Adaptive multi-sensor fusion curved surface measurement method based on aggregation value sampling

Abstract

An adaptive multi-sensor fusion curved surface measurement method based on aggregation value sampling is characterized by comprising the following steps: firstly, acquiring a group of low-precision measurement data of a curved surface to be measured, calculating an aggregation value function of the curved surface in combination with a curved surface measurement point value function and a kernel function, and searching a new measurement point sample which maximizes aggregation value increment; measuring the point on the curved surface by using a high-precision sensor to obtain corresponding high-precision measurement data, performing data fusion on the original low-precision measurement data and the high-precision measurement data to obtain a fusion measurement reconstructed curved surface, and comparing the fusion measurement reconstructed curved surface with a set measurement termination standard; and if the standard is not met, repeatedly and iteratively executing the steps to adaptively expand the high-precision measurement data until a measurement termination standard is met, stopping iteration and outputting a final fusion measurement reconstruction curved surface. According to the method, the measurement efficiency can be remarkably improved while the measurement precision is ensured, so that high-precision and high-efficiency measurement of the curved surface is realized.

Description

Technical Field

[0001] The present invention relates to a measurement technology, in particular to a surface measurement technology, specifically to an adaptive multi-sensor fusion surface measurement method based on aggregated value sampling. Background Art

[0002] The digital reconstruction of free-form surfaces is widely used in key industrial manufacturing fields such as aerospace, vehicle engineering, automation, and optics. The precise reconstruction of free-form surfaces is an important means to ensure product quality control and promote process industry optimization. With the growing demand for high-precision and high-efficiency surface measurement in modern manufacturing, the integration of multi-sensor measurement data such as laser scanners and touch probes has become increasingly important. Laser measurement can quickly acquire high-resolution point clouds, but its accuracy is relatively low; contact measurement has high accuracy but low measurement efficiency. The integration of the two aims to use contact measurement to compensate for the low accuracy of laser measurement. Therefore, the multi-sensor fusion technology of adaptive sampling is used to iteratively guide the generation of probe data by maximizing the aggregate value, reducing the sampling method's dependence on the stability of the surface reconstruction algorithm, thereby ensuring reconstruction accuracy while maximizing measurement efficiency.

[0003] Patent CN108388909A invented a complex surface adaptive sampling method, which obtains the number of sampling points by setting the sampling accuracy, and combines the MacQueen K-means algorithm with the simulated annealing algorithm for adaptive sampling. This method uses a single measurement method, which makes it difficult to ensure its measurement efficiency while achieving high-precision measurement. CN117609939A invented a surface measurement method for multi-source data fusion, which divides two sets of measurement data sets with different accuracy and quantity into multiple subsets, and uses the error index of the low-precision measurement subset to calculate the membership of each subset, thereby compensating the low-precision measurement data to complete data fusion. However, this method does not constrain the amount of high-precision data, and the final fusion accuracy is susceptible to fluctuations due to changes in the amount of high-precision data. Therefore, there is a need for a surface measurement method that combines adaptive sampling and data fusion, which compensates for the measurement error of low-precision measurement data by continuously iterating newly added high-precision data points, and achieves high-precision and efficient surface fusion measurement. Summary of the Invention

[0004] The purpose of the present invention is to address the problems that common surface sampling methods are difficult to ensure their measurement efficiency and common data fusion methods rely on high-precision data volume to ensure stability. An adaptive multi-sensor fusion surface measurement method based on aggregated value sampling is invented. It combines adaptive sampling with data fusion, and by continuously iterating and adding high-precision data points, it maximizes the measurement efficiency while ensuring the final fusion accuracy.

[0005] The technical solution of the present invention is:

[0006] An adaptive multi-sensor fusion surface measurement method based on aggregated value sampling, characterized by comprising the following steps:

[0007] Step 1: For the surface to be measured, obtain a set of low-precision measurement data. Each measurement point in this set of data consists of three-dimensional spatial coordinates in the form of x, y, and z. Calculate the value function of the measurement point on the surface, and calculate the value aggregation function of the surface based on the measurement point value function and the kernel function.

[0008] Step 2: Define the expected value aggregation function of the sample set as the aggregate value of the sample, find a new sample that can maximize the incremental aggregate value of the entire sample set, and use a high-precision sensor to measure the point on the surface to obtain the corresponding high-precision measurement data. Each measurement point in this data set consists of three-dimensional spatial coordinates in the form of x, y, and z.

[0009] Step 3: Fuse the original low-precision measurement data with the high-precision measurement data to obtain a fused measurement reconstructed surface;

[0010] Step 4: Set the measurement termination criteria. If the fused measurement reconstructed surface does not meet the measurement termination criteria, repeatedly iteratively execute steps 2 and 3 above, adaptively expand the high-precision measurement data, until the fused measurement reconstructed surface meets the measurement termination criteria, stop the iteration, and output the final fused measurement reconstructed surface.

[0011] The low-precision measurement data is surface measurement data obtained by a three-dimensional vision camera, a structured light sensor, an ultrasonic measuring instrument or other sensors.

[0012] The method for solving the value aggregation function includes:

[0013] A measurement point value function v(x) is defined for the surface being measured to evaluate the value of each point on the surface for surface reconstruction. These value functions can include: a state value function; an action value function; an accumulation value function; or a Gaussian curvature value function. This patent uses the Gaussian curvature value function, which can be solved using CAD models and laser measurement data.

[0014] Solve the kernel function k(x,x * ), the kernel function includes: Laplace kernel function; or Sigmoid kernel function; or cosine similarity kernel function; or Gaussian radial basis kernel function. In this patent, Gaussian radial basis kernel function is used.

[0015] The calculation method of the value aggregation function is expressed as:

[0016] v′(x,x *)=v(x)k(x,x * )

[0017] The method for calculating the expectation of the value aggregation function of the sample set as the aggregate value of the sample includes:

[0018] For the set s={x1,x2…,x m}, select the upper bound of the individual aggregate value function in the set to obtain the value aggregation function v′(x,S):

[0019] v′(x,S)=v(x)max{k(x,x1),…,k(x,x m )}

[0020] Then the overall value of the collection can be expressed as:

[0021] v agg (S)=∫p(x)v′(x,S)dx

[0022] Where p(x) is the probability density function of the sample. The aggregate value of the set in the sample space N can be expressed as:

[0023]

[0024] The search for new samples that can maximize the aggregate value increment of the entire sample set can be expressed as:

[0025]

[0026] where x n+1 The new sample to be sampled.

[0027] The high-precision measurement data includes surface measurement data obtained by a contact probe, a profilometer or other sensors.

[0028] The method of fusing the original low-precision measurement data with the high-precision measurement data includes: residual approximation; or weighted fusion; or implicit fusion; or multi-level B-spline. The residual approximation data fusion method process is:

[0029] Use regression method to calculate the fitting surface function f of low-precision data set l (x,y), and then calculate each high-precision data point and the fitting surface function f l The difference between (x, y) obtains the residual r of each high-precision data point i .

[0030] Using the discrete residual r between two data sets iTrain the residual model r(x,y), combine the fitted surface model of the low-precision dataset with the residual model, and obtain the fused measurement reconstructed surface:

[0031] f(x,y)=f l (x,y)+r(x,y)

[0032] The regression methods include: Gaussian process regression; or neural network regression; or fuzzy forest regression. The surface fitting model established by Gaussian process regression can be expressed as:

[0033]

[0034] Among them, μ * is the predicted mean, ∑ * is the covariance, K * =κ(X,x * ),K ** =κ(x * ,x * ) and K = κ (X, X) is the covariance matrix, and κ is the pre-defined kernel function. After model prediction, the predicted mean can be obtained as the fitting surface function

[0035] The measurement termination criteria include: calculating the maximum absolute error of the fused measurement reconstructed surface; or analyzing the uncertainty of the fused measurement reconstructed surface; or judging the convergence of the error of the fused measurement reconstructed surface. The process of calculating the maximum absolute error of the fused measurement reconstructed surface includes:

[0036] For additional high-precision sample datasets in Calculate the difference between each high-precision point and the fused measurement reconstructed surface f(x,y):

[0037]

[0038] If the maximum absolute error If the given threshold of the measurement termination standard is exceeded, the above steps of maximizing the aggregation value, fitting the surface calculation error, etc. are repeatedly and iteratively executed to adaptively expand the high-precision measurement data; if the maximum absolute error If the value is lower than the given threshold of the measurement termination criterion, the iteration is stopped and the final fused measurement reconstructed surface is output.

[0039] The beneficial effects of the present invention are:

[0040] The present invention maximizes the aggregation value, continuously and iteratively adds high-precision samples, and continuously improves the accuracy of the reconstructed surface by using the newly added high-precision samples. While ensuring the measurement accuracy, it can significantly improve the measurement efficiency, thereby achieving high-precision and high-efficiency measurement of the surface. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 This is a flow chart of an adaptive multi-sensor fusion surface measurement method based on aggregated value sampling for realizing surface measurement according to an embodiment of the present invention.

[0042] Figure 2 The figure is a schematic diagram of a set of low-precision measurement data on a surface to be measured according to an embodiment of the present invention.

[0043] Figure 3 This is a schematic diagram of obtaining corresponding high-precision measurement data by measuring a new sample point on the surface to be measured according to an embodiment of the present invention.

[0044] Figure 4 This is a distribution diagram of absolute errors between the fused measurement reconstructed surface obtained after initial data fusion according to an embodiment of the present invention and the additional high-precision sample data.

[0045] Figure 5 This is a distribution diagram of absolute errors between the fused measurement reconstructed surface obtained after the first iterative data fusion according to an embodiment of the present invention and the additional high-precision sample data.

[0046] Figure 6 This is a distribution diagram of absolute errors between the fused measurement reconstructed surface obtained after the second iterative data fusion according to an embodiment of the present invention and the additional high-precision sample data.

[0047] Figure 7 The fused measurements are reconstructed into a surface map for the final output. DETAILED DESCRIPTION

[0048] The present invention will be further described below with reference to the accompanying drawings and examples.

[0049] like Figure 1-7 shown.

[0050] The adaptive multi-sensor fusion surface measurement method based on aggregate value sampling of the present invention can be used to iteratively find new samples with maximized aggregate value increments, use high-precision sensors to measure the point on the surface to obtain corresponding high-precision measurement data, use high-precision measurement data and low-precision data to perform data fusion, continuously iteratively generate new fused measurement reconstructed surfaces, and finally output high-precision fused measurement reconstructed surfaces that meet the measurement termination criteria.

[0051] An adaptive multi-sensor fusion surface measurement method based on aggregated value sampling, comprising the following steps (such as Figure 1 shown):

[0052] Step 1: Obtain a set of low-precision measurement data of the surface to be measured and calculate the value aggregation function of the surface

[0053] Assume that the surface to be measured is composed of the following functions:

[0054] f(x,y)=3·cosxsiny+3,x,y∈[0,4]

[0055] Both low-precision measurement data and high-precision measurement data can be obtained on this surface. Low-precision measurement data has complete surface information but low accuracy. In order to simulate the real measurement environment, a large number of data points are sampled on the surface and simplified, and σ is added. 2 = 0.002mm Gaussian noise and The systematic error of in In the implementation case, 1000 low-precision points are selected, that is, m = 1000, such as Figure 2 shown.

[0056] After obtaining the low-precision measurement data of the surface to be measured, it is necessary to calculate the Gaussian curvature of the low-precision measurement data. Methods for calculating Gaussian curvature include: principal curvature method; or covariance matrix method; or local fitting method. In this implementation case, the local fitting method is used. For each low-precision data point, the nearest n data points are found through nearest neighbor search, and these data points are fitted into a quadratic surface. The principal curvature is then extracted from the fitted quadratic surface parameters, and the Gaussian curvature v(x) is calculated as the value function of the measurement point of the surface to be measured. The aggregate value function of the surface to be measured can then be obtained:

[0057] v′(x,x * )=v(x)k(x,x * )

[0058] where k(x,x * ) is the kernel function, which describes the sample point x * The degree of aggregation of its neighborhood information. In this patent, the Gaussian radial basis kernel function is used. Value aggregation function v′(x,x * ) can be interpreted as when the training data already contains sample x * When , the model not only absorbs the sample x * , and also absorbs part of the value of its neighborhood sample x.

[0059] Step 2: Calculate the expectation of the value aggregation function of the sample set as the aggregate value of the sample, find new samples that can maximize the incremental aggregate value of the entire sample set, and use a high-precision sensor to measure the point on the surface to obtain the corresponding high-precision measurement data.

[0060] For existing low-precision datasets Select the upper bound of the individual aggregate value function in the set to obtain the value aggregation function v′(d S ,D S ):

[0061]

[0062] Then the overall value of the collection can be expressed as:

[0063]

[0064] where p(d S ) is the probability density function of the sample. The aggregate value of the set in the sample space N can be expressed as:

[0065]

[0066] Under this definition, the high-value sample sampling problem can be transformed into the problem of maximizing the overall value of the sample set, that is, solving The new sample that maximizes the aggregate value increment of the entire sample set can be expressed as:

[0067]

[0068] in The new sample to be sampled can be obtained by sampling a high-precision data set D T .

[0069] A set of high-precision measurement data sets sampled such as Figure 3 As shown in the figure, the blue surface is the surface to be measured, and the red points are high-precision measurement data points. The x, y, z three-dimensional coordinates of the high-precision data points are as follows:

[0070] Serial number 1 2 3 4 5 6 7 8 9 10 11 12 x 0.127 2.187 1.011 3.427 0.163 0.478 3.165 3.918 1.219 2.461 3.372 2.687 y 0.228 1.165 1.312 1.627 1.659 3.328 3.738 0.826 2.602 2.780 2.889 0.226 z 3.673 1.407 4.540 0.126 5.949 2.506 4.685 1.426 3.531 2.175 2.270 2.396

[0071] Step 3: Fuse the original low-precision measurement data with the high-precision measurement data, use the Gaussian process regression method to establish a fitting surface model for the low-precision data set, and solve the residual model between the fitting surface model and the high-precision measurement data. Combine the fitting surface model and the residual model to reconstruct the surface, and calculate the maximum absolute error between the fused measurement reconstructed surface and the additional high-precision test data.

[0072] Data fusion methods include: residual approximation; weighted fusion; implicit fusion; or multi-level B-spline. In this implementation case, the residual approximation method is used. The GP fitting surface function of the low-precision data set is obtained by using the Gaussian process regression model. For a given low-precision dataset D S ={X,y}, the Gaussian process regression fitting surface model result can be expressed as:

[0073]

[0074] Among them, μ * is the predicted mean, ∑ * is the covariance, K * =κ(X,x * ),K ** =κ(x * ,x * ) and K = κ (X, X) is the covariance matrix, κ is the pre-defined kernel function. After model prediction, the predicted mean GP (D S ). Then calculate each high-precision data point and the fitting surface function f S The difference between (x, y) obtains the residual r of each high-precision data point i , as shown in the following table.

[0075] Serial number 1 2 3 4 5 6 7 8 9 10 11 12 <![CDATA[r i ]]> 0.172 1.207 -1.171 1.740 -2.017 1.354 -2.491 -0.158 -0.195 0.390 -0.273 -0.170

[0076] Using two data sets to get the discrete residual r i After that, the GP model can be trained to obtain the residual model r(x,y). The fitted surface model of the low-precision dataset is combined with the residual model to obtain the fused measurement reconstructed surface f(x,y):

[0077] f(x,y)=f S (x,y)+r(x,y)

[0078] For additional high-precision sample dataset D T , calculate the difference between each high-precision point and the fusion measurement reconstructed surface f(x,y) The absolute error E between the high-precision point and the fused measurement reconstructed surface can be obtained:

[0079]

[0080] The absolute error calculated is Figure 4 and the following table:

[0081] Serial number 1 2 3 4 5 6 7 8 9 10 11 12 E 0.013 0.049 0.038 0.066 0.065 0.075 0.086 0.015 0.007 0.025 0.005 0.013

[0082] Step 4: If the maximum absolute error exceeds the threshold given by the measurement termination criterion, repeat steps 2 and 3 above iteratively, adaptively expand the high-precision measurement data, until the maximum absolute error is lower than the threshold given by the measurement termination criterion, stop the iteration and output the final fused measurement reconstructed surface.

[0083] In this implementation, the maximum absolute error threshold for the measurement termination criteria was set to 0.02 mm. The maximum absolute error after the initial data fusion was 0.086 mm, which did not meet the standard requirement. Steps 2 and 3 were repeated. The first iteration yielded the newly added high-precision data shown in the following table.

[0084]

[0085]

[0086] The absolute error calculated in the first iteration is as follows Figure 5 and shown in the table below.

[0087] Serial number 1 2 3 4 5 6 7 8 9 E 0.008 0.026 0.017 0.035 0.031 0.038 0.041 0.001 0.005

[0088] Serial number 10 11 12 13 14 15 16 17 E 0.012 0.001 0.004 0.002 0.015 0.023 0.041 0.029

[0089] The maximum absolute error after the first iteration of data fusion was 0.041mm, which did not meet the standard requirements. Steps 2 and 3 were repeated. The second iteration obtained the additional high-precision data shown in the following table.

[0090]

[0091] Serial number 11 12 13 14 15 16 17 18 19 x 3.372 2.687 1.258 0.082 1.366 3.912 2.178 2.001 3.099 y 2.889 0.226 0.379 2.266 3.732 3.785 1.926 3.365 0.947 z 2.270 2.396 3.342 5.927 4.220 4.113 1.395 3.278 0.567

[0092] The absolute error calculated by the second iteration is as follows Figure 6 and shown in the table below.

[0093] Serial number 1 2 3 4 5 6 7 8 9 10 E 0.002 0.009 0.007 0.012 0.012 0.015 0.016 0.002 0.002 0.005

[0094] Serial number 11 12 13 14 15 16 17 18 19 E 0.001 0.003 0.002 0.005 0.010 0.016 0.011 0.001 0.010

[0095] The maximum absolute error after the second iteration of data fusion is 0.016mm, which meets the standard requirements. The iteration is stopped and the final fusion measurement and reconstruction surface is output. The final output fusion measurement and reconstruction surface is as follows Figure 7 shown.

[0096] The parts not involved in the present invention are the same as those in the prior art and are implemented using the prior art.

Claims

1. An adaptive multi-sensor fusion surface measurement method based on aggregated value sampling, characterized in that: The following steps are involved: Step 1: For the surface to be measured, obtain a set of low-precision measurement data. Each measurement point in this set of data consists of three-dimensional spatial coordinates in the form of x, y, and z. Calculate the value function of the measurement point on the surface, and calculate the value aggregation function of the surface based on the measurement point value function and the kernel function. Step 2: Define the expected value aggregation function of the sample set as the aggregate value of the sample, find a new sample that can maximize the incremental aggregate value of the entire sample set, and use a high-precision sensor to measure the point on the surface to obtain the corresponding high-precision measurement data. Each measurement point in this data set consists of three-dimensional spatial coordinates in the form of x, y, and z. Step 3: Fuse the original low-precision measurement data with the high-precision measurement data to obtain a fused measurement reconstructed surface; Step 4: Set the measurement termination criteria. If the fused measurement reconstructed surface does not meet the measurement termination criteria, repeatedly iteratively execute steps 2 and 3 above, adaptively expand the high-precision measurement data, until the fused measurement reconstructed surface meets the measurement termination criteria, stop the iteration, and output the final fused measurement reconstructed surface.

2. The method according to claim 1, characterized in that The low-precision measurement data is surface measurement data obtained by a three-dimensional vision camera, a structured light sensor, an ultrasonic measuring instrument or other sensors.

3. The method according to claim 1, characterized in that The method for solving the value aggregation function includes: Define the measurement point value function v(x) of the surface to be measured, which is used to evaluate the value of each point on the surface for surface reconstruction. The measurement point value function includes: state value function; or action value function; or accumulation value function; or Gaussian curvature value function. Solve the kernel function k(x,x * ), the kernel function includes: Laplace kernel function; or Sigmoid kernel function; or cosine similarity kernel function; or Gaussian radial basis kernel function; The calculation method of the value aggregation function is expressed as: v′(x,x * )=v(x)k(x,x * ) Where x and x * is the sample point.

4. The method according to claim 1, wherein The method for calculating the expectation of the value aggregation function of the sample set as the aggregate value of the sample includes: For the sample set S, select the upper bound of the individual aggregate value function in the set to obtain the value aggregation function v ′ (x, S), the overall value of the set can be expressed as: v agg (S)=∫p(x)v′(x,S)dx Where p(x) is the probability density function of the sample; the aggregate value of the set on the sample space N is expressed as:

5. The method according to claim 1, wherein The method of finding a new sample that can maximize the aggregate value increment of the entire sample set is: where x n+1 is the new sample to be sampled, is the overall value of the sample set.

6. The method according to claim 1, characterized in that The high-precision measurement data includes surface measurement data obtained by a contact probe, a profilometer or other sensors.

7. The method according to claim 1, characterized in that The method for fusing the original low-precision measurement data with the high-precision measurement data includes: residual approximation; or weighted fusion; or implicit fusion; or multi-level B-spline; wherein the residual approximation data fusion method process is: Use regression method to calculate the fitting surface function f of low-precision data set l (x,y), and then calculate each high-precision data point and the fitting surface function f l The difference between (x, y) obtains the residual r of each high-precision data point i . Using the discrete residual r between two data sets i Train the residual model r(x,y), combine the fitted surface model of the low-precision dataset with the residual model, and obtain the fused measurement reconstructed surface: f(x,y)=f l (x,y)+r(x,y)。 8. The method according to claim 7, characterized in that The regression methods include: Gaussian process regression; or neural network regression; or fuzzy forest regression; wherein for a given low-precision data set The surface fitting model established by Gaussian process regression is: Among them, μ * is the predicted mean, ∑ * is the covariance, K * =κ(X,x * ),K ** =κ(x * ,x * ) and K = κ (X, X) is the covariance matrix, κ is the pre-defined kernel function; after model prediction, the predicted mean can be obtained as the fitting surface function 9. The method according to claim 1, characterized in that The measurement termination criteria include: calculating the maximum absolute error of the fused measurement reconstructed surface; or analyzing the uncertainty of the fused measurement reconstructed surface; or judging the convergence of the error of the fused measurement reconstructed surface; wherein the process of calculating the maximum absolute error of the fused measurement reconstructed surface includes: For additional high-precision sample datasets in Calculate the difference between each high-precision point and the fused measurement reconstructed surface f(x,y): If the maximum absolute error If the measurement termination standard exceeds the given threshold, the above steps of maximizing the aggregation value and data fusion calculation error are repeatedly and iteratively executed to adaptively expand the high-precision measurement data; if the maximum absolute error If the value is lower than the given threshold of the measurement termination criterion, the iteration is stopped and the final fused measurement reconstructed surface is output.

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