CN108983300B - Transient electromagnetic tunnel advanced prediction method under tunnel boring machine construction condition - Google Patents
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Abstract
The invention discloses an advanced prediction method of a transient electromagnetic tunnel under the construction condition of a tunnel boring machine, which comprises the steps of firstly subtracting TBM mechanism theory response from collected signals, removing partial TBM response, and converting transient electromagnetic diffusion field signals into virtual wave field signals meeting the independent component analysis requirements through mathematical transformation relation and corresponding signal processing; secondly, TBM interference separation is carried out by adopting an information independent component analysis algorithm, and a tunnel transient electromagnetic geological characteristic signal is extracted; and finally, realizing inversion imaging of the underground medium virtual wave field by using Born approximate inversion, realizing the explanation of the front geological abnormality of the tunnel face by combining the definition of the global apparent resistivity, and completing the transient electromagnetic advanced geological forecast of the TBM excavation tunnel. The method can effectively extract low-resistance geological abnormal information in front of the tunnel face, suppress the interference of the TBM machine and effectively solve the key problem of advanced prediction of a transient electromagnetic method in the TBM construction tunnel.
Description
Technical Field
The invention belongs to the field of geophysical detection, and particularly relates to an advanced forecasting method for a transient electromagnetic tunnel under the construction condition of a tunnel boring machine.
Background
Tunnels and underground projects in western regions of China have the characteristics of large buried depth, long tunnel lines, complex geology and dangerous terrain, and a full-face Tunnel Boring Machine (TBM) is mainly adopted for excavation. However, in the TBM construction tunnel, due to the serious electromagnetic response interference of large-scale metal equipment, the application of the transient electromagnetic method in the TBM construction tunnel is difficult greatly. How to effectively extract low-resistance geological abnormal information in front of a tunnel face and suppress TBM machine interference becomes a key problem of whether the advanced prediction of the transient electromagnetic method can be successfully applied to TBM construction of a tunnel.
Because the electromagnetic response of the TBM machine is strong and coincides with the response of the underground medium in time and frequency, the traditional denoising method is difficult to obtain good effect. In the aspect of transient electromagnetic TBM interference elimination, researchers try to calculate total response containing TBM and underground anomaly, pure anomaly response without TBM influence and pure TBM response based on an FDTD forward modeling method, directly subtract the response of the TBM from a total field (containing the TBM and the total response of the underground anomaly) to obtain the response of the pure underground anomaly, eliminate the TBM interference based on a numerical simulation method, and obtain a good effect in the aspect of realizing a theoretical model.
Disclosure of Invention
Aiming at the defects or shortcomings of the prior art, the invention aims to provide an advanced forecasting method for a transient electromagnetic tunnel under the construction condition of a tunnel boring machine, solve the problem of advanced forecasting of the transient electromagnetic tunnel under the construction condition of a TBM (tunnel boring machine), and meet the requirement of advanced tunnel detection.
In order to realize the task, the invention adopts the following technical scheme:
a transient electromagnetic tunnel advanced forecasting method under the construction condition of a tunnel boring machine comprises the following steps:
step 2, separating TBM interference signals by adopting a minimum mutual information independent component analysis algorithm;
and 3, performing inversion imaging on the underground medium virtual wave field, and realizing the explanation of the geological anomaly in front of the tunnel face by combining the definition of the global apparent resistivity.
Further, the method for determining the TBM mechanistic response described in step 1 includes:
according to a design drawing of the TBM machine, three-dimensional modeling is carried out on the structure of the TBM machine and the material properties of parts by adopting a computer modeling mode, a TBM three-dimensional model under a tunnel environment for a time domain finite difference method is generated in a computer, and then transient electromagnetic loop source response characteristics, namely TBM mechanism theory response, of the TBM machine under the tunnel environment are calculated by the time domain finite difference method.
Further, the conversion expression for converting the transient electromagnetic attenuation signal into a virtual wave field signal satisfying the independent component analysis requirement in step 1 is as follows:
in the above equation, x, y, z are spatial coordinates, t is a time variable, τ is a virtual time variable, f (x, y, z, t) is a transient electromagnetic attenuation signal, and U (x, y, z, τ) is a virtual wavefield signal.
Further, when the virtual wave field signal conversion is performed in step 1, firstly, a time window is set for the acquired transient electromagnetic attenuation signal, the time window is slid on the time sequence of the acquired transient electromagnetic attenuation signal, and the wave field inverse conversion is performed on the transient electromagnetic attenuation signal selected in the time window after each sliding according to formula 1; secondly, performing inverse wave field transformation on the acquired transient electromagnetic attenuation signals according to a formula 1 by using a regularization method; and finally, superposing the results of the two wave field inverse transformations to obtain a virtual wave field signal of the acquired transient electromagnetic attenuation signal.
Further, the minimum mutual information independent component analysis algorithm in step 2 adopts a mutual information minimization criterion, which is expressed as:
in the above formula, x is the inverse transformed virtual wave field signal, y is the output signal, y isiIs the element in the output signal y, m is the output signal number, B is the separation matrix, log | B | is the separation matrix information metric, H (-) is the information entropy.
Further, the minimum mutual information independent component analysis algorithm adopted in the step 2 is optimized by adopting a natural gradient method, and the conventional gradient is replaced by the natural gradient, so that the inverse calculation of the separation matrix during parameter adjustment is simplified, and the stability of the calculation is ensured.
Further, the inversion method adopted for performing the underground medium virtual wave field inversion imaging in the step 3 is a Born approximation method.
Further, the method for performing underground medium virtual wave field inversion imaging comprises the following steps: the velocity disturbance can be obtained by solving the following integral equation, and the interface position of the underground medium is obtained to realize inversion imaging:
in the above formula, UkIs an incident field UsFor scattered field, α (r) is the spatial velocity perturbation, C0(r) is the background velocity of the medium, G (r)gR, ω) is a uniform full-space background velocity model Green's function, rsIs the position of the excitation source, rgFor the reception point position, ω is the frequency of the electromagnetic field.
Further, the global apparent resistivity definition includes the following steps:
firstly, calculating transient electromagnetic response formed by loop sources in a uniform full-space medium, then continuously changing resistivity values of the uniform full space, obtaining corresponding transient electromagnetic response, and analyzing a functional relation between the transient electromagnetic response and the uniform full-space resistivity; and finally, performing Taylor expansion on the function of the transient electromagnetic response on the uniform full-space resistivity by using an inverse function principle, and determining an iterative calculation resistivity value range according to the functional relation between the transient electromagnetic response and the uniform full-space resistivity to realize the iterative calculation of the global apparent resistivity.
The utility model provides a transient electromagnetic tunnel advance forecasting system under tunnel boring machine construction condition, includes virtual wave field signal conversion module, interference signal separation module and the explanation module that connects gradually, wherein:
the virtual wave field signal conversion module is used for subtracting TBM mechanism theory response in the acquired signals to obtain overcorrected or undercorrected transient electromagnetic attenuation signals and converting the transient electromagnetic attenuation signals into virtual wave field signals meeting the independent component analysis requirements;
the interference signal separation module adopts a minimum mutual information independent component analysis algorithm to separate TBM interference signals;
the interpretation module is used for performing inversion imaging of the underground medium virtual wave field and realizing the interpretation of the geological anomaly in front of the tunnel face by combining the definition of the global apparent resistivity.
Compared with the prior art, the invention has the following technical characteristics:
1. the method not only obtains stable wave field transformation, but also realizes multi-resolution analysis of the wave field, and utilizes the minimum mutual information independent component analysis algorithm to separate the TBM interference to realize geological disaster characteristic signal extraction and TBM strong interference suppression on the premise of transient electromagnetic wave field transformation, thereby ensuring the effective application of the advanced prediction of the transient electromagnetic tunnel in the TBM tunnel.
2. According to the method, a Born inversion interface and apparent resistivity imaging results are comprehensively interpreted, virtual wave equation backscattering inversion is approximately realized, a geologic body in front of a tunnel face is imaged, low-resistance abnormal delineation is facilitated, transient electromagnetic advanced prediction of the TBM tunnel is realized, the problem of advanced prediction of the transient electromagnetic tunnel under the TBM construction condition is solved, and the requirement of tunnel advanced detection is met.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
FIG. 2 is a schematic diagram of an independent component algorithm;
Detailed Description
Referring to fig. 1, the invention discloses an advanced forecasting method for a transient electromagnetic tunnel under the construction condition of a tunnel boring machine, which comprises the following steps:
step 1.1, acquiring theoretical response of TBM (tunnel boring machine)
The method comprises the following steps of firstly, according to a design drawing of a main model TBM machine in the market, carrying out three-dimensional modeling on the structure of the TBM machine and the material attributes of parts in a computer modeling mode, and generating a TBM three-dimensional model in a tunnel environment for a Finite Difference Time Domain (FDTD) method in a computer; secondly, transient electromagnetic loop source response characteristics of the TBM machine in the tunnel environment, namely TBM mechanism theory response, are calculated through an FDTD method.
Step 1.2, Stable Multi-resolution wavefield transforms
And subtracting the TBM mechanistic response in the acquired signal to obtain overcorrected or undercorrected transient electromagnetic attenuation information. The overcorrection and the undercorrection of the transient electromagnetic attenuation information respectively mean that in the process of subtracting the TBM mechanism theory response, the information subtracted inevitably comprises two situations that not only the theoretical response of the TBM machine is contained, but also geological information and the theoretical response of the TBM machine is not completely removed. Because the overcorrected or undercorrected transient electromagnetic attenuation information does not completely meet the assumption that the independent component requires a signal to be zero mean value, and the seismic wave scattering field meets the basic assumption of independent component analysis, the transient field is converted into a virtual wave field meeting a wave equation through a mathematical transformation relation, and the basic assumption of independent component analysis is met.
The conversion expression for converting the transient electromagnetic attenuation signal into the virtual wave field signal meeting the independent component analysis requirement is as follows:
in the above equation, x, y, z are spatial coordinates, t is a time variable, τ is a virtual time variable, f (x, y, z, t) is a transient electromagnetic attenuation signal, and U (x, y, z, τ) is a virtual wavefield signal.
The expression is a first Fredholm integral equation, which is a typical ill-posed problem, and the transient electromagnetic sampling time range is wide, so that the ill-posed problem is more serious.
Because the larger the order number of the wave field transformation coefficient matrix is, the more serious the ill-condition degree of the equation is, in order to ensure the high-precision wave field transformation and simultaneously avoid the connection problem of each time interval, the specific method of adopting the wave field transformation is as follows:
firstly, setting a time window for an acquired transient electromagnetic attenuation signal (after TBM mechanism theory response is subtracted), sliding the time window on the time sequence of the acquired transient electromagnetic attenuation signal, and performing wave field inverse transformation on the transient electromagnetic attenuation signal selected in the time window after each sliding according to a formula 1; specifically, the width of the time window can be set arbitrarily in theory, and is selected according to the experience of an operator in actual operation; after the time window is determined, a part of signals are selected from the acquired transient electromagnetic attenuation signals (sequences) for wave field inverse transformation, then smaller time shift is given for moving sliding of the time window, and the part of signals selected by sliding each time are subjected to wave field inverse transformation similarly, so that the scanning of the whole sampling time is completed; the selection of the time shift size can be set at will theoretically, and in actual operation, the selection can be made according to the experience of an operator, and the direction of the time shift is generally from the beginning of the data to the end of the data.
Secondly, performing wave field inverse transformation on the acquired transient electromagnetic attenuation signals (all data) by using a regularization method according to formula 1, and taking the result as a 'mark post' of the evaluation of the wave field inverse transformation result of the part signals in the window.
And finally, superposing the results of the two wave field inverse transformations to obtain a virtual wave field signal of the acquired transient electromagnetic attenuation signal. Specifically, the correlation between the wave field inverse transformation result of the partial signal acquired each time in the time window and the regularized wave field inverse transformation result of the transient electromagnetic attenuation signal (all data) is judged; and if the correlation is larger than a threshold value (selected according to experience), performing correlation superposition on the two results to finish the inverse wave field transformation. Since the virtual wavefield has a higher correlation in wavefields of the same time period (i.e., scattered waves from the same geologic body), the wavefields of the time-segmented scans are coherently superimposed by coherent filtering to obtain wavefields of the entire sampling time sequence. The method not only obtains stable wave field transformation, but also realizes multi-resolution analysis of the wave field.
Step 2, separating TBM interference signals by adopting a minimum mutual information independent component analysis algorithm;
referring to fig. 2, the independent component algorithm is to gradually separate the mixed signal from the observation signal x (t) through the separation matrix B under the assumption that the components of the source signal are independent from each other, so that the output y (t) approaches the source signal. The independent component algorithm is actually an optimization process, i.e., under the meaning that a certain measure independence criterion is optimal, the separated independent components are enabled to approach each source signal to the maximum extent.
The blind signal separation of the TBM interference signal and the transient electromagnetic attenuation signal by utilizing the minimum mutual information independent component analysis algorithm comprises two aspects: optimization criteria and an optimization algorithm.
Wherein, the optimization criterion adopts mutual information minimization criterion, which is expressed as:
in the above formula, x is the inverse transformed virtual wave field signal, y is the output signal, y isiIs the element in the output signal y, m is the output signal number, B is the separation matrix, log | B | is the separation matrix information metric, H (-) is the information entropy.
The criterion for minimizing the mutual information is as follows:
let the probability density function of the n-dimensional column vector y be Py(y) each component yiHas a probability density function of Pi(yi) Then the minimum criterion of mutual information is that mutual information i (y) obtains a minimum value:
wherein,
is Py(y) and
the larger the KL value is, the more dissimilar the two are, and when the two are the same, the KL value is 0.
The minimum mutual information independent component analysis algorithm is optimized by adopting a natural gradient method, and the conventional gradient is replaced by the natural gradient, so that the inverse calculation of a separation matrix during parameter adjustment is simplified, and the calculation stability is ensured. Because the objective function I (y, B) is a function of the separation matrix B, the separation matrix B is gradually adjusted to enable the objective function to obtain a minimum value to complete the optimization process, and the corresponding output signal y is the output signal after the blind signal separation. The adjustment amount Δ B of the adjustment separation matrix B is expressed as follows:
in the above equation, y is the output signal, μ is the tuning parameter, and B is the separation matrix.
The above equation is expanded, and the final tuning parameters involve inverting the separation matrix; matrix inversion tends to be computationally intensive, while matrix condition numbers are large and tend to be computationally unstable. The method adopts a natural gradient method for optimization, replaces the conventional gradient with the natural gradient, can avoid inverting the separation matrix, not only saves the calculated amount, but also has stable calculation. Of course, the parameters in the manipulated parameters still need to be converted into higher order statistics of the isolated signal for calculation.
The minimum mutual information minimization criterion and the minimum mutual information independent component analysis algorithm based on natural gradient optimization are adopted to have invariance to the sequencing and amplitude proportion change of each output independent component, and the property enables the subsequent true amplitude to be relatively easy to recover.
And 3, performing inversion imaging on the underground medium virtual wave field, and realizing the explanation of the geological anomaly in front of the tunnel face by combining the definition of the global apparent resistivity.
In this embodiment, the inversion method adopted by the inversion imaging is a Born approximation method. The wave field signals subjected to independent component analysis only retain the relative amplitude of the amplitude, so that the calculation of the television resistivity of the underground medium is not facilitated, the velocity analysis of the virtual wave field is very difficult, and the realization of offset imaging is not facilitated. And the Born approximation method inverse scattering inversion only needs to give a uniform background speed, does not need to carry out accurate speed analysis, and is more suitable for inversion imaging of the separated virtual wave field.
After signal separation is completed in step 2, the TBM interference signals in the virtual wavefield U (r, τ) (i.e., U (x, y, z, τ)) are removed, and the residual component in the virtual wavefield U (r, τ) can reflect the subsurface medium information and satisfy the wave equation, where r represents the spatial coordinates (x, y, z) and τ is the virtual time variable. According to the scattering theoryTo discuss, the total field U (r, τ) is decomposed into an incident field UiAnd the scattered field UsAnd (4) summing. The following integral equation can be obtained according to Green's theorem and Born approximation:
in the above formula, UkIs an incident field, UsFor scattered field, α (r) is the spatial velocity perturbation, C0(r) is the background velocity of the medium, G (r)gR, ω) is a uniform full-space background velocity model Green's function, rsIs the position of the excitation source, rgFor the reception point position, ω is the frequency of the electromagnetic field.
The velocity disturbance can be obtained by solving the integral equation, and the position of the underground medium electrical property difference interface is determined according to the distribution condition of the velocity disturbance value in the space, so that inversion imaging is realized.
Meanwhile, apparent resistivity calculation is carried out by utilizing transient electromagnetic attenuation signals for eliminating theoretical TBM response, approximate electric distribution characteristics in front of the tunnel face can be given, and speed information is provided for Born approximate inversion. After the signal extraction is finished, the amplitude of the characteristic information can be recovered, and the apparent resistivity can be calculated by using the recovered attenuation signal. From the result of the apparent resistivity calculation, a low-resistivity region in front of the tunnel face can be finally defined to serve as a detection basis for forecasting the water-containing structure in front of the tunnel face.
In order to calculate the apparent resistivity of the transient electromagnetic attenuation signal, the global apparent resistance definition needs to be carried out on the transient electromagnetic attenuation signal observed by a multi-point array (namely, multi-component), firstly, the transient electromagnetic response formed by loop sources in a uniform full-space medium is calculated, then, the resistivity value of the uniform full space is continuously changed, the corresponding transient electromagnetic response is obtained, and the functional relation between the response and the uniform full-space resistivity is analyzed (for example, whether the response is a monotonic function, whether an extreme point exists, and the like); and finally, performing Taylor expansion on the function of the transient electromagnetic response on the uniform full-space resistivity by using an inverse function principle, and determining an iterative calculation resistivity value range according to the functional relation between the transient electromagnetic response and the uniform full-space resistivity to realize the iterative calculation of the global apparent resistivity.
In conclusion, the advanced prediction method for the transient electromagnetic tunnel under the construction condition of the tunnel boring machine, provided by the invention, can realize geological disaster characteristic signal extraction and TBM strong interference suppression by utilizing an independent component analysis algorithm on the premise of transient electromagnetic wave field transformation, and can realize the advanced prediction of the transient electromagnetic tunnel of the TBM by introducing the Born approximation into the inverse scattering three-dimensional inversion of the transient electromagnetic advanced prediction virtual wave field, thereby being beneficial to low-resistance abnormal delineation and improving the accuracy of the advanced prediction of the transient electromagnetic tunnel in the TBM.
Claims (2)
1. A transient electromagnetic tunnel advanced forecasting method under the construction condition of a tunnel boring machine is characterized by comprising the following steps:
step 1, subtracting TBM mechanism theory response in an acquired signal to obtain an overcorrected or undercorrected transient electromagnetic attenuation signal, and converting the transient electromagnetic attenuation signal into a virtual wave field signal meeting the independent component analysis requirement;
step 2, separating TBM interference signals by adopting a minimum mutual information independent component analysis algorithm;
step 3, performing inversion imaging on the underground medium virtual wave field, and realizing the explanation of the geological anomaly in front of the tunnel face by combining the definition of the global apparent resistivity;
the method for determining the TBM mechanistic response in the step 1 comprises the following steps:
according to a design drawing of the TBM machine, three-dimensional modeling is carried out on the structure of the TBM machine and the material properties of parts in a computer modeling mode, a TBM three-dimensional model in a tunnel environment for a time domain finite difference method is generated in a computer, and then transient electromagnetic loop source response characteristics, namely TBM mechanism theory response, of the TBM machine in the tunnel environment are calculated through the time domain finite difference method;
the conversion expression for converting the transient electromagnetic attenuation signal into a virtual wave field signal satisfying the independent component analysis requirement in step 1 is:
in the above formula, x, y, z are spatial coordinates, t is a time variable, τ is a virtual time variable, f (x, y, z, t) is a transient electromagnetic attenuation signal, and U (x, y, z, τ) is a virtual wave field signal;
step 1, when virtual wave field signal conversion is carried out, firstly, setting a time window for the acquired transient electromagnetic attenuation signal, sliding the time window on the time sequence of the acquired transient electromagnetic attenuation signal, and carrying out wave field inverse conversion on the transient electromagnetic attenuation signal selected in the time window after each sliding according to formula 1; secondly, performing inverse wave field transformation on the acquired transient electromagnetic attenuation signals according to a formula 1 by using a regularization method; finally, superposing the results of the two wave field inverse transformations to obtain a virtual wave field signal of the acquired transient electromagnetic attenuation signal;
the minimum mutual information independent component analysis algorithm in the step 2 adopts a mutual information minimization criterion, which is expressed as:
in the above formula, x is the inverse transformed virtual wave field signal, y is the output signal, y isiIs an element in the output signal y, m is the output signal number, B is the separation matrix, log | B | is the separation matrix information measure, H (-) is the information entropy;
the minimum mutual information independent component analysis algorithm adopted in the step 2 is optimized by adopting a natural gradient method, and the conventional gradient is replaced by the natural gradient, so that the inverse calculation of a separation matrix during parameter adjustment is simplified, and the calculation stability is ensured;
the inversion method adopted for performing underground medium virtual wave field inversion imaging in the step 3 is a Born approximation method;
the method for carrying out inversion imaging on the underground medium virtual wave field comprises the following steps: the velocity disturbance can be obtained by solving the following integral equation, and the interface position of the underground medium is obtained to realize inversion imaging:
in the above formula, UkFor incident field, UsFor scattered field, α (r) is the spatial velocity perturbation, C0(r) is the background velocity of the medium, G (r)gR, ω) is a uniform full-space background velocity model Green's function, rsIs the position of the excitation source, rgFor the reception point position, ω is the frequency of the electromagnetic field.
2. The advanced forecasting method for the transient electromagnetic tunnel under the construction condition of the tunnel boring machine according to claim 1, characterized in that the global apparent resistivity definition comprises the following steps:
firstly, calculating transient electromagnetic response formed by loop sources in a uniform full-space medium, then continuously changing resistivity values of the uniform full space, obtaining corresponding transient electromagnetic response, and analyzing a functional relation between the transient electromagnetic response and the uniform full-space resistivity; and finally, performing Taylor expansion on the function of the transient electromagnetic response on the uniform full-space resistivity by using an inverse function principle, and determining an iterative calculation resistivity value range according to the functional relation between the transient electromagnetic response and the uniform full-space resistivity to realize the iterative calculation of the global apparent resistivity.
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