A method for detecting outliers in slope deformation monitoring data

Abstract

The application discloses a kind of detection methods for outlier in slope deformation monitoring data, comprising the following steps: calculating the estimated value of measured data sequence in slope deformation monitoring data;The difference sequence of estimated value and measured value in slope deformation monitoring data is calculated;Mirror image processing is carried out on the difference sequence;Threshold is calculated to the difference sequence after mirror image;According to the threshold calculated, outlier in slope monitoring data is judged.The estimation result of measured value is good, and the outlier detection result is ideal, which can realize accurate, efficient and intelligent outlier detection.

Description

Technical Field

[0001] This invention belongs to the field of slope monitoring technology, and in particular relates to a method for detecting outliers in slope deformation monitoring data. Background Technology

[0002] Construction projects in high mountains and canyons often encounter various slope safety issues, as slope stability significantly impacts project safety. Therefore, slope safety monitoring is typically conducted, collecting data on slope deformation, groundwater levels, cracks, and microseismic activity for in-depth analysis. This allows for a better understanding and control of slope changes, ultimately ensuring slope safety and stability. However, a small number of outliers inevitably appear during data collection. These outliers may be caused by environmental interference or instrument malfunction, or they may contain crucial information about slope behavior changes; their causes are complex. Failure to promptly identify outliers will negatively impact subsequent data analysis and the accurate assessment of slope deformation.

[0003] Outlier detection methods typically include clustering-based, classification-based, statistical, or other algorithm-based approaches. Regardless of the algorithm, a suitable threshold needs to be determined as the criterion for determining whether data is an outlier. In hydropower engineering, statistical probability methods are commonly used to detect outliers in slope monitoring data, with the Raida criterion (3σ criterion) being the most widely applied. This method assumes that the data follows a normal distribution and uses three times the standard deviation σ of the data as the outlier criterion. If a data point exceeds 3σ, its occurrence is considered a low-probability event and thus an outlier. However, slope deformation monitoring data usually exhibits a certain trend and clearly does not conform to a normal distribution. Therefore, based on historical data, a regression model is typically established using methods such as statistical regression, neural networks, and time series analysis to estimate the deformation monitoring data. Then, a stationary difference sequence is obtained between the estimated and measured values, and a 3σ criterion is established on this difference sequence. When new data is acquired, it is only necessary to calculate whether the difference between the new value and the estimated value satisfies the 3σ criterion to detect whether the new data is an outlier. In building a regression model, it is essential to ensure that the training data consists of normal data; otherwise, outliers will negatively impact the modeling process. Therefore, for newly obtained experimental data, outlier detection is still necessary before modeling or other data analysis. While manual detection can be used when the data is limited, it is insufficient for large datasets and the demands of intelligent detection. Summary of the Invention

[0004] The purpose of this invention is to provide a method for detecting outliers in slope deformation monitoring data. This method provides good estimation results for measured values ​​and ideal outlier detection results, enabling accurate, efficient, and intelligent outlier detection.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for detecting outliers in slope deformation monitoring data, characterized by comprising the following steps:

[0007] S1, calculate the estimated value of the measured data sequence in the slope deformation monitoring data;

[0008] S2, calculate the sequence of differences between estimated and measured values ​​in the slope deformation monitoring data;

[0009] S3, mirror the difference sequence;

[0010] S4, calculate the threshold for the mirrored difference sequence;

[0011] S5, based on the calculated threshold, identifies outliers in the slope monitoring data.

[0012] Preferably, in step S1, the specific method for calculating the estimated value of the measured data sequence in the slope deformation monitoring data is the weighted moving average method.

[0013] Preferably, in step S1, the specific steps for calculating the estimated value of the measured data sequence in the slope deformation monitoring data include:

[0014] S101, calculate the estimated values ​​of the measured data at time c+1 and subsequent times;

[0015] S102, calculate the estimated value of the measured data at time c.

[0016] Preferably, in step S101, the formula for calculating the estimated values ​​of the measured data at time c+1 and subsequent times is as follows:

[0017]

[0018] Where: x' i Let x be the measured value at time i. i The estimated values; i = c+1, c+2, ..., n; x i-j Let be the measured data at time ij; j = 1, 2, ..., c; ω j For x i The weights corresponding to the data at the first j-th time step;

[0019] Preferably, the weight ω is calculated. j The specific steps include:

[0020] A1, Calculate the measured value x i c differences Δ between the first c measured values j x i The calculation formula is as follows:

[0021] Δ j x i =x i -x i-j

[0022] Where, x i Let x be the measured data at time i; i = c+1, c+2, ..., n; i-j Let be the measured data at time ij; j = 1, 2, ..., c;

[0023] A2, calculate the absolute value of the c differences |Δ j x i The formula for calculating | and s is as follows:

[0024]

[0025] Among them, |Δ j x i |for Δ j x i The absolute value of; j = 1, 2, ..., c;

[0026] A3, calculate the c variables w respectively. j The calculation formula is as follows:

[0027]

[0028] Where s is the absolute value of c differences |Δ j x i | and |Δ j x i |for Δ j x i The absolute value; j = 1, 2, ..., c; Δ j x i ≠0;

[0029] A4, calculate c variables w j The formulas for calculating S and S are as follows:

[0030]

[0031] Among them, w j There are c variables; j = 1, 2, ..., c;

[0032] A5, calculate the c weights ω respectively. j The calculation formula is as follows:

[0033]

[0034] Among them, w jThere are c variables; S has c variables w j The sum of; j = 1, 2, ..., c.

[0035] Preferably, in step S102, the formula for calculating the estimated value of the measured data at time c is as follows:

[0036]

[0037] Where: x′ i Let x be the measured value at time i. i Estimates; i = 1, 2, ..., c; x i+j The measured data is at time i+j; j = 1, 2, ..., c; ω j For x i The weights corresponding to the data at time j;

[0038] Preferably, the weight ω is calculated. j The specific steps include:

[0039] B1, Calculate the measured value x i The c differences Δ between the last c measured values j x i The calculation formula is as follows:

[0040] Δ j x i =x i+j -x i

[0041] Where, x i Let x be the measured data at time i; i = 1, 2, ..., c; i+j Let be the measured data at time i+j; j = 1, 2, ..., c.

[0042] B2, calculate the absolute value of the c differences |Δ j x i The formula for calculating | and s is as follows:

[0043]

[0044] Among them, |Δ j x i |for Δ j x i The absolute value of; j = 1, 2, ..., c;

[0045] B3, calculate the c variables w respectively. j The calculation formula is as follows:

[0046]

[0047] Where s is the absolute value of c differences |Δ j x i | and |Δ j x i |for Δ j x i The absolute value; j = 1, 2, ..., c; Δ j x i ≠0;

[0048] B4, calculate c variables w j The formulas for calculating S and S are as follows:

[0049]

[0050] Among them, w j There are c variables; j = 1, 2, ..., c;

[0051] B5, calculate the c weights ω respectively. j The calculation formula is as follows:

[0052]

[0053] Among them, w j There are c variables; S has c variables w j The sum of; j = 1, 2, ..., c.

[0054] Preferably, in step S3, the specific method of mirroring is as follows: take the opposite number of the difference sequence between the estimated value and the measured value, and then merge the two sequences into one sequence.

[0055] The beneficial effects of this invention are as follows: a weight calculation method is proposed for the weighted moving average (WMA) method, and then combined with the weighted moving average and the 3σ criterion, outlier detection can be performed on the original monitoring data, so as to discover outliers in the original data in a timely and accurate manner, and provide high-quality data for subsequent data analysis and modeling calculations. Attached Figure Description

[0056] Figure 1 The measured value and the added outliers together constitute the value to be detected.

[0057] Figure 2 These are the values ​​to be detected and the estimated values.

[0058] Figure 3 This is a sequence of differences between the value to be detected and the estimated value.

[0059] Figure 4 This is the outlier detection result of the mirrored difference sequence.

[0060] Figure 5 The results are for detecting outliers in the value to be detected.

[0061] Figure 6 This is a flowchart of the present invention. Detailed Implementation

[0062] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0063] Before performing outlier detection, the parameter 'c' must be determined to define the range of values ​​for the calculated estimate. 'c' represents the number of the preceding or following 'c' data points in the measured data sequence that are strongly correlated with a given data point. The value of 'c' is typically determined using correlation analysis, expert experience analysis, or a combination of methods. The methods for determining the value of 'c' are existing techniques and will not be described in detail here. After determining the parameter 'c', outlier detection can proceed.

[0064] like Figure 6 As shown, a method for detecting outliers in slope deformation monitoring data includes the following steps:

[0065] S1, calculate the estimated value of the measured data sequence in the slope deformation monitoring data.

[0066] Moving average is the basis of weighted moving average. Moving average works by progressively shifting the time series data, assigning equal weights to the observations of the previous n periods, and then averaging them to predict the data for the next period. The formula is as follows:

[0067]

[0068] Wherein: F i x is the estimated value at time i; i-n Let be the measured value at time in; n is the range of values.

[0069] The weighted moving average assigns different weights to data from the previous n periods to estimate data for the next period. The formula is as follows:

[0070] F i =(ω1x i-1 +ω2x i-2 +…+ω n x i-n (2)

[0071] Where: ω n Let be the weight corresponding to the measured value at time in.

[0072] The calculation of weights in the weighted moving average method is crucial, as the appropriateness of the weights directly affects the accuracy of the estimation results. Generally speaking, the most recent data is the best predictor of future conditions, and therefore should have a larger weight. This aligns perfectly with the slope deformation process; therefore, the weighted moving average method can be used to calculate the estimated values ​​of the measured data series in slope deformation monitoring data.

[0073] S101, calculate the estimated values ​​of the measured data at time c+1 and subsequent times.

[0074] Let a set of measured data sequences be represented as X = {x1, x2, ..., x...} n The formula for calculating the estimated value based on the weighted moving average method is as follows:

[0075]

[0076] Where: x′ i Let x be the measured value at time i. i The estimated values; i = c+1, c+2, ..., n; x i-j Let be the measured data at time ij; j = 1, 2, ..., c; ω j For x i The weights corresponding to the data at the first j-th time step;

[0077] Estimated value x′ i The initial value corresponds to the measured value at time c+1. ​​From equation (3), we know that the estimated value x′ i It is derived from the measured value x i The first c measured values ​​are multiplied by their corresponding weights and then summed to determine the result, with the calculation of the weights being the most critical step.

[0078] Calculate the weight ω j The specific steps include:

[0079] A1, Calculate the measured value x i c differences Δ between the first c measured values j x i The calculation formula is as follows:

[0080] Δ j x i =x i -x i-j (4)

[0081] Where, x i Let x be the measured data at time i; i = c+1, c+2, ..., n; i-j Let be the measured data at time ij; j = 1, 2, ..., c.

[0082] Δ jx i The absolute value is |Δ j x i |

[0083] A2, calculate the absolute value of the c differences |Δ j x i The formula for calculating | and s is as follows:

[0084]

[0085] Among them, |Δ j x i |for Δ j x i The absolute value of; j = 1, 2, ..., c.

[0086] A3, calculate the c variables w respectively. j The calculation formula is as follows:

[0087]

[0088] Where s is the absolute value of c differences |Δ j x i | and |Δ j x i |for Δ j x i The absolute value; j = 1, 2, ..., c; Δ j x i ≠0.

[0089] When Δ j x i When x is 0, that is, x i =x i-j This will cause equation (6) to be uncalculated. According to the idea of ​​this algorithm, x i-j The weight of is the largest, so let the estimated value x′ be . i =x i At that time, it is not necessary to calculate the estimated value.

[0090] A4, calculate c variables w j The formulas for calculating S and S are as follows:

[0091]

[0092] Among them, w j Let there be c variables; j = 1, 2, ..., c.

[0093] A5, calculate the c weights ω respectively. j The calculation formula is as follows:

[0094]

[0095] Among them, w j There are c variables; S has c variables w j The sum of; j = 1, 2, ..., c.

[0096] As shown in the above formula, as the estimated values ​​are calculated at different times, the weights can be adaptively adjusted based on the distance between the measured value at that time and the previous c times, where the measured value x i The smaller the distance to a value at time c, the greater the weight; the greater the distance, the smaller the weight. This is to reduce the weight of outliers on the estimated value, thereby improving the accuracy of the estimated value.

[0097] The adaptive weighting method can effectively avoid the influence of outliers in the original data on the estimated values.

[0098] S102, calculate the estimated value of the measured data at time c.

[0099] Due to the estimated value x′ i The initial value corresponds to the measured value at time c+1, which will miss the first c estimated values. To ensure that the lengths of the estimated and measured data sequences are the same, it is also necessary to calculate the estimated values ​​of the measured data at the first c times. The calculation method is as follows:

[0100] Let a set of measured data sequences be represented as X = {x1, x2, ..., x...} n The formula for calculating the estimated value based on the weighted moving average method is as follows:

[0101]

[0102] Where: x′ i Let x be the measured value at time i. i Estimates; i = 1, 2, ..., c; x i+j The measured data is at time i+j; j = 1, 2, ..., c; ω j For x i The weights corresponding to the data at time j;

[0103] Estimated value x′ i The initial value corresponds to the measured value at time 1. As shown in equation (9), by performing reverse calculation on the measured data, the estimated value x′ is obtained. i It is derived from the measured value x i The last c measured values ​​are multiplied by their corresponding weights and then summed to determine the result, with the calculation of the weights being the most critical step.

[0104] Calculate the weight ω j The specific steps include:

[0105] B1, Calculate the measured value x iThe c differences Δ between the last c measured values j x i The calculation formula is as follows:

[0106] Its absolute value is |Δ j x i |

[0107] Δ j x i =x i+j -x i (10)

[0108] Where, x i Let x be the measured data at time i; i = 1, 2, ..., c; i+j Let be the measured data at time i+j; j = 1, 2, ..., c.

[0109] B2, calculate the absolute value of the c differences |Δ j x i The formula for calculating | and s is as follows:

[0110]

[0111] Among them, |Δ j x i |for Δ j x i The absolute value of; j = 1, 2, ..., c.

[0112] B3, calculate the c variables w respectively. j The calculation formula is as follows:

[0113]

[0114] Where s represents c absolute values ​​|Δ j x i | and |Δ j x i |for Δ j x i The absolute value; j = 1, 2, ..., c; Δ j x i ≠0.

[0115] When Δ j x i When x is 0, that is, x i =x i-j This will cause equation (12) to be uncalculated. According to the idea of ​​this algorithm, x i-j The weight of is the largest, so let the estimated value x′ be . i =x i At that time, it is not necessary to calculate the estimated value.

[0116] B4, calculate c variables w j The formulas for calculating S and S are as follows:

[0117]

[0118] Among them, w j There are c variables.

[0119] B5, calculate the c weights ω respectively. j The calculation formula is as follows:

[0120]

[0121] Among them, w j There are c variables; S has c variables w j The sum of; j = 1, 2, ..., c.

[0122] S2, calculate the sequence of differences between estimated and measured values ​​in the slope deformation monitoring data.

[0123] Calculate the estimated value x′ i Compared with the measured value x i The difference Δx i The calculation formula is as follows:

[0124] Δx i =x i -x′ i (15)

[0125] Where, x′ i This is an estimated value; x i These are measured values.

[0126] According to Δx i A stable and reliable difference sequence ΔX can be obtained, ΔX = {Δx1, Δx2, ..., Δx}. n}

[0127] S3, mirror the difference sequence.

[0128] Because the trend in the measured data can lead to an asymmetric distribution in the difference sequence, it is necessary to mirror the difference sequence ΔX between the estimated value and the measured value. The specific method is to take the opposite of the difference sequence between the estimated value and the measured value, and then merge the two sequences into one sequence.

[0129] For Δx i Take the opposite number, i.e., -Δx i This forms the sequence ΔX′={-Δx1,-Δx2,…,-Δx nThen, merge the two sequences ΔX and ΔX′ into one sequence, i.e., ΔX″={Δx1, -Δx1, Δx2, -Δx2, ..., Δx n -Δx n}

[0130] S4, calculate the threshold for the difference sequence after mirroring.

[0131] Using ΔX″ as a sample, calculate its standard deviation σ based on 3σ, and then determine the threshold T.

[0132] Using ΔX″ as a sample, for ease of expression and calculation, let the mirrored difference sequence ΔX″ be {x1, x2, ..., x...} 2n}, its mean is:

[0133]

[0134] Where, x i Let i be the i-th data in the mirrored difference sequence; i = 1, 2, ..., 2n.

[0135] The standard deviation is:

[0136]

[0137] Where, x i Let be the i-th data point in the mirrored difference sequence; i = 1, 2, ..., 2n; u is the mean of the mirrored difference sequence.

[0138] The threshold T is:

[0139] T=±kσ (18)

[0140] Where k is the standard deviation coefficient, usually taken as 3; σ is the standard deviation of the mirrored difference sequence.

[0141] If the outlier test results are not ideal, the k value can be adjusted and recalculated based on expert experience to achieve the desired test results.

[0142] S5, based on the calculated threshold, identifies outliers in the slope monitoring data.

[0143] Determine the estimated value x' i Compared with the measured value x i The difference Δx i , when |Δx i When |>T, x i Values ​​that are not outliers are considered outliers, while those that are not are considered normal values.

[0144] The invention is further verified and illustrated through experiments using the following examples.

[0145] A high, tilted slope was equipped with surface and deep deformation monitoring instruments to monitor the slope deformation process. This paper uses data from the deep-mounted rod displacement gauges for outlier detection and analysis, covering the period from January 2020 to October 2022. The monitoring data showed a slow, monotonically increasing trend, with minor fluctuations and step-like changes in some areas. This is attributed to the instrument's insufficient accuracy to measure such minute changes. The WMA-3σ method was used for outlier detection. Since the measured outliers were not significant, five artificially added outliers were used as the values ​​to be detected in the calculations. Specific data can be found in [link to data]. Figure 1 .

[0146] Based on relevant analysis and expert experience, the parameter c and the standard deviation coefficient k in the WMA-3σ method are both selected as 3. The estimated results during the testing process are shown below. Figure 2 The sequence of differences between the detected value and the estimated value is shown in [reference needed]. Figure 3 See the mirrored difference sequence. Figure 4 The outlier test results for the values ​​to be tested are shown in [link to test results]. Figure 5 .

[0147] Depend on Figure 2 As can be seen, the changes in the measured values ​​and their estimated values ​​are very similar, and the two sets of data almost overlap. However, the outliers in the detected values ​​do not appear in the estimated values. This is one of the characteristics of the WMA-3σ method, which can estimate the trend and pattern of the original sequence well without being affected by outliers. Figure 3 In the sequence of differences between the detected value and the estimated value, there are significantly more positive numbers with larger absolute values ​​than negative numbers. This is due to the monotonically increasing trend of the detected values, which is detrimental to the calculation of 3σ, because the 3σ criterion assumes that the sample data is normally distributed and should have a certain degree of symmetry. Therefore, the difference sequence was mirrored. Figure 4 In the process, the difference sequence after mirroring exhibits symmetry. A 3σ threshold was calculated for it, and 10 data points were found to be outside the threshold range, thus identified as outliers. Figure 5 As can be seen, the 10 outliers in the difference sequence correspond to the outliers in the values ​​to be detected, including 5 artificially added outliers and 5 step values. The step values, with their large changes compared to the previous data, are also outliers and can therefore be detected by this method. The above test results show that this method has good detection performance and can be used to detect outliers in slope deformation monitoring data.

[0148] Based on this embodiment, the following conclusions can be drawn:

[0149] (1) The measured slope deformation data changes smoothly and stably in the short term and has strong autocorrelation. For the weighted moving average algorithm, the adaptive weight calculation method is adopted, which can estimate the measured data well. The variation law, trend and local variation characteristics of the estimated value are highly similar to the measured data and are not affected by outliers in the measured data.

[0150] (2) Over the long term, slope deformation monitoring data exhibits a monotonic trend, meaning that the total amount of positive changes exceeds the total amount of negative changes, resulting in an asymmetric difference sequence between the estimated and measured values. To better meet the application conditions of the 3σ criterion, this paper proposes a mirroring process for the difference sequence, which can effectively solve the asymmetry problem and thus better apply the 3σ criterion to establish the threshold.

[0151] (3) The WMA-3σ method can accurately detect outliers in measured data, including single-point mutation outliers and step outliers. Under normal circumstances, based on the monitoring data of different measuring points or different instruments, satisfactory outlier detection results can be obtained by appropriately adjusting the parameter k through trial calculation or expert experience. This has important reference value for outlier testing of measured data and for developing real-time, efficient, and intelligent data processing methods.

[0152] (4) Outlier detection has always been a key and challenging aspect of various data analysis tasks. The selection of the threshold is a crucial issue, and the occurrence of outliers is complex and varied, making it difficult to establish a single method applicable to all types of outlier detection. This paper combines the WMA method and optimizes the theoretically mature and widely used 3σ criterion. This method is only applicable to outlier detection under normal circumstances and can meet the general needs of data analysis in engineering.

[0153] The WMA-3σ method calculates estimates based on time series data. Its calculation process requires minimal sample data, and its threshold calculation and outlier detection procedures are simple, resulting in high detection efficiency. When a large amount of historical data is available, the calculated threshold is representative, enabling outlier detection not only on historical data but also on future measured values, thus providing a degree of real-time capability. When outliers are present, the algorithm significantly reduces the weight of their contribution to the estimate, thereby mitigating their impact on the accuracy of the estimate and demonstrating robustness.

Claims

1. A method for detecting outliers in slope deformation monitoring data, characterized in that, Includes the following steps: S1, calculate the estimated value of the measured data sequence in the slope deformation monitoring data; S2, calculate the sequence of differences between estimated and measured values ​​in the slope deformation monitoring data; S3, mirror the difference sequence; In S3, the specific method of mirroring is as follows: take the opposite number of the difference sequence between the estimated value and the measured value, and then merge the two sequences into one sequence; S4, calculate the threshold for the mirrored difference sequence; In step S4, the specific steps for calculating the threshold are as follows: Let the difference sequence after mirroring for }, its mean is: in, x i The difference sequence after mirroring i One data point; i =1, 2, ..., 2n ; The standard deviation is: in, x i The difference sequence after mirroring i There are 1, 2, ..., 1 data point; i = 1, 2, ... 2n ; u The mean of the difference sequence after mirroring; The threshold T is: T= in, k σ is the standard deviation coefficient; σ is the standard deviation of the mirrored difference sequence. If the outlier test results are not ideal, combine expert experience with... k The values ​​were adjusted and recalculated to achieve the desired test results; S5. Based on the calculated threshold, identify outliers in the slope monitoring data; In step S5, the specific steps for identifying outliers in slope monitoring data are as follows: Determine the estimated value. Compared with measured values x i The difference ,when >T, x i Values ​​that are not outliers are considered outliers, while those that are not are considered normal values.

2. The method for detecting outliers in slope deformation monitoring data according to claim 1, characterized in that, In S1, the specific method for calculating the estimated value of the measured data sequence in the slope deformation monitoring data is the weighted moving average method.

3. The method for detecting outliers in slope deformation monitoring data according to claim 1, characterized in that, In step S1, the specific steps for calculating the estimated value of the measured data sequence in the slope deformation monitoring data include: S101, Calculate the measured data c Estimates for time +1 and subsequent times; S102, Before calculating the measured data c The estimated value of the time.

4. The method for detecting outliers in slope deformation monitoring data according to claim 3, characterized in that, In step S101, the measured data is calculated. c The formula for calculating the estimated values ​​at time +1 and thereafter is: in: For the first i Real-time measured value x i The estimated value; i = c+1 , c+2 , ..., n ; x i-j For the first i - j Actual measured data at any given time; j =1, 2, ..., c ; for x i forward j Weights corresponding to time-series data; .

5. The method for detecting outliers in slope deformation monitoring data according to claim 4, characterized in that, Calculate weights The specific steps include: A1, Calculate the measured value x i Compared to the past c Between the measured values c Individual differences The calculation formula is as follows: in, x i For the first i Actual measured data at any given time; i = c+1 , c+2 , ..., n ; x i-j For the first i - j Actual measured data at any given time; j =1, 2, ..., c ; A2, Calculation c The absolute value of each difference and s The calculation formula is as follows: in, for The absolute value; j =1, 2, ..., c ; A3, calculate respectively c Variables w j The calculation formula is as follows: in, s for c The absolute value of each difference The sum of; for The absolute value; j =1, 2, ..., c ; ≠0; A4, Calculation c Variables w j and S The calculation formula is as follows: in, w j for c One variable; j =1, 2, ..., c ; A5, calculate separately c Weights ω j The calculation formula is as follows: in, w j for c One variable; S for c Variables w j The sum of; j =1, 2, ..., c .

6. The method for detecting outliers in slope deformation monitoring data according to claim 3, characterized in that, In step S102, before calculating the measured data... c The formula for calculating the estimated value of time is: in: For the first i Real-time measured value x i The estimated value; i =1,2,..., c ; x i+j For the first i + j Actual measured data at any given time; j =1, 2, ..., c ; ω j for x i back j Weights corresponding to time-series data; .

7. The method for detecting outliers in slope deformation monitoring data according to claim 6, characterized in that, Calculate weights ω j The specific steps include: B1, Calculate the measured value x i After c Between the measured values c Individual differences The calculation formula is as follows: in, x i For the first i Actual measured data at any given time; i =1, 2, ..., c ; For the first i+j Actual measured data at any given time; j =1, 2, ..., c ; B2, Calculation c The absolute value of each difference and s The calculation formula is as follows: in, for The absolute value; j =1, 2, ..., c ; B3, calculate separately c Variables w j The calculation formula is as follows: in, s for c The absolute value of each difference The sum of; for The absolute value; j =1, 2, ..., c ; ≠0; B4, Calculation c Variables w j and S The calculation formula is as follows: in, w j for c One variable; j =1, 2, ..., c ; B5, calculate separately c Weights ω j The calculation formula is as follows: in, w j for c One variable; S for c Variables w j The sum of; j =1, 2, ..., c .

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