A waveform inversion method and system for tunnel seismic prediction ahead

Abstract

This application belongs to the technical field of tunnel advanced detection. Specifically, it is a tunnel seismic advanced detection waveform inversion method and system, including: performing forward simulation based on an initial velocity model and a seismic source to obtain a simulated seismic record of simulated seismic waves; establishing an objective function with the minimum difference between the observed seismic data and the simulated seismic record; using an enhanced whale optimization algorithm to perform inversion optimization on the objective function, and repeatedly iterating to update the initial velocity model until the inversion reaches the minimum value of the objective function, solving the problem that in tunnel space waveform inversion, as the problem dimension increases, the inversion accuracy decreases. The method of this application improves the global search and local development capabilities, and improves the inversion accuracy and convergence speed.

Description

Technical Field

[0001] This application belongs to the technical field of tunnel advanced detection, and more specifically, it is a waveform inversion method and system for tunnel seismic advanced detection. Background Art

[0002] During the tunnel excavation process, complex geological conditions such as faults, karst caves, and soft surrounding rocks are often encountered, and these factors are likely to trigger geological disasters. Therefore, accurately grasping geological information before tunnel construction is crucial for reducing risks. Full waveform inversion (FWI), as a high-resolution seismic imaging method, reconstructs the underground velocity structure by precisely matching the measured waveform with the simulated waveform. However, its application in tunnel detection has the defect of being highly sensitive to the initial model and easily falling into local minima, which limits its inversion accuracy in tunnel advanced detection.

[0003] The unscented hybrid simulated annealing algorithm (UHSA) has been successfully applied to the inversion research of tunnel velocity models. This algorithm combines the global optimization ability of the simulated annealing algorithm (SA) and the local optimization ability of the unscented Kalman filter (UKF), significantly improving the inversion accuracy. However, as the problem dimension increases, UHSA is prone to falling into local optimal solutions, especially when the number of velocity bodies increases, and the inversion accuracy of the algorithm significantly decreases. Summary of the Invention

[0004] The technical problem to be solved by this application is to provide a waveform inversion method for tunnel seismic advanced detection, which solves the problem that the inversion accuracy decreases as the problem dimension increases in the waveform inversion of the tunnel space.

[0005] This application is implemented as follows:

[0006] A waveform inversion method for tunnel seismic advanced detection includes: performing forward simulation based on the initial velocity model and the seismic source to obtain the simulated seismic record of the simulated seismic wave; establishing an objective function with the minimum difference between the observed seismic data and the simulated seismic record; using the enhanced whale optimization algorithm to perform inversion optimization on the objective function, and repeatedly iterating to update the initial velocity model until the inversion reaches the minimum value of the objective function.

[0007] The step of using the enhanced whale optimization algorithm to perform inversion optimization on the objective function includes:

[0008] Initializing the parameters of the enhanced whale optimization algorithm, where the parameters include the initial value of the iteration number, the maximum iteration number, and the frequency factor.

[0009] Generating an initial population, generating the initial population using the piecewise Chebyshev-logistic mapping, and adding the reverse solution of the current individual to the initial population.

[0010] Adjusting the non-linear convergence factor.

[0011] Update the first coefficient vector , the second system vector , the first random number and the second random number ; According to the values of the first coefficient vector and the second random number , trigger operations including a shrinking enclosure mechanism, a random search mechanism, a bubble net attack mechanism, and a frequency fluctuation mechanism;

[0012] Judge whether the maximum number of iterations or the preset termination condition is reached. If the termination condition is satisfied, output the optimal individual position and the fitness value of the optimal individual.

[0013] Furthermore, when generating the initial population, a piecewise Chebyshev - Logistic map is used to generate the initial population, and the reverse solution of the current individual is added to the initial population, including:

[0014] Generating the reverse solution of the current individual to increase population diversity is expressed as: , where represents the reverse solution of the current individual, represents the lower limit of the individual position variable, represents the upper limit of the individual position variable, represents the -th position variable of the -th individual, and the calculation method is: , represents the -th chaotic variable, is updated as: , the perturbation factor , represents the population size, is a parameter to control the behavior of the Logistic map.

[0015] Furthermore, adjusting the non - linear convergence factor includes: , represents the non - linear convergence factor, represents the maximum number of iterations, represents the number of iterations.

[0016] Furthermore, the shrinking enclosure mechanism includes: when is satisfied and , the global optimal individual represents the prey space coordinates, and other individuals gradually approach the global optimal individual by adjusting their own positions. The population update formula is:

[0017] ,

[0018] ,

[0019] Among them, represents the weighted distance between the individual and the prey, represents the position of the individual at moment, is the position of the global optimal individual of the current population, represents the position of the individual at moment;

[0020] The first coefficient vector and the second coefficient vector are calculated by the following formula:

[0021] ,

[0022] ,

[0023] Among them, is the third random number between [0, 1], is the fourth random number between [0, 1], is the non-linear convergence factor.

[0024] Furthermore, the random search mechanism includes: when satisfying , in the iterative process, each individual randomly selects any feasible solution in the current population as the target position with a probability of and expands the search range by moving towards the target position. The population update formula is:

[0025] ,

[0026] ,

[0027] Among them, is the target position randomly selected in the current population, represents the weighted distance between the individual and the prey, represents the position of the individual at moment, represents the position of the individual at moment.

[0028] Furthermore, the bubble net attack mechanism includes: when satisfying , the population update formula is:

[0029] ,

[0030] ,

[0031] Among them, is set to 1, represents the Euclidean distance between an individual and its prey, represents the position of the individual at moment, is the position of the global optimal individual in the current population, represents the position of the individual at moment, is the modulo operation on the iteration number and the frequency factor and is performed.

[0032] Furthermore, the frequency fluctuation mechanism includes: when is satisfied, the update of the population is as follows:

[0033] where

[0034] is the amplitude factor, defined as:

[0035] where

[0036] Among them is the angular frequency, calculated as ; is a random phase angle within the interval, is the oscillation factor, such that the amplitude factor changes periodically with time. By adjusting the angular frequency and the phase angle, the frequency and phase of the oscillation are controlled to guide the search agent to explore in the search space, such that the amplitude of the oscillation gradually decreases as the number of iterations increases, is the modulo operation on the iteration number and the frequency factor and is performed, represents the maximum number of iterations.

[0037] Furthermore, it also includes adopting the low-altitude hovering mechanism of the red-tailed hawk to enhance its local development ability. The specific formula is expressed as:

[0038] where

[0039] where

[0040] where

[0041] where

[0042] After normalization, it replaces and :[[]]

[0043] ,

[0044] wherein, and represent the direction coordinates at a moment, is represented as an adaptive step factor, is the average value of the position, represents the initial value of the radius, represents the angle gain, is the random gain, is the control gain, represents the instantaneous radius value during the search, represents the instantaneous angle during the search, is the position of the global optimal individual of the current population, represents the position of the individual at moment.

[0045] On the other hand, a tunnel seismic forward detection waveform inversion system provided by an embodiment of the present application includes:

[0046] A forward modeling module, configured to perform forward modeling simulation according to an initial velocity model and a seismic source to obtain a simulated seismic record of the simulated seismic wave;

[0047] A target function establishment module, configured to establish a target function with the minimum difference between the observed seismic data and the simulated seismic record;

[0048] An inversion module, configured to perform inversion optimization on the target function by using an enhanced whale optimization algorithm, and update the initial velocity model through repeated iteration until the inversion reaches the minimum value of the target function;

[0049] The performing inversion optimization on the target function by using the enhanced whale optimization algorithm includes:

[0050] Initializing the parameters of the enhanced whale optimization algorithm, where the parameters include the initial value of the number of iterations, the maximum number of iterations, and the frequency factor;

[0051] Generating an initial population, generating the initial population by using a piecewise Chebyshev-logistic mapping, and adding the reverse solution of the current individual to the initial population;

[0052] Adjusting the non-linear convergence factor;

[0053] Updating the first coefficient vector and the second system vector and the first random number and the second random number ; According to the first coefficient vector and the second random number The value of triggers the operations including shrinking and surrounding mechanism, random search mechanism, bubble net attack mechanism and frequency fluctuation mechanism;

[0054] Determine whether the maximum number of iterations or the preset termination condition has been reached. If the termination condition is met, output the optimal individual position and the fitness value of the optimal individual.

[0055] Compared with the prior art, the present application has the following beneficial effects:

[0056] The method of this application improves the ability of global search and local development. By initializing the population, the diversity and distribution uniformity of the initial solution are enhanced; the nonlinear convergence factor is introduced, which can dynamically adjust the weight of exploration and development according to the search stage to better adapt to different optimization needs; the frequency fluctuation mechanism improves the ability to jump out of the local optimum; the low-altitude hovering strategy further optimizes the accuracy of local search. Improve the inversion accuracy and convergence speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] Figure 1 A flowchart of the method proposed in the embodiment of the present application;

[0058] Figure 2 A tunnel model parameter diagram provided in an embodiment of the present application;

[0059] Figure 3 The convergence curve of the whale optimization algorithm and its variants of the enhanced whale optimization algorithm of the embodiment of the present application iterated 500 times in the Bent Cigar function;

[0060] Figure 4 The convergence curve of the whale optimization algorithm and its variants of the enhanced whale optimization algorithm of the embodiment of the present application iterated 500 times in the Levy function;

[0061] Figure 5 A diagram of a concrete debris tunnel model according to an embodiment of the present application;

[0062] Figure 6 The inversion result diagram of concrete residues of the method (a) of the present application and the UHSA algorithm (b) of the embodiment of the present application;

[0063] Figure 7 It is the convergence curve of the concrete residue of the method of the present application and the UHSA algorithm of the embodiment of the present application after 100 iterations;

[0064] Figure 8 The transverse velocity profile diagram (a) of the concrete debris at a longitudinal position of 20m and the transverse velocity profile diagram (b) at a longitudinal position of 60m according to the method and UHSA algorithm of the embodiment of the present application;

[0065] Figure 9 It is the diagram of the inclined layer change model provided by the embodiment of the present application;

[0066] Figure 10 It is the diagram of the inversion results of the inclined layer change of the method (a) of the present application and the UHSA algorithm (b) provided by the embodiment of the present application;

[0067] Figure 11 It is the convergence curve of the inversion of the inclined layer change of the method of the present application and the UHSA algorithm with 100 iterations provided by the embodiment of the present application;

[0068] Figure 12 It is the transverse velocity profile diagram (a) at the longitudinal position of 32 m and the transverse velocity profile diagram (b) at 70 m of the inversion of the inclined layer change of the method of the present application and the UHSA algorithm provided by the embodiment of the present application. Detailed implementation manners

[0069] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application will be further described in detail below in conjunction with embodiments. It should be understood that the specific embodiments described here are only used to explain the present application and are not used to limit the present application.

[0070] See Figure 1 A waveform inversion method for tunnel seismic forward detection shown as follows, including:

[0071] Performing forward simulation according to the initial velocity model and the seismic source to obtain the simulated seismic record of the simulated seismic wave;

[0072] Establishing an objective function with the minimum difference between the observed seismic data and the simulated seismic record;

[0073] Using the enhanced whale optimization algorithm to perform inversion optimization on the objective function, and repeatedly iterating to update the initial velocity model until the inversion reaches the minimum value of the objective function.

[0074] Among them, the initial velocity model can be established by other inversion methods (such as travel time tomography, migration velocity analysis), which is not limited here. The process of forward simulation is to obtain the simulated seismic record of the simulated seismic wave according to the initial velocity model and the seismic source. Simulating the propagation process of the seismic wave through the given parameters of the initial velocity model and the seismic source is the forward simulation. The methods of forward simulation can include: the finite element method, the boundary element method, the pseudo-spectral method, the finite difference method, etc.

[0075] There are many types of objective functions defined for full waveform inversion, which are not limited here. For example, it can include: the least squares form of the difference between the observed seismic data and the simulated seismic record, the cross-correlation weighted norm, the combination of cross-correlation and least squares, etc.

[0076] The optimization process of the objective function is the process of iterative updating of the initial velocity model.

[0077] In one embodiment, to solve the problem of falling into a local optimal solution after optimization, especially when the number of velocity bodies increases and the inversion accuracy significantly decreases, the present application uses an enhanced whale optimization algorithm to inversely optimize the objective function. The steps include:

[0078] Initialize the parameters of the enhanced whale optimization algorithm, where the parameters include the initial value of the number of iterations, the maximum number of iterations, and the frequency factor;

[0079] Generate an initial population. The initial population is generated using a piecewise Chebyshev-Logistic mapping (Chebyshev-Logistic hybrid mapping), and the reverse solution of the current individual is generated and added to the initial population to improve the uniformity of the population distribution by means of the piecewise Chebyshev-Logistic mapping. The chaotic variables generated by the piecewise Chebyshev-Logistic mapping introduce violent oscillations in the low-value region using the Chebyshev mapping, while maintaining the traversal uniformity in the high-value region using the Logistic mapping, thus combining the advantages of the two mappings and effectively avoiding the problem of uneven coverage caused by random initialization. To further improve the coverage range of the population, a reverse learning strategy is adopted, which increases the population diversity by generating the reverse solution of the current individual.

[0080] Adjust the non-linear convergence factor; the non-linear convergence factor optimizes the balance between exploration and exploitation, with a dynamic adjustment behavior that enables it to widely explore the search space in the initial stage of the search and concentrate on developing potential optimal solutions in the later stage of the search. In the embodiment of the present application, in the early iterations, the convergence factor maintains a high steady state to maintain the global exploration persistence of the enhanced whale optimization algorithm; in the later iterations, the value of the convergence factor implements an exponential decay to enhance the local development intensity and improve the convergence accuracy.

[0081] Update the first coefficient vector and the second system vector as well as the first random number and the second random number ; according to the values of the first coefficient vector and the second random number , trigger operations including a shrinking encircling mechanism, a random search mechanism, a bubble net attack mechanism, and a frequency fluctuation mechanism;

[0082] Among them, the first coefficient vector is used to control the moving distance of the whale or individual towards the global optimal solution, and the second system vector is used to control the moving direction of the whale towards the global optimal solution;

[0083] Determine whether the maximum number of iterations or the preset termination condition is reached. If the termination condition is satisfied, output the position of the optimal individual and the fitness value of the optimal individual. The position of the optimal individual is the global optimal solution.

[0084] In one embodiment, a piecewise Chebyshev - logistic map is used to generate the initial population, and the reverse solution of the current individual is added to the initial population, including:

[0085] Generating the reverse solution of the current individual to increase population diversity is expressed as: , where represents the reverse solution of the current individual, represents the lower limit of the individual position variable, represents the upper limit of the individual position variable, represents the th th position variable of the th individual, and the calculation method is: represents the th chaotic variable, The update of is: , the perturbation factor represents the population size, is a parameter to control the behavior of the logistic map.

[0086] Then, fitness evaluation and sorting are performed on the population and its anti - population, and the top 50% of individuals with the best fitness values are selected based on the sorting results to form the initial population.

[0087] In one embodiment, adjusting the non - linear convergence factor includes: , represents the non - linear convergence factor, represents the maximum number of iterations, represents the number of iterations.

[0088] A higher non - linear convergence factor value significantly increases the probability of , so that the enhanced whale optimization algorithm is more inclined to global exploration. As the iteration progresses, in the middle and late stages, the non - linear convergence factor value rapidly decreases, enhancing the local development ability of the enhanced whale optimization algorithm. The enhanced whale optimization algorithm equipped with the non - linear convergence factor shows better global exploration performance in the early stage, and this characteristic enables it to effectively get rid of the limitation of local minima and avoid premature convergence.

[0089] In one embodiment, according to the first coefficient vector and the second random number The value triggers operations including a shrinking encirclement mechanism, a random search mechanism, a bubble net attack mechanism, and a frequency fluctuation mechanism.

[0090] Among them, the shrinking encirclement mechanism. When , it is, the shrinking encirclement mechanism is triggered. Under the framework of the enhanced whale optimization algorithm, the global optimal individual represents the prey space coordinates, and other individuals gradually approach the global optimal individual by adjusting their own positions. The population update formula is:

[0091] ,

[0092] ,

[0093] Among them, among them, represents the weighted distance between an individual and the prey, represents the position of the individual at the moment, is the position of the global optimal individual of the current population, represents the position of the individual at the moment; the first coefficient vector and the second coefficient vector are calculated by the following formula:

[0094] ,

[0095] ,

[0096] Among them, is the third random number between [0, 1], is the fourth random number between [0, 1].

[0097] When , it is, the random search mechanism is triggered. During the iteration process, each individual randomly selects any feasible solution in the current population as the target position with as the probability, and expands the search range by moving towards this target position, thus enhancing the diversity and exploration ability of the algorithm. The position update equation is:

[0098] ,

[0099] ,

[0100] Among them, is the target position randomly selected in the current population, represents the weighted distance between an individual and the prey, represents the position of the individual at the moment, Indicates the position of an individual at moment.

[0101] Bubble net attack mechanism: When , is satisfied, the population update formula is:

[0102] ,

[0103] ,

[0104] where is set to 1, represents the Euclidean distance between an individual and its prey, indicates the position of an individual at moment, is the position of the global best individual in the current population, indicates the position of an individual at moment, is the modulo operation on the iteration number and the frequency factor . Humpback whales swim towards their prey along a spiral trajectory while continuously releasing bubbles to form an enclosure net, forcing the fish school to gather in the central area. This behavior is simulated through spiral motion.

[0105] When , is satisfied, the frequency fluctuation mechanism is triggered, and the population is updated as follows:

[0106] ,

[0107] is the amplitude factor, defined as:

[0108] ,

[0109] where is the angular frequency, calculated as ; is a random phase angle within the interval, is the oscillation factor, which causes the amplitude factor to change periodically with time. By adjusting the angular frequency and the phase angle, the frequency and phase of the oscillation are controlled to guide the search agent to explore the search space, causing the amplitude of the oscillation to gradually decrease as the number of iterations increases, is the modulo operation on the iteration number and the frequency factor , Indicates the maximum number of iterations. To dynamically adjust the search rhythm of the population, a frequency factor is introduced , which controls the timing of vibration. Every iterations trigger a fluctuation.

[0110] To enhance the local development mechanism. The low-altitude hovering mechanism of the red-tailed hawk is introduced into the whale optimization algorithm. After obtaining the range of the general global optimal individual position obtained by the whale optimization algorithm, the low-altitude hovering mechanism of the red-tailed hawk is used to approach the optimal solution to enhance the local development ability. The whale optimization algorithm combined with the low-altitude hovering mechanism of the red-tailed hawk is called the enhanced whale optimization algorithm. The specific formula is as follows: The specific formula is expressed as:

[0111] ,

[0112] ,

[0113] ,

[0114] ,

[0115] After normalization, replace and :

[0116] ,

[0117] Among them, and represent the direction coordinates at time is expressed as the adaptive step factor, is the average value of the position, represents the initial value of the radius, represents the angle gain, is the random gain, is the control gain, represents the instantaneous radius value during search, represents the instantaneous angle during search, is the position of the global optimal individual of the current population, represents the position of the individual at time.

[0118] This application embodiment also provides a tunnel seismic advanced detection waveform inversion system, including:

[0119] A forward modeling module, configured to perform forward modeling according to the initial velocity model and the seismic source to obtain a simulated seismic record of the simulated seismic wave;

[0120] A target function establishment module, configured to establish a target function with the minimum difference between the observed seismic data and the simulated seismic record;

[0121] An inversion module, which is used to perform inversion optimization on the objective function by using an enhanced whale optimization algorithm, and update the initial velocity model through repeated iteration until the inversion reaches the minimum value of the objective function;

[0122] The inversion optimization of the objective function by using the enhanced whale optimization algorithm includes:

[0123] Initialize the parameters of the enhanced whale optimization algorithm, and the parameters include the initial value of the number of iterations, the maximum number of iterations, and the frequency factor;

[0124] Generate an initial population, generate the initial population by using a piecewise Chebyshev-Logistic mapping, and add the reverse solution of the current individual to the initial population;

[0125] Adjust the non-linear convergence factor;

[0126] Update the first coefficient vector and the second system vector and the first random number and the second random number ; According to the values of the first coefficient vector and the second random number , trigger operations including a shrinking encircling mechanism, a random search mechanism, a bubble net attack mechanism, and a frequency fluctuation mechanism;

[0127] Judge whether the maximum number of iterations or a preset termination condition is reached. If the termination condition is satisfied, output the optimal individual position and the fitness value of the optimal individual.

[0128] This application uses a simulation experimental environment to verify the effects of the embodiments of this application, including:

[0129] The construction of a tunnel model. Refer to Figure 2 for the tunnel model parameter diagram. Use the tunnel model to study the acoustic wave propagation. The specific tunnel model parameters are as follows. The total length of the tunnel model is 150 meters, of which the tunnel section length is 50 meters and the width is 15 meters. The upper and lower walls of the tunnel section are 40 meters and 45 meters away from the edge of the tunnel model respectively. To achieve high-quality acoustic wave signal acquisition, a total of 20 receivers are arranged in the tunnel model, including 8 on each of the upper and lower walls of the tunnel (both are arranged in an equally spaced manner) and 4 on the tunnel face. The seismic source contains 3 excitation points, which are located at the uppermost, middle, and lowermost positions of the tunnel face respectively. In the setting of the acoustic wave propagation speed, the speed inside the tunnel is 340 m / s and the background speed is 3000 m / s.

[0130] Setting of forward modeling parameters. The Ricker wavelet (Mexican hat wave) is used as the excitation source of seismic waves, and its central frequency is set to 10 Hz for generating observed seismic data. The numerical simulation part is implemented based on the regular grid finite difference method, and the grid size is 100×150. To ensure the simulation accuracy, the finite difference operator adopts a second-order accuracy in the time dimension and a fourth-order accuracy in the space dimension.

[0131] Setting of inversion parameters: The population size of the enhanced whale optimization algorithm is set to 300, and the fluctuation frequency is set to 5. The number of runs of the unscented Kalman filter in each iteration is set to 10. Objective function:

[0132] ,

[0133] where, are model parameters, is the number of traces of the observed seismic data, and are respectively the -th trace of the observed seismic data and the simulated seismic data.

[0134] The UHSA algorithm (Ultra-High-Speed Acoustic Full-Waveform Inversion method) is selected as the comparison algorithm. The UHSA algorithm is a meta-heuristic algorithm specifically designed for the global inversion problem of tunnel space, with high efficiency and robustness, and can effectively handle complex geological inversion tasks. Through its application in the tunnel scenario, the UHSA algorithm has demonstrated its significant advantages in global optimization and parameter inversion, making it an ideal choice for comparison with the method of this application.

[0135] To verify the excellent performance of the method of the embodiment of this application in the waveform inversion of tunnel space, this application conducts a qualitative analysis of the synergistic effect of each enhancement mechanism based on the Bent Cigar function and the Levy function.

[0136] The Bent Cigar function presents a deep bowl-shaped structure, with relatively small function values near the global minimum point, and the function values increase rapidly as it moves away from the minimum point. The Levy function presents a complex multi-peak structure, with multiple local minimum points and one global minimum point, and the function surface has large fluctuations, making it difficult to optimize.

[0137] See Figure 3 for the convergence curve of the whale optimization algorithm and its variants of the enhanced whale optimization algorithm of the embodiment of this application iterated 500 times in the Bent Cigar function and see Figure 4The convergence curves of the enhanced whale optimization algorithm and its variants of the embodiments of the present application in the whale optimization algorithm after 500 iterations in the Levy function. In the Bent Cigar function and the Levy function, 500-iteration tests are performed on each improved variant of the enhanced whale optimization algorithm. Among them, CLM & RLI is the introduction of the whale optimization algorithm and the reverse learning initialization strategy; NCF is the addition of a non-linear convergence factor; FFM is the addition of a frequency fluctuation mechanism; LSS is the adoption of an increased low-altitude hovering strategy; LSS & FFM is a variant of the whale optimization algorithm that combines the low-altitude hovering strategy and the frequency fluctuation mechanism. The whale optimization algorithm refers to WOA, and the variants of the whale optimization algorithm refer to the method of the present application. It can be seen that the fitness value of the method of the present application changes significantly with the number of iterations.

[0138] For the inversion of concrete residues, refer to Figure 5 the concrete residue tunnel model diagram in. The real model is set as a model with a high-speed anomaly and a low-speed anomaly, which are 25 meters and 45 meters away from the tunnel face respectively. The speed of the high-speed anomaly is 5000 m / s, and the speed of the low-speed anomaly is 1000 m / s. The refers to the speed, and the speed here and in the following content all refers to the longitudinal wave speed. By comparing the inversion results of the method of the present application and the UHSA algorithm, refer to Figure 6 (a) the concrete residue inversion result diagram of the method of the present application in Figure 6 and (b) the concrete residue inversion result diagram of the UHSA algorithm in. It can be seen that the method of the present application locates the positions of the two velocity anomalies very accurately, while the UHSA algorithm fails to correctly identify the positions of the anomalies. Further analyze the convergence curves of the method of the present application and the UHSA algorithm in 100 iterations, refer to Figure 7 the convergence curves of the method of the present application and the UHSA algorithm for concrete residues after 100 iterations provided in the embodiments of the present application. It can be found that in the first 10 iterations, the fitness value of the method of the present application rapidly drops from about 4.5 to nearly 3.5, showing the characteristic of rapid convergence. In contrast, the fitness value of the UHSA algorithm only slightly drops from about 5.5 to about 5.4 in the initial stage (the first 10 iterations), with very little change, and then tends to be stable, with an obviously slower convergence speed.

[0139] Refer to Figure 8 (a) is the transverse velocity profile diagram at the longitudinal position of 20 m of the concrete residues of the method of the present application and the UHSA algorithm in Figure 8In figure (b), it shows the transverse velocity profile at the longitudinal position of 60 m for the method of this application and the UHSA algorithm for the concrete residue. By intercepting the transverse velocity profiles at the longitudinal positions of 20 m and 60 m for comparison, the velocity and positioning of the method of this application are highly consistent with the actual velocity of the real model. Especially, the low-velocity anomaly is accurately located within the actual velocity region. However, it can be seen from the UHSA velocity that there is a large gap from the actual velocity and the existence of the low-velocity anomaly cannot be identified. At the same time, the inversion result of the high-velocity anomaly by the method of this application also shows high accuracy and can better reflect the characteristics of the real model, while the UHSA algorithm still fails to accurately locate the high-velocity anomaly. This result further verifies the superior performance of the method of this application in the inversion of complex geological models.

[0140] Inversion of inclined layer changes. See Figure 9 For the model diagram of inclined layer changes, the real model is set as a model with a high-velocity inclined layer and a low-velocity inclined layer, which are 30 m and 58 m away from the tunnel face respectively. Among them, the velocity of the high-velocity anomaly is 5000 m / s, and the velocity of the low-velocity anomaly is 1000 m / s. From the inversion results of the method of this application and the UHSA algorithm, Figure 10 In figure (a), it shows the inversion result of the inclined layer changes of the method of this application provided by the embodiment of this application and Figure 10 In figure (b), it shows the inversion result diagram of the inclined layer changes of the UHSA algorithm. It can be seen that the fitness value of the method of this application decreases significantly with the number of iterations. Figure 11 For the convergence curves of the inversion of inclined layer changes by the method of this application and the UHSA algorithm shown in the figure after 100 iterations, the velocity of the method of this application is highly consistent with the actual velocity, and there are only slight deviations at the boundary of the velocity body. However, there is a large gap between the UHS velocity of the inversion result of the UHSA algorithm and the actual velocity, and the low-velocity anomaly cannot be identified. According to the comparison results of the convergence curves of the method of this application and the UHSA algorithm in 100 iterations, the method of this application drops rapidly in the first 10 iterations and then continuously converges to the optimal solution. In contrast, the UHSA algorithm falls into a local optimum from the beginning and fails to further converge.

[0141] See Figure 12 In figure (a), it shows the transverse velocity profile at the longitudinal position of 32 m for the inversion of inclined layer changes of the method of this application and the UHSA algorithm provided by the embodiment of this application and Figure 12 In figure (b), it shows the transverse velocity profile at 70 m. By intercepting the transverse velocity profiles at the longitudinal positions of 32 m and 70 m, the inversion result of the method of this application fully reflects the velocity distribution and velocity values of the real model. In the intervals of 30 m to 100 m and 25 m to 100 m of the velocity profile, the velocity curves of the method of this application basically fit the real velocity model. In contrast, there are large gaps in the shape and velocity values of the velocity body inverted by the UHSA algorithm from the real model.

[0142] In the embodiments of the present application, in population initialization, a segmented Chebyshev-Logistic hybrid mapping is used to generate chaotic variables. By introducing the Chebyshev mapping in the low-value region to produce violent oscillations, and at the same time using the Logistic mapping to maintain the uniformity of traversal in the high-value region, the advantages of the two mappings are combined, effectively avoiding the problem of uneven coverage caused by random initialization. To further improve the coverage range of the population, a reverse learning strategy is adopted to increase population diversity by generating the reverse solution of the current individual. According to the qualitative analysis of each enhancement mechanism, it can be found that in the Bent Cigar function, the convergence value of the CLM & RLI curve is lower than that of the traditional WOA. This shows that the population initialization method adopted in the embodiments of the present application provides a proxy closer to the global optimal solution in the initial stage of iteration.

[0143] In the embodiments of the present application, non-linear convergence factor adjustment. A higher non-linear convergence factor value significantly increases the probability, making the algorithm more inclined to global exploration. As the algorithm iterates, in the middle and late stages the value drops rapidly, enhancing the local exploitation ability of the algorithm. According to the qualitative analysis of each enhancement mechanism, it can be found that the algorithm equipped with the non-linear convergence factor (NCF) exhibits better global exploration performance in the early stage. This characteristic enables it to effectively break away from the limitation of local minima and avoid premature convergence. This performance advantage is fully verified in the tests of the Bent Cigar function and Levy function selected in the present application.

[0144] In the embodiments of the present application, the role of the frequency fluctuation mechanism is to enhance the ability of the whale optimization algorithm to jump out of local optimal solutions. In the traditional random search mechanism, an individual randomly selects any individual in the population and approaches it. This method lacks consideration of historical information and position distribution. Therefore, in multimodal functions, especially in cases like the Levy function where the number of local optimal solutions is large and the distribution is complex, it is easy to fall into local optima and difficult to find the global optimal solution. The frequency fluctuation mechanism proposed in the embodiments of the present application improves this problem by adjusting the volatility in the search process. According to the qualitative analysis of each enhancement mechanism, the FFM curve shows a continuous downward trend throughout the iteration process. Compared with the standard whale optimization algorithm, this curve can find a solution better than the previous generation in each generation, always maintaining a negative slope, thus effectively avoiding the problem of falling into local extreme points.

[0145] The method of the embodiment of the present application combines the low-altitude hovering strategy of the red-tailed hawk with the spiral predation strategy of the whale optimization algorithm, thereby achieving stronger local development ability. According to the qualitative analysis of each enhancement mechanism, the convergence ability of the method of the present application is particularly obvious in the convergence curve of the Bent Cigar function, with a higher slope in the early stage of the convergence curve and a significantly accelerated convergence speed. However, the stronger development ability is more likely to fall into local extreme points. In the Levy function, the LLS curve falls into the local optimal solution earlier than the original whale optimization algorithm. It is worth noting that by combining the frequency fluctuation mechanism and the low-altitude hovering mechanism, the enhanced whale optimization algorithm can more effectively jump out of local extreme points while improving the convergence speed and accuracy. Compared with the original whale optimization algorithm, the whale optimization algorithm only containing the frequency fluctuation mechanism, and the whale optimization algorithm only containing the low-altitude hovering strategy, this combined strategy shows better convergence results (LSS & FFM curves) in both the Bent Cigar function and Levy function tests.

[0146] Through in-depth analysis of the enhancement mechanism, the method of the present application integrates the Chebyshev-Logistic hybrid mapping and the population initialization method of reverse learning, the non-linear convergence factor, the frequency fluctuation mechanism, and the low-altitude hovering strategy of the red-tailed hawk, thereby achieving optimization in terms of global search ability and local development ability. Specifically, the synergistic effect of the Chebyshev-Logistic hybrid mapping and reverse learning effectively improves the uniformity and diversity of the initial population distribution; the non-linear convergence factor can dynamically adjust the balance between exploration and development of the algorithm to adapt to the optimization requirements at different stages; the introduction of the frequency fluctuation mechanism enhances the ability of the algorithm to get rid of local extreme values; and the low-altitude hovering strategy of the red-tailed hawk further improves the accuracy and efficiency of local convergence. The experimental results show that the method of the embodiment of the present application is superior to the UHSA algorithm in terms of inversion accuracy and convergence speed, fully verifying the effectiveness and superiority of the above enhancement mechanism.

[0147] The above are only the preferred embodiments of the present application and are not intended to limit the present application. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A waveform inversion method for tunnel seismic prediction ahead, characterized in that, Including: Performing forward simulation based on the initial velocity model and the seismic source to obtain the simulated seismic record of the simulated seismic wave; Establishing an objective function with the minimum difference between the observed seismic data and the simulated seismic record; Using the enhanced whale optimization algorithm to perform inversion optimization on the objective function, and repeatedly iterating to update the initial velocity model until the inversion reaches the minimum value of the objective function; The performing inversion optimization on the objective function using the enhanced whale optimization algorithm includes: Initializing the parameters of the enhanced whale optimization algorithm, and the parameters include the initial value of the iteration number, the maximum iteration number, and the frequency factor; Generating an initial population, using a piecewise Chebyshev-Logistic map to generate the initial population, and adding the reverse solution of the current individual to the initial population; Adjusting the non-linear convergence factor; Update the first coefficient vector , the second system vector , the first random number and the second random number ; According to the values of the first coefficient vector and the second random number , trigger operations including a contraction enclosure mechanism, a random search mechanism, a bubble net attack mechanism, and a frequency fluctuation mechanism; Judging whether the maximum iteration number or the preset termination condition is reached. If the termination condition is satisfied, output the position of the optimal individual and the fitness value of the optimal individual.

2. The waveform inversion method for tunnel seismic prediction ahead according to claim 1, wherein, The generating an initial population, using a piecewise Chebyshev-Logistic map to generate the initial population, and adding the reverse solution of the current individual to the initial population includes: The generation of the reverse solution of the current individual to increase population diversity is expressed as: , where represents the reverse solution of the current individual, represents the lower limit of the individual position variable, represents the upper limit of the individual position variable, represents the -th position variable of the -th individual, and the calculation method is: represents the -th chaotic variable, is updated as: , Perturbation factor , represents the population size, is a parameter for controlling the behavior of the logistic map.

3. The tunnel seismic pre-detection waveform inversion method according to claim 1, characterized in that Adjust the non - linear convergence factor, including: , represents the non - linear convergence factor, represents the maximum number of iterations, represents the number of iterations.

4. The tunnel seismic prediction waveform inversion method according to claim 1, characterized in that The shrinking and encircling mechanism includes: satisfying ,and When , the global optimal individual represents the spatial coordinates of the prey, and other individuals gradually approach the global optimal individual by adjusting their own positions. The population update formula is: ， ， Among them, represents the weighted distance between an individual and its prey, represents the position of the individual at time, is the position of the global optimal individual of the current population, represents the position of the individual at time; The first coefficient vector and the second coefficient vector are calculated by the following formula: ， ， wherein, is the third random number between [0, 1], is the fourth random number between [0, 1], is the non-linear convergence factor.

5. The waveform inversion method for tunnel seismic prediction ahead according to claim 1, characterized in that, The random search mechanism includes: when meeting , , during the iteration process, each individual randomly selects any feasible solution in the current population as the target position with a probability of , and expands the search range by moving towards the target position. The population update formula is: ， ， Among them, is the target position randomly selected from the current population, represents the weighted distance between the individual and the prey, represents the position of the individual at moment, represents the position of the individual at moment.

6. The waveform inversion method for tunnel seismic forward detection according to claim 1, characterized in that The bubble net attack mechanism includes: when meeting , , the population update formula is: ， ， Among them, is set to 1, represents the Euclidean distance between an individual and its prey, represents the position of the individual at time, is the position of the globally optimal individual in the current population, represents the position of the individual at time, is the modulo operation on the iteration number and the frequency factor for the modulo operation.

7. The waveform inversion method for tunnel seismic advanced detection according to claim 1, characterized in that The frequency fluctuation mechanism includes: when satisfying , , the update of the population: ， is the amplitude factor, defined as: ， where is the angular frequency, calculated as ; is a random phase angle within the is the oscillation factor, such that the amplitude factor varies periodically with time. By adjusting the angular frequency and the phase angle, the frequency and phase of the oscillation are controlled to guide the search agent to explore the search space, such that the amplitude of the oscillation gradually decreases as the number of iterations increases, is the modulo operation on the number of iterations and the frequency factor and represents the maximum number of iterations.

8. The waveform inversion method for tunnel seismic advanced detection according to claim 1, wherein It also includes using the low-altitude hovering mechanism of the red-tailed hawk to enhance its local development ability, and the specific formula is expressed as: ， ， ， ， Replacement after normalization and : ， Among them, and represent the direction coordinates at a moment, is expressed as an adaptive step size factor, is the average value of the position, represents the initial value of the radius, represents the angle gain, is the random gain, is the control gain, represents the instantaneous radius value during the search, represents the instantaneous angle during the search, is the position of the globally optimal individual of the current population, represents the individual at the position at a moment.

9. A waveform inversion system for tunnel seismic lead detection, characterized in that, Including: A forward module for performing forward simulation based on the initial velocity model and the seismic source to obtain the simulated seismic record of the simulated seismic wave; An objective function establishment module for establishing an objective function with the minimum difference between the observed seismic data and the simulated seismic record; An inversion module for performing inversion optimization on the objective function using the enhanced whale optimization algorithm, and repeatedly iterating to update the initial velocity model until the inversion reaches the minimum value of the objective function; The performing inversion optimization on the objective function using the enhanced whale optimization algorithm includes: Initializing the parameters of the enhanced whale optimization algorithm, and the parameters include the initial value of the iteration number, the maximum iteration number, and the frequency factor; Generating an initial population, using a piecewise Chebyshev-Logistic map to generate the initial population, and adding the reverse solution of the current individual to the initial population; Adjusting the non-linear convergence factor; Update the first coefficient vector , the second system vector , the first random number and the second random number ; According to the values of the first coefficient vector and the second random number , trigger operations including a contraction enclosure mechanism, a random search mechanism, a bubble net attack mechanism, and a frequency fluctuation mechanism; Judging whether the maximum iteration number or the preset termination condition is reached. If the termination condition is satisfied, output the position of the optimal individual and the fitness value of the optimal individual.

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