阅读说明：本技术 一种航空发动机叶片准散乱点云数据曲面重构方法 (Curved surface reconstruction method for quasi-scattered point cloud data of aero-engine blade ) 是由 张海涛 毛晴 张旭 李杏华 于 2021-09-30 设计创作，主要内容包括：本发明属于航空发动机叶片加工曲面精确评价领域,对于曲面重构非网格数据,已有的NURBS拟合方法过程复杂,且很难兼顾拟合的精度与速度,本发明提出了一种航空发动机叶片准散乱点云数据曲面重构方法,分行NURBS曲线拟合,输出拟合曲线,利用拟合曲线的曲率特征进行参数重采样,结合分层拟合思想与投影迭代求精思想的重采样数据NURBS曲面拟合,构建k次迭代的NURBS曲面,本发明保证数据参数化的质量,也大大缩短投影点的计算时间,重采样方法将参数化的结果、局部峰值、轮廓曲率快速综合,兼具参数采样与曲率采样的优点,通过传递上次迭代中的参数化结果,能够高效准确的获得投影点。(The invention belongs to the field of precise evaluation of a curved surface processed by an aircraft engine blade, and provides a curved surface reconstruction method for quasi-scattered point cloud data of an aircraft engine blade, which is characterized in that the existing NURBS fitting method has a complex process and is difficult to consider the fitting precision and speed k The invention ensures the quality of data parameterization, greatly shortens the calculation time of the projection point, integrates the parameterization result, the local peak value and the contour curvature quickly by the resampling method, has the advantages of parameter sampling and curvature sampling, and can efficiently and accurately obtain the projection point by transmitting the parameterization result in the last iteration.)

1. A curved surface reconstruction method for quasi-scattered point cloud data of an aircraft engine blade is characterized by comprising the following steps:

step 1: line-by-line NURBS curve fitting: fitting a NURBS curve according to the I row data of the quasi-random data Q by using a general NURBS curve fitting methodFind the first row data of quasi-scattered data Q eachData points in the curveAccording to the projection initial valueCarrying out iterative solution to obtain projection parametersCalculating the distance between each data point and the projection point thereof, namely the fitting deviation; calculating the average value of the fitting deviation, if the average value is larger than the set fitting precision value epsilon₀And is less than the maximum number of iterations, orderUpdating a parameterization result, repeating the steps until the average value of the fitting deviation is smaller than a set fitting precision value, and outputting a fitting curve;

step 2: curve parameter resampling based on curvature characteristics: according to the parameterization result of the fitting curve output in the step 1, subdividing the parameter domain to obtain a curvature change graph of the curvature relative to the parameter u, and extracting a local peak point in the curvature change graph; calculating the total volume score of the curve curvature relative to the parameter u, determining a curvature unit for controlling the sampling density according to the total integral value and the number of samples, and sampling the parameter; finally, updating the parameter sampling result according to the local peak point to obtain resampling data;

and step 3: combining the idea of layered fitting and the idea of projection iterative refinement to fit the resampled data NURBS surface, parameterizing in the u direction and the v direction respectively, determining node vectors, solving control points, and constructing the K times of iterative NURBS surface S^(k)(u, v); according toDetermining the initial position of the projection point, and performing iteration by using a Newton method to obtainAt S^(k)Projection parameters on (u, v)Computing resampled data with grid featuresAll data in to S^(k)Average value of distance of (u, v)If the mean value is less than the set fitting accuracy value epsilon₁Then S^(k)(u, v) is the final curved surface, and the curved surface is output; otherwise, updating the parameterization result according to the projection parameters, and performing iterative refinement, namely: for i 0,1, ·, s; j is 0,1, r,carrying out iteration solution again; and when k reaches the maximum iteration number, ending the projection iteration.

2. The method for reconstructing the curved surface of the quasi-dispersed point cloud data of the aircraft engine blade according to claim 1, wherein in the step 1, in the iterative refinement process of NURBS curve fitting, for adjacent k-th iteration and k + 1-th iteration: in the (k + 1) th iteration, the data points are projected to the curve C obtained in the k-th iteration^(k)Finding the data point at C^(k)The parameterization result of the kth iteration is used as the initial projection value of the (k + 1) th iteration, and then the data point is solved at C^(k)Carrying out parameterization on the (k + 1) th iteration; finding the data point at C^(k)After the projection point, the distance between the data point and the projection point is the fitting error of the data point.

3. The method for reconstructing the curved surface of the quasi-dispersed point cloud data of the aircraft engine blade according to claim 1, wherein in the step 2, all operations of resampling are performed on a parameter u; when resampling is executed, the parameterization result is known information and is used as a sampling candidate point on a parameter domain, 3 parameters are inserted between two adjacent parameters to obtain an additional candidate point, the curvatures of all candidate parameters are calculated, and a curvature change graph with the abscissa as a parameter u and the ordinate as a curvature value is obtained.

4. The method for reconstructing the curved surface of the quasi-dispersed point cloud data of the aircraft engine blade as claimed in claim 1, wherein in the step 2, the curvature is in an interval [ u ]_a,u_b]For the integral of_a-u_b|×|curvature(u_a)+curvature(u_b) I/2 represents, from parameter u, a tangent vector to a curve_aGo to parameter u_bWhere the angle of rotation covered is proportional, the total volume score of the curvature with respect to the parameter u is expressed as Σ | u_a-u_b|×|curvature(u_a)+curvature(u_a)|/2。

5. The method for reconstructing the curved surface of the quasi-dispersed point cloud data of the aircraft engine blade according to claim 1, wherein in the step 3, for the calculation of the projection points, the parameterization result of the surface fitting in the kth iteration process is used as the initial value of the projection points, and then the projection points are calculated by combining Newton iteration.

Technical Field

The invention belongs to the field of accurate evaluation of a machining curved surface of an aircraft engine blade, and particularly relates to a curved surface reconstruction method of quasi-scattered point cloud data of an aircraft engine blade.

Background

Complex free-form surfaces are often an important feature of critical parts of large equipment such as aircraft engine blades, steam turbine blades, and the like. The measurement difficulty of the complex curved surface is high, and the measurement information and the design information have no clear corresponding relation due to the fact that certain profile characteristics lack clear reference standards. After the measurement data is obtained, the surface is required to be restated through a modeling technology, and then the restated measurement curved surface and the reference curved surface are unified to the same coordinate system, and then subsequent error evaluation is carried out. In the measuring process, under the influence of factors such as measuring environment, the self geometric complexity of the curved surface and the like, a single measuring sensor is difficult to adopt to obtain enough measuring data points from the same pose at one time, which inevitably increases the difficulty of data processing. In order to realize high-precision quantitative evaluation of the complex free-form surface, an integral scheme of integrating the characteristics of the free-form surface, a data acquisition mode and a data processing method is required to be established.

For the problem of surface reconstruction, reconstruction based on a parameter spline technology is a good choice, a NURBS surface fitting technology of grid data is mature, but for non-grid data, the existing NURBS fitting method is complex in process, and the fitting precision and speed are difficult to take into account. At present, a coordinate measuring machine is generally adopted to measure a complex free-form surface to obtain data, the measured data is often divided into grid data, quasi-random data and completely-random data, and according to respective characteristics of various data, inheritance and general response of a spline technology are comprehensively considered to provide a proper parameter spline reconstruction method.

Disclosure of Invention

The invention overcomes the defects of the prior art, and solves the technical problems that: the curved surface reconstruction method for the quasi-scattered point cloud data of the blades of the aircraft engine is capable of considering both fitting speed and fitting precision for curved surface reconstruction under the background of a coordinate measurement system, and has wide practicability.

In order to solve the technical problems, the invention adopts the technical scheme that:

a curved surface reconstruction method for quasi-scattered point cloud data of an aircraft engine blade comprises the following steps:

step 1: line-by-line NURBS curve fitting: fitting a NURBS curve according to the I row data of the quasi-random data Q by using a general NURBS curve fitting methodObtaining the curve of each data point of the first row of data Q of quasi-random data QAccording to the projection initial valueCarrying out iterative solution to obtain projection parametersCalculating the distance between each data point and the projection point thereof, namely the fitting deviation; calculating the average value of the fitting deviation, if the average value is larger than the set fitting precision value epsilon₀And is less than the maximum number of iterations, orderUpdating a parameterization result, repeating the steps until the average value of the fitting deviation is smaller than a set fitting precision value, and outputting a fitting curve;

step 2: curve parameter resampling based on curvature characteristics: according to the parameterization result of the fitting curve output in the step 1, subdividing the parameter domain to obtain a curvature change graph of the curvature relative to the parameter u, and extracting a local peak point in the curvature change graph; calculating the total volume score of the curve curvature relative to the parameter u, determining a curvature unit for controlling the sampling density according to the total integral value and the number of samples, and sampling the parameter; finally, updating the parameter sampling result according to the local peak point to obtain resampling data;

and step 3: combining the idea of layered fitting and the idea of projection iterative refinement to fit the resampled data NURBS surface, parameterizing in the u direction and the v direction respectively, determining node vectors, solving control points, and constructing the K times of iterative NURBS surface S^(k)(u, v); according toDetermining the initial position of the projection point, and then adopting Newton's methodPerforming iteration to obtainAt S^(k)Projection parameters on (u, v)Computing resampled data with grid featuresAll data in to S^(k)Average value of distance of (u, v)If the mean value is less than the set fitting accuracy value epsilon₁Then S^(k)(u, v) is the final curved surface, and the curved surface is output; otherwise, updating the parameterization result according to the projection parameters, and performing iterative refinement, namely: for i 0,1, ·, s; j is 0,1, r,k ← k +1, and repeating iterative solution; and when k reaches the maximum iteration number, ending the projection iteration.

Further, in step 1, in the iterative refinement process of NURBS curve fitting, for adjacent k-th and k + 1-th iterations: in the (k + 1) th iteration, the data points are projected to the curve C obtained in the k-th iteration^(k)Finding the data point at C^(k)The parameterization result of the kth iteration is used as the initial projection value of the (k + 1) th iteration, and then the data point is solved at C^(k)Carrying out parameterization on the (k + 1) th iteration; finding the data point at C^(k)After the projection point, the distance between the data point and the projection point is the fitting error of the data point.

Further, in step 2, all the operations of resampling are performed on the parameter u; when resampling is executed, the parameterization result is known information and is used as a sampling candidate point on a parameter domain, 3 parameters are inserted between two adjacent parameters to obtain an additional candidate point, the curvatures of all candidate parameters are calculated, and a curvature change graph with the abscissa as a parameter u and the ordinate as a curvature value is obtained.

Further, in step 2, the curvature is in the interval [ u ]_a,u_b]For the integral of_a-u_b|×|curvature(u_a)+curvature(u_b) I/2 represents, from parameter u, a tangent vector to a curve_aGo to parameter u_bThe angle of rotation experienced is proportional and the total volume score of the curvature with respect to the parameter u is expressed as | u_a-u_b|×|curvature(u_a)+curvature(u_a)|/2。

Further, in step 3, for the calculation of the projection points, the parameterization result of the surface fitting in the k iteration process is used as the initial value of the projection points, and then the projection points are calculated by combining the newton iteration.

Compared with the prior art, the invention has the following beneficial effects:

1. the convergence advantage of the classical Newton iteration is established on the basis of good initial value guess, and if the initial value is set unreasonably, the Newton iteration can enter an incorrect search space, so that the algorithm falls into a local optimal solution, and even the solution fails. The method provided by the invention can avoid the problems, parameterization is fused with the calculation of the projection point, the parameterization result of the kth iteration is utilized, the initial projection value of the kth +1 th iteration is given, and then the Newton method is used for solving the data point at C^(k)And (3) performing (k + 1) th iteration parameterization, wherein in the projection iteration optimization process, the quality of data parameterization is ensured, and the calculation time of a projection point is greatly shortened.

2. According to the resampling method based on the parameters and the geometric characteristics, the resampling method quickly integrates the parameterized result, the local peak value and the contour curvature, and has the advantages of parameter sampling and curvature sampling; the resampling method based on the parameters and the geometric characteristics solves the problems of node redundancy and high time overhead in the NURBS surface fitting of the quasi-scattered data.

3. In general, in a fitting method based on an iterative projection idea, calculation of projection points is the most time-consuming part, but the method provided by the invention enables an initial value of Newton iteration to be more reasonable by transmitting a parameterization result in last iteration, well ensures secondary convergence of Newton iteration, and can efficiently and accurately obtain the projection points.

Drawings

Fig. 1 is based on a general scheme of resampled quasi-diffuse data NURBS fitting.

Detailed Description

In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below, and it is obvious that the described embodiments are some embodiments of the present invention, but not all embodiments; all other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

As shown in FIG. 1, the invention discloses a curved surface reconstruction method for quasi-scattered point cloud data of an aircraft engine blade, which is characterized by comprising the following steps:

step 1: line-by-line NURBS curve fitting: fitting a NURBS curve according to the I row data of the quasi-random data Q by using a general NURBS curve fitting methodObtaining the curve of each data point of the first row of data Q of quasi-random data QAccording to the projection initial valueCarrying out iterative solution to obtain projection parametersCalculating the distance between each data point and the projection point thereof, namely the fitting deviation; calculating the average value of the fitting deviation, if the average value is larger than the set fitting precision value epsilon₀And is less than the maximum number of iterations, orderUpdating a parameterization result, repeating the steps until the average value of the fitting deviation is smaller than a set fitting precision value, and outputting a fitting curve; during the iterative refinement of NURBS curve fitting, for adjacent kth and k +1 iterations: in the (k + 1) th iteration, the data points are projected to the curve C obtained in the k-th iteration^(k)Finding the data point at C^(k)The parameterization result of the kth iteration is used as the initial projection value of the (k + 1) th iteration, and then the data point is solved at C^(k)Carrying out parameterization on the (k + 1) th iteration; finding the data point at C^(k)After the projection point, the distance between the data point and the projection point is the fitting error of the data point.

Step 2: curve parameter resampling based on curvature characteristics: according to the parameterization result of the fitting curve output in the step 1, subdividing the parameter domain to obtain a curvature change graph of the curvature relative to the parameter u, and extracting a local peak point in the curvature change graph; calculating the total volume score of curve curvature relative to parameter u, determining a curvature unit for controlling sampling density according to the total integral value and the number of samples, sampling the parameter, performing resampling on the parameter u, wherein when resampling is performed, the result of parameterization is known information, 3 parameters are used as sampling candidate points on a parameter domain, additional candidate points are obtained by inserting 3 parameters between two adjacent parameters, the curvature of all candidate parameters is calculated, and a curvature change graph with the abscissa as parameter u and the ordinate as curvature value is obtained_l(u) p-1 times of continuity, wherein the obtained curvature change graph has fluctuation at a node, the curvature change graph is subjected to smoothing treatment by adopting Gaussian low-pass filtering, and a parameter u corresponding to a local maximum value in the curvature change graph after filtering is stored and is called a local peak point; finally, updating the parameter sampling result according to the local peak point to obtain resampling data; curvature in the interval u_a,u_b]On| u for integration_a-u_b|×|curvature(u_a)+curvature(u_b) I/2 represents, from parameter u, a tangent vector to a curve_aGo to parameter u_bThe angle of rotation experienced is proportional and the total volume score of the curvature with respect to the parameter u is expressed as | u_a-u_b|×|curvature(u_a)+curvature(u_a)|/2。

Dividing the total volume score of curvature into r parts, each part is called integral unit ^ cur of curvature, determining the sampling position on the parameter domain according to ^ cur, and the integral value of curvature between two adjacent sampling parameters is kept unchanged, so that the corner of the tangent vector of the curve is approximately constant for any two adjacent sampling points. Cur well controls the distribution of sampling points, distributing more points to regions where curvature changes rapidly. Therefore, the obtained sampling points can well reflect the overall trend of the curve, and more sampling points are distributed to the area with fast curvature change.

And step 3: combining the idea of layered fitting and the idea of projection iterative refinement to fit the resampled data NURBS surface, parameterizing in the u direction and the v direction respectively, determining node vectors, solving control points, and constructing the K times of iterative NURBS surface S^(k)(u, v); according toDetermining the initial position of the projection point, and performing iteration by using a Newton method to obtainAt S^(k)Projection parameters on (u, v)Computing resampled data with grid featuresAll data in to S^(k)Average value of distance of (u, v)If the average value is less than the set valueAccuracy of fit value ε₁Then S^(k)(u, v) is the final curved surface, and the curved surface is output; otherwise, updating the parameterization result according to the projection parameters, and performing iterative refinement, namely: for i 0,1, ·, s; j is 0,1, r,k ← k +1, and repeating iterative solution; and when k reaches the maximum iteration number, ending the projection iteration. And aiming at the calculation of the projection points, taking the parameterization result of the surface fitting in the kth iteration process as the initial value of the projection points, and then calculating the projection points by combining Newton iteration.

In order to ensure the precision, the automation degree and the universality of the detection of the complex curved surface and aim at the quasi-scattered data, the invention introduces a resampling thought, combines a layered NURBS curved surface fitting thought, and provides a NURBS curved surface fitting method based on a resampling technology.

Finally, it should be noted that: the above embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; while the invention has been described in detail and with reference to the foregoing embodiments, it will be understood by those skilled in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some or all of the technical features may be equivalently replaced; and the modifications or the substitutions do not make the essence of the corresponding technical solutions depart from the scope of the technical solutions of the embodiments of the present invention.