A virtual layered large-thick-wall solid structure outer surface deformation perception method

Abstract

This invention discloses a method for sensing the deformation of the outer surface of a large, thick-walled solid structure based on virtual layering. The method includes constructing a hybrid model comprising a main body and virtual layers; performing unilateral strain measurement on the outer surface of the large, thick-walled solid structure to obtain the biaxial measured strain components of the outer surface; establishing strain relationships on the virtual layers, using only the biaxial measured strain components of the outer surface as data fitting terms, and compensating for the in-plane shear strain components of the outer surface as inversion unknowns under regularization constraints to obtain the displacement field of the virtual layers; and applying the displacement field of the inverted virtual layers as boundary conditions to the hybrid model to obtain the displacement field of the outer surface of the large, thick-walled solid structure. This method can complete the deformation identification of the outer surface of a thick-walled solid structure under unilateral biaxial strain measurement conditions, reducing the dependence on multiaxial or bilateral strain measurements, and is suitable for online deformation monitoring and health assessment of critical thick-walled structures such as large pressure vessels and equipment bases.

Description

Technical Field

[0001] This invention relates to the field of displacement field identification and structural health monitoring technology for thick-walled solid structures, and particularly to a method for sensing the deformation of the outer surface of a virtual layered thick-walled solid structure. Background Technology

[0002] Thick-walled solid structures are widely used in large industrial equipment and special pressure vessels, such as high-pressure vessels, large storage tanks, and key load-bearing components of marine engineering equipment. During long-term service, the stability and safety of these structures have a significant impact on the continuous operation of the equipment system. With the development of engineering equipment towards larger size and higher reliability, online monitoring and health assessment of such thick-walled structures throughout their entire life cycle has become an urgent need. Due to prolonged exposure to complex alternating loads and multi-field coupled environments, thick-walled solid structures may experience fatigue damage or performance degradation. Failure to identify and intervene in a timely manner will adversely affect the normal operation of the engineering system. In particular, thick-walled structures exhibit a significant three-dimensional strain gradient along their thickness, creating a complex correlation between their external surface response and their internal true mechanical state.

[0003] Currently, traditional strain gauge monitoring or optical measurement methods are commonly used in engineering to perceive the structural state. Traditional strain gauges have a mature and reliable engineering foundation, but they can only provide local strain information at a limited number of measurement points, making it difficult to reflect the overall stress state of the structure. Furthermore, for thick-walled solid structures, sensor placement is usually limited by geometric characteristics, and can only be installed on accessible outer surfaces, making it impossible to directly obtain the mechanical response distribution inside the structure. Increasing the number of sensors also leads to a significant increase in deployment complexity and maintenance costs. While optical measurement methods (such as digital image correlation technology) can obtain surface displacement fields, they are sensitive to external conditions such as ambient light and shading, exhibit poor stability in complex real-world scenarios, and cannot directly infer stress changes inside the structure, limiting their application in long-term online monitoring scenarios.

[0004] In recent years, the inverse finite element method (IEM) has attracted attention because it can invert the displacement and stress distribution of structures using surface strain information. IEM, through the combination of numerical models and finite point measurement data, can achieve deformation reconstruction to a certain extent without external load information. However, existing IEM theories are mainly based on the mechanical assumptions of thin-walled structures such as beams, plates, and shells for modeling and derivation, and are not applicable to solid structures where geometric thickness dominates. When this type of method is directly applied to thick-walled solid structures, it faces two main theoretical obstacles: first, the three-dimensional stress-strain distribution of thick-walled structures is complex, and the traditional plate and shell assumptions no longer hold; second, if an attempt is made to directly establish inverse formulas for solid structures, complex three-dimensional constitutive relations and ill-posed inversion problems must be addressed, resulting in difficult solutions and insufficient reliability. Existing methods also lack a two-dimensional equivalent model that can effectively convert the three-dimensional strain of thick-walled solids into a reversible solution form, making it difficult to establish a stable inversion system.

[0005] Furthermore, in most engineering applications, the accessible area of ​​thick-walled solid structures is usually limited to their outer surface, and actual monitoring often only yields unilateral strain data. This unilateral measurement condition provides limited information and makes it difficult to effectively distinguish between the bending and tensile deformation components of the structure. This renders existing inverse analysis methods, which rely on bilateral or multilateral strain, unusable, thus becoming a key bottleneck limiting the perception of deformation in thick-walled structures. In particular, engineering practice often employs a three-dimensional (0°, 45°, 90°) measurement layout, but the outer surface of thick-walled structures often only allows for a limited number of measurement points, making three-dimensional measurements difficult to achieve in many scenarios.

[0006] In summary, existing technologies cannot stably and accurately obtain surface deformation information by relying solely on biaxial strain measurements on one side of the outer surface of a thick-walled solid structure. Therefore, it is necessary to provide a new technical solution to address these issues. Summary of the Invention

[0007] To address the aforementioned technical issues, this application proposes a deformation sensing method for the outer surface of a large, thick-walled solid structure based on virtual layering. This method enables the reversible solution of the virtual layered displacement field in the two-dimensional measured strain direction of the outer surface without altering the mechanical properties of the main structure. Furthermore, by utilizing the equivalent mapping relationship of virtual layering, it ensures that the solution stability and continuity are maintained even with a reduction in the number of measurement directions. This improves the accuracy and reliability of deformation monitoring of large, thick-walled solid structures under single-sided two-dimensional measurement conditions. The method can be used for online deformation identification and health monitoring of key engineering structures such as large equipment bases and thick-walled pressure vessels.

[0008] A method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure includes: Construct a hybrid model that includes a main body and virtual hierarchical components attached to the outer surface of the main body and fully connected by common nodes; Single-sided strain measurement was performed on the outer surface of a large, thick-walled solid structure to obtain the measured strain components in two directions on the outer surface. Strain relationships are established on the virtual layer. Only the two-dimensional measured strain components of the outer surface are used as data fitting terms. The in-plane shear strain components of the outer surface are used as inversion unknowns and compensated under regularization constraints to obtain the displacement field of the virtual layer. The displacement field obtained by inversion is applied as a boundary condition to the hybrid model to obtain the displacement field on the outer surface of the large thick-walled solid structure.

[0009] Optionally, a hybrid model is constructed comprising a main body and virtual hierarchical layers attached to the outer surface of the main body and connected by all common nodes, including: Based on the actual geometric dimensions of the large, thick-walled solid structure, a virtual, layered main body model is established, including the main body and the virtual layer attached to the outer surface of the main body. The virtual layer and the outer surface of the main body achieve geometric and displacement coordination through a common node connection, so that the nodes on the virtual layer and the nodes on the outer surface of the main body are completely coincident in spatial coordinates, share three-dimensional translational degrees of freedom, and establish an equivalent inversion mapping relationship between the virtual layer and the three-dimensional strain of the outer surface within the common node.

[0010] Optionally, the thickness of the main body is the total thickness of the thick-walled solid structure minus the thickness of the virtual layer.

[0011] Optionally, the main body is modeled using Solid185 solid elements, with each node having three translational degrees of freedom.

[0012] Optionally, the elastic modulus, Poisson's ratio, and density of the virtual layer are consistent with those of the main body.

[0013] Optionally, unilateral strain measurements are performed on the outer surface of the thick-walled solid structure to obtain the biaxial measured strain components of the outer surface, including: Based on the structural stress characteristics and monitoring requirements, on the outer surface of thick-walled solid structures... Key areas Deploy a strain measurement network; Measurement points were arranged in areas of stress concentration, geometric discontinuities, and areas of estimated maximum deformation. Single-sided strain measurements were performed at measurement points on the outer surface of a thick-walled solid structure to obtain the two-dimensional measured strain components of the outer surface.

[0014] Optionally, unilateral strain measurements can be performed at measurement points on the outer surface of the thick-walled solid structure, including: At the measurement points on the outer surface of the thick-walled solid structure, single-sided measurements are performed using a two-way layout at 0° and 90°.

[0015] Optionally, strain relationships are established on the virtual layer, using only the measured strain components of the outer surface in two directions as data fitting terms, and the in-plane shear strain components of the outer surface as inversion unknowns, compensated and solved under regularization constraints to obtain the displacement field of the virtual layer, including: Establish the mathematical relationship between displacement and strain on a virtual layer; Under the biaxial measurement conditions of 0° and 90°, data fitting is set only for the biaxial measured strain components, and the in-plane shear strain components of the outer surface are used as inversion unknowns to compensate and solve under regularization constraints. A weighted least squares objective function is constructed, and a virtual layered displacement field is obtained by minimizing the objective function. The virtual layer is discretized, divided into finite element elements, and the relevant matrices and vectors are calculated. Construct the overall solution equations according to the finite element assembly rules; Solving the global equations yields the virtual layered displacement field.

[0016] The above solution process can be achieved using existing inverse analysis methods.

[0017] Compared with the prior art, this application has at least the following beneficial effects: 1. This invention solvates the inversion problem of thick-walled solid structures by setting up virtual layers, constructing a hybrid model that combines virtual and real elements. This transforms the deformation inversion problem of the outer surface of a large, thick-walled solid structure into an equivalent problem solvable on a virtual layer. The virtual layer is connected to the main body via shared nodes, achieving accurate mapping of the mechanical response of the outer surface and providing a stable and computable interface for subsequent inversion. This technical approach avoids the theoretical difficulties of directly constructing an inversion model on the solid structure, transforming the identification of outer surface deformation of thick-walled structures from a complex three-dimensional problem into a mature two-dimensional shell inversion problem, thereby significantly improving the feasibility and solution stability of the method. 2. This invention achieves bidirectional transmission of mechanical response through shared-node connections, improving the accuracy of external surface deformation inversion. Specifically, this invention sets an extremely thin virtual layer on the outer surface of the thick-walled structure, connected to the main body through shared-node connections, ensuring strict consistency between the two in geometric position and displacement degrees of freedom. In actual monitoring, the external surface deformation of the main body can be accurately transmitted to the virtual layer through the shared-node relationship, forming a composite response including membrane and bending effects. During the inversion stage, the displacement field obtained from the virtual layer inversion can be applied inversely to the hybrid model, achieving coordinated deformation of the overall structure. This virtual-real synergy mechanism breaks through the limitations of traditional inverse analysis methods in thick-walled structure applications and lays a structural-level observability foundation for stable external surface deformation identification under constrained directional measurement conditions (single-sided two-way measurement), providing a novel numerical modeling approach for external surface deformation identification of thick-walled structures.

[0018] 3. This invention can stably identify external surface bending deformation even under unilateral biaxial strain measurement conditions. Specifically, given that only unilateral strain of the external surface is typically available for thick-walled structures in engineering practice, this invention utilizes virtual layering to construct an invertible strain-displacement relationship, enabling unilateral biaxial strain measurement to obtain structural deformation information including bending effects. By establishing a weighted least squares objective function model based on virtual layering, this method avoids the dependence of traditional inverse finite element methods on bilateral strain measurement. Furthermore, by introducing constraint relationships between in-plane strain components in the virtual layering, it can correctly distinguish between membrane deformation and bending deformation even under biaxial measurement conditions, thereby solving the problem of difficult bending identification in unilateral biaxial monitoring of thick-walled structures and enhancing the applicability of the method in engineering fields.

[0019] 4. This invention can effectively reconstruct the displacement field of the outer surface and exhibits good robustness to noise and model uncertainties. Specifically, because the virtual layering maintains strict mechanical consistency with the main structure, the inversion model constructed by this invention has strong fault tolerance to measurement noise. Even with limited surface strain information and noise interference, a stable and reliable virtual layered displacement field can still be obtained, further enabling effective reconstruction of the displacement field of the outer surface of thick-walled structures. The two-dimensional inversion domain constructed by the virtual layering reduces the ill-conditioned nature of three-dimensional thick-walled inversion, allowing the method to maintain good solution stability even with high noise levels or limited measurement points. This method demonstrates good robustness in multiple numerical examples, effectively solving the problem of insufficient accuracy of existing methods in thick-walled structure applications.

[0020] 5. This invention significantly reduces the number of sensors required, lowering engineering implementation costs. Compared to traditional methods that require deploying numerous sensors on the inner and outer surfaces of a structure, this invention effectively reconstructs the displacement field of the outer surface of the structure using only unilateral biaxial strain data from a limited number of measuring points. Under the constraint of virtual layering, the in-plane deformation information required for inversion can be obtained from biaxial strain measurements, reducing both the number of measuring points and single-point directional measurements. This advantage not only reduces the number of sensors and wiring complexity but also lowers system construction and maintenance costs, improving the scalability of the project.

[0021] 6. The system deployment of this invention is simple and suitable for long-term online monitoring of large, thick-walled structures. Specifically, the virtual layered inversion method of this invention has high computational efficiency and low computational resource requirements, and can run stably on ordinary industrial computing equipment. Furthermore, since all sensors are installed on the outer surface of the structure, no internal wiring or structural modifications are required, making installation and maintenance convenient and suitable for long-term health monitoring of large, thick-walled structures. Based on the simplified two-dimensional inversion domain of virtual layering, compared to directly processing three-dimensional thick-walled entities, computational complexity and model building workload can be further reduced. This method can be widely applied to deformation monitoring of structures such as large equipment foundations, thick-walled pressure vessels, storage tanks, and marine engineering equipment, and has good engineering application prospects. Attached Figure Description

[0022] The following sections will describe some specific embodiments of the invention in detail by way of example and not limitation, with reference to the accompanying drawings. The same reference numerals in the drawings denote the same or similar parts or portions. Those skilled in the art should understand that these drawings are not necessarily drawn to scale. In the drawings: Figure 1 This is a schematic diagram of the overall process of the present invention; Figure 2 This is a schematic diagram of a hybrid model combining virtual and real elements for a floating nuclear power plant reactor pressure vessel (RPV) in an embodiment of the present invention; wherein, Figure a is a schematic diagram of the floating nuclear power plant reactor pressure vessel (RPV) model, Figure b is a sectional view of the front sidewall of the virtual layer from both the side and top views, and Figure c is a sectional view of the rear sidewall of the virtual layer from both the side and top views. Figure 3 for Figure 2 A magnified view of position A in the middle; Figure 4 This is a schematic diagram showing the reduction of the three-directional sensor deployment scheme to a two-directional sensor deployment scheme in an embodiment of the present invention; Figure 5 This is a schematic diagram of virtual layered unilateral strain measurement in an embodiment of the present invention; Figure 6 This is a spatial simulation result of the displacement field on the outer surface of a thick-walled structure under typical service conditions (steady-state high temperature and high pressure) in an embodiment of the present invention. Figure 7 This is a spatial sensing result of the displacement field on the outer surface of a thick-walled structure under typical service conditions (steady-state high temperature and high pressure) in an embodiment of the present invention. Figure 8 This is a comparison of the displacement time history of a representative node selected along the height of the pressure vessel in this embodiment of the invention during the entire operating cycle; Figure 9 This is a diagram showing the average relative displacement error under strain input superimposed with Gaussian noise of different intensities in an embodiment of the present invention. Detailed Implementation

[0023] To make the objectives, technical solutions, and advantages of this application clearer, the technical solutions of this application will be clearly and completely described below in conjunction with specific embodiments and corresponding drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0024] The thick-walled solid structure in this scheme refers to a solid structure with non-negligible thickness, significant stress and strain gradients along the thickness direction, and which cannot be described by the thin-shell assumption. Existing technologies for deformation monitoring of thick-walled solid structures suffer from the following problems: First, traditional inverse finite element methods are difficult to apply directly to thick-walled solid structures, lacking a modeling mechanism to convert the three-dimensional mechanical response into an invertible solution domain; second, in practical engineering, it is difficult to achieve internal or bilateral strain measurements, only unilateral strain data can be obtained, and traditional methods typically require triaxial (0°, 45°, 90°) measurements, making them unsuitable for limited directional measurement conditions; third, existing monitoring methods have insufficient accuracy, poor robustness, and complex implementation processes under unilateral measurement conditions.

[0025] The present invention proposes a method for sensing the deformation of the outer surface of a thick-walled solid structure based on virtual layering. The overall idea is to take virtual layering technology as the core, and by constructing a hybrid model that combines virtual and real elements, the problem of inverting the deformation of the outer surface of a thick-walled solid structure, which is traditionally difficult to solve directly, is equivalent to an analytical virtual layering inverse problem.

[0026] By constructing a hybrid modeling system that includes a main body and virtual layers attached to and fully connected to the outer surface of the main body, the problem of deformation inversion of the outer surface of a large thick-walled solid structure is transformed from a complex three-dimensional solid inversion problem into a solvable two-dimensional virtual layered inversion problem. The virtual layering achieves an equivalent mapping of the mechanical response of the outer surface through the connection of shared nodes, and the three-dimensional mechanical response of the outer surface of the thick-walled solid is equivalent to a reversibly solvable two-dimensional virtual layered field, which improves the observability under the condition of single-sided strain measurement. At the same time, under the restricted directional measurement condition of reducing from three directions (0°, 45°, 90°) to two directions (0°, 90°), data fitting is set only for the two-directional measured strain components, and the in-plane shear strain component is used as the inversion unknown quantity to compensate for the solution under regularization constraints, thereby maintaining the identifiability and stability of the inversion equation and overcoming the limitation of insufficient inversion information under the condition of single-sided two-directional measurement of thick-walled structures. By using the inversion model constructed with virtual layering, a virtual layered displacement field can be obtained, which can then drive a hybrid model to achieve effective reconstruction of the displacement of the outer surface of a thick-walled solid structure.

[0027] Specifically, this invention proposes a hybrid modeling strategy combining virtual and real elements. The thick-walled solid structure to be monitored is decomposed in the finite element model into a main body composed of Solid185 solid elements and a virtual layer attached to the outer surface of the main body, composed of Shell181 virtual layers. The virtual layer has a certain thickness, and the total thickness of the hybrid model is completely consistent with the original structure. Through the shared node connection between the virtual layer and the outer surface of the main body, bidirectional transmission of mechanical response is achieved. The nodes of the virtual layer and the nodes of the outer surface of the main body are completely overlapped in space and share three-dimensional translational degrees of freedom, ensuring strict displacement continuity. This allows the three-dimensional mechanical response of the outer surface to form a reversibly solvable two-dimensional inversion domain on the virtual layer. Simultaneously, by establishing mathematical constraints between in-plane strain components in the virtual layer, the identifiability of the inversion equations can be maintained even under unilateral constrained directional conditions. Thus, without changing the constitutive relation of the main structure, effective perception of the bending and shear responses of the outer surface can be achieved.

[0028] During the sensing phase, due to the difficulty in deploying sensors inside and on the opposite sides of thick-walled solid structures, this method employs a single-sided biaxial strain measurement scheme. Strain sensors are placed on the accessible outer surface, mounted at the outer surface position of the virtual layer. Through a common-node mechanism, the actual deformation of the outer surface of the main body is synchronously transmitted to the virtual layer, driving it to generate a composite response that simultaneously includes membrane strain and bending strain. This generates in-plane strain input data on the virtual layer that can be used for two-dimensional inversion.

[0029] In the inversion stage, the virtual layer serves not only as the strain sensing interface but also as the computational interface for displacement inversion. This invention constructs an invertible strain-displacement relationship model based on the virtual layer and uses inverse analysis to solve the displacement field of the virtual layer. This invention does not limit the specific form of the inverse algorithm and can construct a weighted least-squares objective function solution model based on the virtual layer. Under the condition that the three-dimensional (0°, 45°, 90°) measurement is reduced to two-dimensional (0°, 90°) measurement, the data fitting term only applies to the measured strain components in the two-dimensional (0°, 90°) directions. The in-plane shear strain component is used as the inversion unknown and compensated for under regularization constraints, allowing the surface strain measured on one side in two directions to be used to invert the displacement field of the virtual layer, breaking through the dependence of traditional methods on two-sided strain measurements. Simultaneously, by establishing mathematical constraints between in-plane strain components within the virtual layer, it maintains the identifiability of the inversion equations under limited directional measurement conditions, achieving stable identification of the outer surface bending components.

[0030] In the forward analysis phase, the virtual layered displacement field obtained by inversion is applied as a displacement boundary condition to the outer surface nodes of the hybrid model. By utilizing the common node relationship between the virtual layer and the main body, the inverted displacement accurately drives the coordinated deformation of the main structure, thereby reconstructing the real displacement field and stress distribution of the outer surface of the thick-walled solid structure.

[0031] This method enables deformation identification of the outer surface of thick-walled solid structures under unilateral biaxial measurement conditions without altering the original structural mechanical properties and geometric consistency. The virtual layering in this system simultaneously performs three functions: mechanical mapping, strain sensing, and displacement transfer. Mechanical mapping transforms the three-dimensional response of the outer surface into an invertible two-dimensional virtual layered solution domain; strain sensing obtains in-plane strain input data under unilateral biaxial measurement; and displacement transfer ensures that the inverted displacement accurately drives the coordinated deformation of the main body. By introducing mathematical constraints between in-plane strain components within the virtual layering, this method maintains good identifiability and stability even under limited directional measurement conditions (reduced from three-dimensional to two-dimensional), overcoming the engineering bottlenecks of difficulty in deploying measurement points and conducting bilateral sensing on thick-walled solid structures. This provides an implementable, effective, stable, and reliable technical solution for monitoring the outer surface of large thick-walled structures.

[0032] like Figure 1 As shown, a method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure includes the following steps: S1. Construct a hybrid model that includes a main body and virtual layers attached to the outer surface of the main body and fully connected by common nodes.

[0033] Specifically, the hybrid model consists of two parts: the main body and the virtual layers, which are geometrically and mechanically consistent.

[0034] In practice, the first step is to establish a main body model that includes the main body and virtual layers attached to the outer surface of the main body, based on the actual geometric dimensions of the large thick-walled solid structure.

[0035] The virtual layer has a certain thickness, and the thickness of the main body is the total thickness of the thick-walled solid structure minus the thickness of the virtual layer. Simultaneously, its material parameters, such as elastic modulus, Poisson's ratio, and density, remain consistent with the main body to ensure the continuity of overall stiffness and mechanical response.

[0036] In this embodiment, the main body is modeled using Solid185 solid elements. Each node has three translational degrees of freedom, which is used to describe the volumetric stress and overall deformation characteristics of the thick-walled structure, and to provide a benchmark for the real three-dimensional strain field for virtual layering, so that the subsequent virtual layering inverse analysis has a three-dimensional to two-dimensional mapping basis.

[0037] Subsequently, an extremely thin Shell181 virtual layer is generated on the outer surface of the main structure as a virtual layer. The thickness of the virtual layer is set to 1 mm, and its material parameters, such as elastic modulus, Poisson's ratio, and density, are consistent with those of the main body to ensure the continuity of overall stiffness and mechanical response. The virtual layer and the outer surface of the main body are connected by common nodes to achieve geometric and displacement coordination. That is, the nodes of the virtual layer and the nodes of the outer surface of the solid element are completely coincident in spatial coordinates and share three-dimensional translational degrees of freedom. An equivalent inversion mapping relationship between the virtual layer and the three-dimensional strain of the outer surface is established within the common nodes, thereby achieving strict continuity of the displacement field at the outer surface. Through the common node connection between the virtual layer and the outer surface of the main body, bidirectional transmission of mechanical response is realized, and the three-dimensional mechanical behavior of the outer surface forms a two-dimensional equivalent solution domain on the virtual layer that can be used for displacement inversion.

[0038] This step completes the establishment of the hybrid model, providing a stable and reliable numerical basis for subsequent single-sided biaxial strain measurement and virtual layered displacement field inversion.

[0039] S2. Perform unilateral strain measurement on the outer surface of a thick-walled solid structure to obtain the two-dimensional measured strain components on the outer surface.

[0040] In practice, based on the structural stress characteristics and monitoring requirements, a strain measurement network is deployed in key areas of the outer surface of the thick-walled solid structure. Measurement points are preferentially placed in stress concentration areas, geometrically discontinuous parts, and areas of estimated maximum deformation to obtain key strain information reflecting the overall deformation state of the structure, which serves as input data for subsequent virtual layered displacement field inversion. Under bidirectional (0°, 90°) measurement conditions, the single-sided strain measurement is reduced from a tridirectional (0°, 45°, 90°) deployment to a bidirectional (0°, 90°) deployment. In the subsequent inversion process, mathematical constraints and regularization constraints between strain components within the virtual layer will be combined to achieve compensation for missing directional information.

[0041] S3. Establish strain relationships on the virtual layer, using only the measured strain components of the outer surface in two directions as data fitting terms, and use the in-plane shear strain components of the outer surface as inversion unknowns to compensate and solve under regularization constraints to obtain the displacement field of the virtual layer.

[0042] This step utilizes the unilateral biaxial strain data measured in S2 and solves for the displacement field of the virtual layer based on an inversion model constructed from the virtual layer. This invention does not limit the specific inversion algorithm; any inverse analysis method capable of solving the displacement field based on the virtual layer strain can be used. The specific implementation process may include: establishing a mathematical relationship between the virtual layer membrane strain and bending strain using the geometric and thickness characteristics of the virtual layer; constructing a weighted least squares objective function based on this, and obtaining the virtual layer displacement field by minimizing the objective function; discretizing the virtual layer into finite element elements and calculating the relevant element matrices and vectors; forming an overall solution equation according to finite element assembly rules; and solving the overall equation to obtain the displacement field distribution of the virtual layer. By introducing the half-thickness parameter of the virtual layer, a unified relationship can be established between the unilateral biaxial strain measurement and the virtual layer membrane-bending response. Combined with the in-plane strain component constraints within the virtual layer, a complete and identifiable displacement field can still be obtained under biaxial measurement conditions. Simultaneously, techniques such as weight adjustment and regularization can be combined to improve the stability and noise resistance of the inversion process. It should be noted that the inversion solution is based only on virtual hierarchical units and does not involve the solution of the main body structure, ensuring that the inversion process is efficient and stable.

[0043] S4. Apply the virtual layered displacement field obtained by inversion as a boundary condition to the hybrid model to obtain the displacement field on the outer surface of the large thick-walled solid structure.

[0044] The displacement field obtained by inversion is used as a displacement boundary condition and directly applied to the outer surface nodes of the hybrid solid model. The displacement field reconstruction of the outer surface of the thick-walled solid structure is obtained through a forward analysis.

[0045] Example

[0046] like Figure 2 and Figure 3 As shown, this embodiment establishes a hybrid finite element model of the thick-walled shell of the floating nuclear power plant reactor pressure vessel (RPV) by introducing the concept of virtual layering while maintaining the real geometric features. The left side is a three-dimensional model of the complete RPV, which includes structures such as the upper head, cylinder, and inlet / outlet water pipes. The whole model is discretized using Solid185 three-dimensional solid elements to describe the stress and deformation response of the thick-walled pressure vessel under service conditions.

[0047] To achieve deformation inversion based on unilateral biaxial strain measurement on the outer surface, the thick wall is subjected to virtual layering. The middle section shows a view of a local cross-section, i.e., the model before virtual layering. The cylinder wall thickness is represented by solid Solid185 elements, and the cross-section consists of only a single thick-walled solid. In the model after virtual layering, while maintaining the original solid wall thickness, the cross-section is conceptually divided into a main body and a virtual layered part. The main body is still composed of Solid185 elements, representing the majority of the thick-walled volume; a layer of Shell181 elements is attached to its outer surface, forming an outer virtual layer.

[0048] Enlarged view of the part as shown Figure 3 As shown, the outer virtual layer, i.e., the outermost virtual layer, is arranged closely to the outer surface of the solid cylinder. During modeling, the RPV thick-walled solid is first meshed, and then a Shell181 element layer is directly generated using the nodes on the outer surface of the solid elements through a shared-node technique. This ensures that the virtual layer and the corresponding solid surface are geometrically perfectly aligned, with consistent node coordinates and shared degrees of freedom. During calculation, these shared nodes bear unified displacement and rotation degrees of freedom, thus guaranteeing complete coordination between the virtual layer and the solid thick wall during deformation, without relative slippage or separation.

[0049] To ensure the mechanical consistency of the hybrid model, the virtual layer and the solid cylinder are given the same material properties, namely the same elastic modulus, Poisson's ratio, and density. In this way, on the one hand, the original overall stiffness and mass distribution of the thick-walled structure are maintained, and on the other hand, the deformation monitoring problem of the outer surface of the thick-walled structure is transformed into a virtual layered inverse finite element problem through the outer Shell181 virtual layer. This provides a reliable numerical basis for subsequent inner surface deformation sensing and displacement field reconstruction based on unilateral biaxial surface strain.

[0050] Please refer to the appendix. Figure 4 , Figure 4 This diagram illustrates the reduction of a three-dimensional sensor deployment scheme to a two-dimensional sensor deployment scheme. The left side shows the commonly used 0° / 45° / 90° three-dimensional deployment method in traditional strain measurement schemes; the right side shows the measurement method adopted in this invention, which retains only the 0° / 90° two-dimensional configuration. This invention utilizes a virtual layered strain relationship, combined with mathematical and regularization constraints between strain components within the virtual layer, to maintain the identifiability of the inversion equation under two-dimensional measurement conditions, thereby eliminating the need for strain measurement in the 45° direction and simplifying the measurement deployment.

[0051] Please refer to the appendix. Figure 5 , Figure 5 This is a schematic diagram of the virtual layered unilateral biaxial strain measurement in this invention, illustrating the specific scheme for performing biaxial (0°, 90°) strain measurement on the outer surface of the virtual layer, which specifically includes the following process: A coordinate system is established with the virtual layer's mid-surface as the X–Y plane and the normal direction as the Z-axis. Here, Z = +h indicates that the measurement surface is located on the outer surface (upper surface) of the virtual layer, and this measurement surface coincides with the outer surface of the hybrid model. The parameter h is half the thickness of the virtual layer; in this embodiment, the total thickness of the virtual layer is 1mm, therefore h = 0.5mm. It should be noted that the total thickness of the virtual layer, 2h = 1mm, is indicated in the attached figure.

[0052] Biaxial strain gauges are arranged on the outer surface, and the corresponding surface strain measurements are obtained along the 0° and 90° directions, i.e., the biaxial measured strain components of the outer surface. and Although the physical layout direction is reduced from the traditional three-dimensional 0° / 45° / 90° to two-dimensional 0° / 90°, the in-plane strain relationship of virtual layering is used to obtain the bi-dimensional measured strain components in the subsequent inversion process. , As input for data fitting, and using in-plane shear strain components

[0053] The unknowns in the inversion are compensated for under regularization constraints. This results in a one-sided surface strain vector used for subsequent inversion calculations. When deploying sensor networks, stress concentration areas and geometric discontinuities should still be covered to ensure that the main deformation modes can be captured.

[0054] In the bidirectional measurement scheme of this invention, each measuring point directly obtains surface strain observation values ​​in two directions using strain gauges arranged along the 0° and 90° directions. The missing shear strain component is not obtained through direct measurement, but is treated as an undetermined variable on a virtual layer, and is used in the inversion model. , Solve them together. By introducing the geometric compatibility relationship between in-plane strain components and membrane-bending constraints into the virtual layering, the measured strain components in both directions of the outer surface can be reconstructed during the inversion process. and and the in-plane shear strain components of the outer surface The complete single-sided surface strain vector included .

[0055] The inversion method employed in this invention uses virtual stratification as the core inversion interface. By establishing a mathematical relationship between unilateral biaxial surface strain and the displacement state of the virtual stratification, and using inverse analysis to solve the surface strain data, the displacement distribution of the virtual stratification is obtained. This invention does not limit the specific form of the inverse analysis method; it can combine numerical methods such as finite element discretization, weighted least squares objective function solving, and regularization to construct the overall inversion process. Under the condition of only deploying biaxial (0° and 90°) strain sensors, the in-plane shear strain components that are not directly measured are...

[0056] As the unknown quantity in the inversion, it is retained in the virtual layered strain field and solved together with geometric compatibility conditions, material constitutive relations, membrane-bending constraints and measured strain components to achieve equivalent compensation for missing strain information.

[0057] In practical engineering scenarios, due to geometric and accessibility limitations of thick-walled solid structures, strain measurement points can usually only be arranged on the outer surface of the structure. This invention adopts a single-sided biaxial (0°, 90°) measurement scheme, allowing each measurement point to directly obtain the biaxial measured strain components. and

[0058] Compared to the traditional three-dimensional (0° / 45° / 90°) measurement method, the in-plane shear strain component... Instead of being directly provided by sensors, the strain components are treated as undetermined variables in a virtual layered strain field. In subsequent inversion processes, these components are compensated for by considering the geometric compatibility requirements between strain components within the virtual layer, membrane-bending constraints, and regularization constraints. Thus, a complete set of unilateral surface strain components can be generated during the inversion process for calculation, expressed as: ; In the formula, For the strain vector of one side of the virtual layered outer surface; The X-direction normal strain observation value is obtained directly from the strain gauge along the 0° direction; The strain observations in the Y direction are obtained directly from the strain gauge along the 90° direction. The shear strain components in the X–Y plane are not directly acquired by the sensor under biaxial measurement conditions, but are obtained as unknowns in the inversion model through compensation.

[0059] After obtaining the biaxial measured strain input, a strain description consistent with the displacement field needs to be established on the virtual layer, so that the strain measured on the outer surface... , It can constrain the displacement state of virtual layers and make It participates in the solution process as an unknown. The virtual layered outer surface is located at... Its surface strain is jointly determined by the membrane strain term corresponding to the mid-surface deformation and the term reflecting the bending effect. The bending contribution is related to the positional parameter from the mid-surface. Related. This invention only applies to bidirectional measurement conditions. , Set data fitting constraints, and at the same time The missing orientation information is retained as a variable to be determined. The mathematical constraints and regularization constraints within the virtual layer are used to compensate for the missing orientation information, thereby providing a unified, identifiable and stable input organization for the subsequent virtual layer displacement field inversion.

[0060] To further formalize the strain description of the virtual layered outer surface, this embodiment employs a first-order shear deformation displacement assumption to parameterize the displacement state of the virtual layer. A method is established with the mid-surface of the virtual layer as... Plane, normal direction is The coordinate system of the axes. The surface displacement components in the virtual layer are denoted as... , , The mid-plane corner is denoted as , The virtual layered outer surface is located at ,in The virtual layer thickness is half; in this embodiment, the total virtual layer thickness is... ,therefore .

[0061] exist At the outer surface, the in-plane strain components can be given by the mid-surface displacement and rotation variables, and written as: ; ; ; In the formula, , These correspond to the measured components of the outer surface directly obtained from the strain gauges in two directions (0° and 90°); The in-plane shear strain component of the outer surface is not directly provided by the sensor under biaxial measurement conditions, but is retained as an unknown in the inversion and compensated for under regularization constraints.

[0062] Therefore, the strain vector on one side of the virtual layered outer surface can be expressed as:

[0063] It is important to emphasize that, under two-way measurement conditions, the consistency of subsequent data depends solely on the two measured components. , supply; Instead of being used as an independent measurement input for data fitting, it is stably obtained during the inversion process through mathematical and regularization constraints within the virtual layer, thereby reducing the number of directions measured while maintaining the identifiability and stability of the solution. This organization method belongs to the information compensation mechanism of this invention under single-sided two-way measurement conditions, and is not a simple replacement of the three-way measurement input form with a two-way input.

[0064] After establishing the expression for the external surface strain, a weighted least squares objective function is further constructed for inverting the virtual layered displacement field, unifying the two-dimensional measured constraints and shear component compensation within the same inversion framework. For the virtual layered... For each finite element element, the objective function is defined as: ； In the formula, is the virtual layered element node degree of freedom vector (including three-dimensional translation and rotation degrees of freedom); 𝐴𝑒 represents the projection region of the virtual layered finite element on the mid-surface of the structure geometry, that is, the two-dimensional integral domain corresponding to the element position on the mid-surface, used for unified integral calculation of strain constraints, regularization terms and objective functions; d𝐴 is the area micro-element on the mid-surface region, and the relevant area integrals are all performed at the element scale, and the overall inversion model is formed through global assembly.

[0065] Biaxial external surface strain components obtained from element degree of freedom calculation Defined as: ; Actual input for: ; This is a measurement weight matrix used to coordinate the weights of different measurement points and different components; This represents the bending-related quantity constituted by the rotation angle gradient; , These are the bending regularization coefficient and the shear regularization coefficient, respectively. The first term applies only to measurable data. The first step is to perform data fitting; the third step provides the necessary regularization constraints to ensure stable solution even in the absence of direct measurement.

[0066] Discretize the above objective function and then... Taking the minimum, we can obtain the unit linear equation: ; In the formula, It is a unit matrix; It is a unit vector.

[0067] Among them, the unit matrix

[0068] It can be written as: ; Unit vector Formed solely from biaxial measured strain input: ; In the formula, To map the node degrees of freedom to The strain matrix; The bending correlation matrix; To map the node degrees of freedom to The matrix. Due to the two-way measurement Since it is not included in the data fitting input, its solution stability is determined by... This provides a way to avoid equation degradation and ensure identifiability under two-dimensional measurement conditions.

[0069] The equations of each element in the virtual layer are assembled according to the finite element assembly rules to obtain the overall linear equation system: ; In the formula, For the overall matrix, For virtual hierarchical overall degree of freedom vector, This is the right-hand term of the whole. The assembly process follows the requirements of finite element continuity and consistency, and transforms the element matrix in the local coordinate system to the global coordinate system when necessary.

[0070] Under the bidirectional (0°, 90°) unilateral strain measurement conditions of this invention, the overall right end term Only the two measured strain components , Data fitting terms are assembled; in-plane shear strain components Instead of being used as an independent measurement in the data fitting input, it is used through the overall matrix. The corresponding shearing regularization term is constrained, thus maintaining the identifiability and stability of the equation system under direction-shortening conditions. The overall system size depends on the degree of discretization and the number of nodes.

[0071] To avoid singularities in the equations due to potential rigid body displacement modes in the overall system, necessary displacement boundary conditions or equivalent constraints are applied to the virtual layer before solving (by directly modifying the system matrix, using the penalty function method, or the Lagrange multiplier method). The virtual layered displacement field is then obtained by solving the aforementioned equations. Furthermore, the strain and stress distribution of the virtual layer and the main structure can be calculated. The displacement field of the virtual layer obtained by inversion is applied as a displacement boundary condition to the outer surface nodes of the hybrid model that are completely connected with the virtual layer. The synchronous displacement relationship of the shared nodes is used to drive the coordinated deformation of the main body, thereby reconstructing the displacement field of the outer surface of the large thick-walled solid structure.

[0072] Equivalently, the overall equilibrium condition can be written in residual form: ; Based on the aforementioned expression of external surface strain and the weighted least squares objective function, the inversion solution from single-sided two-dimensional surface strain to displacement field can be achieved on a virtual layer. Since the virtual layer is completely nodally connected to the main structure's external surface, external surface deformation can be equivalently mapped to the invertible displacement state of the virtual layer, thus transforming the deformation inversion of the thick-walled solid structure's external surface from a three-dimensional solid problem into a two-dimensional solution problem on a virtual layer. This is especially true when the directional measurement is from three dimensions (…). ) reduced to two directions ( When this invention is applied, it only applies to the two-dimensional measured strain components. , Set data fitting constraints and include unmeasured in-plane shear strain components. As unknowns in the inversion process, and through regularization constraints, stable compensation is achieved during the solution process, thereby reducing the number of directional measurements while maintaining the identifiability of the equations and the stability of the solution. Thus, limited unilateral biaxial surface strain data can still simultaneously characterize tensile and bending effects on a virtual layer, and further drive the coordinated deformation of the main body through the synchronous relationship of common node displacements, realizing the reconstruction of the displacement field of the outer surface of the thick-walled solid structure. This is suitable for the identification of deformation and health monitoring of the outer surface of thick-walled structures.

[0073] Finally, the virtual layered displacement field obtained through the virtual layered inverse analysis method is applied as a displacement boundary condition to the hybrid model to obtain the displacement field of the outer surface of the large thick-walled solid structure. Relying on the displacement coordination relationship between the virtual layered structure and the outer surface of the main structure, which are completely connected at common nodes, the inverted displacement can be synchronously transferred to the nodes of the outer surface of the solid structure, thereby realizing the reconstruction of the displacement field of the outer surface and ensuring that the reconstruction result is consistent with the actual deformation response of the outer surface of the structure.

[0074] Figure 6 and Figure 7 The results of identifying the displacement field of the outer surface of a thick-walled structure using the virtual layered inverse finite element method of this invention under typical service conditions (steady-state high temperature and high pressure) are presented. Spatial simulation results and spatial sensing results of the displacement field of the outer surface of the thick-walled structure under typical service conditions (steady-state high temperature and high pressure) show that the spatial distribution of displacement is basically the same in both cases. That is, the inverted displacement distribution is highly consistent with the direct finite element calculation, with the maximum relative error maintained at 1.698%. The verification results demonstrate that this invention can achieve high-precision spatial identification of outer surface deformation under complex thermo-pressure coupling, exhibiting significant engineering applicability.

[0075] Figure 8 The displacement time histories of representative nodes selected along the height of the pressure vessel are compared throughout the entire operating cycle of loading-heating-steady-cooling. The inversion curves obtained by the virtual layered inverse finite element method and the direct finite element method show a high degree of consistency in amplitude, trend, and inflection point location. The results indicate that the present invention can achieve real-time deformation tracking of thick-walled structures over long periods and in multiple stages.

[0076] Appendix Figure 9 The average relative displacement error is presented under the condition of strain input superimposed with Gaussian noise of different intensities (SNR=40, 35, 30, 25dB). As the noise increases, the recognition error rises slightly, but the overall error remains at a low level acceptable for engineering. The results show that the present invention still has good noise resistance and inversion stability in low signal-to-noise ratio environments.

[0077] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0078] It should be noted that the terms "first," "second," etc., used in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of this application described herein can be implemented in sequences other than those illustrated or described herein.

[0079] It should be noted that the above mathematical expressions, strain relations, objective function construction methods, and discrete solution steps are only used to exemplify an optional inversion implementation process and are not intended to limit the present invention. The core of the present invention lies in: a hybrid modeling mechanism based on virtual layering and complete shared-node connections on the outer surface of the main structure, and under unilateral bidirectional (0°, 90°) measurement conditions, using only... , As input for data fitting, and This serves as an invertible mechanism for compensating and solving for inversion unknowns under regularization constraints. Without deviating from the core mechanism described above, in practical applications, this process can be implemented using inverse analysis methods suitable for virtual layered displacement inversion.

[0080] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure, characterized in that, include: Construct a hybrid model that includes a main body and virtual hierarchical components attached to the outer surface of the main body and fully connected by common nodes; Single-sided strain measurement was performed on the outer surface of a large, thick-walled solid structure to obtain the measured strain components in two directions on the outer surface. Strain relationships are established on the virtual layer. Only the two-dimensional measured strain components of the outer surface are used as data fitting terms. The in-plane shear strain components of the outer surface are used as inversion unknowns and compensated under regularization constraints to obtain the displacement field of the virtual layer. The displacement field obtained by inversion is applied as a boundary condition to the hybrid model to obtain the displacement field on the outer surface of the large thick-walled solid structure.

2. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 1, characterized in that, Construct a hybrid model comprising a main body and virtual hierarchical layers attached to the outer surface of the main body and fully interconnected with common nodes, including: Based on the actual geometric dimensions of the large, thick-walled solid structure, a virtual, layered main body model is established, including the main body and the virtual layer attached to the outer surface of the main body. The virtual layer and the outer surface of the main body achieve geometric and displacement coordination through a common node connection, so that the nodes on the virtual layer and the nodes on the outer surface of the main body are completely coincident in spatial coordinates, share three-dimensional translational degrees of freedom, and establish an equivalent inversion mapping relationship between the virtual layer and the three-dimensional strain of the outer surface within the common node.

3. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 2, characterized in that, The thickness of the main body is the total thickness of the thick-walled solid structure minus the thickness of the virtual layer.

4. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 3, characterized in that, The main body is modeled using Solid185 solid elements, and each node has three translational degrees of freedom.

5. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 4, characterized in that, The elastic modulus, Poisson's ratio, and density of the virtual layer are consistent with those of the main body.

6. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 5, characterized in that, Single-sided strain measurements were performed on the outer surface of a thick-walled solid structure to obtain the biaxial measured strain components of the outer surface, including: Based on the structural stress characteristics and monitoring requirements, on the outer surface of thick-walled solid structures... Key areas Deploy a strain measurement network; Measurement points were arranged in areas of stress concentration, geometric discontinuities, and areas of estimated maximum deformation. Single-sided strain measurements were performed at measurement points on the outer surface of a thick-walled solid structure to obtain the two-dimensional measured strain components of the outer surface.

7. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 6, characterized in that, Single-sided strain measurements were performed at measurement points on the outer surface of the thick-walled solid structure, including: At the measurement points on the outer surface of the thick-walled solid structure, single-sided measurements are performed using a two-way layout at 0° and 90°.

8. The method for sensing the deformation of the outer surface of a virtual layered, thick-walled solid structure as described in claim 7, characterized in that, Strain relationships are established on the virtual layer. Only the measured strain components in both directions of the outer surface are used as data fitting terms. The in-plane shear strain components of the outer surface are used as inversion unknowns and compensated for under regularization constraints to obtain the displacement field of the virtual layer, including: Establish the mathematical relationship between displacement and strain on a virtual layer; Under the biaxial measurement conditions of 0° and 90°, data fitting is set only for the biaxial measured strain components, and the in-plane shear strain components of the outer surface are used as inversion unknowns to compensate and solve under regularization constraints. A weighted least squares objective function is constructed, and a virtual layered displacement field is obtained by minimizing the objective function. The virtual layer is discretized, divided into finite element elements, and the relevant matrices and vectors are calculated. Construct the overall solution equations according to the finite element assembly rules; Solving the global equations yields the virtual layered displacement field.

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