Optimization method of engineering monitoring data

Abstract

The invention relates to the technical field of engineering monitoring, provides an engineering monitoring data optimization method, and is used for solving the problems of large data error and high discreteness. The core of the method is that data credibility is optimized through synchronous acquisition and fusion of double-source data in combination with a Kalman filtering thought. The method comprises the following steps: performing weighted fusion on two groups of monitoring data to generate an optimal value and an error; recursively calculating a recursive value according to a time sequence, and inhibiting error accumulation; and performing self-inspection on six items of data including actual acquisition, recursion and fusion, eliminating abnormal values based on a mean value, a median and a threshold value, and finally determining a reliable truth-like value. Compared with the prior art, the method has the advantages that the data consistency is remarkably improved, human and equipment errors are reduced, and the processing efficiency is optimized. Taking Guangzhou Xiaozhou station monitoring as an example, it is verified that the method can effectively smooth a monitoring curve and restore a real deformation trend. The method is suitable for various engineering monitoring scenes, provides high-precision data support for safety evaluation, and is wide in application prospect.

Description

Technical Field

[0001] The present invention belongs to the field of engineering monitoring, and particularly relates to an optimization method for engineering monitoring data. Background Art

[0002] In the field of engineering monitoring, the acquisition of monitoring point data is a crucial link, and its accuracy and reliability directly affect the assessment and judgment of the engineering safety status. Currently, there are mainly two ways to collect monitoring point data: engineering measurement determination type and direct equipment acquisition type.

[0003] The engineering measurement determination type relies on mature engineering measurement theories and methods to obtain data by measuring the elevation and plane coordinates of each monitoring point. This method has been widely used in monitoring projects such as the settlement, inclination, and horizontal displacement of buildings and structures. Due to the use of precise measurement techniques, it can better control the errors in the three-dimensional coordinate data of the monitored points to be measured, thereby ensuring that the monitoring data obtained by converting the three-dimensional coordinates of adjacent monitoring points has a relatively high credibility. However, although the engineering measurement determination type performs excellently in terms of data accuracy, its monitoring data still needs to be calculated through monitoring operation algorithms, and the propagation of errors may cause the original small errors to be amplified or reduced during the calculation process, resulting in a relatively large fluctuation range of the errors in the finally obtained monitoring data, enhancing the discreteness of the data, and reducing the credibility of the data.

[0004] On the other hand, the direct equipment acquisition type is to directly measure the data of specific monitoring items by using special tools or instruments. This method is mainly applied to monitoring projects such as support axial force, groundwater level, cracks in the ground surface and buildings and structures, blasting vibration velocity, and deep horizontal displacement of soil and walls. Although the direct equipment acquisition type has the advantages of simple operation and direct reading and recording, since it lacks a rigorous adjustment calculation process like the engineering measurement determination type to reduce errors, the data obtained often contains relatively large errors, and the data credibility is relatively low. In addition, the data accuracy of the direct equipment acquisition type is directly affected by the proficiency and experience of monitoring personnel. When the same monitoring point is collected by different personnel, the results may vary greatly, further increasing the error distribution range of the data.

[0005] In summary, the existing engineering monitoring data acquisition technologies have prominent problems such as relatively large monitoring data errors, strong data discreteness, and low credibility. Especially for the monitoring data of the direct equipment acquisition type, due to the lack of a complete error processing program, its data quality is even more difficult to guarantee. Summary of the Invention

[0006] In view of these problems, this application aims to draw on the ideas of data fusion, iteration, and Kalman filter in the field of information technology to limit the monitoring data errors and eliminate the monitoring data items with excessive discreteness, so as to obtain the optimal reliable approximate true value that can best reflect the deformation of the monitored object.

[0007] To achieve the above object, the technical solution provided by the present invention is as follows.

[0008] An optimization method for engineering monitoring data specifically includes the following steps:

[0009] Step 1: Two groups of monitoring teams use different instruments to collect data at the same monitoring point, and compare the two sets of data at the same point.

[0010] Step 2: Perform fusion processing on the data of the two groups of monitoring teams at the same monitoring point in the same time period:

[0011] Monitoring teams No. 1 and No. 2 collect two monitoring data at monitoring point A in the first time period, which are respectively denoted as l A-11 and l A-21 , and their corresponding mean square errors are m A-11 and m A-21 . Use and formulas to calculate the fused data L A-1 and the mean square error m A-1 at this monitoring point in the same time period; if you want to calculate the fused data l A-2 and the mean square error m A-2 collected at point A in the second time period, you can calculate according to the l A-12 and l A-22 collected at point A in the second time period and their corresponding mean square errors are m A-12 and m A-22 , and apply formulas (1-2) and (3) again. Repeating this way, the fused monitoring values at any time for any point A can be calculated;

[0012] Step 3: Calculate the recursive data of the same monitoring point for different monitoring teams in different time periods according to the time series:

[0013] The collection of monitoring point A in the first time period is called the initial value collection. The results of the initial value collection can use the fused monitoring data l A-1 and the mean square error m A-1 at point A. After the monitoring teams No. 1 and No. 2 collect the second monitoring value at point A, the recursive monitoring data and mean square error of each group at point A need to be calculated according to L K = L k-1 + K K ×(l k - L k-1 )(5) and formulas respectively; repeating this way, the recursive monitoring values and their mean square errors of monitoring team No. 1 at point A in any time series 1 2 3...K can be calculated. The calculation method of the recursive monitoring values and their mean square errors of monitoring team No. 2 in any time series is the same as the above method;

[0014] Step 4: Conduct data self-check on the actually collected monitoring data at the same point and the total of 6 newly generated data in the above steps, and eliminate data with excessive deviation:

[0015] Taking point A in the nth time period as an example, through the above calculations, 6 monitoring data of point A in the nth time period will be obtained, namely the actual collected value l of the first monitoring team A-1n , the recursive value L A-1n , the actual collected value l of the second monitoring team A-2n , the recursive value L A-2n , the actual collected fusion value L' of the first and second monitoring teams A-n , the recursive fusion value L of the first and second monitoring teams A-n ; Calculate the arithmetic mean, median and mean error of the arithmetic mean of the above 6 values of point A in the nth time period; Use to represent the set of observed values of point A in the nth time period; Use y to represent the arithmetic mean of , and m to represent the median of , that is and (1) Set a threshold ξ, and identify whether there are elements with excessive dispersion in by calculating the difference between y and m. The difference between y and m can be expressed as |y - m|. When |y - m| ≤ ξ, it indicates that all elements in are truly valid. If |y - m| > ξ, it indicates that there are elements with excessive dispersion in , and then eliminate them through subsequent steps.

[0016] The specific elimination process is as follows:

[0017] Calculate the mean error of the arithmetic mean of M y :

[0018]

[0019] With y as the center and 2M y as the radius, enclose a data set {y ± 2M y}, and find the elements in that are not in this data set, and then eliminate this element to form a new data set; Repeat multiple times until |y - m| of the finally formed data set ≤ ξ and then stop.

[0020] When the condition |y - m| ≤ ξ is satisfied, take the arithmetic mean of as the optimal reliable approximate true value of point A in the nth time period, that is

[0021] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0022] 1. Improve data accuracy: By means of the concept of data fusion and recursive calculation, combined with the idea of the Kalman filter, the error of the monitoring data is effectively limited. This method can significantly reduce the error influence caused by human operation and instrument equipment, making the monitoring data more accurate and reliable.

[0023] 2. Enhance data consistency: By fusing multiple groups of monitoring data at the same monitoring point in the same time period, the method of the present invention can ensure higher consistency of the data collected by different monitoring teams, reducing the data deviation caused by the operation differences of different monitoring teams.

[0024] 3. Optimize the data processing flow: The present invention proposes a systematic data processing flow, including steps such as data fusion, recursive calculation, and data self-check, effectively eliminating data items with too large discreteness, so as to obtain the optimal and reliable approximate true value.

[0025] This process not only improves the data processing efficiency, but also ensures the accuracy and stability of the processing results.

[0026] 4. Improve the quality of engineering monitoring: Applying the method of the present invention to the field of engineering monitoring can provide more accurate and reliable monitoring data analysis and judgment opinions for project supervision and management work, helping to timely discover and handle potential risks during the construction process, thereby improving the overall engineering quality and safety.

[0027] 5. Broad application prospects: The method of the present invention is applicable to various engineering construction fields, especially in the field of engineering monitoring, with broad application prospects. By promoting this method, the level and effect of engineering monitoring can be significantly improved, providing strong technical support for engineering construction. BRIEF DESCRIPTION OF THE DRAWINGS

[0028] Figure 1 is the flow chart of the technical solution of the present invention.

[0029] Figure 2 is the flow chart of step S2 of the present invention.

[0030] Figure 3 is the flow chart of step S3 of the present invention.

[0031] Figure 4 is the flow chart of step S4 of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0032] The present invention will be further described in detail below in conjunction with specific embodiments, but the embodiments of the present invention include, but are not limited to, the scope represented by the following embodiments.

[0033] 1. Calculation of the data fusion concept

[0034] Collect monitoring data for a certain monitoring point. Let the collected value of the No. 1 monitoring instrument be l1, and its collection mean square error be m1; the collected value of the No. 2 monitoring instrument be l2, and its collection mean square error be m2. Assume that since the collection accuracy of the No. 2 monitoring instrument is lower than that of the No. 1 monitoring instrument, then m2 > m1. Then the most probable value L of the monitoring data at this monitoring point is calculated as follows:

[0035] L = l1 + K × (l2 - l1)...............................(1-1)

[0036] L = (1 - K) × l1 + Kl2...............................(1-2)

[0037] In equation (1), K is the ratio coefficient of the mean square error. Apply the law of error propagation to equation (1-2) to calculate the mean square error m of the most probable value L L .

[0038]

[0039] To make m L minimum, take the derivative of equation (2) with respect to K and set it to zero, that is obtain:

[0040]

[0041] 2. Calculation with the concept of recursion

[0042] Collect monitoring data for a certain monitoring point. At this time, only one monitoring instrument is used for collection. To improve the collection accuracy, the monitoring point is collected K times. The first collected value is recorded as l1, the second collected value is recorded as l2,..., and the Kth collected value is recorded as l k , and finally take the arithmetic mean (the most probable value) L K as the final collected value.

[0043]

[0044] In equation (4), l k-1 is the collected value of the (k - 1)th time, and L k-1 is the arithmetic mean of the collected values from the 1st to the (k - 1)th time.

[0045] When the number of collections is determined, in equation (4) is a fixed value. For the convenience of expression, is denoted as K K , then equation (4) can be expressed as equation (5)

[0046] L K = Lk-1 +K K ×(l k -L k-1 )............................(5)

[0047] (5) The connotation of formula (5) is to use the quasi-true value collected last time by the same monitoring instrument to recursively calculate the quasi-true value collected next time, which is similar to the expression of formula (1-1). At this time, the calculation method of formula (3) can be applied to calculate K K , as shown in formula (6).

[0048]

[0049] In formula (6) is the mean square error of the arithmetic mean of the collected values from the 1st to the (k - 1)th time, is the mean square error of the kth collected value.

[0050] Through the above data fusion and recursive calculation, it is found that the expressions of the above formulas (1), (3), (5), and (6) are consistent with the principle formula of the Kalman filter in terms of the expression form. Therefore, referring to the calculation of its state update equation P K , it can be known that and satisfy the following relationship:

[0051]

[0052] In formula (7) is the mean square error of the arithmetic mean of the collected values from the 1st to the (k - 2)th time, and K K-1 is the mean square error ratio coefficient of the (k - 1)th time.

[0053] 3. Calculation of the optimal reliable quasi-true value

[0054] In actual monitoring work, in order to improve the authenticity and effectiveness of data, usually two groups of monitoring teams use different instruments to collect data at the same monitoring point, and compare the two groups of data at the same point to ensure data consistency. However, due to the existence of measurement errors, it is sometimes difficult to ensure data consistency. Therefore, the measured data needs to be optimized based on the above formulas (1)-(7) as follows.

[0055] 3.1 Perform fusion processing on the data of two groups of monitoring teams at the same monitoring point in the same time period.

[0056] Monitoring teams No. 1 and No. 2 collect two monitoring data at monitoring point A in the 1st time period, which are respectively recorded as l A-11 and l A-21 , and their corresponding mean square errors are m A-11 and m A-21, the fused data L of this monitoring point during the same time period can be calculated by applying equations (1-2), (2), and (3). A-1 and the mean error m A-1 . If you want to calculate the fused data l A-2 and the mean error m A-2 collected at point A during the second time period, A-12 and l A-22 and their corresponding mean error is m A-12 and m A-22 , applying equations (1-2) and (3) again and repeating this process, the fused monitoring values at any time for any point A can be calculated. Taking the second time period as an example, the calculation of the collected data L' A-2 is as follows:

[0057] L' A-2 = (1 - K) × l A-12 + K × l A-22

[0058]

[0059] 3.2 Calculate the recursive data of the same monitoring point with different numbers of monitoring teams in different time periods according to the time series.

[0060] During the monitoring work, the recursive data of monitoring point A by the No. 1 and No. 2 monitoring teams each time should be calculated according to the time series. The purpose is to reduce the error in the process of collecting monitoring data, thereby improving the collection accuracy.

[0061] The collection of monitoring point A in the first time period is called the initial value collection. The result of the initial value collection can use the fused monitoring data l A-1 and the mean error m A-1 . After the No. 1 and No. 2 monitoring teams collect the monitoring values of point A for the second time, the recursive monitoring data and mean error of each group at point A should be calculated according to equations (5) and (6). The following takes the No. 1 monitoring team as an example.

[0062] Assume that the actual collected value of point A by the No. 1 monitoring team in the second time period is l A-12 , and the mean error is m A-12 , then the recursive monitoring value L A-12 of point A in the second time period and its mean error The results are equations (8)-(10).

[0063] L A-12 = L A-1 + K2 × (l A-12 - L A-1 )............................(8)

[0064]

[0065] Assume that the actual measured value of Point A by the 1st monitoring team in the third time period is l A-13 , and the mean square error is m A-13 , then the recursive monitoring value L of Point A in the third time period A-13 and its mean square error The results are given by equations (10) and (11).

[0066] L A-13 = L A-12 + K3×(l A-13 - L A-12 )........................(11)

[0067]

[0068] In the above manner, by repeating this process, the recursive monitoring values and their mean square errors of Point A by the 1st monitoring team in any time series 1, 2, 3,..., K can be calculated. The calculation method for the recursive monitoring values and their mean square errors of the 2nd monitoring team in any time series is similar to the above.

[0069] 3.3 Perform fusion processing on the recursive data of different monitoring teams at the same monitoring point in the same time period.

[0070] Assume that it is necessary to calculate the recursively fused data L of the 1st and 2nd monitoring teams at Point A in the third time period A-3 , then calculated according to equations (1 - 2) and (3):

[0071] L A-3 = (1 - K)×L A-13 + K×L A-23 ........................(14)

[0072]

[0073] In equation (14), L A-13 is the recursive monitoring value of Point A by the 1st monitoring team in the third time period, and L A-23 is the recursive monitoring value of Point A by the 2nd monitoring team in the third time period. In equation (15), is the mean square error of the recursive monitoring value of Point A by the 1st monitoring team in the third time period, is the mean square error of the recursive monitoring value of Point A by the 2nd monitoring team in the third time period.

[0074] 3.4 Perform data self-check on the monitoring data actually collected at the same point and the total 6 items of data newly generated in the above "Steps 3.1 - 3.3", and eliminate the data with too large deviations.

[0075] Taking point A in the third time period as an example, at this time, 6 monitoring data of point A in the third time period will be obtained through the above calculations, which are the actual measured value l of the first monitoring team A-13 , the recursive value L A-13 , the actual measured value l of the second monitoring team A-23 , the recursive value L A-23 , the actual measurement fusion value L' of the first and second monitoring teams A-3 , the recursive fusion value L of the first and second monitoring teams A-3 . Calculate the arithmetic mean, median, and mean error of the arithmetic mean of the above 6 values of point A in the third (3) time period.

[0076] Use to represent the set of observed values of point A in the third (3) time period, use y to represent the arithmetic mean of , and use m to represent the median of , that is

[0077] (1) Set a threshold ξ, and identify whether there are elements with too large discreteness in by calculating the difference between y and m. The difference between y and m can be expressed as |y - m|. When |y - m| ≤ ξ, it indicates that all elements in are truly valid. If |y - m| > ξ, it indicates that there are elements with too large discreteness in, and then eliminate them through the subsequent steps (2) and (3).

[0078] (2) Calculate the mean error of the arithmetic mean of M y

[0079]

[0080] (3) Taking y as the center and 2M y as the radius, enclose a data set {y ± 2M y}, find the elements in that are not in this data set, and thus eliminate this element to form a new data set

[0081] (4) Repeat the above steps (1)--(3) until |y - m| of the finally formed data set ≤ ξ and then stop.

[0082] 3.5 Determination of the optimal reliable approximate true value

[0083] When the condition |y - m| ≤ ξ is satisfied, take The arithmetic mean is used as the optimal reliable approximate true value of point A in the third time period, that is

[0084] The above is illustrated by taking the optimal reliable approximate true value of point A in the third time period as an example, and its calculation principle can be extended to the calculation of the optimal reliable approximate true value of any point A' in the nth time period, and the result is denoted as

[0085] Embodiment

[0086] The above "technical solution content" theoretically explains the principle and steps of the optimization algorithm. Next, taking the monitoring data of Xiamao Station on the Guangzhou Fangbai Intercity Railway as an example, it is illustrated how to optimize it. See the following description for details.

[0087] Taking the deep horizontal displacement monitoring of the wall of ZQT2-2 at Xiamao Station as an example, the depth of the monitoring point ZQT2-2 is 42 meters. The horizontal displacement deformation of the retaining structure wall is measured every 0.5 meters along its depth. This monitoring work is monitored by the monitoring team of the construction unit and the third-party monitoring team respectively. The monitoring team of the construction unit monitors every day, with a measurement mean error of 4 mm, and the calculation period is from June 7, 2024 to July 14, 2024; the third-party monitoring team monitors every three days, with a measurement mean error of 6 mm, and the calculation period is from June 8, 2024 to July 14, 2024; within the calculation period, through the principle of recursion and fusion, that is, using the formula (1)-(7), the cumulative deformation value of the optimal approximate true value of the monitoring point ZQT2-2 on July 14 is calculated.

[0088] In the "Xiamao Station ZQT2-2 (Example Algorithm)" EXCEL table, the operation steps are as follows:

[0089] 1. List the monitoring data and mean error (measured error) actually measured by the monitoring team of the construction unit from June 7 to July 14 in the label of "ZQT2-2 6.7-7.14 Construction Monitoring Data Self-Recursion". Taking June 7 and its monitoring value as the initial date and initial value, calculate the recursive cumulative change amount of each measured date through the recursive method of formula (5)-(7) until the recursive cumulative change value and its mean error of the monitoring team of the construction unit on July 14 are calculated.

[0090] 2. List the monitoring data and mean error (measured error) actually measured by the third-party monitoring team from June 8 to July 14 in the label of "ZQT2-2 6.8-7.14 Third-Party Data Self-Recursion". Taking June 8 and its monitoring value as the initial date and initial value, calculate the recursive cumulative change amount of each measured date through the recursive method of formula (5)-(7) until the recursive cumulative change value and its mean error of the monitoring team of the construction unit on July 14 are calculated.

[0091] 3. List the measured values and mean errors of the construction party and the third party at the ZQT2-2 point on July 14th within the label "ZQT2-2 7.14 Construction Party and Third Party Measured Data Fusion", and calculate the cumulative change values and their mean errors after fusion between the two parties at every 0.5-meter depth according to equations (2) and (3).

[0092] 4. List the recursive optimal cumulative change values and their mean errors of the construction party and the third party at the ZQT2-2 point on July 14th within the label "ZQT2-2 6.7 Construction and Third Party Self-Recursive Data Fusion in the Same Time Period", and calculate the cumulative change values and their mean errors after fusion between the two parties at every 0.5-meter depth according to equations (2) and (3).

[0093] 5. Through the calculations in the above four steps, six cumulative change values (measured values, recursive values, and fusion values) at every 0.5-meter depth of the ZQT2-2 point will be obtained. Calculate the "7.14 Optimal Apparent Value and Its Mean Error" at every 0.5-meter depth through the method of "Data Self-Check, Eliminate Data with Excessive Deviations" (let ξ = 0.3) in Section 3.4 above, and draw the monitoring curve of the change along the depth with the calculated 7.14 optimal apparent value. For details, see the label "Determination of 7.14 Optimal Apparent Value".

[0094] In the label "7.14 ZQT2-2 Monitoring Curve Comparison", it can be found that there are many similarities and differences between the monitoring curve after recursive fusion calculation and the monitoring curves of the third party and the construction unit (measured). Through the algorithm of this patent, the data errors of the two monitoring teams are reduced, the monitoring curve is smoother and easier to express, and it is more consistent with the actual deformation form, which better reflects the objective deformation of the monitored object.

[0095] In summary, this invention patent proposes an innovative engineering monitoring data optimization method. Through the concepts of data fusion and recursive calculation, it effectively solves the problems of large mean errors and poor data consistency in existing engineering monitoring data. In practical applications, this method can significantly improve the accuracy and consistency of monitoring data, providing more reliable data support for project supervision and management work.

[0096] Through the implementation of this invention, the error effects brought by manual operations and instrument equipment are successfully reduced, making the monitoring data more accurate and reliable. At the same time, the application of this method also improves the quality and efficiency of engineering monitoring, providing strong technical support for engineering construction.

[0097] The engineering monitoring data optimization method proposed by this invention has significant beneficial effects and broad application prospects, and is worthy of popularization and application in the field of engineering construction.

Claims

1. A method for optimizing engineering monitoring data, characterized in that: The specific steps include: Step 1: Two monitoring teams use different instruments to collect data from the same monitoring point, and compare the two sets of data at the same point; Step 2: Fusion processing of the data of two monitoring teams at the same monitoring point and in the same time period: Monitoring teams 1 and 2 collect two monitoring data from monitoring point A in the first time period, which are recorded as l and A-11 and l A-21 , and its corresponding mean error is m A-11 and m A-21 , use L = (1-K) × l1 + Kl2 (1-2), and The formula is used to calculate the fused data L of the monitoring point in the same time period. A-1 and mean error m A-1 ; If you want to calculate the fused data collected at point A in the second time period l A-2 and mean error m A-2 , according to the second time period A point position collection l A-12 and l A-22 The corresponding mean error is m A-12 and m A-22 , apply (1-2) and (3) again, and repeat this process to calculate the fusion monitoring value of any point A at any time; Step 3: According to the time series, calculate the recursive data of the same monitoring point with different monitoring teams in different time periods: The collection of the first time period of monitoring point A is called initial value collection. The result of initial value collection can be used to calculate the monitoring data after fusion at point A. A-1 and mean error m A-1 After the No. 1 and No. 2 monitoring teams collect the second monitoring value of point A, they should K =L k-1 +K K ×(l k -L k-1 )(5) and The recursive monitoring data and mean square error of point A of each group are calculated by the formula respectively; in this way, the recursive monitoring value and mean square error of monitoring team No. 1 at point A in any time series 1 2 3…K can be calculated back and forth. The calculation method of the recursive monitoring value and mean square error of monitoring team No. 2 in any time series is consistent with the above method; Step 4: Perform a self-check on the monitoring data actually collected at the same point and the 6 newly generated data in the above steps, and remove the data with excessive deviation: Taking point A in the nth time period as an example, the above calculation will obtain 6 monitoring data of point A in the nth time period, which are the actual sampling value of monitoring team No. 1, A-1n , recursive value L A-1n , the actual value collected by the No. 2 monitoring team A-2n , recursive value L A-2n , the actual fusion value L' of monitoring teams 1 and 2 A-n , the recursive fusion value L of monitoring teams 1 and 2 A-n ; Calculate the arithmetic mean, median and error in the arithmetic mean of the above 6 values ​​of point A in the nth time period; use Represents the set of observations of point A in the nth time period; y is used to represent The arithmetic mean of The median of and (1) Set a threshold ξ and identify the Is there an element with too large a discrete value in the matrix? The difference between y and m can be expressed as |ym|. When |ym|≤ξ, it indicates All elements in are real and valid. If |ym|>ξ, it means If there are elements with too large discreteness, they will be removed in the subsequent steps.

2. The method for optimizing engineering monitoring data according to claim 1, characterized in that: In step 4, the specific elimination process is: Calculate M y The arithmetic mean error of : With y as the center, 2M y Define a data set for the radius {y±2M y }, find The elements that are not in this data set are removed to form a new Data set; repeat multiple times until the final data set is formed Stop when |ym|≤ξ.

3. The method for optimizing engineering monitoring data according to claim 2, characterized in that: When the condition |ym|≤ξ is satisfied, take The arithmetic mean of is taken as the optimal reliable plausibility value of point A in the nth time period, that is

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