A method for predicting the pose of tunnel boring machines based on dynamic modeling

Abstract

This invention provides a method for predicting the tunnel boring machine (TBM) posture based on dynamic modeling, comprising the following steps: S1: Obtaining historical TBM posture information and posture change rate based on the TBM guidance system; S2: Determining the TBM posture transformation matrix; S3: Determining the TBM propulsion system parameters; S4: Establishing the dynamic equations of the TBM propulsion system; S5: Establishing the state-space model of the TBM propulsion system; S6: Establishing the equivalent load estimation model of the TBM; S7: Establishing the TBM tunneling posture prediction model. This method has high prediction accuracy and engineering applicability, and can provide a theoretical basis for TBM operators or automatic control systems to adjust the TBM posture.

Description

Technical Field

[0001] This invention belongs to the field of tunnel boring machine (TBM) construction, specifically relating to a method for predicting the posture of a TBM tunneling machine based on dynamic modeling. Background Technology

[0002] Shield tunneling, with its advantages of high construction speed, high safety, and low environmental pollution, has gradually become the mainstream method for tunnel construction. However, during shield tunneling, factors such as varying constraints from the surrounding rock and unreasonable operating parameter settings make precise control of the shield's position and attitude difficult, inevitably causing the shield's trajectory to deviate from the tunnel's design axis. Improper shield position control can easily lead to the shield tail squeezing the tunnel segments, resulting in problems such as segment misalignment, damage, and leakage. Furthermore, deviations from the tunnel's design axis significantly reduce the quality of the completed tunnel, creating potential safety hazards for future operation. Therefore, precise control of the shield's position is crucial for ensuring safe and efficient shield tunneling.

[0003] Currently, most shield tunneling machine (TBM) posture control relies on feedback control. The TBM operator or the automatic control system adjusts the TBM propulsion system parameters based on manual experience or a specific control strategy, using the TBM's posture deviation measured by the shield's guidance system, to achieve this adjustment. However, due to the large inertia caused by the TBM's own mass and the time lag in the hydraulic system control, feedback-based posture control methods suffer from significant lag, easily leading to serpentine movement of the TBM. If the TBM's posture deviation could be predicted and controlled before it deviates during tunneling, the control lag could be effectively eliminated, improving the accuracy of TBM posture control.

[0004] With the development of artificial intelligence and big data technologies, current shield tunneling posture prediction mainly utilizes a large amount of historical data generated during shield tunneling to establish posture prediction models using data-driven modeling. However, existing data-driven shield tunneling posture prediction models are essentially black-box models with poor interpretability. The inherent contradiction between the accuracy and generalization ability of data-driven models means that a model with high prediction accuracy in one project may not be applicable to another. Retraining the model for new projects requires additional time, which greatly limits the practical engineering application of the model. Summary of the Invention

[0005] The present invention aims to provide a method for predicting the pose of tunnel boring machines based on dynamic modeling, in order to solve the above problems.

[0006] The technical solution of this invention is:

[0007] A method for predicting the pose of a tunnel boring machine (TBM) based on dynamic modeling includes the following steps:

[0008] S1: Obtain historical shield posture information and posture change rate based on the shield guidance system;

[0009] S2: Determine the shield tunneling posture transformation matrix;

[0010] S3: Determine the parameters of the tunnel boring machine propulsion system;

[0011] S4: Establish the dynamic equations of the tunnel boring machine propulsion system;

[0012] S5: Establish the state-space model of the tunnel boring machine propulsion system;

[0013] S6: Establish an equivalent load estimation model for the tunnel boring machine;

[0014] S7: Establish a shield tunneling posture prediction model.

[0015] Preferably, in S1,

[0016] The shield tunneling pose vector q = [xyz ψ θ φ] T and pose change rate vector

[0017] Where (x,y,z) represents the position coordinates of the center of the ball joint distribution circle in front of the tunnel boring machine's propulsion cylinder; (ψ,θ,φ) represents the three attitude angles of the tunnel boring machine: roll angle, pitch angle, and yaw angle.

[0018] Preferably, in S2,

[0019] The formula for calculating the shield tunneling posture transformation matrix is:

[0020]

[0021] in, and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows:

[0022]

[0023]

[0024] Where c represents the cosine function cos; s represents the sine function sin.

[0025] Preferably, in S3,

[0026] The parameters of the tunnel boring machine propulsion system include: coordinate B of the ball joint behind the propulsion cylinder. i ; Shield body centroid position vector r G Shield mass M G Shield body inertial tensor A I M ; Shield propulsion system propulsion force vector F d=[F1 F2…F n ] T , where n is the total number of hydraulic cylinders.

[0027] Preferably, in S4,

[0028] The dynamic equations of the tunnel boring machine propulsion system are:

[0029]

[0030] Among them, F T The equivalent load experienced during shield tunneling; the formulas for calculating other coefficients are:

[0031]

[0032] Where E3 is a third-order identity matrix; A u i Let g be the unit direction vector of the i-th propulsion cylinder, i = 1, 2, 3, ..., n; g = [0 0 -9.8] T ω is the gravitational acceleration vector; ω is the angular velocity of the shield. A u i T0 The formula for calculating ω is:

[0033]

[0034]

[0035]

[0036]

[0037] Preferably, in S5,

[0038] The state-space model of the tunnel boring machine propulsion system is

[0039]

[0040] Y = X1 = HX (11)

[0041] Among them, X1=q=[xyz ψ θ φ] T Indicates the pose of the system. This represents the rate of change of the system's pose. Represents the state vector of the system; U = F d =[F1 F2…F n ] T This represents the system's control input; H = [E6 0 6×6 [] represents the system's output matrix; Y = [xyz ψ θ φ] TThe output pose vector of the system is represented by h1(X) and h2(X). The formulas for calculating h1(X) and h2(X) are as follows:

[0042] h1(X)=M -1 (F T -CX2-G) (12)

[0043] h2(X)=M -1 J T (13)

[0044] Preferably, the establishment of the shield tunneling equivalent load estimation model in S6 specifically includes:

[0045] By rearranging and performing backward difference on formula (4), the formula for estimating the equivalent load of the tunnel boring machine is:

[0046]

[0047] Among them, F T (k) represents the shield equivalent load at time k; U(k) represents the shield propulsion system control input at time k; M(k), C(k), G(k) and J(k) represent the values ​​of parameters M, C, G and J in formula (5) at time k, respectively; X(k) represents the system state vector at time k; X(k-1) represents the system state vector at time k-1; T s D1 = [0] is the system sampling interval time; 6×6 E6],D2=[E6 0 6×6 ].

[0048] Preferably, the shield tunneling pose prediction model is established in S7, specifically including:

[0049] (1) One-step prediction

[0050] The equivalent load of the tunnel boring machine at time k is estimated as follows:

[0051]

[0052] The system state vector at time k is predicted to be at time k+1 in the future.

[0053] X p (k+1|k)=X(k)+T s f(X(k),U(k),F T (k)) (16)

[0054] (2) Two-step prediction

[0055] The equivalent load of the tunnel boring machine at time k+1 is estimated as follows:

[0056]

[0057] The system state vector at time k is predicted to be the state vector at time k+2.

[0058] X p (k+2|k)=X p (k+1|k)+T s f(X p (k+1|k),U(k+1),F T (k+1)) (18)

[0059] (3)N p Step prediction

[0060] k+N p The estimated equivalent load of the tunnel boring machine at time -1 is:

[0061]

[0062] Predict the future k+N at time k. p The system state vector at time t is

[0063]

[0064] According to formula (10), at time k, for the future N p The formula for predicting the posture state of a tunnel boring machine is as follows:

[0065] The beneficial effects of this invention are as follows:

[0066] This invention provides a shield tunneling posture prediction method based on dynamic modeling, which includes three parts: dynamic modeling, shield load estimation model and shield posture prediction model. It has high prediction accuracy and engineering applicability, and can provide a theoretical basis for shield operators or automatic control systems to adjust shield posture. Attached Figure Description

[0067] Figure 1 A flowchart illustrating a shield tunneling pose prediction method based on dynamic modeling, provided for an embodiment of the present invention;

[0068] Figure 2 A diagram showing the zonal arrangement of hydraulic cylinders in a shield propulsion system for a shield tunneling posture prediction method based on dynamic modeling, provided in an embodiment of the present invention.

[0069] Figure 3 This is a schematic diagram of the multi-step prediction results of the shield tunneling posture of a shield tunneling posture prediction method based on dynamic modeling provided in an embodiment of the present invention. Detailed Implementation

[0070] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. The embodiments of the present invention are not limited thereto.

[0071] Example 1

[0072] like Figure 1 As shown, a shield tunneling pose prediction method based on dynamic modeling includes the following steps:

[0073] S1: Obtain historical shield posture information and posture change rate based on the shield guidance system;

[0074] S2: Determine the shield tunneling posture transformation matrix;

[0075] S3: Determine the parameters of the tunnel boring machine propulsion system;

[0076] S4: Establish the dynamic equations of the tunnel boring machine propulsion system;

[0077] S5: Establish the state-space model of the tunnel boring machine propulsion system;

[0078] S6: Establish an equivalent load estimation model for the tunnel boring machine;

[0079] S7: Establish a shield tunneling posture prediction model.

[0080] In step one, the shield tunneling guidance system acquires historical shield posture information and posture change rate, including the shield posture vector q = [xyz ψ θ φ]. T and pose change rate vector The above parameters can be acquired through the tunnel boring machine's guidance system;

[0081] The shield tunneling pose transformation matrix in step two can be determined by the following formula:

[0082]

[0083] in, and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows:

[0084]

[0085]

[0086] Where c represents the cosine function cos; s represents the sine function sin.

[0087] The shield tunneling propulsion system parameters in step three can be determined based on engineering data: coordinate B of the ball joint behind the propulsion cylinder. i It can be determined by the arrangement of the propulsion system cylinders, such as Figure 2As shown; the shield's center of mass position vector r G = [1.2m + 0m + -3m]; Shield mass M G =3×10 6 kg; shield body inertia tensor A I M =diag(27000000,31298700,4320000)kgm 2 The shield tunneling propulsion system has an appropriate propulsion force F. d =[F1 F2…F n ] T It can be read by the tunnel boring machine propulsion system; the total number of propulsion cylinders n = 56; the sampling interval time T s =30s.

[0088] The dynamic equations of the shield propulsion system in step four can be established using the Kane method, as shown in the following equation.

[0089]

[0090] Among them, F T The equivalent load experienced during shield tunneling; the formulas for calculating other coefficients are:

[0091]

[0092] Where E3 is a third-order identity matrix; A u i Let be the unit direction vector of the i-th propulsion cylinder, i = 1, 2, 3, ..., n; A u i T0 and The calculation formula is:

[0093]

[0094]

[0095]

[0096] The state-space model of the tunnel boring machine propulsion system in step five can be represented as follows:

[0097]

[0098] Y = X1 = CX (31)

[0099] Among them, X1=q=[xyz ψ θ φ] T Indicates the pose of the system. This represents the rate of change of the system's pose. Represents the state vector of the system; U = F d =[F1 F2…Fn ] T This represents the system's control input; C = [E6 0 6×6 [] represents the system's output matrix; Y = [xyz ψ θ φ] T This represents the system's output pose vector. The formulas for calculating h1(X) and h2(X) are:

[0100] h1(X)=M -1 (F T -CX2-G) (32)

[0101] h2(X)=M -1 J T (33)

[0102] The equivalent load on the tunnel boring machine in step six can be estimated using the following formula.

[0103]

[0104] Among them, F T (k) represents the shield equivalent load at time k; U(k) represents the shield propulsion system control input at time k; M(k), C(k), G(k) and J(k) represent the values ​​of parameters M, C, G and J in formula (5) at time k, respectively; X(k) represents the system state vector at time k; X(k-1) represents the system state vector at time k-1; T s D1 = [0] is the system sampling interval time; 6×6 [E6], D2 = [E6 0] 6×6 ]

[0105] The shield tunneling posture in step seven can be predicted using the following formula.

[0106] (1) One-step prediction

[0107] The equivalent load of the tunnel boring machine at time k is estimated as follows:

[0108]

[0109] The system state vector at time k is predicted to be at time k+1 in the future.

[0110] X p (k+1|k)=X(k)+T s f(X(k),U(k),F T (k)) (36)

[0111] (2) Two-step prediction

[0112] The equivalent load of the tunnel boring machine at time k+1 is estimated as follows:

[0113]

[0114] The system state vector at time k is predicted to be the state vector at time k+2.

[0115] X p (k+2|k)=X p (k+1|k)+T s f(X p (k+1|k),U(k+1),F T (k+1)) (38)

[0116] (3)N p Step prediction

[0117] k+N p The estimated equivalent load of the tunnel boring machine at time -1 is:

[0118]

[0119] Predict the future k+N at time k. p The system state vector at time t is

[0120]

[0121] According to formula (10), at time k, for the future N p The formula for predicting the posture state of a tunnel boring machine is as follows:

[0122]

[0123] The above can achieve the prediction of future N at time k. p The shield tunneling posture prediction at this stage, and the multi-step prediction of the shield tunneling posture at other times, can be determined using the same method. Through the above process, Figure 3 N is given p A schematic diagram of the multi-step prediction results of the shield tunneling posture at time 5. Figure 3 It can be seen that the pose prediction values ​​and the actual pose values ​​over time from step k+1 to step k+5 basically coincide, indicating that the shield tunneling pose prediction method proposed in this invention has high prediction accuracy. The relative error curve shows that the pose prediction accuracy is highest at step k+1. As the number of prediction steps increases, the relative error of pose prediction gradually increases, reaching its maximum at step k+5. The relative errors of pose prediction are all on the order of 10. -4 As can be seen below, the shield tunneling posture prediction method of this invention can predict the future multi-step posture of the shield with high accuracy, providing a theoretical basis for the shield operator or automatic control system to adjust the shield posture.

[0124] Those skilled in the art will understand that the accompanying drawings are merely schematic diagrams of one embodiment, and the processes depicted in the drawings are not necessarily essential for implementing the present invention.

Claims

1. A method for predicting the pose of a tunnel boring machine based on dynamic modeling, characterized in that, Includes the following steps: S1: Obtain historical shield posture information and posture change rate based on the shield guidance system; S2: Determine the shield tunneling posture transformation matrix; S3: Determine the parameters of the tunnel boring machine propulsion system; S4: Establish the dynamic equations of the tunnel boring machine propulsion system; S5: Establish the state-space model of the tunnel boring machine propulsion system; S6: Establish an equivalent load estimation model for the tunnel boring machine; S7: Establish a shield tunneling posture prediction model; in, In S4, The dynamic equations of the tunnel boring machine propulsion system are: Among them, F T The equivalent load experienced by the tunnel boring machine during tunneling; M, C, G, and J are the coefficients of the dynamic equations of the tunnel boring machine propulsion system; In S5, The state-space model of the tunnel boring machine propulsion system is Y = X1 = HX (3) Among them, X1=q=[xy zψθφ] T Indicates the pose of the system. This represents the rate of change of the system's pose. Represents the state vector of the system; U = F d =[F1 F2 … F n ] T Indicates the system's control input; H = [E60] 6×6 [] represents the system's output matrix; Y = [xyz ψ θ φ] T The output pose vector of the system is represented by h1(X) and h2(X). The formulas for calculating h1(X) and h2(X) are as follows: h1(X)=M -1 (F T -CX2-G) (4) h2(X)=M -1 J T (5) Among them, the parameters M, C, G and J constitute the dynamic equations of the shield propulsion system; The specific steps for establishing the shield tunneling equivalent load estimation model in S6 include: By rearranging and performing backward difference on formula (1), the formula for estimating the equivalent load of the tunnel boring machine is: Among them, F T (k) represents the equivalent load of the shield at time k; U(k) represents the control input of the shield propulsion system at time k; M(k), C(k), G(k) and J(k) represent the values ​​of parameters M, C, G and J at time k, respectively; X(k) represents the state vector of the system at time k; X(k-1) represents the state vector of the system at time k-1; T s D1 = [0] is the system sampling interval time; 6×6 E6],D2=[E60 6×6 ].

2. The shield tunneling pose prediction method based on dynamic modeling according to claim 1, characterized in that, In S1, The shield tunneling pose vector q = [xyz ψ θ φ] T and pose change rate vector Where (x,y,z) represents the position coordinates of the center of the ball joint distribution circle in front of the tunnel boring machine's propulsion cylinder; (ψ,θ,φ) represents the three attitude angles of the tunnel boring machine: roll angle, pitch angle, and yaw angle.

3. The shield tunneling pose prediction method based on dynamic modeling according to claim 2, characterized in that, In S2, The formula for calculating the shield tunneling posture transformation matrix is: in, and Let represent the attitude matrix and position vector of the tunnel boring machine (TBM), respectively, and their calculation formulas are as follows: Where c represents the cosine function cos; s represents the sine function sin.

4. The shield tunneling pose prediction method based on dynamic modeling according to claim 3, characterized in that, In S3, The parameters of the tunnel boring machine propulsion system include: coordinate B of the ball joint behind the propulsion cylinder. i ; Shield body centroid position vector r G Shield mass M G Shield body inertial tensor A I M ; Shield propulsion system propulsion force vector F d =[F1 F2 … F n ] T , where n is the total number of hydraulic cylinders.

5. The shield tunneling pose prediction method based on dynamic modeling according to claim 4, characterized in that, The shield tunneling pose prediction model is established in S7, specifically including: (1) One-step prediction The equivalent load of the tunnel boring machine at time k is estimated as follows: The system state vector at time k is predicted to be at time k+1 in the future. X p (k+1|k)=X(k)+T s f(X(k),U(k),F T (k)) (11) (2) Two-step prediction The equivalent load of the tunnel boring machine at time k+1 is estimated as follows: The system state vector at time k is predicted to be the state vector at time k+2. X p (k+2|k)=X p (k+1|k)+T s f(X p (k+1|k),U(k+1),F T (k+1)) (13) (3)N p Step prediction k+N p The estimated equivalent load of the tunnel boring machine at time -1 is: Predict the future k+N at time k. p The system state vector at time t is According to formula (2), at time k, for the future N p The formula for predicting the posture state of a tunnel boring machine is as follows:

6. The shield tunneling pose prediction method based on dynamic modeling according to claim 1, characterized in that, In S4, The formulas for calculating the coefficients M, C, G, and J are as follows: Where E3 is a third-order identity matrix; A u i Let g be the unit direction vector of the i-th propulsion cylinder, i = 1, 2, 3, ..., n; g = [0, 0, -9, 8]. T ω is the gravitational acceleration vector; ω is the angular velocity of the shield. A u i T0 The formula for calculating ω is:

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