Flame ablation test platform and verification method for trailing cable under static and dynamic loads

Abstract

The invention provides a flame ablation test platform and verification method for a towing cable under static and dynamic loads, and relates to the technical field of cables, the flame ablation test platform comprises an ablation device, a tension tester, a temperature sensing system, a light source, an optical power meter, a resistance tester and a stress-strain monitoring device, the ablation device is used for jetting flame to the towing cable; the towing cable is wound on the tension testing machine, and the tension testing machine provides required static and dynamic working loads; a probe of the temperature sensing system is in contact with the surface of the towrope and a core part, and is used for monitoring the flame temperature in real time, feeding back the flame temperature to the ablation device for dynamic adjustment and synchronously providing monitoring data; according to the invention, a stress and temperature field composite simulation technology is combined, ablation resistance test and correction under static and dynamic stretching are realized, and comprehensive analysis and monitoring verification, supporting structure optimization and application verification of the towing cable under a comprehensive state of flame ablation and static and dynamic loads are realized.

Description

Technical Field

[0001] The present invention relates to the field of cable technology, and in particular to a flame ablation test platform and a verification method for a towing cable under static and dynamic loads. Background Art

[0002] Composite towing cables can be widely used in aviation, ships, etc. to provide optical signals and power transmission for devices near the engine. They also need to withstand the instantaneous impact force, static and dynamic loads and other comprehensive stresses during towing. When released, they need to withstand static or dynamic loads of more than 6000N under composite working conditions such as high temperature ablation at 1000℃. At the same time, the strain under working load and high temperature is controlled within 1%;

[0003] According to the above requirements, it is necessary to conduct adaptability verification for the actual application conditions of the tow cable to ensure the stability of its photoelectric transmission under high load, high and low temperature, and flame ablation. However, there is currently no relevant comprehensive design and verification means. Therefore, the present invention proposes a flame ablation test platform and verification method for a tow cable under static and dynamic loads to solve the problems existing in the prior art. Summary of the invention

[0004] In view of the above problems, the present invention proposes a flame ablation test platform and verification method for towing cables under static and dynamic loads, combines stress and temperature field composite simulation technology to realize ablation resistance testing and correction under static and dynamic tension, and realizes comprehensive analysis and monitoring verification of towing cable strain and temperature field under the comprehensive conditions of flame ablation and static and dynamic loads, as well as support structure optimization and application verification.

[0005] To achieve the purpose of the present invention, the present invention is implemented through the following technical solutions: a flame ablation test platform under static and dynamic loads of a towing cable, comprising an ablation device, a tensile testing machine, a temperature sensing system, a light source, an optical power meter, a resistance tester and a stress-strain monitoring device, wherein the ablation device is used to spray flames to the towing cable; the towing cable is wound on the tensile testing machine, and the tensile testing machine provides the required static and dynamic working loads; the probe of the temperature sensing system contacts the surface and core components of the towing cable, and is used to monitor the flame temperature in real time and feed it back to the ablation device for dynamic adjustment, and simultaneously provide monitoring data;

[0006] The light source is used to connect to the optical unit at one end of the streamer to provide an excitation light source; the optical power meter is used to connect to the optical unit at the other end of the streamer to test the change of optical performance; the resistance tester is used to monitor the electrical performance change data of the streamer; the stress strain monitoring device is used to monitor the optical fiber strain in the streamer.

[0007] A further improvement is that the tensile testing machine is static or dynamic.

[0008] A further improvement is that the resistance tester includes a DC resistance tester and an insulation resistance tester, and the DC resistance tester and the insulation resistance tester are used to monitor the electrical performance change data of the DC resistance and insulation resistance of the tow cable.

[0009] A method for verifying flame erosion of a towing cable under static and dynamic loads comprises the following steps:

[0010] The three-dimensional temperature field of the towed cable is reconstructed by decoupling the mixed signal of strain and temperature under dynamic airborne conditions, dividing the node elements of the flexible towed cable structure, and using the three-dimensional thermal conduction differential equation and finite element method.

[0011] Based on the core part of the tow cable, the strain and temperature are measured, and the structural strain distribution and temperature field distribution are inversely calculated through simulation and analytical method of axial thermal deformation of thin-walled circular tubes;

[0012] According to the algorithm and discrete data, the strain difference and temperature difference are calculated back and used as the added value of the simulation strain difference and temperature difference to compare and analyze the results;

[0013] According to the inverse finite element principle, a structure-oriented adaptive function matrix is ​​constructed to solve the unit strain vector, thereby inverting the strain distribution characteristics of the towed cable structure.

[0014] According to the strain distribution characteristics of the towline, auxiliary identification of the towline tension is carried out.

[0015] Further improvement is: oriented to the node unit division of the flexible tow cable structure, including the following steps:

[0016] The tow cable section is divided into 8-node arc segment units, and the unit node coordinates are assumed to satisfy the following formula:

[0017] r A =r B =r C =r D = r1 r E =r F =r G =r H =r2

[0018]

[0019] h C =h D =h G =h H =h1 h A =h B =h E =h F =h2

[0020]

[0021] The mesh tangent vector τ and the unit distance vector d are perpendicular to each other, that is, τ·d=0. The diffusion term of the heat conduction equation between arc segment units of the same size meets the temperature field inversion conditions of conventional units. The unit surface sizes of arc segment units in various directions are different, and the unit area calculation expression is:

[0022]

[0023] Wherein, Ah-1 represents the unit surface area of ​​the arc unit at height h1, Ah+1 represents the unit surface area of ​​the arc unit at height h2, Ar-1 represents the unit surface area of ​​the arc unit at radius r1, Ar+1 represents the unit surface area of ​​the arc unit at radius r2, Indicates the arc unit at an angle The unit surface area at Indicates the arc unit at an angle The unit surface area at .

[0024] Further improvements are: based on the three-dimensional heat conduction differential equation and finite element, the three-dimensional temperature field reconstruction of the towline is realized, including the following steps:

[0025] Substituting the area calculation formula of formula (1-2) into the conventional volume unit temperature field inversion equation and simplifying it, we can get:

[0026]

[0027] Where k is the thermal conductivity of the structural material, n is the unit external normal vector of the control volume unit boundary, is the temperature gradient, Te is the center temperature of the structural unit body, Ti is the center temperature of the unit body adjacent to the i-th surface of the unit body, is the temperature gradient on the i-th surface of the unit cell;

[0028] Simplify equation (1-3) and let the arc segment unit of the structure division be calculated. The temperature field reconstruction calculation formula based on the arc segment unit division structure can be obtained:

[0029]

[0030] Further improvement is: inverse calculation of temperature field distribution, including the following steps:

[0031] Let the radius corresponding to the unit center point be r e , knowing Δr=1, then r1=r e -0.5, r2 = r e +0.5, and then from formula (1-4) we know the unit center temperature T eThe temperature value of is only related to the radius information of the structural unit, and it can be seen from formula (1-2) that A h-1 =A h+1 , That is, the heat of the arc segment unit is non-uniformly distributed along the radius r;

[0032] The heat transfer problem in the radial direction of the arc segment unit is converted into a one-dimensional linear problem, and equation (1-4) is processed. The temperature relationship in the radial direction is known to be r1+r2=2r e ,get:

[0033] r1(T r-1 -T e )+r2(T r+1 -T e )=0(1-5);

[0034] Based on r2-r e =r e -r1, and then according to formula (1-5), we get:

[0035]

[0036] Assume T = f(r), then we get its first-order derivative form:

[0037]

[0038] Assume that the inner and outer radii of the arc segment structure are r min 、r max , in a certain radial direction r min 、r max The corresponding temperature value is T min , T max , it is known that T m1 =f(r min ), T m2 =f(r max ), combined with formula (1-7), the expression of T = f (r) is:

[0039]

[0040] It is known that each node of the arc unit satisfies the relationship (1-1). Combining the relationship (1-8), we can get the value of any position in the internal space of the arc unit. Temperature of point The calculation formula is:

[0041]

[0042] The expressions corresponding to T1 and T2 in formula (1-9) are:

[0043] T1=N AT A +N B T B +N C T C +N D T D

[0044] T2=N E T E +N F T F +N G T G +N H T H (1-10);

[0045] Where TA~TH are the temperature values ​​corresponding to the unit nodes A~H, and the expressions of the coefficients in formula (1-10) are:

[0046]

[0047] Substitute the coefficients calculated by formula (1-11) into formula (1-10), and combine with formula (1-9) to obtain the coefficients at any position in the unit grid: Temperature value at

[0048] Each arc segment unit is assembled to form a volume unit model for the streamer, and the temperature field inversion method inside each unit is combined to realize the global measurement of the streamer temperature field inversion.

[0049] The beneficial effects of the present invention are:

[0050] 1. The present invention combines stress and temperature field composite simulation technology to realize ablation resistance testing and correction under static and dynamic tension, and realizes the comprehensive analysis and monitoring verification of tow cable strain and temperature field under the comprehensive state of flame ablation, static and dynamic load, as well as the optimization and application verification of supporting structure.

[0051] 2. The present invention builds a flame ablation test platform for towing cables under static and dynamic loads, realizes the verification of the tensile properties and temperature resistance adaptability of the towing cables, tests the stability of their photoelectric transmission under static and dynamic loads and flame ablation, and solves the problems of ablation resistance testing under static and dynamic tension, and monitoring of optical fiber strain and temperature field distribution in structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a front view of the platform of the present invention;

[0053] Figure 2 A schematic diagram of the arc segment unit form and unit grid node setting of the present invention;

[0054] Figure 3Schematic diagram of adjacent nodes of the present invention.

[0055] Among them: 1. Ablation device; 2. Tensile testing machine; 3. Temperature sensing system; 4. Light source; 5. Optical power meter; 6. Resistance tester; 7. Stress and strain monitoring equipment; 8. Tow cable. DETAILED DESCRIPTION

[0056] In order to deepen the understanding of the present invention, the present invention will be further described in detail below in conjunction with examples. The examples are only used to explain the present invention and do not constitute a limitation on the protection scope of the present invention.

[0057] Embodiment 1

[0058] according to Figure 1 As shown, this embodiment proposes a flame ablation test platform under static and dynamic loads of a towing cable, including an ablation device 1, a tensile testing machine 2, a temperature sensing system 3, a light source 4, an optical power meter 5, a resistance tester 6 and a stress and strain monitoring device 7. The ablation device 1 is used to spray flames to the towing cable 8; the towing cable 8 is wound on the tensile testing machine 2, and the tensile testing machine 2 provides the required static and dynamic working loads; the probe of the temperature sensing system 3 is in contact with the surface and core components of the towing cable 8, and is used to monitor the flame temperature in real time and feed it back to the ablation device 1 for dynamic adjustment, and simultaneously provide monitoring data to provide support for subsequent temperature field distribution and three-dimensional temperature field reconstruction;

[0059] The light source 4 is used to connect with the optical unit at one end of the streamer 8 to provide an excitation light source; the optical power meter 5 is used to connect with the optical unit at the other end of the streamer 8 to test the optical performance change; the resistance tester 6 is used to monitor the electrical performance change data of the streamer 8; the stress strain monitoring device 7 is used to monitor the optical fiber strain in the streamer 8. A flame ablation test platform under static and dynamic loads of the streamer is built to verify the tensile properties and temperature resistance adaptability of the streamer, and test the stability of its photoelectric transmission under static and dynamic loads and flame ablation, solving the problems of ablation resistance test under static and dynamic tension, and monitoring the optical fiber strain and temperature field distribution in the structure.

[0060] The tensile tester 2 is static or dynamic. The resistance tester 6 includes a DC resistance tester and an insulation resistance tester, and the DC resistance tester and the insulation resistance tester are used to monitor the electrical performance change data of the DC resistance and the insulation resistance of the tow cable 8.

[0061] Embodiment 2

[0062] according to Figure 1 , 2 As shown in FIG. 3 , this embodiment proposes a method for verifying flame ablation of a towing cable under static and dynamic loads, comprising the following steps:

[0063] The mixed signal decoupling of strain and temperature of fiber Bragg grating sensor under dynamic airborne is adopted, and the node unit division of flexible towed cable structure is adopted. Based on three-dimensional heat conduction differential equation and finite element, the three-dimensional temperature field reconstruction of towed cable is realized. The fiber sensor is attached to the core part of the towed cable to measure strain and temperature. Through simulation and analytical methods such as axial thermal deformation of thin-walled circular tube, the structural strain distribution and temperature field distribution are inversely calculated. In the dynamic airborne environment, the fiber Bragg grating sensor will be affected by strain and temperature at the same time, resulting in the output signal of the sensor being a mixed signal of strain and temperature. In order to accurately obtain strain and temperature information, signal decoupling is required. An effective decoupling method is to use analytical modal decomposition technology. This method first collects the mixed signal output by the fiber Bragg grating sensor, and then uses the analytical modal decomposition method to decompose the signal into multiple intrinsic mode functions. Since the strain signal caused by dynamic load usually has a faster change speed, while the signal caused by temperature change is relatively slow, the fast-changing signal can be attributed to strain, and the slow-changing signal can be attributed to temperature. Finally, through reconstruction technology, the time domain response signals of strain and temperature can be obtained respectively. The key to this method is to accurately extract and separate the fast and slow fiber Bragg grating dynamic response frequency components, namely the intrinsic mode function. Through this method, only one fiber Bragg grating sensor can be used to monitor and demodulate the strain and temperature signals separately. The flexible streamer structure also plays an important role in the dynamic airborne environment. The division of its node units is of great significance for the performance analysis and optimal design of the structure. Based on the idea of ​​finite element, the flexible streamer structure can be discretized into nodes and units. The nodes are the key points of the streamer structure, and the units are the parts connecting the nodes.

[0064] According to the algorithm and discrete data, the strain difference and temperature difference are inversely calculated as the value-added of the simulation strain difference and temperature difference, and the results are compared and analyzed. At the same time, according to the inverse finite element principle, a structure-oriented adaptive function matrix is ​​constructed to solve the unit strain vector, thereby inverting the strain distribution characteristics of the tow cable structure. On this basis, according to the strain distribution characteristics of the tow cable, the subsequent tow cable tension identification is assisted. After obtaining the temperature field distribution, the strain distribution of the cable can be further inverted. Strain difference calculation: According to the algorithm and discrete data, the strain difference is calculated as the value-added of the simulation strain difference. Inverse finite element principle: Using the inverse finite element principle, an adaptive function matrix for the structure is constructed to solve the unit strain vector. Strain distribution characteristics: According to the unit strain vector, the strain distribution characteristics of the cable structure are inverted. Assisting the subsequent cable tension identification: After obtaining the strain distribution characteristics of the cable, the subsequent cable tension identification work is assisted. This includes: Tension model establishment: According to the material properties, geometric shape, etc. of the cable, a relationship model between tension and strain is established. Tension calculation: Substitute the strain distribution characteristics obtained by inversion into the tension model to calculate the tension distribution of the cable. Result verification: Verify the accuracy of the calculation results through experiments or other methods, and continuously optimize the model and decoupling algorithm.

[0065] Specifically: Divide the cable section into 8-node arc units. The node coordinates of the arc unit and the relationship between adjacent nodes are as follows: Figure 2 , 3 As shown, assuming Figure 2 , 3 The unit node coordinate values ​​shown in satisfy the following formula:

[0066] r A =r B =r C =r D = r1 r E =r F =r G =r H =r2

[0067]

[0068] h C =h D =h G =h H =h1 h A =h B =h E =h F =h2

[0069]

[0070] Depend on Figure 3 It can be seen that the grid tangent vector τ and the unit distance vector d are perpendicular to each other, that is, τ·d=0. Therefore, the diffusion term of the heat conduction equation between arc segment units of the same size meets the temperature field inversion conditions of conventional units. The unit surface sizes of arc segment units in all directions are different, and the unit area calculation expression is:

[0071]

[0072] Where Ah-1 represents the unit surface area of ​​the arc unit at height h1, Ah+1 represents the unit surface area of ​​the arc unit at height h2, Ar-1 represents the unit surface area of ​​the arc unit at radius r1, and Ar+1 represents the unit surface area of ​​the arc unit at radius r2. Indicates the arc unit at an angle The unit surface area at Indicates the arc unit at an angle The unit surface area at .

[0073] Substituting the area calculation formula of formula (1-2) into the conventional volume unit temperature field inversion equation and simplifying it, we can get:

[0074]

[0075] Where k is the thermal conductivity of the structural material, n is the unit external normal vector of the control volume unit boundary, is the temperature gradient, Te is the center temperature of the structural unit body, Ti is the center temperature of the unit body adjacent to the i-th surface of the unit body, is the temperature gradient on the i-th surface of the unit cell.

[0076] Simplify equation (1-3) and let the arc segment unit of the structure division be calculated. The temperature field reconstruction calculation formula based on the arc segment unit division structure can be obtained:

[0077]

[0078] Assume that the radius corresponding to the unit center point is r e , knowing Δr=1, then r1=r e -0.5, r2 = r e +0.5, and then from formula (1-4) we can know the unit center temperature T e The temperature value of is only related to the radius information of the structural unit, and it can be seen from formula (1-2) that A h-1 =A h+1 , That is, the heat of the arc segment unit is non-uniformly distributed along the radius r.

[0079] The heat transfer problem in the radial direction of the arc segment unit is converted into a one-dimensional linear problem, and equation (1-4) is processed. The temperature relationship in the radial direction is known to be r1+r2=2r e , we can get:

[0080] r1(T r-1 -T e )+r2(T r+1 -T e )=0(1-5)

[0081] Considering r2+r e =r e -r1, and then according to formula (1-5), we can infer that:

[0082]

[0083] Assume T = f(r), then we can get its first-order derivative form:

[0084]

[0085] Assume that the inner and outer radii of the arc segment are r min 、r max , in a certain radial direction r min、r max The corresponding temperature value is T min , T max , it is known that T m1 =f(r min ), T m2 =f(r max ), combined with formula (1-7), we can get the expression of T = f (r):

[0086]

[0087] It is known that each node of the arc unit satisfies the relationship (1-1). Combining the relationship (1-8), we can get the value of any position in the internal space of the arc unit. Temperature of point The calculation formula is:

[0088]

[0089] The expressions corresponding to T1 and T2 in formula (1-9) are:

[0090] T1=N A T A +N B T B +N C T C +N D T D

[0091] T2=N E T E +N F T F +N G T G +N H T H (1-10)

[0092] Among them, TA~TH is Figure 2 The temperature values ​​corresponding to the unit nodes A~H. The expressions of the coefficients in formula (1-10) are:

[0093]

[0094] Substitute the coefficients calculated by formula (1-11) into formula (1-10) and combine them with formula (1-9) to obtain Temperature value at

[0095] Finally, each arc segment unit is assembled to form a volume unit model for the streamer. Combined with the temperature field inversion method inside each unit, the temperature field inversion of the streamer with approximate global measurement is realized.

[0096] The present invention combines stress and temperature field composite simulation technology to realize ablation resistance testing and correction under static and dynamic stretching, and realizes comprehensive analysis and monitoring verification of tow cable strain and temperature field under flame ablation and static and dynamic load combined conditions, as well as support structure optimization and application verification. At the same time, a flame ablation test platform under static and dynamic loads for tow cables is built to verify the tensile properties and temperature resistance adaptability of tow cables, and to test the stability of their photoelectric transmission under static and dynamic loads and flame ablation, solving the problems of ablation resistance testing under static and dynamic stretching, and monitoring of optical fiber strain and temperature field distribution in structures.

[0097] The above shows and describes the basic principles, main features and advantages of the present invention. It should be understood by those skilled in the art that the present invention is not limited to the above embodiments. The above embodiments and descriptions are only for explaining the principles of the present invention. Without departing from the spirit and scope of the present invention, the present invention may have various changes and improvements, which fall within the scope of the present invention. The scope of protection of the present invention is defined by the attached claims and their equivalents.

Claims

1. A flame ablation test platform for a towing cable under static and dynamic loads, comprising an ablation device (1), a tensile testing machine (2), a temperature sensing system (3), a light source (4), an optical power meter (5), a resistance tester (6) and a stress and strain monitoring device (7), characterized in that: The ablation device (1) is used to spray flames onto the tow cable (8); the tow cable (8) is wound around the tensile testing machine (2), and the tensile testing machine (2) provides the required static and dynamic working loads; the probe of the temperature sensing system (3) is in contact with the surface and core components of the tow cable (8), and is used to monitor the flame temperature in real time and feed it back to the ablation device (1) for dynamic adjustment, and simultaneously provide monitoring data; The light source (4) is used to connect to the optical unit at one end of the streamer (8) to provide an excitation light source; the optical power meter (5) is used to connect to the optical unit at the other end of the streamer (8) to test the change of optical performance; the resistance tester (6) is used to monitor the electrical performance change data of the streamer (8); and the stress strain monitoring device (7) is used to monitor the optical fiber strain in the streamer (8).

2. A flame ablation test platform for towing cables under static and dynamic loads according to claim 1, characterized in that: The tensile testing machine (2) is static or dynamic.

3. The flame ablation test platform for towing cables under static and dynamic loads according to claim 1, characterized in that: The resistance tester (6) comprises a DC resistance tester and an insulation resistance tester, and the DC resistance tester and the insulation resistance tester are used to monitor the electrical performance change data of the DC resistance and the insulation resistance of the tow cable (8).

4. A method for verifying flame ablation of a towing cable under static and dynamic loads, using a flame ablation test platform for towing cable under static and dynamic loads as described in any one of claims 1 to 3, characterized in that: The following steps are involved: The three-dimensional temperature field of the towed cable is reconstructed by decoupling the mixed signal of strain and temperature under dynamic airborne conditions, dividing the node elements of the flexible towed cable structure, and using the three-dimensional thermal conduction differential equation and finite element method. Based on the core part of the tow cable, the strain and temperature are measured, and the structural strain distribution and temperature field distribution are calculated through simulation and analytical method of axial thermal deformation of thin-walled circular tubes; According to the algorithm and discrete data, the strain difference and temperature difference are calculated back and used as the added value of the simulation strain difference and temperature difference to compare and analyze the results; According to the inverse finite element principle, a structure-oriented adaptive function matrix is ​​constructed to solve the unit strain vector, thereby inverting the strain distribution characteristics of the towed cable structure. According to the strain distribution characteristics of the towline, auxiliary identification of the towline tension is carried out.

5. The method for verifying flame ablation of a towing cable under static and dynamic loads according to claim 4, characterized in that: The node unit division for the flexible streamer structure includes the following steps: The tow cable section is divided into 8-node arc segment units, and the unit node coordinates are assumed to satisfy the following formula: The mesh tangent vector τ and the unit distance vector d are perpendicular to each other, that is, τ·d=0. The diffusion term of the heat conduction equation between arc segment units of the same size meets the temperature field inversion conditions of conventional units. The unit surface sizes of arc segment units in various directions are different, and the unit area calculation expression is: Wherein, Ah-1 represents the unit surface area of ​​the arc unit at height h1, Ah+1 represents the unit surface area of ​​the arc unit at height h2, Ar-1 represents the unit surface area of ​​the arc unit at radius r1, Ar+1 represents the unit surface area of ​​the arc unit at radius r2, Indicates the arc unit at an angle The unit surface area at Indicates the arc unit at an angle The unit surface area at .

6. The method for verifying flame ablation of a towing cable under static and dynamic loads according to claim 5, characterized in that: Based on the three-dimensional heat conduction differential equation and finite element method, the three-dimensional temperature field reconstruction of the streamer is realized, which includes the following steps: Substituting the area calculation formula of formula (1-2) into the conventional volume unit temperature field inversion equation and simplifying it, we can get: Where k is the thermal conductivity of the structural material, n is the unit external normal vector of the control volume unit boundary, is the temperature gradient, Te is the center temperature of the structural unit body, Ti is the center temperature of the unit body adjacent to the i-th surface of the unit body, is the temperature gradient on the i-th surface of the unit cell; Simplify equation (1-3) and let the arc segment unit of the structure division be calculated. The temperature field reconstruction calculation formula based on the arc segment unit division structure can be obtained:

7. The method for verifying flame ablation of a towing cable under static and dynamic loads according to claim 6, characterized in that: The temperature field distribution is calculated in reverse, including the following steps: Let the radius corresponding to the unit center point be r e , knowing Δr=1, then r1=r e -0.5, r2=r e +0.5, and then from formula (1-4) we know the unit center temperature T e The temperature value of is only related to the radius information of the structural unit, and it can be seen from formula (1-2) that That is, the heat of the arc segment unit is non-uniformly distributed along the radius r; The heat transfer problem in the radial direction of the arc segment unit is converted into a one-dimensional linear problem, and equation (1-4) is processed. The temperature relationship in the radial direction is known to be r1+r2=2r e ,get: r1(T r-1 -T e )+r2(T r+1 -T e )=0 (1-5); Based on r2-r e =r e -r1, and then according to formula (1-5), we get: Assume T = f(r), then we get its first-order derivative form: Assume that the inner and outer radii of the arc segment structure are r min 、r max , in a certain radial direction r min 、r max The corresponding temperature value is T min , T max , it is known that T m1 =f(r min ), T m2 =f(r max ), combined with formula (1-7), the expression of T = f (r) is: It is known that each node of the arc unit satisfies the relationship (1-1). Combining the relationship (1-8), we can get the value of any position in the internal space of the arc unit. Temperature of point The calculation formula is: The expressions corresponding to T1 and T2 in formula (1-9) are: T1=N A T A +N B T B +N C T C +N D T D T2=N E T E +N F T F +N G T G +N H T H (1-10); Where TA~TH are the temperature values ​​corresponding to the unit nodes A~H, and the expressions of the coefficients in formula (1-10) are: Substitute the coefficients calculated by formula (1-11) into formula (1-10), and combine with formula (1-9) to obtain the coefficients at any position in the unit grid: Temperature value at Each divided arc segment unit is assembled to form a volume unit model for the streamer, and the temperature field inversion method inside each unit is combined to realize the global measurement of the streamer temperature field inversion.

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