Artificial metamaterial-based LVDT sensor and design method thereof

Abstract

The invention discloses an LVDT sensor based on an artificial metamaterial and a design method of the LVDT sensor. The LVDT sensor comprises a shell, a coil, the artificial metamaterial and an iron core which are arranged in a nested mode from outside to inside. The artificial metamaterial comprises metamaterial units which are periodically arranged in the axial direction; each metamaterial unit is formed by compounding a first dielectric material and a second dielectric material which have different magnetic conductivities; the projection of each metamaterial unit on the two-dimensional plane is of a rectangular structure, the rectangular structure comprises sub-rectangular structures formed by the projection of the first dielectric material and the projection of the second dielectric material on the two-dimensional plane, the length of each sub-rectangular structure represents the filling proportion of the corresponding dielectric material in the metamaterial unit, and the width of each sub-rectangular structure represents the spatial distribution of the metamaterial unit; the electromagnetic characteristics of the metamaterial units are regulated and controlled by changing the length and width of the sub-rectangular structure of the projection of the first dielectric material, and the action range of the artificial metamaterial is regulated and controlled by changing the periodic number of the metamaterial units arranged in the axial direction.

Description

Technical Field

[0001] This invention belongs to the field of linear variable differential transformer sensor technology, specifically relating to an LVDT sensor based on artificial metamaterials and its design method. Background Technology

[0002] Linear Variable Differential Transformers (LVDTs), as high-precision electromechanical displacement sensors, play an irreplaceable role in aerospace, precision instruments, industrial automation, and medical devices due to their long lifespan, high reliability, and strong environmental adaptability. Especially in applications such as aerospace servo actuation systems, aircraft control surface inspection, and minimally invasive surgical instrument positioning, not only are excellent repeatability and stability required of the sensors, but stringent demands are also placed on their ability to achieve high-precision measurements within confined spaces. Therefore, the core performance indicators of LVDT sensors (sensitivity and linearity) directly affect the accuracy and reliability of the entire measurement system.

[0003] From a working principle perspective, the performance of an LVDT sensor is essentially determined by its internal magnetic field distribution. In the design of LVDT sensors based on structural optimization, the magnetic field distribution mainly depends on the geometry and arrangement of the magnetic material, which is a "passive" approach to magnetic circuit construction. This design method has inherent limitations. When using high-permeability materials or increasing the cross-sectional area of ​​the magnetic core to improve sensitivity, although the coupled magnetic field can be enhanced, it can also lead to excessive concentration of magnetic flux in the coil end region, causing edge effects and exacerbating the nonlinearity of the magnetic field distribution, thereby impairing the linearity of the sensor. Conversely, if the magnetic core structure is cut or other contour designs are adopted to improve linearity, the effective magnetic flux will be reduced, the signal strength will decrease, and sensitivity will be sacrificed. This difficult trade-off between sensitivity and linearity has plagued the design and optimization of traditional LVDT sensors, becoming a major technical bottleneck restricting further performance breakthroughs in high-precision and miniaturized applications.

[0004] With current technology, LVDT sensors are increasingly focusing on structural optimization to improve their performance. Structural design primarily encompasses several key components of the LVDT sensor, such as the coil, core, and frame. Fundamentally, optimizing the structural design directly impacts the sensor's physical characteristics and operating principle, thus possessing broad application potential and development prospects.

[0005] For example, invention patent (publication number CN118969466A, invention title: An LVDT Coil Structure) proposes: by setting a winding skeleton as an insulating layer, magnetic lines of force are prevented from directly reaching the secondary coil from the primary coil, thereby reducing magnetic circuit saturation; at the same time, the number of coil turns at both ends of the primary coil is increased, increasing the magnetic field strength in the nonlinear region at both ends, thereby increasing the magnetic flux of the secondary coil, ultimately increasing the linear range of the LVDT sensor. Another invention patent (publication number CN110736429A, invention title: A Winding Structure for Improving LVDT Linearity) proposes: by setting specific winding segmentation parts, including short winding skeletons and vertical winding partitions, the advantages of a "double-cone" winding structure are achieved to improve the linear accuracy of the LVDT. For example, invention patent (publication number CN119687768A, invention title: A High-Sensitivity LVDT Sensor) proposes: by replacing the solid iron core with a hollow iron core structure with an axially penetrating inner hole and axial slots, the hollow structure significantly reduces the induced eddy current loss generated by the iron core under high-frequency excitation; at the same time, the axial slots further divide the magnetic circuit of the iron core in the circumferential direction, optimizing the magnetic flux distribution. This structure can improve the sensor sensitivity while maintaining the linearity essentially unchanged. Another invention patent (publication number CN119687769A, invention title: A High-Linearity LVDT Sensor) proposes: by replacing the traditional single-segment continuous primary coil with a three-segment structure consisting of a primary main coil and two symmetrical primary compensation coils, with intervals between segments and physical isolation using separator rings on the frame. This design compensates for the gain drop caused by magnetic field diffusion at the ends of the traditional LVDT, achieving a reduction in the minimum length of the sensor coil while maintaining linearity.

[0006] The aforementioned invention patents are all LVDT sensor performance improvement schemes based on structural optimization, mainly achieved through geometric correction or topological reconstruction of macroscopic components such as coils, windings, and cores. Although these schemes have achieved significant results, they still have the following limitations: (1) The degree of freedom for optimization is limited by the structural space. When increasing the number of coil turns to enhance the magnetic field, using segmented windings to compensate for nonlinearity, and hollowing out and slotting the iron core to suppress eddy currents, the adjustment angle is limited within the limited housing space of the sensor. Specifically, increasing the number of turns requires sacrificing the wire diameter, resulting in an increase in coil resistance; complex winding structures require more axial or radial space; and changes to the shape of the iron core may weaken its mechanical strength.

[0007] (2) Problems of manufacturing difficulties that accompany the optimization design. For example, the precision winding of multi-layer segmented coils, the integrated machining of the skeleton with micro-separating rings, and the deep hole and narrow slot cutting of thin-walled hollow iron cores all place stringent requirements on processing equipment, process routes and operating accuracy.

[0008] (3) The optimized structure may produce other adverse effects while improving a certain index. Specifically, the increase in the number of coil turns or density will aggravate copper loss and skin effect; the hollow design of the iron core may reduce eddy currents but may also change its mechanical vibration characteristics; the complex magnetic circuit structure will make thermal management more difficult, and local temperature rise may cause material parameter drift, thereby affecting the long-term stability and measurement accuracy of the sensor.

[0009] (4) Optimization and adjustment rely heavily on trial and error, the coupling relationship between parameters is complex, there is a lack of systematic optimization methods, and it is difficult to efficiently obtain the global optimal solution that satisfies multiple indicators (high sensitivity, high linearity). Summary of the Invention

[0010] To address the aforementioned problems in the existing technology, this invention provides an LVDT sensor based on artificial metamaterials and its design method. The technical problem to be solved by this invention is achieved through the following technical solution: In a first aspect, embodiments of the present invention provide an LVDT sensor based on artificial metamaterials, the LVDT sensor comprising a shell, a coil, an artificial metamaterial, and an iron core nested from the outside in; wherein... The artificial metamaterial comprises several metamaterial units arranged periodically along the axial direction. Each metamaterial unit is composed of two dielectric materials, a first dielectric material and a second dielectric material, with different magnetic permeabilities. Each metamaterial unit is projected onto a two-dimensional plane as a rectangular structure, which includes sub-rectangular structures projected onto the two-dimensional plane by the first dielectric material and the second dielectric material, respectively. The length of the sub-rectangular structure represents the filling ratio of the corresponding dielectric material in the metamaterial unit, and the width of the sub-rectangular structure represents the spatial distribution of the metamaterial unit. The electromagnetic properties of the metamaterial unit can be controlled by changing the length and width of the sub-rectangular structure projected onto the two-dimensional plane by the first dielectric material, and the range of action of the artificial metamaterial can be controlled by changing the number of periods in which the metamaterial units are arranged along the axial direction.

[0011] In one embodiment of the present invention, the permeability of the first medium is greater than that of the second medium.

[0012] In one embodiment of the present invention, the first medium includes at least one of ferrite, silicon steel sheet, amorphous alloy and nanocrystalline alloy.

[0013] In one embodiment of the present invention, the second medium includes at least one of air, plastic, and ceramic.

[0014] In one embodiment of the present invention, the length of the sub-rectangular structure corresponding to the first medium is greater than the length of the sub-rectangular structure corresponding to the second medium, and the width of the sub-rectangular structure corresponding to the first medium is equal to the width of the sub-rectangular structure corresponding to the second medium.

[0015] In one embodiment of the invention, the artificial metamaterial covers at least the effective sensing range of the coil in the axial direction.

[0016] In one embodiment of the present invention, the artificial metamaterial is fixed to the inner wall of the coil by adhesive bonding or thermal fitting.

[0017] Secondly, embodiments of the present invention provide a design method for an LVDT sensor based on artificial metamaterials, used to design any of the LVDT sensors based on artificial metamaterials described in the first aspect, the corresponding design method including: A parameter optimization model for artificial metamaterials is established. The objective of the parameter optimization model is to maximize the performance index of the LVDT sensor. The optimized parameters are the parameter combinations of the artificial metamaterials. The parameter combinations include the length and width of the sub-rectangular structure corresponding to the projection of the first dielectric material in the metamaterial unit onto the two-dimensional plane, and the number of cycles of the metamaterial units arranged axially. The optimal parameter combination of the artificial metamaterial is obtained by iterative optimization of the parameter optimization model. The optimal artificial metamaterial is determined based on the optimal parameter combination; An LVDT sensor based on artificial metamaterials is formed by nesting an outer shell, coil, optimal artificial metamaterial, and iron core from the outside in.

[0018] In one embodiment of the present invention, maximizing the performance of the LVDT sensor includes maximizing the sensitivity of the LVDT sensor and minimizing the nonlinear error of the LVDT sensor.

[0019] In one embodiment of the present invention, the parameter optimization model is iteratively optimized to obtain the optimal parameter combination of the artificial metamaterial, including: By employing multi-objective optimization algorithms, particle swarm optimization algorithms, or simulated annealing algorithms, the parameter optimization model is iteratively optimized to obtain the optimal parameter combination of the artificial metamaterial.

[0020] The beneficial effects of this invention are: This invention proposes an LVDT sensor based on artificial metamaterials. Addressing the inherent contradiction between linearity and sensitivity in traditional LVDTs, this invention does not directly improve existing LVDT cores or coils. Instead, it innovatively introduces an independent, functional artificial metamaterial into the magnetic circuit of the LVDT sensor, enabling active and precise design of the internal magnetic field distribution. By designing the metamaterial unit composite structure and periodic arrangement of this artificial metamaterial to form a novel magnetic circuit matrix for the LVDT sensor, it provides two independently and actively controllable design dimensions for LVDT magnetic circuit design: unit equivalent permeability and axial action domain. Within this two-dimensional design space, by changing the filling ratio of the two dielectric materials in the metamaterial unit and the arrangement of the metamaterial units, continuous and precise control of the local "equivalent permeability" of the matrix can be achieved without significantly altering the macroscopic shape and volume of the LVDT sensor. This transforms permeability from a fixed material property into a variable that can be adjusted as needed, aiming to precisely adjust sensor performance to meet specific performance indicators (such as high linearity, high sensitivity, or a balance between the two). The artificial metamaterial of this invention can be directly embedded in the inherent annular gap between the core and coil of an existing LVDT sensor. As an independent functional component, it does not require changes to the main topology of the sensor, coil parameters, or a significant increase in volume, thus reducing the process complexity and cost of improving existing LVDT sensors and has potential for engineering and industrialization.

[0021] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the structure of an LVDT sensor based on artificial metamaterials provided in an embodiment of the present invention; Figure 2 These are different parameter pairs provided in the embodiments of the present invention. Figure 1 The diagram below illustrates the performance impact of the LVDT sensor. Figure 3 This is a flowchart illustrating a design method for an LVDT sensor based on artificial metamaterials provided in an embodiment of the present invention. Detailed Implementation

[0023] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0024] To overcome the limitations imposed by macroscopic structural optimization, this invention adopts a different approach than additive or subtractive design of traditional LVDT component shapes. Instead, it seeks breakthroughs at a more fundamental level by controlling the equivalent electromagnetic properties of the material itself, proposing an LVDT sensor based on artificial metamaterials and its design method.

[0025] Firstly, please see Figure 1 This invention provides an LVDT sensor based on artificial metamaterials. The LVDT sensor includes a shell, a coil, an artificial metamaterial, and an iron core nested from the outside in. The artificial metamaterial comprises several metamaterial units arranged periodically along the axial direction. Each metamaterial unit is composed of two dielectric materials with different magnetic permeabilities: a first dielectric material and a second dielectric material. Each metamaterial unit is projected as a rectangular structure on a two-dimensional plane. This rectangular structure includes sub-rectangular structures projected by the first and second dielectric materials respectively on the two-dimensional plane. The length of the sub-rectangular structure represents the filling ratio of the corresponding dielectric material in the metamaterial unit, and the width of the sub-rectangular structure represents the spatial distribution of the metamaterial unit. The electromagnetic properties of the metamaterial unit are controlled by changing the length and width of the sub-rectangular structures projected by the first dielectric material, and the effective range of the artificial metamaterial is controlled by changing the number of periods in the axial arrangement of the metamaterial units. The coil includes one primary coil and two secondary coils, with the primary coil positioned between the two secondary coils.

[0026] Unlike traditional LVDT sensors, this invention adds an artificial metamaterial between the outer circumferential surface of the iron core and the inner circumferential surface of the coil. This artificial metamaterial occupies the underutilized annular air gap region in traditional LVDT sensors and preferably covers at least the effective sensing range of the coil (two secondary coils) axially. In terms of connectivity, the artificial metamaterial can be fixed to the inner wall of the coil via adhesive bonding, heat sealing, or other integral molding methods, forming a static annular sleeve structure closely adjacent to the iron core.

[0027] The artificial metamaterial of this invention is an artificially designed two-dimensional periodic structure. Specifically, the artificial metamaterial layer is composed of identical metamaterial units arranged periodically along the axial direction. Each metamaterial unit is a basic functional body constituting the artificial metamaterial. Each metamaterial unit is composed of two dielectric materials with different magnetic permeabilities: a first dielectric material and a second dielectric material. The magnetic permeability of the first dielectric material is greater than that of the second dielectric material. The first dielectric material includes at least one of ferrite, silicon steel sheet, amorphous alloy, and nanocrystalline alloy, but is not limited to these materials and their combinations. The second dielectric material includes at least one of air, plastic, and ceramic, but is not limited to these materials and their combinations. In a preferred embodiment of this invention, the first dielectric material is ferrite, serving as a high-permeability dielectric (see...). Figure 1 The green portion in the image), the second dielectric material is air, used as a low-permeability dielectric (see...). Figure 1The purple portion (in the image) is combined according to a defined shape. Specifically, in a two-dimensional axisymmetric model embodiment, the projection of each metamaterial unit is a rectangular structure, which is divided into two sub-rectangular structures, one of which is filled with ferrite (see...). Figure 1 The green part in the image), another sub-rectangular structure is filled with air (see the green part in the image). Figure 1 (The purple part in the image) The length h1 of the sub-rectangular structure corresponding to the first medium is greater than the length h-h1 of the sub-rectangular structure corresponding to the second medium, where h is the length of the rectangular structure projected by the metamaterial unit, and the width of the sub-rectangular structure corresponding to the first medium is equal to the width of the sub-rectangular structure corresponding to the second medium. Figure 1 The electromagnetic properties of the metamaterial unit can be controlled by changing the length h1 and width w of the two sub-rectangular structures. Furthermore, the effective range of the artificial metamaterial can be controlled by changing the number of cycles in which the metamaterial units are arranged axially.

[0028] As can be seen, the LVDT sensor based on artificial metamaterials proposed in this invention has multi-dimensional, independently adjustable design freedom, specifically: The first degree of design freedom is the continuous control of the equivalent permeability of the metamaterial unit. By changing the volume ratio of the first and second dielectric materials within each metamaterial unit, the macroscopic equivalent permeability of the metamaterial unit can be continuously and precisely adjusted. Specifically, for example, increasing the volume ratio of ferrite increases the... Figure 1 Increasing h1 in the metamaterial unit increases its equivalent permeability; increasing the volumetric filling ratio of air decreases its equivalent permeability. The equivalent permeability of the metamaterial unit determines the magnetic field conductivity in that region. Decreasing the equivalent permeability is equivalent to introducing controllable magnetoresistance within the metamaterial unit, which forces the magnetic flux lines to disperse, thereby optimizing the uniformity of the magnetic field distribution in space. This directly corresponds to an improvement in the linearity of the LVDT sensor. Conversely, increasing the equivalent permeability is beneficial for converging and enhancing the local magnetic field strength, providing a basis for improving sensitivity. Furthermore, by changing the geometry of the metamaterial unit (e.g., h1), the equivalent permeability can be further improved. Figure 1 The width (w) alters the spatial distribution of the metamaterial elements. The parameter w can be designed separately from the internal filling ratio of the metamaterial elements. By controlling the parameter w, the continuity and stability of magnetic flux conduction within the metamaterial elements can be changed, thereby optimizing the uniformity of the axial magnetic field distribution. Therefore, this design freedom can collaboratively reconcile and optimize the trade-off between linearity and sensitivity.

[0029] Building upon the established principle of controlling the equivalent permeability through the internal structure of metamaterial units (the first degree of design freedom), this invention further introduces the number of cycles N of the axial metamaterial units as a second independent degree of design freedom. This degree of freedom allows for the control of the spatial coverage and intensity of the magnetic field by managing the number of repeating metamaterial units along the sensor's axis. The axial arrangement cycle number refers to the total number of identical metamaterial units arranged along the sensor's axis. Given a fixed metamaterial unit geometry, the cycle number directly determines the total axial coverage length of the artificial metamaterial. By changing the cycle number, the physical effect of the artificial metamaterial along the main path of the magnetic field can be adjusted.

[0030] Traditional magnetic circuit optimization is one-dimensional, such as changing only the material or only the shape. This invention, by independently and collaboratively adjusting different parameters, provides a multi-dimensional tuning target for magnetic circuit design. For different application scenarios, such as requiring high linearity or high sensitivity, or seeking a balance between the two, different parameter combinations can be found to design the desired sensor performance. This design breaks away from the traditional passive design approach and transforms into an active control design approach.

[0031] To demonstrate the effectiveness of the aforementioned design freedoms, this invention uses simulations to show their impact on the performance of LVDT sensors. Figure 2 (a) shows the trend of the effect of the filling ratio (length) parameter h1 of the first dielectric material on the sensitivity S and nonlinear error t when the metamaterial unit parameter h is fixed. It can be seen that the sensitivity S and nonlinear error t exhibit a clear and controllable relationship with the change of h1, proving that sensitivity and linearity can be adjusted through h1. Similarly, the parameter w also has a significant and regular effect on the sensitivity S and nonlinear error t, such as... Figure 2 As shown in (b). Furthermore, the effect of the number of axially arranged periods N of the metamaterial units on the linearity of the LVDT sensor is not monotonically changing. Figure 2 (c) shows the influence trend of N on the nonlinear error t under specific h1 and w. From the above analysis, it can be seen that this complex relationship involving multiple parameters and non-monotonicity makes it difficult to find the optimal design using traditional trial-and-error methods. This is precisely the necessity and advantage of introducing an optimization design method in this invention.

[0032] It should be noted that each metamaterial unit in this embodiment of the invention is not limited to being filled with two different magnetic permeability media materials, but can also be filled with more different magnetic permeability media materials, such as three different magnetic permeability media materials. The electromagnetic properties of the metamaterial unit can be controlled by changing the length and width of the sub-rectangular structure projected by any two media materials on the two-dimensional plane. Other filling cases are similar. The projection of each metamaterial unit on the two-dimensional plane is not limited to a rectangular structure, but can also be any regular or irregular shape such as a circle, hexagon, or trapezoid. The electromagnetic properties of the metamaterial unit can be controlled by changing the structural parameters corresponding to the projection. For artificial metamaterials, the metamaterial units are not limited to periodic arrangement, but can also vary in spatial distribution according to a certain functional gradient, thereby achieving a more complex spatial distribution of magnetic permeability.

[0033] In summary, the LVDT sensor based on artificial metamaterials proposed in this invention addresses the inherent contradiction between linearity and sensitivity in traditional LVDTs. Instead of directly improving the existing core or coil structure of LVDTs, it innovatively introduces an independent, functional artificial metamaterial into the magnetic circuit of the LVDT sensor, enabling active and precise design of the internal magnetic field distribution. By designing the metamaterial unit composite structure and periodic arrangement of this artificial metamaterial to form a novel magnetic circuit matrix for the LVDT sensor, two independently and actively controllable design dimensions—unit equivalent permeability and axial action domain—are provided for LVDT magnetic circuit design. Within this two-dimensional design space, by changing the filling ratio of the two dielectric materials in the metamaterial unit and the arrangement of the metamaterial units, continuous and precise control of the local "equivalent permeability" of the matrix can be achieved without significantly altering the macroscopic shape and volume of the LVDT sensor. This transforms permeability from a fixed material property into a variable that can be adjusted as needed, aiming to precisely adjust the sensor performance to meet specific performance indicators (such as high linearity, high sensitivity, or a balance between the two). The artificial metamaterial of this invention can be directly embedded in the inherent annular gap between the core and coil of an existing LVDT sensor. As an independent functional component, it does not require changes to the main topology of the sensor, coil parameters, or a significant increase in volume, thus reducing the process complexity and cost of improving existing LVDT sensors and has potential for engineering and industrialization.

[0034] Secondly, to optimize the overall performance of the LVDT sensor, this invention further provides a supporting design method. The most important aspect of this method is the automatic search for the optimal parameter combination (h1, w, N) of the artificial metamaterial by establishing a parameterized model and applying an algorithm. For details, please refer to [link to relevant documentation]. Figure 3This invention provides a design method for an LVDT sensor based on artificial metamaterials, used to design any of the LVDT sensors based on artificial metamaterials described in the first aspect. The corresponding design method includes: S10. Establish a parameter optimization model for artificial metamaterials. The objective of the parameter optimization model is to maximize the performance index of the LVDT sensor. The optimization parameters are the parameter combinations of the artificial metamaterials. The parameter combinations include the length and width of the sub-rectangular structure corresponding to the projection of the first medium material in the metamaterial unit onto the two-dimensional plane, and the number of cycles of the metamaterial units arranged in the axial direction. S20. Iteratively optimize the parameter optimization model to obtain the optimal parameter combination of the artificial metamaterial; S30. Determine the optimal artificial metamaterial based on the optimal parameter combination; S40. The outer shell, coil, optimal artificial metamaterial and iron core are nested from the outside to the inside to form an LVDT sensor based on artificial metamaterial.

[0035] To efficiently determine the optimal parameter combination (h1, w, N) of artificial metamaterials and achieve precise performance design, this invention provides the following method: Key adjustable parameters of the artificial metamaterial are defined as design variables. For example, h1 is the length of the sub-rectangular structure corresponding to the projection of the first dielectric material in the metamaterial unit onto a two-dimensional plane, used to control the volume filling ratio of the dielectric; w is the width of the metamaterial unit, which is also the width of the sub-rectangular structure corresponding to the projection of the first dielectric material onto a two-dimensional plane, used to control the spatial distribution of the magnetic circuit; N is the number of axial arrangement periods of the metamaterial unit. The core performance indicators of the LVDT sensor are defined as optimization objectives. This invention mainly aims to maximize the sensitivity S of the LVDT sensor and minimize its nonlinear error t. Based on the electromagnetic field simulation software COMSOL Multiphysics, a parameterized finite element analysis model is established between the design variables (h1, w, N) and the optimization objectives (S, t). This model can automatically calculate the magnetic field distribution and output performance of the LVDT sensor under any given parameter combination.

[0036] In embodiment S20 of the present invention, the parameter optimization model is iteratively optimized to obtain the optimal parameter combination of the artificial metamaterial. This includes: using a multi-objective optimization algorithm, a particle swarm optimization algorithm, or a simulated annealing algorithm to iteratively optimize the parameter optimization model to obtain the optimal parameter combination of the artificial metamaterial.

[0037] Taking a multi-objective optimization algorithm as an example: A reasonable range of values ​​for the design variables (h1, w, N) is set, and the algorithm population is initialized. The algorithm iteration process includes: a) generating a new set of candidate parameter combinations; b) calling the aforementioned parameterized finite element model to calculate the sensitivity S and nonlinear error t corresponding to this set of parameters; c) selecting the best-performing solution set based on the Pareto optimality criterion. Steps ac and ac are repeated until the iteration count or performance convergence condition is met, and the optimal solution set is output. Taking the Non-Dominated Sorting Genetic Algorithm (NSGA-II) as an example, the multi-objective optimization algorithm encodes each parameter combination (h1, w, N) as a chromosome, using (S, t) as the objective function. The algorithm iteratively evolves the population by simulating selection, crossover, and mutation operations in biological evolution, eventually converging to a set of non-dominated solutions that achieve the best balance among multiple objectives. When the algorithm outputs one or more sets of Pareto optimal solutions (i.e., h1, w, N), they are used to guide the specific design and manufacturing of artificial metamaterials in this invention. That is, based on the results of the algorithm output, the geometric dimensions of the first dielectric material and the second dielectric material in each metamaterial unit and the arrangement period of the metamaterial unit are accurately determined, thereby realizing the on-demand customization of sensor performance.

[0038] It should be noted that the optimization algorithm of this invention is not limited to multi-objective optimization algorithms, particle swarm optimization algorithms, or simulated annealing algorithms; it can also be other optimization algorithms.

[0039] The design method for LVDT sensors based on artificial metamaterials proposed in this invention, combined with optimization algorithms, transforms the design process from "trial and error based on experience" to "model optimization," significantly improving design efficiency and the optimality of structural design. It innovatively introduces an independent, functional artificial metamaterial into the magnetic circuit of the LVDT sensor, enabling active and precise design of the internal magnetic field distribution. By designing the metamaterial unit composite structure and periodic arrangement of this artificial metamaterial to form a novel magnetic circuit matrix for the LVDT sensor, it provides two independently and actively controllable design dimensions for LVDT magnetic circuit design: unit equivalent permeability and axial action domain. Within this two-dimensional design space, by changing the filling ratio of the two dielectric materials in the metamaterial unit and the arrangement of the metamaterial units, continuous and precise control of the local "equivalent permeability" of the matrix can be achieved without significantly altering the macroscopic shape and volume of the LVDT sensor. This transforms permeability from a fixed material property into a variable that can be adjusted as needed, aiming to precisely adjust the sensor performance to meet specific performance indicators (such as high linearity, high sensitivity, or a balance between the two). The artificial metamaterial of this invention can be directly embedded in the inherent annular gap between the core and coil of an existing LVDT sensor. As an independent functional component, it does not require changes to the main topology of the sensor, coil parameters, or a significant increase in volume, thus reducing the process complexity and cost of improving existing LVDT sensors and has potential for engineering and industrialization.

[0040] As for the design method embodiment of the second aspect, since it is basically similar to the structural embodiment of the first aspect, the description is relatively simple. For relevant details, please refer to the description of the structural embodiment of the first aspect.

[0041] In the description of this invention, it should be understood that the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0042] Although the invention has been described herein in conjunction with various embodiments, those skilled in the art, by reviewing the specification and accompanying drawings, will understand and implement other variations of the disclosed embodiments in carrying out the claimed invention. In the specification, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality. While certain measures are described in different embodiments, this does not mean that these measures cannot be combined to produce good results.

[0043] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. An LVDT sensor based on artificial metamaterials, characterized in that, The LVDT sensor comprises a shell, a coil, an artificial metamaterial, and an iron core, nested from the outside in; wherein... The artificial metamaterial comprises several metamaterial units arranged periodically along the axial direction. Each metamaterial unit is composed of two dielectric materials, a first dielectric material and a second dielectric material, with different magnetic permeabilities. Each metamaterial unit is projected onto a two-dimensional plane as a rectangular structure, which includes sub-rectangular structures projected onto the two-dimensional plane by the first dielectric material and the second dielectric material, respectively. The length of the sub-rectangular structure represents the filling ratio of the corresponding dielectric material in the metamaterial unit, and the width of the sub-rectangular structure represents the spatial distribution of the metamaterial unit. The electromagnetic properties of the metamaterial unit can be controlled by changing the length and width of the sub-rectangular structure projected onto the two-dimensional plane by the first dielectric material, and the range of action of the artificial metamaterial can be controlled by changing the number of periods in which the metamaterial units are arranged along the axial direction.

2. The LVDT sensor based on artificial metamaterials according to claim 1, characterized in that, The permeability of the first medium is greater than that of the second medium.

3. The LVDT sensor based on artificial metamaterials according to claim 1, characterized in that, The first medium includes at least one of ferrite, silicon steel sheet, amorphous alloy and nanocrystalline alloy.

4. The LVDT sensor based on artificial metamaterials according to claim 1, characterized in that, The second medium includes at least one of air, plastic, and ceramic.

5. The LVDT sensor based on artificial metamaterials according to claim 1, characterized in that, The length of the sub-rectangular structure corresponding to the first medium is greater than the length of the sub-rectangular structure corresponding to the second medium, and the width of the sub-rectangular structure corresponding to the first medium is equal to the width of the sub-rectangular structure corresponding to the second medium.

6. The LVDT sensor based on artificial metamaterials according to claim 1, characterized in that, The artificial metamaterial covers at least the effective induction range of the coil in the axial direction.

7. The LVDT sensor based on artificial metamaterials according to claim 1, characterized in that, Artificial metamaterials are fixed to the inner wall of the coil by adhesive bonding or heat fitting.

8. A design method for an LVDT sensor based on artificial metamaterials, characterized in that, The design method for the LVDT sensor based on artificial metamaterials as described in any one of claims 1 to 7 includes: A parameter optimization model for artificial metamaterials is established. The objective of the parameter optimization model is to maximize the performance index of the LVDT sensor. The optimized parameters are the parameter combinations of the artificial metamaterials. The parameter combinations include the length and width of the sub-rectangular structure corresponding to the projection of the first dielectric material in the metamaterial unit onto the two-dimensional plane, and the number of cycles of the metamaterial units arranged axially. The optimal parameter combination of the artificial metamaterial is obtained by iterative optimization of the parameter optimization model. The optimal artificial metamaterial is determined based on the optimal parameter combination; An LVDT sensor based on artificial metamaterials is formed by nesting an outer shell, coil, optimal artificial metamaterial, and iron core from the outside in.

9. The design method of the LVDT sensor based on artificial metamaterials according to claim 8, characterized in that, Maximizing the performance metrics of an LVDT sensor includes maximizing its sensitivity and minimizing its nonlinearity error.

10. The design method of the LVDT sensor based on artificial metamaterials according to claim 8, characterized in that, The parameter optimization model is iteratively optimized to obtain the optimal parameter combination of the artificial metamaterial, including: By employing multi-objective optimization algorithms, particle swarm optimization algorithms, or simulated annealing algorithms, the parameter optimization model is iteratively optimized to obtain the optimal parameter combination of the artificial metamaterial.

Images