CN114066720B - Tensor regression-based three-dimensional surface morphology prediction method, device and readable medium - Google Patents
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Abstract
The invention provides a three-dimensional surface morphology prediction method, a device and a readable medium based on tensor regression, which comprise the steps of measuring to obtain space coordinate data of a three-dimensional surface, processing the measured data, and mapping coordinate values in a three-dimensional Euclidean space onto a two-dimensional plane through space mapping; establishing a tensor regression model, and solving a model parameter tensor according to known sample measurement data; and predicting the new sample according to the established tensor regression model to obtain the surface morphology of the new sample. The invention can be applied to three-dimensional surfaces with any shape, establishes a tensor regression model containing evolution information through historical data, can effectively predict the three-dimensional surface morphology of a future machined part, improves the defect that the surface morphology of the machined part can only be evaluated afterwards in a method relying on machining process parameters and signal monitoring, and predicts the surface morphology of the next part according to the existing measurement data so as to perform advanced control.
Description
Technical Field
The invention relates to surface morphology prediction of a processed part, in particular to a three-dimensional surface morphology prediction method and system based on tensor regression.
Background
In the processing process of complex-shape parts such as engine cylinder heads, aerospace valves, blades and the like, the surface morphology of the parts is an important control object in the processing of the parts, and has important influence on the functional performance of the parts. The advanced prediction of surface topography may facilitate optimizing process parameters and improving quality control of the manufacturing process. The traditional shape prediction method only can predict the part being processed at the current moment according to specific process parameters through monitoring the processing parameters and signals, but cannot predict the surface shape of the next part. With the development of the measurement technology, the high-definition measurement technology can measure the surface of the part on the premise of no contact and short time, so that large-scale point cloud data is obtained, and the three-dimensional surface morphology information of the part is comprehensively and detailed. For a plurality of continuous machined parts, the surface information of the historical parts obtained based on high-definition measurement comprises the evolution process of the surface morphology of the parts, and the change rule of the surface can be obtained by mining the change information of the process, so that the surface morphology of the next part to be machined is predicted, and the defect that the surface morphology of the machined part can only be evaluated afterwards in the traditional method is overcome. And predicting the surface morphology of the next part to be processed according to the historical measurement data, so as to perform advanced control.
In the prior art, the invention patent with the name of CN113204852A is a method and a system for predicting the milling surface morphology of a ball-end milling cutter, which are used for predicting the three-dimensional surface morphology of a milling surface according to the movement track of a cutting edge and processing parameters. However, due to the complex geometry of the cutting edge and the curved trajectory, it is difficult to consider the influence of all factors in a single model, and it is difficult to accurately predict the surface appearance.
Su Changqing et al in the paper "shaft hole characteristic error separation and surface morphology prediction based on harmonic theory" ("journal of the military industry", 10 th edition, 1956-1963 pages) describe a shaft hole shape error separation method based on harmonic theory, performing harmonic separation according to the shape characteristics of shaft hole parts, calculating harmonic errors, and predicting the surface morphology of the parts according to the deviation degree of measurement points. However, the method is only suitable for the shape of the part with periodic errors in the shaft hole type, and cannot be expanded to the three-dimensional surface with any shape.
Disclosure of Invention
1. Object of the invention
Aiming at the defects in the prior art, the invention aims to provide a tensor regression-based three-dimensional surface morphology prediction method and system.
2. The invention adopts the technical proposal that
The invention provides a three-dimensional surface morphology prediction method based on tensor regression, which comprises the following steps:
step 1: surface measurement, namely measuring the three-dimensional surface of the existing sample to obtain coordinate data representing the surface morphology in a three-dimensional space;
step 2: data processing, mapping coordinate values in a three-dimensional Euclidean space onto a two-dimensional plane, and representing each of three Cartesian coordinates (x, y, z) in the coordinate data as a function of a surface coordinate (u, v);
step 3: establishing a tensor regression model, for the existing M samples, taking the surface coordinates (u, v) of each sample as a prediction variable and taking (x, y, z) in a Cartesian coordinate system as a response variable, establishing the tensor regression model,
step 4: solving the model parameter tensor according to the measurement data of the existing M samples and the corresponding surface coordinates,
step 5: and predicting the morphology, namely predicting the surface morphology of the future processed part according to the established tensor regression model.
Preferably, in step 1, a non-contact high-definition surface measuring instrument is used to measure a three-dimensional surface, so as to obtain point cloud data in a three-dimensional space.
Preferably, the step 2 includes:
for surfaces in three-dimensional space, described by two parameters, in three surface components (x, y, z), the surface coordinates (u, v) are used for the respective representation by a spatial mapping algorithm, specifically:
thus p:i.e. the parameterization of the point p from the three-dimensional space S to the surface coordinates (u, v); modeling three coordinates (x, y, z) of point p with (u, v); the two-dimensional mapping of the point coordinates is performed by the isomap algorithm.
Preferably, in step 3, a linear tensor regression model is built, specifically:
the establishment of the prediction variable and the response variable are respectively as follows:definition of the definitionFor predicting the variables, surface parameter coordinates (u i ,v i ) The corresponding response variable is +.>I.e. three coordinate values obtained by surface measurement. Where i is the i-th measurement point of the sample surface, u i For the ith measurement point, v is mapped by two dimensions to the value in the u direction i The value in the v direction is mapped by two dimensions for the i-th measurement point. X is x i ,y i ,z i The method is characterized in that the method is respectively the numerical values of the ith measuring point in the x, y and z directions under a three-dimensional Cartesian coordinate system, wherein N is the number of surface measuring points, M is the number of samples, and a tensor regression model is established as follows: /> Wherein ε is the error term, ">For model regression parameters>And epsilon are tensor forms, and the tensor space where epsilon is located is: />
Assuming that the tensor regression model is linear, the error term epsilon obeys Gaussian distribution prediction variablesAnd response variable +.>The linear relation formula between the two is as follows:
preferably, the step 5 includes: and predicting the new sample according to the established tensor regression model and the surface coordinates (u, v) to obtain the surface morphology of the new sample.
The invention provides a three-dimensional surface morphology prediction device based on tensor regression, which comprises a memory and a processor, wherein the memory stores a computer program, and the processor realizes the steps of the method when executing the computer program.
The present invention proposes a computer readable storage medium having stored thereon a computer program which, when executed by a processor, implements the method steps.
3. The invention has the beneficial effects that
(1) The method can be used for three-dimensional surfaces with any shapes, has wide applicability to surface topography prediction, and solves the problem that the existing surface topography prediction technical method cannot be applied to any three-dimensional surfaces;
(2) The method can be used for large-scale point cloud data based on high-definition measurement equipment, and solves the problem that the existing surface morphology prediction technical method cannot be suitable for large-scale data;
(3) The invention predicts the surface morphology of the unprocessed part by the processed part based on the historical measurement information of the surface morphology of the part, and can perform advanced control.
Drawings
FIG. 1 is a flow chart of a tensor regression-based three-dimensional surface morphology prediction method and system provided by the invention;
FIG. 2 is a flow chart of an isomap algorithm used in the present invention;
FIG. 3 is a schematic diagram of two-dimensional mapping of three coordinate components of a surface provided by the present invention;
FIG. 4 is a flow chart of a low rank tensor learning algorithm used in the present invention;
FIG. 5 is a schematic illustration of the combustion chamber surface of an engine cylinder head according to the present invention, as measured by the high definition measurement technique, meeting the specification requirements;
FIG. 6 is a predictive view of the engine head combustion chamber surface of the present invention.
Detailed Description
The following description of the embodiments of the present invention will be made more apparent and fully by reference to the accompanying drawings, in which embodiments of the invention are shown, and in which it is evident that the embodiments shown are only some, but not all embodiments of the invention. All other embodiments, which can be made by a person skilled in the art without any inventive effort, are intended to be within the scope of the present invention.
Examples of the present invention will be described in further detail below with reference to the accompanying drawings.
Example 1
Referring to fig. 1, a method and a system for predicting three-dimensional surface morphology based on tensor regression include the following steps:
step 1: and (5) surface measurement. And measuring the three-dimensional surface of the existing sample to obtain coordinate data of the surface morphology in the three-dimensional space, wherein the coordinate value of each measuring point is expressed as p (x, y, z).
Step 2: and (5) data processing. Specifically, the coordinate values of the measurement points are spatially mapped. For a surface embedded in three-dimensional space, two parameters can be described, namely a point p (w) on the surface can be represented by two parameters:
thus p:i.e. a parameterization of the point p from the three-dimensional space S to the surface coordinates (u, v). Three coordinates (x, y, z) of point p can be modeled with (u, v). In this step, two-dimensional mapping of the point coordinates is performed by the isomap algorithm, and the algorithm flow is shown in fig. 2. Fig. 3 shows the mapping of this algorithm to a sinusoidal three-dimensional surface p (x, y, z) with its three parameter components.
Step 3: and establishing a tensor regression model. For the existing M samples, obtaining measurement coordinates and mapping surfaces of the part surfaces through the steps 1 and 2, and establishing a predicted variable tensor Where N is the number of surface measurement points and M is the number of samples measured. Establishing a response variable tensorWhere N is the number of surface measurement points and M is the number of samples.
Based on predicted variablesAnd response variable +.>The established tensor regression model is as follows: />Wherein ε is the error term, "> For model regression parameters>
Assuming that the tensor regression model is linear, the error term epsilon obeys Gaussian distribution prediction variablesAnd response variable +.>The linear relation formula between the two is as follows:
step 4: and solving a model parameter tensor. The model parameters are solved by a low rank tensor learning algorithm, the algorithm flow is shown in fig. 4. And solving a model parameter tensor according to the measurement data of the existing M samples and the corresponding surface coordinates.
Step 5: and (5) predicting morphology. Calculating the minimum and maximum values in the u, v directions in the first M samples, taking the minimum and maximum values as sampling point boundaries, and sampling at equal intervals in the u, v directions to obtain samples to be predictedAnd predicting the surface morphology of the next part according to the established tensor regression model.
The invention will be further described with reference to the accompanying drawings, taking a model of an in-line four-cylinder engine cylinder head produced by an automobile engine plant as an example.
In this example, the cylinder head combustion chamber surface morphology prediction is taken as an example to illustrate the implementation process.
As shown in fig. 1, a method and a system for predicting three-dimensional surface morphology based on tensor regression include the following steps:
step 1: the surfaces of the combustion chambers of the 16 engine cylinder covers which are continuously processed are measured through a high-definition measuring instrument, and the measurement result of a single combustion chamber is shown in fig. 5, so that point cloud data of the surfaces of the combustion chambers are obtained.
Step 2: and (5) data processing. The three-dimensional combustion chamber surface is mapped onto a two-dimensional plane by the isomap algorithm, and the three-dimensional coordinates of the measurement points in each sample are expressed as a function of the surface coordinates (u, v). Because the number of the measurement points of each sample is different, for each measurement sample, random sampling is carried out on the mapped (u, v) plane, and the corresponding coordinate (x, y, z) value is extracted, so that the input variable structure of each sample is ensured to be the same. Here 5000 points are sampled for each combustion chamber surface sample.
Step 3: and establishing a tensor regression model. And establishing a tensor regression model according to the existing 16 measurement samples. The predicted variable and the response variable are respectively: establishing a tensor regression model: />
Step 4: and solving a model parameter tensor. Based on the measured data of the existing sample and the corresponding surface coordinates, model parameter tensors are obtained by a low-rank tensor learning algorithmAnd solving.
Step 5: and (5) predicting morphology. Calculating the minimum and maximum values in the u, v directions in the first 16 samples, taking the minimum and maximum values as sampling point boundaries, and sampling at equal intervals in the u, v directions to obtain samples to be predictedValues are brought into the tensor model, based on the solved model parameter tensor +.>Calculate +.17 for sample>And predicting the surface morphology of the 17 th sample part of the next sample part. FIG. 6 shows the morphology prediction results and the measured values of sample 17. The error in calculating the predicted and true measured values is 16.85.
The foregoing is only a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present invention should be included in the scope of the present invention. Therefore, the protection scope of the present invention should be subject to the protection scope of the claims.
Claims (7)
1. The three-dimensional surface morphology prediction method based on tensor regression is characterized by comprising the following steps of:
step 1: surface measurement, namely measuring the three-dimensional surface of the existing sample to obtain coordinate data representing the surface morphology in a three-dimensional space;
step 2: data processing, mapping coordinate values in a three-dimensional Euclidean space onto a two-dimensional plane, and representing each of three Cartesian coordinates (x, y, z) in the coordinate data as a function of a surface coordinate (u, v);
step 3: establishing a tensor regression model, for the existing M samples, taking the surface coordinates (u, v) of each sample as a prediction variable and taking (x, y, z) in a Cartesian coordinate system as a response variable, establishing the tensor regression model,
step 4: solving the model parameter tensor according to the measurement data of the existing M samples and the corresponding surface coordinates,
step 5: and predicting the morphology, namely predicting the surface morphology of the future processed part according to the established tensor regression model.
2. The tensor regression-based three-dimensional surface morphology prediction method according to claim 1, wherein in step 1, the three-dimensional surface is measured using a non-contact high-definition surface measuring instrument to obtain point cloud data in a three-dimensional space.
3. The tensor regression-based three-dimensional surface topography prediction method according to claim 1, wherein the step 2 comprises:
for surfaces in three-dimensional space, described by two parameters, in three surface components (x, y, z), the surface coordinates (u, v) are used for the respective representation by a spatial mapping algorithm, specifically:
thus p:i.e. the parameterization of the point p from the three-dimensional space S to the surface coordinates (u, v); modeling three coordinates (x, y, z) of point p with (u, v); and carrying out two-dimensional mapping of the point coordinates by using an isomap algorithm.
4. The tensor regression-based three-dimensional surface morphology prediction method according to claim 3, wherein the linear tensor regression model is built in step 3, specifically:
the establishment of the prediction variable and the response variable are respectively as follows:definitions->For predicting the variables, surface parameter coordinates (u i ,v i ) The corresponding response variable is +.>Namely three coordinate values obtained by surface measurement; where i is the i-th measurement point of the sample surface, u i For the ith measurement point, v is mapped by two dimensions to the value in the u direction i For the ith measurement point, x is x by two-dimensionally mapping the values in the v direction i ,y i ,z i The values of the ith measuring point in the x, y and z directions under a three-dimensional Cartesian coordinate system are respectively obtained; wherein N is the number of surface measurement points, M is the number of samples, and the established tensor regression model is: />Wherein ε is the error term, ">For model regression parameters>And epsilon are tensor forms, and the tensor space where epsilon is located is: />
Assuming that the tensor regression model is linear, the error term epsilon obeys Gaussian distribution prediction variablesAnd response variable +.>The linear relation formula between the two is as follows:
5. the method for predicting three-dimensional surface morphology based on tensor regression according to claim 1, wherein the step 5 comprises: and predicting the new sample according to the established tensor regression model and the surface coordinates (u, v) to obtain the surface morphology of the new sample.
6. A tensor regression-based three-dimensional surface topography prediction device comprising a memory and a processor, the memory storing a computer program, characterized in that; the processor, when executing the computer program, implements the method steps of any of claims 1-5.
7. A computer-readable storage medium having stored thereon a computer program, characterized by: the computer program implementing the method steps of any of claims 1-5 when executed by a processor.
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