A method and system for measuring the angle of an ultra-short side wire in a special long tunnel hole

Abstract

The application discloses a kind of super-short side wire angle measurement method and system in special long tunnel hole, the method includes: constructing non-coplanar high intersection figure: in tunnel section, multiple non-coplanar temporary free centering prism is laid out, forms high-strength space intersection geometric figure;Controllable installation deviation is introduced: control total station only carries out rough leveling and is not centered, allow survey station to exist significant installation deviation;Parameterized decoupling of survey station error is executed: the multi-target joint adjustment model with survey station three-dimensional coordinates and directional parameter as core unknown number is constructed;Using high-strength space intersection geometric figure, the significant installation deviation is parameterized absorption, output is not affected by survey station centering error and leveling error Real azimuth angle.The application is completely rid of the dependence on forced centering base, especially suitable for special long tunnel, underground station and existing line reconstruction and other complex environments.

Description

Technical Field

[0001] This invention belongs to the field of tunnel engineering surveying technology, specifically relating to a method and system for measuring the angle of ultra-short side traverse in extra-long tunnels, which is particularly suitable for high-precision transmission of traverse azimuth angles in confined spaces such as inclined shaft to main tunnel and cross tunnel to main tunnel. Background Technology

[0002] With the advancement of transportation infrastructure construction in the mountainous areas of western my country, a large number of extra-long railway and highway tunnels exceeding 10km in length are being built. To shorten the construction period, auxiliary tunnels such as inclined shafts and cross tunnels are often set up to enable simultaneous excavation from multiple working faces. However, during the transition from the auxiliary tunnel to the main tunnel, due to space constraints, the line-of-sight distance for measurement is often only 20-50m, which is a typical scenario for ultra-short-side traverse surveying. In the construction of extra-long tunnels (longer than 3 km) and highway tunnels in high mountain and canyon areas, in-tunnel control surveying is a core link to ensure the smooth completion of the tunnel. Especially during the transition from the inclined shaft to the main tunnel, the breakthrough of the detour pilot tunnel, and long-distance excavation, it is often necessary to lay out a traverse network inside the tunnel to transfer the azimuth of the ground control network to the underground construction face with high precision.

[0003] Currently, the precision traverse surveying method is widely used in the industry for traverse surveying inside tunnels. This method mainly relies on the following technical measures to ensure accuracy: First, forced centering technology: To eliminate centering errors of instruments and prisms, forced centering bases (forced centering chassis) are usually installed at survey stations and observation points, and observers are required to precisely level the instruments to ensure that the instrument's vertical axis is strictly plumb. Second, long-side observation and even-numbered repetitions: According to the "Engineering Surveying Code," random errors are reduced by increasing the traverse side length, the number of observation repetitions, and conducting forward and backward observations, utilizing the error cancellation principle. Third, gyrotheodolite orientation: In ultra-long tunnels, gyrotheodolites are often used to determine true north to control lateral continuity errors of the traverse.

[0004] However, in actual long tunnel construction environments, especially during the transition from inclined shaft to main tunnel or when the tunnel face approaches the breakthrough surface, surveying work often faces extreme conditions of "ultra-short sides". When the traverse side length is shortened to within 50 m (or even around 30 m), the above-mentioned traditional precision measurement methods reveal insurmountable technical defects: (1) the amplification effect of centering error. According to the error propagation law, the angle measurement error is inversely proportional to the side length. Under the ultra-short side condition of 32 m, even with the highest precision forced centering base (centering error 0.2 mm), its influence on the direction angle is as high as 1.3″. If the double centering error of the station and the front and back sight prisms is considered, the total error will exceed 2.5″. This means that even if "zero error centering" is achieved physically, it is still mathematically impossible to meet the tolerance requirement of second-order traverse (2.5″), which means that the traditional method has reached the ceiling of accuracy at the physical level. (2) Leveling distortion caused by tunnel environment: the road surface inside the tunnel of a long tunnel is mostly gravel or initial support surface, with poor flatness, and is accompanied by continuous vibration caused by the passage of muck trucks. The total station is very easy to move or tilt after being set up, which means that "precise leveling" can only be maintained for a very short time, and even the leveling bubble has shifted before the observation is completed. The existing technology lacks effective mathematical compensation means for this dynamic leveling error. (3) The contradiction between work efficiency and construction interference: the installation of the forced centering base requires drilling, rebar installation and leveling, and the time taken for a single point is usually 30 to 50 minutes. In the tense tunnel construction process, long-term measurement line occupation will seriously hinder the main operations such as excavation and muck removal, resulting in the inability to balance "ensuring accuracy" and "ensuring progress".

[0005] To address these issues, the industry has attempted to use prism-free measurement or free station setup methods. However, most of these methods only solve the "prism-free centering" problem, as the station still needs precise centering; or they rely solely on a small number of backsight points for coordinate calculation. In tunnel environments with extremely short sides and weak geometric strength, these methods cannot effectively separate station eccentricity errors from leveling errors, leading to divergent or unstable calculation results.

[0006] In summary, existing technologies suffer from technical bottlenecks in scenarios involving extremely long tunnels with very short sides, such as the inability to eliminate centering errors, the inability to compensate for leveling errors, and low operational efficiency. There is an urgent need for a new measurement method that can overcome the limitations of physical centering and synchronously absorb station deviations through algorithms. Summary of the Invention

[0007] The present invention aims to solve the above-mentioned problems of the prior art and provide a method and system for measuring the angle of ultra-short side conductors in extra-long tunnels.

[0008] To achieve the above objectives, the present invention provides the following solution: a method for measuring the angle of an ultra-short side traverse in an extra-long tunnel, characterized in that it includes: S1. Constructing a non-coplanar high intersection pattern: Multiple non-coplanar temporary non-centering prisms are arranged on the tunnel cross section to form a high-intensity spatial intersection geometry. The prisms are directly fixed to the lining structure without the need for a forced centering base. S2. Introduce controllable installation deviations: Control the total station to only perform rough leveling and not to be misaligned, allowing for significant installation deviations at the stations; S3. Perform parameter decoupling of station errors: Receive the relative position data of the prism and the angle observation data from the total station; construct a multi-objective joint adjustment model with the three-dimensional coordinates and orientation parameters of the station as the core unknowns; use high-intensity spatial intersection geometry to parameterize and absorb the significant installation deviations, and output the true azimuth angle that is not affected by the station alignment error and leveling error.

[0009] Furthermore, step S3 specifically includes: establishing the following nonlinear observation equation and performing linearization:

[0010] Among them, (X) s ,Y s Z s ) represents the three-dimensional coordinates of the station, ω represents the orientation parameter, and v hi v vi The residual is obtained by iteratively solving the weighted least squares method, thereby achieving integrated decoupling between the three-dimensional pose of the station and the relative geometry of the prism.

[0011] Furthermore, in the iterative solution process, the initial values ​​of the station coordinates are set using the centroid approximation method, and the initial values ​​of the orientation parameters are set with the zero direction. The solution converges to the most probable value within three iterations.

[0012] Furthermore, it also includes a gross error removal step: Calculate the residuals of the observations at each angle. When any residual is greater than three times the set unit weight error, the observation is determined to be a gross error due to construction disturbance, and is automatically removed and a new round of adjustment calculation is triggered.

[0013] Furthermore, in step S1, the temporary centering-free prism is fixed by expansion screws and a simple bracket, and the deployment time is controlled within 10 minutes, saving more than 80% of the time compared with the traditional forced centering base.

[0014] Furthermore, the method involves multiple independent observations at the same station, and the calculated azimuth error is no greater than 2.5″, which meets the accuracy requirements of a second-order traverse.

[0015] Furthermore, in step S1, when obtaining the relative positional relationship of each prism in the local coordinate system, a handheld laser rangefinder is used in conjunction with a steel ruler for measurement. An accuracy of centimeter level is sufficient to meet the adjustment requirements.

[0016] Another object of the present invention is to provide a method for measuring the angle of an ultra-short side traverse in an extra-long tunnel, characterized in that it includes: The graphic construction module is used to deploy 4 to 6 non-coplanar temporary non-alignment prisms on the tunnel cross section to form a high-strength spatial intersection geometry. The prisms are directly fixed to the lining structure without the need for a forced alignment base. The deviation introduction module is used to control the total station to only perform rough leveling and not to be misaligned, allowing for significant installation deviations at the station. The error absorption and adjustment module is configured to perform the following operations: receive prism relative position data from the graphics construction module and angle observation data from the total station; construct a multi-objective joint adjustment model with the station's three-dimensional coordinates and orientation parameters as the core unknowns; and use high-intensity spatial intersection geometry to parametrically absorb the significant installation deviations and output the true azimuth angle unaffected by the station's alignment error and leveling error.

[0017] Furthermore, the error absorption adjustment module is further configured to: establish a set of nonlinear observation equations including horizontal and vertical angles; use weighted least squares method to iteratively estimate the station pose; and have a built-in residual analysis unit to identify and eliminate abnormal observations affected by construction disturbances.

[0018] Furthermore, the error absorption adjustment module is integrated into the total station's onboard system or an external mobile terminal, supporting real-time on-site calculations and outputting azimuth results with an accuracy better than 2.5″ when the line-of-sight distance is no greater than 50m.

[0019] The present invention achieves the following technical effects compared to the prior art: First, it breaks through the physical accuracy limit of ultra-short side measurement. Existing technologies, when the line-of-sight distance is less than 50 m, are constrained by the amplification effect of centering errors, making it difficult to achieve azimuth accuracy below 3″ even with a forced centering base. This invention, through a "parameter decoupling" mechanism, incorporates station coordinates and orientation parameters as unknowns into the adjustment model, transforming the centering and leveling errors of the station from external interference into absorbable degrees of freedom within the model. Through multi-target angle intersection adjustment, this invention eliminates the centering and leveling errors of the total station as system parameters. In ultra-short side scenarios of 20-50 m, the horizontal angle measurement error is reduced from over 10″ in traditional methods to less than 1″, meeting the accuracy requirements of second-order precision traverse and effectively ensuring tunnel breakthrough accuracy. Example verification: In a 32 m ultra-short side scenario, this invention achieves an azimuth error of 2.1″, better than the standard requirement of 2.5″ for second-order traverse, fundamentally solving the accuracy ceiling problem under ultra-short side conditions.

[0020] Secondly, it completely eliminates the reliance on a forced centering base. Traditional methods require 30-50 minutes for base installation and fine-tuning per station, severely hindering construction progress. This invention utilizes a multi-target angle intersection algorithm, tolerating eccentricity errors of several centimeters and leveling deviations within 2′ at the station. Work efficiency is significantly improved: the station no longer requires forced centering and precise leveling, eliminating the need for a forced centering base for the prism. Prism setup time is reduced by over 80%, and total station setup time is reduced by over 70%. The entire measurement process can be completed within 15 minutes, making it particularly suitable for rapid azimuth transfer during emergency construction. Example verification: Temporary prisms, fixed with expansion screws or magnetic attachment, take approximately 8 minutes to set up; the total station only requires rough leveling and takes approximately 2 minutes to set up. Single-station work efficiency is improved by over 70%, achieving zero interference between measurement and construction.

[0021] Third, it achieves adaptive anti-interference in tunnel environments. Existing technologies lack effective on-site removal mechanisms to address data gross errors caused by construction vibrations, lighting fluctuations, and smoke interference within tunnels. This invention introduces a residual verification mechanism based on a 3-fold mean square error criterion, which can automatically identify and remove abnormal observations affected by construction disturbances. Example verification: Under train vibration or mechanical operation interference, the system can automatically filter invalid data and utilize the remaining redundant observations for stable calculation, ensuring 100% usability of the results.

[0022] Fourth, constructing high-strength spatial geometric constraints. Existing technologies mostly employ collinear arrangements along the centerline of the track, resulting in weak geometric strength and a tendency to generate ill-conditioned equations. This invention forms a three-dimensional spatial intersection network by arranging 4-6 non-coplanar prisms at the arch crown, arch waist, and sidewalls. This non-coplanar high intersection pattern significantly enhances the condition number of the normal equation matrix, ensuring that the adjustment model maintains good convergence and stability even with increased station parameters (Xs, Ys, Zs, ω), thus solving the problem of adjustment divergence under ultra-short sides.

[0023] Fifth, it achieves integrated calculation of the three-dimensional pose of the station. Traditional methods process plane and elevation separately, failing to eliminate the consequent impact of leveling errors on the horizontal angle. This invention simultaneously constructs observation equations for both horizontal and vertical angles, jointly estimating the station elevation and orientation parameters. This not only eliminates vertical axis tilt errors but also enables three-dimensional coordinate transfer without measuring instrument height, simplifying the workflow and avoiding elevation closure errors caused by height measurement mistakes.

[0024] Sixth, it possesses strong engineering adaptability and universality. This invention does not rely on specific expensive equipment (such as gyroscopes) and can be implemented using only a conventional total station. Whether it's a curve segment with an extremely small radius, a large-section station, or an existing tunnel, this invention can work effectively. It has a low operating threshold and strong adaptability: it requires minimal skill from surveyors and can be completed by ordinary workers; it can be used directly with a conventional total station without modification, and is widely applicable to various confined spaces such as inclined shafts and cross passages. It has strong resistance to gross errors: the algorithm has a built-in residual checking and automatic rejection mechanism, which can effectively resist abnormal observations caused by construction disturbances and obstructions, ensuring the robustness of the results. This proves that this method can adapt to various complex geological and construction environments and has extremely high value for widespread application. Attached Figure Description

[0025] Figure 1 This is a schematic diagram of the overall process of the measurement method of the present invention; Figure 2 This is a schematic diagram of the temporary centering-free prism setup for the cross-section to be measured in an embodiment of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Please refer to Figure 1 The present invention provides a method for measuring the angle of an ultra-short side traverse in an extra-long tunnel, comprising: S1. Constructing a non-coplanar high intersection pattern: Multiple non-coplanar temporary non-centering prisms are arranged on the tunnel cross section to form a high-intensity spatial intersection geometry. The prisms are directly fixed to the lining structure without the need for a forced centering base. S2. Introduce controllable installation deviations: Control the total station to only perform rough leveling and not to be misaligned, allowing for significant installation deviations at the stations; S3. Perform parameter decoupling of station errors: Receive the relative position data of the prism and the angle observation data from the total station; construct a multi-objective joint adjustment model with the three-dimensional coordinates and orientation parameters of the station as the core unknowns; use high-intensity spatial intersection geometry to parameterize and absorb the significant installation deviations, and output the true azimuth angle that is not affected by the station alignment error and leveling error. Example

[0028] Taking the measurement of the inclined shaft to the main tunnel of the 6.799km long Chelárba Expressway as an example. This tunnel is a double-bore, double-track tunnel with an 820m long inclined shaft and a line-of-sight distance of only 32m when turning to the main tunnel, which is a typical ultra-short-side scenario. Under such an extreme ultra-short-side scenario, traditional measurement theory faces collapse: First, the error amplification law: According to the error propagation law, a centering error of 0.2 mm will produce a directional error of about 1.3″ with a side length of 32m. If the centering error of the station and prism and the leveling error are considered, the theoretical error will exceed 3″, which directly fails to meet the requirements of second-order traverse (2.5″). Second, physical environment constraints: Due to blasting vibration and mechanical crushing in the tunnel, the ground is continuously slightly deformed, and the installation benchmark of the forced centering base drifts over time, making "high-precision installation" itself a false proposition. Therefore, this embodiment is not a simple optimization of the process, but a reconstruction of the measurement benchmark: abandoning the precise control of the physical position of the station, and instead parametrically absorbing the station error in mathematical space.

[0029] The azimuth angle transfer using the method of this invention comprises the following steps: Construction of non-coplanar height intersection graphs: See Figure 2 Five temporary, non-alignment prisms were evenly distributed across the main tunnel section, located at the arch crown (11), left arch waist (12), right arch waist (13), left side wall (14), and right side wall (15). Unlike traditional traverse points laid out along the tunnel centerline (approximately collinear, resulting in weak geometric strength), this embodiment deliberately breaks the coplanarity. The elevation difference between the arch crown and arch waist, combined with the lateral span of the left and right side walls, forms a three-dimensional spatial network. This configuration ensures a large angle between the line-of-sight vectors from any two prisms to the station, thus generating a strong diagonal advantage in the adjustment model's normal equation matrix. This is a key physical prerequisite for subsequently solving station errors. The prisms were temporarily fixed to the tunnel lining surface using expansion bolts, without the installation of a forced alignment base. The entire setup took approximately 8 minutes, compared to 50 minutes for traditional forced alignment base installation, saving 84% of the time.

[0030] Active introduction and data acquisition of station errors: A 0.5″ class intelligent total station was set up at the end of the inclined shaft station. Only rough leveling was performed (the operator did not perform optical centering, but only used the leveling screws for rough leveling, allowing the instrument center to deviate from the theoretical station position by several centimeters, and allowing the leveling bubble to deviate from the center by about 1.5′, with an actual leveling error of about 1.5′, meeting the 2′ requirement). The setup process took about 2 minutes. Then, the horizontal and vertical angles of 5 prisms were observed in sequence, with 2 observations for each prism, for a total observation time of about 6 minutes. In traditional surveying, these are called "gross errors" or "residual errors"; however, in this embodiment, these deviations are treated as unknown parameters to be solved. By allowing the station to be in an "unstable state," the time loss of on-site leveling is eliminated, while forcing the algorithm to rely on redundant observations to invert the true azimuth. 2 observations were performed for each prism, and the horizontal angle H was recorded. i With vertical angle V i .

[0031] The multi-target angle intersection algorithm is used for solution, specifically: Using the left wall prism as the origin, the local relative coordinates of the other four prisms can be measured with a handheld laser rangefinder and a steel ruler, with an accuracy of centimeters.

[0032] Let the coordinates of the station be (X) s ,Y s The orientation parameter is ω (i.e., the azimuth angle corresponding to the zero direction of the scale). For each prism i, its local coordinates are (X... i ,Y i The observed horizontal angle is H. i An observation equation can be established:

[0033] Where V i This is the residual. Similarly, for vertical angle observations, the elevation-related equations can be derived. This yields the equation containing (X... s ,Y s Error equations for unknowns such as ,ω).

[0034] The weighted least squares method is used for iterative solution. The initial values ​​can be set as the centroids of each prism point with the station coordinates, and the orientation parameter is 0. After three iterations, the solution converges, obtaining (X... s ,Y s The most probable values ​​of ω and ω.

[0035] A residual check is performed. Let the unit weight error be σ. When the residual of a certain observation is greater than 3σ, the value is automatically removed and the adjustment is repeated. No values ​​exceeding the limit were found in this embodiment.

[0036] The final solution yields the station orientation parameter ω, which is the true azimuth angle, completely eliminating the influence of the station on centering and leveling.

[0037] Decoupling and Adjustment of Station Errors: The core improvement in this embodiment is to regard the station as a "floating origin". This includes: (1) Local coordinate system and relative geometric constraints, with the left wall prism P4 as the local coordinate origin (0,0,0). The relative slope distance and height difference between each prism are obtained using a handheld laser rangefinder to construct a local approximate coordinate system. (2) Establishing a nonlinear observation model with error parameters, assuming the real physical coordinates of station S are (X s ,Y s Z s The orientation parameter of the i-th prism is ω (i.e., the zero direction of the scale). For the i-th prism, the following rigorous observation equation is established:

[0038] Among them, H i obs and V i obs These are the raw observations collected by the total station.

[0039] Error absorption mechanism: In the adjustment model, (X) s ,Y s Z s All parameters (X, ω) are set as unknowns. Absorption of the mean square error: The physical offset of the station center is directly reflected in (X... s ,Y s In the solution results, regardless of where the instrument is set up, the ω obtained from the adjustment is the true orientation relative to that actual location. Absorption of leveling error: vertical angle V i The introduction of this method establishes elevation constraints. If the total station is not leveled, its line of sight may have a slight tilt, which will be controlled by Z. s The elevation observation equation is automatically compensated through iterative calculation, thereby eliminating the cascading effect of vertical axis tilt error on horizontal angle. Iteration and Gross Error Removal: The Gauss-Newton method is used for iterative solution. The initial value is set as the centroid of the prism group, and convergence is achieved after 3 iterations. The standardized residuals are calculated; if the residual v of a certain observation... i If the value is >3σ (usually caused by vibrations from passing vehicles), the measured data should be discarded and the data adjusted again to ensure robustness of the solution. Accuracy Verification and Breakthrough Results: Accuracy statistics were obtained from 10 independent experiments conducted under the same 32 m side conditions. The results are shown in Table 1.

[0040]

[0041] This embodiment achieves the counterintuitive effect of "the more relaxed the physical control, the higher the mathematical accuracy." In traditional methods, physical installation errors (centering, leveling) are the upper limit of accuracy; however, in this invention, the arbitrariness of physical installation is transformed into redundant observations by the algorithm, which in turn improves the strength of the model. The single-station operation time is reduced from 60 minutes in the traditional scheme to 16 minutes, improving efficiency by 73%, and there is no need to wait for vibration to dissipate. This method completely eliminates the dependence on forced centering bases and stable bedrock, making it particularly suitable for unstable and space-constrained engineering environments such as tunnels, subways, and underground utility tunnels.

[0042] In contrast, in the same scenario, 10 repeated observations were conducted using the traditional forced centering method (both the station and the prism are equipped with forced centering bases for precise centering and leveling). The azimuth error was 11.2″, which could not meet the specification requirements.

[0043] Furthermore, a simulation was conducted on a scheme where only the prism was not required to be aligned, but the measuring station was forced to be aligned (similar to existing technologies). A station alignment error of 0.2 mm still contributed approximately 1.3″ of error on a 32m side. Combined with the difficulty of achieving high precision in leveling within the tunnel, the angular measurement error was approximately 4-5″, lower than that of this invention. This demonstrates that this invention, by simultaneously absorbing station alignment and leveling errors through overall adjustment, possesses significant advantages.

[0044] Subsequently, the tunnel was guided to complete using the azimuth angle provided by this invention, and the final completion error was only 11mm, far less than the 50mm limit, verifying the effectiveness of the invention.

[0045] Example 2: Tunnel with extremely small radius curve segment (extreme geometric constraint scenario) Scenario and Engineering Background: A highway tunnel in a mountainous area enters a horizontal curve section with a radius of 300 m at K3+200. The tunnel has a clear width of 10.5 m, a shallow arch depth, and severe water seepage on the lining surface. During traverse surveying at this location, the foresight and backsight distances are only 28 m due to the curve's obstruction, and the slippery ground makes it impossible to install a forced centering base.

[0046] Technical Solution Implementation: S1. Constructing a non-coplanar height intersection diagram: On the slippery lining surface, five reflectors (replacing prisms) are attached using waterproof adhesive: P1: Arch crown (avoiding seepage points), P2: Left arch waist, P3: Right arch waist, P4: Left maintenance access road, P5: Right cable trench. S2. Introducing controllable installation deviation: The total station is set up at the station without centering; only coarse leveling is performed using a circular bubble level (leveling error approximately 1.8′). Due to the slippery ground, the instrument experienced a slight slippage of approximately 2 mm during the observation process. S3. Implementing error parameter decoupling: A local coordinate system is established with P4 as the origin; the observation equation is constructed, treating the station coordinates (Xs, Ys) and orientation parameter ω as unknowns; key processing: the displacement caused by instrument slippage is captured by the adjustment model as the change in station coordinates, while the orientation parameter ω remains stable between the two observations.

[0047] Station setup and angle observation (introducing controllable installation deviation): A 0.5″ total station was set up on the platform outside the curve. Counterintuitive operation: No optical centering was performed; only coarse leveling was done using a circular bubble level (measured leveling error approximately 1.8′). Dynamic interference: During the observation period, a muck truck drove by quickly, causing the instrument to slip physically by approximately 2 mm. Observation data: Two observations were performed for each prism, and the horizontal angle H was recorded. i With vertical angle V i .

[0048] Multi-target angle intersection adjustment (error parameter decoupling): A local coordinate system is established, with P4 (left wall) as the origin (0,0,0). The slope distances between points are measured using a handheld rangefinder to construct approximate coordinates. The observation equations and parameter absorption are then constructed, resulting in the following rigorous observation equations:

[0049] Set the station coordinates (X) s ,Y s Set as an unknown. Handling instrument slippage: The 2 mm slippage caused by the slag removal vehicle is represented in the adjustment model as the station coordinates (X... s ,Y s The change in azimuth is considered. Since the observations are collected before and after the sliding motion, the adjustment solution automatically fits an "equivalent station position," while the orientation parameter ω (azimuth angle), as an independent unknown, is unaffected by the physical displacement of the station and maintains its theoretical stability. The weighted least squares method is used, and convergence is achieved after three iterations.

[0050] The implementation results are shown in Table 2.

[0051]

[0052] This invention demonstrates that even under extreme conditions of instrument physical instability (slippage), it can still output a stable azimuth angle through parameter decoupling, supporting "synchronous absorption of station deviations".

[0053] Example 3: Large-section station tunnel (multi-station collaborative scenario) Scenario and Engineering Background: A subway station tunnel, a large-section structure with two islands and four tracks, has an excavation width of 25 meters. Due to the construction machinery occupying most of the space, surveyors can only conduct measurements on a narrow sidewall platform. At this point, the survey station is far from the tunnel center, and the line of sight must penetrate a complex steel support network, forming an irregular, ultra-short side network.

[0054] Technical Solution Implementation: S1. Construct a non-coplanar elevation intersection diagram. Six temporary prisms (one more than usual to enhance diagram strength) are placed at different elevations on the station sidewalls: three at the arch crown and upper step (high elevation), and three at the sidewalls and lower step (low elevation). High elevation group: P1 (arch crown center), P2 (left arch waist), P3 (right arch waist). Low elevation group: P4 (left side wall), P5 (right side wall), P6 (side of the central column). S2. Introduce controllable installation deviations. Due to the narrow platform, the tripod opening angle is limited during total station setup, significantly increasing the centering error (estimated > 5 mm). Only rough leveling is performed. S3. Perform error parameter decoupling. Utilize the spatial three-dimensional network formed by the six prisms to establish elevation constraint equations including vertical angles. Employ weighted least squares adjustment, focusing on the elevation parameter Zs. In large-section scenarios, vertical angle observations are extremely sensitive to station elevation errors. By using prism constraints, vertical axis errors caused by instrument tilt are effectively eliminated.

[0055] Multi-target angle intersection adjustment (3D pose decoupling) introduces a vertical angle equation. Unlike small cross-sections, large cross-sections have large elevation differences and abundant vertical angle observations. An observation equation incorporating vertical angles is constructed:

[0056] Error absorption mechanism: The station elevation Z s Incorporating unknowns. Elimination of vertical axis tilt: Tilt of the line of sight caused by instrument misalignment will change all vertical angle readings. The adjustment model calculates the actual tilt of the instrument by comparing the geometric relationship between the vertical and horizontal angles of the six prisms, and subtracts it from the observations, thereby eliminating the leveling error.

[0057] The implementation results are shown in Table 3.

[0058]

[0059] This invention demonstrates that, in scenarios with large cross sections and multiple prisms (6 in total), the introduction of vertical angle observation achieves integrated decoupling of three-dimensional pose.

[0060] Example 4: Reconstruction of Existing Railway Tunnel (Non-destructive Installation Scenario) Scenario and Engineering Background: An operational railway tunnel is undergoing electrification upgrades, requiring the installation of control points on the existing lining surface. Constraints: Drilling holes in the lining is strictly prohibited (expansion bolts cannot be installed), and train intervals (maintenance windows) are only 2 hours.

[0061] Technical Solution Implementation: S1. Construct a non-coplanar height intersection diagram and use a magnetic base prism to attach it to steel embedded parts (such as fire hydrants and cable supports) in the tunnel. P1: Fire hydrant valve. P2: Cable support crossarm. P3: Passing hole door frame angle iron. P4: Ventilation pipe flange. P5: Trackside signal box. These points are not ideal measurement markers; their positions are random and vary in height. However, this invention does not require forced alignment, so it does not affect use. S2. Introduce controllable installation deviations by setting up a total station on the ballast beside the track. Due to the softness of the ballast, leveling the instrument is extremely difficult, and trains passing by will cause micro-vibrations. Only rough leveling is performed. S3. Perform error parameter decoupling and establish observation equations. Gross error elimination mechanism: Vibrations caused by passing trains result in gross errors (residuals > 3σ) in some sets of observations. The adjustment system automatically identifies and eliminates these disturbed observations, and uses the remaining stable observations to complete the calculation. Gross error removal process: After the first adjustment, calculate the residuals v of each observation. i The residual |v3| for observation P3 was found to be 12.5′′, far exceeding the set three-times mean square error limit (3σ=6′′). Automatic diagnosis: This observation was determined to be a gross error due to train vibration interference. Removal and recalculation: The second set of data for P3 was automatically removed, and the remaining nine observations were used to recalculate the adjustment.

[0062] The implementation results are shown in Table 4.

[0063]

[0064] This demonstrates that even when the prism cannot be precisely positioned and environmental vibrations are significant, the present invention can still ensure the reliability of the results by relying on the gross error elimination step.

[0065] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them. Those skilled in the art should understand that modifications can be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for measuring the angle of an ultra-short side traverse in an extra-long tunnel, characterized in that, include: S1. Constructing a non-coplanar high intersection pattern: Multiple non-coplanar temporary non-centering prisms are arranged on the tunnel cross section to form a high-intensity spatial intersection geometry. The prisms are directly fixed to the lining structure without the need for a forced centering base. S2. Introduce controllable installation deviations: Control the total station to only perform rough leveling and not to be misaligned, allowing for significant installation deviations at the stations; S3. Perform parameter decoupling of station errors: Receive the relative position data of the prism and the angle observation data from the total station; construct a multi-objective joint adjustment model with the three-dimensional coordinates and orientation parameters of the station as the core unknowns; use high-intensity spatial intersection geometry to parameterize and absorb the significant installation deviations, and output the true azimuth angle that is not affected by the station alignment error and leveling error.

2. The measurement method according to claim 1, characterized in that, Step S3 specifically includes: establishing the following nonlinear observation equations and performing linearization: Among them, (X) s ,Y s Z s ) represents the three-dimensional coordinates of the station, ω represents the orientation parameter, and v hi v vi The residual is obtained by iteratively solving the weighted least squares method, thereby achieving integrated decoupling between the three-dimensional pose of the station and the relative geometry of the prism.

3. The method according to claim 2, characterized in that, During the iterative solution process, the initial values ​​of the station coordinates are set using the centroid approximation method, and the initial values ​​of the orientation parameters are set with the zero direction. The solution converges to the most probable value within three iterations.

4. The method according to claim 1, characterized in that, It also includes a gross error removal step: Calculate the residuals of the observations at each angle. When any residual is greater than three times the set unit weight error, the observation is determined to be a gross error due to construction disturbance, and is automatically removed and a new round of adjustment calculation is triggered.

5. The method according to claim 1, characterized in that, In step S1, the temporary centering-free prism is fixed by expansion screws and a simple bracket, and the deployment time is controlled within 10 minutes.

6. The method according to claim 1, characterized in that, The method involves multiple independent observations at the same station, and the calculated azimuth error is no greater than 2.5″.

7. The method according to claim 1, characterized in that, In step S1, when obtaining the relative positional relationship of each prism in the local coordinate system, a handheld laser rangefinder is used in conjunction with a steel ruler for measurement.

8. A method for measuring the angle of an ultra-short side traverse in an extra-long tunnel, characterized in that, include: The graphic construction module is used to deploy multiple non-coplanar temporary non-alignment prisms on the tunnel cross section to form a high-strength spatial intersection geometry. The prisms are directly fixed to the lining structure without the need for a forced alignment base. The deviation introduction module is used to control the total station to only perform rough leveling and not to be misaligned, allowing for significant installation deviations at the station; The error absorption and adjustment module is configured to perform the following operations: receive prism relative position data from the graphics construction module and angle observation data from the total station; construct a multi-objective joint adjustment model with the station's three-dimensional coordinates and orientation parameters as the core unknowns; and use high-intensity spatial intersection geometry to parametrically absorb the significant installation deviations and output the true azimuth angle unaffected by the station's alignment error and leveling error.

9. The system according to claim 8, characterized in that, The error absorption adjustment module is further configured to: establish a set of nonlinear observation equations including horizontal and vertical angles; use weighted least squares method to iteratively estimate the station pose; and use built-in residual analysis to identify and remove abnormal observation values ​​affected by construction disturbances.

10. The system according to claim 8, characterized in that, The error absorption adjustment module is integrated into the total station's onboard system or an external mobile terminal, supports real-time on-site calculation, and outputs azimuth results with an accuracy better than 2.5″ under the condition that the line-of-sight distance is no more than 50m.

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