Force-thermal coupling deformation measurement method for airborne array SAR (Synthetic Aperture Radar)

Abstract

The invention discloses a force-thermal coupling deformation measurement method for an airborne array SAR (Synthetic Aperture Radar), which can realize high-precision measurement of force-induced deformation and thermal deformation. Firstly, fiber grating strain sensors and temperature sensors are symmetrically pasted on the upper surface and the lower surface of a wing, the strain and the temperature of the surface of the wing are measured respectively, strain decoupling is achieved based on temperature compensation and up-down difference, discrete strain data are obtained, a continuous force-induced strain function is obtained through quadratic polynomial fitting, and high-precision bending deformation is obtained; secondly, solving the temperature difference between the upper surface and the lower surface of the wing based on a temperature sensor, obtaining a continuous temperature difference function through spline interpolation, and substituting the continuous temperature difference function into the axial thermal expansion deformation measurement model to obtain axial thermal displacement; and finally, establishing a wing force thermal coupling deformation measurement model based on the force-induced bending deformation and the axial thermal displacement, and inputting the length of each measurement point to obtain the axial displacement, the longitudinal displacement and the rotation angle of the wing under the measurement coordinate system.

Description

Technical Field

[0001] This invention relates to the field of airborne remote sensing technology, and in particular to a force-thermal coupling deformation measurement method for airborne array SAR, which can be applied to motion compensation of distributed imaging payloads such as flexible baseline array antenna SAR under force-thermal coupling conditions on airfoils. Background Technology

[0002] Array Synthetic Aperture Radar (SAR), as a new generation of airborne remote sensing system installed under the wings, has attracted increasing attention and is gradually becoming an important research direction because it can achieve all-weather three-dimensional imaging.

[0003] To achieve high-definition imaging, array SAR requires that each antenna undergo uniform and stable ideal linear motion. However, due to factors such as airflow disturbances and solar radiation, the flexible baseline of the wing will experience significant force-thermal coupling deformation, causing uncertain relative motion between the antenna elements, resulting in blurred and distorted images.

[0004] In recent years, fiber Bragg grating (FBG) sensors have been widely used for deformation measurement of various structures due to their ability to measure strain and temperature. Compared with non-contact measurement methods, the FBG method has higher stability. FBG sensors, used in FBG-based deformation measurement, offer advantages such as light weight, non-conductivity, resistance to high and low temperatures, and immunity to electromagnetic interference, making them ideal for measuring the deformation of flexible wing arms during flight.

[0005] Fiber optic strain sensors are affected by the combined effects of temperature and strain when measuring deformation; failure to decouple them will affect their measurement accuracy. Existing strain decoupling methods are mainly divided into two categories: one is to use a single temperature sensor to compensate for all strain sensors, which can eliminate most of the influence of temperature changes, but cannot achieve strain decoupling caused by multiple complex external forces and ignores the spatial temperature gradient; the other is to achieve strain decoupling through differential strain sensors on the upper and lower surfaces, which can solve the strain coupling problem in the case of single bending deformation to a certain extent, but cannot handle multidimensional composite bending deformation and ignores the temperature gradient between the upper and lower surfaces.

[0006] Existing methods for measuring fiber Bragg grating (FBG) sensor deformation and decoupling fiber Bragg grating strain typically utilize reference gratings or differential principles to eliminate temperature-sensitive parameters of the FBG, decoupling the actual coupled deformation of the wing into deformation caused purely by external forces. These methods generally only yield force-induced deformation and cannot measure the force-thermal coupling deformation of the wing or similar structural beams. Array SAR places extremely high demands on the motion parameters of each antenna element; ignoring the influence of thermal deformation on the deformation of the flexible baseline and considering only force-induced deformation is insufficient to meet the requirements of array SAR.

[0007] In summary, flexible baseline array antenna SAR urgently needs to achieve force-thermal coupling deformation measurement to further improve the accuracy of flexible baseline motion compensation. Summary of the Invention

[0008] This invention addresses the significant measurement errors caused by deformation due to temperature gradients on the upper and lower surfaces of an airfoil under force-thermal coupling conditions. It proposes a force-thermal coupling deformation measurement method for airborne array SAR. This method involves symmetrically deploying fiber optic strain and temperature sensors on the upper and lower surfaces of the airfoil to simultaneously acquire surface strain and temperature data. Strain decoupling is achieved through temperature compensation and upper / lower surface differential measurement. A continuous force-induced strain function is obtained using quadratic polynomial fitting and substituted into a piecewise circular arc bending model to solve for high-precision bending deformation. Simultaneously, the temperature difference between the upper and lower surfaces is calculated from the temperature sensors and interpolated using spline interpolation to obtain a continuous temperature difference function, which is then substituted into an axial thermal expansion model to solve for axial thermal displacement. Based on this, a force-thermal coupling deformation measurement model is constructed. By inputting the lengths of each measurement point, the axial displacement, longitudinal displacement, and rotation angle of the airfoil in the measurement coordinate system can be obtained. This method effectively improves the deformation measurement accuracy of the airfoil under force-thermal coupling conditions, providing reliable deformation compensation information for array SAR imaging.

[0009] To achieve the above objectives, the present invention provides the following technical solution:

[0010] A force-thermal coupling deformation measurement method for airborne array SAR includes the following steps:

[0011] Step 1: Layout of FBG strain sensor and temperature sensor:

[0012] An FBG strain sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG strain sensors for each cross-sectional structure are located at points A and B, respectively. The bending strain of the wing around the neutral axis at points A and B is obtained. An FBG temperature sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG temperature sensors for each cross-sectional structure are located at points A and B, respectively. The temperature T at the upper and lower surfaces of the wing is obtained. A ,T B ;

[0013] Step 2: Solve for bending deformation:

[0014] A combination of temperature compensation and upper / lower differential methods is used to decouple the strain data measured by the FBG strain sensor, obtaining discrete strain data Δε. A continuous force-induced strain function ε(l) is then obtained through quadratic polynomial fitting. This function is substituted into a bending deformation measurement model based on the piecewise circular arc assumption to obtain the high-precision bending deformation ε. b (l);

[0015] Step 3: Solve for axial thermal displacement:

[0016] Temperature data T measured using an FBG temperature sensor A ,T B To solve for the temperature difference ΔT between the upper and lower surfaces of the wing, spline interpolation is performed on the discrete temperature difference data to obtain the continuous temperature difference function T(l). Then, the axial thermal displacement Δε of the wing is calculated based on the principle of thermal expansion. r ;

[0017] Step 4: Establish a force-thermal coupling deformation measurement model for the wing:

[0018] For bending deformation ε b (l) After one integration, it is linearly superimposed with the initial angle function η(l) to obtain the bending angle function Δθ(l); the wing is divided into n segments with different radii. According to the bending deformation principle with constant wing length, the bending angle function Δθ(l) and the thermal axial displacement Δε r The axial displacement function Δx for each segment is obtained. i i = 1, 2, L, n; according to the axial displacement function Δx i Similarly, the deflection function Δz for the i-th segment is obtained. i By adding up the displacement deformations of each segment, the wing displacement deformation functions Δx(l) and Δz(l) in the measurement coordinate system (O; x, y, z) can be obtained, thus realizing the force-thermal coupling deformation measurement.

[0019] Furthermore, the specific process of step one is as follows:

[0020] In the measurement coordinate system (x, y, z), two strings of FBG strain sensors are attached at points A and B on a cross-section of the wing. The straight line AB is perpendicular to the neutral axis, and the length of AB is c(l). Because the aircraft wing has a cantilever beam-like structure, the strain at the root is large and changes drastically. Therefore, the FBG strain sensors are densely attached at the wing root and sparsely attached at the wingtip. Two strings of FBG temperature sensors are also attached at points A and B on a cross-section of the wing. They are arranged according to the principle of equidistant spacing to ensure that each temperature sensor is placed at a location with drastic temperature changes.

[0021] Furthermore, the specific process of step two is as follows:

[0022] The FBG strain sensor is a narrowband reflective low-pass filter with a center wavelength of:

[0023] λ B =2n eff Λ

[0024] In the formula, n eff Λ represents the effective refractive index of the fiber core; Λ represents the grating spacing that varies with strain and temperature.

[0025] Under stress-free conditions, the Bragg wavelength shift of a fiber Bragg grating is expressed by the following equation:

[0026] Δλ B,T / λ B =ΔΛ / Λ+Δn eff / n eff

[0027] In the formula, α and ξ represent the coefficient of thermal expansion and the thermo-optical coefficient, respectively, and the temperature sensitivity coefficient is expressed as:

[0028] K T =Δλ B,T / ΔT=λ B The center wavelength Δλ of the (α+ξ)FBG strain sensor B Simultaneously subjected to strain ε M Influenced by temperature drift ΔT, strain ε M As shown below:

[0029]

[0030] In the formula, K ε K is the strain sensitivity coefficient. T This refers to the temperature sensitivity coefficient.

[0031] The strains measured by the FBG sensor at points A and B are as follows:

[0032]

[0033] In the formula, These are the strains produced by bending around the neutral axis at points A and B, respectively; ε z ε is the strain produced by bending perpendicular to the neutral axis; T This is the strain caused by temperature drift;

[0034] The strain due to the mixture of calculation errors is specifically represented as follows:

[0035]

[0036] The method employs upper and lower differential temperature compensation. Local compensation is performed at the nearest measurement point using a reference grating, followed by temperature compensation based on the upper and lower differential principle. The corresponding strain change is expressed as:

[0037] 2Δε=[Δλ A / λ A -Δλ B / λ B -K C / K T (Δλ A,T / λ A,T -Δλ B,T / λ B,T )] / K ε

[0038] In the formula, K C Δλ represents the temperature sensitivity coefficient of the reference grating. A and Δλ B Δλ represents the change in the center wavelength of the strain sensors on the upper and lower surfaces, respectively. A,T and Δλ B,T These represent the changes in the center wavelength of the upper and lower surface temperature sensors, respectively.

[0039] Furthermore, the strain ε of each section is first fitted using the least squares method, and then a quadratic polynomial is used as the bending strain fitting curve.

[0040] Furthermore, the bending strain fitting curve is specifically represented by a quadratic polynomial:

[0041] ε b (l)=a2l 2 +a1l 1 +a0

[0042] In the formula, a0, a1, and a2 are the coefficients obtained from the fitting.

[0043] Furthermore, the specific process of step three is as follows:

[0044] In the measurement coordinate system (x, y, z), FBG temperature sensors are attached at points A and B on a certain cross section of the wing. The straight line AB is perpendicular to the neutral axis, and the length of AB is c(l). Based on the placement of the temperature sensors, the temperature difference between the upper and lower surfaces of the wing can be calculated. A continuous temperature function is obtained by spline interpolation fitting, and the specific formula is as follows:

[0045] S(x)=S i (x) x∈[x i ,x i+1 ]

[0046] in

[0047] S i(x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 .

[0048] Furthermore, in step three, based on the principle of thermal expansion, the axial thermal displacement of the wing is expressed as:

[0049] Δl r =l0αΔT

[0050] In the formula, Δl r ΔT is the thermal displacement, α is the coefficient of thermal expansion, and ΔT is the temperature change.

[0051] By solving the axial displacement Δε caused by local temperature changes r The axial thermal displacement can then be obtained by integrating along the wing length direction:

[0052]

[0053] In the formula, The temperature gradient is represented as:

[0054] Furthermore, in step four, the formula for calculating the wing's bending angle function Δθ(l) is as follows:

[0055]

[0056] Furthermore, in step four, the wing is divided into n segments with different radii, and the axial displacement function Δx of the i-th segment is... i Represented as:

[0057] Δx i =ν / [1-cos(Δθ) i -Δθ i-1 )]sinΔθ i-1 +[Δl z -ν / sin(Δθ i -Δθ i-1 )]cosΔθ i-1 +Δl z sinΔθ i-1 tan(Δθ i-1 / 2)

[0058] In the formula, Δl z ν represents the sum of the deformation caused by external force and the deformation caused by thermal force; ν represents the ratio of the length of the wing element to the change in its angle, expressed as: v = Δl z / (Δθ i -Δθ i-1 );

[0059] Based on the obtained Δx i The deflection function Δz of the i-th segment i for:

[0060] Δz i =(Δl) z -Δx i )tanΔθ i-1 +[1-cos(Δθ i -Δθ i-1 )] / νcosΔθ i-1

[0061] By superimposing the displacement and deformation of each wing micro-element, the wing displacement and deformation represented in the measurement coordinate system can be obtained.

[0062] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0063] This invention provides a force-thermal coupling deformation measurement method for airborne array SAR. By improving the strain decoupling method, it eliminates thermal deformation errors caused by temperature gradients. It establishes separate models for bending deformation and axial thermal displacement, enabling the calculation of both and reducing measurement errors caused by neglecting thermal deformation. A force-thermal coupling deformation measurement model based on the piecewise circular arc assumption and the principle of thermal expansion is established. By inputting the lengths of each measurement point, the axial displacement, longitudinal displacement, and rotation angle of the wing in the measurement coordinate system can be obtained. This method effectively improves the deformation measurement accuracy of the wing under force-thermal coupling conditions, reduces measurement errors caused by spatial temperature gradients when measuring force-thermal coupling deformation, and improves the deformation measurement accuracy of the sensor array under force-thermal coupling conditions. The overall design of this measurement method is scientifically sound, safe, reliable, and suitable for widespread application. Attached Figure Description

[0064] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in this invention. For those skilled in the art, other drawings can be obtained based on these drawings.

[0065] Figure 1 This is a flowchart of a force-thermal coupling deformation measurement method for airborne array SAR provided in an embodiment of the present invention.

[0066] Figure 2 This is a schematic diagram of the array SAR wing sensor arrangement provided in an embodiment of the present invention.

[0067] Figure 3This is a schematic diagram of the i-th wing segment provided in an embodiment of the present invention. Detailed Implementation

[0068] To better understand this technical solution, the method of the present invention will be described in detail below with reference to the accompanying drawings.

[0069] This invention provides a force-thermal coupling deformation measurement method for airborne array SAR, such as... Figure 1-3 As shown, it includes the following steps:

[0070] Step 1: Layout of FBG strain sensor and temperature sensor.

[0071] An FBG strain sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG strain sensors for each cross-sectional structure are located at points A and B, respectively. The bending strain of the wing around the neutral axis at points A and B is obtained. An FBG temperature sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG temperature sensors for each cross-sectional structure are located at points A and B, respectively. The temperature T at the upper and lower surfaces of the wing is obtained. A ,T B ;

[0072] Step 2: Solve for bending deformation.

[0073] A combination of temperature compensation and upper / lower differential methods is used to decouple the strain data measured by the FBG strain sensor, obtaining discrete strain data Δε. A continuous force-induced strain function ε(l) is then obtained through quadratic polynomial fitting. This function is substituted into a bending deformation measurement model based on the piecewise circular arc assumption to obtain the high-precision bending deformation ε. b (l);

[0074] Step 3: Solve for the axial thermal displacement.

[0075] Temperature data T measured using an FBG temperature sensor A ,T B To solve for the temperature difference ΔT between the upper and lower surfaces of the wing, spline interpolation is performed on the discrete temperature difference data to obtain the continuous temperature difference function T(l). Then, the axial thermal displacement Δε of the wing is calculated based on the principle of thermal expansion. r ;

[0076] Step 4: Establish a force-thermal coupling deformation measurement model for the wing.

[0077] For bending deformation ε b(l) After one integration, it is linearly superimposed with the initial angle function η(l) to obtain the bending angle function Δθ(l); the wing is divided into n segments with different radii. According to the bending deformation principle with constant wing length, the bending angle function Δθ(l) and the thermal axial displacement Δε r The axial displacement function Δx for each segment is obtained. i i = 1, 2, L, n; according to the axial displacement function Δx i Similarly, the deflection function Δz for the i-th segment is obtained. i By adding up the displacement deformations of each segment, the wing displacement deformation functions Δx(l) and Δz(l) in the measurement coordinate system (O; x, y, z) can be obtained, thus realizing the force-thermal coupling deformation measurement.

[0078] To better illustrate the design principles of this invention, specific operational embodiments are provided below:

[0079] Example 1

[0080] A force-thermal coupling deformation measurement method for airborne array SAR includes:

[0081] Step 1: Layout of FBG strain sensor and temperature sensor.

[0082] An FBG strain sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG strain sensors for each cross-sectional structure are located at points A and B, respectively. The bending strain of the wing around the neutral axis at points A and B is obtained. An FBG temperature sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG temperature sensors for each cross-sectional structure are located at points A and B, respectively. The temperature T at the upper and lower surfaces of the wing is obtained. A ,T B .

[0083] The specific steps are as follows:

[0084] In the measurement coordinate system (x,y,z), Figure 2 FBG strain sensors are attached to points A and B on a cross section of the wing. The straight line AB is perpendicular to the neutral axis and the length of AB is c(l).

[0085] As an example, because aircraft wings have a cantilever beam-like structure, the strain at the root is large and changes drastically. Therefore, FBG strain sensors are densely attached at the wing root and sparsely attached at the wingtip. Two strings of FBG temperature sensors are attached at points A and B on a certain cross-section of the wing, arranged according to the principle of equidistance to ensure that each temperature sensor is placed at a location with drastic temperature changes.

[0086] Step 2: Solve for bending deformation.

[0087] A combination of temperature compensation and upper / lower differential methods is used to decouple the strain data measured by the FBG strain sensor, obtaining discrete strain data Δε. A continuous force-induced strain function ε(l) is then obtained through quadratic polynomial fitting. This function is substituted into a bending deformation measurement model based on the piecewise circular arc assumption to obtain the high-precision bending deformation ε. b (l);

[0088] The specific steps are as follows:

[0089] The FBG strain sensor is a narrowband reflective low-pass filter with a center wavelength of:

[0090] λ B =2n eff Λ (1)

[0091] In the formula, n eff Λ represents the effective refractive index of the fiber core; Λ represents the grating spacing that varies with strain and temperature.

[0092] Therefore, the center wavelength Δλ of the FBG strain sensor B Simultaneously subjected to strain ε M The influence of temperature drift ΔT, and strain ε M As shown below:

[0093]

[0094] In the formula, K ε K is the strain sensitivity coefficient. T This refers to the temperature sensitivity coefficient.

[0095] As an example, the strains measured by the FBG sensor at points A and B are as follows:

[0096]

[0097] In the formula, These are the strains produced by bending around the neutral axis at points A and B, respectively; ε z ε is the strain produced by bending perpendicular to the neutral axis; T The strain is caused by temperature drift; subtracting equation (4) from equation (3) yields the calculated strain due to error mixing, as shown below:

[0098]

[0099] The method employs upper and lower differential temperature compensation. Local compensation is performed at the nearest measurement point using a reference grating, followed by temperature compensation based on the upper and lower differential principle. The corresponding strain change is expressed as:

[0100] 2Δε=[Δλ A / λA -Δλ B / λ B -K C / K T (Δλ A,T / λ A,T -Δλ B,T / λ B,T )] / K ε (6)

[0101] In the formula, K C Δλ represents the temperature sensitivity coefficient of the reference grating. A and Δλ B Δλ represents the change in the center wavelength of the strain sensors on the upper and lower surfaces, respectively. A,T and Δλ B,T These represent the changes in the center wavelength of the upper and lower surface temperature sensors, respectively.

[0102] As an example, in order to minimize errors, the least squares method is used for data fitting, and to make it more consistent with the law of strain change, a quadratic polynomial is used as the bending strain fitting curve.

[0103] Using a quadratic polynomial as the bending strain fitting function can achieve higher accuracy, specifically expressed as:

[0104] ε b (l)=a2l 2 +a1l 1 +a0 (7)

[0105] In the formula, a0, a1, and a2 are the coefficients obtained from the fitting.

[0106] Step 3: Solve for the axial thermal displacement.

[0107] Temperature data T measured using an FBG temperature sensor A ,T B To solve for the temperature difference ΔT between the upper and lower surfaces of the wing, spline interpolation is performed on the discrete temperature difference data to obtain the continuous temperature difference function T(l). Then, the axial thermal displacement Δε of the wing is calculated based on the principle of thermal expansion. r ;

[0108] An FBG temperature sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG temperature sensors for each cross-sectional structure are located at points A and B, respectively. The temperatures T on the upper and lower surfaces of the wing are then obtained. A ,T B Subtracting the two values ​​yields the temperature difference ΔT between the upper and lower surfaces of the wing. Using spline interpolation, a continuous temperature function T(l) is obtained. Then, based on the principle of thermal expansion, the axial thermal displacement Δε of the wing can be calculated. r ;

[0109] The specific steps are as follows:

[0110] In the measurement coordinate system (x,y,z), Figure 2 FBG temperature sensors are attached to points A and B on a cross-section of the wing. The straight line AB is perpendicular to the neutral axis, and the length of AB is c(l). The temperature difference between the upper and lower surfaces of the wing can be obtained by subtracting the temperature data measured at points A and B on the cross-section of the wing.

[0111] As an example, spline interpolation is used to fit the discrete temperature difference data of the upper and lower surfaces of the wing to obtain the continuous temperature function ΔT(l). The specific representation of the temperature fitting curve using spline interpolation is as follows:

[0112] S(x)=S i (x) x∈[x i ,x i+1 (8)

[0113] in

[0114] S i (x)=a i +b i (xx i )+c i (xx i ) 2 +d i (xx i ) 3 (9)

[0115] As an example, based on the fundamental theory of thermoelasticity and the principle of thermal expansion, the mechanical behavior of an airfoil under localized temperature changes can be described by the thermal displacement as follows:

[0116] Δl r =l0αΔT (10)

[0117] In the formula, Δl r ΔT represents the thermal deformation, α represents the coefficient of thermal expansion, and ΔT represents the temperature change.

[0118] Experimental airfoils typically have a large aspect ratio, and thermal stress deformation mainly considers the axial displacement of the airfoil, as well as the component of vertical expansion after bending. This is addressed by solving for the axial displacement Δε caused by local temperature changes. r The axial thermal displacement can be obtained by integrating along the wing length direction.

[0119]

[0120] In the formula, The temperature gradient can be expressed as:

[0121] Step 4: Establish a force-thermal coupling deformation measurement model for the wing.

[0122] For bending deformation ε b (l) After one integration, it is linearly superimposed with the initial angle function η(l) to obtain the bending angle function Δθ(l); the wing is divided into n segments with different radii. According to the bending deformation principle with constant wing length, the bending angle function Δθ(l) and the thermal axial displacement Δε r The axial displacement function Δx for each segment is obtained. i i = 1, 2, L, n; according to the axial displacement function Δx i Similarly, the deflection function Δz for the i-th segment is obtained. i By adding up the displacement deformations of each segment, the wing displacement deformation functions Δx(l) and Δz(l) in the measurement coordinate system (O; x, y, z) can be obtained, thus realizing the force-thermal coupling deformation measurement.

[0123] As an example, the calculation of the beam plane bending rotation function Δθ(l);

[0124] Based on the initial angle function and the bending strain function, the bending angle function of the wing can be given by the following formula:

[0125]

[0126] As an example, the calculation of the axial displacement function Δx(l) and deflection function Δz(l) of a beam under planar bending deformation is as follows:

[0127] like Figure 3 As shown, to achieve displacement deformation measurement, the wing is divided into n segments with different radii. Based on the bending deformation principle with constant wing length, the axial displacement of the wing can be obtained through geometric relationships. The force-induced deformation and the thermal axial displacement elements are linearly superimposed, and the axial displacement function Δx of the i-th segment is obtained. i It can be represented as:

[0128]

[0129] In the formula, Δl z ν represents the sum of deformation caused by external force and thermal deformation; ν represents the ratio of the change in length of the wing element to the change in its angle, which can be expressed as v = Δl. z / (Δθ i -Δθ i-1 Similarly, based on the obtained Δx i The deflection function Δz of the i-th segment can be obtained. i for:

[0130] Δz i =(Δl) z -Δx i )tanΔθi-1 +[1-cos(Δθ i -Δθ i-1 )] / νcosΔθ i-1 (14)

[0131] By superimposing the displacement and deformation of each wing micro-element, the wing displacement and deformation represented in the measurement coordinate system can be obtained.

[0132] In summary, the force-thermal coupling deformation measurement method for airborne array SAR provided by this invention firstly involves symmetrically attaching fiber optic strain sensors and temperature sensors to the upper and lower surfaces of an airfoil to measure the surface strain and temperature. Strain decoupling is achieved based on temperature compensation and upper / lower surface differential to obtain discrete strain data. A continuous force-induced strain function is obtained through quadratic polynomial fitting and substituted into a bending deformation measurement model based on the piecewise circular arc assumption to obtain high-precision bending deformation. Secondly, the temperature difference between the upper and lower surfaces of the airfoil is calculated based on the temperature sensors. A continuous temperature difference function is obtained through spline interpolation and substituted into the axial thermal expansion deformation measurement model to obtain the axial thermal displacement. Finally, a force-thermal coupling deformation measurement model for the airfoil is established based on the force-induced bending deformation and axial thermal displacement. By inputting the lengths of each measuring point, the axial displacement, longitudinal displacement, and rotation angle of the airfoil in the measurement coordinate system can be obtained. This method can improve the deformation measurement accuracy of the airfoil under force-thermal coupling conditions, providing accurate deformation information for array SAR.

[0133] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. However, these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring deformation by force-thermal coupling in airborne array SAR, characterized in that, Includes the following steps: Step 1: Layout of FBG strain sensor and temperature sensor: An FBG strain sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG strain sensors for each cross-sectional structure are located at points A and B, respectively. The bending strain of the wing around the neutral axis at points A and B is obtained. An FBG temperature sensor is attached to the upper and lower surfaces of each cross-sectional structure of the wing. The two FBG temperature sensors for each cross-sectional structure are located at points A and B, respectively. The temperature T at the upper and lower surfaces of the wing is obtained. A ,T B ; Step 2: Solve for bending deformation: A combination of temperature compensation and upper / lower differential methods is used to decouple the strain data measured by the FBG strain sensor, obtaining discrete strain data Δε. A continuous force-induced strain function ε(l) is then obtained through quadratic polynomial fitting. This function is substituted into a bending deformation measurement model based on the piecewise circular arc assumption to obtain the high-precision bending deformation ε. b (l); Step 3: Solve for axial thermal displacement: Temperature data T measured using an FBG temperature sensor A ,T B To solve for the temperature difference ΔT between the upper and lower surfaces of the wing, spline interpolation is performed on the discrete temperature difference data to obtain the continuous temperature difference function T(l). Then, the axial thermal displacement Δε of the wing is calculated based on the principle of thermal expansion. r ; Step 4: Establish a force-thermal coupling deformation measurement model for the wing: For bending deformation ε b (l) After one integration, it is linearly superimposed with the initial angle function η(l) to obtain the bending angle function Δθ(l); the wing is divided into n segments with different radii. According to the bending deformation principle with constant wing length, the bending angle function Δθ(l) and the thermal axial displacement Δε r The axial displacement function Δx for each segment is obtained. i i = 1, 2, L, n; according to the axial displacement function Δx i Similarly, the deflection function Δz for the i-th segment is obtained. i By adding up the displacement deformations of each segment, the wing displacement deformation functions Δx(l) and Δz(l) in the measurement coordinate system (O; x, y, z) can be obtained, thus realizing the force-thermal coupling deformation measurement.

2. The method for measuring force-thermal coupling deformation for airborne array SAR according to claim 1, characterized in that, The specific process of step one is as follows: In the measurement coordinate system (x, y, z), two strings of FBG strain sensors are attached at points A and B on a cross-section of the wing. The straight line AB is perpendicular to the neutral axis, and the length of AB is c(l). Because the aircraft wing has a cantilever beam-like structure, the strain at the root is large and changes drastically. Therefore, the FBG strain sensors are densely attached at the wing root and sparsely attached at the wingtip. Two strings of FBG temperature sensors are also attached at points A and B on a cross-section of the wing. They are arranged according to the principle of equidistant spacing to ensure that each temperature sensor is placed at a location with drastic temperature changes.

3. The method for measuring force-thermal coupling deformation for airborne array SAR according to claim 1, characterized in that, The specific process of step two is as follows: The FBG strain sensor is a narrowband reflective low-pass filter with a center wavelength of: l B =2n eff L In the formula, n eff Λ represents the effective refractive index of the fiber core; Λ represents the grating spacing that varies with strain and temperature. Under stress-free conditions, the Bragg wavelength shift of a fiber Bragg grating is expressed by the following equation: Dl B,T / l B =ΔΛ / Λ+Δn eff / n eff In the formula, α and ξ represent the coefficient of thermal expansion and the thermo-optical coefficient, respectively, and the temperature sensitivity coefficient is expressed as: K T =Δλ B,T / ΔT=λ B The center wavelength Δλ of the (α+ξ)FBG strain sensor B Simultaneously subjected to strain ε M Influenced by temperature drift ΔT, strain ε M As shown below: In the formula, K ε K is the strain sensitivity coefficient; T This refers to the temperature sensitivity coefficient. The strains measured by the FBG sensor at points A and B are as follows: In the formula, These are the strains produced by bending around the neutral axis at points A and B, respectively; ε z ε is the strain produced by bending perpendicular to the neutral axis; T This is the strain caused by temperature drift; The strain due to the mixture of calculation errors is specifically represented as follows: The method employs upper and lower differential temperature compensation. Local compensation is performed at the nearest measurement point using a reference grating, followed by temperature compensation based on the upper and lower differential principle. The corresponding strain change is expressed as: 2D=[Dl A / l A -Dl B / l B -K C / K T (Dl A,T / l A,T -Dl B,T / l B,T )] / K ε In the formula, K C Δλ represents the temperature sensitivity coefficient of the reference grating. A and Δλ B Δλ represents the change in the center wavelength of the strain sensors on the upper and lower surfaces, respectively. A,T and Δλ B,T These represent the changes in the center wavelength of the upper and lower surface temperature sensors, respectively.

4. The method for measuring force-thermal coupling deformation for airborne array SAR according to claim 3, characterized in that, The strain ε of each section is first fitted using the least squares method, and then a quadratic polynomial is used as the bending strain fitting curve.

5. The force-thermal coupling deformation measurement method for airborne array SAR according to claim 4, characterized in that, The bending strain fitting curve is specifically represented by a quadratic polynomial: ε b (l)=a2l 2 +a1l 1 +a0 In the formula, a0, a1, and a2 are the coefficients obtained from the fitting.

6. The force-thermal coupling deformation measurement method for airborne array SAR according to claim 1, characterized in that, The specific process of step three is as follows: In the measurement coordinate system (x, y, z), FBG temperature sensors are attached at points A and B on a certain cross section of the wing. The straight line AB is perpendicular to the neutral axis, and the length of AB is c(l). Based on the placement of the temperature sensors, the temperature difference between the upper and lower surfaces of the wing can be calculated. A continuous temperature function is obtained by spline interpolation fitting, and the specific formula is as follows: S(x)=S i (x)x∈[x i ,x i+1 ] in S i (x)=a i +b i (x-x i )+c i (x-x i ) 2 +d i (x-x i ) 3 。 7. The method for measuring force-thermal coupling deformation for airborne array SAR according to claim 1, characterized in that, In step three, based on the principle of thermal expansion, the axial thermal displacement of the wing is expressed as: Δl r =l0αΔT In the formula, Δl r ΔT is the thermal displacement, α is the coefficient of thermal expansion, and ΔT is the temperature change. By solving the axial displacement Δε caused by local temperature changes r The axial thermal displacement can then be obtained by integrating along the wing length direction: In the formula, The temperature gradient is represented as:

8. The method for measuring force-thermal coupling deformation for airborne array SAR according to claim 1, characterized in that, In step four, the formula for calculating the wing's bending angle function Δθ(l) is as follows:

9. The method for measuring force-thermal coupling deformation for airborne array SAR according to claim 1, characterized in that, In step four, the wing is divided into n segments with different radii. The axial displacement function of the i-th segment is Δx. i Represented as: Δx i =ν / [1-cos(Δθ i -Dth i-1 )]sinΔθ i-1 +[Δl z -ν / sin(Δθ i -Dth i-1 )]cosΔθ i-1 +Δl z sinΔθ i-1 tan(Δθ i-1 / 2) In the formula, Δl z ν represents the sum of the deformation caused by external force and the deformation caused by thermal force; ν represents the ratio of the length of the wing element to the change in its angle, expressed as: v = Δl z / (Δθ i -Δθ i-1 ) Based on the obtained Δx i The deflection function Δz of the i-th segment i for: Δz i =(Δl z -Dx i )tanΔθ i-1 +[1-cos(Δθ i -Dth i-1 )] / νcosΔθ i-1 By superimposing the displacement and deformation of each wing micro-element, the wing displacement and deformation represented in the measurement coordinate system can be obtained.

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