A tunnel surrounding rock deformation prediction method based on time series and inversion analysis

Abstract

The application discloses a tunnel surrounding rock deformation prediction method based on time series and inversion analysis, and comprises the following steps: S1, setting tunnel monitoring points, collecting, testing and preprocessing relevant data obtained by the tunnel monitoring points to obtain pretreatment data; S2, analyzing the surrounding rock level, buried depth and support structure of the monitoring section of each tunnel monitoring point, setting tunnel monitoring reference control values and early warning values; S3, obtaining the management level of the monitoring section of each tunnel monitoring point according to the pretreatment data combined with the tunnel monitoring reference control values and early warning values, analyzing each management level and determining the section for time series analysis and inversion analysis; and S4, collecting the time series data of the section for time series analysis and inversion analysis, and adopting a wavelet-time series analysis model to predict the deformation of the surrounding rock. The application can timely make an advanced prediction on the geological conditions in front of the tunnel and accurately judge the stability of the surrounding rock.

Description

Technical Field

[0001] The present invention belongs to the field of tunnel surrounding rock deformation prediction, and in particular relates to a tunnel surrounding rock deformation prediction method based on time series and inversion analysis. Background Art

[0002] my country has a vast territory and complex topography. With the rapid development of the economy, the pace of road construction in my country is also accelerating. As an important component of road construction, the number of tunnels is also increasing. Due to the particularity of tunnel structure, deformation of tunnel surrounding rock will make the safety of construction and vehicle operation unguaranteed. Therefore, how to scientifically predict, monitor and control the deformation of tunnel surrounding rock has become an urgent problem to be solved.

[0003] For a complex mountain highway or railway stretching over thousands of miles, the sheer number of tunnels, complex construction conditions, and geological environment make it difficult to predict and control tunnel surrounding rock deformation. Furthermore, the nature and stability of the tunnel rock mass are unclear, and the factors influencing surrounding rock stability are numerous and complex, making quantitative analysis difficult. With the introduction and application of the New Austrian Tunneling Method (NATM), my country's tunnel construction technology has greatly advanced, and the scale of tunnel construction has increased. The resulting large amount of field monitoring data has provided researchers with an alternative approach to determining rock mass parameters: inverse analysis. Monitoring and measurement, as one of the three key elements of the NATM, plays a crucial role in the overall tunnel construction process. Prompting timely access to first-hand data from on-site monitoring and collecting information on stress, strain, and displacement changes between the surrounding rock and the support structure during tunnel excavation is crucial for subsequent construction control. In recent years, deformation analysis and predictive modeling have become increasingly popular research areas. For a long time, deformation data analysis and processing have assumed that the observed data are independent or uncorrelated. This type of statistical method is a static data processing method. Although each observation is obtained under relatively independent conditions, these observations are interdependent and have a "memory" characteristic, forming a dynamic data model. Therefore, the single linearity and static limitations of traditional time series prediction models, which ignore the influence of the construction process, make it difficult to quickly and effectively predict and analyze the deformation of specific tunnel surrounding rocks in actual projects. Summary of the Invention

[0004] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a method for predicting tunnel surrounding rock deformation based on time series and inversion analysis.

[0005] To achieve the above object, the technical solution adopted by the present invention is:

[0006] A method for predicting tunnel surrounding rock deformation based on time series and inversion analysis includes the following steps:

[0007] S1. Setting up tunnel monitoring points, and collecting, inspecting, and preprocessing relevant data obtained from the tunnel monitoring points to obtain preprocessed data;

[0008] S2. Analyze the surrounding rock grade, burial depth, and support structure of the monitoring section of each tunnel monitoring point set in step S1 based on the tunnel engineering geological conditions and the preprocessed data obtained in step S1, and set tunnel monitoring benchmark control values ​​and warning values ​​based on the analysis results;

[0009] S3. Based on the pre-processed data obtained in step S1 and the tunnel monitoring benchmark control value and warning value obtained in step S2, the management level of the monitoring section of each tunnel monitoring point is obtained, and each management level is analyzed to determine the section for time series analysis and inversion analysis;

[0010] S4. Collecting the time series data of the cross section obtained from the time series analysis and inversion analysis in step S3, and using a wavelet-time series analysis model to predict the deformation of the surrounding rock.

[0011] Preferably, in step S1, the inspection and preprocessing process of the tunnel-related data includes the removal of singular data, zero mean processing and stationarity inspection operations.

[0012] Preferably, in step S1, the setting of the tunnel monitoring points is divided into external monitoring points and internal monitoring points according to the measurement location. The external monitoring points are buried in the ground surface and are used to monitor the surface settlement in the area affected by tunnel excavation; the internal monitoring points are buried around the excavated surrounding rock and inside the support structure to monitor the deformation of the surrounding rock and the internal force of the support.

[0013] Preferably, in step S4, the time series data is obtained by the following method:

[0014] The cross section of the time series analysis and inversion analysis in step S3 is monitored, and the monitored displacement data are collected in chronological order according to the monitoring frequency to form a time series.

[0015] Preferably, in step S4, the time series data needs to be inspected and preprocessed before using the wavelet-time series analysis model for predictive analysis. The data inspection and preprocessing include the removal of singular data, zero mean processing and stationarity inspection operations.

[0016] Preferably, in step S4, the wavelet-time series analysis model is established by the following method:

[0017] S41. Selection of wavelet basis and determination of number of layers and coefficients;

[0018] S42, wavelet threshold denoising, reconstruction coefficients, reconstruction time series analysis model;

[0019] S43, selecting the type of the reconstructed time series analysis model to determine the type of the time series model;

[0020] S44, determining the order of the time series model obtained in step S43 to obtain the order of the wavelet-time series model;

[0021] S45, estimating the parameters of the time series model obtained in step S43 to obtain the parameters of the wavelet-time series model;

[0022] S46, testing the applicability of the order of the time series model obtained in step S44, and further determining the final order of the time series model;

[0023] S47. Determine a wavelet-time series analysis model based on the time series model type obtained in step S43, the final order of the time series model obtained in step S46, and the parameters of the time series model obtained in step S45.

[0024] Preferably, in step S42, the time series analysis model is established by the following method:

[0025] S421. Select and determine the type of the time series model.

[0026] S422, determining the order of the time series model obtained in step S421 to obtain the order of the time series model;

[0027] S423, estimating the parameters of the time series model obtained in step S421 to obtain the parameters of the time series model;

[0028] S424, testing the applicability of the order of the time series model obtained in step S422, and further determining the final order of the time series model;

[0029] S425 , determining a time series analysis model according to the time series model type obtained in step S421 , the final order of the time series model obtained in step S424 , and the parameters of the time series model obtained in step S423 .

[0030] Preferably, step S421 specifically includes the following steps:

[0031] S4211. Determine whether the autocorrelation function has k-step truncation. If so, the time series model is MR(k);

[0032] S4212. If the autocorrelation function does not have k-step truncation, determine whether the partial correlation function has k-step truncation. If so, the model is AR(k); if not, the model is ARMA(p,q).

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] (1) The tunnel surrounding rock deformation prediction method based on time series and inversion analysis provided by the present invention can perform multiple scale refinement analyses on the time series through wavelet analysis by designing a wavelet-time series analysis model, so that the basic characteristic information of the time motion series can be accurately retained;

[0035] (2) The present invention establishes a dynamic inversion analysis and prediction model for surrounding rock deformation through a wavelet-time series model, timely predicts the geological conditions ahead of the tunnel, and accurately judges the stability of the surrounding rock. Based on the feedback information, the tunnel design and construction plan are scientifically and rationally organized. If necessary, the original design of the tunnel support parameters and construction methods must be adjusted and corrected to achieve dynamic information design and construction, ensure smooth tunnel crossing, and improve the tunnel surrounding rock deformation prediction model and application based on time series and inversion analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 This is a flow chart of an algorithm for predicting surrounding rock deformation using a time series model in an embodiment of the present invention;

[0037] Figure 2 is the change diagram of wavelet decomposition coefficients;

[0038] Figure 3 This is the flow chart of wavelet threshold denoising;

[0039] Figure 4 is the change diagram of wavelet reconstruction coefficients;

[0040] Figure 5 Schematic diagram of the layout of surface subsidence observation points;

[0041] Figure 6 This is a schematic diagram of the arrangement of measurement points for vault subsidence and horizontal convergence;

[0042] Figure 7 This is a comparison chart of the vault settlement data before and after wavelet processing;

[0043] Figure 8 This is a comparison chart of data before and after clearance convergence wavelet processing;

[0044] Figure 9 The relative error rate diagram of the in-sample prediction of the vault settlement and clearance convergence monitoring data calculated by the time series model;

[0045] Figure 10 This is a graph of the relative error rate of the in-sample prediction of the vault settlement and clearance convergence monitoring data calculated using the wavelet-time series model. DETAILED DESCRIPTION

[0046] Exemplary embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although exemplary embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth above. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the present disclosure to those skilled in the art.

[0047] The embodiment of the present invention provides a method for predicting tunnel surrounding rock deformation based on time series and inversion analysis, which specifically includes the following steps:

[0048] S1. Set up tunnel monitoring points and collect, inspect, and preprocess relevant data (such as surface settlement at the tunnel entrance and exit sections, vault settlement, and clearance convergence) to obtain preprocessed data.

[0049] The inspection and preprocessing process of the tunnel-related data includes the removal of singular data, zero mean processing and stationarity inspection operations;

[0050] The tunnel monitoring points are divided into external monitoring points and internal monitoring points according to the measurement location. The external monitoring points are buried in the ground surface and are used to monitor the surface settlement in the area affected by tunnel excavation; the internal monitoring points are buried around the excavated surrounding rock and inside the support structure to monitor the deformation of the surrounding rock and the internal force of the support.

[0051] S2. Analyze the surrounding rock grade, burial depth, and support structure of the monitoring section of each tunnel monitoring point set in step S1 based on the tunnel engineering geological conditions and the preprocessed data obtained in step S1, and set tunnel monitoring benchmark control values ​​and warning values ​​based on the analysis results;

[0052] S3. Based on the pre-processed data obtained in step S1 and the tunnel monitoring benchmark control value and warning value obtained in step S2, the management level of the monitoring section of each tunnel monitoring point is obtained, and each management level is analyzed to determine the section for time series analysis and inversion analysis;

[0053] S4. Collecting the time series data of the cross section obtained from the time series analysis and inversion analysis in step S3, and using a wavelet-time series analysis model to predict the deformation of the surrounding rock.

[0054] In step S4, the time series data is obtained by the following method:

[0055] The cross section of the time series analysis and inversion analysis in step S3 is monitored, and the monitored displacement data are collected in chronological order according to the monitoring frequency to form a time series.

[0056] Commonly used time series models in practice include the AR model, the MA model, and the ARMA model. The Autoregressive Integrated Moving Average (ARIMA) model is a non-stationary time series model. When the differencing order I in the ARIMA model is zero, the ARIMA model is also an ARMA model. Therefore, in its special form, the ARIMA model can be considered a stationary time series model.

[0057] In step S42, the time series analysis model is established by the following method:

[0058] S421. Select and determine the type of the time series model.

[0059] Step S421 specifically includes the following steps:

[0060] S4211. Determine whether the autocorrelation function has k-step truncation. If so, the time series model is MR(k);

[0061] S4212. If the autocorrelation function does not have k-step truncation, determine whether the partial correlation function has k-step truncation. If so, the model is AR(k); if not, the model is ARMA(p,q).

[0062] The search starts from the low order, and parameter estimation and model suitability testing are repeatedly performed until a suitable model is found. In the embodiment of the present invention, the ARMA model is selected for performance analysis. Low-order models can be tried one by one. The smaller p+q is, the better.

[0063] According to the observed time series, the calculations are performed according to the following formulas:

[0064]

[0065]

[0066] Where: x t is the observation value of the random process or time series, is the estimated value of the autocorrelation function; is the estimated value of the partial autocorrelation function.

[0067] The estimated value of the autocorrelation function is calculated by the above formula and the estimated partial autocorrelation function Then the type of model is determined based on this.

[0068] S422, determining the order of the time series model obtained in step S421 to obtain the order of the time series model;

[0069] S423, estimating the parameters of the time series model obtained in step S421 to obtain the parameters of the time series model;

[0070] For a stationary time series {x t Fit AR(n) and ARMA(p,q) models respectively and calculate the residuals of the two models respectively (Theoretically, the residual values ​​should be equal at the same time.) From the system perspective, through the sample data {x t The white noise sequences of the AR(n) and ARMA(p,q) models fitted can be considered equal, so the AR(n) model can be fitted using process data first. The white noise sequence required for fitting the ARMA(p,q) model can be obtained by calculating the AR model residual sequence, and then estimating the ARMA model parameters. The calculation process is as follows:

[0071] ① Using data sample {x t}First fit the AR(n)(n≥p+q) model and estimate the model parameters

[0072] ② The residual sequence from t=n+1 to t=N is calculated by the following formula: Perform the transformation:

[0073]

[0074] ③Substitute the calculation obtained in step ② into the following formula:

[0075]

[0076] Where: x t is a time series sample; is the residual sequence; are model parameters; θ j (j=1, 2, ..., q) is the sliding average coefficient;

[0077] The following linear equations can be obtained, which can be expressed in matrix form:

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] ④ In the matrix x in t 、 If the values ​​of are known, the ARMA model parameters can be obtained using the least squares method, and the parameter matrix

[0084]

[0085] S424, testing the applicability of the order of the time series model obtained in step S422, and further determining the final order of the time series model;

[0086] The most basic principle of model applicability testing is to test the disturbance sequence Is it a white noise sequence? From the perspective of mathematical statistics, it is mainly to test the residual sequence for model fitting. Whether it is a white noise sequence; the applicability test of the model can be roughly divided into the following four types: a: Directly test the residual sequence through the autocorrelation coefficient criterion, Q-criterion, serial correlation criterion, etc. b: to test whether it is white noise; b: to test whether the residual sum of squares or the variance of the residual sequence is significantly reduced through the residual sum of squares (residual variance) criterion and the F-criterion; c: Akaike information criteria such as the minimum final forecast error criterion, Akaike information criterion (AIC), and Bayesian information criterion (BIC); d: for different application purposes and different parameter estimation methods, the applicability is tested through criteria that are suitable for the application purpose, criteria that are suitable for the parameter estimation method, empirical criteria, etc. that can meet special requirements.

[0087] Of the aforementioned adaptability testing methods, the AIC and BIC criteria are widely used in practical engineering due to their simple calculations and ease of operation. Furthermore, these two criteria effectively address the issue of increased error due to increasing model order. The resulting fitted model order closely approximates the actual system.

[0088] S425 , determining a time series analysis model based on the time series model type obtained in step S421 , the final order of the time series model obtained in step S424 , and the parameters of the time series model obtained in step S423 .

[0089] In step S4, the time series data needs to be inspected and preprocessed before using the wavelet-time series analysis model for prediction analysis. The inspection and preprocessing of the data include the removal of singular data, zero mean processing and stationarity inspection operations, specifically:

[0090] (1) Data collection, data testing, and data preprocessing; the main operations of data preprocessing include the removal of singular data, zero mean processing, and stationarity testing;

[0091] a: Eliminate singular data

[0092] The operational data obtained on-site will inevitably contain some singular data. These singular data are generally gross errors caused by accidental measurement errors, instrument physical distortion, etc., which will seriously affect the accuracy of time series analysis results. However, determining whether a set of data contains singular data with gross errors and whether to eliminate them is a matter that requires sufficient theoretical basis. The Laida criterion can be used to determine whether the measurement data contains gross errors. Its principle is as follows:

[0093] Given a time series {x1, x2, ...x n}, calculate its arithmetic mean and residual error The standard error is calculated according to the Bessel formula:

[0094]

[0095] For the sequence {x1, x2, ...x n} for a specific value, if its residual error Δx i (1≤i≤n) satisfies |Δx i |>3σ, the data is considered to be a singular value containing gross errors and needs to be eliminated.

[0096] b: Zero mean processing

[0097] When the time series {x i If} is a stationary series but has a non-zero mean, it needs to be processed with zero mean. The steps are as follows:

[0098] Estimate the time series {x t The mean of

[0099] According to the formula to process;

[0100] Get the zero mean {y t}sequence, the sequence processed by zero mean is still recorded as {x t}.

[0101] c: Stationarity test

[0102] Stationarity is a key characteristic of random processes. The stationarity of a time series is related to the data sampling interval, but not the sampling start time. A prerequisite for time series analysis is that the series must be stationary. However, most field data is non-stationary, so it needs to be stabilized before modeling.

[0103] The definition of a stationary series is:

[0104] If the time series {x t The following two conditions are met:

[0105] ① Take any t, μ t =E(x t )=c, where c is a constant;

[0106] ② Take any t, s, k, γ (t, s) = γ (k, k + st);

[0107] Then the time series {x t} is a stationary series.

[0108] The time series stationarity test methods mainly include parametric test method and non-parametric test method. The non-parametric test method is also called the runs test method. This method only requires a set of measured data and does not require any form of distribution law to be assumed for the data. It is more widely used in practice.

[0109] The following is a brief discussion of non-parametric test methods:

[0110] Define the run as a set of symbol sequences that divide the sequence into two unrelated classes without changing the random sequence. For time series:

[0111] ①Calculate the mean of the sequence

[0112] ②If It is represented by the symbol "+"; otherwise it is represented by "-", thus obtaining a set of symbol sequences. A run is represented by a continuous sequence of identical symbols.

[0113] ③ By calculating the time series {x t The total number of runs of} is r, and the calculated statistical quantity z is:

[0114]

[0115] in, N3=N1+N2, N1 and N2 are the runs of the symbols “+” and “-” respectively;

[0116] ④If |z|≤1.96, the sample data is stationary, otherwise it is not stationary;

[0117] ⑤If the output sequence is non-stationary, it can be converted into a stationary random number sequence by performing one or more difference processing on it.

[0118] In step S4, the wavelet-time series analysis model is established by the following method:

[0119] S41. Selection of wavelet basis and determination of number of layers and coefficients;

[0120] First, we need to select the wavelet basis function and follow the "four principles": orthogonality, linear phase, continuity, and compact support. Several common wavelets are as follows:

[0121] a:Haar wavelet

[0122] Haar function

[0123]

[0124] This is the simplest orthogonal wavelet, namely

[0125]

[0126] It is a compactly supported wavelet, meaning that its function values ​​can only be between 0 and 1. Because it is the simplest orthogonal wavelet, its calculation is relatively simple, but it is discontinuous and non-differentiable, meaning it has no smoothness. There is only one such wavelet, and its localization performance is limited by that of the square wave, so it is rarely used in practical applications.

[0127] b:Daubechies(dbN) wavelet system

[0128] The characteristics of this wavelet are The discrete orthogonal wavelet can be obtained from the scaling function. The support domain of the sum scaling function is from 0 to 2N-1. With N vanishing moments, that is There is an Nth-order zero at ω = 0. When N = 1, db1 is the Haar wavelet; when N > 1, dbN begins to become not completely symmetric. It does not show the expression, but the coefficients of the two-scale equation {h k The square of the modulus of the transfer function of} has an explicit expression. Assume that:

[0129]

[0130] in is the binomial coefficient, then

[0131]

[0132]

[0133] c: Symlets (symN) wavelet system

[0134] The asymmetry of the db function causes significant distortion of the time series, especially around edges and details, which is extremely detrimental to image processing. Therefore, a nearly symmetric wavelet function was proposed based on the db function. SymN has an advantage over dbN in terms of symmetry, and also has good orthogonality and biorthogonality.

[0135] d: Coiflet (coifN) wavelet system

[0136] The Coiflet function is also a Daubechies-derived wavelet function and similarly exhibits better symmetry than db. However, coifN has a longer support length. However, increasing support length degrades the performance of tight supports and increases computational time, resulting in lower efficiency. coifN also has a larger vanishing moment. While a larger vanishing moment reduces the number of wavelet coefficients to zero, facilitating data compression and noise elimination, the support length increases with increasing lattice length.

[0137] e:Biorthogonal(biorNr.Nb) wavelet system

[0138] Biorthogonal function systems have good symmetry and are widely used in signal sequence reconstruction. They have the following forms:

[0139] Nr value 1 2 3 4 5 6 Nd value 1,3,5 2,4,6,8 1,3,5,7,9 4 5 8

[0140] Among them, r means reconstruction and d means decomposition. For example, bior2.8 means using a function bior8 for decomposition and another function bior2 for reconstruction.

[0141] f:Morlet(morl) wavelet

[0142] The Morlet function is It has no scaling function, compact support, or orthogonality, but it can be seen from the expression that it has infinite order smoothness, that is, regularity.

[0143] g:Mexican Hat (mexh) wavelet

[0144] The function is

[0145]

[0146] It is obtained by taking the second derivative of a Gaussian function and is named after the image that looks like a cross section of a Mexican hat. It has good compact support, but like the Morlet wavelet, it does not have a scaling function and is therefore not orthogonal.

[0147] h:Meyer wavelet

[0148] Meyer waves are orthogonal waves with compact support and arbitrary regularity (smoothness).

[0149] Based on the introduction of the above wavelets, the embodiment of the present invention selects db3, which has the best denoising effect among the respective wavelet systems.

[0150] Different time series have their own ideal number of decomposition layers for denoising. A few experiments based on your needs or requirements will yield the desired result. Excessive decomposition layers can burden the computation and lead to loss of the original sequence, resulting in significant deviations in the reconstruction of time samples. Too few layers can lead to ineffective denoising. Generally, the lowest number of layers that produces a smooth time series curve is sufficient. In this embodiment, three-layer wavelet decomposition is sufficient.

[0151] Wavelet transform is the process of changing a time series into a main time series and a series of noise series. The main time series can be approximated by the coefficient w a The noise sequence can be represented by the sum of products of detail coefficients and wavelet basis.

[0152] Basic wavelet definition: Wavelet is a function space L 2 (R) A function or signal sequence that satisfies the following conditions

[0153]

[0154] The above formula is called the "admissibility condition". Here, R * =R-(0) represents all non-zero real numbers.

[0155] if The above formula can be further expressed as

[0156]

[0157] because A standard orthogonal basis can be "created" by transformation, so it can also be called It is the mother wavelet or wavelet basis, which is why a wavelet basis can represent any approximation function.

[0158]

[0159] Where a is the scale factor, which represents the frequency information of the signal and plays a role of expansion and contraction, and a≠0; τ is the translation factor, which represents the time sequence of the signal and plays a role of translation.

[0160] The continuous wavelet transform can be expressed as

[0161]

[0162] Taking the three-layer wavelet as an example, the change of wavelet decomposition coefficient can be expressed as

[0163]

[0164]

[0165] in, is the scale factor; is the wavelet decomposition coefficient of each layer.

[0166] The change of wavelet decomposition coefficients is shown in the figure Figure 2 shown.

[0167] S42, wavelet threshold denoising, reconstruction coefficients, reconstruction time series analysis model;

[0168] Wavelet denoising principle: Try to make the variance of the denoised time series as small as possible compared with the original time series. In addition, the denoised time series cannot reduce the regularity of the original series. The principle of threshold denoising is to process the wavelet coefficients after wavelet decomposition of the noisy time series, that is, compare the size with the set domain value, and discard all coefficients smaller than the set value. Finally, use the processed wavelet coefficients to reconstruct the time series to obtain the denoised time series. The wavelet threshold denoising process is as follows: Figure 3 shown.

[0169] Wavelet reconstruction is also called inverse wavelet transform. Figure 4 The wavelet reconstruction coefficient can be obtained intuitively, and then the wavelet reconstruction coefficient formula can be obtained.

[0170] Wavelet coefficient reconstruction uses the Mallat algorithm to reconstruct the time series. The reconstruction algorithm is as follows:

[0171]

[0172]

[0173] Where h and g are low-pass and high-pass filters respectively; j is the scale number in the scale space.

[0174] S43, selecting the type of the reconstructed time series analysis model to determine the type of the time series model;

[0175] S44, determining the order of the time series model obtained in step S43 to obtain the order of the wavelet-time series model;

[0176] S45, estimating the parameters of the time series model obtained in step S43 to obtain the parameters of the wavelet-time series model;

[0177] S46, testing the applicability of the order of the time series model obtained in step S44, and further determining the final order of the time series model;

[0178] S47. Determine a wavelet-time series analysis model based on the time series model type obtained in step S43, the final order of the time series model obtained in step S46, and the parameters of the time series model obtained in step S45.

[0179] The following example uses the Niuliantang Tunnel to verify the deformation prediction analysis results of the surrounding rock using the method provided by the embodiment of the present invention.

[0180] S1. Setting up tunnel monitoring points, and collecting, inspecting, and preprocessing relevant data obtained from the tunnel monitoring points to obtain preprocessed data;

[0181] (1) Measuring points outside the cave

[0182] Surface settlement observation points of the shallow buried section outside the Niuliantang Tunnel are as follows: Figure 5 shown.

[0183] 1) Surface subsidence

[0184] The horizontal layout range of the lateral surface settlement measurement points should be larger than the width of the predicted sliding rupture surface on both sides, and at least one section should be set up for each tunnel entrance. The number of measurement points in a single cross section should be no less than 11, and the measurement points should be densely arranged near the tunnel centerline. The distance between adjacent measurement points should be controlled at 2 to 3 meters, and the distance between measurement points on both sides of the arch is 3 to 4 meters. The distance between measurement points can be appropriately increased away from the tunnel centerline, and the maximum distance shall not be greater than 5 meters.

[0185] At the shallow buried biased tunnel entrance, in addition to the lateral surface settlement monitoring, it is necessary to measure the horizontal and longitudinal displacement at the same time. The shallow buried section of the tunnel entrance is arranged with a section every 10 to 15 meters, and the remaining sections should be arranged according to the requirements of the specifications, and the measurement points should be arranged in the cross section where the clearance convergence measurement points are located in the tunnel.

[0186] (2) Measurement points inside the cave

[0187] The measurement points in the tunnel are mainly for the arch settlement and clearance convergence measurement points. The arrangement of the arch settlement and horizontal convergence measurement points of Niuliantang Tunnel is shown in Figure 6 .

[0188] 1) Layout of settlement convergence points

[0189] Vault subsidence measurement points are used to assess the stability of the tunnel vault surrounding rock, while perimeter convergence points are used to assess the stability of the surrounding rock, the adequacy of the initial support design and construction methods, and to determine the timing of secondary lining placement. Sections are arranged every 10-15 meters in fully to strongly weathered Grade V surrounding rock sections. Generally, sections are arranged every 10-20 meters in Grade V surrounding rock sections, every 20-40 meters in Grade IV surrounding rock sections, and every 30-50 meters in Grade III surrounding rock sections. Measurement points are generally placed along the vault centerline. When the surrounding rock is poor, three measurement points are set on the vault.

[0190] The arrangement of peripheral convergence measurement points should be in the same section as that of vault settlement measurement. 1 to 3 pairs of measurement points should be arranged in each section according to the excavation method (1 pair of measurement points for each step). Bottom heave measurement points are generally arranged in a section every 20 to 40 meters in Grade V surrounding rock areas. In principle, the measurement points should be arranged on the center line of the inverted arch, and the measurement points should be arranged in the same section as that of vault settlement and horizontal convergence measurement. The measurement points and measurement frequency should be increased in areas with larger deformation.

[0191] S2. Analyze the surrounding rock grade, burial depth, and support structure of the monitoring section of each tunnel monitoring point set in step S1 based on the tunnel engineering geological conditions and the preprocessed data obtained in step S1, and set tunnel monitoring benchmark control values ​​and warning values ​​based on the analysis results;

[0192] By consulting relevant specifications and literature, and combining the engineering geological conditions of the Niuliantang Tunnel with on-site monitoring and measurement data, we analyzed factors such as the surrounding rock grade, burial depth, and support structure of the monitoring section where the measuring points were set. The allowable deformation of the tunnel vault settlement, surface settlement, and clearance convergence during construction was designed to be 20 mm, and the monitoring and early warning benchmark control values ​​were set as shown in Table 1 below.

[0193] Table 1 Tunnel monitoring benchmark control values ​​and warning values

[0194]

[0195] S3. Based on the pre-processed data obtained in step S1 and the tunnel monitoring benchmark control value and warning value obtained in step S2, the management level of the monitoring section of each tunnel monitoring point is obtained, and each management level is analyzed to determine the section for time series analysis and inversion analysis;

[0196] To ensure personnel safety during tunnel construction, collected displacement monitoring data served as the basis for monitoring and early warning of surrounding rock deformation. This early warning result, combined with observations inside and outside the tunnel entrance, served as a feedback and evaluation criterion for on-site construction management. Therefore, based on the relevant assessments of monitoring results in the standard, the early warning levels for surface settlement, vault settlement, and clearance convergence at the entrance and exit sections of the left and right tunnels of the Niuliantang Tunnel were managed. The results are shown in Table 2 below.

[0197] Table 2 Tunnel surrounding rock deformation monitoring management level table

[0198]

[0199]

[0200] Table 2 shows that the deformation rate at surface settlement measuring point YK4+680, located at the right tunnel exit, is within the normal range and is classified as normal. ZK2+025, ZK2+065, ZK2+100, and ZK4+555, ZK4+580, and ZK4+640 are monitoring sections at the left tunnel entrance and exit. ZK4+555 and ZK4+580 have two clearance convergence lines, so the cumulative convergence value and convergence rate need to be presented separately. Among the three sections at the left tunnel entrance, the initial deformation rate of the crown settlement at ZK2+065 is the highest, exceeding the settlement control baseline. The management level is classified as alarm. Effective monitoring should be carried out during the initial construction phase, with enhanced initial support construction and timely follow-up on the invert arch and secondary lining. However, the clearance convergence initial deformation rate of the left and right tunnels does not meet the requirements. The management level is mostly alarm or early warning. The deformation rate of some sections far exceeds the control benchmark value. Therefore, engineering measures should be taken immediately to control the deformation of the surrounding rock.

[0201] Therefore, based on the above analysis of tunnel monitoring data, section ZK2+065 was selected as the section for time series analysis and inversion analysis.

[0202] S4. Collecting the time series data of the cross section obtained from the time series analysis and inversion analysis in step S3, and using a wavelet-time series analysis model to predict the deformation of the surrounding rock.

[0203] Taking the processing and analysis of monitoring data from tunnel projects as an example, during the surrounding rock deformation monitoring process, displacement sensors placed at measuring points acquire displacement data in chronological order according to the monitoring frequency specified in the construction plan, forming a time series. A time series model is established based on the differential form of the deformation data. Data features are then extracted and judged based on the model to generate displacement data prediction results. Based on the early warning level control analysis of the Niuliantang Tunnel vault settlement and clearance convergence monitoring data in S2, section ZK2+065 was selected as the primary analysis section for the prediction analysis of surrounding rock deformation values.

[0204] In addition, in order to further illustrate the rationality of using the wavelet-time series analysis method to predict the surrounding rock deformation value, the ZK2+065 section was selected, and the time series model and wavelet-time series model were used to predict the surrounding rock deformation of the section.

[0205] (1) Effect of time series model

[0206] The prediction process of the time series model is as follows Figure 1 The cross-section was measured from August 6 to August 27, 2021, for a total of 18 days. The arch settlement measurement lines were uniformly numbered GD01, and the clearance convergence lines were uniformly numbered SL01. The specific monitoring data of the time series model are shown in Table 1 below. Based on the established ARMA (p, q) model, static prediction of the existing measured sample data values ​​can be used to obtain the model's in-sample prediction values, as shown in Table 3 below.

[0207] Table 3 Section vault settlement and clearance convergence measurement data, sample prediction data Unit: mm

[0208]

[0209]

[0210]

[0211] Combining the predicted value with the measured value, the error between the two is calculated. The maximum relative error of the prediction within the sample of the monitoring data of the arch settlement and clearance convergence of the ZK2+065 section is 4.8% and 2.69%, respectively. Figure 7 shown.

[0212] (2) Effect of wavelet-time series model

[0213] The present invention uses Matlab to realize wavelet analysis, adopts db3, decomposes the number of layers into 3, and performs global threshold denoising on the measured data. Figure 7 and Figure 8 These are the data of vault settlement and clearance convergence before and after wavelet processing, respectively.

[0214] Based on the established ARMA (p, q) model, static prediction of the sample data values ​​after wavelet analysis can obtain the model's in-sample prediction value. The prediction results are shown in Table 4 below.

[0215] Table 2 Measured and predicted data of cross-section vault settlement and clearance convergence Unit: mm

[0216]

[0217]

[0218] Combining the wavelet analysis prediction value with the measured value, the error between the two is calculated. The relative maximum error of the prediction within the sample of the ZK2+065 section vault settlement and clearance convergence monitoring data is 4.17% and 1.09%, respectively. Figure 8 shown.

[0219] pass Figure 9 and Figure 10 The results show that the maximum relative errors of the model for the in-sample predictions of the crown settlement and clearance convergence monitoring data at section ZK2+065 using the interval series analysis were 4.8% and 2.69%, respectively. The maximum relative errors of the model for the in-sample predictions of the crown settlement and clearance convergence monitoring data at section ZK2+065 using the wavelet-time series model were 4.17% and 1.09%, respectively. Starting from the ninth day, the relative error rates of the model for the crown settlement predictions at each section tended to be stable, ranging from 2% to -2%. The relative error rates of the model for the clearance convergence predictions at each section tended to be stable, ranging from 2% to -2%. The overall error rate was low, and the model's prediction accuracy met the requirements, providing a reference for the design and construction of similar tunnel projects.

[0220] Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if such changes and modifications fall within the scope of the claims and their equivalents, the present invention is intended to include such changes and modifications.

Claims

1. A tunnel surrounding rock deformation prediction method based on time series and inversion analysis, characterized in that: The following steps are involved: S1. Setting up tunnel monitoring points, and collecting, inspecting, and preprocessing relevant data obtained from the tunnel monitoring points to obtain preprocessed data; In step S1, the inspection and preprocessing process of the tunnel-related data includes the removal of singular data, zero mean processing and stationarity inspection operations; S2. Analyze the surrounding rock grade, burial depth, and support structure of the monitoring section of each tunnel monitoring point set in step S1 based on the tunnel engineering geological conditions and the preprocessed data obtained in step S1, and set tunnel monitoring benchmark control values ​​and warning values ​​based on the analysis results; S3. Based on the pre-processed data obtained in step S1 and the tunnel monitoring benchmark control value and warning value obtained in step S2, the management level of the monitoring section of each tunnel monitoring point is obtained, and each management level is analyzed to determine the section for time series analysis and inversion analysis; S4, collecting the time series data of the cross section obtained from the time series analysis and inversion analysis in step S3, and using a wavelet-time series analysis model to predict the deformation of the surrounding rock. The wavelet-time series analysis model is established by the following method: S41. Selection of wavelet basis and determination of number of layers and coefficients; S42, wavelet threshold denoising, reconstruction coefficients, reconstruction time series analysis model; S43, selecting the type of the reconstructed time series analysis model to determine the type of the time series model; S44, determining the order of the time series model obtained in step S43 to obtain the order of the wavelet-time series model; S45, estimating the parameters of the time series model obtained in step S43 to obtain the parameters of the wavelet-time series model; S46, testing the applicability of the order of the time series model obtained in step S44, and further determining the final order of the time series model; S47, determining a wavelet-time series analysis model based on the time series model type obtained in step S43, the final order of the time series model obtained in step S46, and the parameters of the time series model obtained in step S45; In step S42, the time series analysis model is established by the following method: S421. Select and determine the type of the time series model. S422, determining the order of the time series model obtained in step S421 to obtain the order of the time series model; S423, estimating the parameters of the time series model obtained in step S421 to obtain the parameters of the time series model; S424, testing the applicability of the order of the time series model obtained in step S422, and further determining the final order of the time series model; S425. Determine a time series analysis model based on the time series model type obtained in step S421, the final order of the time series model obtained in step S424, and the parameters of the time series model obtained in step S423; Step S421 specifically includes the following steps: S4211. Determine whether the autocorrelation function has k-step truncation. If so, the time series model is MR(k). S4212. If the autocorrelation function does not have k-step truncation, determine whether the partial correlation function has k-step truncation. If so, the model is AR(k); if not, the model is ARMA(p,q).

2. The tunnel surrounding rock deformation prediction method based on time series and inversion analysis according to claim 1 is characterized in that: In step S1, the tunnel monitoring points are divided into external monitoring points and internal monitoring points according to the measurement location. The external monitoring points are buried in the ground surface to monitor the surface settlement in the area affected by tunnel excavation; the internal monitoring points are buried around the excavated surrounding rock and inside the support structure to monitor the deformation of the surrounding rock and the internal force of the support.

3. The tunnel surrounding rock deformation prediction method based on time series and inversion analysis according to claim 1 is characterized in that: In step S4, the time series data is obtained by the following method: The cross section of the time series analysis and inversion analysis in step S3 is monitored, and the monitored displacement data are collected in chronological order according to the monitoring frequency to form a time series.

4. The tunnel surrounding rock deformation prediction method based on time series and inversion analysis according to claim 1 is characterized in that: In step S4, the time series data needs to be inspected and preprocessed before using the wavelet-time series analysis model for prediction analysis. The data inspection and preprocessing include the removal of singular data, zero mean processing and stationarity inspection operations.

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