Earth and rockfill dam monitoring data abnormal value identification method based on wavelet variable separation

Abstract

The invention relates to the technical field of data exception identification, and discloses an earth and rockfill dam monitoring data exception value identification method based on wavelet variable separation. Comprising the following steps: step 1, acquiring safety monitoring time sequence data of the earth and rockfill dam; 2, according to earth and rockfill dam data, influence factors of stress deformation and seepage of the earth and rockfill dam are determined; 3, separating an environment component and an aging component in the monitoring time sequence data by adopting a wavelet method to obtain time sequence data of which the influence factors in the step 2 are removed; 4, performing abnormal value identification on the time sequence data obtained in the step 3 to obtain a preliminary identification result; 5, discriminating the preliminary recognition result obtained in the step 4 by adopting a space-time comparison method to obtain a recognition result; according to the method, the environment component and the aging component in the monitoring data are separated, so that noise interference is reduced, and the accuracy of anomaly recognition is improved; and evaluating the reliability of anomaly recognition by combining monitoring data space-time comparison.

Description

Technical Field

[0001] The present invention relates to the technical field of data anomaly recognition, and in particular to a method for recognizing abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation. Background Art

[0002] The monitoring data of earth-rock dam is the basis for the performance analysis and evaluation of high earth-rock dams. However, the operating environment of earth-rock dams is complex, and a lot of data is collected. The instruments are prone to abnormalities during the construction and operation stages. In addition, due to the negligence of engineers, the probability of data errors is high. Therefore, it is very necessary to identify outliers before analyzing the data.

[0003] Abnormal values ​​of monitoring data are caused by measurement errors. Measurement errors can be divided into systematic errors, random errors and gross errors according to their causes and characteristics. Errors that remain constant or change according to a certain rule are called systematic errors. The former is called custom systematic errors, and the latter is called variable systematic errors. This type of error is mostly caused by the instrument itself. For example, the 0 scale is not aligned or the conversion calculation parameters are inaccurate. The absolute value and positive and negative signs of the error change in an unpredictable way, which is called a random error. The random error of dam monitoring is generally within the allowable measurement error and is usually not considered. Gross errors are errors caused by the carelessness of the surveyor or temporary failure of the instrument.

[0004] Common methods for identifying outliers in safety monitoring data include the Raitt criterion, Chauvenet criterion, Grubbs criterion, t criterion, Dixon criterion, etc. In recent years, the method derived by Stephane Mallat to calculate the Lipshitz index using wavelet decomposition and identify gross errors through the Lipshitz index has been widely used in many fields.

[0005] The defects of current error identification methods are summarized as follows: identification methods mostly draw on the theory of repeatable test data identification, mainly for static error identification; lack of consideration of environmental factors; anomaly identification research is mostly focused on gross error identification; identification mostly starts from isolated measurement points, without considering the spatial and temporal comparison of measured values, and reliability needs to be improved.

[0006] Earth-rock dam safety monitoring belongs to dynamic measurement, and its data series changes continuously over time. Moreover, the deformation and seepage of earth-rock dam are the result of the joint action of environmental quantities such as water level and temperature. The error identification method based solely on digital smoothness is difficult to obtain satisfactory results. Therefore, it is necessary to consider the influence of environmental quantities and combine the time-space comparison of measured values ​​to explore a method suitable for the abnormal identification of dynamic measurements in earth-rock dam safety monitoring. Summary of the invention

[0007] The present invention aims at solving the problems in the prior art and provides a method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation.

[0008] The technical solution adopted by the present invention is: a method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation, comprising the following steps:

[0009] Step 1: Obtain earth-rock dam safety monitoring time series data;

[0010] Step 2: Determine the influencing factors of stress, deformation and seepage of earth-rock dam based on the data of earth-rock dam;

[0011] Step 3: Use the wavelet method to separate the environmental component and the time-effect component in the monitoring time series data, and obtain the time series data without the influencing factors in step 2;

[0012] Step 4: Perform outlier identification on the time series data obtained in step 3 to obtain preliminary identification results;

[0013] Step 5: Use the time-space comparison method to judge the preliminary recognition result obtained in step 4 to obtain the recognition result.

[0014] Furthermore, the factors affecting the stress, deformation and seepage of the earth-rock dam include:

[0015] The stress and deformation influencing factors of earth-rock dam are the depth below the dam crest H, H 2 , height of core wall from dam base h, h 2 、h 3 , water level change Δh, first water storage level h f and time-effect factor e -ct ;

[0016] The seepage influencing factors are the filling height H, H 2 , water level h, rheological influence e -ct , water temperature T′, average water level J.

[0017] Furthermore, the process of determining the stress-deformation influencing factor of the earth-rock dam is as follows:

[0018] The stress deformation of earth-rock dam is divided into the deformation during construction caused by filling load, the instantaneous deformation caused by water load and the long-term deformation related to time. Functions are constructed respectively to determine the influencing factors. The specific process is as follows:

[0019] S111: The construction function of the deformation caused by the filling load of the earth-rock dam during the construction period is as follows:

[0020]

[0021] Where: S H is the total settlement at depth H, H is the depth below the dam crest, z is the height of the earth-rock dam, m v is the volume compression coefficient, γ is the compacted bulk density of the soil, and δ is the thickness of the soil layer;

[0022] S112: The function of water load and earth-rock dam deformation includes the earth-rock dam deformation function considering water pressure, wetting deformation and buoyancy;

[0023] Considering the water pressure condition, the deformation of the core wall at a height h from the dam base caused by the water pressure is:

[0024] y=y fk +y θd

[0025] Among them: y is the deformation, y fk is the horizontal displacement of point k caused by the shear force of the dam body, y θd is the dam body rotation angle θ d Horizontal displacement of point k caused by

[0026] First water storage curve h f It is a single influencing factor reflecting the soil wetting characteristics;

[0027] The dam body below the water infiltration line is affected by buoyancy, and the buoyancy force F on the unit soil is:

[0028] F=γ+γ w -γ ε

[0029] Where: γ is the compacted bulk density of soil, γ w is the water specific gravity, γ ε is the saturated bulk density;

[0030] Establish regression models for the savings period and the operation period;

[0031] The initial accumulation model is as follows:

[0032]

[0033] The runtime model is as follows:

[0034]

[0035] Where: Y(t) is the deformation of the dam at time t, i is the time index ranging from 1 to 6, corresponding to the current day, the previous 15 days, the previous 30 days, the previous 60 days, and the previous 90 days, j is the description (h it -h0) is the power of the nonlinear effect, ranging from 1 to 3, a0 is a constant term, h it is the average water level in the corresponding time period, h0 is the dam foundation elevation, e -ct To consider the time factor, a ij , a4, a5 and a6 are all factors to be determined;

[0036] S113: Considering the rheological properties of soil, the formula of rheological exponential curve is as follows:

[0037] ε(t)=ε f (1-e ct )

[0038] Where: ε(t) is the flow variable at time t, ε f is the final flow variable at t→∞.

[0039] Furthermore, the process of determining the seepage influencing factor is as follows:

[0040] S121: Construct the expression of unsteady seepage field of earth-rock dam and determine the initial and boundary conditions;

[0041] S122: According to the variational method, the stationary point extreme value is obtained through the universal function, and the expression of S121 is solved;

[0042] S123: According to the extreme value and solution result of step S122, the influencing factors of the earth-rock dam are determined to be the permeability coefficient, the upstream water head h1, the downstream water head h2 and the water supply degree;

[0043] S124: Obtaining the influencing factor of the influencing factor on the seepage in step S123;

[0044] Confirmation process of upstream and downstream head influence factors on seepage:

[0045] Determine the functional relationship between dam body seepage and upstream and downstream water levels:

[0046]

[0047] Where: h x is the seepage pressure head at any point, L is the horizontal distance from the seepage point to the y-axis, x is the horizontal distance from any point on the infiltration line to the y-axis, and the horizontal distance between the y-axis and the infiltration point is m1 is the upstream slope coefficient, h1 is the upstream water level, and h2 is the downstream water level;

[0048] Establish a seepage statistical regression model:

[0049] The regression model for the initial accumulation period is as follows:

[0050] P(t)=a0+a1(h i1 -h0)+a2H 1 +a3H 2 +a4T+a5e -ct

[0051] The running period regression model is as follows:

[0052] P(t)=a0+a1(h i1 -h0)+a2T+a3e -ct

[0053] Where: P(t) is the seepage head at time t, a1, a2 and a3 are all factors to be determined, h i1 is the average upstream water level in the corresponding time period;

[0054] Factors affecting seepage coefficient on seepage:

[0055] Determining the seepage effect based on the empirical formula of permeability coefficient requires considering the effect of external loads that affect the porosity ratio;

[0056] Considering the influence of temperature, the osmotic pressure model is constructed as follows:

[0057]

[0058] Factors affecting water supply on seepage:

[0059] According to the empirical formula of water supply degree, determine the factor affecting seepage of water supply degree;

[0060] Considering the hysteresis effect of rainfall on seepage, a rainfall model is constructed:

[0061]

[0062] Where: Q(t) is the seepage rate at time t, J t is the average water level over a period of time, h i is the average water level in the corresponding time period, i is 1-3, corresponding to the current day, 2-7 days before, 8-15 days before, a 11 、a 12 、a 3+i The factor to be sought.

[0063] Furthermore, the specific process of step 3 is as follows:

[0064] S31: Determine the approximate space V of the earth-rock dam deformation seepage data and environmental measurement data f j ; j is the scale level, f j ∈V j ;

[0065] S32: The environmental measurement data f j decomposed into multiple bands;

[0066] S33: Environmental measurement data f j By removing the high-frequency decomposition coefficients, the environmental impact is removed from the deformation and seepage data of the earth-rock dam, and new deformation and seepage coefficients are obtained. The wavelet coefficients are obtained according to the scale coefficients, and the monitoring data without environmental impact is obtained.

[0067] Furthermore, in step 4, outliers are identified by comparing with historical measurements of the sequence and similar points in space, judging residuals and Lipschitz index.

[0068] Furthermore, the process of identifying outliers by comparing with historical measurements of the sequence and similar points in space is as follows:

[0069] S411: Separate the alignment sequence z and the sequence to be identified x to obtain z ε and x ε ; Calculate z ε and x ε The average value of

[0070] S412: Calculate the variance estimates of z and x and z respectively ε and x ε An estimate of the variance of the mean of ;

[0071] S413: using interval probability to determine whether there is an error; determining the error judgment criteria for the same measuring point and different measuring points according to the variance estimation value in step S412;

[0072] Get the possible confidence level of the error. If the error judgment standard does not meet the given confidence interval, there is a fixed value error, which is an outlier.

[0073] Furthermore, the process of identifying outliers by using the residual judgment method in step 4 is as follows:

[0074] S421: Calculate data residuals and sort them in the order of measurement;

[0075] S422: Test the residuals using the Abbe test method to determine whether there are outliers.

[0076] Furthermore, the process of identifying outliers using the Lipschitz index in step 4 is as follows:

[0077] If the Lipschitz index is positive, it is the wavelet transform modulus of the signal point and is a normal value;

[0078] If the Lipschitz index is negative, it is the wavelet transform modulus of the noise point and is an outlier.

[0079] Furthermore, the temporal-spatial comparison method is used to judge the preliminary recognition results obtained in step 4 as follows:

[0080] S51: Assume that the confidence level of error identification at a certain measuring point of a high earth-rock dam on a certain day is a i , 0≤a i ≤1; then the recognition result for n consecutive days is a={a1,a2...a n}, the error comparison identification result of the measured value on the jth day for the measuring point i is bij, and the spatial comparison result b of m measuring points for n consecutive days is:

[0081]

[0082] S52: The time-space comparison results of the measuring points a&b are:

[0083]

[0084] Determine whether H0: a&b=1 is true, where H0 is the expected value of a&b;

[0085] S53: If H0 holds true for a t distribution T~t(n-1) with n-1 degrees of freedom, and a given identification significance level α, then If it is established, there is an error in the measuring point; is the critical value of the significance level α in the t distribution with n-1 degrees of freedom (looked up from the t distribution table), and T is the actual calculated value of the t statistic.

[0086] The beneficial effects of the present invention are:

[0087] (1) The method of the present invention reduces noise interference and improves the accuracy of anomaly identification by separating the environmental component and the time component in the monitoring data;

[0088] (2) The present invention combines the temporal and spatial comparison of monitoring data to evaluate the reliability of anomaly identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 It is a schematic diagram of the process of the present invention.

[0090] Figure 2 Schematic diagram of settlement calculation of earth-rock dam during construction period in an embodiment of the present invention.

[0091] Figure 3 Schematic diagram of calculation of horizontal displacement of the k-point of the core wall in an embodiment of the present invention.

[0092] Figure 4 It is the unloading and loading deformation curve of soil in the embodiment of the present invention.

[0093] Figure 5 Schematic diagram of comparison of statistical regression complex correlation coefficients of dam body deformation in the initial storage period in an embodiment of the present invention, a is the Longtoushi core wall rockfill dam, and b is the Shiziping core wall rockfill dam.

[0094] Figure 6 Schematic diagram of comparison of statistical regression complex correlation coefficients of dam body deformation during operation in an embodiment of the present invention, a is the Longtoushi core wall rockfill dam, and b is the Shiziping core wall rockfill dam.

[0095] Figure 7 Schematic diagram of calculation of seepage line of earth-rock dam in an embodiment of the present invention.

[0096] Figure 8Schematic diagram of comparison of statistical regression coefficients of dam body seepage pressure in the initial storage period in the embodiment of the present invention, a is the Longtoushi core wall rockfill dam, b is the Shiziping core wall rockfill dam.

[0097] Fig. 9 Schematic diagram of comparison of statistical regression complex correlation coefficients of dam body seepage pressure during operation in an embodiment of the present invention, a is the Longtoushi core wall rockfill dam, and b is the Shiziping core wall rockfill dam.

[0098] Fig.10 Schematic diagram of comparison of the complex correlation coefficient of the seepage pressure of the dragon head stone in the embodiment of the present invention, a is the atmospheric temperature, and b is the temperature of the measuring point.

[0099] Fig.11 Schematic diagram of the effect of rainfall lag on Yele seepage in an embodiment of the present invention.

[0100] Fig.12 Schematic diagram of the decomposition algorithm of measured data of earth-rock dam in an embodiment of the present invention.

[0101] Fig.13 Schematic diagram of an algorithm for reconstructing deformation and seepage influencing factors of earth-rock dams in an embodiment of the present invention.

[0102] Fig.14 Schematic diagram of the wavelet decomposition results of the vertical deformation of the Shiziping core rockfill dam in an embodiment of the present invention.

[0103] Fig.15 Schematic diagram of the wavelet separation results of the vertical deformation pollution sequence of the Shiziping core rockfill dam in an embodiment of the present invention.

[0104] Fig.16 This is a schematic diagram of the inclinometer data for the core wall of the Yele asphalt core wall dam in an embodiment of the present invention.

[0105] Fig.17 Schematic diagram of the vertical monitoring sequence of the Shiziping core rockfill dam crest in an embodiment of the present invention.

[0106] Fig.18 It is a schematic diagram for comparing the statistical regression multiple correlation coefficient of the osmotic pressure in the initial storage period between the method of the present invention and the traditional method.

[0107] Fig.19 It is a schematic diagram for comparing the statistical regression multiple correlation coefficient of osmotic pressure during operation between the method of the present invention and the traditional method. DETAILED DESCRIPTION

[0108] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

[0109] like Figure 1 As shown, a method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation includes the following steps:

[0110] Step 1: Obtain earth-rock dam safety monitoring time series data;

[0111] Step 2: Determine the influencing factors of stress, deformation and seepage of earth-rock dam based on the data of earth-rock dam;

[0112] The stress and deformation influencing factors of earth-rock dam are the depth below the dam crest H, H 2 , height of core wall from dam base h, h 2 、h 3 , water level change Δh, first water storage level h f and time-effect factor e -ct ;

[0113] The seepage influencing factors are the filling height H, H 2 , water level h, rheological influence e -ct , water temperature T′, average water level J.

[0114] Step 3: Use the wavelet method to separate the environmental component and the time-effect component in the monitoring time series data, and obtain the time series data without the influencing factors in step 2;

[0115] The specific process is as follows:

[0116] S31: Determine the approximate space V of the earth-rock dam deformation seepage data and environmental measurement data f j ; j is the scale level, f j ∈V j ;

[0117] S32: The environmental measurement data f j decomposed into multiple bands;

[0118] S33: Environmental measurement data f j By removing the high-frequency decomposition coefficients, the environmental impact is removed from the deformation and seepage data of the earth-rock dam, and new deformation and seepage coefficients are obtained. The wavelet coefficients are obtained according to the scale coefficients, and the monitoring data without environmental impact is obtained.

[0119] Step 4: Perform outlier identification on the time series data obtained in step 3 to obtain preliminary identification results;

[0120] Outliers are identified by comparing with historical measurements of the sequence and similar points in space, judging residuals and Lipschitz index.

[0121] Step 5: Use the time-space comparison method to judge the preliminary recognition result obtained in step 4 to obtain the recognition result.

[0122] The process of using the time-space comparison method to judge the preliminary recognition results obtained in step 4 is as follows:

[0123] S51: Assume that the confidence level of error identification at a certain measuring point of a high earth-rock dam on a certain day is a i , 0≤a i ≤1; then the recognition result for n consecutive days is a={a1,a2...a n}, the error comparison identification result of the measured value on the jth day for the measuring point i is bij, and the spatial comparison result b of m measuring points for n consecutive days is:

[0124]

[0125] S52: The time-space comparison results of the measuring points a&b are:

[0126]

[0127] Determine whether H0: a&b=1 is true, where H0 is the expected value of a&b;

[0128] S53: If H0 holds true for a t distribution T~t(n-1) with n-1 degrees of freedom, and a given identification significance level α, then If it is established, there is an error in the measuring point; is the critical value of the significance level α in the t-distribution with n-1 degrees of freedom (summarized and found from the t-distribution table), and T is the actual calculated value of the t-statistic.

[0129] The present invention will be further described below in conjunction with specific real time.

[0130] A method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation comprises the following steps:

[0131] Step 1: Obtain earth-rock dam safety monitoring time series data y i (i=1,2,...,n);

[0132] y i =y ie +y it +y io

[0133] Where: y ie is the environmental impact component, y it In order to consider the time-varying components such as material rheology, y io is a series containing measurement errors.

[0134] Step 2: Determine the influencing factors of stress, deformation and seepage of earth-rock dam based on the earth-rock dam data

[0135] Based on the analysis of original observation data of multiple earth-rock dams, the functional relationship between influencing factors such as water level, temperature, filling load, time effect and deformation and seepage of earth-rock dams is established to determine the main influencing factors of stress deformation and seepage during the construction period, initial storage period and operation period of earth-rock dams, and appropriate influencing factors are selected according to the attributes of the measuring points.

[0136] The process is as follows:

[0137] The process of determining the stress and deformation influencing factors of earth-rock dam is as follows:

[0138] The stress deformation of earth-rock dam is divided into the deformation during construction caused by filling load, the instantaneous deformation caused by water load and the long-term deformation related to time. Functions are constructed respectively to determine the influencing factors. The 60-day lag effect of water level needs to be considered during the initial storage period, and the 30-day lag effect of water level needs to be considered during the operation period. The specific process is as follows:

[0139] S111: The construction function of the deformation caused by the filling load of the earth-rock dam during the construction period is as follows:

[0140]

[0141] Where: S H is the total settlement at depth H, H is the depth below the dam crest, z is the height of the earth-rock dam, m v is the volume compression coefficient, γ is the compacted bulk density of the soil, and δ is the thickness of the soil layer.

[0142] The deformation of the earth-rock dam during construction caused by the filling load is deduced according to the graded filling method, and the calculation is as follows: Figure 2 As shown, the compression of the soil layer with a thickness of dδ is dS H =m v σ H dδ, which determines that the settlement deformation during the construction period of the earth-rock dam is a function of the first and second powers of the filling height.

[0143] S112: The function of water load and earth-rock dam deformation includes the earth-rock dam deformation function considering water pressure, wetting deformation and buoyancy;

[0144] Assuming that the soil deformation is small, the foundation and the dam body are approximately regarded as elastic deformation, and the water load acts on the core wall, the core wall and the dam body medium are continuous, according to the elastic body deformation calculation method, the deformation of the core wall caused by water pressure at a height h from the dam base surface is:

[0145] y=y fk +y θd

[0146] Among them: y is the deformation, y fk is the horizontal displacement of point k caused by the shear force of the dam body, y θd is the dam body rotation angle θ dThe horizontal displacement of point k caused by Figure 3 shown.

[0147] The shear level of the dam body is:

[0148]

[0149] Among them, Q is the shear force caused by water pressure, which is proportional to the square of the water depth; K is the shear force distribution coefficient, which is about 1.2, μ d is the Poisson's ratio of small deformation of earth dam, E d is the small deformation elastic modulus of soil, A is the horizontal upstream cross-sectional area of ​​the dam body;

[0150] The horizontal displacement caused by the dam body rotation is:

[0151]

[0152] Among them, M is the bending moment caused by water pressure, which is proportional to the cube of the water depth, and I is the moment of inertia of the horizontal section of the dam;

[0153] Therefore, it is determined that the deformation of the core wall point k caused by the water level in front of the dam is a function of the square and cubic power of the water depth. If the dam body and the dam foundation are taken as continuous cutoffs, the deformation of the dam body can also be approximately considered as a function of the square and cubic power of the water depth. At the same time, it is considered that the deformation of the actual soil body caused by loading and unloading is different. Figure 4 As shown, the influence of water level change Δh is considered.

[0154] First water storage curve h f is a single influencing factor reflecting the soil wetting characteristics; when h(t)≥h(t) max ,h f (t)=h(t), when h(t) <h(t) max ,h f (t) = h f (t-1), h(t) is the water level at time t, h(t) max is the highest water level before time t; h f (t) is the first water storage level at time t; h f (t-1) is the first water storage level before time t.

[0155] After the reservoir is filled with water, as the water level rises, the dam body below the infiltration line is affected by buoyancy, and the buoyancy force F per unit soil is:

[0156] F=γ+γ w -γ ε

[0157] Where: γ is the compacted bulk density of soil, γ w is the water specific gravity, γ ε is the saturated bulk density;

[0158] The buoyancy force can be considered as reducing the bulk density of the soil, that is, changing γ, which can be reflected by h.

[0159] Finally, the factors affecting water pressure are determined to be h, h 2 、h 3 , Δh, h f .

[0160] Establish regression models for the savings period and the operation period.

[0161] A regression analysis was conducted on the existing engineering data to obtain the lag effect interval, and the original monitoring data of high core rockfill dams such as Longtoushi (dam height 72.5m), Shiziping (dam height 136m), Pubugou (dam height 186m) and Nuozhadu (dam height 261.5m) were selected.

[0162] The initial accumulation model is as follows:

[0163]

[0164] The runtime model is as follows:

[0165]

[0166] Where: Y(t) is the deformation of the dam at time t, i is the time index, and j is the description (h it -h0) is the power of the nonlinear effect, a0 is a constant term, h it is the average water level in the corresponding time period, h0 is the dam foundation elevation, e -ct is the time factor, a ij , a4, a5 and a6 are all factors to be determined;

[0167] Among them, i ranges from 1 to 6, corresponding to the current day, 15 days before, 30 days before, 60 days before, and 90 days before. The results of the model complex correlation coefficient comparison considering the different lag effects of water level factors are as follows: Figure 5 and Figure 6 The 60-day water level is considered in the initial storage period, and the 30-day water level is considered as the hysteresis interval in the operation period.

[0168] S113: Considering the rheological properties of soil, the formula of rheological exponential curve is as follows:

[0169] ε(t)=ε f (1-e ct )

[0170] Where: ε(t) is the flow variable at time t, ε f is the final flow rate when t→∞. The time factor affecting the flow rate is determined as e -ct .

[0171] According to S111 to S113, the main influencing factors of the deformation of earth-rock dams during the initial storage period are H and H 2 、e -ct The main factors affecting stress are H and e -ct ; The main influencing factors of deformation during the water storage period are H and H 2 ,h,h 2 、h 3 , Δh, h f 、e -ct , h Considering the 60-day lag effect, the main influencing factors of stress are H, h, and h 2 , Δh, h f 、e -ct ; The main influencing factors of deformation during operation are h and h 2 、h 3 , Δh, h f 、e -ct The main factors affecting stress are h and h 2 , Δh, h f 、e -ct , h takes into account the 30-day lag effect. Among them, H is the filling height, H 2 is the square of the filling height, e -ct is the time factor, h, h 2 、h 3 are the first, second and third powers of the water head respectively, Δh is the change in water level, h f For the water storage level.

[0172] The process of determining the seepage influencing factor is as follows:

[0173] S121: Construct the expression of unsteady seepage field of earth-rock dam and determine the initial and boundary conditions;

[0174] The flow field expression is:

[0175]

[0176] Where h′ is the hydraulic head function, x, y and z are spatial coordinates, t is the time coordinate, k x , k y and k z are the permeability coefficients in the x, y and z directions, s t It is the unit water storage capacity of soil.

[0177] The initial condition of unsteady seepage is determined as: h′| t＝0 =H0(x,y,z), the boundary condition is h′| Γ1 =H0(x,y,z,t) and Where Γ1 and Γ2 are both boundaries, k nis the permeability coefficient in the n direction, n is the normal vector of the boundary Γ2, and q is the seepage rate per unit area.

[0178] S122: According to the variational method, the stationary point extreme value is obtained through the universal function, and the expression of S121 is solved;

[0179] The generic function is:

[0180]

[0181] Where Ω is a region in three-dimensional space.

[0182] The solution process is as follows:

[0183] 1) Take the derivative of the unit stationary point and get the matrix solution equation as follows: Among them, [K] is the total permeability matrix; [S] is the matrix calculated by unit water storage and location; [p] is the matrix determined by water supply degree and boundary node coordinates; [F] is a constant term, which is calculated based on the upstream and downstream heads.

[0184] 2) Take implicit finite differences for the matrix solution time t in 1) and do not consider soil compressibility, that is, [S] is 0, and we get [p] is the water supply degree, and Δt is the time step.

[0185] S123: According to the extreme value and solution result of step S122, the influencing factors of the earth-rock dam are determined to be the permeability coefficient K, the upstream water head h1, the downstream water head h2 and the water supply degree;

[0186] S124: Obtaining the influencing factor of the influencing factor on the seepage in step S123;

[0187] Confirmation process of upstream and downstream head influence factors on seepage:

[0188] According to the hydraulic principle, the functional relationship between the dam body seepage and the upstream and downstream water levels is obtained:

[0189]

[0190] Where: h x is the seepage pressure head at any point, L is the horizontal distance from the seepage point to the y-axis, x is the horizontal distance from any point on the infiltration line to the y-axis, and the horizontal distance between the y-axis and the infiltration point is m1 is the upstream slope coefficient, h1 is the upstream water level, and h2 is the downstream water level; the calculation process is as follows Figure 7 As shown, it can be seen that the seepage pressure has a first-order relationship with the upstream water level.

[0191] Based on the analysis of the original data of the existing projects, the hysteresis effect of water level on seepage is obtained, and a statistical regression model of seepage is established:

[0192] The regression model for the initial accumulation period is as follows:

[0193] P(t)=a0+a1(h i1 -h0)+a2H 1 +a3H 2 +a4T+a5e -ct

[0194] The running period regression model is as follows:

[0195] P(t)=a0+a1(h i1 -h0)+a2T+a3e -ct

[0196] Where: P(t) is the seepage head at time t, a1, a2 and a3 are all factors to be determined, h i1 is the average upstream water level in the corresponding time period; i and j are 1 to 6, corresponding to the average water level of the day, the previous 15 days, the previous 30 days, the previous 60 days, and the previous 90 days; the meanings of other symbols are the same as before. According to the negative correlation coefficient results of the seepage statistical regression model, Figure 8 and Fig. 9 As shown in the figure, it can be seen that the lag effect of the water level in the first 30 days is considered in the initial storage period, and the lag effect of the water level in the first 15 days is considered in the operation period.

[0197] Factors affecting seepage coefficient on seepage:

[0198] 1) According to the empirical formula of permeability coefficient Where k is the soil permeability coefficient, d 10 is the effective particle size, e is the porosity ratio, and the external load that affects the porosity ratio needs to be considered when determining the seepage, that is, the influencing factors of filling height H and H 2 , water level h, rheological influence factor e -ct .

[0199] 2) The permeability coefficient is linearly related to the water temperature T, and the hysteresis effect of temperature on seepage is obtained. Based on the temperature correction formula K T K is the permeability coefficient considering the hydrological effect. 20 is the permeability coefficient at water temperature of 20°C.

[0200] The osmotic pressure model is constructed as follows:

[0201]

[0202] Among them, h i0 is the average downstream water level in the corresponding time period;

[0203] According to the negative correlation coefficient results of the osmotic pressure model, such as Fig.10As shown in the figure, when the atmospheric temperature is used as the temperature factor, the temperature of the previous 90 days is considered, and when the temperature of the instrument measuring point is used as the temperature factor, the temperature of the previous 15 days is considered.

[0204] Factors affecting water supply on seepage:

[0205] 1) According to the empirical formula of water supply degree and μ = an, where μ is the unit water supply, n is the porosity, and a is the reduction coefficient; the factors that determine the water supply degree and the seepage coefficient are the same, that is, the filling height H, H 2 , water level h, rheological influence factor e -ct .

[0206] Considering the hysteresis effect of rainfall on seepage, the rainfall model is constructed using the data of Longtou core rockfill dam:

[0207]

[0208] Where: Q(t) is the seepage rate at time t, J t is the average water level over a period of time, h i is the average water level in the corresponding time period, a 11 、a 12 、a 3+i The factor to be sought.

[0209] i is 1-3, corresponding to the current day, 2-7 days before, 8-15 days before; J t is the average water level over a period of time; t is the current day, the previous 15 days, the previous 30 days, the previous 60 days, the previous 90 days, the previous 180 days; e -ct is the time-effect factor; the results are as follows Fig.11 As shown in Figure 2, the influence of available rainfall is mainly due to the rainfall duration in the previous 30 days.

[0210] Through the above process, it can be determined that the main influencing factors of the seepage pressure of earth-rock dam in the initial storage period are H, H 2 ,h,e -ct , T, the main influencing factors of seepage are H, H 2 ,h,e -ct , T, J, water level considers the influence of water level in the previous 30 days; if atmospheric temperature is used, the temperature in the previous 90 days is considered; if point temperature is used, the temperature in the previous 15 days is considered; rainfall considers the influence of rainfall in 30 days; the main influencing factors of seepage pressure during earth-rock dam operation period are h, e -ct , T, the main influencing factors of seepage are h, e -ct , T, J, where the water level takes into account the influence of the water level in the previous 15 days; if the atmospheric temperature is used as the temperature, the temperature in the previous 90 days is considered; if the measuring point temperature is used, the temperature in the previous 15 days is considered; and the rainfall takes into account the influence of the rainfall in the previous 30 days.

[0211] Step 3: Use the wavelet method to separate the environmental component and the time-effect component in the monitoring time series data, and obtain the time series data without the influencing factors in step 2;

[0212] The specific process is as follows:

[0213] S31: Initialization, determine the approximate space V of the earth-rock dam deformation seepage data and environmental measurement data f j ; j is the scale level, f j ∈V j ; make||f j -f||minimum, that is, f j Yes j The best approximation in .

[0214] S32: Decomposition, decomposing the measured data into multiple bands for filtering; f is obtained by initialization j ∈V j , then the decomposition algorithm scale coefficient and Find {c j-1,k} k∈Z and {d j-1,k} k∈Z Among them, C l-1,k is the scale coefficient at position k on scale l-1, is the filter coefficient, c ln is the scale coefficient on a certain scale n, d l-1,k is the detail coefficient at position k on scale l-1, is the coefficient of the high-pass filter, c j-1,k is the scale coefficient at position k on scale j-1, d j-1,k is the detail coefficient at position k at scale j-1, and Z is an integer set.

[0215] Coming soon j Decompose into f j =f j-1 +ω j-1 ,in ω j-1 =Σ k∈Z d j-1,k ψ j-1,k (x)∈W j-1 , for f j-1 ∈V j-1 、f j-2 ∈V j-2 …f j-n ∈V j-n Similarly, multiple layers can be decomposed as needed. The decomposed statements are determined by the actual situation. j ={c j,k} k∈Z, D j ={d j,k} k∈Z , the decomposition process is as follows Fig.12 shown.

[0216] Among them, ω j-1 is the detailed information of the function at scale j-1, is the evaluation value of the scaling function at a specific scale j-1 and position k, C j-1,k is the scale coefficient at position k on scale j-1, d j-1,k is the detail coefficient at position k on scale j-1, ψ j-1,k (x) is the evaluation value of the wavelet function at scale j-1 and position k, W j-1 is the representation of the wavelet space at scale j-1.

[0217] S33: Reconstruction of environmental measurement data f j By removing the high-frequency decomposition coefficient, the deformation and seepage data of earth-rock dams are freed from environmental influences, and new deformation and seepage coefficients {Nd j-1,k} k∈Z , according to the scale factor {Nc j-1,k} k∈Z According to the reconstruction algorithm, the wavelet coefficients {Nc l,k} k∈Z , get the monitoring data without environmental impact, the process is as follows Fig.13 .

[0218] Based on the vertical deformation data of the core rockfill dam of Shiziping, a fixed value pollution sequence was injected from October 15, 2013. The pollution sequence is normally distributed with expected values ​​of 0.1, 0.2, 0.4, 0.6, 0.8, and 1.2. The decomposition effect of the measured values ​​of the pollution sequence is shown in Fig.14 .

[0219] Step 4: Perform outlier identification on the time series data obtained in step 3 to obtain preliminary identification results;

[0220] Outliers are identified by comparing with historical measurements of the sequence and similar points in space, judging residuals and Lipschitz index.

[0221] (1) The process of outlier identification by comparing with historical measurements of the sequence and similar points in space is as follows:

[0222] S411: Align the sequence z (z1, z2, z3...z m ) and the sequence to be identified x(x1, x2, x3...x n ), separated by environmental factors and time-effect factors to obtain z ε and x ε ; Calculate zε and x ε The average

[0223] S412: Since the means of the two sequences should satisfy a certain constant μ i The normal distribution N(μ i ,σ 2 ), calculate the variance estimate of the series and The variance estimate of

[0224] S413: Use interval probability to determine whether there is an error; if the comparison is for the same measuring point, if there is no fixed value error, then Should satisfy normal distribution in Error identification is the judgment standard; if it is a comparison of different measuring points, if there is no fixed value error, Should satisfy normal distribution Error identification is the judgment standard; the possible confidence level of the error is obtained by looking up the normal distribution table. If the standard does not meet the given confidence interval, the mean does not meet the normal distribution, and there is a fixed value error. The system customization error for the same point comparison is The fixed value system error of different measuring points is right Fig.14 The sequence is used to identify the fixed value system error, and the results are shown in Table 1. Fig.14 As can be seen from Table 1, this method can identify various errors, and the error identification value accuracy is relatively high. The larger the injected error, the greater the confidence, and the more obvious the distinction.

[0225] Table 1. Identification results of the fixed value error of the vertical deformation pollution sequence of the Shiziping core rockfill dam

[0226]

[0227] (2) The process of outlier identification using the residual judgment method is as follows:

[0228] S421: Calculate data residuals Sort by measurement order;

[0229] S422: Test the residuals using the Abbe test to determine whether there are outliers. First, calculate and B = (v1-v2) 2 +(v2-v3) 2 +...+(v n-1 -v n ) 2 +(v n -v1)2 , and then calculate and like There is a systematic variable error. Fig.15 Based on the external vertical deformation data of the Shiziping core rockfill dam, the environmental quantity, time effect and constant value separation were carried out after the pollution sequence with a step gradient of 0.1 was injected from October and 15, 2013. The variable value systematic error was identified for the data. The Abbe test value of the sequence was 0.232, which was greater than the standard value of 0.164, and it was considered that there was a variable value error.

[0230] (3) The process of identifying outliers using the Lipschitz index is as follows:

[0231] If the Lipschitz index is positive, it is the wavelet transform modulus of the signal point and is a normal value;

[0232] If the Lipschitz index is negative, it is the wavelet transform modulus of the noise point and is an outlier.

[0233] Get the sequence after separating the environmental and time components

[0234] set up is the j-layer wavelet decomposition of function f(x), then the Lipschitz index a is expressed as Assume that the actual number of wavelet decomposition layers is J, and let Assume that when 2 j Full hours, there K0 and a0 are constants, then E(a,k)=Σ j∈J (a j -k2 ja ) 2 . Let J = 5, then After simplification, calculation is required

[0235] When J = 5, if Among them, a1, a2, a4, and a5 are the modulus values ​​of the wavelet coefficients at the point x = x0 at each layer. The Lipschitz index is positive, which is the modulus value of the wavelet transform of the signal point and is a normal value. Then the Lipschitz index is negative, which is the wavelet transform modulus of the noise point and is an outlier. The same is true for other decomposition levels. Fig.16 The sequence is used for gross error identification. When the 3σ criterion is used, the 3σ value of the sequence is 6.53, which cannot be identified. The 4-layer Daubechies wavelet decomposition is used to obtain the wavelet coefficient list and solve The positive and negative values ​​of the four abnormal points are -0.275, -0.375, -0.421, and -0.15, all of which are negative values ​​and can be correctly identified.

[0236] Step 5: Use the time-space comparison method to judge the preliminary recognition results obtained in step 4 and obtain the recognition results

[0237] S51: Except for large instantaneous changes caused by extreme environments such as earthquakes, dams are continuously changing under the combined effects of external environment and internal factors. Therefore, the reliability of identification is judged by subsequent changes in measured values.

[0238] Assume that the confidence level of error identification at a certain measuring point of a high earth-rock dam on a certain day is a i , 0≤a i ≤1 (1 is error, 0 is non-error, and the interval is fuzzy); then the recognition result for n consecutive days is a={a1,a2...a n}, the error comparison and identification result of the measured value on the jth day for the measuring point i is b ij , for n consecutive days, the spatial comparison result b of m measuring points is:

[0239]

[0240] S52: The time-space comparison results of the measuring points a&b are:

[0241]

[0242] Determine whether H0:a&b=1 is true, where H0 is the expected value of a&b; determine the time-space error robustness assessment based on whether the expected value of a&b is 1.

[0243] S53: Use probability test method to construct t statistic in is the sequence average, S 2 is the sample variance.

[0244] If H0 holds true for a t distribution T~t(n-1) with n-1 degrees of freedom, and a given identification significance level α, then If it is established, there is an error in the measuring point; is the critical value of the significance level α in the t distribution with n-1 degrees of freedom (summarized and searched from the t distribution table), and T is the value of the actual calculated t statistic. The vertical monitoring sequence of the top of the Shiziping core rockfill dam is used as the verification object, see Fig.17 The results of the spatiotemporal comparison are shown in Table 2. In the figure, identification points 1 and 4 are overall lifting points, which are stable after lifting and are non-abnormal points; monitoring point 2 is an abnormal sharp point; monitoring point 3 is a fluctuating point and an abnormal value. In the isolated point determination, they are all judged as abnormal values. After combining the spatiotemporal comparison, identification points 1 and 4 are effectively judged as non-abnormal values.

[0245] Table 2. Confidence of spatiotemporal stability identification of gross errors in vertical monitoring of Shiziping core rockfill dam crest

[0246]

[0247]

[0248] In order to further illustrate the effect of the present invention, the model of the present invention is compared with the existing traditional model, and the comparison results of the multiple correlation coefficients are as follows: Fig.18 and Fig.19 As shown in the figure, it can be seen that the stress deformation and seepage regression model of the earth-rock dam constructed by the present invention has high accuracy. And considering the influence of environmental factors, the average coefficient of complex correlation is significantly higher than that of the traditional model.

[0249] The method of the present invention separates the environmental component and the time-effect component of the measured value, which solves the defect that the previous method is not suitable for dynamic monitoring. The accuracy of outlier identification is high. Since the influencing factors are selected based on the functional relationship between each influencing factor and the stress, deformation and seepage of the earth-rock dam and the properties of the measuring point, and the wavelet method is used to separate the environmental component and the time-effect component of the measured value of the measuring point to eliminate the environmental impact, the misjudgment caused by excessive changes in the measured value caused by the sudden change of the environmental quantity is effectively avoided. Compared with the 3σ criterion, the accuracy of outlier identification is improved. The reliability of the gross error identification results is improved. Considering the spatiotemporal stability of the overall change of the dam, the misjudgment of isolated points is effectively avoided by comparing the subsequent changes in the measured values.

Claims

1. A method for identifying abnormal values ​​in earth-rock dam monitoring data based on wavelet variable separation, characterized in that: The following steps are involved: Step 1: Obtain earth-rock dam safety monitoring time series data; Step 2: Determine the influencing factors of stress, deformation and seepage of earth-rock dam based on the data of earth-rock dam; Step 3: Use the wavelet method to separate the environmental component and the time-effect component in the monitoring time series data, and obtain the time series data without the influencing factors in step 2; Step 4: Perform outlier identification on the time series data obtained in step 3 to obtain preliminary identification results; Step 5: Use the time-space comparison method to judge the preliminary recognition result obtained in step 4 to obtain the recognition result.

2. According to claim 1, a method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation is characterized in that: The factors affecting the stress, deformation and seepage of earth-rock dams include: The stress and deformation influencing factors of earth-rock dam are the depth below the dam crest H, H 2 , height of core wall from dam base h, h 2 、h 3 , water level change Δh, first water storage level h f and time-effect factor e -ct ; The seepage influencing factors are the filling height H, H 2 , water level h, rheological influence e -ct , water temperature T′, average water level J.

3. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 2 is characterized in that: The process of determining the stress and deformation influencing factors of earth-rock dam is as follows: The stress deformation of earth-rock dam is divided into the deformation during construction caused by filling load, the instantaneous deformation caused by water load and the long-term deformation related to time. Functions are constructed respectively to determine the influencing factors. The specific process is as follows: S111: The construction function of the deformation caused by the filling load of the earth-rock dam during the construction period is as follows: Where: S H is the total settlement at depth H, H is the depth below the dam crest, z is the height of the earth-rock dam, m v is the volume compression coefficient, γ is the compacted bulk density of the soil, and δ is the thickness of the soil layer; S112: The function of water load and earth-rock dam deformation includes the earth-rock dam deformation function considering water pressure, wetting deformation and buoyancy; Considering the water pressure condition, the deformation of the core wall at a height h from the dam base caused by the water pressure is: Among them: y is the deformation, y fk is the horizontal displacement of point k caused by the shear force of the dam body, y θd is the dam body rotation angle θ d Horizontal displacement of point k caused by First water storage curve h f It is a single influencing factor reflecting the soil wetting characteristics; The dam body below the water infiltration line is affected by buoyancy, and the buoyancy force F on the unit soil is: F=γ+γ w -c ε Where: γ is the compacted bulk density of soil, γ w is the water specific gravity, γ ε is the saturated bulk density; Establish regression models for the savings period and the operation period; The initial accumulation model is as follows: The runtime model is as follows: Where: Y(t) is the deformation at time t, i is the time index, and j describes (h it -h0) is the power of the nonlinear effect, a0 is the constant term, a ij is the coefficient of the water level model to be determined, h it is the average water level in the corresponding time period, h0 is the dam foundation elevation, e -ct To consider the time factor, a4, a5 and a6 are all factors to be determined; S113: Considering the rheological properties of soil, the formula of rheological exponential curve is as follows: ε(t)=ε f (1-e ct ) Where: ε(t) is the flow variable at time t, ε f is the final flow variable at t→∞, c is the first day flow variable at t=0, accounting for ε f The ratio of ct The influencing factor of time.

4. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 3 is characterized in that: The process of determining the seepage influencing factor is as follows: S121: Construct the expression of unsteady seepage field of earth-rock dam and determine the initial and boundary conditions; S122: According to the variational method, the stationary point extreme value is obtained through the universal function, and the expression of S121 is solved; S123: According to the extreme value and solution result of step S122, the influencing factors of the earth-rock dam are determined to be the permeability coefficient, the upstream water head h1, the downstream water head h2 and the water supply degree; S124: Obtaining the influencing factor of the influencing factor on the seepage in step S123; Confirmation process of upstream and downstream head influence factors on seepage: Determine the functional relationship between dam body seepage and upstream and downstream water levels: Where: h x is the seepage pressure head at any point, L is the horizontal distance from the seepage point to the y-axis, x is the horizontal distance from any point on the infiltration line to the y-axis, and the horizontal distance between the y-axis and the infiltration point is m1 is the upstream slope coefficient, h1 is the upstream water level, and h2 is the downstream water level; Establish a seepage statistical regression model: The regression model for the initial accumulation period is as follows: P(t)=a0+a1(h i1 -h0)+a2H 1 +a3H 2 +a4T+a5e -ct The running period regression model is as follows: P(t)=a0+a1(h i1 -h0)+a2T+a3e -ct Where: P(t) is the seepage pressure at time t, a1, a2 and a3 are all factors to be determined, h i1 is the average upstream water level in the corresponding time period; Factors affecting seepage coefficient on seepage: Determining the seepage effect based on the empirical formula of permeability coefficient requires considering the effect of external loads that affect the porosity ratio; Considering the influence of temperature, the osmotic pressure model is constructed as follows: Among them, h i0 is the average downstream water level in the corresponding time period; Factors affecting water supply on seepage: According to the empirical formula of water supply degree, determine the factor affecting seepage of water supply degree; Considering the hysteresis effect of rainfall on seepage, a rainfall model is constructed: Where: Q(t) is the seepage rate at time t, J t is the average water level over a period of time, h i is the average water level in the corresponding time period, a 11 、a 12 、a 3+i The factor to be sought.

5. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 1 is characterized in that: The specific process of step 3 is as follows: S31: Determine the approximate space V of the earth-rock dam deformation seepage data and environmental measurement data f j ; j is the scale level, f j ∈V j ; S32: The environmental measurement data f j decomposed into multiple bands; S33: Environmental measurement data j By removing the high-frequency decomposition coefficients, the environmental impact is removed from the deformation and seepage data of the earth-rock dam, and new deformation and seepage coefficients are obtained. The wavelet coefficients are obtained according to the scale coefficients, and the monitoring data without environmental impact is obtained.

6. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 1 is characterized in that: In step 4, outliers are identified by comparing with historical values ​​of the sequence and similar points in space, judging residuals and Lipschitz index.

7. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 6 is characterized in that: The process of identifying outliers by comparing with historical measurements of the sequence and similar points in space is as follows: S411: Separate the alignment sequence z and the sequence to be identified x to obtain z ε and x ε ; Calculate z ε and x ε The average value of S412: Calculate the variance estimates of z and x and z respectively ε and x ε An estimate of the variance of the mean of ; S413: using interval probability to determine whether there is an error; determining the error judgment criteria for the same measuring point and different measuring points according to the variance estimation value in step S412; Get the possible confidence level of the error. If the error judgment standard does not meet the given confidence interval, there is a fixed value error, which is an outlier.

8. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 6 is characterized in that: The process of using the residual judgment method to identify outliers in step 6 is as follows: S421: Calculate data residuals and sort them in the order of measurement; S422: Test the residuals using the Abbe test method to determine whether there are outliers.

9. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 6 is characterized in that: The process of identifying outliers using the Lipschitz index in step 6 is as follows: If the Lipschitz index is positive, it is the wavelet transform modulus of the signal point and is a normal value; If the Lipschitz index is negative, it is the wavelet transform modulus of the noise point and is an outlier.

10. The method for identifying abnormal values ​​of earth-rock dam monitoring data based on wavelet variable separation according to claim 1, characterized in that: The process of using the time-space comparison method to judge the preliminary recognition results obtained in step 4 is as follows: S51: Assume that the confidence level of error identification at a certain measuring point of a high earth-rock dam on a certain day is a i , 0≤a i ≤1; then the recognition result for n consecutive days is a={a1,a2...a n }, the error comparison and identification result of the measured value on the jth day for the measuring point i is b ij , for n consecutive days, the spatial comparison result b of m measuring points is: S52: The time-space comparison results of the measuring points a&b are: Determine whether H0: a&b=1 is true, where H0 is the expected value of a&b; S53: If H0 holds true for a t distribution T~t(n-1) with n-1 degrees of freedom, and a given identification significance level α, then If it is established, there is an error in the measuring point; is the critical value of the significance level α in the t-distribution with n-1 degrees of freedom (summarized and found from the t-distribution table), and T is the actual calculated value of the t-statistic.

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