Intelligent Stress Monitoring Method for Ellipsoidal Reticulated Shell Structures Based on Multi-Sensor Fusion

Abstract

The present invention relates to the technical field of stress monitoring, and more particularly, to an intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion. The method includes: Step 1: Represent the ellipsoidal reticulated shell structure using parametric equations; deploy strain sensors at the optimal layout positions; Step 2: Based on the parametric equations, construct the metric tensor of the spherical surface of the ellipsoidal reticulated shell structure; correct the original strain values measured by the strain sensors in combination with the metric tensor to obtain the true strain values; Step 3: Based on the true strain values and the metric tensor, construct a strain field interpolation function for the spherical surface of the ellipsoidal reticulated shell structure to characterize the strain values at any point of the ellipsoidal reticulated shell structure; Step 4: Establish a stress-strain relationship considering the influence of curvature to obtain the stress distribution function of the ellipsoidal reticulated shell structure to characterize the stress values at any point of the ellipsoidal reticulated shell structure. The present invention significantly improves the accuracy and calculation efficiency of stress monitoring.

Description

Technical Field

[0001] The present invention belongs to the technical field of stress monitoring, and particularly relates to an intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion. Background Art

[0002] With the continuous development of modern engineering structures, complex curved surface reticulated shell structures have been widely used in fields such as architecture, bridges, aerospace, and ocean engineering. Due to its excellent mechanical properties and material utilization rate, the reticulated shell structure shows significant advantages in the design of large-span buildings and lightweight structures. Among them, the ellipsoidal reticulated shell structure can effectively reduce wind loads and snow loads due to its streamlined design, and is widely used in large buildings such as stadiums, exhibition centers, and airport terminals. However, due to its complex geometric characteristics, traditional stress monitoring methods still have many problems in terms of accuracy and applicability, and it is difficult to meet the requirements of modern intelligent monitoring systems.

[0003] In existing engineering practices, the stress monitoring of reticulated shell structures mainly relies on the layout of sensor arrays and combines finite element analysis to simulate the stress conditions of the structure. However, this method has multiple technical bottlenecks. First of all, finite element analysis requires high-precision mesh generation. For complex curved surface structures, the computational cost of high-precision mesh generation is extremely high, and it is easy to introduce discretization errors. In addition, the accuracy of the finite element method depends to a large extent on the setting of boundary conditions, and the boundary conditions in the actual engineering environment are often difficult to accurately determine, resulting in a deviation between the simulation results and the actual stress state. Secondly, traditional sensor layout methods are usually based on experience or the principle of uniform distribution, without considering the geometric characteristics of the reticulated shell structure, which may lead to insufficient monitoring of stress concentration areas or waste of sensor resources. Especially in the ellipsoidal reticulated shell structure, due to the uneven curvature distribution in each area, the method of uniformly arranging sensors is difficult to effectively capture the stress changes in key stress areas. Summary of the Invention

[0004] The main objective of the present invention is to provide an intelligent stress monitoring method for ellipsoidal reticulated shell structures based on multi-sensor fusion. Through optimizing the sensor layout strategy, strain field interpolation based on differential geometry, high-precision stress calculation, and curvature correction, accurate force analysis of complex reticulated shell structures is achieved. This method uses Gaussian curvature to optimize the sensor layout, improving the monitoring accuracy in key stress areas, and combines the metric tensor to correct the interpolation calculation to ensure the continuity and accuracy of the strain field. Meanwhile, by adopting the thin shell theory and membrane moment matrix, and introducing curvature influence correction, the stress calculation can more realistically reflect the stress state of the reticulated shell structure, especially with higher accuracy in high-curvature areas. Compared with traditional methods, the present invention significantly improves the accuracy and calculation efficiency of stress monitoring, reduces the dependence on finite element analysis, makes the monitoring system more efficient and stable, and is applicable to the long-term health monitoring of complex structures such as large-span buildings, aerospace, and ocean engineering, providing solid technical support for structural safety assessment and optimal design.

[0005] To solve the above problems, the technical solution of the present invention is implemented as follows:

[0006] An intelligent stress monitoring method for ellipsoidal reticulated shell structures based on multi-sensor fusion, the method comprising:

[0007] Step 1: Represent the ellipsoidal reticulated shell structure using parametric equations; determine the optimal positions for sensor placement based on the Gaussian curvature distribution of the ellipsoidal reticulated shell structure, and deploy strain sensors at the optimal positions.

[0008] Step 2: Based on the parametric equations, construct the metric tensor of the spherical surface of the ellipsoidal reticulated shell structure; correct the original strain values measured by the strain sensors in combination with the metric tensor to obtain the true strain values.

[0009] Step 3: Based on the true strain values and the metric tensor, construct a strain field interpolation function for the spherical surface of the ellipsoidal reticulated shell structure to characterize the strain values at any point of the ellipsoidal reticulated shell structure.

[0010] Step 4: Based on the strain field interpolation function, in combination with the membrane force matrix of the ellipsoidal reticulated shell structure, establish a stress-strain relationship considering the influence of curvature to obtain the stress distribution function of the ellipsoidal reticulated shell structure to characterize the stress values at any point of the ellipsoidal reticulated shell structure.

[0011] Further, the parametric equations are expressed as:

[0012]

[0013] where is the position vector of a point on the spherical surface of the ellipsoidal reticulated shell structure; , and They are the triaxial length parameters of the ellipsoidal reticulated shell structure, corresponding to the X-axis, Y-axis, and Z-axis directions respectively; is the polar angle with the Z-axis; is the azimuth angle with the XY plane.

[0014] Furthermore, through the following formula, the Gaussian curvature distribution of the ellipsoidal reticulated shell structure is established :

[0015]

[0016] where, is the Gaussian curvature at the point on the spherical surface of the ellipsoidal reticulated shell structure. The stress gradient change is more significant in the area with a larger Gaussian curvature; a curvature distribution threshold is set; if is greater than the set curvature distribution threshold , then strain sensors are arranged at this point.

[0017] Furthermore, the metric tensor of the spherical surface of the ellipsoidal reticulated shell structure is expressed by the following formula:

[0018]

[0019] where, the indices and represent the local coordinate components on the ellipsoidal surface, that is, along the parametric coordinates and directions; when , , it corresponds to the metric component along the direction; when , or , , it corresponds to the coupled metric components and directions ; when , , it corresponds to the metric component along the direction.

[0020] Furthermore, through the following formula, the original strain value measured by the strain sensor is corrected by combining with the metric tensor to obtain the true strain value :

[0021]

[0022] where, is the determinant of the metric tensor; is the strain-curvature compensation coefficient.

[0023] Furthermore, the strain-curvature compensation coefficient is calculated using the following formula:

[0024]

[0025] where is the thickness of the shell of the ellipsoidal reticulated shell structure; is the Poisson's ratio of the material of the ellipsoidal reticulated shell structure; is the local principal curvature radius of the ellipsoidal reticulated shell structure.

[0026] Furthermore, the strain field interpolation function is expressed using the following formula:

[0027]

[0028] where is the number of strain sensors; is an integer subscript index; represents the true strain value corresponding to the original strain value obtained by the th strain sensor; represents the position where the th strain sensor is arranged

[0029] Furthermore, the stress distribution function is expressed using the following formula :

[0030]

[0031] where is the elastic modulus of the material of the ellipsoidal reticulated shell structure; is the curvature influence coefficient, and its value range is from 0.05 to 0.5; is the membrane force matrix.

[0032] Furthermore, the membrane force matrix is calculated using the following formula:

[0033]

[0034] where is the first principal curvature at point ; is the second principal curvature at point ;

[0035] The intelligent stress monitoring method for ellipsoidal reticulated shell structures based on multi-sensor fusion of the present invention has the following beneficial effects: By optimizing the sensor layout scheme, the present invention improves the representativeness and measurement accuracy of strain data. In the prior art, the layout of sensors usually adopts uniform distribution or experience-based optimization methods, without fully considering the geometric characteristics and local stress change characteristics of the reticulated shell structure, resulting in insufficient monitoring accuracy in key stress-bearing areas or low utilization rate of sensor resources. The present invention calculates the curvature distribution of the reticulated shell structure and sets a reasonable curvature threshold, enabling sensors to be preferentially arranged in high-curvature areas. This optimization strategy ensures that the sensors can cover the areas with the most significant stress changes, making the measurement data more accurate, avoiding over-layout in low-curvature areas, and improving the efficiency of the entire monitoring system. In addition, the method of the present invention can be adaptively adjusted according to the geometric characteristics of different reticulated shell structures, thus being applicable to various types of reticulated shell structures without additional experimental calibration. Secondly, based on the principle of differential geometry, the present invention proposes a new strain field interpolation method, significantly improving the accuracy of constructing a continuous strain field from limited measurement data. In the prior art, interpolation methods usually rely on Euclidean distance or traditional interpolation algorithms, without considering the curved surface geometric characteristics of the reticulated shell structure, resulting in large errors in interpolation calculations, especially obvious in high-curvature areas. The present invention combines the metric tensor information of the reticulated shell structure, enabling the interpolation calculation to correct the influence of local geometric scales, thereby improving the interpolation accuracy. In addition, by introducing a weighting factor of Gaussian curvature, the interpolation accuracy in high-curvature areas is further enhanced, ensuring that the interpolation calculation can accurately reflect the true situation of local strain distribution. This improvement makes the strain calculation of the entire reticulated shell structure more accurate, especially in stress concentration areas, where the interpolation error is significantly reduced, providing more reliable input data for subsequent stress calculations. In terms of stress calculation, the present invention realizes a more accurate stress distribution calculation through the combination of curvature correction and thin shell theory. Traditional stress calculation methods usually assume that the structure is planar or adopt simple linear elastic theory, without fully considering the curvature effect, which leads to large errors in stress calculations in high-curvature areas. The present invention introduces a curvature correction factor in the stress calculation process, enabling the stress calculation in high-curvature areas to be adaptively adjusted, thus being more in line with the actual stress situation. In addition, by introducing the membrane moment matrix of thin shell theory, the stress calculation can simultaneously consider the bending stiffness and direction coupling effect of the structure, enabling the stress influence in different directions to be more accurately described. This improvement makes the stress calculation in high-curvature areas more accurate, and at the same time, it can maintain the stability of the calculation in low-curvature areas, ensuring that the stress analysis of the entire reticulated shell structure is more physically meaningful. Description of the Drawings

[0036] Figure 1It is a schematic flowchart of a method for analyzing the stress of spherical reticulated shell structure nodes based on refined simulation optimization provided by an embodiment of the present invention. Specific embodiments

[0037] In order to enable those skilled in the art to better understand the solution of the present invention, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without making creative efforts shall fall within the protection scope of the present invention.

[0038] Example 1, refer to Figure 1 : An intelligent stress monitoring method for ellipsoidal reticulated shell structures based on multi-sensor fusion, the method includes:

[0039] Step 1: Represent the ellipsoidal reticulated shell structure with parametric equations; determine the optimal sensor layout positions based on the Gaussian curvature distribution of the ellipsoidal reticulated shell structure, and deploy strain sensors at the optimal layout positions;

[0040] Gaussian curvature is an important geometric quantity that measures the local bending characteristics of the surface of the reticulated shell structure. It determines the gradient change of stress on the surface. The magnitude of Gaussian curvature reflects the complexity of the force in the local area. That is, in the area with a larger Gaussian curvature, the external load may cause a more significant strain response, while the area with a smaller Gaussian curvature often shows a more uniform force distribution. Therefore, in the present invention, the optimal layout positions of strain sensors are determined by calculating the Gaussian curvature distribution, so that the monitoring system can preferentially cover the areas with a larger stress gradient, thereby improving the representativeness and effectiveness of the measurement data. Traditional strain monitoring methods often adopt a uniform sensor layout method or rely on engineering experience to select key measuring points, and these methods ignore the geometric characteristics of the reticulated shell structure, which may lead to insufficient monitoring accuracy in key stress concentration areas or waste of resources caused by redundant sensor layout. In contrast, the present invention uses the distribution of Gaussian curvature to optimize the sensor layout strategy, which not only ensures the sensor density in the key stress areas, but also avoids redundant monitoring of areas insensitive to stress changes, improving the efficiency and accuracy of data acquisition.

[0041] In the optimization process of sensor layout, the present invention sets a curvature distribution threshold. When the Gaussian curvature is greater than this threshold, it is considered that the stress change at this point is relatively drastic, and sensors should be preferentially arranged. The rationality of this strategy stems from the mechanics principle of thin-shell structures, that is, in regions with larger curvature, external loads often cause greater stress concentration, leading to more significant structural deformation. Arranging sensors in these regions can capture the stress changes of the structure under external loads more accurately, thereby enhancing the reliability of the entire monitoring system. In addition, using Gaussian curvature for optimized layout also has the effect of reducing measurement errors. Since the strain measurement of thin-shell structures is usually affected by local curvature, if sensors are arranged in low-curvature regions, the measured strain values may not be sufficient to reflect the overall stress state, while arranging sensors in high-curvature regions can more accurately reflect the influence of local geometry on stress distribution. After completing the sensor layout, the present invention further considers the spatial distribution uniformity among sensors to avoid uneven data acquisition caused by over-concentration or dispersion of sensors. In regions with larger Gaussian curvature, although sensors should be preferentially arranged, it is still necessary to ensure the reasonable distribution of these sensors on the reticulated shell surface, thereby ensuring the comprehensiveness of measurement data and the accuracy of interpolation calculation. Therefore, in the process of sensor layout, the concept of geodesic distance also needs to be combined to ensure that the spacing between adjacent sensors is not too large to avoid the accumulation of interpolation errors. At the same time, the layout strategy needs to take into account engineering feasibility, avoid arranging sensors in areas where it is difficult to install sensors on the structure, and comprehensively consider the convenience of wiring and signal acquisition systems.

[0042] Step 2: Based on the parametric equations, construct the metric tensor of the spherical surface of the ellipsoidal reticulated shell structure; correct the original strain values measured by the strain sensors by combining with the metric tensor to obtain the true strain values;

[0043] Due to the non-uniform curvature distribution of the ellipsoidal reticulated shell structure, its local geometric characteristics will affect the measurement results of strain. Therefore, relying solely on the direct readings of sensors cannot accurately characterize the actual strain distribution. The present invention eliminates the measurement deviation caused by curvature changes and provides strain data that more conforms to the actual stress state by establishing a metric tensor, enabling the measured original strain data to be mapped into a canonical geometric space. The metric tensor is an important tool in differential geometry to describe the intrinsic geometric properties of a surface, which is used to measure the distance, angle, and local scale deformation between two points on the surface. When the ellipsoidal reticulated shell structure is subjected to external loads, the strain on its surface is not only affected by mechanical properties but also restricted by the surface geometric shape. Therefore, traditional plane strain measurement methods cannot be directly applied to stress calculation of complex surfaces. By constructing the metric tensor, the stretching deformation of the local area on the reticulated shell surface can be described in a parametric coordinate system, thus providing an accurate mathematical model for strain correction.

[0044] The construction of the metric tensor depends on the parametric equations of the ellipsoidal reticulated shell. By calculating the derivatives of the parametric equations, the components of two tangential basis vectors on the surface can be obtained, and further calculate their inner product, and then the components of the metric tensor can be obtained. The role of the metric tensor is that it provides a way to describe the deformation degree of the local surface and is used to correct the original strain values measured by the sensors. Due to the geometric characteristics of the reticulated shell structure, there may be a certain deviation between the strain values measured by the sensors and the actual structural deformation. For example, in the high-curvature region, due to the stretching effect of the local coordinate system, the measured values may be amplified or reduced. If not corrected, it may lead to the accumulation of stress calculation errors and affect the accuracy of the entire monitoring system. The present invention constructs a strain correction factor by calculating the determinant of the metric tensor and combining the Gaussian curvature distribution, so that the original strain measurement values can be converted into real strain data. This correction process takes into account the geometric characteristics of the structure, so that the corrected strain data can better reflect the actual stress state of the reticulated shell structure. In addition to correcting measurement errors, the introduction of the metric tensor can also provide a more accurate description of the strain field. In the traditional strain monitoring method, the measured strain is usually based on the local coordinate system, and this method cannot directly reflect the change trend of the strain on the entire surface of the structure. In the present invention, through the calculation of the metric tensor, a complete strain distribution model can be constructed, so that the strain data can be reasonably interpolated on the entire surface of the ellipsoidal reticulated shell and used for subsequent stress calculation. In addition, the metric tensor also enables the data between sensors to be fused under a unified geometric framework, thereby improving the overall consistency and accuracy of strain measurement. This feature is particularly important for the stress analysis of complex reticulated shell structures, because it can ensure that the strain data measured at different positions can be correctly interpreted without data incompatibility caused by different coordinate systems.

[0045] Step 3: Based on the true strain values and the metric tensor, construct a strain field interpolation function for the spherical surface of the ellipsoidal reticulated shell structure to characterize the strain values at any point of the ellipsoidal reticulated shell structure;

[0046] The method of the present invention first uses the real strain data measured by the already deployed sensors as input, and based on the geometric characteristics of the reticulated shell structure, interpolates and expands the data of these discrete measurement points so that a continuous strain field is formed on the entire surface of the reticulated shell. Since the curvatures of different regions of the ellipsoidal reticulated shell are different, the influence weights of the data of different measurement points on an unmeasured point should also be different during the interpolation process. Therefore, the present invention introduces a weight distribution based on Gaussian curvature, making the regions with larger curvatures contribute more to the interpolation calculation, thereby ensuring higher interpolation accuracy in the key stress regions. The core idea of this strategy is that the regions with larger Gaussian curvatures are often subjected to more complex forces and have larger local strain gradient changes. Therefore, the measurement data from these regions should be more important for the interpolation process. In the regions with smaller curvatures, since the strain changes are relatively gentle and the strain differences between adjacent measurement points are small, the interpolation calculation depends relatively less on these regions. In this way, the present invention realizes an adaptive interpolation method, enabling the construction of the strain field to more accurately reflect the true stress state of the structure.

[0047] In addition, to further improve the accuracy of the interpolation calculation, the present invention uses the determinant of the metric tensor as a scale factor in the interpolation calculation, so that not only the geometric relationship between the measurement points is considered during the interpolation process, but also the calculation error caused by the local stretching effect on the surface of the reticulated shell is compensated. Since the local geometric scales at different positions on the surface of the reticulated shell structure are different, simply using the Euclidean distance for interpolation calculation may lead to large errors. Therefore, through the determinant of the metric tensor, the influence of different measurement points during the interpolation process can be scaled, enabling the measurement data to be more reasonably distributed in the interpolation calculation, thereby improving the overall calculation accuracy. At the same time, the present invention also combines geodesic distance calculation, enabling the interpolation calculation between adjacent measurement points to consider the true spatial distribution of the structure, rather than just a simple distance calculation based on the rectangular coordinate system, which is often ignored in traditional methods but is an important link for improving the interpolation accuracy of the ellipsoidal reticulated shell structure.

[0048] Traditional strain field interpolation methods are usually based on planar interpolation or triangular grid interpolation, but these methods have significant limitations when dealing with complex curved surface structures. The planar interpolation method assumes that the measurement points are distributed in a flat area and cannot correctly handle the non-uniform geometric shape of the ellipsoidal reticulated shell. Although the triangular grid interpolation method can adapt to a certain curved surface shape, due to its interpolation calculation being based on a linear assumption, large errors may occur in areas with large strain gradients. The present invention constructs a non-uniform interpolation weight distribution by combining the metric tensor and Gaussian curvature information, enabling the interpolation calculation to not only adapt to the geometric characteristics of the curved surface but also self-adaptively adjust the interpolation result to make it more consistent with the actual deformation of the structure. In addition, the interpolation method of the present invention also has strong anti-noise ability. In practical engineering applications, due to sensor measurement errors or environmental interference, the measured strain data may contain a certain amount of noise. If the traditional interpolation method is directly used for calculation, it may lead to error propagation, causing the final strain field calculation result to deviate from the actual situation. The present invention reduces the influence of local measurement errors and improves the stability of the final interpolation result by introducing a curvature compensation factor in the interpolation calculation, enabling the measurement data in high-curvature regions to be smoothed to a certain extent during the interpolation process. In contrast, when faced with noisy data, traditional methods often require additional filtering steps, while the interpolation method of the present invention has considered the influence of noise during the construction process and can directly achieve the anti-noise function during the calculation process, improving the efficiency and accuracy of data processing.

[0049] Step 4: Based on the strain field interpolation function, combined with the membrane force matrix of the ellipsoidal reticulated shell structure, establish a stress-strain relationship considering curvature effects to obtain the stress distribution function of the ellipsoidal reticulated shell structure, so as to characterize the stress value of any point on the ellipsoidal reticulated shell structure.

[0050] The calculation of stress usually depends on the constitutive relationship of materials. In general, the relationship between stress and strain of materials is described by Hooke's law, that is, stress is equal to the elastic modulus multiplied by strain. However, in an ellipsoidal reticulated shell structure, due to the non-uniform curvature of the surface, the local stress not only depends on the properties of the material itself, but is also modulated by geometric factors. Therefore, directly using traditional stress calculation methods may lead to large errors. To solve this problem, the present invention introduces a curvature influence correction factor in the stress calculation process, so that the final stress calculation can reflect the influence of the local geometric shape. This correction factor is jointly determined by the Gaussian curvature, local principal curvature, and the thickness parameter of the reticulated shell structure. It can adjust the degree of curvature influence in stress calculation, thereby ensuring the calculation accuracy. In high-curvature regions, due to stronger geometric constraints on the surface, external loads may cause more significant stress concentration. Therefore, the correction factor will play a magnifying role in these regions to accurately characterize the stress state. In low-curvature regions, since the surface stress is relatively uniform, the correction factor will tend to be a smaller value to avoid calculation errors caused by overcorrection.

[0051] To further improve the accuracy of stress calculation, the present invention optimizes the stress calculation in combination with the membrane force matrix. The membrane force matrix is a matrix form that describes the local stress state of a thin-shell structure. It reflects the bending stiffness of the reticulated shell structure in different directions and the influence of the Poisson effect. Traditional stress calculation methods usually describe stress in scalar form. In the present invention, due to considering the influence of the curvature of the structure, the matrix form needs to be introduced in the stress calculation to accurately describe the stress conditions in different directions. The construction of the membrane force matrix depends on the local principal curvature and the structure thickness parameter. It can not only describe the bending stiffness of the local area, but also provide a correction for the Poisson effect, so that the finally calculated stress distribution can more conform to the actual stress state of the structure. Especially in the region with non-uniform curvature distribution, the membrane force matrix can effectively adjust the anisotropic influence in stress calculation, thereby improving the calculation accuracy. Under the calculation framework of the present invention, the final stress distribution function is jointly calculated based on the strain field interpolation result, elastic modulus, membrane force matrix, and curvature correction factor. The advantage of this calculation method is that it can not only provide more accurate stress calculation results, but also ensure the continuity of the calculation, so that the stress distribution changes smoothly on the entire surface of the reticulated shell structure. Compared with the traditional finite element analysis method, the method of the present invention does not need to establish a high-precision mesh division model, but directly calculates the stress distribution through mathematical modeling, thereby greatly improving the calculation efficiency. In addition, since the present invention adopts a multi-sensor fusion method, it can comprehensively utilize the data of multiple sensors during the stress calculation process, improve the robustness and noise resistance of the calculation, and avoid the influence of single-measurement point data errors on the overall calculation result.

[0052] Example 2: The parametric equation is expressed as:

[0053]

[0054] Among them, is the position vector of a point on the spherical surface of the ellipsoidal reticulated shell structure; , and are the triaxial length parameters of the ellipsoidal reticulated shell structure, corresponding to the X-axis, Y-axis, and Z-axis directions respectively; is the polar angle with respect to the Z-axis; is the azimuth angle with respect to the XY plane.

[0055] Specifically, in the method of the present invention, the shape of the ellipsoidal reticulated shell structure is jointly determined by three principal axis length parameters , and , which respectively correspond to the dimensions of the ellipsoid in the , , directions. This parameterization method enables the geometric shape of the reticulated shell to be flexibly controlled by adjusting these three parameters and can be applied to ellipsoidal structures of different shapes. When , the equation describes a standard spherical surface, while when , , take different values, different shapes of ellipsoids can be represented, such as prolate ellipsoids, oblate ellipsoids, etc., so as to meet different engineering requirements. The parameter represents the polar angle, which is used to describe the vertical position of a point on the ellipsoidal surface, that is, the angle between the point and the axis, represents the north pole, represents the south pole, and represents the equatorial position. The parameter is the azimuth angle, which defines the rotation angle of the point in the plane. Its range is from to , meaning that the entire ellipsoidal surface can be completely covered.

[0056] The advantage of this parameterization method is that it enables any point on the ellipsoidal surface to be represented by It can be uniquely determined without using complex constraint equations in the traditional Cartesian coordinate system. This not only greatly simplifies the complexity of the geometric calculation of the reticulated shell, but also makes tasks such as strain calculation, curvature analysis, and sensor layout optimization on the curved surface more intuitive and efficient. Especially in the process of optimizing the layout of strain sensors, since the present invention uses Gaussian curvature to optimize the position distribution of sensors, the parametric model can directly provide the geometric information required for curvature calculation, thus achieving an adaptive optimal layout. In addition, in the processes of strain correction, stress calculation, and interpolation, the construction of the metric tensor also depends on this parametric equation. Therefore, this parametric equation is not only a tool for describing the geometric shape, but also the basis for all subsequent mechanical analyses. In traditional stress analysis methods, the reticulated shell structure is often simplified to a planar model or finite element calculations are performed using discrete point clouds, and these methods are prone to large geometric errors when dealing with complex curved surfaces. Through parametric modeling of the present invention, all calculations can be directly performed on the ellipsoidal surface without relying on finite element discretization, thus avoiding calculation deviations caused by uneven mesh division or discrete errors. Especially in the process of stress calculation, the parametric model can provide accurate local coordinate information, enabling the calculation of key physical quantities such as the metric tensor, strain field, and membrane force matrix to maintain high precision, which is crucial for the accuracy of the intelligent monitoring system.

[0057] Example 3: Establish the Gaussian curvature distribution of the ellipsoidal reticulated shell structure through the following formula :

[0058]

[0059] where is the Gaussian curvature at the point on the spherical surface of the ellipsoidal reticulated shell structure. The stress gradient change is more significant in the region with a larger Gaussian curvature; set a curvature distribution threshold ; if is greater than the set curvature distribution threshold , then strain sensors are arranged at this point.

[0060] Specifically, the calculation formula of Gaussian curvature directly depends on the parametric equation of the ellipsoidal reticulated shell and is derived in combination with its principal curvature information. In the ellipsoidal reticulated shell structure, the Gaussian curvature is not only affected by the three-axis length parameters of the reticulated shell, but also related to the polar angle and the azimuth angle . Specifically, the calculation of Gaussian curvature involves the fundamental quadratic form coefficients of the local surface, and these coefficients are obtained by calculating the determinants of the first fundamental form and the second fundamental form. For the ellipsoidal reticulated shell, its Gaussian curvature distribution can be expressed as a function depending on , where the numerator part is , represents the volume scale of the ellipsoid, and the denominator is the square of the product of the principal curvatures of the local point on the ellipsoid surface, reflecting the influence of the local geometry of the point on the Gaussian curvature.

[0061] The physical meaning of Gaussian curvature is that it describes the intrinsic curvature of a surface at a certain point. For a plane or simple surface, Gaussian curvature can be zero or a constant, but for an ellipsoidal lattice shell structure, due to the different degrees of curvature in various directions, the Gaussian curvature presents a non-uniform distribution. In areas with larger Gaussian curvature, local structures are more susceptible to external loads, and thus stress changes more dramatically, which are usually the key stress-bearing parts of the structure. Therefore, the core idea of the present invention is to use Gaussian curvature to guide the sensor layout strategy so that the sensors can preferentially cover areas where stress changes significantly, thereby improving the accuracy of stress monitoring. In order to achieve this optimization goal, the present invention sets a Gaussian curvature threshold. , which is used to screen the key locations where sensors need to be deployed. When the threshold is exceeded, it is considered that the point belongs to an area with significant stress changes, so strain sensors should be arranged at this point. For those areas with smaller Gaussian curvature, due to the lower stress gradient, the necessity of sensor arrangement is weak, so the density of sensors can be reduced to optimize the utilization of measurement resources. Such a layout strategy can ensure that the sensor distribution matches the stress distribution, so that the measured data is representative and does not cause waste of sensor resources. Compared with the traditional uniform layout or empirical layout method, the Gaussian curvature optimization layout method of the present invention has significant technical advantages. Traditional methods usually rely on the experience judgment of engineers or the results of finite element analysis to determine the sensor layout position. Although this method is effective to a certain extent, it often lacks mathematical rigor and is easily interfered by human factors. The present invention calculates the Gaussian curvature through a strict mathematical model, and arranges the sensor based on a scientifically set threshold, so that the entire layout process has a higher degree of automation, while also ensuring the efficiency and accuracy of data acquisition. In addition, since the calculation of Gaussian curvature only depends on the geometric parameters of the structure and does not require additional experiments or simulation calculations, this method not only has low computational cost, but is also applicable to ellipsoidal lattice shell structures of different specifications and shapes and has strong universality.

[0062] Example 4: The metric tensor of the spherical surface of the ellipsoidal lattice shell structure is expressed using the following formula:

[0063]

[0064] Among them, the index and Represents the local coordinate components on the ellipsoid, that is, along the parameterized coordinate and Direction; when , When, it corresponds to the metric component along the direction ; when , or , When, it corresponds to and The coupled metric component in the direction ; when , When, it corresponds to the metric component along the direction .

[0065] Specifically, in an ellipsoidal reticulated shell structure, the metric tensor is the core mathematical tool for describing local geometric scale changes. Its essence is to establish the conversion relationship between local coordinates and global coordinates by describing the change relationship of infinitesimal displacements on the surface, so as to accurately calculate strain, stress, and geodesic distance at different positions. In the present invention, through parametric modeling, first, the polar angle and the azimuth angle are used to determine the point positions on the ellipsoid surface, and based on this, the metric tensor is derived to enable it to describe the geometric characteristics of the local area of the surface. Each element of this matrix reflects the stretching degree of the local area of the surface in different directions and takes into account the coupling effect in different directions. First, represents the metric component along the polar angle direction :

[0066]

[0067] This component determines the local scale change along the polar angle direction. It is not only affected by the ellipsoid major axis parameter , but also related to the spatial position of the point ( ). For example, at the top ( ) or bottom ( ) of the ellipsoid, is mainly determined by , while in the equatorial region ( ), it is jointly determined by and . This change reflects the surface scale differences in different regions and provides a mathematical basis for subsequent strain correction.

[0068] In the azimuth angle direction, the metric component is given by the following formula:

[0069]

[0070] This component describes the local scale variation of the ellipsoidal surface in the horizontal direction. Its value depends on and the lengths of the axes, as well as the value of the polar angle . When or , this component becomes zero, meaning that at the top and bottom of the ellipsoid, the motion in the azimuthal direction does not result in actual displacement. While in the equatorial region ( ), this component takes the maximum value, reflecting the scale variation in the horizontal direction. Due to and having different values, the metric components in the direction also vary at different azimuthal angles. This non-uniformity determines the geometric characteristics of the reticulated shell structure in different regions, thus affecting the distribution of strain and stress.

[0071] In addition, on the ellipsoidal surface, the motions in different directions are not completely independent but are coupled with each other. To describe this coupling relationship, the term in the metric tensor is defined as:

[0072]

[0073] This term describes the degree of coupling between the polar angle direction and the azimuthal angle direction. Due to , the curvature changes differently in different regions. Therefore, at certain positions, the displacement in the direction will affect the geometric scale variation in the direction. Especially in high-curvature regions, such as near the equator or specific local areas, this coupling effect is particularly significant. For example, at the poles ( or ), due to , is also zero, indicating that near the poles, the metrics in the polar angle and azimuthal angle directions are independent. While in the equatorial region, the geometric scales in the and directions have a stronger mutual influence, and this characteristic needs to be particularly considered in the calculation of strain and stress.

[0074] In the intelligent monitoring system, the introduction of the metric tensor plays a role in multiple key aspects. First, during the strain correction process, the original data measured by the sensors needs to be transformed by the metric tensor to correct the measurement errors caused by local geometric scale changes. The determinant of the metric tensor is used to calculate the local area dilation factor, ensuring that the measured data can accurately reflect the true structural deformation. Second, during the strain field interpolation calculation process, the metric tensor is used to correct the geodesic distance, making the interpolation calculation more conform to the geometric shape of the ellipsoidal reticulated shell and improving the interpolation accuracy. In the traditional method, the interpolation between measurement points is usually based on the Euclidean distance, while in the method of the present invention, the interpolation calculation is based on the corrected distance of the metric tensor, thus more accurately reflecting the surface geometry. In addition, during the stress calculation process, the metric tensor determines the numerical value of the local stress distribution, enabling the calculation results to correctly reflect the actual stress conditions of the structure. Compared with the traditional finite element method, the present invention constructs the metric tensor of the ellipsoidal reticulated shell, enabling all calculations to be carried out within a strict mathematical framework, avoiding mesh division errors, and improving the calculation accuracy. In addition, since this method is completely based on parametric modeling and does not depend on discretized meshes, it is applicable to ellipsoidal reticulated shell structures of different shapes and has strong generality. Generally speaking, the metric tensor construction method of the present invention not only improves the calculation accuracy but also provides a solid mathematical foundation for the intelligent monitoring system, thereby enhancing its applicability and reliability in practical engineering.

[0075] Example 5: Through the following formula, the original strain value measured by the strain sensor is corrected by combining with the metric tensor to obtain the true strain value :

[0076]

[0077] where is the determinant of the metric tensor; is the strain-curvature compensation coefficient.

[0078] Specifically, is the determinant of the metric tensor, which is used to describe the area deformation of the surface of the ellipsoidal reticulated shell in the local area. Since the strain data measured by the sensor is measured in the local coordinate system, and the strain calculation needs to be uniformly processed in the global coordinate system, it is necessary to use the determinant of the metric tensor for correction to ensure that the measured strain data is consistent with the actual geometric deformation of the structure. In different regions, takes different values, and its magnitude determines the local scale dilation situation in that region. For example, in the high-curvature region, may be smaller, indicating that the local area in this region is smaller, while in the low-curvature region, It may be relatively large, indicating that the area of the local region is large. Therefore, in the high-curvature region, the strain measurement value needs to be amplified, while in the low-curvature region, the strain measurement value needs to be reduced to ensure data consistency.

[0079] Secondly, the Gaussian curvature reflects the local bending degree of the surface at a certain point. In traditional strain measurement, the influence of curvature is often ignored, assuming that the structure is planar, thus resulting in measurement errors. In the present invention, this term is used to correct the strain distortion effect caused by local curvature. Specifically, in the region with a large Gaussian curvature, a large bending deformation will occur when the local surface is stressed, which may lead to a relatively large strain value measured by the sensor. Therefore, it is necessary to perform a certain scaling correction on the measurement data to make it more accurately reflect the actual stress situation. In the region with a small Gaussian curvature, the surface is relatively flat, and the strain measurement value is closer to the true strain value, so the correction amplitude is smaller.

[0080] In addition, this term introduces the strain-curvature compensation factor , further considering the influence of the structural bending stiffness on strain measurement. This compensation factor is used to describe the interaction between the material and the geometric form, and its value depends on the thickness of the structure, Poisson's ratio, and the local curvature radius. Generally speaking, in a thinner shell structure, the influence of local curvature on strain measurement is greater, so the compensation factor takes a larger value, while in a thicker structure, the influence of local curvature is relatively smaller, so takes a smaller value. By introducing this compensation factor, the present invention can dynamically adjust the strain correction amplitude, making the finally obtained true strain value more in line with physical laws.

[0081] Overall, this strain correction method has significant advantages compared to traditional methods. Traditional strain measurement methods usually assume that the strain value measured by the sensor is directly equal to the true strain value without considering the geometric effects of the structure, which may lead to the accumulation of measurement errors. The method of the present invention combines metric tensor and Gaussian curvature information, enabling precise correction of strain measurement data and improving the accuracy and consistency of measurement data. In addition, this method has strong self - adaptability and can be applied to different ellipsoidal reticulated shell structures without additional experimental calibration, so it has strong engineering practical value. In practical engineering applications, this strain correction method can significantly improve the reliability of the structural health monitoring system. For complex ellipsoidal reticulated shell structures, traditional methods have large strain measurement errors in high - curvature regions, while the method of the present invention can effectively correct this error, making the stress monitoring data of the entire reticulated shell structure more accurate and thus improving the reliability of safety assessment. Especially in the fields of large - span buildings, aerospace structures, and ocean engineering, accurate strain measurement is crucial for the long - term stability of structures. Therefore, the strain correction method of the present invention can provide more accurate monitoring data for these key structures, thereby enhancing engineering safety.

[0082] Example 6: Strain - curvature compensation coefficient It is calculated using the following formula:

[0083]

[0084] where is the thickness of the shell of the ellipsoidal reticulated shell structure; is the Poisson's ratio of the material of the ellipsoidal reticulated shell structure; is the local principal curvature radius of the ellipsoidal reticulated shell structure.

[0085] Specifically, the physical meaning of this formula is that it describes the degree to which the strain measurement value is affected by curvature during the bending deformation of the curved surface structure. The larger the compensation coefficient , the more significant the influence of curvature on strain measurement, so a greater correction is required in the measurement data; conversely, if is smaller, it indicates that the influence of local curvature on the measurement data is weaker, and the correction amplitude can be appropriately reduced. First, the role of the shell thickness in the formula reflects the stiffness characteristics of the thin - shell structure. In the classical thin - shell theory, the bending stiffness of the structure is usually proportional to the square of the thickness. Therefore, in the formula of the present invention, the numerator part of contains . When the structure is thicker, the bending stiffness of the shell is larger, and the influence of local geometric inhomogeneity on strain measurement is relatively small. Therefore A smaller value indicates a reduced need for compensation correction. When the shell is thinner, the bending stiffness of the structure is smaller, and the influence of local curvature is more likely to be manifested, resulting in a relatively large deviation in the strain measurement value. Therefore, a larger value is required, and stronger compensation correction is needed. Therefore, this formula can dynamically adapt to reticulated shell structures of different thicknesses to ensure the rationality of compensation calculation.

[0086] Secondly, the Poisson's ratio reflects the elastic properties of the material, that is, when the material is subjected to stress, the deformation of the material in the direction perpendicular to the stress application direction. For materials with a relatively large Poisson's ratio, the transverse deformation is more obvious. Therefore, when bending, the influence of local curvature on strain measurement is more significant, resulting in a relatively large strain measurement error. Therefore, in the formula of the present invention, the Poisson's ratio appears in the denominator in the form of , indicating that when the Poisson's ratio increases, the compensation coefficient also increases to enhance the correction ability of the measurement data. For materials with a relatively small Poisson's ratio, such as certain ceramics or high-stiffness alloys, since their transverse deformation is weak and the strain measurement data is less affected by curvature, the compensation coefficient is also small, indicating a reduced need for compensation correction. Finally, the local principal curvature radius directly determines the local geometric characteristics of the ellipsoidal reticulated shell structure. The principal curvature radius is an important parameter describing the degree of surface bending. The smaller its value, the greater the curvature, that is, the surface of this area is more obviously bent and the local stress distribution is more complex. Therefore, in the formula of the present invention, appears in the denominator, indicating that in the area with a larger curvature, the compensation coefficient takes a larger value and stronger compensation correction is required to reduce the measurement error. When takes a larger value, it indicates that the curvature of this area is smaller, the bending deformation of the structure is relatively weak, and the influence on strain measurement is also smaller. Therefore, the compensation coefficient takes a smaller value and the intensity of compensation correction is reduced. This calculation method of the compensation coefficient has significant advantages compared with the traditional method. The traditional strain measurement method usually assumes that the measured value can directly reflect the true strain state without considering the influence of local curvature on the measurement result. Especially in the high-curvature area, this kind of neglect may lead to the accumulation of measurement errors, thereby affecting the accuracy of the entire structural health monitoring. The present invention makes the measurement data adaptively adjust the compensation amplitude by accurately calculating the compensation coefficient , combined with Gaussian curvature and metric tensor information, thereby improving the reliability and accuracy of strain measurement.

[0087] In practical engineering applications, the compensation coefficient calculation method of the present invention can greatly improve the measurement accuracy of intelligent monitoring systems. Especially in fields such as large-span reticulated shells, aerospace structures, and ocean engineering, stress monitoring of complex curved surfaces is crucial for structural safety. Although traditional finite element analysis methods can be used to calculate local stress and strain distributions, their calculation costs are relatively high, and they are sensitive to the quality of mesh generation. Therefore, there are certain limitations in practical applications. The method of the present invention can directly correct measurement data without complex mesh generation by analytically calculating the compensation coefficient , making the strain monitoring system more efficient and accurate, and applicable to ellipsoidal reticulated shell structures of various shapes and specifications. In addition, this method also has strong adaptability. Since the calculation of the compensation coefficient is completely based on the geometric parameters and material properties of the structure, it can adapt to different engineering requirements. For example, in the application scenario of thin-shell structures, takes a larger value to ensure high-precision measurement data; while in the application of thick-shell structures, takes a smaller value to avoid error accumulation caused by overcorrection. This adaptive characteristic makes the method of the present invention not only applicable to large-span building structures, but also can be applied to micro-scale precision engineering fields such as biomedical devices and microelectromechanical systems, providing a highly versatile and computationally efficient solution for stress monitoring in various application environments.

[0088] Example 7: Strain field interpolation function It is expressed by the following formula:

[0089]

[0090] Among them, is the number of strain sensors; is an integer subscript index; represents the true strain value corresponding to the original strain value obtained by the th strain sensor; represents the Gaussian curvature at the position where the th strain sensor is arranged.

[0091] Specifically, represents the determinant of the metric tensor of the ellipsoidal reticulated shell at the position , which describes the local scale stretching characteristics of the curved surface at this point. In this formula, the first term of the interpolation weight: It is used to correct the geometric scale differences between different measurement points, so that the interpolation calculation can maintain local geometric consistency. For example, in a high-curvature region, the determinant of the metric tensor is usually small, indicating that the local area of this region is small, while in a low-curvature region, the determinant of the metric tensor is large, indicating that the local area of this region is large. Therefore, when performing interpolation calculations, higher weights need to be assigned to the measurement data from high-curvature regions to ensure that the interpolation results can correctly reflect the strain change trend in this region.

[0092] Secondly, the second term of the interpolation weight: It is used to correct the influence of Gaussian curvature. Gaussian curvature describes the local bending degree of the surface at this point, and it determines the change of the stress gradient. In high-curvature regions, the local stress state is more complex and the gradient of the strain distribution is larger. Therefore, the interpolation calculation needs to more accurately reflect this change trend. By introducing the ratio of Gaussian curvature as the interpolation weight, the method of the present invention can ensure that the measurement data from high-curvature regions has a greater impact on the interpolation calculation, while the data from low-curvature regions has a relatively smaller impact. For example, in the top or bottom (where the Gaussian curvature is large) region of an ellipsoidal reticulated shell, the interpolation calculation will give priority to the measurement data of nearby measurement points with similar Gaussian curvature to ensure that the interpolation results can accurately reflect the local strain change.

[0093] Compared with traditional linear interpolation or planar interpolation methods, the interpolation method of the present invention has significant technical advantages. Traditional methods usually perform interpolation based on Euclidean coordinates without considering the geometric characteristics of the surface. This method is prone to introducing errors in complex surface structures, resulting in the interpolation results deviating from the actual situation. In contrast, the method of the present invention performs weighted interpolation based on the metric tensor and Gaussian curvature, enabling the calculation results to more accurately match the actual morphology of the structure and improving the accuracy of strain field reconstruction. In addition, the method also has strong adaptability. In ellipsoidal reticulated shell structures of different shapes and scales, since the calculation of the metric tensor and Gaussian curvature completely depends on geometric parameters, this interpolation method can be applied to structures of different specifications without additional parameter adjustment. This characteristic makes the method applicable not only to conventional large-span building reticulated shell structures but also to complex aerospace structures, ocean engineering structures, etc., providing a high-precision and highly robust calculation scheme for stress monitoring of these key engineering structures. In practical engineering applications, the interpolation method of the present invention can significantly improve the accuracy and stability of strain monitoring. For large-span reticulated shell structures, traditional finite element methods usually require constructing high-density grids to ensure calculation accuracy, while this method can accurately reconstruct the strain field of the entire structure through mathematical interpolation based on limited measurement point data, thereby reducing the calculation cost and improving the calculation efficiency. In addition, the method can effectively suppress the influence of measurement noise and improve the reliability of the monitoring system. In practical applications, since there may be certain noise in the sensor measurement data, directly using these data for interpolation calculation may lead to error propagation. However, the method of the present invention reduces the sensitivity of the interpolation calculation to measurement errors through Gaussian curvature weighting and metric tensor correction, thereby improving the stability of the final calculation results.

[0094] Example 8: The stress distribution function is expressed by the following formula :

[0095]

[0096] where is the elastic modulus of the material of the ellipsoidal reticulated shell structure; is the curvature influence coefficient, and its value range is from 0.05 to 0.5; is the membrane force matrix.

[0097] Specifically, is directly related to the elastic modulus of the material and the strain , which is consistent with the classical linear elasticity theory, that is, stress is equal to material stiffness multiplied by strain. However, due to the complex geometric characteristics of the surface of the ellipsoidal reticulated shell structure, the present invention further considers the modulation effect of curvature on stress. To describe this effect, a curvature correction term is introduced into the formula: ; Among them, The value range is between 0.05 and 0.5, which is used to adjust the influence of curvature on stress. The physical meaning of this term is that it reflects how the local curvature of the reticulated shell affects the stress distribution. When the structure deforms under external loads, the local stress in the high-curvature region is often greater than that in the low-curvature region. Therefore, this correction term is needed to adapt the calculation results. For example, when is larger, the value of this correction term is also larger, indicating that the stress amplification effect in this region is more significant. While in the region where is smaller, this correction term approaches 1, indicating that the local stress is mainly determined by the elastic response of the material.

[0098] In addition, in order to further correct the geometric influence in the calculation, the reciprocal of the square root of the determinant of the metric tensor is introduced in the formula: ; The role of this term is to correct the influence of local geometric scale on stress. In the ellipsoidal reticulated shell structure, the change of local geometric scale will cause the same strain to produce different stress responses in different regions. For example, in the high-curvature region, the local area is small, and the stress borne by the material is usually large. While in the low-curvature region, the local area is large, and the stress distribution of the material is more uniform. Through this correction term, it can be ensured that the stress calculation can adapt to the scale changes of different geometric regions, making the calculation results more in line with physical reality. Finally, the formula includes the membrane force matrix , which is used to describe the membrane force effect of the reticulated shell structure. The membrane force matrix is an important parameter in the analysis of thin shell mechanics, and it is used to characterize the influence of the additional stress generated during the bending deformation of the structure. Since the ellipsoidal reticulated shell structure not only has a membrane force effect when stressed, but may also exhibit bending stress, the stress calculation method of the present invention comprehensively considers these two effects, making the calculated stress value more accurate. The specific form of the membrane force matrix depends on the geometric parameters and material properties of the structure, and its value can be obtained through the derivation of thin shell theory. Compared with the traditional plane stress calculation method, the stress distribution calculation method of the present invention has significant technical advantages. The traditional method usually assumes that the stress is only related to strain and material stiffness, without considering the geometric characteristics and curvature influence of the structure, so large errors may occur in complex curved surface structures. The method of the present invention makes the calculation result more accurately reflect the true stress state of the reticulated shell structure by introducing a curvature correction term, a metric tensor correction term, and a membrane force matrix. In addition, this method also has strong self - adaptability and can be applied to ellipsoidal reticulated shell structures of different shapes and specifications without additional experimental data or finite element analysis, and is suitable for a variety of engineering scenarios, such as large - span buildings, aerospace structures, ocean engineering, etc. In practical engineering applications, this stress calculation method can significantly improve the accuracy of structural health monitoring. For example, in large - span reticulated shell buildings, the traditional stress calculation method may not be able to accurately predict the location of local stress concentration, while the method of the present invention makes the stress estimation of key stress - bearing areas more accurate by combining curvature influence and membrane force matrix calculation, thereby improving the reliability of safety assessment. In addition, in the fields of aerospace and ocean engineering, this method can also be used to analyze the stress distribution of composite thin shell structures, providing an important theoretical basis for the optimal design of lightweight structures.

[0099] Example 9: Membrane Force Matrix It is calculated using the following formula:

[0100]

[0101] where is the first principal curvature at point ; is the second principal curvature at point .

[0102] Specifically, the construction of the membrane force matrix is based on the first and second principal curvatures of the ellipsoidal reticulated shell surface. These two parameters determine the geometric bending degree of the local area and directly affect the stress transfer characteristics of this area. For thin-shell structures, the greater the local principal curvature, the more significant its stiffness effect, and thus the stress values generated under the same load will also change. Therefore, in the present invention, by introducing the square term of the principal curvature, the stress behavior of the thin-shell structure is corrected, so that the stress calculation can not only consider the elastic response of the material, but also adaptively adjust the stress amplification effect in the high-curvature area. In addition, the thickness of the shell is also an important factor affecting the mechanical behavior of the thin shell. In the construction of the membrane force matrix, the square term of the shell thickness appears in the correction factor, and this design conforms to the classical thin-shell theory, that is, the stiffness of the shell varies with the square of the thickness. In the thicker reticulated shell area, the local structural stiffness is higher, the thin-shell effect is weaker, and the correction effect of the membrane force matrix is relatively small; while in the thinner area, the thin-shell effect is significant, and the influence of local stress is more sensitive, so the correction effect of the membrane force matrix is stronger, thus ensuring the calculation accuracy.

[0103] In the construction of the membrane force matrix, in addition to the influence of the principal curvature and thickness, the Poisson's ratio is also introduced as a key adjustment parameter. The Poisson's ratio reflects the lateral deformation ability of the material, and it has different value ranges in different materials. In the method of the present invention, the role of the Poisson's ratio is mainly reflected in the cross-term correction of the principal curvature, that is, when the shell structure is stressed in one direction, the Poisson effect will cause deformation in the other direction, and this interaction is particularly significant in the high-curvature area. Therefore, in the non-diagonal terms of the membrane force matrix, the Poisson's ratio is used as a coupling factor, which determines the degree of mutual influence between the two principal curvatures. When the Poisson's ratio is large, the force-coupling effect in different directions is enhanced, so the value of the cross-correction term of the membrane force matrix increases, and when the Poisson's ratio is small, the coupling effect is weak, and the corresponding correction amplitude decreases. This design enables the method of the present invention to adapt to ellipsoidal reticulated shell structures of different material types, and improves the universality and adaptability of stress calculation.

[0104] In the actual stress analysis of the ellipsoidal reticulated shell structure, the high-curvature region is usually the location of stress concentration, while the stress distribution in the low-curvature region is relatively uniform. The traditional plane stress calculation method cannot accurately reflect this difference, so it is necessary to correct the stress conditions in different regions through the membrane force matrix. The method of the present invention constructs a membrane force matrix based on the principal curvature, so that in the high-curvature region, the local stress can be additionally corrected to more accurately describe the stress concentration phenomenon. In the low-curvature region, due to the strong stiffness of the shell, the change of local stress is relatively gentle, and the correction effect of the membrane force matrix is relatively small, thus ensuring the stability of the calculation. This method of dynamically adjusting the stress calculation accuracy based on geometric characteristics makes the method of the present invention more in line with the actual engineering requirements than the traditional method, and is particularly suitable for the real-time stress monitoring of large-span reticulated shell structures. In the actual application of the intelligent monitoring system, the introduction of the membrane force matrix not only improves the accuracy of stress calculation, but also enhances the stability of the monitoring data. In the traditional finite element method, the stress analysis of thin-shell structures usually relies on high-density mesh division, while the method of the present invention can obtain high-precision stress calculation results even at a lower mesh density through the correction of the membrane force matrix, thereby reducing the calculation cost and improving the calculation efficiency. In addition, since the calculation of the membrane force matrix is completely based on the geometric parameters of the structure, it can adapt to ellipsoidal reticulated shell structures of different specifications without additional experimental calibration. This method is not only applicable to conventional large-span building reticulated shell structures, but also can be applied to fields such as complex aerospace structures and ocean engineering structures, providing a high-precision and high-robustness calculation scheme for the stress monitoring of these key engineering structures.

[0105] As described above, the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An intelligent stress monitoring method for ellipsoidal reticulated shell structures based on multi-sensor fusion, characterized in that, The method includes the following steps: Step 1: Represent the ellipsoidal reticulated shell structure with parametric equations; determine the optimal sensor layout positions based on the Gaussian curvature distribution of the ellipsoidal reticulated shell structure, and deploy strain sensors at the optimal layout positions; Step 2: Based on the parametric equations, construct the metric tensor of the spherical surface of the ellipsoidal reticulated shell structure; correct the original strain values measured by the strain sensors by combining with the metric tensor to obtain the true strain values; Step 3: Based on the true strain values and the metric tensor, construct the strain field interpolation function of the spherical surface of the ellipsoidal reticulated shell structure to characterize the strain values at any point of the ellipsoidal reticulated shell structure; Step 4: Based on the strain field interpolation function, combine with the membrane force matrix of the ellipsoidal reticulated shell structure to establish the stress-strain relationship considering the influence of curvature, and obtain the stress distribution function of the ellipsoidal reticulated shell structure to characterize the stress values at any point of the ellipsoidal reticulated shell structure; Membrane force matrix Calculated using the following formula: wherein, is the first principal curvature at point ; is the second principal curvature at point ; is the shell thickness of the ellipsoidal reticulated shell structure; is the Poisson's ratio of the material of the ellipsoidal reticulated shell structure.

2. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 1, characterized in that, The parametric equations are expressed as: Among them, is the position vector of a point on the spherical surface of the ellipsoidal reticulated shell structure; , and are the triaxial length parameters of the ellipsoidal reticulated shell structure, corresponding to the X-axis, Y-axis, and Z-axis directions respectively; is the polar angle with respect to the Z-axis; is the azimuth angle with respect to the XY plane.

3. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 2, characterized in that Establish the Gaussian curvature distribution of the ellipsoidal reticulated shell structure through the following formula : Among them, is the Gaussian curvature at the point on the spherical surface of the ellipsoidal reticulated shell structure. The stress gradient changes more significantly in the region with a larger Gaussian curvature. Set a curvature distribution threshold . If is greater than the set curvature distribution threshold , then strain sensors are arranged at this point.

4. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 3, characterized in that The metric tensor of the spherical surface of the ellipsoidal reticulated shell structure is expressed using the following formula: where the indices and represent local coordinate components on the ellipsoid surface, i.e., along the parametric coordinates and ; when , , the corresponding one is the metric component along the direction; when , or , , the corresponding one is the coupled metric component and in the direction; when , , the corresponding one is the metric component along the direction.

5. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 4, wherein, The original strain value measured by the strain sensor is corrected by the following formula in combination with the metric tensor to obtain the true strain value as follows: ； Among them, is the determinant of the metric tensor; is the strain-curvature compensation coefficient.

6. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 5, characterized in that Strain-curvature compensation coefficient Calculated using the following formula: Among them, is the shell thickness of the ellipsoidal reticulated shell structure; is the Poisson's ratio of the material of the ellipsoidal reticulated shell structure; is the local principal curvature radius of the ellipsoidal reticulated shell structure.

7. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 6, characterized in that, Strain field interpolation function It is expressed by the following formula: Among them, is the number of strain sensors; is an integer subscript index; represents the true strain value corresponding to the original strain value obtained by the th strain sensor; represents the th position where the strain sensor is arranged and the Gaussian curvature at that position.

8. The intelligent stress monitoring method for an ellipsoidal reticulated shell structure based on multi-sensor fusion according to claim 7, characterized in that The stress distribution function is expressed by the following formula :[[]]END]] Among them, is the elastic modulus of the material of the ellipsoidal reticulated shell structure; is the curvature influence coefficient, and its value range is from 0.05 to 0.5; is the membrane force matrix.

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