and specifically includes:
Extracting all coherence points in the main image, selecting qualified coherence points with amplitude deviation lower than a preset threshold value from all the coherence points by a amplitude stabilizing method, and constructing a coherence point candidate set by using the qualified coherence points;
calculating coherence coefficients of all qualified coherence points in the coherence point candidate set, and defining the qualified coherence points with the coherence coefficients larger than a preset coefficient as target coherence points:
;
Wherein, The coefficient of coherence is represented by a coefficient of coherence,Representing the maximum number of interferograms in the interferogram set,An imaginary unit representing a complex number,Representing the phase of the differential interference,Representing the phase of the spatial low-pass filtering,Representing the estimated phase of the residual terrain,Represented in the largest interferogram setAn interference pattern;
Constructing a triangular net according to the target coherent points, calculating the interference phases of all qualified coherent points in the triangular net, inputting all the interference phases into a constructed deformation model, and outputting a spatial correction phase, wherein the interference phases are calculated as follows:
;
Wherein, The phase of the interference is represented by,Representing deformation phase; Representing a residual terrain phase; Represents the atmospheric phase; representing the track error phase; Representing noise phase;
The deformation model is expressed as:
;
Wherein, An interference phase representing the target coherence point,Representing the average value of the interference phases of the other coherence points in the coherence point candidate set,Representing the residual terrain phase error of the target coherence point,A noise phase representing the target coherence point,Representing noise phases of other coherent points in the coherent point candidate set;
Estimating and eliminating atmospheric errors and orbit errors of all the coherent points by using a space-time filtering method to obtain deformation data of all the coherent points;
Constructing a three-dimensional coordinate system, and inputting the deformation data into the three-dimensional coordinate system to obtain a first deformation inversion result of the target region in the three-dimensional coordinate system;
The three-dimensional coordinate system takes the central point of the target area as a coordinate origin, takes the flight direction of a radar satellite as a P axis and takes the oblique distance direction as a Q axis, and a G axis is constructed according to the P axis and the Q axis;
Constructing a geocentric coordinate system, and acquiring satellite coordinates of a plurality of navigation satellites in the geocentric coordinate system;
calculating station coordinates of the observation station in the geodetic coordinate system according to the satellite coordinates and the preprocessing data by a calculation algorithm, wherein the calculation algorithm is as follows:
;
Wherein, Represent the firstThe satellite coordinates of the individual navigation satellites,The coordinates of the measuring station are indicated,Representing the observation station to the firstThe distance of the individual navigation satellites;
Inputting the station coordinates into a constructed space correlation error model, outputting corrected first baseline vector data, and representing the first baseline vector data in the geodetic coordinate system.
Optionally, the sea-filling airport deformation evaluation method combining InSAR and GNSS, wherein the transferring the first baseline vector data to a constructed station coordinate system to obtain second baseline vector data in the station coordinate system, and transferring the second baseline vector data to the three-dimensional coordinate system to obtain third baseline vector data in the three-dimensional coordinate system specifically includes:
A station heart coordinate system is built, wherein the station heart coordinate system takes a coordinate origin of the three-dimensional coordinate system as a coordinate origin, a north-right side of a meridian line as an M axis, a east-right side of the meridian line as an F axis, and an N axis is built according to the M axis and the F axis;
transferring the first baseline vector data in the geocentric coordinate system to the station core coordinate system according to the coordinate conversion relation between the geocentric coordinate system and the station core coordinate system to obtain second baseline vector data:
;
Wherein, Representing the coordinates of any point in the station-core coordinate system,A transformation matrix representing a coordinate system is presented,Representing the coordinates of the arbitrary point in the geocentric coordinate system,A rectangular coordinate representing an origin in the geocentric coordinate system,Geodetic longitude representing the origin of the station-to-station coordinate system,A geodetic latitude representing an origin of the station-core coordinate system;
acquiring longitude and latitude of a central point of a target area, acquiring orbit parameters and attitude parameters of the radar satellite, and determining a coordinate system rotation matrix according to the longitude and latitude, the orbit parameters and the attitude parameters;
inputting the second baseline vector data into the three-dimensional coordinate system by using the coordinate system rotation matrix to obtain third baseline vector data:
;
Wherein, Representing the third baseline vector data,Representing the rotation matrix of the coordinate system,Representing the second baseline vector data,、AndRespectively representing that the second baseline vector data are respectively in the station-center coordinate systemA shaft(s),Shaft and method for producing the sameThe amount of deformation of the shaft,、AndRespectively representing the third baseline vector data in the three-dimensional coordinate systemA shaft(s),Shaft and method for producing the sameThe amount of deformation of the shaft,Representing the transpose.
Optionally, the method for evaluating the airport deformation of the sea-filling area by combining the InSAR and the GNSS includes the steps of constructing a fitting estimation model, acquiring longitude and latitude information of any point in the target area, inputting the longitude and latitude information into the fitting estimation model, and outputting a deformation vector, wherein the method specifically includes the steps of:
Estimating an instrument error and an atmospheric error of the first deformation inversion result by a fitting recursion method, and correcting the instrument error and the atmospheric error to obtain a second deformation inversion result;
according to the second deformation inversion result, the third baseline vector data is projected to the direction of the sight line axis in the three-dimensional coordinate system, and a projection result is obtained:
;
Wherein, Representing the projection result of a point in the target area in the direction of the line of sight axis,、AndThe second deformation inversion results respectively representing the certain point are in the geocentric coordinate systemA shaft(s),Shaft and method for producing the sameA unit projection vector in the axial direction;、 And Third baseline vector data representing the point in the east-west direction, the north-south direction and the vertical upward direction respectively;
Wherein, ;
Wherein,Representing an angle of incidence of the radar satellite sensor signal emissions; an azimuth angle representing the flight of the radar satellite sensor;
Calculating a difference between the projection result and the second deformation inversion result:
;
Wherein, Representing the difference between the projection result and the second deformation inversion result,A second deformation inversion result representing a point;
fitting the difference values to obtain fitting estimation parameters, and constructing a fitting estimation model according to the fitting estimation parameters:
;
Wherein, 、、、、AndAll of which represent the fit estimation parameters,Indicating the latitude of a certain point,A longitude indicating a certain point is indicated,Representing the random signal(s),Representing a noise vector when a certain point is observed;
And acquiring longitude and latitude information of the target area, inputting the longitude and latitude information into the fitting estimation model, and outputting a deformation vector of the target area.
Optionally, the method for evaluating deformation of sea-filling area airport by combining InSAR and GNSS includes constructing a data fusion model, inputting the third baseline vector data and the deformation vector to the data fusion model, outputting a deformation result, and generating a deformation monitoring result and an evaluation report of the target area according to the deformation result, wherein the method specifically includes:
Constructing an observation equation:
;
;
;
Wherein, Indicating that the target area is inThe observed value of the time of day,Representation ofThe observation equation for the moment of time designs the matrix,Is shown inThe state of the system at the moment in time,Is shown inThe observed noise vector for the moment in time,Third baseline vector data representing east-west,Third baseline vector data representing north-south directions,Third baseline vector data representing the vertical direction,Indicating that the target area is inThe second deformation at the moment inverts the result,、AndRespectively representing deformation amounts of the target region in the east-west direction, the south-north direction and the vertical direction in the third baseline vector data,、AndRepresenting the deformation rate of the target region in the east-west, north-south and vertical up third baseline vector data respectively,Representing a discrete point in time of the device,Representing a transpose;
and (3) constructing a state equation:
;
;
;
Wherein, Is shown inThe equation of state for the moment of time,Is shown inThe system state transition matrix is used at the moment,Is shown inThe time of day state equation,Representing data fusion model inThe noise vector for the moment of time,Is shown inThe system dynamics at time instant is a noise distribution matrix,The identity matrix of 3*3 is represented,A time period representing deformation of the target area;
according to the observation equation and the state equation, filtering and recursing the third baseline vector data and the deformation vector to obtain a system gain matrix;
Constructing a data fusion model according to the system gain matrix, inputting the third baseline vector data and the deformation vector into the data fusion model, and outputting a deformation result;
and generating a deformation monitoring result and an evaluation report of the target area according to the deformation result.
Optionally, the sea-filling airport deformation evaluation method combining InSAR and GNSS, wherein the filtering recursion is performed on the third baseline vector data and the deformation vector according to the observation equation and the state equation to obtain a system gain matrix, specifically includes:
according to the state equation, obtaining an optimal estimated value of the state of the data fusion model, and predicting the state of the data fusion model at the next moment according to the optimal estimated value to obtain a state predicted value:
;
Wherein, Is shown inThe time of day state prediction value,Is shown inFusing the time data with the optimal estimated value of the model state;
Constructing a state prediction error variance matrix, and updating the state prediction error variance matrix in real time:
;
Wherein, Representation ofProcess noise covariance matrix of time of day,Representing data fusion model inA noise vector at a time;
and performing filtering recursion on the third baseline vector data and the deformation vector according to the state prediction error variance matrix to obtain a system gain matrix:
;
Wherein, Is shown inA matrix of system gains at the moment in time,Is shown inAn observation noise covariance matrix at a moment;
Constructing a state estimation error matrix according to the state predicted value:
;
updating the state estimation error matrix in real time to obtain a state estimation error variance matrix, wherein the formula is as follows:
;
Wherein, Representing the identity matrix;
and estimating the optimal estimated value of the data fusion model state in real time according to the state estimation error matrix and the state estimation error variance matrix.
In addition, in order to achieve the above object, the present invention further provides a sea-filling airport deformation evaluation system combining InSAR and GNSS, wherein the sea-filling airport deformation evaluation system combining InSAR and GNSS includes:
The data preprocessing module is used for acquiring an image set and observation data of a target area, selecting a main image from the image set according to a preset rule, and preprocessing the observation data to obtain preprocessed data;
The data resolving module is used for extracting coherent points from the main image by adopting a dual-threshold strategy based on amplitude dispersion and a coherence coefficient, performing deformation inversion on the target area according to the coherent points to obtain a first deformation inversion result in a constructed three-dimensional coordinate system, and resolving the preprocessed data by a resolving algorithm to obtain first baseline vector data of an observation station in a geocentric coordinate system;
The data conversion module is used for transferring the first baseline vector data to a constructed station center coordinate system to obtain second baseline vector data in the station center coordinate system, and transferring the second baseline vector data to the three-dimensional coordinate system to obtain third baseline vector data in the three-dimensional coordinate system;
The data fitting module is used for constructing a fitting estimation model, acquiring longitude and latitude information of any point in the target area, inputting the longitude and latitude information into the fitting estimation model and outputting a deformation vector;
The data fusion module is used for constructing a data fusion model, inputting the third baseline vector data and the deformation vector into the data fusion model, outputting a deformation result, and generating a deformation monitoring result and a risk assessment report of the target area according to the deformation result.
In addition, to achieve the above object, the present invention also provides a terminal, wherein the terminal includes: the method comprises the steps of a memory, a processor and a sea-filling airport deformation evaluation program which is stored in the memory and can run on the processor and is combined with the InSAR and the GNSS, wherein the sea-filling airport deformation evaluation program of the combined InSAR and the GNSS is executed by the processor to realize the sea-filling airport deformation evaluation method of the combined InSAR and the GNSS.
In addition, in order to achieve the above object, the present invention further provides a computer readable storage medium, wherein the computer readable storage medium stores a sea-filling airport deformation evaluation program of a combined InSAR and a GNSS, and the step of the sea-filling airport deformation evaluation method of the combined InSAR and the GNSS is implemented when the sea-filling airport deformation evaluation program of the combined InSAR and the GNSS is executed by a processor.
In the method, an image set and observation data of a target area are obtained, a main image is selected from the image set according to a preset rule, and the observation data is preprocessed to obtain preprocessed data; extracting coherent points from the main image by adopting a dual-threshold strategy based on amplitude dispersion and a coherence coefficient, performing deformation inversion on the target area according to the coherent points to obtain a first deformation inversion result in a constructed three-dimensional coordinate system, and resolving the preprocessing data by a resolving algorithm to obtain first baseline vector data of an observation station in a geocentric coordinate system; transferring the first baseline vector data to a constructed station-core coordinate system to obtain second baseline vector data in the station-core coordinate system, and transferring the second baseline vector data to the three-dimensional coordinate system to obtain third baseline vector data in the three-dimensional coordinate system; constructing a fitting estimation model, acquiring longitude and latitude information of any point in the target area, inputting the longitude and latitude information into the fitting estimation model, and outputting a deformation vector; and constructing a data fusion model, inputting the third baseline vector data and the deformation vector into the data fusion model, outputting a deformation result, and generating a deformation monitoring result and a risk assessment report of the target area according to the deformation result. According to the invention, the subsidence information of the airport surface of the sea-filling area is obtained by utilizing satellite and synthetic aperture radar interferometry, the deformation inversion result is corrected and fused by taking the base line vector data as a reference, the subsidence monitoring precision of the airport surface of the sea-filling area is improved, the accuracy and reliability of the subsidence result are ensured, and the subsidence risk of the airport of the sea-filling area is estimated based on the fused subsidence information.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear and clear, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The sea-filling airport deformation evaluation method combining InSAR and GNSS according to the preferred embodiment of the invention, as shown in figure 1, comprises the following steps:
Step S10, acquiring an image set and observation data of a target area, selecting a main image from the image set according to a preset rule, and preprocessing the observation data to obtain preprocessed data.
The airport is used as a high-standard infrastructure engineering, the internal facilities, the ground surface and the like of the airport are influenced by geological environment changes, base structures, dynamic and static loads and the like, and the airport in the sea-filling area has infrastructures such as buildings, roads and the like, namely a large number of permanent scatterers exist, and high coherence can be maintained at a long time sequence, so that as shown in fig. 2, the PS-InSAR technology (permanent scatterer synthetic aperture radar interferometry, PERSISTENT SCATTERER Interferometric Synthetic Aperture Radar) is applied to acquire the surface deformation information of the airport in the sea-filling area, and the accurate deformation observables are ensured to be provided for the infrastructures such as the roads, the buildings and the like in the airport in the sea-filling area.
Specifically, a SAR (synthetic aperture radar ) image set and observation data of a target area are obtained; randomly selecting a target image from the SAR image set, respectively performing interference calculation on the target image and other images in the SAR image set to obtain interferograms respectively corresponding to the target image and the other images in the SAR image set, and constructing an interference atlas by using all the interferograms; continuing to select other images in the SAR image set as target images to perform interference calculation until all images in the SAR image set are completely calculated as target images, so as to obtain a plurality of interference atlas; according to the time base line, the space base line and the Doppler frequency, calculating the overall coherence coefficient of each interference atlas, taking a target image corresponding to the interference atlas with the maximum overall coherence coefficient as a main image, and calculating the overall coherence coefficient as: ; wherein, Representing the overall coherence coefficient of the signal,The spatial coherence coefficient is represented by a spatial coherence coefficient,The coefficient of temporal coherence is represented as such,The doppler coherence coefficient is represented as such,Representing a thermal noise coherence coefficient; and carrying out data calibration processing on the observed data, and carrying out format conversion processing on the calibrated observed data to obtain preprocessed data.
The method comprises the steps of selecting an optimal interference combination pair according to an optimal strategy of a time base line, a space base line and Doppler frequency, and introducing an overall coherence coefficient as a main basis for selecting a main image: firstly, the main image refers to a SAR image which is selected to perform interference calculation with the slave image, the interference image can be obtained after interference, then the overall coherence coefficient is introduced, the value of each interference image is calculated, and then the main image is selected in reverse by comparing the overall coherence coefficients among the interference images to determine the main image. And (3) calibrating the observed data of the target area while determining the main image, wherein the calibration comprises preprocessing operations such as data format conversion, parameter setting and the like, so as to obtain preprocessed data. Due to the support of high-resolution X-band SAR data, permanent scatterer deformation details of airport facilities can be continuously monitored through a PS-InSAR technology, so that accuracy of deformation data is improved.
And S20, extracting coherent points from the main image by adopting a dual-threshold strategy based on amplitude dispersion and a coherence coefficient, performing deformation inversion on the target area according to the coherent points to obtain a first deformation inversion result in a constructed three-dimensional coordinate system, and resolving the preprocessed data by a resolving algorithm to obtain first baseline vector data of an observation station in a geocentric coordinate system.
And extracting stable PS points (coherent points) which are not influenced by spatial decoherence and atmospheric phase positions in the main image, establishing a phase model on each PS point, constructing an equation set by using phase values of a plurality of interferograms, and carrying out iterative solution to finally obtain the airport surface subsidence field in millimeter level.
Specifically, all coherence points in the main image are extracted, qualified coherence points with amplitude deviation lower than a preset threshold value are selected from all the coherence points through a amplitude stabilizing method, and a coherence point candidate set is constructed by using the qualified coherence points; calculating coherence coefficients of all qualified coherence points in the coherence point candidate set, and defining the qualified coherence points with the coherence coefficients larger than a preset coefficient as target coherence points: ; wherein, The coefficient of coherence is represented by a coefficient of coherence,Representing the maximum number of interferograms in the interferogram set,An imaginary unit representing a complex number,Representing the phase of the differential interference,Representing the phase of the spatial low-pass filtering,Representing the estimated phase of the residual terrain,Represented in the largest interferogram setAn interference pattern; constructing a triangular net according to the target coherent points, calculating the interference phases of all qualified coherent points in the triangular net, inputting all the interference phases into a constructed deformation model, and outputting a spatial correction phase, wherein the interference phases are calculated as follows: ; wherein, The phase of the interference is represented by,Representing deformation phase; Representing a residual terrain phase; Represents the atmospheric phase; representing the track error phase; representing noise phase; the deformation model is expressed as: ; wherein, An interference phase representing the target coherence point,Representing the average value of the interference phases of the other coherence points in the coherence point candidate set,Representing the residual terrain phase error of the target coherence point,A noise phase representing the target coherence point,Representing noise phases of other coherent points in the coherent point candidate set; estimating and eliminating atmospheric errors and orbit errors of all the coherent points by using a space-time filtering method to obtain deformation data of all the coherent points; constructing a three-dimensional coordinate system, and inputting the deformation data into the three-dimensional coordinate system to obtain a first deformation inversion result of the target region in the three-dimensional coordinate system; the three-dimensional coordinate system takes the central point of the target area as a coordinate origin, takes the flight direction of a radar satellite as a P axis and takes the oblique distance direction as a Q axis, and a G axis is constructed according to the P axis and the Q axis; constructing a geocentric coordinate system, and acquiring satellite coordinates of a plurality of navigation satellites in the geocentric coordinate system; calculating station coordinates of the observation station in the geodetic coordinate system according to the satellite coordinates and the preprocessing data by a calculation algorithm, wherein the calculation algorithm is as follows: ; wherein, Represent the firstThe satellite coordinates of the individual navigation satellites,The coordinates of the measuring station are indicated,Representing the observation station to the firstThe distance of the individual navigation satellites; inputting the station coordinates into a constructed space correlation error model, outputting corrected first baseline vector data, and representing the first baseline vector data in the geodetic coordinate system.
Extracting coherent points in a determined main image, reflecting phase stability through an approximation method of amplitude stability, setting an initial amplitude dispersion threshold to select qualified PS points to construct a candidate set, performing gridding treatment on candidate point targets to improve the point target density and estimation accuracy of a low coherence area, performing weight adjustment according to a coherence coefficient gamma, and performing iterative screening for multiple rounds to identify PS point targets meeting conditions in an airport of a sea-filling area, removing adjacent pseudo-coherent point targets, eliminating side lobe effects, and accurately acquiring a final PS point set.
Furthermore, a space-time combined analysis method is designed aiming at the specific requirements of the airport of the sea-filling area so as to accurately identify key PS point targets, in the aspect of space analysis, the PS point targets of the airport runway, the parking apron, the airport terminal and related infrastructures are particularly focused on according to the accurate geographic position information of the airport facilities of the sea-filling area, the selected PS points can be guaranteed to accurately reflect the deformation behaviors of the airport facilities of the sea-filling area, the elevation errors of the PS points are estimated by using a least square method, and the atmospheric and rail errors of the PS points are estimated and eliminated by adopting space-time filtering so as to obtain the average deformation rate and the time sequence deformation phase along the LOS (Line of Sight) direction, and meanwhile, the interference generated by surrounding non-target areas is reduced. In terms of time analysis, the phase stability of the target point is evaluated by applying a time sequence analysis technology and taking the maximum likelihood estimated value of the target point in the time sequence as a standard, and meanwhile, a threshold value is set, for example, the total coherence is greater than 0.7, so that the airport facility PS point has high stability and reliability in time. For specific coastal zone characteristics, further comprehensive consideration of elevation data and surrounding environmental factors is performed to rationalize PS points, excluding point targets that may be located on auxiliary buildings (these targets do not directly contribute to monitoring the deformation of the main facilities of the sea-fill airport). Through the process, a group of PS point target sets capable of accurately representing the deformation of airport facilities are finally screened, the accuracy and efficiency of the extraction of PS points of airport facilities in a sea-filling area are remarkably improved through the space-time comprehensive screening method, a set of high-accuracy technical framework is provided for the deformation monitoring of the airport facilities in the sea-filling area, and potential structural risks and geological changes of airports are timely found and evaluated by a booster airport security department.
When a GNSS (global navigation satellite system ) station is utilized to acquire airport deformation of a sea-fill area, baseline calculation is firstly needed, four satellites are needed in the calculation process, the calculation is carried out through satellite coordinates, differential correction is then carried out (a reference station sends observation data to a control center, a space correlation error model is built, the space correlation error between the station and the reference station is estimated, network carrier phase differential correction information is generated by combining the reference station observation data, correction information is corrected based on the correction information), the position accuracy is improved, errors such as atmospheric delay and multipath interference are eliminated, finally, three-dimensional coordinates of the station are obtained through calculation, airport station deformation information is acquired through comparing the station coordinates of different time points, the station arrangement position is generally selected, the open non-shielding position is selected as far as possible, and the relative high point is selected as possible, so that an interference source is avoided.
And step S30, transferring the first baseline vector data to a constructed station-core coordinate system to obtain second baseline vector data in the station-core coordinate system, and transferring the second baseline vector data to the three-dimensional coordinate system to obtain third baseline vector data in the three-dimensional coordinate system.
In order to smoothly correct the InSAR observation value and realize the subsequent data fusion of the GNSS and the InSAR, the InSAR observation value and the coordinate system where the GNSS observation value is located need to be unified. Since describing the sedimentation deformation of a point on the ground in the station-core coordinate system has a more intuitive effect, and the GNSS observations are generally located in the earth-core coordinate system, it is necessary to convert the GNSS observations into the station-core coordinate system first.
Specifically, as shown in fig. 3, a station coordinate system is constructed, wherein the station coordinate system uses a coordinate origin of the three-dimensional coordinate system as a coordinate origin, uses the north direction of a meridian as an M axis, uses the east direction of the meridian as an F axis, and constructs an N axis according to the M axis and the F axis; transferring the first baseline vector data in the geocentric coordinate system to the station core coordinate system according to the coordinate conversion relation between the geocentric coordinate system and the station core coordinate system to obtain second baseline vector data: ; wherein, Representing the coordinates of any point in the station-core coordinate system,A transformation matrix representing a coordinate system is presented,Representing the coordinates of the arbitrary point in the geocentric coordinate system,A rectangular coordinate representing an origin in the geocentric coordinate system,Geodetic longitude representing the origin of the station-to-station coordinate system,A geodetic latitude representing an origin of the station-core coordinate system; acquiring longitude and latitude of a central point of a target area, acquiring orbit parameters and attitude parameters of the radar satellite, and determining a coordinate system rotation matrix according to the longitude and latitude, the orbit parameters and the attitude parameters; inputting the second baseline vector data into the three-dimensional coordinate system by using the coordinate system rotation matrix to obtain third baseline vector data: ; wherein, Representing the third baseline vector data,Representing the rotation matrix of the coordinate system,Representing the second baseline vector data,、AndRespectively representing that the second baseline vector data are respectively in the station-center coordinate systemA shaft(s),Shaft and method for producing the sameThe amount of deformation of the shaft,、AndRespectively representing the third baseline vector data in the three-dimensional coordinate systemA shaft(s),Shaft and method for producing the sameThe amount of deformation of the shaft,Representing the transpose.
The GNSS observations are converted from the geocentric coordinate system into the station-centric coordinate system through the coordinate system conversion. For InSAR observations, a three-dimensional coordinate system O-PGQ is established: the observed point is taken as an origin of the three-dimensional coordinate system, the flight direction of the radar satellite is taken as a P axis, the inclined distance direction is taken as a Q axis, the G axis and the P and Q axes form a left-hand coordinate system, and the three axes of the P axis, the G axis and the Q axis jointly form the three-dimensional coordinate system.
Further, after the three-dimensional coordinate system O-PGQ is established, the GNSS observed value needs to be converted into the O-PGQ coordinate system from the station-core coordinate system, so that the coordinate system of the GNSS observed value and the InSAR observed value is unified. What is observed by InSAR monitoring technology is a one-dimensional deformation of a point in the O-PGQ coordinate system, which can be expressed as; The GNSS monitoring technique observes a three-dimensional deformation of a point in the station-center coordinate system O-MFN, which can be expressed asAnd then converting the GNSS three-dimensional deformation in the station core coordinate system into a three-dimensional coordinate system through vector conversion, and realizing the goal of unifying the GNSS observation value and the InSAR observation value coordinate system through the conversion of the two coordinate systems.
And S40, constructing a fitting estimation model, acquiring longitude and latitude information of any point in the target area, inputting the longitude and latitude information into the fitting estimation model, and outputting a deformation vector.
After the coordinate system of the GNSS observation value and the InSAR observation value is unified, the GNSS observation result may be used as a reference standard to compensate for systematic errors such as atmospheric errors in the InSAR monitoring, and the InSAR observation result may be corrected appropriately.
Specifically, estimating an instrument error and an atmospheric error of the first deformation inversion result by a fitting recursion method, and correcting the instrument error and the atmospheric error to obtain a second deformation inversion result; according to the second deformation inversion result, the third baseline vector data is projected to the direction of the sight line axis in the three-dimensional coordinate system, and a projection result is obtained: ; wherein, Representing the projection result of a point in the target area in the direction of the line of sight axis,、AndThe second deformation inversion results respectively representing the certain point are in the geocentric coordinate systemA shaft(s),Shaft and method for producing the sameA unit projection vector in the axial direction;、 And Third baseline vector data representing the point in the east-west direction, the north-south direction and the vertical upward direction respectively; wherein,; Wherein,Representing an angle of incidence of the radar satellite sensor signal emissions; An azimuth angle representing the flight of the radar satellite sensor; calculating a difference between the projection result and the second deformation inversion result: ; wherein, Representing the difference between the projection result and the second deformation inversion result,A second deformation inversion result representing a point;
fitting the difference values to obtain fitting estimation parameters, and constructing a fitting estimation model according to the fitting estimation parameters: ; wherein, 、、、、AndAll of which represent the fit estimation parameters,Indicating the latitude of a certain point,A longitude indicating a certain point is indicated,Representing the random signal(s),Representing a noise vector when a certain point is observed; and acquiring longitude and latitude information of the target area, inputting the longitude and latitude information into the fitting estimation model, and outputting a deformation vector of the target area.
The main method used in the step is a fitting estimation method, and the abnormal earth surface deformation observed value caused by systematic errors such as instrument errors and atmospheric interference can be identified and corrected by inputting the InSAR observed value into a built fitting estimation model for fitting estimation recursion estimation, so that earth surface deformation deviation obtained by InSAR observation is reduced or eliminated, and the GNSS observed value is firstly projected onto the sight line (LOS direction) because the observed result obtained by the InSAR monitoring technology is the sight line. The formula in the step S40 is solved simultaneously, so that fitting estimation parameters in a fitting estimation model can be obtained, the fitting estimation model is constructed according to the fitting estimation parameters, then, the corrected value of any monitored point on the airport ground can be obtained by substituting the longitude and latitude of the monitored point into the fitting estimation model, and then, the corrected InSAR line-of-sight deformation of the monitored point is corrected by using the corrected value to obtain the corrected InSAR line-of-sight deformation(I.e., the deformation vector of the target region).
And S50, constructing a data fusion model, inputting the third baseline vector data and the deformation vector into the data fusion model, outputting a deformation result, and generating a deformation monitoring result and a risk assessment report of the target area according to the deformation result.
Wherein, as shown in FIG. 4, the corrected InSAR line-of-sight deformation is obtainedThe method can be fused with the GNSS line-of-sight deformation quantity to obtain higher-precision airport surface subsidence information, and accurate evaluation of airport safety is realized. Through the combined application of the GNSS and InSAR technologies, complementation can be realized in the aspects of measurement precision, spatial resolution and the like, and the accuracy and reliability of ground surface deformation monitoring are greatly improved. Based on the consideration of actual conditions such as coastal geographic positions at the sea-filling airport, a GNSS-InSAR data fusion model is established by utilizing a Kalman filtering principle, so that the data fusion of GNSS and InSAR is realized, and high-precision surface deformation information of the sea-filling airport is obtained.
Before data fusion, the relative weights of the InSAR and the GNSS data are set, so that the respective advantages of the InSAR and the GNSS data can be ensured to be fully exerted in the fusion process, and errors caused by different data source differences and different measurement accuracy are reduced: firstly, performing calculation and analysis on GNSS data and corrected InSAR data to obtain accuracy indexes of each data, such as standard deviation, root mean square error and the like, and providing important basis for subsequent weight distribution; secondly, setting initial weights for InSAR and GNSS data according to priori knowledge or expert experience, and carrying out data fusion on the InSAR and the GNSS data according to the set initial weights, wherein in the fusion process, the matching of the two data in time and space needs to be ensured so as to obtain an accurate fusion result; then, comparing the fused airport surface deformation result of the sea-filled area with the deformation result of the single remote sensing data (namely, the deformation data obtained through a single measurement mode), and calculating errors between the two, wherein the error information provides an important basis for subsequently adjusting the weight of the data source; then, according to error analysis of the fusion result, adjusting the relative weight between the InSAR and the GNSS data, if the error between the fusion result and a certain data source is larger, properly reducing the weight of the data source in fusion, otherwise, if the error between the fusion result and the certain data source is smaller, properly increasing the weight of the data source in fusion; finally, in order to ensure the accuracy and reliability of the weight distribution, repeated data fusion and weight adjustment are required to be performed for a plurality of times until the preset iteration times are reached, at this time, iteration can be stopped, a final weight distribution scheme is obtained, and fusion of InSAR and GNSS data is performed.
Specifically, an observation equation is constructed:;; ; wherein, Indicating that the target area is inThe observed value of the time of day,Representation ofThe observation equation for the moment of time designs the matrix,Is shown inThe state of the system at the moment in time,Is shown inThe observed noise vector for the moment in time,Third baseline vector data representing east-west,Third baseline vector data representing north-south directions,Third baseline vector data representing the vertical direction,Indicating that the target area is inThe second deformation at the moment inverts the result,、AndRespectively representing deformation amounts of the target region in the east-west direction, the south-north direction and the vertical direction in the third baseline vector data,、AndRepresenting the deformation rate of the target region in the east-west, north-south and vertical up third baseline vector data respectively,Representing a discrete point in time of the device,Representing a transpose; and (3) constructing a state equation:;; ; wherein, Is shown inThe equation of state for the moment of time,Is shown inThe system state transition matrix is used at the moment,Is shown inThe time of day state equation,Representing data fusion model inThe noise vector for the moment of time,Is shown inThe system dynamics at time instant is a noise distribution matrix,The identity matrix of 3*3 is represented,A time period representing deformation of the target area; according to the observation equation and the state equation, filtering and recursing the third baseline vector data and the deformation vector to obtain a system gain matrix; constructing a data fusion model according to the system gain matrix, inputting the third baseline vector data and the deformation vector into the data fusion model, and outputting a deformation result; and generating a deformation monitoring result and an evaluation report of the target area according to the deformation result.
Further, according to the state equation, an optimal estimated value of the state of the data fusion model is obtained, and the state of the data fusion model at the next moment is predicted according to the optimal estimated value, so that a state predicted value is obtained: ; wherein, Is shown inThe time of day state prediction value,Is shown inFusing the time data with the optimal estimated value of the model state; constructing a state prediction error variance matrix, and updating the state prediction error variance matrix in real time: ; wherein, Representation ofProcess noise covariance matrix of time of day,Representing data fusion model inA noise vector at a time; and performing filtering recursion on the third baseline vector data and the deformation vector according to the state prediction error variance matrix to obtain a system gain matrix: ; wherein, Is shown inA matrix of system gains at the moment in time,Is shown inAn observation noise covariance matrix at a moment; constructing a state estimation error matrix according to the state predicted value: ; updating the state estimation error matrix in real time to obtain a state estimation error variance matrix, wherein the formula is as follows: ; wherein, Representing the identity matrix; and estimating the optimal estimated value of the data fusion model state in real time according to the state estimation error matrix and the state estimation error variance matrix.
Firstly, an observation equation and a state equation of a data fusion model are established, a system state transition matrix and acquired GNSS and InSAR observation data are introduced, the introduced sea-fill airport surface deformation observation data are continuously filtered and recursively subjected to the aim of minimizing the mean square error of system state estimation, and the optimal estimation of the system state is acquired after the system state and the mean square error are updated for a plurality of times, so that the optimal fusion of the GNSS and the InSAR data is realized. Through the formula in the step S50, a GNSS-InSAR data fusion model is formed, after the construction of the fusion model is completed, the estimated value of the system state or parameter of the model at the initial moment is set, the GNSS observed values and the InSAR observed values of all points are input into the observation equation in the fusion model for fusion operation, data fusion is finally realized through repeated filtering recursion, the characteristics of GNSS and InSAR are fully utilized by fused data, the characteristic trend of the earth surface deformation of an airport in a sea-fill area can be accurately reflected, and the obtained airport earth surface deformation result is more accurate and reliable.
Furthermore, after the airport surface deformation result of the target area is obtained according to the steps, the invention also designs a sea-filling area airport comprehensive risk assessment model based on the fused settlement information, and a plurality of risk factors of airport deformation are brought into a comprehensive risk assessment system by referring to the accumulated settlement and flatness standard in the existing standard, and different evaluation indexes and different grading standards are designed for main facilities of the airport. In order to refine the standard and integrate multiple influencing factors, an evaluation system is respectively established for each key facility and a secondary fuzzy comprehensive evaluation method is used, as shown in fig. 5, so as to realize more comprehensive airport facility risk evaluation in the sea-filling area.
The indexes of various risk factors are subjected to unified quantification treatment, certain deformation risk factors have no clear judgment standard, certain factors with ambiguity (such as aging degree of facilities, structural form of buildings and the like) exist, or due to subjective reasons, experts have different opinions on the image degree of certain influence factors, and the deformation risk factors with unified weights are difficult to be determined directly by a statistical method, and are analyzed and treated by a analytic hierarchy process and a fuzzy comprehensive judgment method:
1. Establishing a fuzzy comprehensive judgment comment set: according to the deformation risk classification method of urban infrastructure, the airport accident risk level is combined, and on the basis of meeting the classification and refinement requirements of all facility evaluation indexes, the deformation risk of the sea-filling airport is classified into 5 grades of high risk, higher risk, medium risk, low risk and no risk, and the grades are respectively represented by v1, v2, v3, v4 and v 5. Namely: v= { V1, V2, V3, V4, V5} = { high risk, higher risk, stroke risk, low risk, no risk }.
2. Establishing a fuzzy comprehensive judgment index system: adopting a second-level fuzzy comprehensive evaluation, wherein the target layer is B, namely the deformation risk level of airport facilities in the sea-filled area; the criterion layer is U, and the index system is mainly selected from three aspects: u1 airport deformation conditions, U2 airport facility conditions, U3 airport environmental factors; the scheme layer is U, wherein the U1 airport deformation condition comprises: u11 facility deformation rate, u12 facility cumulative deformation amount; the U2 airport facility conditions include: u21 facilities are distant from the coastline, u22 facilities aging degree, u23 facilities construction influence level and u24 facilities heavy load level; u3 airport environmental factors include: u31 airport geological soil type, u32 sea facing sea level altitude, u33 extreme weather probability (desk lamp, heavy rain, high temperature), u34 groundwater level change.
3. Dividing the evaluation grade of the index system: the secondary indexes in the index system of the road and the building facilities are also classified according to 5 grades of the fuzzy comprehensive evaluation comment set, for example, the risk grade classification of u12 accumulated deformation indexes of the road facilities is performed according to 5 grades of each index, and the grade classification as shown in table 2 is performed by referring to the standard of table 1. Firstly, two standards of accumulated sedimentation and flatness are used, the accumulated deformation risk level of the facility is determined by combining the two standards, the facility deformation trend is reflected by using the facility average deformation rate index U11 (as shown in table 3), and the deformation current situation U1 in the comprehensive evaluation index is reflected by fully utilizing the fusion data result of the GNSS and the InSAR.
Table 1: airport road facility deformation standard meter
Table 2: index grade dividing table
Table 3: deformation rate index grading table
4. Determining a judgment membership function: in the established evaluation index system, indexes such as deformation rate, accumulated deformation, sea level height, underground water level and the like can be quantitatively described, and the quantitative evaluation indexes are designed and described by using a ridge membership function, because the defect that a broken line keeps a fixed slope can be avoided to a certain extent by the ridge membership function, the ridge membership function is distributed as follows:
Smaller size:
;
intermediate type:
;
Larger size:
;
Wherein, 、、AndAll represent segment indicators of the ridge membership function.
In the evaluation index system, qualitative indexes such as aging degree, construction influence and geological conditions are considered in addition to quantitative indexes, and the membership function of the indexes can be constructed through comparison analysis. For each index, it was classified into five ratings, namely, "fully met", "substantially met", "partially met", "substantially not met" and "fully not met", and values of 1, 0.75, 0.5, 0.25, 0 were assigned, respectively. Based on this, a single index evaluation matrix corresponding to each rating is formed, in such a way that qualitative indexes are quantitatively evaluated.
5. Determining the weight of a fuzzy comprehensive judgment index system: the weight of each evaluation index is set by a analytic hierarchy process, a questionnaire is issued to students, technical experts and site constructors with intensive experience in the field, and a hierarchical judgment matrix of the index is constructed by comprehensively analyzing relevant documents and data and questionnaire investigation results. For example, when fuzzy comprehensive evaluation of airport runway deformation risk in sea-fill area is performed, four levels of judgment matrixes are involved, wherein each level of judgment matrixes comprises 1 first-level evaluation index judgment matrix and 3 second-level index judgment matrixes (as shown in fig. 5), a plurality of indexes in the same level are compared in pairs, the relative importance of each factor in each level is judged in a numerical form, so as to form each level of judgment matrixes, weight values of each level are obtained through matrix operation, and consistency test is performed on the results:
;
;
Wherein, Indicating the random consistency of the judgment matrix,Represents the maximum eigenvalue of the judgment matrix,The number of the indexes is represented,Representing the random uniformity ratio of the decision matrix,Representing the average random consistency index of the judgment matrix; when (when)When or,And acquiring various risk index weights meeting the criteria of the analytic hierarchy process.
6. Calculating a fuzzy comprehensive evaluation vector: and calculating the membership value of each index on each grade by using the selected membership function, and establishing a first-level fuzzy evaluation matrix and a second-level fuzzy evaluation matrix according to the membership value. And calculating by using a fuzzy operator of weighted average to obtain a fuzzy evaluation vector, and finally, selecting a corresponding judgment element as a final evaluation result by adopting a maximum membership principle.
7. And carrying out fuzzy comprehensive evaluation on deformation risks aiming at different facilities of the airport: through the technical process, comprehensive fuzzy evaluation of deformation risks of different facilities of the airport in the sea-filled area is completed, comprehensive deformation risk levels of target areas (such as facilities of airport runways, slideways, apron, airport terminals and the like) at a certain monitoring moment are obtained, and if the airport InSAR-GNSS fusion deformation monitoring and risk evaluation of the facilities are integrated into an airport safety operation platform, the capability of the airport for resisting the deformation risks can be improved to a great extent, and the safety of airport operation is enhanced.
According to the invention, the subsidence information of the airport surface of the sea-filling area is acquired by utilizing satellite and synthetic aperture radar interferometry, the baseline vector data is used as a reference, deformation inversion results are corrected and fused based on Kalman filtering, the subsidence monitoring precision of the airport surface of the sea-filling area is improved, the accuracy and reliability of the subsidence results are ensured, finally, deformation risk assessment systems of different facilities are established according to various deformation factors of the airport facilities of the sea-filling area, and the surface deformation monitoring and risk assessment of the airport of the sea-filling area are realized by utilizing fuzzy comprehensive assessment.
Further, as shown in fig. 6, the invention further provides a sea-filling airport deformation evaluation system based on the combined InSAR and GNSS, wherein the sea-filling airport deformation evaluation system based on the combined InSAR and GNSS comprises:
The data preprocessing module 51 is configured to obtain an image set and observation data of a target area, select a main image from the image set according to a preset rule, and preprocess the observation data to obtain preprocessed data;
The data resolving module 52 is configured to extract coherent points from the main image by using a dual-threshold strategy based on amplitude dispersion and a coherence coefficient, perform deformation inversion on the target area according to the coherent points to obtain a first deformation inversion result in a constructed three-dimensional coordinate system, and resolve the preprocessed data by using a resolving algorithm to obtain first baseline vector data of the observation station in a geocentric coordinate system;
The data conversion module 53 is configured to transfer the first baseline vector data to a constructed station-core coordinate system, obtain second baseline vector data in the station-core coordinate system, and transfer the second baseline vector data to the three-dimensional coordinate system, obtain third baseline vector data in the three-dimensional coordinate system;
the data fitting module 54 is configured to construct a fitting estimation model, obtain longitude and latitude information of any point in the target area, input the longitude and latitude information to the fitting estimation model, and output a deformation vector;
The data fusion module 55 is configured to construct a data fusion model, input the third baseline vector data and the deformation vector data to the data fusion model, output a deformation result, and generate a deformation monitoring result and a risk assessment report of the target area according to the deformation result.
Further, as shown in fig. 7, the invention further provides a terminal based on the sea-filling airport deformation evaluation method and system combining InSAR and GNSS, which comprises a processor 10, a memory 20 and a display 30. Fig. 7 shows only some of the components of the terminal, but it should be understood that not all of the illustrated components are required to be implemented and that more or fewer components may alternatively be implemented.
The memory 20 may in some embodiments be an internal storage unit of the terminal, such as a hard disk or a memory of the terminal. The memory 20 may in other embodiments also be an external storage device of the terminal, such as a plug-in hard disk provided on the terminal, a smart memory card (SMART MEDIA CARD, SMC), a Secure Digital (SD) card, a flash memory card (FLASH CARD), etc. Further, the memory 20 may also include both an internal storage unit and an external storage device of the terminal. The memory 20 is used for storing application software installed in the terminal and various data, such as program codes of the installation terminal. The memory 20 may also be used to temporarily store data that has been output or is to be output. In an embodiment, the memory 20 stores a sea-filling airport deformation evaluation program 40 of the combined InSAR and GNSS, and the sea-filling airport deformation evaluation program 40 of the combined InSAR and GNSS can be executed by the processor 10, so as to implement the sea-filling airport deformation evaluation method of the combined InSAR and GNSS in the present application.
The processor 10 may be a central processing unit (Central Processing Unit, CPU), microprocessor or other data processing chip in some embodiments, for executing program codes or processing data stored in the memory 20, such as performing the sea-fill airport deformation assessment method of the combined InSAR and GNSS.
The display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch, or the like in some embodiments. The display 30 is used for displaying information at the terminal and for displaying a visual user interface. The components 10-30 of the terminal communicate with each other via a system bus.
In one embodiment, the steps of the sea-fill airport deformation evaluation method combining InSAR and GNSS as described above are implemented when the processor 10 executes the sea-fill airport deformation evaluation program 40 combining InSAR and GNSS in the memory 20.
The invention also provides a computer readable storage medium, wherein the computer readable storage medium stores a sea-filling airport deformation evaluation program of the combined InSAR and the GNSS, and the sea-filling airport deformation evaluation program of the combined InSAR and the GNSS realizes the steps of the sea-filling airport deformation evaluation method of the combined InSAR and the GNSS when being executed by a processor.
In summary, the present invention provides a sea-filling airport deformation evaluation method and related equipment combining InSAR and GNSS, the method comprising: acquiring an image set and observation data of a target area, selecting a main image and preprocessing the observation data; extracting coherent points by using a double-threshold strategy, performing deformation inversion on a target area to obtain a deformation inversion result, and resolving the preprocessed data by a resolving algorithm to obtain baseline vector data; and carrying out fusion processing on the baseline vector data and the deformation inversion result through a data fusion model, outputting a deformation result, and generating a deformation monitoring result and an evaluation report of the target area according to the deformation result. According to the invention, the subsidence information of the airport surface of the sea-filling area is obtained by utilizing satellite and synthetic aperture radar interferometry, the deformation inversion result is corrected and fused by taking the base line vector data as a reference, the subsidence monitoring precision of the airport surface of the sea-filling area is improved, the accuracy and reliability of the subsidence result are ensured, and the subsidence risk of the airport of the sea-filling area is estimated based on the fused subsidence information.
It should be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising one … …" does not exclude the presence of other like elements in a process, method, article, or terminal that comprises the element.
Of course, those skilled in the art will appreciate that implementing all or part of the above described methods may be accomplished by a computer program for instructing relevant hardware (e.g., processor, controller, etc.), the program may be stored on a computer readable storage medium, and the program may include the above described methods when executed. The computer readable storage medium may be a memory, a magnetic disk, an optical disk, etc.
It is to be understood that the invention is not limited in its application to the examples described above, but is capable of modification and variation in light of the above teachings by those skilled in the art, and that all such modifications and variations are intended to be included within the scope of the appended claims.