Hearth center line online determination method based on expansion detector

Abstract

The invention discloses a hearth center line on-line determination method based on an expansion detector, which comprises the following steps of: combining hearth geometrical characteristics with a water wall expansion detector signal to form an absolute coordinate sample, and fitting front, rear, left and right wall surfaces by adopting random sample consensus RANSAC and an overall least square method to obtain a wall surface equation during on-line operation; a closed quadrangle is obtained by horizontally transecting four wall surfaces, the center of gravity of the quadrangle is solved, and the geometric center line of the hearth is determined through an RANSAC algorithm by taking three-dimensional coordinates of the centers of gravity of a plurality of sections as samples, so that the center line of the hearth is predicted under the non-stop condition; the predicted center line of the hearth is compared with the designed center line, so that the deviation angle of the center line can be obtained; the deviation angle of the center line can be used as an alternative index for boiler operation state evaluation and fault early warning, and the potential of improving the boiler operation safety is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of boiler detection, and in particular to an online method for determining a furnace centerline based on an expansion detector. Background Art

[0002] In order to allow each part of the boiler body to have sufficient thermal expansion, large power station boilers adopt a fully suspended structure. In order to calculate the thermal expansion displacement of power station boilers more accurately, so as to carry out system stress analysis and sealing design, an expansion center that remains unchanged under various working conditions is generally artificially specified as the zero point for thermal expansion displacement calculation. The position of the expansion center is determined by the furnace type. For various forms of single-furnace boilers, the vertical expansion zero point of the boiler is set at the top of the large plate beam, and the depth and width expansion zero points of the boiler are set at the center of the furnace.

[0003] When the boiler is running, the geometric center of the boiler furnace may deviate from its design condition as the operating conditions change, and the deviation state cannot be directly measured at present; if the furnace centerline can be determined online when the boiler is running, it will be of great significance for the boiler furnace expansion monitoring and boiler combustion state diagnosis. Summary of the invention

[0004] In view of the problems existing in the prior art, the present invention provides an online method for determining the center line of a furnace based on an expansion detector, which has a reasonable design and high calculation accuracy.

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

[0006] A method for online determination of a furnace centerline based on an expansion detector comprises the following steps:

[0007] Step 1) coordinate data acquisition; the starting point of the furnace center is set at the furnace top pipe as the zero point of the Z axis; the X axis takes the symmetric center line of the furnace in the direction of the front and rear walls, and the Y axis takes the symmetric center line of the furnace in the direction of the left and right side walls; expansion detectors are arranged on the front, rear, left and right walls respectively, and the three-dimensional expansion value of each installation point is obtained through the expansion detector; the geometric characteristics of the furnace are combined with the three-dimensional expansion signal of the water-cooled wall to form the absolute coordinates during online operation;

[0008] Step 2) Eliminate abnormal values ​​of the expansion detector; Construct a matrix P for the synthesized three-dimensional coordinates f (t), P b (t), P l (t) and P r (t), using the RANSAC algorithm to remove outliers and improve the wall fitting accuracy;

[0009] Step 3) after eliminating the expansion detector data points of the front, rear, left and right walls, the equations of the four walls are determined in a three-dimensional coordinate system;

[0010] Step 4) Obtain centerline data by horizontally cross-sectioning the four walls; after obtaining the plane equations of the front wall, rear wall, left wall, and right wall at time t, cross-section the four walls with a horizontal plane, and take the center of gravity of the quadrilateral to construct a data sample for subsequent determination of the furnace centerline;

[0011] Step 5) Determine the furnace center line: The furnace center point matrix P obtained in step 4) g , the RANSAC algorithm is used to determine the furnace centerline.

[0012] Furthermore, the specific process of step 1) is as follows:

[0013] Step 1.1) Obtaining coordinate data of cold expansion detector: Assume that N f expansion detector, with matrix P f (0) represents the three-dimensional coordinates of the front wall expansion detector in the cold state, where The number of expansion detectors installed on the rear wall is N b , with the matrix P b (0) indicates the installation coordinates of the expansion detector on the rear wall in the cold state; the number of expansion detectors installed on the left wall is N l , with the matrix P l (0) indicates the installation coordinates of the expansion detector on the left wall in the cold state; the number of expansion detectors installed on the right wall is N r , with the matrix P r (0) represents the installation coordinates of the right wall expansion detector in the cold state; where P f (0), P b (0), P l (0) and P r (0) According to the furnace geometry and the installation position of the expansion detector, data collection is completed in an offline state;

[0014] Step 1.2) Acquisition of expansion detector coordinate data during operation: Assume that N r expansion detectors, and the three-dimensional readings obtained from expansion detector i at time t when the boiler is running are and The X- and Y-direction readings are consistent with the theoretical expansion direction; thus, the absolute coordinate P of the expansion detector i at time t is obtained. r i (t):

[0015]

[0016] N r The three-dimensional coordinates of the data from the expansion detectors form a matrix P r (t); Similarly, the three-dimensional coordinates of the other three walls constitute the matrix P b(t), matrix P f (t) and the matrix P l (t).

[0017] Furthermore, the specific process of step 2) is as follows:

[0018] Step 2.1) Group the expansion detectors according to the front, rear, left and right walls of the furnace, and use the four surface data to fit the furnace wall surface; where the matrix P f (t) for front wall fitting, P b (t) for back wall fitting, P l (t) is used for left wall fitting, P r (t) is used for right wall fitting;

[0019] Step 2.2) Expansion detector outlier removal based on RANSAC: Taking the previous wall fitting as an example, from the data matrix P f (t) Randomly select three points and determine whether the three points are collinear. If so, reselect the points. If not, calculate the plane equations corresponding to the three points.

[0020] z=ax+by+c (3)

[0021] Calculate the matrix P f The distance from each point in (t) to the plane shown in formula (3):

[0022]

[0023] Calculate the distance d from each point to the plane i Standard Deviation of:

[0024]

[0025] Where n = N f -3, Take the threshold t = 2σ; when d i >tThe point is considered an invalid point and deleted; otherwise, it is retained as a valid point and the number of valid points is counted; repeat the above steps, iterate K times, compare and select the model with the largest number of valid points, and record the number of valid points as M f ;

[0026] Step 2.3) Back wall matrix P b (t), left wall matrix P l (t) and the right wall matrix P r (t) is also processed using the RANSAC algorithm in step 2.2), the abnormal data in the data matrix is ​​deleted, and the number of valid points of the back wall, left wall, and right wall are recorded as M respectively. b 、M l and Mr .

[0027] Furthermore, the specific process of step 3) is as follows:

[0028] Step 3.1) Taking the front wall as an example, plane fitting based on the overall least squares method;

[0029] Assume the front wall plane equation is:

[0030] z=ax+by+c (6)

[0031] Use the M obtained in step 2) f Valid points {(x i ,y i ,z i )i=1,2,…,M f}, considering that there are errors in the three directions of x, y, and z, formula (6) can be rewritten as:

[0032] z+υ z =a(x+υ x )+b(y+υ y )+c (7)

[0033] In the formula, υ x ,υ y ,υ z are the error correction values ​​in the X, Y, and Z directions respectively; formula (7) is rearranged as follows:

[0034] (A+E A )X=L+E L (8)

[0035] in,

[0036] Step 3.2) Use the matrix singular value decomposition method to solve equation (8) and obtain:

[0037] X=(A T A-Ω 2 I) -1 A T L (9)

[0038] Where Ω is the minimum eigenvalue of the augmented matrix [AL]. After obtaining the solution through equation (9), we can then replace X = [abc] T Substituting into equation (6) we can obtain the front wall plane equation;

[0039] Step 3.3) The plane equations of the rear wall, the left wall and the right wall are also calculated using steps 3.1 and 3.2, that is, the plane equations of the four walls of the furnace at time t when the boiler is running are obtained.

[0040] Furthermore, the specific process of step 4) is as follows:

[0041] Step 4.1) Take a horizontal plane and cut through the four walls to obtain a closed quadrilateral. Let the coordinates of the center of gravity of the quadrilateral be (x gk ,y gk ,z k ), where z k Depending on the horizontal section position, x gk and gk Represents the centroid of a quadrilateral; the number of cross-sections is N s , then we get N s The center of gravity of each horizontal section is the intersection of the center line of the furnace and the cross section, passing through N s The centerline equation of the furnace can be determined by the coordinates of the center of gravity; s The coordinates of the center of gravity obtained by the second cross-section are expressed as a matrix P g ;

[0042] Step 4.2) Find the centroid of the horizontally cut quadrilateral:

[0043] Take the origin (0,0,0) as the starting point of the furnace center, the distance z k The horizontal section k intersects with the four wall planes to form a quadrilateral. The coordinates of the four vertices of the quadrilateral are (x 1 ,y 1 )、(x 2 ,y 2 )、(x 3 ,y 3 ) and (x 4 ,y 4 ), then the coordinates of the center of gravity of the quadrilateral (x gk ,y gk ) is calculated as follows:

[0044]

[0045] The coordinates of the center of gravity of the joint quadrilateral (x gk ,y gk ) and distance z k The furnace center point (x gk ,y gk ,z k ); Repeat the above process until the cross section N s times, get N s points in three-dimensional space, defined as the matrix P g .

[0046] Furthermore, the specific process of step 5) is as follows:

[0047] Step 5.1) Use the RANSAC algorithm to determine the equation of the line. Since the furnace adopts a hanging structure, the center line passes through the hanging point (0,0,0), so from the matrix P g Calculate the center point of i sections, denoted as (x i ,y i ,z i ), that is, determine the center line equation;

[0048] Step 5.2) Calculate the distance d from all other points to the line, by setting the threshold T d , all d <T d The points are called interior points, and the number of interior points is counted;

[0049] Step 5.3) Repeat steps 5.1) and 5.2), set the number of loops N, and at the end of the loop, select the one with the largest number of internal points as the optimal result. The straight line equation at this time is the center line of the furnace at time t.

[0050] The design ideas of the present invention are as follows: ① The geometric characteristics of the furnace are first combined with the signal of the water-cooled wall expansion detector to form an absolute coordinate sample, and then the random sample consensus (RANSAC) and the overall least squares method are used to fit the front, rear, left and right walls to obtain the wall equation during online operation; ② A closed quadrilateral is obtained by horizontally cross-cutting the four walls and the center of gravity of the quadrilateral is obtained. The three-dimensional coordinates of the center of gravity of multiple sections are used as samples, and the furnace geometric center line is determined by the RANSAC algorithm to achieve the prediction of the furnace center line without stopping the machine; ③ The predicted furnace center line is compared with the designed center line to obtain the offset angle of the center line; the offset angle of the center line can be used as an alternative indicator for boiler operation status evaluation and fault warning, and has the potential to improve the safety of boiler operation.

[0051] The beneficial effects of the present invention are as follows:

[0052] 1. The present invention proposes a method for online prediction of the furnace centerline by combining furnace geometric features with the signal of the water-cooled wall expansion detector. The deviation angle of the centerline can be used as an indicator for boiler operation status evaluation and fault warning, which has the potential to improve boiler operation safety;

[0053] 2. The present invention classifies the data according to the installation positions of the expansion detectors on the four walls, and adopts the RANSAC algorithm to propose abnormal data and fit the plane equations of the front, back, left and right walls using the overall least squares method; the wall fitting accuracy is improved by eliminating abnormal data and considering errors;

[0054] 3. The present invention predicts the center line of the furnace by horizontally cutting four walls and using the centroid coordinates of multiple cross-sectional quadrilaterals. When the RANSAC algorithm determines the center line, the origin is used as one of the straight line determination points. By reducing the degree of freedom, the physical constraint of the center line passing through the origin is ensured, making this patent more feasible on site. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 A schematic diagram for determining the centerline of the furnace of the present invention;

[0056] Figure 2 It is a schematic diagram of coordinate synthesis of the expansion detector of the present invention;

[0057] Figure 3 A flow chart of online determination of the boiler centerline based on expansion detection of the present invention;

[0058] Figure 4 It is a horizontal cross-sectional schematic diagram of the present invention;

[0059] Figure 5 It is a schematic diagram of the centroid of the quadrilateral of the four walls of the furnace of the present invention. DETAILED DESCRIPTION

[0060] The present invention is further described below in conjunction with the accompanying drawings.

[0061] A method for online determination of a furnace centerline based on an expansion detector, characterized in that it comprises the following steps:

[0062] Step 1: Acquire coordinate data. Figure 1 The figure shows the schematic diagram of online determination of the center line of the suspended boiler furnace. The starting point of the furnace center is set at the furnace top pipe as the zero point of the Z axis; the X axis takes the symmetric center line of the furnace in the direction of the front and rear walls, and the Y axis takes the symmetric center line of the furnace in the direction of the left and right side walls. Figure 1 As shown. Different numbers of expansion detectors are arranged on the front, rear, left and right walls, up to dozens in total, and the three-dimensional expansion value of each installation point can be obtained through the expansion detector. The present invention combines the furnace geometric features with the three-dimensional expansion signal of the water-cooled wall to form the absolute coordinates during online operation, and performs subsequent processing based on the sample, so the data acquisition process can be divided into the following two sub-steps.

[0063] Step 1.1, obtain the coordinate data of the cold expansion detector. Figure 1 As shown in the figure, point o is selected as the origin of the coordinates. According to the boiler design parameters and the installation position of the expansion detector, the three-dimensional coordinates of each expansion detector when the boiler is cold can be obtained. f expansion detector, with matrix P f (0) represents the three-dimensional coordinates of the front wall expansion detector in the cold state, where The number of expansion detectors installed on the rear wall is N b , with the matrix P b (0) indicates the installation coordinates of the expansion detector on the rear wall in the cold state; the number of expansion detectors installed on the left wall is N l , with the matrix P l (0) indicates the installation coordinates of the expansion detector on the left wall in the cold state; the number of expansion detectors installed on the right wall is N r , with the matrix P r (0) indicates the installation coordinates of the expansion detector on the right wall in the cold state. f (0), P b (0), P l (0) and P r (0) According to the geometric dimensions of the furnace and the installation position of the expansion detector, data collection is completed in an offline state.

[0064] Step 1.2, acquisition of expansion detector coordinate data during operation. When the boiler is cold, the three-dimensional expansion value of the expansion detector is generally set to 0, and the expansion reading represents the relative change between the boiler operation and the cold state. When the boiler is running, the water-cooled wall will deform according to the operating state, and three-dimensional expansion will occur at the expansion detection installation point, which is expressed by the expansion detector reading.

[0065] Figure 2 In the right wall, N r expansion detectors, and the three-dimensional readings obtained from expansion detector i at time t when the boiler is running are and The X- and Y-axis readings are consistent with the theoretical expansion direction of the point. This allows us to obtain the absolute coordinates of the expansion detector i at time t.

[0066]

[0067] The absolute coordinates of the other expansion detectors on the right wall are processed in the same way. r After the data of the expansion detectors are processed, the synthesized three-dimensional coordinates form a matrix P r (t). The absolute coordinates of the rear wall expansion detector are also processed in a similar way, such as Figure 2 As shown, at time t, a three-dimensional reading is obtained from the rear wall expansion detector i and Then the absolute coordinates of the rear wall expansion detector i at time t are Can be expressed as

[0068]

[0069] Back Wall N bAfter the data of the expansion detectors are processed, the three-dimensional coordinates at time t are combined into a matrix P b (t). The absolute coordinates of the expansion detectors of the front wall and the left wall are processed in the same way to obtain the matrices P f (t) and P l (t), I will not repeat it here, the process is shown in Figure 3 shown.

[0070] Step 2: Remove abnormal values ​​of the expansion detector. f (t), P b (t), P l (t) and P r There may be abnormal data values ​​in (t). The RANSAC algorithm is used to remove the abnormal values ​​and improve the wall fitting accuracy.

[0071] Step 2.1, group the expansion detectors according to the front, rear, left and right walls of the furnace, and use the data of the four surfaces to fit the furnace wall surface. Data matrix P f (t) for front wall fitting, P b (t) for back wall fitting, P l (t) is used for left wall fitting, P r (t) is used for right wall fitting.

[0072] Step 2.2, RANSAC-based expansion detector outlier removal. Take the previous wall fitting as an example to illustrate. From the data matrix P f Randomly select 3 points from (t) and determine whether these 3 points are collinear. If they are collinear, reselect them. If they are not collinear, calculate the plane equation corresponding to these 3 points.

[0073] z=ax+by+c (3)

[0074] Calculate P f The distances from other points in (t) to the plane shown in equation (3)

[0075]

[0076] Calculate the distance d from each point to the plane i Standard Deviation

[0077]

[0078] Where n = N f -3, Take the threshold value t = 2σ. When d i>tThe point is considered an invalid point and deleted; otherwise, it is considered a valid point and retained, and the number of valid points is counted. Repeat the above steps, iterate k times, compare and select the model with the largest number of valid points, and record the number of valid points as M f The number of iterations k can be inferred based on the specific situation.

[0079] Step 2.3, back wall data matrix P b (t), left wall data matrix P l (t) and the right wall data matrix P r (t) is also processed using RANSAC as shown in step 2.2, the abnormal data in the data matrix is ​​deleted, and the number of valid points of the back wall, left wall, and right wall are recorded as M respectively. b 、M l and M r .

[0080] Step 3: After removing the expansion detector data points of the front, rear, left and right walls, Figure 1 Determine the equations of the four walls in the three-dimensional coordinate system shown in the figure. The process is shown in Figure 3 shown.

[0081] Step 3.1, take the front wall as an example to illustrate the plane fitting based on the global least squares method. The global least squares method is an improved algorithm developed on the basis of the least squares method.

[0082] Assume the front wall plane equation is

[0083] z=ax+by+c (6)

[0084] Using the M obtained in step 2 f Valid points {(x i ,y i ,z i )i=1,2,…,M f}, considering that there are errors in the three directions of x, y, and z, formula (6) can be rewritten as

[0085] z+υ z =a(x+υ x )+b(y+υ y )+c (7)

[0086] In the formula, υ x ,υ y ,υ z are the error correction values ​​in the three directions of X, Y, and Z respectively. Formula (7) can be rearranged as

[0087] (A+E A )X=L+E L (8)

[0088] in,

[0089] Step 3.2, use the matrix singular value decomposition method to solve equation (8), and we can get

[0090] X=(A T A-Ω 2 I) -1 A T L (9)

[0091] Where Ω is the minimum eigenvalue of the augmented matrix [AL]. The matrix singular value decomposition algorithm is not described here. After obtaining the solution through equation (9), we can replace X = [abc] T Substituting into equation (6) we can obtain the front wall plane equation.

[0092] Step 3.3, the plane equations of the back wall, left wall and right wall are also calculated using steps 3.1 and 3.2, such as Figure 3 As shown, the plane equations of the four walls of the furnace at time t when the boiler is running can be obtained.

[0093] Step 4: Obtain centerline data by horizontally cross-sectioning the four walls. After obtaining the plane equations of the front wall, rear wall, left wall, and right wall at time t, cross-section the four walls with a horizontal plane, and take the center of gravity of the quadrilateral to construct a data sample for subsequent determination of the furnace centerline.

[0094] Step 4.1, take a horizontal plane and cross the four walls to obtain a closed quadrilateral. Let the coordinates of the center of gravity of the quadrilateral be (x gk ,y gk ,z k ), where z k Depending on the horizontal section position, x gk and gk represents the centroid of the quadrilateral. The number of cross-sections is N s , we can get N s The barycentric coordinates, such as Figure 4 The center of gravity of the quadrilateral of each horizontal section is the intersection of the center line of the furnace and the cross section, passing through N s The centerline equation of the furnace can be determined by the coordinates of the center of gravity. s The coordinates of the center of gravity obtained by the second cross-section are expressed as a matrix P g .

[0095] Step 4.2, find the centroid of the horizontally cut quadrilateral. Take the distance z from the origin (0,0,0) k The horizontal section k of intersects with the four wall planes to form a quadrilateral, such as Figure 5 As shown. The coordinates of the four vertices of the quadrilateral are (x 1 ,y1 )、(x 2 ,y 2 )、(x 3 ,y 3 ) and (x 4 ,y 4 ), then the coordinates of the center of gravity of the quadrilateral (x gk ,y gk ) can be calculated as follows

[0096]

[0097]

[0098] The coordinates of the center of gravity of the joint quadrilateral (x gk ,y gk ) and distance z k The furnace center point (x gk ,y gk ,z k ). Repeat the above process until the intersection of N s times, we can get N s points in three-dimensional space, defined as the matrix P g .

[0099] Step 5: Determine the center line of the furnace. The furnace center point matrix P obtained in step 4 g , the RANSAC algorithm is used to determine the furnace centerline.

[0100] Step 5.1, the present invention uses the RANSAC algorithm to determine the straight line equation. Since the furnace adopts a hanging structure, the center line passes through the hanging point (0,0,0), so from the matrix P g Calculate the i interface center points, denoted as (x i ,y i ,z i ), the pre-centerline equation can be determined.

[0101] Step 5.2, calculate the distance d from all other points to the line, by setting the threshold T d , all d <T d The points are called interior points, and the number of interior points is counted.

[0102] Step 5.3, repeat steps 5.1 and 5.2, set the number of loops N, and at the end of the loop, select the one with the largest number of internal points as the optimal result. The equation of the straight line at this time is the center line of the furnace at time t.

[0103] In the process of determining the furnace centerline, two parameters need to be adjusted: threshold T dThis patent uses the RANSAC algorithm to determine the center line of the furnace. When selecting points, the origin (0,0,0) is fixed as one of the points to ensure that the center line of the furnace passes through the hanging point. If the least square method is used, it is difficult to ensure this physical constraint.

[0104] The present invention combines the furnace geometric characteristics with the water-cooled wall expansion detector signal to predict the furnace centerline online when the boiler is running. The offset angle of the centerline can be used as an indicator for boiler operating status evaluation and fault warning, and has the potential to improve the safety of boiler operation.

[0105] The RANSAC+global least squares method proposed in the present invention can improve the fitting accuracy of the four walls, and the adopted RANSAC centerline determination method can meet the physical constraint that the centerline passes through the origin, and has stronger on-site feasibility.

[0106] The above embodiments are only preferred embodiments of the present invention and are not limitations of the technical solutions of the present invention. Any technical solution that can be implemented on the basis of the above embodiments without creative work should be deemed to fall within the scope of protection of the patent of the present invention.

Claims

1. A method for online determination of the center line of a furnace based on an expansion detector, characterized in that: The following steps are involved: Step 1) Coordinate data acquisition; the starting point of the furnace center is set at the furnace top pipe as the zero point of the Z axis; the X axis takes the symmetric center line of the furnace in the direction of the front and rear walls, and the Y axis takes the symmetric center line of the furnace in the direction of the left and right side walls; expansion detectors are arranged on the front, rear, left and right walls respectively, and the three-dimensional expansion value of each installation point is obtained through the expansion detector; the geometric characteristics of the furnace are combined with the three-dimensional expansion signal of the water-cooled wall to form the absolute coordinates during online operation, and after data processing, the three-dimensional coordinates of the front, rear, left and right walls are obtained to form a matrix P f (t), P b (t), P l (t) and P r (t); Step 2) Eliminate abnormal values ​​of the expansion detector; Construct a matrix P for the synthesized three-dimensional coordinates f (t), P b (t), P l (t) and P r (t), using the RANSAC algorithm to remove outliers and improve the wall fitting accuracy; Step 3) after eliminating the expansion detector data points of the front, rear, left and right walls, the equations of the four walls are determined in a three-dimensional coordinate system; Step 4) Obtain centerline data by horizontally cross-sectioning the four walls; after obtaining the plane equations of the front wall, rear wall, left wall, and right wall at time t, cross-section the four walls with a horizontal plane, take the center of gravity of the quadrilateral to construct a data sample, and obtain the furnace center point matrix P g ; Step 5) Determine the furnace center line: The furnace center point matrix P obtained in step 4) g , the RANSAC algorithm is used to determine the furnace centerline.

2. The method for online determination of the furnace centerline based on an expansion detector according to claim 1, characterized in that: The specific process of step 1) is as follows: Step 1.1) Obtaining coordinate data of cold expansion detector: Assume that the front wall is installed with N f expansion detector, with matrix P f (0) represents the three-dimensional coordinates of the front wall expansion detector in the cold state, where The number of expansion detectors installed on the rear wall is N b , with the matrix P b (0) indicates the installation coordinates of the expansion detector on the rear wall in the cold state; the number of expansion detectors installed on the left wall is N l , with the matrix P l (0) indicates the installation coordinates of the expansion detector on the left wall in the cold state; the number of expansion detectors installed on the right wall is N r , with the matrix P r (0) indicates the installation coordinates of the expansion detector on the right wall in the cold state; Step 1.2) Acquisition of expansion detector coordinate data during operation: Assume that N r expansion detectors, and the three-dimensional readings obtained from expansion detector i at time t when the boiler is running are and The X- and Y-direction readings are consistent with the theoretical expansion direction; thus, the absolute coordinates of the expansion detector i at time t are obtained. N r The three-dimensional coordinates of the data from the expansion detectors form a matrix P r (t); Similarly, the three-dimensional coordinates of the other three walls constitute the matrix P b (t), matrix P f (t) and the matrix P l (t).

3. The method for online determination of the furnace centerline based on an expansion detector according to claim 1, characterized in that: The specific process of step 2) is as follows: Step 2.1) Group the expansion detectors according to the front, rear, left and right walls of the furnace, and use the four surface data to fit the furnace wall surface; where the matrix P f (t) for front wall fitting, P b (t) for back wall fitting, P l (t) is used for left wall fitting, P r (t) is used for right wall fitting; Step 2.2) Expansion detector outlier removal based on RANSAC: Taking the previous wall fitting as an example, from the data matrix P f Randomly select three points in (t) and determine whether the three points are collinear. If they are collinear, reselect them. If they are not collinear, calculate the plane equation corresponding to the three points: z=ax+by+c (3) Calculate the matrix P f The distance from each point in (t) to the plane shown in formula (3): Calculate the distance d from each point to the plane i Standard Deviation of: Where n = N f -3, Take the threshold t = 2σ; when d i >tThe point is considered an invalid point and deleted; otherwise, it is retained as a valid point and the number of valid points is counted; repeat the above steps, iterate K times, compare and select the model with the largest number of valid points, and record the number of valid points as M f ; Step 2.3) Back wall matrix P b (t), left wall matrix P l (t) and the right wall matrix P r (t) is also processed using the RANSAC algorithm in step 2.2), the abnormal data in the data matrix is ​​deleted, and the number of valid points of the back wall, left wall, and right wall are recorded as M respectively. b 、M l and M r .

4. The method for online determination of the furnace centerline based on an expansion detector according to claim 1, characterized in that: The specific process of step 3) is as follows: Step 3.1) Taking the front wall as an example, plane fitting based on the overall least squares method; Assume the front wall plane equation is: z=ax+by+c (6) Use the M obtained in step 2) f Valid points {(x i ,y i ,z i )i=1,2,…,M f }, considering x, There are errors in the y and z directions, and equation (6) can be rewritten as: z+u z =a(x+υ x )+b(y+υ y )+c (7) In the formula, υ x ,υ y ,υ z are the error correction values ​​in the X, Y, and Z directions respectively, and a, b, and c are polynomial coefficients; formula (7) is rearranged as follows: (A+E A )X=L+E L (8) Among them, Step 3.2) Use the matrix singular value decomposition method to solve equation (8) and obtain: X=(A T A-Ω 2 I) -1 A T L (9) Where Ω is the minimum eigenvalue of the augmented matrix [AL]. After obtaining the solution through equation (9), we can then replace X = [abc] T Substituting into equation (6) we obtain the front wall plane equation, where I represents the unit matrix; Step 3.3) The plane equations of the rear wall, the left wall and the right wall are also calculated using steps 3.1 and 3.2, that is, the plane equations of the four walls of the furnace at time t when the boiler is running are obtained.

5. The method for online determination of the furnace centerline based on an expansion detector according to claim 1, characterized in that: The specific process of step 4) is as follows: Step 4.1) Take a horizontal plane and cut through the four walls to obtain a closed quadrilateral. Let the coordinates of the center of gravity of the quadrilateral be (x gk ,y gk ,z k ), where z k Depending on the horizontal section position, x gk and gk Represents the centroid of a quadrilateral; the number of cross-sections is N s , then we get N s The center of gravity of each horizontal section is the intersection of the center line of the furnace and the cross section, passing through N s The centerline equation of the furnace can be determined by the coordinates of the center of gravity; s The coordinates of the center of gravity obtained by the second cross-section are expressed as a matrix P g ; Step 4.2) Find the centroid of the horizontally cut quadrilateral: Take the distance z from the origin (0,0,0) k The horizontal section k of the quadrilateral intersects with the planes of the four walls to form a quadrilateral, where the origin (0,0,0) is the starting point of the furnace center; the coordinates of the four vertices of the quadrilateral are (x1,y1), (x2,y2), (x3,y3) and (x4,y4), then the coordinates of the centroid of the quadrilateral (x gk ,y gk ) is calculated as follows: The coordinates of the center of gravity of the joint quadrilateral (x gk ,y gk ) and distance z k The furnace center point (x gk ,y gk ,z k ); Repeat the above process until the cross section N s times, get N s points in three-dimensional space, defined as the matrix P g .

6. The method for online determination of the furnace centerline based on an expansion detector according to claim 1, characterized in that: The specific process of step 5) is as follows: Step 5.1) Use the RANSAC algorithm to determine the equation of the straight line. Since the furnace adopts a suspended structure, the center line passes through the origin (0,0,0), so from the matrix P g The center points of the i cross sections are calculated in sequence, denoted as (x i ,y i ,z i ), which is determined as the pre-centerline equation; Step 5.2) Calculate the distance d from other intersection points to the straight line by setting the threshold T d , all d <T d The point of becomes the interior point; Step 5.3) Repeat steps 5.1) and 5.2), set the number of cycles N, and when the cycle ends, the one with the most internal points is taken as the optimal result, and the straight line equation at this time is the center line of the furnace at time t.

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