Method for modeling measurement point errors in blade profile detection based on line laser

Abstract

The application discloses a kind of based on line laser's blade profile detection measuring point error modeling method, comprising: the discrete error calibration stage based on rectangular block, rectangular block is regarded as calibration reference, through motion platform to decoupling control observation distance and observation angle, traverse pose parameter space and collect point cloud data, based on the planeness of rectangular block known, the single-point measurement error under each discrete pose node is calculated, and discrete error dataset is formed;Continuous error model construction stage based on data driving, discrete error dataset is regarded as training sample, and data-driven model is used to train with pose parameter as input and measurement error as output, and the continuity error prediction model that can predict measurement error under any observation pose is obtained.The application realizes the quantitative modeling of line laser sensor measuring point error and observation pose, provides quantization boundary for considering the view point planning of measuring point precision constraint, and is suitable for the precision detection field of complex curved surface parts such as blade.

Description

Technical Field

[0001] This invention belongs to the field of precision measurement technology, specifically relating to a method for modeling the error of measuring points in blade profile detection based on line laser. Background Technology

[0002] Blades are key components in aero-engines and gas turbines, crucial for energy conversion. The dimensional and shape accuracy of their blades plays a decisive role in the engine's aerodynamic performance and operational efficiency. Even minute geometric defects can significantly impact engine performance and operational safety under extreme conditions of high temperature and pressure. Therefore, precise three-dimensional inspection of blade profiles during manufacturing and maintenance is essential for ensuring product quality, guiding process optimization, and preventing accidents.

[0003] Due to the complex structure and occlusion of the blade surface, a single scan cannot obtain complete 3D data. Therefore, detection from multiple perspectives and stitching together of the point cloud data are necessary. Viewpoint planning is the process of pre-determining a series of observation poses for the line laser sensor to acquire complete 3D data. Many current viewpoint planning methods focus on achieving full geometric coverage of the surface, but they generally suffer from a key limitation: they fail to adequately consider the accuracy constraints of individual measurement points.

[0004] For line laser scanning, the measurement accuracy of each data point is not constant; it highly depends on the relative position of the line laser sensor and the surface being measured during acquisition, primarily the scanning distance (observation distance) and the angle between the laser beam and the normal to the surface being measured (observation angle). Figure 1 As shown, inappropriate observation distances or angles can significantly reduce point cloud accuracy. For example, excessively large observation angles can lead to laser echo energy attenuation and introduce signal noise; observation distances that deviate from the depth of field will produce a defocusing effect, reducing measurement accuracy.

[0005] Therefore, how to quantify the measurement error of a line laser sensor under different observation poses, and provide a quantified boundary for viewpoint planning that considers the accuracy constraints of the measurement point, has become a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0006] The purpose of this invention is to provide a method for modeling measurement point errors in blade profile detection based on line laser. By combining physical experiments with data-driven models, a mapping relationship between observation pose and measurement error is established, laying the foundation for subsequent viewpoint planning that constrains measurement point accuracy.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: A method for modeling measurement point errors in blade profile detection based on line laser, comprising: S1: Discrete error calibration stage based on rectangular blocks; Using a rectangular block with known flatness as a calibration reference, the observation distance and observation angle of the line laser sensor are decoupled and controlled by a motion platform. The preset pose parameter space is traversed to collect point cloud data of the line laser sensor measuring the rectangular block at each discrete pose node. Based on the flatness of the rectangular block, the single-point measurement error at each discrete pose node is calculated to form a discrete error dataset. S2: Data-driven continuous error model construction phase; Using the discrete error dataset as training samples, a multilayer perceptron neural network is trained with observation distance and observation angle as inputs and measurement error amplitude as output to obtain a continuous error prediction model that can predict measurement errors under any observation pose.

[0008] Furthermore, the motion platform includes a turntable for controlling the observation angle and a translation axis for controlling the observation distance. The rectangular gauge block is vertically fixed to the center of the turntable, and the line laser sensor is mounted on the translation axis and can move along the optical axis of the line laser sensor. The direction of observation is reciprocated; the observation distance traverses the entire range along the optical axis of the laser sensor with a step size Δd, and the observation angle rotates with a step size Δθ within the range of [-90°, 90°], and n sets of point cloud data are continuously triggered to be acquired at each discrete pose node.

[0009] Furthermore, before traversing the pose parameter space, a motion platform pose calibration step is included to establish the initial spatial pose relationship between the line laser sensor, the turntable, and the rectangular block, so that the origin of the line laser sensor coordinate system is... Turntable Center The overlap constraint between the rectangular block's working surface and the rectangular block's working surface includes the following steps: Step 1: Establish parallel constraints; adjust the angle of the turntable so that the projection of the working surface of the rectangular block within the field of view of the line laser sensor is parallel to the coordinate system of the line laser sensor. The axes are parallel; Step 2: Align the rotation center; drive the turntable to perform equal-amplitude 90° symmetrical rotations clockwise and counterclockwise, and record the extreme coordinate values ​​of the working surface of the rectangular gauge block at different angles. and Solve for the center of the turntable In the coordinate system of online laser sensor Offset The offset is compensated by translating the line laser sensor. This enables the line laser sensor The shaft passes through the rotation center of the turntable. ; Step 3: Depth reference calibration; Drive the turntable again for a 90° symmetrical rotation with equal amplitude clockwise and counterclockwise, measuring the coordinate values ​​of the working surface of the rectangular block at different angles. Translate the rectangular block to make the rotation center coincide with the working surface; Drive the turntable again for a 90° symmetrical rotation with equal amplitude clockwise and counterclockwise, measuring the coordinate values ​​of both sides of the rectangular block along the optical axis of the line laser sensor. Translate the rectangular block to make the rotation center bisect the working surface; Adjust the pose of the line laser sensor by translating along the optical axis of the line laser sensor, so that the line laser sensor... The axis is collinear with the working surface.

[0010] Furthermore, the method for calculating the single-point measurement error includes: At each discrete pose node, the point cloud data acquired by the line laser sensor is obtained. The first row vector represents the line laser sensor. The coordinate information is shown in the first row, and the remaining rows represent the coordinates of each measurement. The measured value corresponding to the coordinate; The center of the line laser sensor's field of view is selected as the measurement point p to be evaluated, and its corresponding column index is denoted as p. Select Both sides The column indexes constitute the index set. For each row of data in the index set Perform line fitting on the above, and obtain the fitted lines respectively. ; Calculate the maximum distance between each row of measurement points and both sides of the fitted straight line. , ; The straightness error of a single measurement is calculated based on the maximum distance between the two sides of the fitted straight line. , Flatness of the rectangular block; The single-point measurement error is calculated based on the straightness error of a single measurement. , This refers to the scanning distance (observation distance). θ is the angle between the laser beam and the normal to the surface being measured (observation angle), and n is the total number of point cloud data collected.

[0011] Furthermore, the discrete error dataset is preprocessed, and the supervision target is defined as the error magnitude with an upper limit constraint. ,in It is a constant.

[0012] Furthermore, the multilayer perceptron neural network adopts a two-dimensional input and one-dimensional output design, and the hidden layers adopt a symmetrical topological configuration of [2,64,128,256,128,64,1]. Each hidden layer is composed of a linear transformation layer and a ReLU activation function, and batch normalization processing is introduced between layers.

[0013] Furthermore, the mean squared error is used as the loss function, and the Adam optimizer is used to train the multilayer perceptron neural network, with an initial learning rate set to 1×10⁻⁶. -3 The learning rate decays to 0.5 of the previous stage every 4000 iterations, for a total of 50000 iterations.

[0014] Compared with the prior art, the present invention has the following beneficial effects: (1) Quantitative modeling of the measurement point error and observation pose of the line laser sensor was realized; through decoupling experimental design, the influence of observation distance and observation angle on measurement accuracy was separated, providing quantitative accuracy boundary constraints for viewpoint planning.

[0015] (2) Precision position calibration eliminates the eccentricity measurement deviation introduced by the unknown rotation axis of the turntable, ensuring the reliability of subsequent error measurement.

[0016] (3) Combining discrete experiments with data-driven approaches; transforming limited discrete experimental data into a global continuous error prediction surface through a neural network model, which not only makes up for the limitations of experimental data in spatial sampling, but also realizes the error prediction capability under arbitrary pose parameter combinations.

[0017] (4) The generated error spatial distribution heat map intuitively shows the “optimal measurement range” and “accuracy failure boundary” of the line laser sensor, providing direct guidance for viewpoint planning in actual detection. Attached Figure Description

[0018] Figure 1 Here is a schematic diagram of the optical constraints of a line laser sensor; (a) optical constraint of observation distance; (b) optical constraint of observation angle.

[0019] Figure 2 A schematic diagram of the experimental design scheme for measuring point error calibration; (a) keep the observation distance constant and change the observation angle; (b) keep the observation angle constant and change the observation distance.

[0020] Figure 3 This is a schematic diagram for calibrating the initial spatial pose relationship of the experiment.

[0021] Figure 4 A schematic diagram is established to establish the parallel constraint between the sensor coordinate system and the working surface of the gauge block.

[0022] Figure 5This is a schematic diagram showing the sensor coordinate system coinciding with the rotation center of the turntable.

[0023] Figure 6 Schematic diagram for depth benchmark calibration and coordinate origin establishment; (a) Rotation center coincides with working surface; (b) Rotation center is aligned with the working surface of the component blocks; (c) Coordinate origin is established.

[0024] Figure 7 This is a schematic diagram illustrating the principle of measuring point error calculation.

[0025] Figure 8 A scatter plot is used to verify the consistency between the actual error magnitude and the neural network prediction.

[0026] Figure 9 This is a data-driven heatmap showing the spatial distribution of errors at continuous measurement points.

[0027] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments.

[0028] This embodiment provides a method for modeling the measurement point error of blade profile detection based on line laser, which mainly includes two stages: a discrete error calibration stage based on rectangular gauge blocks and a continuous error model construction stage based on data-driven methods.

[0029] Discrete error calibration stage based on rectangular gauge blocks: High-precision standard rectangular gauge blocks are introduced, and controlled variable experiments are designed to quantitatively obtain the measurement deviation distribution of the line laser sensor under different spatial poses, providing quantitative precision boundary constraints for viewpoint planning of complex surfaces.

[0030] This embodiment uses flatness. The rectangular gauge block; through the coordinated movement of the turntable and the translation axis, it can traverse any node in the "observation distance-observation angle" parameter space, thereby realizing the comprehensive calibration of the quantitative error of the measuring point under complex scanning conditions.

[0031] like Figure 2 As shown, a rectangular gauge block is vertically fixed to the center of the turntable. Controlled rotation of the turntable in the horizontal plane causes the working surface of the rectangular gauge block to deflect at an angle relative to the line laser sensor, thus simulating changes in the observed angle. Simultaneously, a linear translation axis moves the line laser sensor along its optical axis. The direction of the laser sensor's reference center is changed by switching it from forward to reverse. The spatial observation distance between the sensor and the rectangular gauge block surface is used to cover the full range and depth of field of the line laser sensor. Through the coordinated stepping motion of the turntable and the translation axis, the experiment can traverse any node in the "observation distance-observation angle" parameter space, thereby achieving comprehensive calibration of the quantitative error of the measurement point under complex scanning conditions.

[0032] To achieve decoupled calibration of observation distance and observation angle, the initial spatial pose relationship between the line laser sensor, turntable axis, and rectangular gauge block needs to be established through precise calibration before operation. For example... Figure 3 As shown, this embodiment uses the rectangular block itself as the calibration medium, and establishes the imaging origin of the line laser sensor based on the principle of geometric symmetry. Turntable Center The overlap constraint between the rectangular gauge block and the working surface is used to eliminate the eccentric measurement deviation introduced by the unknown rotation axis of the turntable.

[0033] This embodiment uses a three-step precision calibration method: Step 1: Establish parallel constraints; such as Figure 4 As shown, the coordinate system of the line laser sensor is established. The axis is parallel to the working surface AB of the rectangular block. Initially, the placement of the rectangular block ABCD on the turntable is random. By fine-tuning the turntable angle, the projection of the rectangular block's working surface (side AB) into the field of view of the line laser sensor is aligned with the line laser sensor's position. The axes are parallel to ensure that subsequent angular deflections are based on an ideal, direct observation (incident angle of 0°).

[0034] Step 2: Align the rotation center; as shown... Figure 5 As shown, the coordinate system of the line laser sensor is realized. Shaft and Rotation Center of Turntable The coincidence. Determine the center of rotation. The position of the rectangular gauge block in the coordinate system is crucial for achieving the target. By driving the turntable to perform equal-amplitude 90° symmetrical rotations clockwise and counterclockwise, the extreme coordinate values ​​of the rectangular gauge block's working surface AB at different angles are recorded. and By utilizing the property of geometric central symmetry, the center of the turntable can be calculated. In the coordinate system of online laser sensor Offset and through The line laser sensor is moved along the translation axis to compensate for this offset, so that the reference optical axis of the line laser sensor (i.e., (Axis) precisely passes through the center of rotation of the turntable .

[0035] Step 3: Depth baseline calibration; such as... Figure 6As shown in (a), after completing Based on the alignment of direction and angle, the turntable is driven to perform equal-amplitude 90° symmetrical rotations clockwise and counterclockwise respectively, and the coordinate values ​​of side AB are measured again. and (at this time The rectangular block moves a distance by translating left / right. , making Then the rectangular block working surface AB and the center of rotation are... coincide.

[0036] To further improve the rotation center Bisect the working surface AB of the rectangular gauge block, as shown Figure 6 As shown in (b), similarly, the turntable is driven to perform symmetrical rotations of 90° clockwise and counterclockwise with equal amplitudes, and the two sides of the rectangular block are measured at... To coordinate values and The distance moved by translating the rectangular block forward / backward Make .

[0037] Subsequently, to establish the origin of the coordinate system, such as Figure 6 (c) shows the direction of the laser sensor's optical axis along the line ( The pose of the line laser sensor is adjusted by translating the axis, so that the line laser sensor... The axis is collinear with the working surface AB of the rectangular gauge block, meaning the working surface AB is measured to be on... The coordinate value of the direction is 0.

[0038] At this point, the imaging origin of the line laser sensor is... Turntable Center The three surfaces—the rotary table, the rectangular gauge block, and the control surface—are aligned. Under this reference, the rotation degree of the rotary table is equivalent to the observation angle, and the displacement increment of the translation axis is equivalent to the change in the observation distance.

[0039] Since the pose space is continuous, it is impossible to obtain the global continuous error distribution through exhaustive experimental calibration. This embodiment adopts a discrete sampling strategy, which uses a regular discrete grid to capture the nonlinear gradient of the error as the pose changes with representative sample points.

[0040] In terms of specific sampling design, this embodiment constructs a two-dimensional discrete grid covering the entire optical constraint space. The observation distance traverses the entire range along the optical axis of the line laser sensor with a step size of Δd (e.g., from -12.5mm to 12.5mm, Δd=0.5mm) to characterize the impact of defocusing on accuracy; the observation angle rotates within the range of [-90°, 90°] with a step size of Δθ (e.g., Δθ=5°) to capture signal noise caused by echo energy attenuation.

[0041] To suppress random fluctuations, n frames of point cloud data are continuously acquired at each grid node, and environmental vibrations and thermal noise from the photosensitive element are filtered out by temporal averaging. The measurement data is represented as a matrix. Where n is the number of repeated sampling frames and m is the number of grid nodes. First row of data. , representing the line laser sensor at each grid node. To coordinate information; each column Linear laser sensor To the corresponding node The n sets of repeated measurements.

[0042] like Figure 7 As shown, select column index Let p be the central location (i.e., the test point to be evaluated), and denote the set of column indices on its left and right sides. , This represents the total number of indices within the set. For index Both sides Each column is indexed. For each row of data, an index set is used. Perform line fitting on the above, and obtain the fitted lines respectively. Calculate the distance of each measuring point in the row relative to the fitted line, and record the maximum distances between the measuring points in each row and the two sides of the fitted line. , .

[0043] Single measurement of rectangular gauge block The straightness error in the vicinity is Under these measurement conditions, the measurement error at measuring point p is: , This refers to the scanning distance (observation distance). The angle between the laser beam and the normal to the surface being measured (observation angle).

[0044] Using the above method, for each discrete pose node The corresponding single-point measurement error can be calculated for each. To form a discrete error dataset .

[0045] The data-driven continuous error model construction phase: After obtaining a finite discrete error set, this embodiment uses a multilayer perceptron (MLP) neural network to construct a continuous prediction model for single-point measurement errors to obtain the global continuous error distribution. Specifically, it includes the following steps: Step 1: Training sample construction; for each discrete node, extract its physical pose parameters as the input feature vector. Considering that a small number of outliers may occur during the discrete calibration process due to sudden environmental vibrations or light spot distortion, this embodiment defines the supervision target as the error amplitude with an upper limit constraint in order to enhance the model's generalization ability and robustness. ,in The value is a constant, and in this embodiment it is taken as 0.01 mm; by setting an upper limit for the error. This allows the model to focus on learning the evolution of errors within a typical measurement range, avoiding the interference of extreme noise on the smoothness of the fitted surface. Since the model aims to predict the range of accuracy fluctuations, the output only retains the magnitude of the error.

[0046] Step 2: Network Architecture Design; This embodiment uses a Multilayer Perceptron (MLP) to establish a nonlinear mapping relationship from the input space to the error space. The network adopts a two-dimensional input and one-dimensional output design, and the hidden layers use a symmetrical topology configuration [2, 64, 128, 256, 128, 64, 1] to balance the model's expressive power and computational efficiency. Each hidden layer consists of a linear transformation layer and a ReLU activation function, and batch normalization is introduced between layers to accelerate convergence and improve the numerical stability of the training process.

[0047] The final continuous error estimation model can be expressed as: ,in, For prediction error, For discrete pose nodes, This is the set of weight parameters obtained by the network learning.

[0048] Step 3: Model training; In this embodiment, mean squared error (MSE) is used as the loss function to minimize the deviation between the network predictions and the experimental calibration values.

[0049] loss function , For prediction error, Let N be the true error and N be the total number of errors.

[0050] The optimization algorithm uses the Adam optimizer, with an initial learning rate set to 1×10⁻⁶. -3 The training process was iterated 50,000 times. To balance the convergence speed in the early stages with the fitting accuracy in the later stages, a segmented learning rate decay strategy was implemented: after every 4,000 iterations, the learning rate was decayed to 0.5 of the previous stage.

[0051] Step 4: Model Validation and Application; This embodiment first quantitatively evaluates the network's fitting accuracy by calculating the mean squared error of the entire sample set, ensuring that the model can faithfully reproduce the statistical characteristics of the experimental calibration data. To visually verify the consistency of the model's predictions, a scatter plot comparing the actual experimental error magnitude and the neural network's predicted magnitude is plotted, as shown below. Figure 8As shown, the scatter points are highly concentrated near the 45° diagonal, indicating a strong correlation between the predicted and experimental values ​​across the entire measurement range. The model effectively captures the mapping relationship between observed pose and measurement accuracy.

[0052] A heatmap of the spatial distribution of errors at continuous measurement points under full-space pose (observation distance and observation angle) is generated using a trained error model, such as... Figure 9 As shown in the figure, this heatmap not only finely depicts the gradient trend of error as optical constraints change, but also intuitively reveals the "optimal measurement range" and "accuracy failure boundary" of the line laser sensor.

[0053] In summary, the originally isolated discrete calibration point set is transformed into a high-fidelity, analytically analyzable continuous error prediction surface. This continuous model not only compensates for the limitations of spatial sampling of experimental data, but also enables the prediction of errors in arbitrary parameter combinations. The corresponding error prediction values ​​can be obtained directly, which provides key quantitative boundary support for viewpoint planning for subsequent a priori control of measurement point errors.

[0054] This embodiment provides a method for modeling measurement point errors in blade profile inspection based on line laser technology. This method establishes a quantitative mapping relationship between the observation pose of the line laser sensor and the measurement error, providing crucial data support for viewpoint planning that considers measurement point accuracy constraints. This method can be widely applied to the precision 3D inspection of complex curved surface parts such as aero-engine blades, gas turbine blades, and wind turbine blades, demonstrating significant industrial practical value and application prospects.

[0055] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for modeling measurement point errors in blade profile detection based on line laser, characterized in that, Includes the following steps: S1: Discrete error calibration stage based on rectangular blocks; Using a rectangular block with known flatness as a calibration reference, the observation distance and observation angle of the line laser sensor are decoupled and controlled by a motion platform. The preset pose parameter space is traversed to collect point cloud data of the line laser sensor measuring the rectangular block at each discrete pose node. Based on the flatness of the rectangular block, the single-point measurement error at each discrete pose node is calculated to form a discrete error dataset. S2: Data-driven continuous error model construction phase; Using the discrete error dataset as training samples, a multilayer perceptron neural network is trained with observation distance and observation angle as inputs and measurement error amplitude as output to obtain a continuous error prediction model that can predict measurement errors under any observation pose.

2. The method for modeling measurement point errors of blade profile detection based on line laser as described in claim 1, characterized in that, The motion platform includes a turntable for controlling the observation angle and a translation axis for controlling the observation distance. The rectangular block is vertically fixed at the center of the turntable. The line laser sensor is mounted on the translation axis and can reciprocate along the optical axis of the line laser sensor. The observation distance traverses the entire range along the optical axis of the line laser sensor with a step size Δd. The observation angle rotates with a step size Δθ within the range of [-90°, 90°] and continuously triggers the acquisition of n sets of point cloud data at each discrete pose node.

3. The method for modeling measurement point errors of blade profile detection based on line laser as described in claim 2, characterized in that, Before traversing the pose parameter space, a motion platform pose calibration step is included to establish the initial spatial pose relationship between the line laser sensor, the turntable, and the rectangular block, so that the origin of the line laser sensor coordinate system is set to... Turntable Center The overlap constraint between the rectangular block's working surface and the rectangular block's working surface includes the following steps: Step 1: Establish parallel constraints; adjust the angle of the turntable so that the projection of the working surface of the rectangular block within the field of view of the line laser sensor is parallel to the coordinate system of the line laser sensor. The axes are parallel; Step 2: Align the rotation center; drive the turntable to perform equal-amplitude 90° symmetrical rotations clockwise and counterclockwise, and record the extreme coordinate values ​​of the working surface of the rectangular gauge block at different angles. and Solve for the center of the turntable In the coordinate system of online laser sensor Offset The offset is compensated by translating the line laser sensor. This enables the line laser sensor The shaft passes through the rotation center of the turntable. ; Step 3: Depth reference calibration; Drive the turntable again for a 90° symmetrical rotation with equal amplitude clockwise and counterclockwise, measuring the coordinate values ​​of the working surface of the rectangular block at different angles. Translate the rectangular block to make the rotation center coincide with the working surface; Drive the turntable again for a 90° symmetrical rotation with equal amplitude clockwise and counterclockwise, measuring the coordinate values ​​of both sides of the rectangular block along the optical axis of the line laser sensor. Translate the rectangular block to make the rotation center bisect the working surface; Adjust the pose of the line laser sensor by translating along the optical axis of the line laser sensor, so that the line laser sensor... The axis is collinear with the working surface.

4. The method for modeling measurement point errors of blade profile detection based on line laser as described in claim 1, characterized in that, The method for calculating the single-point measurement error includes: At each discrete pose node, the point cloud data acquired by the line laser sensor is obtained. The first row vector represents the line laser sensor. The coordinate information is shown in the first row, and the remaining rows represent the coordinates of each measurement. The measured value corresponding to the coordinate; The center of the line laser sensor's field of view is selected as the measurement point p to be evaluated, and its corresponding column index is denoted as p. Select Both sides The column indexes constitute the index set. For each row of data in the index set Perform line fitting on the above, and obtain the fitted lines respectively. ; Calculate the maximum distance between each row of measurement points and both sides of the fitted straight line. , ; The straightness error of a single measurement is calculated based on the maximum distance between the two sides of the fitted straight line. , Flatness of the rectangular block; The single-point measurement error is calculated based on the straightness error of a single measurement. , For observation distance, 'n' represents the observation angle, and 'n' represents the total number of point cloud data collected.

5. The method for modeling measurement point errors of blade profile detection based on line laser as described in claim 1, characterized in that, The discrete error dataset is preprocessed, and the supervision target is defined as the error magnitude with an upper limit constraint. ,in It is a constant.

6. The method for modeling measurement point errors of blade profile detection based on line laser as described in claim 1, characterized in that, The multilayer perceptron neural network adopts a two-dimensional input and one-dimensional output design. The hidden layers adopt a symmetrical topological configuration of [2,64,128,256,128,64,1]. Each hidden layer consists of a linear transformation layer and a ReLU activation function, and batch normalization is introduced between layers.

7. The method for modeling measurement point errors of blade profile detection based on line laser as described in claim 6, characterized in that, Mean squared error was used as the loss function, and the Adam optimizer was used to train the multilayer perceptron neural network with an initial learning rate of 1×10⁻⁶. -3 The learning rate decays to 0.5 of the previous stage every 4000 iterations, for a total of 50000 iterations.

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