Pile integrity detection method based on stress wave analysis
By symmetrically arranging sensors on the top of the foundation pile, building a three-dimensional reflected image and using the detection network to judge the integrity of the foundation pile, the problem of failure to effectively consider the differences in reflected signals at different locations at multiple time points and other factors in the prior art, and the accuracy of foundation pile integrity detection is improved.
Patent Information
- Application Number
- CN202411762884.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-03
- Publication Date
- 2025-08-22
- Estimated Expiration
- 2044-12-03
AI Technical Summary
The prior art fails to effectively consider the differences in reflected signal at different locations at multiple time points and the influence of other factors in the foundation pile integrity detection, resulting in inaccurate detection of detection results.
Multiple sensors are used to obtain reflected signals at the symmetrical position of the center point on the top of the foundation pile, and a three-dimensional reflected image is constructed through Fourier transform. The position comparison detection network and spectrum detection network are used to extract features, and the foundation pile integrity is judged in combination with the fusion network to reduce the influence of other factors.
It realizes more accurate detection of foundation pile integrity, can effectively identify foundation pile defects and reduce interference from other factors, and improves the accuracy of detection.
Smart Images

Figure CN119669693B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the field of computer technology, and in particular to a pile integrity detection method based on stress wave analysis. Background Art
[0002] A foundation pile is considered a continuous, homogeneous elastic rod. When stress waves propagate through the pile, they generate reflected waves when they encounter defects. Sensors mounted on the pile top receive these reflected wave signals, which are then used to analyze the pile's integrity. Currently, stress waves are often generated by applying an excitation signal along the pile axis from a platform on the pile top. Two acceleration sensors are installed along the pile side, and two acceleration curves are collected simultaneously. The distance between the two sensors and the time difference in their responses determine the average wave velocity of the pile, thereby assessing pile integrity. Pile foundation integrity can also be tested by generating super-seismic waves and flexural waves. However, this approach fails to account for the differences in reflected signals received at different locations at multiple time points, nor does it consider how to eliminate other factors that may affect the reflected waves. Summary of the Invention
[0003] The purpose of the present invention is to provide a pile integrity detection method based on stress wave analysis to solve the above-mentioned problems existing in the prior art.
[0004] An embodiment of the present invention provides a method for detecting pile integrity based on stress wave analysis, comprising:
[0005] Acquiring reflection signals at multiple locations at multiple time points; the reflection signals at the multiple locations represent signals of reflected waves received by multiple sensors at the top of the foundation pile; the multiple sensors are placed at multiple locations on a straight line passing through the center point of the top of the foundation pile; the multiple sensors are symmetrical about the center point of the top of the foundation pile;
[0006] According to the reflection signals at the multiple time points, one dimension is mapped into two dimensions by Fourier transform to obtain a reflection image; multiple reflection images are obtained corresponding to the multiple positions; the reflection image represents the reflection signal that changes with the time point;
[0007] Arranging the reflection images at multiple positions in sequence according to position order to obtain a three-dimensional reflection image; the three-dimensional reflection image contains information about time changes and position changes;
[0008] Obtaining a first detection feature based on the three-dimensional reflection image through a position comparison detection network; the first detection feature represents changes in the reflected wave at different positions at the same time point;
[0009] Obtaining a second detection feature based on the three-dimensional reflection image through a spectrum detection network; the second detection feature represents a characteristic of a reflection wave changing over time;
[0010] The first detection feature and multiple second detection features are input into a fusion network to determine whether the foundation pile is complete.
[0011] Optionally, the position comparison detection network includes a first detection network and a reflection wave convolution network;
[0012] The first detection network includes multiple two-dimensional position convolution kernels of size 2*n; the width of the two-dimensional position convolution kernel is in the same direction as the width of the three-dimensional reflection image, and the height of the two-dimensional position convolution kernel is in the same direction as the height of the three-dimensional reflection image.
[0013] Optionally, the reflected wave convolutional network is a temporal convolutional network with a switch structure between the input layer and the intermediate layer.
[0014] Optionally, the spectrum detection network includes a plurality of three-dimensional position convolution kernels of size q*u*n;
[0015] The width of the 3D position convolution kernel is in the same direction as the length of the 3D reflection image, the height of the 3D position convolution kernel is in the same direction as the height of the 3D reflection image, and the depth of the 3D position convolution kernel is in the same direction as the width of the 3D reflection image.
[0016] Optionally, obtaining a first detection feature based on the three-dimensional reflection image through a position comparison detection network includes:
[0017] Using the two-dimensional position convolution kernel of the first detection network, convolution is performed on the three-dimensional reflection image in the width direction with a step size of 1 to obtain m position change vectors; one time point corresponds to one position change vector; and one position change vector contains u-1 elements;
[0018] Superimposing m position change vectors into a two-dimensional time matrix; the two-dimensional time matrix represents the characteristics of position changes corresponding to multiple time points;
[0019] According to the width direction of the three-dimensional reflection image, the two-dimensional time matrix is divided into u-1 position vectors; two adjacent positions correspond to one position vector;
[0020] Based on the plurality of position vectors, features are first detected.
[0021] Optionally, the first detection feature based on multiple position vectors includes:
[0022] Adjusting a reflection wave convolutional network based on the multiple position vectors;
[0023] averaging the values of corresponding subscripts in the plurality of position vectors to obtain an adjusted position vector, wherein the adjusted position vector includes m elements;
[0024] According to the time points from early to late, the adjusted position vectors are sequentially input into the adjusted reflected wave convolution network to obtain the first detection feature.
[0025] Optionally, adjusting the reflected wave convolution network based on the multiple position vectors includes:
[0026] Associating two position vectors whose positions are symmetrical to obtain an associated position feature set;
[0027] Calculating the difference between the values of the corresponding subscripts of the two position vectors in the associated position feature set using a Euclidean distance algorithm to obtain a difference vector; the number of elements in the difference vector is equal to the number of elements in the position vector;
[0028] Calculating the variance of the values in the difference vector to obtain a position discrimination value; the position discrimination value of 1 indicates that the reflected wave received at the position corresponding to the associated position feature set is affected by other factors; the position discrimination value of 0 indicates that the reflected wave received at the position corresponding to the associated position feature set is not affected by other factors;
[0029] The reflected wave convolutional network is adjusted according to the position discrimination value.
[0030] Optionally, obtaining a second detection characteristic based on the three-dimensional reflection image through a spectrum detection network includes:
[0031] Dividing the three-dimensional reflection image by time points to obtain m / q time reflection images;
[0032] In time sequence, m / q time reflection images are superimposed in the direction of the time point to obtain a superimposed time image; the width of the superimposed time image is (m / q)*u;
[0033] The three-dimensional position convolution kernel of the spectrum detection network is convolved on the superimposed time image with a step size of 1 to obtain a second detection feature; the second detection feature represents the change in the overall feature of the reflected wave formed at multiple positions.
[0034] Optionally, obtaining a second detection feature based on the three-dimensional reflection image through a spectrum detection network includes:
[0035] The height of the three-dimensional reflection image is n, the length is m, and the width is u; n, m, and u are positive integers; the height of the three-dimensional reflection image represents the frequency range of 0-n in the three-dimensional reflection image; the length of the three-dimensional reflection image represents the three-dimensional reflection image composed of m time points; and the length of the three-dimensional reflection image represents the three-dimensional reflection image composed of u positions.
[0036] Optionally, adjusting the reflected wave time convolution network according to the position discrimination value includes:
[0037] If the position discrimination value is 0, the value in the switch structure is set to 1;
[0038] Obtaining an influence ratio; the influence ratio indicates reducing the attention level of unaffected positions;
[0039] If the position discrimination value is 1, the value in the switch structure is set to the influence ratio to obtain an adjusted reflected wave time convolution network; the adjusted reflected wave time convolution network indicates that the attention level of the reflected signal at the affected position is reduced.
[0040] Compared with the prior art, the embodiments of the present invention achieve the following beneficial effects:
[0041] An embodiment of the present invention also provides a method for detecting pile integrity based on stress wave analysis.
[0042] In the present invention, sensors are placed at multiple locations symmetrically around a central point to acquire reflected signals. The reflected signals at multiple locations at multiple time points are converted from one dimension to two dimensions to construct a three-dimensional reflection image. A two-dimensional position convolution kernel is constructed that can extract changes in the reflected signals of stress waves received at multiple locations at a single time point. Based on the identical characteristics of the reflected signals received at symmetrical locations, it is determined whether there is a sudden change in the reflected signals at two adjacent locations at each time point. Because a sudden change indicates the influence of factors other than pile defects, an influence ratio is stored in the switch structure to reduce the influence of other factors. Furthermore, a characteristic of the three-dimensional position convolution kernel of the spectrum detection network is found for determining the overall changes in the reflected signals received at multiple locations at multiple time points. This achieves the technical effect of more accurately determining the integrity of the pile by using the changes in the reflected signals of two adjacent locations detected at multiple identical time points and the changes in the reflected signals received at the overall location at multiple time points. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] Figure 1 This is a flow chart of a pile integrity detection method based on stress wave analysis provided by an embodiment of the present invention.
[0044] Figure 2 It is a schematic diagram of a three-dimensional reflection image in a pile integrity detection method based on stress wave analysis provided by an embodiment of the present invention being convolved by a two-dimensional position convolution kernel of a first detection network.
[0045] Figure 3 It is a schematic diagram of a partial structure of a reflection wave convolution network in a pile integrity detection method based on stress wave analysis provided by an embodiment of the present invention.
[0046] Figure 4This is a schematic diagram of the positions of multiple sensors on the top of a pile in a pile integrity detection method based on stress wave analysis provided by an embodiment of the present invention. DETAILED DESCRIPTION
[0047] The present invention will be described in detail below with reference to the accompanying drawings.
[0048] Example 1
[0049] like Figure 1 As shown, an embodiment of the present invention provides a pile integrity detection method based on stress wave analysis, the method comprising:
[0050] S101: Acquire reflection signals at multiple positions at multiple time points; the reflection signals at the multiple positions represent signals of reflected waves received by multiple sensors at the top of the foundation pile; the multiple sensors are placed at multiple positions on a straight line passing through the center point of the top of the foundation pile; the multiple sensors are symmetrical about the center point of the top of the foundation pile.
[0051] In this embodiment, a transmitter for emitting stress waves is installed at the center point of the top of the foundation pile, and sensors are installed at multiple positions on a straight line passing through the center point of the top of the foundation pile. The sensors are used to receive signals of reflected waves when the stress waves encounter defects in the pile body.
[0052] The signal of the reflected wave indicates that the stress wave emitted by the foundation pile encounters a defect in the pile body when propagating downward along the pile body, generating a reflected wave.
[0053] S102: According to the reflection signals at the multiple time points, one dimension is mapped to two dimensions through Fourier transform to obtain a reflection image; multiple reflection images are obtained corresponding to multiple positions; the reflection image represents the reflection signal that changes with time points.
[0054] In this embodiment, the Fourier transform used is the Discrete Fourier Transform (DFT).
[0055] The reflection image is a two-dimensional spectrum diagram; the length of the reflection image represents a time point, the height of the reflection image represents the frequency of the reflection signal, and the pixels in the reflection image represent the amplitude.
[0056] S103: Arranging the reflection images at multiple positions in sequence according to position order to obtain a three-dimensional reflection image; the three-dimensional reflection image includes information on time changes and position changes.
[0057] The three-dimensional reflection image has a height of n, a length of m, and a width of u; n, m, and u are positive integers.
[0058] Wherein, the three-dimensional reflection image is as follows Figure 2 shown.
[0059] S104: Obtain a first detection feature based on the three-dimensional reflection image through a position comparison detection network; the first detection feature represents changes in different positions at the same time point.
[0060] S105: Obtaining a second detection feature based on the three-dimensional reflection image through a spectrum detection network; the second detection feature represents a feature of a reflection wave that changes over time;
[0061] S106: Input the first detection feature and multiple second detection features into a fusion network to determine whether the pile is complete.
[0062] The fusion network is a fully connected neural network (Fully Connected Neural Network), and the output layer has two neurons, one neuron indicates that the foundation pile is complete, and the other neuron indicates that the foundation pile is incomplete.
[0063] Optionally, the position comparison detection network includes a first detection network and a reflection wave convolution network.
[0064] In this embodiment, the first detection network is a convolutional neural network (CNN).
[0065] The first detection network includes multiple two-dimensional position convolution kernels of size 2*n; the width of the two-dimensional position convolution kernel is in the same direction as the width of the three-dimensional reflection image, and the height of the two-dimensional position convolution kernel is in the same direction as the height of the three-dimensional reflection image.
[0066] Among them, such as Figure 2 Because the width of the 2D position convolution kernel and the width of the 3D reflection image are in the same direction, the 2 in the 2D position convolution kernel corresponds to u in the 3D reflection image. Because the height of the 2D position convolution kernel and the height of the 3D reflection image are in the same direction, the n in the 2D position convolution kernel corresponds to n in the 3D reflection image.
[0067] Optionally, the reflected wave convolutional network is a temporal convolutional network with a switch structure between the input layer and the intermediate layer.
[0068] In this embodiment, the reflected wave convolution network is a temporal convolution network (TCN) with a switch structure.
[0069] Among them, part of the structure of the reflected wave convolutional network is as follows Figure 3 shown.
[0070] Optionally, the spectrum detection network includes multiple three-dimensional position convolution kernels with sizes of q*u*n.
[0071] Wherein, the spectrum detection network is a three-dimensional convolutional neural network (3D Convolutional Neural Networks, 3DCNN).
[0072] The width of the 3D position convolution kernel is in the same direction as the length of the 3D reflection image, the height of the 3D position convolution kernel is in the same direction as the height of the 3D reflection image, and the depth of the 3D position convolution kernel is in the same direction as the width of the 3D reflection image.
[0073] Wherein, q is a positive integer.
[0074] Optionally, obtaining a first detection feature based on the three-dimensional reflection image through a position comparison detection network includes:
[0075] Using the two-dimensional position convolution kernel of the first detection network, convolution is performed on the three-dimensional reflection image in the width direction with a step size of 1 to obtain m position change vectors; one time point corresponds to one position change vector; and one position change vector contains u-1 elements;
[0076] The m position change vectors are superimposed to form a two-dimensional time matrix; the two-dimensional time matrix represents the characteristics of the position changes corresponding to multiple time points.
[0077] The size of the two-dimensional time matrix is m*(u-1).
[0078] The position change vectors are sequentially superimposed into a dimensional time matrix according to the order of their positions in the three-dimensional reflection image.
[0079] According to the width direction of the three-dimensional reflection image, the two-dimensional time matrix is divided into u-1 position vectors; two adjacent positions correspond to one position vector.
[0080] Among them, such as Figure 2 As shown, the wide direction of the three-dimensional reflection image is the direction corresponding to u.
[0081] The position vector represents the value of the reflection signal at two adjacent positions at a time point.
[0082] Based on the plurality of position vectors, features are first detected.
[0083] Optionally, the first detection feature based on multiple position vectors includes:
[0084] Adjusting a reflection wave convolutional network based on the multiple position vectors;
[0085] The values of corresponding subscripts in the plurality of position vectors are averaged to obtain an adjusted position vector; the adjusted position vector includes m elements.
[0086] The adjusted position vector represents the expression of the characteristics of the changes of multiple positions at a time point using an average value.
[0087] According to the time points from early to late, the adjusted position vectors are sequentially input into the adjusted reflected wave convolution network to obtain the first detection feature.
[0088] Optionally, adjusting the reflected wave convolution network based on the multiple position vectors includes:
[0089] Correlate two position vectors whose positions are symmetrical to obtain a set of correlated position features;
[0090] The associated position feature set includes two position vectors.
[0091] Among them, such as Figure 4 As shown, the multiple sensors are symmetrical with the center point of the top of the foundation pile, that is, with "position 3" as the center point, "position 1" and position "5" are symmetrical, "position 2" and position "4" are symmetrical, and the position vectors corresponding to "position 1" and position "5" are symmetrical with the position vectors corresponding to "position 2" and position "4".
[0092] The difference between the values of the corresponding subscripts of the two position vectors in the associated position feature set is calculated by using the Euclidean distance algorithm to obtain a difference vector.
[0093] Here, if the values with subscript 0 in the two position vectors in the associated position feature set are calculated using the Euclidean distance algorithm, the values with subscript 0 in the difference vector are obtained.
[0094] The difference vector represents the difference in the change of the reflected waves at the same time point at the symmetrical position.
[0095] The variance of the values in the gap vector is calculated to obtain a position discrimination value; the position discrimination value of 1 indicates that the reflected wave received at the corresponding position of the associated position feature set is affected by other factors; the position discrimination value of 0 indicates that the reflected wave received at the corresponding position of the associated position feature set is not affected by other factors.
[0096] The position determination value is used to determine whether the difference between the reflected waves at multiple time points in a symmetrical position changes suddenly.
[0097] The reflected wave convolutional network is adjusted according to the position discrimination value.
[0098] Optionally, obtaining a second detection feature based on the three-dimensional reflection image through a spectrum detection network includes:
[0099] The three-dimensional reflection image is divided into time points to obtain m / q time reflection images.
[0100] Wherein, q represents the number of time points for segmentation and is a positive integer.
[0101] In time sequence, m / q time reflection images are superimposed in the direction of the time point to obtain a superimposed time image; the width of the superimposed time image is (m / q)*u.
[0102] The length of the superimposed time image is q, and the height is n.
[0103] The three-dimensional position convolution kernel of the spectrum detection network is convolved on the superimposed time image with a step size of 1 to obtain a second detection feature; the second detection feature represents the change in the overall feature of the reflected wave formed at multiple positions.
[0104] Among them, the convolution direction of the three-dimensional position convolution kernel is consistent with the wide direction of the superimposed time image.
[0105] Optionally, adjusting the reflected wave time convolution network according to the position discrimination value includes:
[0106] If the position discrimination value is 0, the value in the switch structure is set to 1;
[0107] An influence ratio is obtained; the influence ratio indicates that the attention level of unaffected positions is reduced.
[0108] In this embodiment, the influence ratio is 0.75.
[0109] If the position discrimination value is 1, the value in the switch structure is set to the influence ratio to obtain an adjusted reflected wave time convolution network; the adjusted reflected wave time convolution network indicates that the attention level of the reflected signal at the affected position is reduced.
[0110] Similarly, it should be understood that in order to streamline the present disclosure and aid in understanding one or more of the various inventive aspects, in the above description of exemplary embodiments of the invention, various features of the invention are sometimes grouped together into a single embodiment, figure, or description thereof. However, this disclosed method should not be interpreted as reflecting an intention that the claimed invention requires more features than are expressly recited in each claim. Rather, as reflected in the claims below, inventive aspects lie in less than all the features of the individual embodiments disclosed above. Accordingly, the claims following the detailed description are hereby expressly incorporated into this detailed description, with each claim standing on its own as a separate embodiment of the invention.
Claims
1. A pile integrity detection method based on stress wave analysis, characterized in that: include: Acquiring reflection signals at multiple locations at multiple time points; the reflection signals at the multiple locations represent signals of reflected waves received by multiple sensors at the top of the foundation pile; The plurality of sensors are placed at a plurality of positions on a straight line passing through the center point of the top of the foundation pile; the plurality of sensors are symmetrical with respect to the center point of the top of the foundation pile; According to the reflection signals at the multiple time points, mapping one dimension into two dimensions by Fourier transform to obtain a reflection image; A plurality of reflection images are obtained corresponding to the plurality of positions; the reflection images represent reflection signals that change with time points; Arranging the reflection images at multiple positions in sequence according to position order to obtain a three-dimensional reflection image; the three-dimensional reflection image contains information about time changes and position changes; Obtaining a first detection feature based on the three-dimensional reflection image through a position comparison detection network; the first detection feature represents changes in the reflected wave at different positions at the same time point; Obtaining a second detection feature based on the three-dimensional reflection image through a spectrum detection network; the second detection feature represents a characteristic of a reflection wave changing over time; The first detection feature and multiple second detection features are input into a fusion network to determine whether the foundation pile is complete.
2. The pile integrity detection method based on stress wave analysis according to claim 1 is characterized in that: The position comparison detection network includes a first detection network and a reflection wave convolution network; The first detection network includes multiple two-dimensional position convolution kernels of size 2*n; the width of the two-dimensional position convolution kernel is in the same direction as the width of the three-dimensional reflection image, and the height of the two-dimensional position convolution kernel is in the same direction as the height of the three-dimensional reflection image.
3. The pile integrity detection method based on stress wave analysis according to claim 2 is characterized in that: The reflected wave convolutional network is a temporal convolutional network with a switch structure between the input layer and the middle layer.
4. The pile integrity detection method based on stress wave analysis according to claim 1 is characterized in that: The spectrum detection network includes a plurality of three-dimensional position convolution kernels of size q*u*n; The width of the 3D position convolution kernel is in the same direction as the length of the 3D reflection image, the height of the 3D position convolution kernel is in the same direction as the height of the 3D reflection image, and the depth of the 3D position convolution kernel is in the same direction as the width of the 3D reflection image.
5. The pile integrity detection method based on stress wave analysis according to claim 3 is characterized in that: The obtaining of a first detection feature based on the three-dimensional reflection image through a position contrast detection network includes: The two-dimensional position convolution kernel of the first detection network is used to convolve the three-dimensional reflection image in the width direction with a step size of 1 to obtain m position change vectors; one time point corresponds to one position change vector; and one position change vector contains u-1 elements; Superimposing m position change vectors into a two-dimensional time matrix; the two-dimensional time matrix represents the characteristics of position changes corresponding to multiple time points; According to the width direction of the three-dimensional reflection image, the two-dimensional time matrix is divided into u-1 position vectors; two adjacent positions correspond to one position vector; Based on the multiple position vectors, a first detection feature is obtained.
6. The pile integrity detection method based on stress wave analysis according to claim 5 is characterized in that: The obtaining of a first detection feature based on the multiple position vectors includes: Adjusting a reflection wave convolutional network based on the multiple position vectors; averaging the values of corresponding subscripts in the plurality of position vectors to obtain an adjusted position vector, wherein the adjusted position vector includes m elements; According to the time points from early to late, the adjusted position vectors are sequentially input into the adjusted reflected wave convolution network to obtain the first detection feature.
7. The pile integrity detection method based on stress wave analysis according to claim 6 is characterized in that: The adjusting the reflected wave convolution network based on the multiple position vectors includes: Associating two position vectors whose positions are symmetrical to obtain an associated position feature set; Calculating the difference between the values of the corresponding subscripts of the two position vectors in the associated position feature set using a Euclidean distance algorithm to obtain a difference vector; the number of elements in the difference vector is equal to the number of elements in the position vector; Calculating the variance of the values in the difference vector to obtain a position discrimination value; the position discrimination value of 1 indicates that the reflected wave received at the position corresponding to the associated position feature set is affected by other factors; the position discrimination value of 0 indicates that the reflected wave received at the position corresponding to the associated position feature set is not affected by other factors; The reflected wave convolutional network is adjusted according to the position discrimination value.
8. The pile integrity detection method based on stress wave analysis according to claim 4 is characterized in that: The obtaining of a second detection characteristic based on the three-dimensional reflection image through a spectrum detection network includes: Dividing the three-dimensional reflection image by time points to obtain m / q time reflection images; In time sequence, m / q time reflection images are superimposed in the direction of the time point to obtain a superimposed time image; the width of the superimposed time image is (m / q)*u; The three-dimensional position convolution kernel of the spectrum detection network is convolved on the superimposed time image with a step size of 1 to obtain a second detection feature; the second detection feature represents the change in the overall feature of the reflected wave formed at multiple positions.
9. The pile integrity detection method based on stress wave analysis according to claim 3 is characterized in that: The obtaining of a second detection feature based on the three-dimensional reflection image through a spectrum detection network includes: The height of the three-dimensional reflection image is n, the length is m, and the width is u; n, m, and u are positive integers; the height of the three-dimensional reflection image represents the frequency range of 0-n in the three-dimensional reflection image; the length of the three-dimensional reflection image represents the three-dimensional reflection image composed of m time points; and the length of the three-dimensional reflection image represents the three-dimensional reflection image composed of u positions.
10. The pile integrity detection method based on stress wave analysis according to claim 7, characterized in that: The adjusting of the reflected wave time convolution network according to the position discrimination value includes: If the position discrimination value is 0, the value in the switch structure is set to 1; Obtaining an influence ratio; the influence ratio indicates reducing the attention level of unaffected positions; If the position discrimination value is 1, the value in the switch structure is set to the influence ratio to obtain an adjusted reflected wave time convolution network; the adjusted reflected wave time convolution network indicates that the attention level of the reflected signal at the affected position is reduced.
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