Pile sinking geometric parameter determination method

Abstract

The invention discloses a pile sinking geometric parameter determination method which comprises the following steps: (1) acquiring three-dimensional coordinate data of a plurality of measuring points on the surface of a pile sinking, and preprocessing the three-dimensional coordinate data; (2) judging the number of required alternative axis vectors and calculating the alternative axis vectors by using the distribution indexes of the measuring points; (3) calculating a pile sinking radius and an error degree corresponding to each alternative axis vector; (4) the optimal initial value of the pile sinking geometric parameter is screened out according to the minimum error degree; and (5) the optimal pile sinking geometric parameters are fitted according to the optimal initial value. The method is suitable for various measuring point distribution conditions, pile sinking geometric parameters are rapidly, accurately and stably determined, the pile sinking geometric parameters are compared with design values, deviation is calculated, and whether engineering requirements are met or not is rapidly and accurately judged.

Description

Technical Field

[0001] This invention relates to the field of geotechnical engineering surveying, and in particular to a method for determining the geometric parameters of pile driving. Background Technology

[0002] The geometric parameters of pile driving include the direction vector of the pile axis, the coordinates of a point on the axis, and the radius of the cross-section circle. Accurate acquisition of these parameters is crucial for evaluating the quality of pile driving construction (such as verticality and cross-sectional integrity) and bearing capacity, and is of great significance in pile foundation engineering for buildings, bridges, and other projects.

[0003] Currently, the determination of pile driving geometric parameters mainly relies on feature extraction of measurement point data, among which principal component analysis (PCA) is one of the commonly used techniques. This method approximates the pile axis by finding the direction (eigenvector) with the largest data variance, but it has significant defects in practical applications: (1) Sensitive to the distribution of measurement points: It is only effective when the measurement points are ideally distributed (such as "long and narrow type" evenly distributed along the pile length or "short and fat type" evenly distributed along the cross section). When the measurement points form a "weak geometric distribution" (such as sparse and uneven) due to construction obstruction and measurement limitations, the eigenvector deviates greatly from the real axis, and the accuracy drops sharply; (2) Lack of distribution adaptability: Existing methods do not dynamically adjust the calculation strategy for different measurement point distribution types. For scenarios where the difference in eigenvalues ​​is not significant (such as λ1≈λ2≈λ3), it is difficult to effectively distinguish the axis direction from the interference direction; (3) Initial value dependence problem: Some methods optimize parameters through fitting algorithms (such as the least squares method), but the selection of initial values ​​depends on human experience or the assumption of ideal distribution. Under non-ideal distribution, it is easy to fall into local optima, resulting in convergence failure or excessive error.

[0004] Therefore, there is an urgent need for a method to determine the geometric parameters of pile driving that can adapt to different measurement point distributions, find reliable initial values, and maintain high accuracy even under weak geometric distributions. Summary of the Invention

[0005] Purpose of the invention: This invention discloses a method for determining the geometric parameters of pile driving, aiming to solve the problem that existing methods are unable to accurately estimate the geometric parameters of pile driving when the pile driving measurement points have a weak geometric distribution.

[0006] Technical solution: A method for determining the geometric parameters of pile driving, comprising the following steps:

[0007] (1) Obtain the three-dimensional coordinate data of multiple measuring points on the surface of the pile and preprocess the three-dimensional coordinate data;

[0008] (2) Use the measurement point distribution index to determine the number of candidate axis vectors needed and to calculate the candidate axis vectors;

[0009] (3) Calculate the pile radius and error degree corresponding to each candidate axis vector;

[0010] (4) Select the corresponding candidate axis vectors based on the minimum error degree, and use the coordinates of a point on the axis and the pile radius as the best initial values ​​of the pile geometric parameters.

[0011] (5) Fit the optimal pile driving geometric parameters based on the best initial value.

[0012] Beneficial effects: This invention is applicable to various measuring point distributions, and can quickly, accurately and stably determine the geometric parameters of pile driving, including the direction vector of the axis, the coordinates of a point on the axis, and the radius of the bottom circle; it can compare the geometric parameters of pile driving with the design values, calculate the deviation, and quickly and accurately determine whether the engineering requirements are met. Attached Figure Description

[0013] Figure 1 This is a flowchart of a method for determining the geometric parameters of pile driving. Detailed Implementation

[0014] The technical solution of the present invention will be further described below with reference to the accompanying drawings.

[0015] like Figure 1 As shown, the present invention provides a technical solution:

[0016] A method for determining the geometric parameters of pile driving includes the following steps:

[0017] (1) Obtain the three-dimensional coordinate data of multiple measuring points on the surface of the pile and preprocess the three-dimensional coordinate data;

[0018] (2) Use the measurement point distribution index to determine the number of candidate axis vectors needed and to calculate the candidate axis vectors;

[0019] (3) Calculate the pile radius and error degree corresponding to each candidate axis vector;

[0020] (4) Select the corresponding candidate axis vectors based on the minimum error degree, and use the coordinates of a point on the axis and the pile radius as the best initial values ​​of the pile geometric parameters.

[0021] (5) Fit the optimal pile driving geometric parameters based on the best initial value.

[0022] Furthermore, step (1) includes:

[0023] Obtain the three-dimensional coordinate data of multiple measuring points on the surface of the driven pile, denoted as {(x i ,y i ,z i Let |i = 1, 2, ..., n}, where n is the number of measurement points; preprocess the three-dimensional coordinate data:

[0024]

[0025] Obtain new coordinates (x′)i ,y′ i ,z′ i ).

[0026] Furthermore, obtaining the measurement point distribution index includes the following steps:

[0027] Construct matrix A:

[0028]

[0029] Solve the equation:

[0030] |λE-A|=0

[0031] The solutions are sorted from largest to smallest and denoted as λ1, λ2, and λ3, where λ1 ≥ λ2 ≥ λ3; E represents the third-order identity matrix.

[0032] The above λ i Substitute the following equations to solve for the corresponding three-dimensional direction vector V. i

[0033] λ i V i =AV i

[0034] Among them, V i =(a i ,b i ,c i ) T a i ,b i ,c i These represent the components of the direction vector along the X, Y, and Z axes, respectively.

[0035] Calculate the distribution index of the measuring points:

[0036]

[0037] Obtain the distribution indices s1 and s2 of the measurement points.

[0038] Furthermore, the formula for calculating the number of candidate axis vectors is as follows:

[0039]

[0040] Where m is the number of candidate axis vectors in each group, and s1 and s2 are the distribution indices of the measuring points.

[0041] Furthermore, calculate the candidate axis vectors and construct the candidate axis vector set e = {e1, e2, ..., e}. m} and n={n1,n2,…,n m}, candidate axis vector e k nk Calculation formula:

[0042] e k =V1cosθ k +V2sinθ k

[0043] n k =V1cosθ k +V3sinθ k

[0044] Where, θ k Let k be the weighted angle, and k = 0, 1, 2, ..., m.

[0045] The weighted angle is calculated as follows:

[0046]

[0047] Furthermore, the pile driving radius corresponding to each candidate axis vector. And error degree d j :

[0048]

[0049] in, This represents the distance from the i-th measuring point to the j-th candidate axis. When 1 ≤ j ≤ m, l j For the candidate axis vector e k When m+1≤j≤2m, l j For the candidate axis vector n k .

[0050] Furthermore, step (4) includes processing 2m error degrees d j Select the minimum value d from the middle min Find the candidate axis vector l corresponding to the minimum value. best and radius As the optimal initial values ​​for the geometric parameters of the pile driving.

[0051] Furthermore, step (5) includes:

[0052] The Z0 coordinate component of a point on the candidate axis corresponding to the optimal initial value is 0, with H = (X0, Y0, a, b, c, r). T Let X0 and Y0 be the vector of geometric parameters to be determined for pile driving, where X0 and Y0 are initially 0, and (a, b, c) are initially l. best The initial value of r in the three components along the X, Y, and Z axes is...

[0053] Construct the error function v:

[0054] v = B * HL

[0055] in, f i =(x i -X0) 2 +(y i -Y0) 2 +(z i -Z0) 2 -(a(x i -X0)+b(y i -Y0)+c(z i -Z0)) 2 -r 2 ,

[0056] Parameter estimation is performed through iteration:

[0057] h=(B T B) -1 B T l

[0058] H j+1 =H j +h

[0059] Where h is the parameter correction value for each iteration, j = 0, 1, 2, ..., N-1, and N represents the maximum allowed number of iterations. The iteration terminates when the iteration termination condition is met.

[0060] Furthermore, the iteration terminates when one of the following conditions is met: (1) j > N-1, (2) the absolute values ​​of the parameter correction values ​​h of the three parameters X0, Y0, and r are all less than 1e-5, and the absolute values ​​of the parameter correction values ​​h of the three parameters a, b, and c are all less than 1e-8.

Claims

1. A method for determining the geometric parameters of pile driving, characterized in that, Includes the following steps: (1) Obtain the three-dimensional coordinate data of multiple measuring points on the surface of the pile and preprocess the three-dimensional coordinate data; (2) Use the measurement point distribution index to determine the number of candidate axis vectors needed and to calculate the candidate axis vectors; (3) Calculate the pile radius and error degree corresponding to each candidate axis vector; (4) Select the optimal initial values ​​of pile driving geometric parameters based on the minimum error; (5) Fit the optimal pile driving geometric parameters based on the best initial value.

2. The method for determining the geometric parameters of pile driving according to claim 1, characterized in that, Step (1) includes: Obtain the three-dimensional coordinate data of multiple measuring points on the surface of the driven pile, denoted as {(x i ,y i ,z i Let |i = 1, 2, ..., n}, where n is the number of measurement points; preprocess the three-dimensional coordinate data: Obtain new coordinates (x′) i ,y′ i ,z′ i ).

3. The method for determining the geometric parameters of pile driving according to claim 1, characterized in that, The acquisition of the measurement point distribution index includes the following steps: Construct matrix A: Solve the equation: |λE-A|=0 The solutions are sorted from largest to smallest and denoted as λ1, λ2, and λ3, where λ1 ≥ λ2 ≥ λ3; E represents the third-order identity matrix. The above λ i Substitute the following equations to solve for the corresponding three-dimensional direction vector V. i λ i V i =OFF i Among them, V i =(a i ,b i ,c i ) T a i ,b i ,c i These represent the components of the direction vector along the X, Y, and Z axes, respectively. Calculate the distribution index of the measuring points: Obtain the distribution indices s1 and s2 of the measurement points.

4. The method for determining the geometric parameters of pile driving according to claim 1, characterized in that, The formula for calculating the number of candidate axis vectors is as follows: Where m is the number of candidate axis vectors in each group, and s1 and s2 are the distribution indices of the measuring points.

5. The method for determining the geometric parameters of pile driving according to claim 3, characterized in that, The calculation of candidate axis vectors constructs a candidate axis vector set e = {e1, e2, ..., e...} m } and n={n1,n2,…,n m }, candidate axis vector e k n k Calculation formula: e k =V1cosθ k +V2sinθ k n k =V1cosθ k +V3sinθ k Where, θ k Let k be the weighted angle, and k = 0, 1, 2, ..., m.

6. The method for determining the geometric parameters of pile driving according to claim 5, characterized in that, The weighted angle is calculated as follows:

7. The method for determining the geometric parameters of pile driving according to claim 1, characterized in that, Calculate the pile driving radius corresponding to each candidate axis vector. And error degree d j : in, This represents the distance from the i-th measuring point to the j-th candidate axis. When 1 ≤ j ≤ m, l j For the candidate axis vector e k When m+1≤j≤2m, l j For the candidate axis vector n k .

8. The method for determining the geometric parameters of pile driving according to claim 7, characterized in that, Step (4) includes calculating from 2m error degrees d j Select the minimum value d from the middle min Find the candidate axis vector l corresponding to the minimum value. best and radius As the optimal initial values ​​for the geometric parameters of the pile driving.

9. The method for determining the geometric parameters of pile driving according to claim 1, characterized in that, Step (5) includes: The Z0 coordinate component of a point on the candidate axis corresponding to the optimal initial value is 0, with H = (X0, Y0, a, b, c, r). T Let X0 and Y0 be the vector of geometric parameters to be determined for pile driving, where X0 and Y0 are initially 0, and (a, b, c) are initially l. best The initial value of r in the three components along the X, Y, and Z axes is... Construct the error function v: v = B * HL wherein, f i = (x i - X0) 2 + (y i - Y0) 2 + (z i - Z0) 2 - (a(x i - X0)+b(y i - Y0)+c(z i - Z0)) 2 - r 2 , Parameter estimation is performed through iteration: h=(B T B) -1 B T l H j+1 =H j +h Where h is the parameter correction value for each iteration, j = 0, 1, 2, ..., N-1, and N represents the maximum allowed number of iterations. The iteration terminates when the iteration termination condition is met.

10. The method for determining the geometric parameters of pile driving according to claim 9, characterized in that, The iteration termination condition is that the iteration terminates when one of the following conditions is met: (1) j > N-1; (2) the absolute values ​​of the parameter correction values ​​h of the three parameters X0, Y0, and r are all less than 1e-5, and the absolute values ​​of the parameter correction values ​​h of the three parameters a, b, and c are all less than 1e-8.

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