Electromechanical integration modeling and optimization method for very-low-frequency thirteen-tower antenna

Abstract

The invention discloses an electromechanical integration modeling and optimizing method for a very-low-frequency thirteen-tower antenna. The method comprises the following steps: (1) inputting very-low-frequency antenna structure parameters, load parameters and electromagnetic parameters; (2) setting an optimization design variable as the initial prestress of the antenna inhaul cable; (3) constructing a complete structural finite element model; (4) applying a multi-source load to the structural finite element model, and solving and obtaining node displacement information of the antenna under the action of the multi-source load; (5) judging whether the structural response corresponding to the current design variable meets a constraint function or not; (6) calculating a key electrical performance index under a multi-source load; (7) judging whether the current optimal objective function value meets a preset convergence criterion or not; (8) updating the Gaussian process agent model; and step (9), outputting global optimal design and corresponding structure response and electrical performance parameters. According to the invention, performance maintenance and quick response of the very-low-frequency antenna in an extreme environment are realized.

Description

Technical Field

[0001] This invention belongs to the field of antenna technology, specifically relating to a method for electromechanical integration modeling and optimization of a very low frequency thirteen-tower antenna. Background Technology

[0002] The very low frequency (VLF) 13-tower antenna system is primarily used for long-range communication from submarines, featuring stable propagation and strong penetration. The system consists of thirteen antenna towers, six rhomboid antenna panels, and a bottom-lead feed network, forming a large, symmetrical, top-loaded, vertically grounded antenna array. As a typical electrically small antenna (its size is much smaller than the wavelength), it improves radiation performance by adding a top load at the top of the bottom lead to enhance the current distribution in the vertical section.

[0003] The top load consists of multiple open-ended top capacitive wires, whose sag and structural shape vary with the environment, thus affecting the antenna's electrical performance. Under extreme conditions, this effect often leads to a decline in antenna electrical performance. Therefore, establishing an electromechanical integration optimization model under multi-source loads is crucial for improving antenna electrical performance under harsh conditions.

[0004] The impact on very low frequency (VLF) transmitting antennas is increasingly attracting the attention of researchers, and some meaningful research conclusions have been reached.

[0005] In his paper "A Virtual Temperature-Based Method for Finding the Shape of Very Low Frequency Antenna Networks" (2015 National Antenna Conference, 2015:781-784), Guo Rui proposed a rapid shape-finding method for large very low frequency antennas with complex network designs. This method optimizes sag by adjusting the virtual temperature and expansion coefficient, and its feasibility and efficiency are verified through single-wire and complex network examples. Yan Yalong et al., in their paper "Combined Electromechanical Analysis for a Very-Low-Frequency Complex Structure T-Type Transmitting Antenna" (Progress In Electromagnetics Research M, 2018, 63:107-117), proposed a combined electromechanical analysis method for very low frequency T-type transmitting antennas. This method uses the finite element method for structural modeling and antenna sag optimization, aiming for minimum sag, and combines this with the method of moments for electrical performance analysis. The results demonstrate that this method effectively improves antenna radiation efficiency with minimal impact on the radiation pattern.

[0006] The aforementioned traditional optimization methods, which focus on minimizing cable sag, can improve the geometric regularity of the structure by tightening the cable shape, but they have several drawbacks. First, at the structural level, a single sag target can easily lead to an imbalance in stress distribution. For example, some cables may have stress redundancy due to over-tensioning, while others may have near-zero stress, resulting in inefficient use of material resources and creating potential safety hazards such as localized structural fatigue. Second, at the electromechanical coupling level, traditional methods completely ignore the intrinsic relationship between structural form and electromagnetic performance. Structures obtained solely through sag constraints often suffer from distorted antenna current distribution due to uneven node displacement, causing a bottleneck in improving core electrical performance such as radiation resistance and radiation efficiency. Third, at the design space level, optimizing sag as a single target significantly compresses the parameter adjustment space, failing to reserve reasonable structural deformation margins for electrical performance optimization. Summary of the Invention

[0007] To overcome the shortcomings of the existing technology, the present invention aims to provide a method for electromechanical integration modeling and optimization of a very low frequency (VLF) 13-tower antenna. This method shifts the optimization objective from simple structural performance indicators to directly addressing the antenna's electrical performance, transforming cable sag into a constraint condition, and constructing an electromechanical integration optimization model. Under the premise of satisfying structural strength and deformation constraints, the key electrical performance indicators under harsh operating conditions are maximized through optimized configuration of the initial prestress of the cables, thereby achieving performance maintenance and rapid response of the VLF antenna in extreme environments.

[0008] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for electromechanical integration modeling and optimization of a very low frequency 13-tower antenna includes the following steps; Step (1): Using the very low frequency antenna structural parameters, load parameters, and electromagnetic parameters as inputs to the electromechanical integration optimization model, the output of the electromechanical integration optimization model is the globally optimal design. ; Step (2): Set the optimization design variable as the initial prestress T of the antenna cable; Step (3): Calculate the spatial morphology of each antenna cable based on the initial prestress T, and construct a complete structural finite element model; Step (4): Apply multi-source loads to the finite element model of the structure, conduct a static finite element analysis of the structure considering geometric nonlinear effects, and solve and obtain the nodal displacement information of the antenna under the action of multi-source loads; Step (5): Determine whether the structural response corresponding to the current design variable satisfies the constraint function. If any constraint is not satisfied, proceed to step (8); otherwise, proceed to step (6). Step (6): Update the electromagnetic mesh based on nodal displacement information and calculate key electrical performance indicators under multi-source loads. , as the objective function value for optimization; Step (7): Determine whether the current optimal objective function value satisfies the preset convergence criterion. If not satisfied, proceed to step (8) Bayesian optimization; if satisfied, proceed to step (9). Step (8): Transfer the current design sample Input the Bayesian optimizer, update the Gaussian process surrogate model, and determine the next set of design variables for evaluation points in the new round of structural analysis based on the acquisition function Expected Improvement Plus; Step (9): Output the globally optimal design The effect of improving radiation performance was verified by comparing the corresponding structural response and electrical performance parameters.

[0009] In step (1), the structural parameters of the thirteen-tower antenna are specifically the antenna geometry and cable material parameters; the load parameters are specifically gravity and icing multi-source load parameters; the electromagnetic parameters include the operating frequency band, feed information, and far-field pattern sampling settings.

[0010] Step (2) specifically involves: In antenna engineering design practice, the shape adjustment of the antenna cable network structure is mainly achieved by changing the initial prestress of the cables, thereby controlling the spatial tension shape of each lead or top load; assuming the antenna system consists of N cables, the th cable... i The initial prestress of the cable is T i ( i If the values ​​are 1, 2, ..., N), then the design variables are expressed as: .

[0011] The specific steps (3) are as follows: In actual operation, the flexible structures of the antenna, such as the cable, lower lead, and top lead wire, will exhibit a suspended shape, i.e., a catenary wire mesh structure, due to the influence of multiple environmental loads such as gravity or icing. The decrease in the sag of the antenna cable will directly change the spatial layout of the antenna conductor, thereby affecting the antenna current distribution and the phase structure of far-field radiation.

[0012] Before applying external loads, to reduce deformation under its own weight, antenna cables are usually prestressed with a prestress T. If the top catenary is considered an ideal catenary, then the finite element model of the antenna structure... for Where a(T) is the catenary parameter, expressed as Where ω is the unit horizontal load and L is the horizontal projection of the cable.

[0013] The finite element model is a finite element model that is only subjected to its own gravity before external loads are applied, and prestress is used to control the antenna shape.

[0014] Step (4) specifically involves: When the very low frequency 13-tower antenna is in service, in addition to its own weight, it also needs to withstand the combined effects of various extreme environmental loads such as strong winds, icing and low temperatures; these are uniformly classified as multi-source loads to characterize the comprehensive stress state of the antenna in complex environments. Increasing temperature loads, such as the contraction of rigging in extremely cold weather, can lead to a sharp increase in tension on the top of the tower.

[0015] Under the action of multiple loads, the total displacement field generated by each element of the antenna can be expressed as the superposition of the load components: in Indicates the first Under the action of a single load, at position Structural displacement caused at the location; This refers to the number of loads.

[0016] Step (5) specifically involves: Based on the structural response corresponding to the current design variables, the first Genlasoze Under given operating conditions, the following must be satisfied: in and These are the lower and upper limits of axial stress, respectively; the upper and lower limits of axial stress are the constraints; the minimum and maximum values ​​are derived from the material safety factor, which is generally a commonly used engineering factor. The minimum sag of the antenna structure is transformed from an objective function into an additional constraint condition to ensure structural safety and stiffness requirements: in, At this point, the antenna is close to an ideal horizontal position. If the antenna is severely deformed and shows obvious bending, and the constraint is not met, proceed to step (8); otherwise, proceed to step (6).

[0017] The specific steps (6) are as follows: The far-field radiation expression for the antenna under multi-source loads, derived from the load disturbance term in step (4), is as follows: in An ideal electric field without load disturbance. This is because the antenna element deviates from its ideal position. The resulting additional phase disturbance The resulting radiation field; The antenna radiated power after adding a multi-source load is expressed as: This formula reflects the effect of structural geometric perturbations on the antenna's radiated power, at which point the antenna's radiation resistance is... in The current at the feed end is denoted as ; the radiation resistance is used as the objective function value for optimization.

[0018] The specific steps (7) are as follows: The radiation resistance obtained in step (6) is used as the objective function value of the optimization model to determine whether the Cauchy convergence criterion is satisfied. If the condition is not met, proceed to step (8); if the condition is met, proceed to step (9).

[0019] The specific steps (8) are as follows: Input the current design sample into the Bayesian optimizer, set the maximum number of objective function evaluations to 500, and the maximum runtime to 8 hours; adopt the expected improvement + acquisition function, set the exploration ratio to 0.7 to balance local optimization and global search, set the Gaussian process active set size to 300, update the Gaussian process surrogate model, and determine the next set of design variables for the evaluation points of the new round of structural analysis.

[0020] The specific steps (9) are as follows: The output includes the global optimal design with optimal prestress distribution for 24 cables and the corresponding structural response (such as initial strain and nodal displacement information) and electrical performance parameters (such as radiation resistance), verifying the effect of radiation performance improvement.

[0021] The beneficial effects of this invention are: This invention uses radiation resistance as the core objective function, the prestress of the very low frequency (VLF) antenna cables as the design variable, and the initial strain boundary of the cables and the minimum structural sag, a concern in traditional design, as constraints. By extracting the load disturbance term from the far-field integral formula, it derives the analytical expression for the far-field radiation of the antenna under multi-source loads, and finally constructs an electromechanical integrated optimization model. Traditional design focuses on reducing cable sag and suppressing structural deformation as core optimization objectives, increasing cable prestress within the material safety threshold to enhance structural stiffness. However, its electromechanical separation design paradigm has inherent defects: it requires first calculating prestress and deformation through structural finite element analysis, and then repeatedly solving the electromagnetic response for each set of parameters in full-wave simulation. This not only results in a lengthy design cycle and extremely low efficiency, but also makes it difficult to overcome the limitations of the complex influence mechanism of electromechanical coupling. This invention avoids the redundant steps of traditional design, which only focuses on structural performance, ignores the complex influence mechanism of electromechanical coupling, and relies on repeated simulation verification. It provides a systematic technical path for the multi-physics collaborative optimization design of broadband VLF antennas under multi-source loads, demonstrating the engineering application value of multidisciplinary optimization of antenna performance.

[0022] 1. In designing the optimization model, this invention fully considers the inherent defects of traditional design, which focuses on structural performance and ignores the impact of electromechanical coupling on electrical performance. Instead, it uses electrical performance indicators such as radiation resistance, which directly determine the communication effect, as the core objective function, thereby achieving precise control over the final service performance of the antenna from the design source.

[0023] 2. The very low frequency (VLF) 13-tower antenna is large in size and complex to model. Traditional design typically divides the analysis process into two modules: structural and electrical performance, lacking efficient collaboration between them. This results in long iterative calculation cycles for both structural and electrical design. This invention defines the VLF antenna cable prestress as a design variable, using the initial strain boundary of the cable and the minimum structural sag (a concern in traditional design) as constraints. By extracting the load disturbance term from the far-field integral formula, the far-field radiation expression of the antenna under multi-source loads is derived. Based on this, an electromechanical integrated optimization model is constructed, achieving coordinated optimization of structural and electrical performance. Attached Figure Description

[0024] Figure 1 The flowchart illustrates the electromechanical integration modeling and optimization of a very low frequency thirteen-tower antenna provided in this embodiment of the invention.

[0025] Figure 2 A schematic diagram showing the results of electromechanical integration modeling and optimization of the very low frequency thirteen-tower antenna provided by this invention. Detailed Implementation

[0026] The present invention will now be described in further detail with reference to the accompanying drawings.

[0027] Please see Figure 1 The flowchart of the rapid modeling method for electromechanical coupling of a very low frequency thirteen-tower antenna provided for the implementation of this invention includes: Step (1): Input the very low frequency antenna structural parameters (antenna geometry and cable material parameters), load parameters (gravity, icing multi-source load parameters), and electromagnetic parameters (operating frequency band, feed information, far-field pattern sampling settings) into the electromechanical integration optimization model. Step (2): In antenna engineering design practice, the shape adjustment of the antenna wire mesh structure is mainly achieved by changing the initial prestress of the cables, thereby controlling the spatial tension shape of each lead or top load; assuming the antenna system consists of N cables, the first... i The initial prestress of the cable is T i ( i If the values ​​are 1, 2, ..., N), then the design variables are expressed as: .

[0028] Step (3): In actual operation, the flexible structures such as the cable, lower lead and top lead wire of the antenna will be suspended due to the influence of multiple environmental loads such as gravity or icing. The decrease in the sag of the antenna cable will directly change the spatial layout of the antenna conductor, thereby affecting the phase structure of the antenna current distribution and far-field radiation.

[0029] Before loading, to reduce deformation under its own weight, a prestress T is applied to the antenna cable. The top capacitive line is considered an ideal catenary. Therefore, the finite element model of the antenna structure... for Where a(T) is the catenary parameter, expressed as Where ω is the unit horizontal load and L is the horizontal projection of the cable.

[0030] Step (4): When the very low frequency thirteen-tower antenna is in service, in addition to its own weight, it also needs to withstand the combined effects of extreme environmental loads such as strong winds and icing. This invention also classifies external harsh loads such as wind and icing into multi-source loads to characterize the comprehensive stress state of the antenna in complex environments. Under the action of multiple loads, the total displacement field generated by each element of the antenna can be expressed as the superposition of the load components: in Indicates the first Under the action of a single load, at position Structural displacement caused at the location; This refers to the number of loads.

[0031] Step (5): Based on the structural response corresponding to the current design variables, the first... Genlasoze Under given operating conditions, the following must be satisfied: .

[0032] in and These represent the lower and upper limits of the axial stress, respectively. The minimum sag of the antenna structure is transformed from an objective function into additional constraints to ensure structural safety and stiffness requirements: in, At this point, the antenna is close to an ideal horizontal position. The antenna is severely deformed and shows obvious bending. If the constraint is not met, proceed to step 8; otherwise, proceed to step 6.

[0033] Step (6): The far-field radiation expression of the antenna under multi-source load is derived from the load disturbance term in step (4). in An ideal electric field without load disturbance. This is because the antenna element deviates from its ideal position. The resulting additional phase disturbance The resulting radiation field; The antenna radiated power after adding a multi-source load is expressed as: This formula reflects the effect of structural geometric perturbations on the antenna's radiated power, at which point the antenna's radiation resistance is... in Let be the feed current. The radiation resistance is used as the objective function value for optimization.

[0034] Step (7): Determine whether the Cauchy convergence criterion is satisfied based on the radiation resistance obtained in step (6) as the objective function value of the optimization model. If the condition is not met, proceed to step (8); if the condition is met, proceed to step (9).

[0035] Step (8): Input the current design sample into the Bayesian optimizer, set the maximum number of objective function evaluations to 500, and the maximum running time to 8 hours; adopt the expected improvement + acquisition function, set the exploration ratio to 0.7 to balance local optimization and global search, set the Gaussian process active set size to 300, update the Gaussian process surrogate model, and determine the next set of design variables for the evaluation points of the new round of structural analysis.

[0036] Step (9): Output the global optimal design containing the optimal prestress distribution of 24 cables and the corresponding structural response (such as initial strain of cables and nodal displacement information) and electrical performance parameters (such as radiation resistance) to verify the radiation performance improvement effect.

[0037] The advantages of this invention can be further illustrated by the following simulation experiments: 1. Simulation conditions: The antenna material and environmental parameters are as follows: the central support tower is 340m high, the outer ring support tower is 310m high, the antenna tower diameter is 1.5m, the guy wire diameter is 60mm, the conductivity is 1.0×107S / m, and it is made of stainless steel; the main radiating conductor is made of bronze wire with a diameter of 2.54cm, conductivity of 5.8×107S / m, yield strength of approximately 140MPa, and is subjected to a load equivalent to 30m of ice thickness.

[0038] 2. Simulation results: The electromechanical integration modeling and optimization method for a very low frequency thirteen-tower antenna of the present invention was adopted. The results are detailed in Table 1. Table 1. Comparison of antenna parameters under ideal conditions, distorted design, conventional design, and electromechanical integrated design. As shown in Table 1, based on this invention, by controlling the structural deformation distribution under icing load through cable prestressing, the maximum deformation of the antenna structure is reduced by 42.52%. The improvement in electrical performance was verified in a scenario with a center operating frequency of 22.5kHz, achieving an increase in radiation resistance of 14.18%. Compared with the traditional design, this scheme still achieved an improvement in radiation resistance of 6.62% under more relaxed structural constraints. Figure 2 This paper compares the full-band electrical performance of ideal conditions, distorted design, traditional design, and integrated optimized design under severe icing conditions. The integrated optimized design further improves the radiation resistance compared to the traditional design. Through structural electromagnetic coupling control, the gain is approximately 0.1Ω across the entire frequency band, and it almost approaches the ideal condition in the low-frequency range. This simulation example verifies the effectiveness of the method presented in this invention.

[0039] This invention extracts the load disturbance term from the far-field integral formula, derives the analytical expression for antenna far-field radiation under multi-source loads, and then constructs an electromechanical integration optimization model. The model uses radiation resistance as the optimization objective and the minimum structural sag, a concern in traditional design, as a constraint. It employs a Bayesian optimization algorithm to overcome the performance bottlenecks of traditional designs, ultimately achieving radiation performance superior to conventional solutions.

[0040] The parts not described in detail in this embodiment are common and well-known methods in the industry, and will not be described in detail here. The above examples are merely illustrative of the present invention and do not constitute a limitation on the scope of protection of the present invention. All designs that are the same as or similar to the present invention are within the scope of protection of the present invention.

Claims

1. A method for electromechanical integration modeling and optimization of a very low frequency thirteen-tower antenna, characterized in that, Comprise the following steps; Step (1): the very low frequency antenna structure parameters, load parameters and electromagnetic parameters as the input of the electromechanical integrated optimization model, the output of the electromechanical integrated optimization model is the global optimal design ; Step (2): set the optimization design variable as the initial prestress T of the antenna cable; Step (3): calculate the spatial form of each antenna cable according to the initial prestress T of the antenna cable, and construct a complete structure finite element model; Step (4): apply multi-source load to the structure finite element model, carry out structure static finite element analysis considering geometric nonlinear effect, solve and obtain the node displacement information of the antenna under the action of multi-source load; Step (5): determine whether the structure response corresponding to the current design variable satisfies the constraint function, if any constraint is not satisfied, jump to step (8); Otherwise, proceed to step (6); Step (6): Update the electromagnetic mesh based on the node displacement information, calculate the key electrical performance indicators under multi-source load , as the optimization objective function value; Step (7): judging whether the current optimal objective function value meets the preset convergence criterion If not, proceed to step (8) Bayesian optimization; if yes, proceed to step (9) Step (8): The current design sample is input into the Bayesian optimizer, the Gaussian process surrogate model is updated, and the next set of design variables is determined based on the acquisition function Expected Improvement Plus for the evaluation points of the new round of structural analysis. Step (9): output global optimal design with corresponding structural response and electrical performance parameters.

2. The method of claim 1, wherein, In the step (1), the input structure parameters of the thirteen tower antenna are specifically antenna geometric dimensions and cable material parameters; The load parameters are specifically the multi-source load parameters of gravity, icing; The electromagnetic parameters include working frequency band, feed information, far field pattern sampling setting.

3. The method of claim 2, wherein, The step (2) is specifically: Suppose the antenna system is composed of N cables, the initial prestress of the i i th cable is T i i , and the initial tension of the i i th cable is T i , i = 1, 2, …, N, then the design variable is represented as 。 4. The method of claim 3, wherein, The step (3) is specifically: In order to reduce the deformation under dead weight, the antenna cable is usually prestressed T before external load is applied. The top contour line is regarded as an ideal catenary line. Then the finite element model of the antenna structure is established is Wherein a(T) is the catenary parameter, which is expressed as Wherein ω is the unit horizontal load, and L is the horizontal projection of the cable.

5. The method of claim 4, wherein, The step (4) is specifically: When the very low frequency thirteen tower antenna is in service, in addition to the self weight, it also needs to bear the comprehensive action of various extreme environmental loads such as wind, icing and low temperature, which are classified as multi-source load to represent the comprehensive stress state of the antenna under complex environment; Under the action of multi-source load, the total displacement field generated by each unit of the antenna is expressed as the superposition of each load component: wherein represents the first class of loads acting alone at positions cause structural displacements; is the number of loads.

6. The method of claim 5, wherein, The step (5) is specifically: According to the structural response corresponding to the current design variable, the first Root cable Must meet in given working conditions wherein and are the lower and upper limits of the axial stress, respectively; the upper and lower limits of the axial stress are the constraints The minimum value and the maximum value are obtained according to the material safety factor; The minimum sag of the antenna structure is converted from the objective function to meet the additional constraint condition to ensure the safety and stiffness requirements of the structure: wherein, At this time, the antenna is close to the ideal horizontal state, At this time, the antenna is close to the ideal horizontal state, At this time, the antenna is close to the ideal horizontal state, 7. The method of claim 6, wherein, The step (6) is specifically: The far field radiation expression of the antenna under the multi-source load is obtained from the load disturbance term in step (4) in An ideal electric field without load disturbance. This is because the antenna element deviates from its ideal position. The resulting additional phase disturbance The resulting radiation field; Then the antenna radiation power expression after adding the multi-source load is This formula reflects the influence of the geometric disturbance of the structure on the antenna radiation power, and the radiation resistance of the antenna at this time is wherein is the current at the feed end; the radiating resistance is taken as the optimization objective function value.

8. The method of claim 7, wherein, The step (7) is specifically: According to the radiation resistance obtained in step (6) as the optimization model objective function value to determine whether to meet the Cauchy convergence criterion , if not, proceed to step (8); if yes, proceed to step (9).

9. The method of claim 8, wherein, The step (8) is specifically: Input the current design sample into the Bayesian optimizer, use the expected improvement + acquisition function, update the Gaussian process surrogate model, determine the next set of design variables for the evaluation point of the new round of structure analysis.

10. The method of claim 8, wherein, The step (9) is specifically: Output the global optimal design containing the optimal prestress distribution of the cable, the corresponding structure response and electrical performance parameters, and verify the radiation performance improvement effect.

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