A method for identifying outliers in monitoring data of earth-rock dams based on wavelet variable separation

Abstract

The invention relates to the technical field of data anomaly identification, and discloses a method for identifying anomalies in earth-rock dam monitoring data based on wavelet variable separation. The method comprises the following steps: step 1: acquiring earth-rock dam safety monitoring time series data; step 2: determining, based on the earth-rock dam data, influencing factors of stress, deformation and seepage of the earth-rock dam; step 3: using a wavelet method to separate environmental components and time-effect components in the monitoring time series data, to obtain time series data with the influencing factors in step 2 removed; step 4: performing outlier identification on the time series data obtained in step 3, to obtain a preliminary identification result; step 5: using a time-space comparison method to discriminate the preliminary identification result obtained in step 4, to obtain an identification result. The method reduces noise interference and improves the accuracy of anomaly identification by separating the environmental components and time-effect components in the monitoring data; and evaluates the reliability of anomaly identification by combining the time-space comparison of the monitoring data.

Description

Technical Field

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

[0002] Monitoring data from earth-rockfill dams is the foundation for analyzing and evaluating the performance of high earth-rockfill dams. However, the complex operating environment of earth-rockfill dams requires extensive data collection. Instruments are prone to anomalies during construction and operation, and due to negligence by engineers, the probability of data errors is high. Therefore, it is essential to identify outliers before analyzing the data.

[0003] Abnormal values in monitoring data are caused by measurement errors, which can be categorized by their causes and characteristics as systematic errors, random errors, and gross errors. Systematic errors are those that remain constant or vary according to a certain pattern. The former is called a custom systematic error, while the latter is called a variable systematic error. These errors are often caused by issues with the instrument itself, such as misalignment of the zero scale or inaccurate conversion calculation parameters. Random errors are those in which the absolute value and sign of the error vary in unpredictable ways. Random errors in dam monitoring are generally within the allowable measurement error and can usually be disregarded. Gross errors are errors caused by carelessness on the part of the surveyor or temporary instrument malfunctions.

[0004] Common methods for identifying outliers in safety monitoring data include the Lait criterion, Chauvenet criterion, Grubbs criterion, t criterion, and Dixon criterion. In recent years, the method derived by Stephane Mallat, which uses wavelet decomposition to calculate the Lipshitz index and then identifies gross errors based on the Lipshitz index, has been widely used in various 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 and are mainly aimed at static error identification; there is a lack of consideration of environmental factors; anomaly identification research mostly focuses on gross error identification; identification often starts from isolated measurement points without considering the temporal and spatial comparison of measurement values, and its reliability needs to be improved.

[0006] Earth-rockfill dam safety monitoring is a dynamic measurement, and its data series changes continuously over time. In addition, the deformation and seepage of earth-rockfill dams are the result of the combined effects of environmental variables such as water level and temperature. Error identification methods based solely on digital smoothness are difficult to achieve satisfactory results. Therefore, it is necessary to consider the influence of environmental variables and combine the spatiotemporal comparison of measured values to explore a method suitable for identifying anomalies in dynamic measurements of earth-rockfill dam safety monitoring. Summary of the Invention

[0007] Aiming at the problems existing in the prior art, the present invention provides a method for identifying abnormal values in 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 in 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 factors affecting stress, deformation and seepage of earth-rock dams based on the earth-rock dam data;

[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: Identify outliers on the time series data obtained in step 3 and obtain preliminary identification results;

[0013] Step 5: Use the spatiotemporal comparison method to judge the preliminary recognition results obtained in step 4 to obtain the recognition results.

[0014] Furthermore, the factors affecting the stress, deformation and seepage of earth-rock dams 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 elevation H, H 2 , water level h, rheological effect e -ct , water temperature T′, average water level J.

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

[0018] The stress and deformation of earth-rock dams are divided into construction deformation caused by filling load, instantaneous deformation caused by water load, and long-term deformation related to time. Functions are constructed for each of them 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 construction is as follows:

[0020]

[0021] Where: S H is the total settlement at depth H, where H is the depth below the dam crest and 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: Functions of water load and earth-rock dam deformation include 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 the 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 k point caused by

[0026] First water storage curve h f It is a separate 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 density of soil, γ w is the water density, γ ε is the saturated bulk density;

[0030] Establish regression models for the savings period and the operating 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 time of the day, the previous 15 days, the previous 30 days, the previous 60 days, and the previous 90 days, and 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 aging factor, a ij , a4, a5 and a6 are all factors to be determined;

[0036] S113: Considering the rheological properties of soil, the formula of the 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 unsteady seepage field expression of earth-rock dam and determine the initial and boundary conditions;

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

[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 head h1, the downstream head h2 and the water supply degree;

[0043] S124: Obtaining the influence factor of the influencing factors 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 regression model for the operational period 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 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 influence factor of water supply degree on seepage;

[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 of 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 is the factor to be determined.

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

[0064] S31: Determine the approximation 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 and removing the environmental impact from the deformation and seepage data of the earth-rock dam, 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 values of the sequence and similar points in space, judging residuals, and using the Lipschitz index.

[0068] Furthermore, the process of identifying outliers by comparing with historical values 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 ε and x ε The variance estimate 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 based on the variance estimate in step S412;

[0072] Obtain 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 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 measurement value on the jth day for the measurement point i is bij, and the spatial comparison result b of m measurement points for n consecutive days is:

[0081]

[0082] S52: The spatiotemporal comparison results of the measurement 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 with n-1 degrees of freedom T~t(n-1), 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 spatiotemporal comparison of monitoring data to evaluate the reliability of anomaly identification. BRIEF DESCRIPTION OF THE DRAWINGS

[0089] Figure 1 Schematic diagram of the process of the present invention.

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

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

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

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

[0097] Figure 9 Schematic diagram of comparison of statistical regression multiple 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] Figure 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] Figure 11 This is a schematic diagram of the impact of rainfall hysteresis on Yele seepage in an embodiment of the present invention.

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

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

[0102] Figure 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] Figure 15 Schematic diagram of the wavelet separation results of the vertical deformation pollution series of the Shiziping core rockfill dam in an embodiment of the present invention.

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

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

[0106] Figure 18 Schematic diagram showing the comparison of 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] Figure 19 Schematic diagram showing comparison of statistical regression multiple correlation coefficients 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 with reference to the accompanying drawings and specific embodiments.

[0109] like Figure 1 As shown in FIG, a method for identifying abnormal values in 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 factors affecting stress, deformation and seepage of earth-rock dams based on the earth-rock dam data;

[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 elevation H, H 2 , water level h, rheological effect 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 approximation 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 and removing the environmental impact from the deformation and seepage data of the earth-rock dam, 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: Identify outliers on the time series data obtained in step 3 and 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 spatiotemporal comparison method to judge the preliminary recognition results obtained in step 4 to obtain the recognition results.

[0122] The process of using the spatiotemporal 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 measurement value on the jth day for the measurement point i is bij, and the spatial comparison result b of m measurement points for n consecutive days is:

[0124]

[0125] S52: The spatiotemporal comparison results of the measurement 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 with n-1 degrees of freedom T~t(n-1), 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 examples.

[0130] A method for identifying abnormal values in earth-rock dam monitoring data based on wavelet variable separation includes 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 factors affecting stress, deformation and seepage of earth-rock dams based on earth-rock dam data

[0135] Based on the analysis of original observation data of multiple earth-rock dams, a functional relationship between influencing factors such as water level, temperature, fill load, and aging 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 properties of the measuring points.

[0136] The process is as follows:

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

[0138] The stress and deformation of earth-rock dams are divided into deformation during construction caused by filling load, instantaneous deformation caused by water load, and long-term deformation related to time. Functions are constructed for each of them to determine the influencing factors. The 60-day lag effect of the water level needs to be considered during the initial storage period, and the 30-day lag effect of the 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 construction 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 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: Functions of water load and earth-rock dam deformation include the earth-rock dam deformation function considering water pressure, wetting deformation and buoyancy;

[0144] Assuming that the soil deformation is small, the foundation and dam body are approximately regarded as elastic deformation, and the water load acts on the core wall. The core wall and the dam body 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 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 the k point 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 the 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] Where 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 body;

[0153] Therefore, it is determined that the deformation of the core wall k point 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 regarded 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 initial water 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 density of soil, γ w is the water density, γ ε is the saturated bulk density;

[0158] The buoyancy 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 hysteresis effect range, and the original monitoring data of high core wall 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 aging 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 time of the day, the previous 15 days, the previous 30 days, the previous 60 days, and the previous 90 days. The results of the comparison of the multiple correlation coefficients of the models considering the different hysteresis effects of the 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 in the operation period as the hysteresis interval.

[0168] S113: Considering the rheological properties of soil, the formula of the 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 variable at t→∞. The time factor affecting the rheology is determined as e -ct .

[0171] According to S111 to S113, the main factors affecting the deformation of earth-rock dams during the initial storage period are H, H 2 、e -ct The main factors affecting stress are H and e -ct The main factors affecting 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, h 2 , Δh, h f 、e -ct ; The main factors affecting deformation during operation are h, 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 aging factor, h, h 2 、h 3 They are the first power, second power and third power of water head respectively, Δh is the change of water level, h f The water storage level.

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

[0173] S121: Construct the unsteady seepage field expression 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), and 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, find the extreme value of the stationary point through the universal function and solve the expression of S121;

[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: Where [K] is the total permeability matrix; [S] is the matrix calculated from the unit water storage and location; [p] is the matrix determined by the water supply degree and the coordinates of the boundary nodes; and [F] is a constant term calculated based on the upstream and downstream heads.

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

[0185] S123: Based on 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 head h1, the downstream head h2 and the water supply degree;

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

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

[0188] According to the hydraulic principles, 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 existing engineering original observation data, the hysteresis effect of water level on seepage is obtained, and a seepage statistical regression model 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 regression model for the operational period 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 factors to be determined, h i1 is the average upstream water level in the corresponding time period; i and j are 1 to 6, which correspond to the average water level of the current 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 Figure 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, and the determination of seepage requires consideration of the external load that affects the porosity, that is, the influencing factors of fill 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, which can be used to obtain the hysteresis effect of temperature on seepage. Based on the temperature correction formula K T K is the conductivity coefficient considering the influence of hydrology. 20 is the permeability coefficient at a 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 Figure 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 instrument measuring point temperature 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 was constructed using the data of Longtoushi 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 is the factor to be determined.

[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 Figure 11 As shown in Figure 2, the influence of available rainfall is mainly due to the rainfall timeliness in the first 30 days.

[0210] Through the above process, it can be determined that the main influencing factors of the seepage pressure of the 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 the water level in the previous 30 days; if the atmospheric temperature is used, 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; rainfall considers the influence of rainfall in the previous 30 days; the main influencing factors of seepage pressure during the operation period of earth-rock dam are h and e -ct , T, the main influencing factors of seepage are h, e -ct , T, J, among which, 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; 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, i.e. f j It is v 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 on scale j-1, and Z is an integer set.

[0215] About to f 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, it can be decomposed into multiple layers as needed. The decomposition statement is determined by the actual situation. j ={c j,k} k∈Z, D j ={d j,k} k∈Z , the decomposition process is as follows Figure 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 Remove the high frequency decomposition coefficient, remove the environmental impact of the deformation and seepage data of the earth-rock dam, and obtain the 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 Figure 13 .

[0218] Based on the vertical deformation data of the Shiziping core rockfill dam, a fixed value pollution sequence was injected from 10th and 15th of 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 value of the pollution sequence is shown in Figure 2. Figure 14 .

[0219] Step 4: Identify outliers on the time series data obtained in step 3 and 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 identifying outliers 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 Average value

[0223] S412: Since the means of the two sequences should satisfy a certain constant μ i 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 the normal distribution in Error identification with For the judgment standard; if it is a comparison of different measuring points, if there is no fixed value error, Should satisfy the normal distribution Error identification with 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 compared at different measuring points is right Figure 14 The fixed value system error identification is performed based on the sequence, and the results are shown in Table 1. Figure 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 injection 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 identifying outliers 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. Figure 15 Based on the external vertical deformation data of the Shiziping core rockfill dam, a pollution sequence with a step gradient of 0.1 was injected starting from October 15, 2013. The environmental quantity, time effect and constant value were separated. The data were used to identify the variable value systematic error. The Abbe test value of the sequence was 0.232, which was greater than the standard value of 0.164, indicating that the variable value error existed.

[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 in each layer, then the Lipschitz index is positive, which is the modulus value of the wavelet transform of the signal point and is a normal value; if The Lipschitz index is negative, which is the wavelet transform modulus of the noise point and an abnormal value. The same applies to other decomposition levels. Figure 16 When the 3σ criterion is used to identify the gross error of the sequence, 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 subject to continuous changes under the combined influence of external environment and internal factors. Therefore, the reliability of identification is judged by the subsequent changes in the 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 intervals are fuzzy segments); then the recognition results for n consecutive days are a={a1,a2...a n}, the error comparison and identification result of the measurement value on day j for measurement point i is b ij , for n consecutive days, the spatial comparison result b of m measurement points is:

[0239]

[0240] S52: The spatiotemporal comparison results of the measurement points a & b are:

[0241]

[0242] Determine whether H0: a&b = 1 is true, where H0 is the expected value of a&b; and determine the robustness of the spatiotemporal error 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 the 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 actual calculated value of the t statistic. The vertical monitoring sequence of the Shiziping core rockfill dam crest is used as the verification object, see Figure 17 The results of the spatiotemporal comparison are shown in Table 2. In the figure, identification points 1 and 4 are overall uplift points that stabilize after the uplift and are therefore non-outliers; monitoring point 2 is an abnormal sharp point; and monitoring point 3 is a fluctuating point and an outlier. In the isolated point determination, both were identified as outliers. However, combined with the spatiotemporal comparison, identification points 1 and 4 are effectively identified as non-outliers.

[0245] Table 2. Confidence of spatiotemporal stability identification of gross errors in vertical monitoring of the 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: Figure 18 and Figure 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. In addition, the influence of environmental factors is taken into account, and 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, solving the defect of the previous method that 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 attributes 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 influence, it effectively avoids the misjudgment caused by excessive changes in the measured value caused by sudden changes in the environmental quantity. Compared with the 3σ criterion, the accuracy of outlier identification is improved. The reliability of the gross error identification results is improved. Taking into account 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 factors affecting stress, deformation and seepage of earth-rock dams based on the earth-rock dam data; 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; the influencing shadows are the environmental factor and the time-effect factor; The specific process is as follows: S31: Determine the approximation 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 f j Remove the high-frequency decomposition coefficients, remove the environmental impact from the deformation and seepage data of the earth-rock dam, and obtain new deformation and seepage coefficients. According to the scale coefficients, the wavelet coefficients are obtained to obtain the monitoring data without environmental impact. Step 4: Identify outliers on the time series data obtained in step 3 and obtain preliminary identification results; Step 5: Use the spatiotemporal comparison method to judge the preliminary recognition results obtained in step 4 to obtain the recognition results.

2. The method for identifying abnormal values in earth-rock dam monitoring data based on wavelet variable separation according to claim 1 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 depth below the dam crest H, H 2 , water level h, time-effect factor e -ct , water temperature T′, average water level J.

3. The method for identifying abnormal values in 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 dams is as follows: The stress and deformation of earth-rock dams are divided into construction deformation caused by filling load, instantaneous deformation caused by water load, and long-term deformation related to time. Functions are constructed for each of them 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 construction is as follows: Where: S H is the total settlement at depth H, where H is the depth below the dam crest and 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: Functions of water load and earth-rock dam deformation include 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 the height h from the dam base caused by the water pressure is: Where: y is the deformation, is the horizontal displacement of point k caused by the shear force of the dam body, is the dam body rotation angle θ d Horizontal displacement of k point caused by First water storage level h f It is a separate influencing factor reflecting the soil wetting characteristics; The dam body below the water infiltration line is affected by buoyancy, and the buoyancy force F per unit soil is: F=γ+γ w -c ε Where: γ is the compacted density of soil, γ w is the water density, γ ε is the saturated bulk density; Establish regression models for the savings period and the operating 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, j describes (h it -h0) is the power of the nonlinear effect, a0 is a constant term, a ij is the coefficient of the water level model to be determined, h i is the average water level in the corresponding time period, h0 is the dam foundation elevation, e -ct is the time-effecting factor, a4, a5 and a6 are all factors to be determined; S113: Considering the rheological properties of soil, the formula of the 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 ratio.

4. The method for identifying abnormal values in 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 unsteady seepage field expression of earth-rock dam and determine the initial and boundary conditions; S122: According to the variational method, find the extreme value of the stationary point through the universal function and solve the expression of S121; 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 head h1, the downstream head h2 and the water supply degree; S124: Obtaining the influence factor of the influencing factors 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 regression model for the operational period 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 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 influence factor of water supply degree on seepage; 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 is the factor to be determined.

5. The method for identifying abnormal values in 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 using the Lipschitz index.

6. The method for identifying abnormal values in earth-rock dam monitoring data based on wavelet variable separation according to claim 5 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 ε and x ε The variance estimate 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 based on the variance estimate in step S412; Obtain 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.

7. The method for identifying abnormal values in earth-rock dam monitoring data based on wavelet variable separation according to claim 1 is characterized in that: The process of identifying outliers using the residual judgment method 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 to determine whether there are outliers.

8. The method for identifying abnormal values in earth-rock dam monitoring data based on wavelet variable separation according to claim 5 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.

9. The method for identifying abnormal values in earth-rock dam monitoring data based on wavelet variable separation according to claim 1 is characterized in that: The process of using the spatiotemporal 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 measurement value on day j for measurement point i is b ij , for n consecutive days, the spatial comparison result b of m measurement points is: S52: The spatiotemporal comparison results of the measurement 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 with n-1 degrees of freedom T~t(n-1), 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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