Temperature indicating paint three-dimensional temperature field reconstruction interpretation method based on prior shape point cloud registration

Abstract

The application provides a temperature indicating paint three-dimensional temperature field reconstruction interpretation method based on prior shape point cloud registration, relates to the testing technical field of hot end components of an aero-engine and a gas turbine, and through obtaining a real surface color point cloud of a measured rotating component after testing and a cold standard three-dimensional model, finite element analysis is carried out by using rotating speed parameters and temperature field prediction parameters under a target working condition, a theoretical deformation amount and a deformation main direction are obtained, and a theoretical deformation reference model is constructed; the theoretical deformation reference model is taken as a target, the real surface color point cloud is taken as a source, non-rigid point cloud registration is executed, the deformation main direction is taken as a direction constraint of a deformation field in the registration process, deformation of the source point cloud along the deformation main direction is limited, and a mapping relationship of the real point cloud to a standard coordinate space is established; color values are mapped to the standard coordinate space based on the mapping relationship, and a three-dimensional temperature field is reconstructed according to a temperature indicating paint color-temperature corresponding relationship. The method realizes accurate temperature field reconstruction of temperature indicating paint data of a deformed blade.

Description

Technical Field

[0001] This invention belongs to the field of testing technology for hot-end components of aero-engines and gas turbines, and specifically relates to a method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration. Background Technology

[0002] Temperature-indicating paint is a coating applied to the surface of high-temperature rotating components such as turbine blades in aero-engines. It undergoes irreversible chemical changes under high-temperature conditions, resulting in different colors. By comparing the color of the temperature-indicating paint after testing with a pre-defined color-temperature correspondence, the highest temperature distribution experienced by the component surface can be deduced. This is an important method for obtaining the overall temperature field in the research and development testing of hot-end components of engines.

[0003] However, turbine blades undergo significant thermal expansion and centrifugal tensile deformation under high-temperature and high-speed conditions. After testing and reverting to a cold state, the blade's geometry differs considerably from the cold-state standard design model, manifesting as radial elongation at the blade tip and slight twisting of the blade body. When using 3D scanning equipment to acquire the colored point cloud of the cold-state blade surface and directly mapping its color values ​​to the cold-state standard 3D model for temperature interpretation, geometric mismatch leads to a misalignment in the correspondence between color values ​​and spatial locations: the color of the blade's leading edge may be incorrectly mapped to the blade root region, and the color of the blade tip region may be incorrectly mapped to the blade root direction. This mapping deviation directly results in a distorted spatial distribution of the reconstructed temperature field, leading to incorrect identification of the high-temperature zone and severely impacting the accuracy of assessments of blade cooling effects and thermal protection design.

[0004] Existing processing methods typically treat the blade as a rigid body and use rigid registration algorithms to align the real point cloud to the standard model. However, rigid registration cannot compensate for the non-uniform thermo-mechanical deformation of the blade under high-temperature conditions. The residual geometric deviation after registration is particularly significant in areas with large deformation, such as the blade tip, and cannot fundamentally solve the color mapping misalignment problem caused by geometric mismatch. Summary of the Invention

[0005] In view of the above-mentioned defects or deficiencies in the prior art, a method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration is provided, including the following steps: Obtain the color point cloud of the actual surface of the rotating component under test after the test under the target working condition, as well as the cold standard three-dimensional model of the rotating component under test; Based on the rotational speed parameters and temperature field prediction parameters of the target working condition, the theoretical deformation amount and main deformation direction of the tested rotating component under the target working condition are obtained through finite element analysis. Based on the cold-state standard three-dimensional model and the theoretical deformation, a theoretical deformation benchmark model is constructed. Using the theoretical deformation reference model as the target and the colored point cloud of the physical surface as the source, non-rigid point cloud registration is performed; during the registration process, the main deformation direction is used as the directional constraint of the deformation field to restrict the source point cloud from deforming along the main deformation direction, and a mapping relationship between the physical point cloud and the standard coordinate space is established. Based on the mapping relationship, the color values ​​of the colored point cloud on the surface of the object are mapped to the standard coordinate space, and the three-dimensional temperature field is reconstructed according to the color-temperature correspondence of the temperature-indicating paint.

[0006] According to the technical solution provided in this application, the step of using the main deformation direction as the directional constraint of the deformation field to limit the deformation of the source point cloud along the main deformation direction includes the following steps: With the main deformation direction as the central axis, a conical constraint space with an allowable deviation angle of ±θ is constructed, wherein ±θ is determined according to the manufacturing tolerance grade of the rotating component under test; In each iteration of the non-rigid point cloud registration, it is determined whether the displacement vector of each sampling point in the source point cloud falls within the cone-shaped constraint space; If the displacement vector falls within the conical constraint space, it is retained; if it exceeds the conical constraint space, it is projected back onto the boundary of the conical constraint space. Continue iterating using the constrained displacement vector until convergence.

[0007] According to the technical solution provided in this application, the step of reconstructing a three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: The measured temperature value is obtained at least one known location point on the surface of the rotating component under test, and the measured temperature value is obtained by installing a contact temperature sensor on the surface of the rotating component under test. In the standard coordinate space, extract the mapped color value corresponding to the known position point; The color value is input into the color-temperature correspondence of the temperature-indicating paint to obtain the predicted temperature value, and the deviation between the measured temperature value and the predicted temperature value is calculated. Using the deviation as a global correction parameter, the color-temperature correspondence of the temperature-indicating paint is shifted and corrected to obtain the corrected color-temperature correspondence. Based on the corrected color-temperature correspondence, a three-dimensional temperature field is reconstructed.

[0008] According to the technical solution provided in this application, ±θ is a permissible deviation angle assigned to the corresponding region based on the local region where each sampling point is located in the cold standard three-dimensional model, including the following steps: The cold standard three-dimensional model is pre-divided into multiple regions, based on the local thickness distribution and / or local stiffness distribution of the rotating component under test. Each region is calibrated with a corresponding allowable deviation angle, wherein the allowable deviation angle of the high stiffness region is smaller than that of the low stiffness region. In each iteration of the non-rigid point cloud registration, for the current sampling point in the source point cloud, according to the region to which it belongs in the cold standard 3D model, the corresponding region allowable deviation angle is retrieved, and a conical constraint space with the main deformation direction as the central axis is constructed, thereby constraining the displacement vector of the sampling point.

[0009] According to the technical solution provided in this application, when extracting the mapped color value corresponding to the known position point in the standard coordinate space, the following steps are performed: Based on the local region to which the known location point belongs in the cold standard 3D model, obtain the allowable deviation angle of the corresponding local region; Using the allowable deviation angle of the region as input, the spatial search radius is determined by a preset mapping function, wherein the spatial search radius corresponding to the low stiffness region is greater than the spatial search radius corresponding to the high stiffness region. A spherical search domain is constructed with the coordinates of the known location point in the standard coordinate space as the center and the spatial search radius as the radius; Extract the color values ​​of all sampling points within the spherical search domain, calculate the color value statistics, and use the color value statistics as the mapped color value corresponding to the known location point.

[0010] According to the technical solution provided in this application, the calculation of color value statistics includes the following steps: Obtain the temperature field prediction parameters of the measured rotating component under the target working condition, and determine the local predicted temperature gradient direction in the spherical search domain based on the temperature field prediction parameters; Using the projection position of the center of the spherical search domain onto the direction of the local estimated temperature gradient as the reference isotherm, calculate the offset of the projection position of each sampling point in the spherical search domain relative to the reference isotherm. Based on the offset, a weight coefficient is assigned to each sampling point, wherein the smaller the offset, the larger the weight coefficient corresponding to the sampling point, and the larger the offset, the smaller the weight coefficient corresponding to the sampling point. The color value statistics are obtained by weighting the color values ​​of all sampling points in the spherical search domain with the weighting coefficients.

[0011] According to the technical solution provided in this application, the following steps are performed during the non-rigid point cloud registration process: For each node in the theoretical deformation reference model, the main deformation direction corresponding to the node is identified, and the position adjustment range of the node along the main deformation direction is determined. The position adjustment range is set according to the uncertainty of the temperature field prediction parameters. In each registration iteration, two parts of the update are performed simultaneously: the first part is to update the deformation parameters of each sampling point in the source point cloud, and the second part is to update the position parameters of each node in the theoretical deformation reference model along its main deformation direction. The two parts of the update aim to jointly minimize the overall registration error between the source point cloud and the theoretical deformation reference model. After iterative convergence, the updated theoretical deformation benchmark model is used as the final target model for mapping the physical point cloud to the standard coordinate space.

[0012] According to the technical solution provided in this application, obtaining the color point cloud of the actual surface of the tested rotating component after testing under target working conditions includes the following steps: A multispectral imaging device is used to add at least one auxiliary spectral channel in addition to the visible light band to obtain a set of multispectral reflectance values ​​for each sampling point. The set of multispectral reflectance values ​​includes the color value corresponding to the visible light band and the auxiliary reflectance value corresponding to the auxiliary spectral channel. A set of multispectral reflectance values ​​for each sampling point are input into a pre-built attachment identification classifier. The attachment identification classifier is obtained by learning the known spectral characteristics of clean temperature-indicating paint samples and the known spectral characteristics of attachment samples, and outputs the determination result of whether the sampling point is an attachment-covered point. For sampling points determined to be free of attached substances, their color values ​​are marked as temperature-indicating paint reading color values; for sampling points determined to be covered by attached substances, a set of multispectral reflectance values ​​are marked as attached substance reading spectral values. The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: For sampling points marked as color values ​​for temperature-indicating paint, the temperature is determined by applying the color-temperature correspondence of the temperature-indicating paint. For sampling points marked as attachment interpretation spectral values, a set of multispectral reflectance values ​​are input into a pre-constructed attachment-temperature mapping model. The attachment-temperature mapping model is established by simultaneously collecting attachment spectral samples at different known temperatures during calibration tests and outputs the estimated temperature value of the attachment corresponding to the sampling point. The temperature reading results corresponding to the color values ​​of the temperature-indicating paint are combined with the estimated temperature values ​​of the attachments corresponding to the spectral values ​​of the attachments to reconstruct a three-dimensional temperature field.

[0013] According to the technical solution provided in this application, before reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint, the following steps are also included: Obtain flow field simulation data of the rotating component under test under the target working condition, and determine the airflow scouring intensity distribution at each position on the surface of the rotating component under test based on the flow field simulation data; Based on the airflow scouring intensity distribution and the continuous operating time of the target working condition, the spatial distribution of coating thinning at each position on the surface of the tested rotating component is calculated. Based on the spatial distribution of the coating thinning amount, the color values ​​mapped to the standard coordinate space are sampled point by point and thinning compensation correction is performed to obtain the compensated color values. The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: Based on the compensated color value, the temperature is determined by applying the pre-calibrated color-temperature correspondence of the temperature-indicating paint, and a three-dimensional temperature field is reconstructed.

[0014] According to the technical solution provided in this application, the thinning compensation correction is performed in a hierarchical iterative manner: First, apply the uncompensated color value to the color-temperature correspondence of the temperature-indicating paint to obtain the initial temperature estimate for each sampling point; Based on the initial temperature estimate, for each sampling point, the coating thinning amount is read from the corresponding spatial distribution of coating thinning amount, and the compensation curve corresponding to the temperature range closest to the initial temperature estimate is selected from the pre-calibrated multi-temperature range coating thinning-color compensation mapping relationship library. Thinning compensation is performed on the color value of the sampling point to obtain the color value after one compensation. Based on the color value after the first compensation, the color-temperature correspondence of the temperature-indicating paint is reapplied to obtain the updated temperature estimate; Repeat the compensation and temperature update steps until the change in temperature estimate between two adjacent iterations is less than the preset convergence threshold. Use the temperature estimate of the last iteration as the final temperature reading result for that sampling point.

[0015] Compared with the prior art, the beneficial effects of this application are as follows: First, it eliminates the color-position mapping deviation caused by the thermal-mechanical deformation of the blade. Finite element analysis is used to obtain the theoretical deformation amount and principal direction of the blade under the target operating condition. This theoretical deformation benchmark model is then used as the registration target. Simultaneously, during the non-rigid registration process, the deformation direction of the source point cloud is constrained by the principal deformation direction, ensuring that the deformation adjustment of the actual point cloud always conforms to the physical laws of the blade's centrifugal stretching and thermal expansion, rather than arbitrary mathematical deformation. The mapping relationship after registration accurately restores the correspondence between each sampling point on the deformed blade surface and the spatial coordinates of the standard model, fundamentally solving the core problem of color misalignment caused by geometric mismatch.

[0016] Second, the physical constraints of the blades are preserved, avoiding deformations that violate engineering realities caused by non-rigid registration. Unlike general unconstrained non-rigid registration algorithms, this method embeds the main deformation direction into the registration process as a directional constraint, restricting the source point cloud to deform only along the radial direction dominated by centrifugal force. This avoids pseudo-deformations such as blade torsion and out-of-plane warping caused by excessive freedom in the algorithm, ensuring that the registration results meet the requirements in terms of both geometric accuracy and physical rationality.

[0017] Third, it achieved accurate localization of the temperature-indicating paint data of deformed blades to the standard design coordinate system. Based on the mapping relationship established by physical constraint registration, the color values ​​of the colored point cloud on the actual surface are accurately mapped to the standard coordinate space of the cold standard 3D model. This ensures that the temperature-indicating paint interpretation results of different batches of blades of the same model have a unified spatial reference benchmark, providing a data foundation for establishing a blade temperature field database and conducting batch statistical analysis. Attached Figure Description

[0018] Other features, objects, and advantages of this application will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 A flowchart illustrating the steps of the three-dimensional temperature field reconstruction and interpretation method for temperature-indicating paint based on prior shape point cloud registration provided in this application. Detailed Implementation

[0019] The present application will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings.

[0020] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other. This application will now be described in detail with reference to the accompanying drawings and embodiments.

[0021] As mentioned in the background section, this application proposes a method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration. Figure 1 As shown, it includes the following steps: S1. Obtain the color point cloud of the actual surface of the rotating component under test after the test under the target working condition, and the cold standard three-dimensional model of the rotating component under test. S2. Based on the rotational speed parameters and temperature field prediction parameters of the target working condition, the theoretical deformation amount and main deformation direction of the tested rotating component under the target working condition are obtained through finite element analysis. S3. Based on the cold-state standard three-dimensional model and the theoretical deformation amount, construct a theoretical deformation benchmark model; S4. Using the theoretical deformation reference model as the target and the colored point cloud of the physical surface as the source, perform non-rigid point cloud registration; during the registration process, use the main deformation direction as the directional constraint of the deformation field to restrict the source point cloud from deforming along the main deformation direction, and establish the mapping relationship between the physical point cloud and the standard coordinate space. S5. Based on the mapping relationship, the color values ​​of the colored point cloud on the surface of the object are mapped to the standard coordinate space, and the three-dimensional temperature field is reconstructed according to the color-temperature correspondence of the temperature-indicating paint.

[0022] The following is a detailed explanation of each step.

[0023] In S1, the tested rotating component refers to blade-like rotating parts in equipment such as aero-engines, gas turbines, steam turbines, and compressors. The physical surface color point cloud refers to the set of discrete sampling points obtained by scanning the surface of the tested rotating component using a 3D scanning device. Each sampling point contains three-dimensional spatial coordinates and a color value, typically represented in the RGB color space. The cold-state standard 3D model refers to the computer-aided design model of the tested rotating component in its design state, usually in STL or STEP format, representing the theoretical geometry of the component in its undeformed state at room temperature.

[0024] In S2, the rotational speed parameter refers to the actual rotational speed of the rotor under the target operating condition, measured in revolutions per minute (rpm), and is directly acquired by the rotational speed sensor on the test bench. The temperature field prediction parameter refers to the predicted surface temperature distribution of the tested rotating component obtained through whole-machine thermal analysis simulation or empirical data from similar models. The finite element analysis process is as follows: the cold-state standard three-dimensional model is discretized into a finite element mesh, and centrifugal load and thermal load are applied simultaneously to each mesh node. The centrifugal load is applied by using the angular velocity ω, converted from the rotational speed parameter, as input, and calculating the centrifugal force on each node. The magnitude of the centrifugal force is the mass of the element associated with that node multiplied by ω² and then multiplied by the distance from that node to the rotation axis. The thermal load is applied by applying the temperature field prediction parameter to the finite element model in the form of nodal temperature boundary conditions, and converting the temperature change into thermal strain through the thermal expansion coefficient of the material. The static equilibrium equations under the above load conditions are solved to obtain the displacement vector of each node. The magnitude of this displacement vector is the theoretical deformation, and the direction of this displacement vector is the principal deformation direction. For rotating blades, the main deformation direction is dominated by the radial component, which is driven by centrifugal force, and superimposed with the thermal expansion component caused by the temperature gradient.

[0025] In S3, the theoretical deformation benchmark model is constructed as follows: The coordinates of each node in the cold standard 3D model are added to the corresponding displacement vector to obtain the deformed node coordinates. Specifically, for the i-th node in the cold standard 3D model, its original coordinates are (xi, yi, zi), and the displacement vector obtained from the finite element analysis is (dxi, dyi, dzi). Then, the coordinates of the corresponding node in the theoretical deformation benchmark model are (xi+dxi, yi+dyi, zi+dzi). All the deformed node coordinates and the original mesh topology together constitute the theoretical deformation benchmark model.

[0026] In S4, the goal of non-rigid point cloud registration is to find a deformation function F such that after transformation F, the overall distance error between each sampled point in the source point cloud P and the target point cloud Q is minimized. The registration process uses a non-rigid extended version of the iterative nearest point algorithm, and the specific execution steps are as follows: S4-1: Initialization. Set the initial position of the source point cloud P to its original sampling coordinates, and set the maximum number of iterations Nmax and the convergence threshold ε.

[0027] S4-2: Establishing the Correspondence. For each sampling point pi in the source point cloud P, search for the point qj in the target point cloud Q that has the closest spatial distance to it, and establish the correspondence between pi and qj. The spatial distance is calculated using Euclidean distance.

[0028] S4-3: Solving the deformation field under the constraint of the principal deformation direction. An energy function E is constructed, consisting of a data term Edata and a smoothing term Esmooth. The data term Edata is the sum of squares of the distances between all corresponding point pairs. The smoothing term Esmooth constrains the difference in displacement vectors between adjacent sampling points, ensuring the smoothness and continuity of the deformation field. The constraint of the principal deformation direction is introduced into the energy function as follows: for each sampling point pi, its displacement vector di is decomposed into a component di_parallel along the principal deformation direction and a component di_perp perpendicular to the principal deformation direction. A penalty term is added to the energy function, which is proportional to the sum of squares of di_perp, with a penalty coefficient of a preset large value λ. Thus, when minimizing the energy function, the optimization algorithm tends to compress di_perp to zero, while allowing di_parallel to adjust freely, thereby achieving the constraint effect that the source point cloud deforms only along the principal deformation direction. The minimization of the energy function is solved using the Levenberg-Marquardt algorithm.

[0029] S4-4: Source point cloud update. Update the position of each sampling point in the source point cloud using the displacement vector obtained from S4-3.

[0030] S4-5: Convergence check. Calculate the average distance between corresponding points in the source point cloud and the target point cloud after this iteration. If the distance is less than the convergence threshold ε, or the number of iterations reaches Nmax, stop the iteration and output the final deformation field F; otherwise, return to S4-2 to continue the iteration.

[0031] After registration convergence, the deformation field F is the mapping relationship from the object point cloud to the standard coordinate space. For any sampling point p in the object point cloud, its corresponding coordinates in the standard coordinate space are obtained by adding the displacement vector of F at that point to the original coordinates of p.

[0032] In S5, mapping the color values ​​of the colored point cloud on the object's surface to the standard coordinate space refers to using the deformation field F established in S4 to assign the RGB color value of each sampling point to its corresponding position in the standard coordinate space. The color-temperature correspondence of the temperature-indicating paint refers to the mapping data obtained through laboratory calibration, typically stored in the form of a lookup table. The calibration method involves heating a sample coated with the temperature-indicating paint at different known temperatures and recording the RGB values ​​after color change, forming a mapping table from RGB values ​​to temperature values. Based on this mapping table, the RGB color value at each position in the standard coordinate space is looked up or interpolated to obtain the temperature value. Then, spatial interpolation is performed on the discrete temperature values ​​to reconstruct the three-dimensional temperature field.

[0033] The core principle of this implementation lies in using finite element analysis to obtain prior knowledge of the deformation of the rotating component under test. This prior knowledge is then embedded into the energy function of non-rigid point cloud registration in the form of a penalty term for the principal deformation direction. This allows the registration algorithm to eliminate geometric mismatch while maintaining the physical rationality of the deformation results. The desired technical effect is to solve the problem that traditional rigid registration cannot compensate for the misalignment between the color of the temperature indicator paint and the spatial coordinates caused by the thermal deformation of the blades, thus eliminating the spatial mapping deviation of the temperature field reconstruction from its geometric root.

[0034] In a preferred embodiment, the step of using the principal deformation direction as the directional constraint of the deformation field to restrict the source point cloud from deforming along the principal deformation direction includes the following steps: With the main deformation direction as the central axis, a conical constraint space with an allowable deviation angle of ±θ is constructed, wherein ±θ is determined according to the manufacturing tolerance grade of the rotating component under test; In each iteration of the non-rigid point cloud registration, it is determined whether the displacement vector of each sampling point in the source point cloud falls within the cone-shaped constraint space; If the displacement vector falls within the conical constraint space, it is retained; if it exceeds the conical constraint space, it is projected back onto the boundary of the conical constraint space. Continue iterating using the constrained displacement vector until convergence.

[0035] Specifically, the conical constraint space refers to a three-dimensional conical region with the main deformation direction as its central axis and ±θ as its semi-cone angle. The semi-cone angle θ is determined as follows: Collect a certain number of physical measurement data of the same model of rotating parts being measured. After rigidly registering each physical measurement data with the cold-state standard three-dimensional model, statistically analyze the geometric deviation distribution of each sampling point, and take the angle value corresponding to the preset quantile of the deviation distribution as θ. For example, taking the deviation angle corresponding to the 95th quantile as θ means that 95% of the manufacturing deviation falls within the ±θ range. In each iteration of the non-rigid point cloud registration, for each sampling point pi in the source point cloud, perform the following operations: First, the displacement vector di of the sampling point is read from the deformation field of the current iteration step. The displacement vector di is a three-dimensional vector, whose starting point is the position of the sampling point pi in the previous iteration, and whose ending point is the new position calculated in this iteration.

[0036] Then, calculate the angle φ between the displacement vector di and the principal deformation direction. The principal deformation direction is a pre-calculated unit vector vi, and the formula for calculating the angle φ is φ=arccos(|di·vi| / |di|), where di·vi represents the dot product of di and vi, and |di| represents the magnitude of di.

[0037] Next, the included angle φ is compared with the half-cone angle θ. If φ ≤ θ, it means that the direction of the displacement vector falls within the conical constraint space, and di remains unchanged. If φ > θ, it means that the displacement vector exceeds the boundary of the conical constraint space and needs to be projected back onto the boundary. The specific method of projection is as follows: calculate a corrected displacement vector di', where the direction of di' is the direction closest to di on the boundary of the conical constraint space, and the angle between this direction and the principal deformation direction (i.e., the vi direction) is exactly equal to θ, and it lies in the plane spanned by di and vi. The correction method is to keep the component along the principal deformation direction unchanged and scale the perpendicular component to the conical boundary: the calculation formula for di' is: first calculate the component di_perp perpendicular to the principal deformation direction and the component di_parallel along the principal deformation direction, and construct di' = di_parallel + (di_perp / |di_perp|) × |di_parallel| × tan(θ), where tan represents the tangent function. The geometric meaning of this formula is to correct the direction of di to the direction of the cone boundary while keeping the component along the principal deformation direction unchanged. The corrected displacement vector di' replaces the original di and participates in the position update of the sampling point in the next iteration.

[0038] Since the displacement vectors that exceed the constraints are projected and corrected in each iteration, as the iteration proceeds, the displacement vector directions of all sampling points in the source point cloud are gradually constrained within the cone-shaped space, and the overall deformation field converges to a solution that satisfies both the data matching accuracy and the physical direction constraints.

[0039] The core principle of this implementation lies in concretizing the abstract constraint of deformation along the main deformation direction into a conical spatial projection operation, ensuring that the displacement direction of the sampling points does not deviate from the physically reasonable range in each iteration. The desired technical effect is to provide tolerance space for minor geometric differences caused by manufacturing tolerances between the actual blade and the standard model, while preserving the physical prior constraints, thus avoiding overly tight constraints that could cause the registration algorithm to fail to converge in local areas with large manufacturing deviations.

[0040] In a preferred embodiment, the step of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: The measured temperature value is obtained at least one known location point on the surface of the rotating component under test, and the measured temperature value is obtained by installing a contact temperature sensor on the surface of the rotating component under test. In the standard coordinate space, extract the mapped color value corresponding to the known position point; The color value is input into the color-temperature correspondence of the temperature-indicating paint to obtain the predicted temperature value, and the deviation between the measured temperature value and the predicted temperature value is calculated. Using the deviation as a global correction parameter, the color-temperature correspondence of the temperature-indicating paint is shifted and corrected to obtain the corrected color-temperature correspondence. Based on the corrected color-temperature correspondence, a three-dimensional temperature field is reconstructed.

[0041] Specifically, in this application scenario, contact temperature sensors are typically thermocouples or crystal thermometers. Known location points refer to the installation positions of these sensors on the surface of the rotating component being measured; their spatial coordinates in the cold-state standard 3D model are pre-recorded and known, denoted as (xk, yk, zk). The measured temperature value T_measured_k refers to the temperature data directly measured by the sensor during the target operating condition test. The mapped color values ​​corresponding to the known location points are extracted in the standard coordinate space. The specific steps are as follows: First, using the mapping relationship established in step S4 by the deformation field F, the coordinates (xk, yk, zk) of the known location point on the cold-state standard 3D model are reverse-mapped back to the physical point cloud space. The reverse mapping method involves searching in the deformation field F for the mapping target point whose spatial coordinates are closest to (xk, yk, zk), thus finding the corresponding source sampling point in the physical point cloud. Since the deformation field F is a mapping between discrete sampling points, nearest neighbor search or bilinear interpolation is used during the reverse mapping. After finding the corresponding sampling point in the physical point cloud, the RGB color value of that sampling point is read and denoted as (Rk, Gk, Bk). This color value is the mapped color value corresponding to the known location point. The color value (Rk, Gk, Bk) is input into the color-temperature correspondence of the temperature-indicating paint to obtain the predicted temperature value T_predicted_k. The color-temperature correspondence of temperature-indicating paint is typically stored in a three-dimensional lookup table. For input RGB values, the lookup table may not have an exact corresponding entry. Trilinear interpolation is used to perform interpolation calculations in the RGB space to obtain the corresponding predicted temperature value. Specifically, trilinear interpolation involves finding the eight vertices of the cube element containing the RGB value in the lookup table, using the normalized distance of the RGB value from each vertex as weights, and then summing the temperature values ​​at the eight vertices using weighted averages. The deviation ΔT_k between the measured temperature value T_measured_k and the predicted temperature value T_predicted_k is calculated as ΔT_k = T_measured_k - T_predicted_k. If multiple contact temperature sensors are installed on the surface of the rotating component being measured, the deviation is calculated for each known location point, and the arithmetic mean or weighted average of all deviations is taken as the global correction parameter ΔT. In weighted averaging, the weights can be assigned based on the reliability and measurement accuracy of each sensor's installation location; for example, a welded thermocouple has a greater weight than a pasted thermocouple. Using the deviation ΔT as the global correction parameter, the color-temperature correspondence of the temperature-indicating paint is comprehensively shifted and corrected. The meaning of global translation correction is that for each entry in the original color-temperature lookup table of the thermochromic paint, while keeping its RGB color value unchanged, its corresponding temperature value is added by ΔT to form a corrected color-temperature lookup table. This operation is equivalent to shifting the entire color-temperature mapping curve along the temperature axis by ΔT. The mathematical essence of this global translation is the assumption that the color-temperature correspondence of the thermochromic paint has undergone additive systematic error under actual experimental conditions, rather than multiplicative error or nonlinear distortion. Based on the corrected color-temperature lookup table, the RGB color values ​​of all valid sampling points in the standard coordinate space are looked up and interpolated to obtain the temperature value of each point. Then, spatial interpolation of the discrete temperature values ​​is performed through Kriging interpolation or radial basis function interpolation to reconstruct the three-dimensional temperature field calibrated by thermocouple measured data.

[0042] In a preferred embodiment, ±θ is assigned a corresponding allowable deviation angle based on the local region where each sampling point is located in the cold standard 3D model, including the following steps: The cold standard three-dimensional model is pre-divided into multiple regions, based on the local thickness distribution and / or local stiffness distribution of the rotating component under test. Each region is calibrated with a corresponding allowable deviation angle, wherein the allowable deviation angle of the high stiffness region is smaller than that of the low stiffness region. In each iteration of the non-rigid point cloud registration, for the current sampling point in the source point cloud, according to the region to which it belongs in the cold standard 3D model, the corresponding region allowable deviation angle is retrieved, and a conical constraint space with the main deformation direction as the central axis is constructed, thereby constraining the displacement vector of the sampling point.

[0043] Specifically, the cold-state standard 3D model is pre-divided into multiple regions based on the local thickness and stiffness distribution of the rotating component under test. Local thickness distribution refers to the distance from each point on the surface of the rotating component along the normal direction to the opposite surface. Regions with larger local thicknesses have higher bending stiffness, and their actual deformation under centrifugal force and thermal load is closer to the theoretical calculation value. Local stiffness distribution refers to the ability of each point on the surface of the rotating component to resist elastic deformation, which is related to factors such as local thickness, material properties, and radius of curvature. The specific steps for region division are as follows: First, the cold-state standard 3D model is meshed using finite element methods, resulting in N mesh elements. For shell element meshes, the thickness value of the element is directly read from the element attribute parameters. For solid element meshes, M sampling points are uniformly taken on the element surface, with M ranging from 4 to 9. A ray is drawn along the surface normal at each sampling point, and the intersection of the ray and the opposite surface is calculated. The distance from the ray's origin to the intersection point is the local thickness at that sampling point. The arithmetic mean of the thicknesses of the M sampling points is taken as the local thickness value of the element. The second step is to sort all N mesh elements in descending order of their local thickness values, resulting in a sorted list. The third step is to set the number of regions, K, which can be between 3 and 5. The partition threshold is calculated by selecting K-1 equal-interval dividing points in the sorted list and using the thickness value corresponding to each dividing point as the boundary threshold between adjacent regions. Alternatively, the boundary threshold can be manually set based on the structural characteristics of the rotating component being tested, for example, using the thickness values ​​at the natural boundaries of the blade root, mid-blade, and tip segments as the threshold. The fourth step is to divide all mesh elements into K regions based on the boundary thresholds, assigning a region label to each mesh element. The region with the largest thickness value is labeled as a high-stiffness region, the region with the smallest thickness value is labeled as a low-stiffness region, and the intermediate regions are labeled as medium-high stiffness, medium stiffness, or medium-low stiffness regions, respectively. Taking aero-engine turbine blades as an example, they are divided into three regions: the blade root region, with a thickness of 3 to 6 millimeters, is classified as a high-stiffness region; the middle section of the blade, with a thickness of 1.5 to 3 millimeters, is classified as a medium-stiffness region; and the blade tip and leading edge, with a thickness of 0.5 to 1.5 millimeters, is classified as a low-stiffness region.

[0044] The allowable deviation angle for each region is calibrated. The calibration is based on the distribution of the deviation angles between the actual and theoretical deformations of the sampling points within that region. Specifically, the calibration process involves collecting physical scan point cloud data from at least 5 to 10 identical rotating components tested under the same target conditions. Each physical point cloud is then rigidly pre-registered with a cold-state standard 3D model. The pre-registration uses an iterative nearest-point algorithm based on the non-deformable region of the leaf root, with the rigid transformation matrix containing six degrees of freedom: rotation and translation. After pre-registration, for each sampling point in the physical point cloud, the displacement vector from the cold-state position to the physical position is calculated and denoted as the actual displacement vector. Simultaneously, the theoretical displacement vector of the corresponding node is retrieved from the finite element analysis results. The angular deviation between the actual and theoretical displacement vectors is calculated by dividing the dot product of the two vectors by the product of their magnitudes, and then taking the inverse cosine. The angular deviation values ​​of all sampling points belonging to the same region are aggregated into a dataset, and the angle value corresponding to the preset quantile of this dataset is calculated as the allowable deviation angle for that region. The preset quantile is 95%, meaning the angle value where 95% of the angle deviations in the dataset are less than or equal to is taken as the permissible deviation angle for that region. Calibration results are stored in a region tolerance table, which records the label, thickness range, and corresponding permissible deviation angle value for each region. Typical calibration results show that the permissible deviation angle for high-stiffness regions is 1 to 3 degrees, for medium-stiffness regions it is 3 to 6 degrees, and for low-stiffness regions it is 6 to 10 degrees.

[0045] In each iteration of non-rigid point cloud registration, for the current sampling point in the source point cloud, the following steps are performed: First, determine the region to which the sampling point belongs in the cold-state standard 3D model by querying the region label of the mesh cell containing the target point. Second, retrieve the region's allowable deviation angle from the region tolerance table. Third, construct a conical constraint space with the main deformation direction as the central axis and the region's allowable deviation angle as the half-cone angle θ_r. Subsequent displacement vector judgment and projection operations are consistent with the above, except that θ in the projection formula is replaced with θ_r corresponding to the current region, i.e., di'=di_parallel+(di_perp / |di_perp|)×|di_parallel|×tan(θ_r).

[0046] The principle of this implementation method lies in associating the structural mechanical properties of the rotating component under test with the constraint parameters of the registration algorithm, so that different regions of the blade adopt constraints with varying degrees of tightness. The desired technical effect is to maintain strict physical constraints in high-stiffness regions to ensure registration accuracy, while appropriately relaxing constraints in low-stiffness regions to avoid the algorithm failing to converge due to reasonable deviations between actual and theoretical deformations. This regionally differentiated constraint strategy balances registration accuracy and algorithm robustness, avoiding the dilemma of a globally uniform cone angle leading to spurious deformation in high-stiffness regions due to excessively loose constraints, and failing to converge in low-stiffness regions due to excessively tight constraints.

[0047] In a preferred embodiment, when extracting the mapped color value corresponding to the known location point in the standard coordinate space, the following steps are performed: Based on the local region to which the known location point belongs in the cold standard 3D model, obtain the allowable deviation angle of the corresponding local region; Using the allowable deviation angle of the region as input, the spatial search radius is determined by a preset mapping function, wherein the spatial search radius corresponding to the low stiffness region is greater than the spatial search radius corresponding to the high stiffness region. A spherical search domain is constructed with the coordinates of the known location point in the standard coordinate space as the center and the spatial search radius as the radius; Extract the color values ​​of all sampling points within the spherical search domain, calculate the color value statistics, and use the color value statistics as the mapped color value corresponding to the known location point.

[0048] Specifically, based on the local region to which the known location point belongs in the cold standard 3D model, the allowable deviation angle of that local region is obtained. The spatial coordinates of the known location point are pre-recorded. These coordinates are mapped onto the cold standard 3D model to determine which mesh cell the coordinates fall within. The region label of that mesh cell is read, and the allowable deviation angle of that region is retrieved from the established region tolerance table.

[0049] Using the allowable deviation angle of the region as input, the spatial search radius is determined through a preset mapping function. The preset mapping function adopts the following linear form: the spatial search radius equals the first coefficient multiplied by the allowable deviation angle of the region plus a second coefficient. The first coefficient ranges from 0.005 to 0.05 mm per degree, and the second coefficient ranges from 0 to 0.1 mm. In a typical parameter setting, the first coefficient is 0.01 mm per degree, and the second coefficient is 0.05 mm. Therefore, when the allowable deviation angle of the region is 2 degrees, the search radius is 0.07 mm; when the allowable deviation angle of the region is 8 degrees, the search radius is 0.13 mm. The first and second coefficients of this linear mapping function are calibrated as follows: Multiple repeated scans and registration tests are performed on the same type of rotating component under test. The registration deviation distribution of the known coordinates of the marker points within each region is statistically analyzed. The 95th quantile of the deviation distribution is used as the required spatial search radius for that region. Least squares linear fitting is performed on multiple sets of allowable deviation angles and corresponding search radius data to obtain the first and second coefficients. This mapping function ensures that the spatial search radius corresponding to the low stiffness region is greater than the spatial search radius corresponding to the high stiffness region.

[0050] A spherical search domain is constructed with the known location point's coordinates in standard coordinate space as the center and the spatial search radius as the radius. This spherical search domain is a sphere in standard coordinate space with a radius equal to the spatial search radius, and its center is located at the known location point. All sampling points within the spherical search domain refer to all sampling points in the colored point cloud of the physical surface after mapping to standard coordinate space in step S4, whose spatial coordinates fall within this sphere.

[0051] Extract the color values ​​of all sampling points within the spherical search domain and calculate the color value statistics. The color value statistics are calculated using a weighted average. For each sampling point within the spherical search domain, calculate its Euclidean distance to the center of the sphere and assign a weight based on this distance. The weighting function uses a Gaussian kernel form, where the weight is equal to the negative square of the distance (e) divided by 2 multiplied by the square of the bandwidth (one-third of the spatial search radius). This weighting function gives sampling points closer to the center of the sphere a weight close to 1, and sampling points at the edge of the sphere a weight of approximately 0.01. Multiply the RGB three-channel color values ​​of each sampling point by its respective weight and sum them to obtain a weighted sum of the three channels. Then divide each of the three weighted sums by the sum of all weights to obtain a weighted average RGB value. This weighted average RGB value is used as the mapped color value corresponding to the known location point and provided for subsequent steps. If the number of sampling points within the spherical search domain is zero, the search radius is expanded to 1.5 times the original value, and the search is repeated until the search domain contains at least 3 sampling points.

[0052] The principle of this implementation is to adaptively determine the color value sampling range near the thermocouple installation location by utilizing the established regional allowable deviation angle information, thus linking the spatial search radius to the registration uncertainty. The desired technical effect is that in low-stiffness regions with low registration accuracy, random registration errors are smoothed by expanding the search range and using statistical measures, avoiding the extraction of incorrect color values ​​due to single-point coordinate deviations; in high-stiffness regions with high registration accuracy, a smaller search radius is used to preserve spatial resolution. This scheme achieves an adaptive balance between color value extraction accuracy and spatial resolution.

[0053] In a preferred embodiment, the calculation of color value statistics includes the following steps: Obtain the temperature field prediction parameters of the rotating component under test under the target working condition, and determine the local predicted temperature gradient direction in the spherical search domain based on the temperature field prediction parameters; Using the projection position of the center of the spherical search domain onto the direction of the local estimated temperature gradient as the reference isotherm, calculate the offset of the projection position of each sampling point in the spherical search domain relative to the reference isotherm. Based on the offset, a weight coefficient is assigned to each sampling point, wherein the smaller the offset, the larger the weight coefficient corresponding to the sampling point, and the larger the offset, the smaller the weight coefficient corresponding to the sampling point. The color value statistics are obtained by weighting the color values ​​of all sampling points in the spherical search domain with the weighting coefficients.

[0054] Specifically, the temperature field prediction parameters of the rotating component under test are obtained under the target operating condition. These temperature field prediction parameters have already been used in step S2 for finite element analysis to calculate the theoretical deformation, and are called again here without the need for additional data acquisition. The temperature field prediction parameters are stored in the form of discrete nodes, each containing spatial coordinates and a temperature prediction value.

[0055] The direction of the locally predicted temperature gradient within the spherical search domain is determined based on the temperature field prediction parameters. The temperature gradient direction is calculated by taking small offsets (0.01 to 0.1 mm) along the positive and negative directions of the three coordinate axes at the center of the spherical search domain. Temperature prediction values ​​at six locations are calculated, and three partial derivatives are calculated using the central difference formula. The partial derivative is calculated as follows: the partial derivative of temperature with respect to x is approximately equal to the temperature value at the center x-coordinate plus the small offset minus the temperature value at the center x-coordinate minus the small offset, divided by twice the small offset. The partial derivatives in the y and z directions are calculated similarly. The vector formed by the three partial derivatives is the temperature gradient vector, and the direction of this vector is the direction of the locally predicted temperature gradient. The magnitude of the temperature gradient vector represents the degree of temperature change.

[0056] The center of the spherical search domain is projected onto the direction of the locally estimated temperature gradient as the reference isotherm. The offset of the projected position of each sampling point within the spherical search domain relative to the reference isotherm is calculated. Specifically, let the coordinates of the center of the spherical search domain be P0, the coordinates of the i-th sampling point be Pi, and the spatial vector between them be Vi, which is equal to Pi minus P0. The projection scalar of Vi onto the temperature gradient direction is equal to the dot product of Vi and the temperature gradient vector divided by the magnitude of the temperature gradient vector. The sign of this projection scalar indicates the direction of deviation of the sampling point relative to the reference isotherm, and the absolute value of the projection scalar represents the deviation distance.

[0057] Based on the magnitude of the offset, a weighting coefficient is assigned to each sampling point. The weighting function adopts a Gaussian kernel form, where the weighting coefficient of the i-th sampling point is equal to the negative of the natural constant e, the square of the offset of that sampling point, divided by 2 multiplied by the square of the temperature gradient bandwidth parameter σ_T. Sampling points with smaller offsets have larger weighting coefficients, and those with larger offsets have smaller weighting coefficients. The value of the temperature gradient bandwidth parameter σ_T is determined jointly based on the magnitude of the locally estimated temperature gradient and the color temperature sensitivity of the temperature-indicating paint. σ_T is independent of the aforementioned bandwidth based on spatial distance. Specifically, the color temperature sensitivity is first calibrated from the color-temperature correspondence of the temperature-indicating paint, with the unit being the color space distance per degree Celsius. The calibration method is to take the average slope of the working temperature range on the color-temperature curve. Then, a tolerable color deviation threshold is determined, ranging from 0.5 to 2 color space distance units. The tolerable color deviation is then converted into a tolerable temperature deviation, which is equal to the color deviation threshold divided by the color temperature sensitivity. The bandwidth parameter is set as the tolerable temperature deviation divided by the magnitude of the temperature gradient vector. Physically, this means that at a distance of one temperature gradient bandwidth parameter σ_T from the reference isotherm, the temperature difference between the sampling point and the reference isotherm is approximately equal to the tolerable temperature deviation, and the weight of this sampling point is approximately 0.6. At a distance of twice the temperature gradient bandwidth parameter σ_T from the reference isotherm, the weight decreases to approximately 0.14. This method ensures that the larger the temperature gradient, the smaller the bandwidth parameter and the narrower the weighting window, effectively suppressing the interference of sampling points with large temperature differences on the average value in high-gradient regions; conversely, the smaller the temperature gradient, the larger the bandwidth parameter and the wider the weighting window, fully utilizing the advantages of a large number of sampling points and good temperature consistency in low-gradient regions.

[0058] The color values ​​of all sampling points within the spherical search domain are weighted and averaged using weighting coefficients. The weighting method involves multiplying the RGB three-channel color value of each sampling point within the spherical search domain by its respective weighting coefficient to obtain a weighted color value. The weighted color values ​​of the same channel from all sampling points are then summed, and this summation is divided by the sum of the weighting coefficients of all sampling points to obtain the weighted average color value for that channel. The weighted average color values ​​of the three channels are combined to form the final weighted average RGB value, which serves as the color value statistic.

[0059] The principle of this implementation is to utilize the prior information on the temperature gradient provided by the temperature field prediction parameters to directionally weight the sampling points within the spherical search domain. This results in sampling points closer to the isothermal surface contributing more to the color value statistics, while those farther away contribute less. The desired technical effect is to avoid color value distortion caused by sampling points with excessively large temperature differences participating in the averaging process in areas with large temperature gradients. This ensures that the extracted color value statistics accurately represent the true color change state of the thermocouple installation location, improving the reliability of subsequent thermocouple correction steps.

[0060] In a preferred embodiment, the following steps are performed during the non-rigid point cloud registration process: For each node in the theoretical deformation reference model, the main deformation direction corresponding to the node is identified, and the position adjustment range of the node along the main deformation direction is determined. The position adjustment range is set according to the uncertainty of the temperature field prediction parameters. In each registration iteration, two parts of the update are performed simultaneously: the first part is to update the deformation parameters of each sampling point in the source point cloud, and the second part is to update the position parameters of each node in the theoretical deformation reference model along its main deformation direction. The two parts of the update aim to jointly minimize the overall registration error between the source point cloud and the theoretical deformation reference model. After iterative convergence, the updated theoretical deformation benchmark model is used as the final target model for mapping the physical point cloud to the standard coordinate space.

[0061] Specifically, in the initialization phase of non-rigid point cloud registration, the following operations are performed on each node in the theoretical deformation reference model: Identify the principal deformation direction corresponding to the node. The principal deformation direction is given by the finite element analysis results in step S2. The principal deformation direction of each node is the direction of its displacement vector, expressed as a unit vector. Determine the position adjustment range of the node along the principal deformation direction. The position adjustment range is set based on the uncertainty of the temperature field prediction parameters.

[0062] The uncertainty of the temperature field prediction parameters is expressed in absolute temperature values, such as ±50 degrees Celsius or ±10%, and is given by the thermal analysis simulation engineer based on the accuracy of the simulation model and the reliability of the boundary conditions. The specific method for converting the uncertainty into a position adjustment range along the principal deformation direction is to perform sensitivity conversion using the linear relationship between temperature load and thermal strain in finite element analysis. For a component with a material linear expansion coefficient of α, the uncertainty of the temperature field prediction parameters is ±δT, the thermal strain caused by temperature change is α multiplied by δT, and the corresponding displacement change along the principal deformation direction is the integral of this thermal strain along the principal deformation direction. In the engineering simplification, for the j-th node, its theoretical deformation is dj, and the characteristic length of the node's location along the principal deformation direction is Lj, which is the distance from the node to the leaf root constraint end along the principal deformation direction. When the uncertainty of the temperature field prediction parameters is ±δT, the position adjustment range of the node along the principal deformation direction is dj ± α·Lj·δT. Taking a typical nickel-based superalloy turbine blade as an example, the coefficient of linear expansion α is approximately 1.5 x 10⁻⁵ per degree Celsius. If a blade tip node has a characteristic length Lj of approximately 100 mm and a temperature uncertainty δT of 50 degrees Celsius, then the half-width of the position adjustment range is α x Lj x δT, which equals 0.075 mm. That is, the radial position adjustment range of the blade tip node is ±0.075 mm. The position adjustment ranges of each node are stored in the form of an interval table for subsequent iterations.

[0063] In each registration iteration, two parts of the update are performed simultaneously. The first part updates the deformation parameters of each sampling point in the source point cloud. The second part updates the position parameters of each node in the theoretical deformation reference model along its principal deformation direction. The goal of both parts of the update is to jointly minimize the overall registration error between the source point cloud and the theoretical deformation reference model. The specific solution for the two parts of the update adopts an alternating optimization strategy, and each iteration includes the following sub-steps.

[0064] Sub-step one: Keep the positions of all nodes in the fixed theoretical deformation reference model unchanged. Using the non-rigid registration method described in step S4, solve for the displacement vectors of each sampling point in the source point cloud. At this point, the target point cloud is the theoretical deformation reference model for the current iteration step. During the solution process, the principal deformation direction is used as the directional constraint of the deformation field, restricting the deformation of each sampling point in the source point cloud along its respective principal deformation direction. After this sub-step is completed, the positions of each sampling point in the source point cloud are updated.

[0065] Sub-step two: Keeping the updated source point cloud positions unchanged, perform one-dimensional optimization on each node in the theoretical deformation benchmark model. For the j-th node, let its current coordinates be Qj, the unit vector of the deformation principal direction be Vj, and the node's position parameter along the deformation principal direction be tj. Then, the node's actual coordinates are Qj plus tj multiplied by Vj. The value of tj ranges from the lower limit to the upper limit of the position adjustment range corresponding to the node. Search for H nearest sampling points corresponding to node j in the updated source point cloud, where H is 3 to 5. Calculate the sum of squared Euclidean distances from these sampling points to node j, which serves as the local registration error function for that node. Search for the tj value that minimizes the local registration error function within a one-dimensional interval, using the golden section method, with a convergence accuracy set to one-hundredth of the half-width of the position adjustment range. Update the position parameter of node j to the searched optimal tj value. Repeat the above operations for all nodes to complete the node position update of the theoretical deformation benchmark model.

[0066] Sub-step 3: Calculate the overall registration error. The overall registration error is the average Euclidean distance from all sampled points in the source point cloud to their nearest point on the theoretical deformation reference model. Determine the convergence condition: Let η be the relative change between the current overall registration error and the overall registration error of the previous iteration. If η is less than a preset relative convergence threshold (ranging from 0.1% to 1%), the convergence condition is met. If the convergence condition is met, stop the iteration; otherwise, return to sub-step 1.

[0067] After iterative convergence, the updated theoretical deformation benchmark model is used as the final target model for mapping the physical point cloud to the standard coordinate space. Since the updated theoretical deformation benchmark model has absorbed and digested the uncertainty of the temperature field prediction parameters, its geometry is closer to the actual deformation state of the measured rotating part under the target working condition. Therefore, the mapping relationship established based on this final target model has higher spatial accuracy.

[0068] The principle behind this implementation is to break away from the assumption of a fixed target point cloud in traditional registration algorithms. It allows the target point cloud to bidirectionally approach the source point cloud within physically reasonable degrees of freedom, achieving a balance between data matching and physical constraints through alternating optimization. The desired technical effect is to eliminate the systematic impact of temperature field prediction errors on registration accuracy, preventing target shape distortion caused by predicted temperature deviations from being transmitted as spatial misalignment in color mapping, thus improving the robustness and accuracy of the entire temperature field reconstruction method from the source of the registration process.

[0069] In a preferred embodiment, obtaining the color point cloud of the actual surface of the rotating component under test after testing under target operating conditions includes the following steps: A multispectral imaging device is used to add at least one auxiliary spectral channel in addition to the visible light band to obtain a set of multispectral reflectance values ​​for each sampling point. The set of multispectral reflectance values ​​includes the color value corresponding to the visible light band and the auxiliary reflectance value corresponding to the auxiliary spectral channel. A set of multispectral reflectance values ​​for each sampling point are input into a pre-built attachment identification classifier. The attachment identification classifier is obtained by learning the known spectral characteristics of clean temperature-indicating paint samples and the known spectral characteristics of attachment samples, and outputs the determination result of whether the sampling point is an attachment-covered point. For sampling points determined to be free of attached substances, their color values ​​are marked as temperature-indicating paint reading color values; for sampling points determined to be covered by attached substances, a set of multispectral reflectance values ​​are marked as attached substance reading spectral values. The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: For sampling points marked as color values ​​for temperature-indicating paint, the temperature is determined by applying the color-temperature correspondence of the temperature-indicating paint. For sampling points marked as attachment interpretation spectral values, a set of multispectral reflectance values ​​are input into a pre-constructed attachment-temperature mapping model. The attachment-temperature mapping model is established by simultaneously collecting attachment spectral samples at different known temperatures during calibration tests and outputs the estimated temperature value of the attachment corresponding to the sampling point. The temperature reading results corresponding to the color values ​​of the temperature-indicating paint are combined with the estimated temperature values ​​of the attachments corresponding to the spectral values ​​of the attachments to reconstruct a three-dimensional temperature field.

[0070] Specifically, a multispectral imaging device is used, adding at least one auxiliary spectral channel in addition to the visible light band to obtain a set of multispectral reflectance values ​​for each sampling point. A multispectral imaging device refers to an imaging device that adds several narrowband spectral channels to the traditional RGB three-channel imaging. The auxiliary spectral channels are typically selected in the near-infrared band, with a wavelength range of 700 nm to 1100 nm, or in the ultraviolet band, with a wavelength range of 300 nm to 400 nm. The selection is based on the fact that the difference in spectral reflectance characteristics between carbon deposits and the temperature-indicating paint color-changing layer in the aforementioned auxiliary bands is greater than the difference in the visible light band. A set of multispectral reflectance values ​​includes the RGB color value corresponding to the visible light band and the auxiliary reflectance value corresponding to the auxiliary spectral channel. The auxiliary reflectance value is the ratio of the reflected light intensity received by that channel to the reflected light intensity of a standard white board, expressed as a percentage.

[0071] A set of multispectral reflectance values ​​for each sampling point is input into a pre-constructed adhering substance identification classifier. The classifier is constructed by collecting samples of known types of clean, temperature-indicating paint and known types of adhering substances, including carbon deposits, oil stains, and oxide layers. Multispectral reflectance values ​​of these samples are acquired using a multispectral imaging device to construct a training dataset. Each training sample contains a set of multispectral reflectance values ​​and a corresponding type label, categorized as either clean, temperature-indicating paint or adhering substance. A support vector machine (SVM) is selected as the classifier model, with a radial basis function (RBF) kernel. The training process involves inputting the training dataset into the SVM model and determining the optimal parameters of the RBF kernel through cross-validation. After training, an adhering substance identification classifier capable of distinguishing between the spectral features of clean, temperature-indicating paint and those of adhering substances is obtained. The classifier outputs the determination result for each sampling point, indicating whether the sampling point is uncovered or covered by adhering substances.

[0072] For sampling points determined to be free of adhering substances, their RGB color values ​​are marked as color values ​​for temperature-indicating paint interpretation. For sampling points determined to be covered by adhering substances, their set of multispectral reflectance values ​​are marked as spectral values ​​for adhering substances interpretation.

[0073] When reconstructing the three-dimensional temperature field, for sampling points marked as color values ​​for temperature-indicating paint, the temperature is determined by applying the color-temperature correspondence of the temperature-indicating paint, and the determination method is the same as step S5.

[0074] For sampling points marked as having spectral values ​​for adhering deposit interpretation, a set of multispectral reflectance values ​​is input into a pre-constructed adhering deposit-temperature mapping model. The adhering deposit-temperature mapping model is constructed as follows: during calibration tests, samples coated with temperature-indicating paint and pre-placed carbon deposits are heated at different known temperatures, with temperature gradient intervals ranging from 10 to 25 degrees Celsius, and the heating time is consistent with the continuous operation time under the target condition. After heating, a set of multispectral reflectance values ​​of the adhering deposit-covered area is collected using a multispectral imaging device at each temperature level. The correspondence between this set of spectral values ​​and the known temperature is recorded, forming an adhering deposit-temperature mapping lookup table with multispectral reflectance values ​​as the index and temperature as the value. The physical basis of this mapping model is that the deposition rate and microstructure of carbon deposits on the blade surface have a monotonic correlation with surface temperature; the higher the temperature, the denser the carbon deposit layer and the lower the spectral reflectance. Through calibration, this correlation can be quantified into a lookupable mapping relationship. For a measured sampling point, a set of its multispectral reflectance values ​​are searched for nearest neighbor or multivariate linear interpolation in the lookup table, and the estimated temperature value of the attachment corresponding to the sampling point is output.

[0075] The temperature readings corresponding to the color values ​​of the temperature-indicating paint and the estimated temperature values ​​of the adhering substances corresponding to the spectral values ​​of the adhering substances are merged. The merging method is to fill the temperature values ​​of the two types of sampling points into the same temperature field dataset according to their respective spatial coordinates in the standard coordinate space, and then perform spatial interpolation on the merged dataset to reconstruct a complete three-dimensional temperature field.

[0076] The principle of this implementation lies in using multispectral imaging to distinguish the spectral differences between the paint and the attached substances. Different temperature interpretation paths are used for the two types of sampling points, transforming the information of the attached substances, which is discarded as interference in traditional methods, into a supplementary source of temperature information. The technical effect it aims to achieve is to avoid erroneous temperature interpretations due to attached substance contamination, and to prevent the loss of temperature data in key areas due to the removal of attached substance coverage points, thereby achieving a complete three-dimensional temperature field reconstruction across the entire domain while ensuring the accuracy of temperature interpretation.

[0077] In a preferred embodiment, before reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint, the following steps are further included: Obtain flow field simulation data of the rotating component under test under the target working condition, and determine the airflow scouring intensity distribution at each position on the surface of the rotating component under test based on the flow field simulation data; Based on the airflow scouring intensity distribution and the continuous operating time of the target working condition, the spatial distribution of coating thinning at each position on the surface of the tested rotating component is calculated. Based on the spatial distribution of the coating thinning amount, the color values ​​mapped to the standard coordinate space are sampled point by point and thinning compensation correction is performed to obtain the compensated color values. The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: Based on the compensated color value, the temperature is determined by applying the pre-calibrated color-temperature correspondence of the temperature-indicating paint, and a three-dimensional temperature field is reconstructed.

[0078] Specifically, flow field simulation data of the tested rotating component under target operating conditions is obtained. The flow field simulation data is obtained through numerical simulation of the target operating conditions using computational fluid dynamics software. The simulation domain includes the surface of the tested rotating component and the surrounding flow channel region. The flow field simulation data includes parameters such as airflow velocity vector and wall shear stress on each grid cell of the tested rotating component surface. Based on the flow field simulation data, the airflow scouring intensity distribution at various locations on the surface of the tested rotating component is determined. The airflow scouring intensity is characterized by wall shear stress or near-wall airflow velocity gradient. For each surface grid cell, the wall shear stress value of that cell is read from the flow field simulation data; a larger wall shear stress value indicates a stronger airflow scouring at that location. The wall shear stress values ​​of all surface grid cells are normalized to the range of 0 to 1. The normalization method is to divide the shear stress value of each cell by the maximum value of the shear stress values ​​of all cells to obtain the airflow scouring intensity distribution.

[0079] Based on the airflow erosion intensity distribution and the continuous operating time under the target condition, the spatial distribution of coating thinning at various locations on the surface of the tested rotating component is calculated. The coating thinning is calculated using an erosion wear model, which assumes that the coating thinning rate is proportional to the airflow erosion intensity. For the i-th surface grid cell, its coating thinning is equal to the erosion wear coefficient multiplied by the airflow erosion intensity value of that cell multiplied by the continuous operating time under the target condition. The erosion wear coefficient is determined through a pre-calibration test. The calibration method involves conducting an erosion test on a flat plate sample coated with a temperature-indicating paint in a wind tunnel with a known erosion intensity and duration. Before and after the test, a high-precision profilometer is used to measure the thickness change of the coating on the sample surface. The thickness change is divided by the product of the erosion intensity and duration to obtain the erosion wear coefficient. Different temperature-indicating paint formulations correspond to different erosion wear coefficients, which are stored in the form of a material parameter table. The calculated spatial distribution of coating thinning is the coating thinning value for each surface grid cell, expressed in micrometers.

[0080] A pre-calibrated coating thinning-color compensation mapping relationship was obtained. This mapping relationship was established by collecting spectra of thermochromic paint samples with different coating thicknesses at a fixed temperature during calibration experiments. The calibration method involved preparing a series of thermochromic paint samples with different coating thicknesses, ranging from 0 micrometers to the original nominal thickness, with thickness intervals of 5 to 10 micrometers. All samples were heated at the same fixed temperature, chosen as the midpoint of the thermochromic paint's color change temperature range. After heating, the color values ​​of each sample were acquired using the same 3D scanning equipment used to acquire the color point cloud of the actual object surface. The correspondence between coating thickness and color values ​​was recorded, forming a coating thinning-color compensation lookup table with coating thinning amount as the index and color compensation value as the output. The color compensation value is represented by the offset of the RGB three channels, indicating the deviation of the color value at that coating thinning amount from the original nominal thickness color value.

[0081] Based on the spatial distribution of coating thinning, the color values ​​mapped to the standard coordinate space are corrected for thinning at each sampling point. For the i-th sampling point in the standard coordinate space, the corresponding coating thinning value is looked up based on its spatial coordinates. The color compensation value corresponding to the coating thinning is read from the coating thinning-color compensation lookup table. The color compensation value is subtracted from the color value of the sampling point to obtain the compensated color value. The physical meaning of this compensation operation is to restore the color that has become lighter due to coating thinning caused by airflow to the color that should be presented at the original nominal thickness, eliminating the interference of coating thinning on the color value.

[0082] Based on the compensated color values, a pre-calibrated color-temperature correspondence for the temperature-indicating paint is applied for temperature interpretation, reconstructing a three-dimensional temperature field. The pre-calibrated color-temperature correspondence refers to a calibration curve established under the original nominal coating thickness conditions, and it uses the same set of data as the original color-temperature correspondence for the temperature-indicating paint. Since the compensated color values ​​have eliminated the interference from coating thinning, applying this calibration relationship yields accurate temperature interpretation results.

[0083] The principle of this implementation is to use flow field simulation data to predict the spatial distribution of coating thinning, and to correct the color value of each sampling point point by point through a pre-calibrated thinning-color compensation relationship, thereby separating the physical thinning effect caused by airflow scouring from the color signal. The desired technical effect is to eliminate the systematic color shift of the temperature-indicating paint caused by coating thinning, ensuring that the temperature reading reflects the true thermochemical color change state rather than an optical artifact caused by coating thickness differences, and significantly improving temperature reading accuracy in areas such as the middle section of the impeller where airflow scouring is severe.

[0084] In a preferred embodiment, the thinning compensation correction is performed in a hierarchical iterative manner: First, apply the uncompensated color value to the color-temperature correspondence of the temperature-indicating paint to obtain the initial temperature estimate for each sampling point; Based on the initial temperature estimate, for each sampling point, the coating thinning amount is read from the corresponding spatial distribution of coating thinning amount, and the compensation curve corresponding to the temperature range closest to the initial temperature estimate is selected from the pre-calibrated multi-temperature range coating thinning-color compensation mapping relationship library. Thinning compensation is performed on the color value of the sampling point to obtain the color value after one compensation. Based on the color value after the first compensation, the color-temperature correspondence of the temperature-indicating paint is reapplied to obtain the updated temperature estimate; Repeat the compensation and temperature update steps until the change in temperature estimate between two adjacent iterations is less than the preset convergence threshold. Use the temperature estimate of the last iteration as the final temperature reading result for that sampling point.

[0085] Specifically, the thinning compensation correction is performed in a hierarchical iterative manner, and the iterative process includes the following steps.

[0086] It should be noted that the temperature estimates in this embodiment refer to the temperature values ​​obtained by converting color values ​​through the color-temperature correspondence of the temperature-indicating paint, which are intermediate variables in the iteration process; the final output after the iteration is completed is called the temperature interpretation result, which is consistent with the aforementioned embodiment.

[0087] The first step is to apply the color-temperature correspondence of the temperature-indicating paint to the uncompensated color value to obtain the initial temperature estimate for each sampling point. The uncompensated color value refers to the original color value after mapping to the standard coordinate space in step S4, which has not yet undergone thinning compensation correction. The application method is to input the color value into the temperature-indicating paint color-temperature lookup table and obtain the corresponding temperature value through trilinear interpolation.

[0088] The second step involves performing the following operations for each sampling point based on the initial temperature estimate: The coating thinning amount is read from the spatial distribution of the coating thinning amount corresponding to that sampling point, which is calculated using the aforementioned method. The compensation curve corresponding to the temperature range closest to the initial temperature estimate is selected from a pre-calibrated multi-temperature range coating thinning-color compensation mapping library. The multi-temperature range coating thinning-color compensation mapping library is established by expanding the fixed temperature of the calibration test to multiple temperature ranges, covering the working temperature range of the temperature-indicating paint, with intervals of 50 to 100 degrees Celsius. At each temperature range, samples with different coating thicknesses are prepared and color values ​​are collected to form the coating thinning-color compensation curve for that temperature range. The collection of compensation curves from all temperature ranges constitutes the multi-temperature range coating thinning-color compensation mapping library. When selecting the temperature range closest to the initial temperature estimate, calculate the absolute value of the difference between the initial temperature estimate and the set value of each temperature range, and take the temperature range with the smallest absolute value. Using the selected compensation curve, perform thinning compensation on the color value of the sampling point to obtain the color value after one compensation. The compensation method is the same as described above, that is, read the color compensation value corresponding to the coating thinning amount from the compensation curve, and subtract the color compensation value from the original color value.

[0089] The third step is to reapply the color-temperature correspondence of the temperature-indicating paint based on the color value after compensation to obtain the updated temperature estimate.

[0090] Fourth, repeat steps two and three. In each iteration, use the temperature estimate updated in the previous iteration to reselect the temperature level and compensation curve, compensate the color value again, and update the temperature estimate again.

[0091] The fifth step is to determine the convergence condition. The convergence condition is that for each sampling point, the absolute value of the change in the temperature estimate between two consecutive iterations is less than a preset convergence threshold, which is between 1 and 5 degrees Celsius. If all sampling points meet the convergence condition, or the number of iterations reaches a preset maximum number of iterations, which is between 5 and 10, then the iteration stops. The temperature estimate from the last iteration is taken as the final temperature reading for that sampling point.

[0092] The principle of this implementation lies in iteratively coupling the two interdependent steps of thinning compensation and temperature interpretation. It dynamically selects a more suitable thinning compensation curve using the updated temperature estimate in each iteration, allowing the compensation amount to adaptively adjust with temperature. The desired technical effect is to eliminate the cross-influence of temperature on the thinning compensation amount itself, so that the thinning compensation is no longer a fixed correction but adaptively matches the actual temperature level of each sampling point. This significantly improves compensation accuracy in areas with large temperature gradients and avoids residual errors caused by the mismatch between the compensation curve and the true temperature.

[0093] The above description is merely a preferred embodiment of this application and an explanation of the technical principles employed. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to technical solutions formed by specific combinations of the above-described technical features, but should also cover other technical solutions formed by arbitrary combinations of the above-described technical features or their equivalents without departing from the inventive concept. For example, technical solutions formed by substituting the above features with (but not limited to) technical features with similar functions disclosed in this application.

Claims

1. A method for reconstructing and interpreting the three-dimensional temperature field of a temperature-indicating paint based on prior shape point cloud registration, characterized in that, Includes the following steps: Obtain the color point cloud of the actual surface of the rotating component under test after the test under the target working condition, as well as the cold standard three-dimensional model of the rotating component under test; Based on the rotational speed parameters and temperature field prediction parameters of the target working condition, the theoretical deformation amount and main deformation direction of the tested rotating component under the target working condition are obtained through finite element analysis. Based on the cold-state standard three-dimensional model and the theoretical deformation, a theoretical deformation benchmark model is constructed. Using the theoretical deformation reference model as the target and the colored point cloud of the physical surface as the source, non-rigid point cloud registration is performed. During the registration process, the main deformation direction is used as the directional constraint of the deformation field to restrict the deformation of the source point cloud along the main deformation direction, and to establish the mapping relationship between the physical point cloud and the standard coordinate space. Based on the mapping relationship, the color values ​​of the colored point cloud on the surface of the object are mapped to the standard coordinate space, and the three-dimensional temperature field is reconstructed according to the color-temperature correspondence of the temperature-indicating paint. The method of using the principal deformation direction as the directional constraint of the deformation field to restrict the source point cloud from deforming along the principal deformation direction includes the following steps: With the main deformation direction as the central axis, a conical constraint space with an allowable deviation angle of ±θ is constructed, wherein ±θ is determined according to the manufacturing tolerance grade of the rotating component under test; In each iteration of the non-rigid point cloud registration, it is determined whether the displacement vector of each sampling point in the source point cloud falls within the cone-shaped constraint space; If the displacement vector falls within the conical constraint space, it is retained; if it exceeds the conical constraint space, it is projected back onto the boundary of the conical constraint space. Continue iterating using the constrained displacement vector until convergence; In the non-rigid point cloud registration process, the following steps are performed: For each node in the theoretical deformation reference model, the main deformation direction corresponding to the node is identified, and the position adjustment range of the node along the main deformation direction is determined. The position adjustment range is set according to the uncertainty of the temperature field prediction parameters. In each registration iteration, two parts of the update are performed simultaneously: the first part is to update the deformation parameters of each sampling point in the source point cloud, and the second part is to update the position parameters of each node in the theoretical deformation reference model along its main deformation direction. The two parts of the update aim to jointly minimize the overall registration error between the source point cloud and the theoretical deformation reference model. After iterative convergence, the updated theoretical deformation benchmark model is used as the final target model for mapping the physical point cloud to the standard coordinate space.

2. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration as described in claim 1, characterized in that, The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: The measured temperature value is obtained at least one known location point on the surface of the rotating component under test, and the measured temperature value is obtained by installing a contact temperature sensor on the surface of the rotating component under test. In the standard coordinate space, extract the mapped color value corresponding to the known position point; The color value is input into the color-temperature correspondence of the temperature-indicating paint to obtain the predicted temperature value, and the deviation between the measured temperature value and the predicted temperature value is calculated. Using the deviation as a global correction parameter, the color-temperature correspondence of the temperature-indicating paint is shifted and corrected to obtain the corrected color-temperature correspondence. Based on the corrected color-temperature correspondence, a three-dimensional temperature field is reconstructed.

3. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration as described in claim 1, characterized in that, The ±θ is a permissible deviation angle assigned to the corresponding region based on the local region where each sampling point is located in the cold standard 3D model, including the following steps: The cold standard three-dimensional model is pre-divided into multiple regions, based on the local thickness distribution and / or local stiffness distribution of the rotating component under test. Each region is calibrated with a corresponding allowable deviation angle, wherein the allowable deviation angle of the high stiffness region is smaller than that of the low stiffness region. In each iteration of the non-rigid point cloud registration, for the current sampling point in the source point cloud, according to the region to which it belongs in the cold standard 3D model, the corresponding region allowable deviation angle is retrieved, and a conical constraint space with the main deformation direction as the central axis is constructed, thereby constraining the displacement vector of the sampling point.

4. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration according to claim 2, characterized in that, When extracting the mapped color value corresponding to the known location point in the standard coordinate space, the following steps are performed: Based on the local region to which the known location point belongs in the cold standard 3D model, obtain the allowable deviation angle of the corresponding local region; Using the allowable deviation angle of the region as input, the spatial search radius is determined by a preset mapping function, wherein the spatial search radius corresponding to the low stiffness region is greater than the spatial search radius corresponding to the high stiffness region. A spherical search domain is constructed with the coordinates of the known location point in the standard coordinate space as the center and the spatial search radius as the radius; Extract the color values ​​of all sampling points within the spherical search domain, calculate the color value statistics, and use the color value statistics as the mapped color value corresponding to the known location point.

5. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration according to claim 4, characterized in that, The calculation of color value statistics includes the following steps: Obtain the temperature field prediction parameters of the rotating component under test under the target working condition, and determine the local predicted temperature gradient direction in the spherical search domain based on the temperature field prediction parameters; Using the projection position of the center of the spherical search domain onto the direction of the local estimated temperature gradient as the reference isotherm, calculate the offset of the projection position of each sampling point in the spherical search domain relative to the reference isotherm. Based on the offset, a weight coefficient is assigned to each sampling point, wherein the smaller the offset, the larger the weight coefficient corresponding to the sampling point, and the larger the offset, the smaller the weight coefficient corresponding to the sampling point. The color value statistics are obtained by weighting the color values ​​of all sampling points in the spherical search domain with the weighting coefficients.

6. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration according to claim 1, characterized in that, The process of obtaining the color point cloud of the actual surface of the rotating component under test after testing under the target working condition includes the following steps: A multispectral imaging device is used to add at least one auxiliary spectral channel in addition to the visible light band to obtain a set of multispectral reflectance values ​​for each sampling point. The set of multispectral reflectance values ​​includes the color value corresponding to the visible light band and the auxiliary reflectance value corresponding to the auxiliary spectral channel. A set of multispectral reflectance values ​​for each sampling point are input into a pre-built attachment identification classifier. The attachment identification classifier is obtained by learning the known spectral characteristics of clean temperature-indicating paint samples and the known spectral characteristics of attachment samples, and outputs the determination result of whether the sampling point is an attachment-covered point. For sampling points determined to be free of attached substances, their color values ​​are marked as temperature-indicating paint reading color values; for sampling points determined to be covered by attached substances, a set of multispectral reflectance values ​​are marked as attached substance reading spectral values. The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: For sampling points marked as color values ​​for temperature-indicating paint, the temperature is determined by applying the color-temperature correspondence of the temperature-indicating paint. For sampling points marked as attachment interpretation spectral values, a set of multispectral reflectance values ​​are input into a pre-constructed attachment-temperature mapping model. The attachment-temperature mapping model is established by simultaneously collecting attachment spectral samples at different known temperatures during calibration tests and outputs the estimated temperature value of the attachment corresponding to the sampling point. The temperature reading results corresponding to the color values ​​of the temperature-indicating paint are combined with the estimated temperature values ​​of the attachments corresponding to the spectral values ​​of the attachments to reconstruct a three-dimensional temperature field.

7. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration as described in claim 1, characterized in that, Before reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint, the following steps are also included: Obtain flow field simulation data of the rotating component under test under the target working condition, and determine the airflow scouring intensity distribution at each position on the surface of the rotating component under test based on the flow field simulation data; Based on the airflow scouring intensity distribution and the continuous operating time of the target working condition, the spatial distribution of coating thinning at each position on the surface of the tested rotating component is calculated. Based on the spatial distribution of the coating thinning amount, the color values ​​mapped to the standard coordinate space are sampled point by point and thinning compensation correction is performed to obtain the compensated color values. The process of reconstructing the three-dimensional temperature field based on the color-temperature correspondence of the temperature-indicating paint includes the following steps: Based on the compensated color value, the temperature is determined by applying the pre-calibrated color-temperature correspondence of the temperature-indicating paint, and a three-dimensional temperature field is reconstructed.

8. The method for reconstructing and interpreting the three-dimensional temperature field of temperature-indicating paint based on prior shape point cloud registration according to claim 7, characterized in that, The thinning compensation correction is performed using a hierarchical iterative approach: First, apply the uncompensated color value to the color-temperature correspondence of the temperature-indicating paint to obtain the initial temperature estimate for each sampling point; Based on the initial temperature estimate, for each sampling point, the coating thinning amount is read from the corresponding spatial distribution of coating thinning amount, and the compensation curve corresponding to the temperature range closest to the initial temperature estimate is selected from the pre-calibrated multi-temperature range coating thinning-color compensation mapping relationship library. Thinning compensation is performed on the color value of the sampling point to obtain the color value after one compensation. Based on the color value after the first compensation, the color-temperature correspondence of the temperature-indicating paint is reapplied to obtain the updated temperature estimate; Repeat the compensation and temperature update steps until the change in temperature estimate between two adjacent iterations is less than the preset convergence threshold. Use the temperature estimate of the last iteration as the final temperature reading result for that sampling point.

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