A Multi-parameter Optimization Method for Suspended Tunnel Structures in Wave Environments

Abstract

This invention relates to a multi-parameter optimization method for suspended tunnel structures under wave conditions, belonging to the field of tunnel structures. Based on existing methods for calculating the dynamic response of suspended tunnels under wave loads, this method uses the maximum horizontal and vertical displacements at key control positions of the suspended tunnel under wave loads as optimization targets to optimize parameters such as the buoyancy ratio, anchor cable inclination angle, anchor cable installation angle, submersion depth, and cross-sectional parameters. Previous methods for optimizing suspended tunnel structures typically use the magnitude of the stress on the structure as the optimization target, neglecting the dynamic response of the structure under wave loads. The proposed method uses the maximum displacement at key control positions as the optimization target. Furthermore, the proposed method comprehensively considers multiple structural parameters, allowing for flexible selection of parameters at key structural positions based on actual design requirements. Therefore, the proposed method has good applicability to different structural design requirements.

Description

Technical Field

[0001] This invention belongs to the field of tunnel structures and relates to a multi-parameter optimization method for suspended tunnel structures in wave environments. Background Technology

[0002] Submerged Floating Tunnels (SFTs) mainly consist of a tube body, anchor cables, foundations, and revetment sections. They possess advantages such as large span capacity, adaptability to deep-water construction, all-weather operation, and good environmental and economic benefits, making them considered one of the most challenging and promising new transportation structures of the 21st century. However, there are currently no real-world examples of submerged tunnel projects, and concerns remain regarding their safety and comfort in complex marine environments. Wave loads are the most significant environmental dynamic loads experienced by submerged tunnels. Therefore, the dynamic response of a submerged tunnel under wave loads is a major factor affecting structural safety and comfort. In the design of submerged tunnels, it is essential to minimize the dynamic response in wave environments. Many factors influence the dynamic response of a submerged tunnel, but previous research indicates that the most significant factors include the submersion depth, the inclination angle of the anchor cables, the installation angle of the anchor cables, the buoyancy ratio of the tube body, and different cross-sectional shapes. Therefore, it is necessary to seek an optimal set of structural design parameters when designing submerged tunnel structures.

[0003] Most existing optimization methods focus on stress optimization of stationary structures, which severs the coupling relationship between tube motion and stress, making the optimization results potentially unreliable. Furthermore, current optimization methods typically only optimize the tube cross-section, neglecting the combined influence of multiple factors on the structure's dynamic response. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a multi-parameter optimization method for suspended tunnel structures in wave environments.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A multi-parameter optimization method for a suspended tunnel structure under wave conditions, the method comprising the following steps:

[0007] S1: Calculate the dynamic response of the structure under wave load.

[0008] Based on existing structural dynamic response calculation methods, including potential flow theory, computational fluid dynamics (CFD), finite element method, and traditional dynamics, the dynamic response of key locations in a suspended tunnel under wave loads is calculated. The 1 / 2 span, 1 / 4 span, and 1 / 8 span locations of the tunnel are selected as the control positions of the structure, and their maximum horizontal and vertical displacements are denoted as: S hi ,S vi, i = 2, 4, 8; representing 1 / 2 span, 1 / 4 span and 1 / 8 span respectively;

[0009] S2: Determine the optimization parameters and their feasible range

[0010] The parameters considered in the design of suspended tunnel segments include: submerged water depth d. s buoyancy ratio R bw Installation angle α, tilt angle β, cross-sectional parameters X = {x1, x2, ..., x n}, where x1, x2, ..., x n This refers to a single decision variable to be optimized, determined based on actual needs, such as cross-sectional height, cross-sectional width, wall thickness, etc.

[0011] The feasible range of the above parameters is determined based on actual design requirements. For cross-sectional parameters, the spatial size of the tunnel remains constant, and the cross-sectional area S of the pipe body is guaranteed. A The area remains constant, ensuring sufficient lane width, ensuring that a certain characteristic width L of the cross section is greater than a certain fixed value, ensuring that the tunnel meets a certain clearance height, and ensuring that a certain characteristic height H of the cross section is greater than a certain specific value.

[0012] The optimization parameters and feasible region are represented as follows:

[0013]

[0014] Where a1, b1, a2, b2, a3, b3 and a4, b4 represent the left and right endpoints of the range of values ​​for submerged water depth, inclination angle, installation angle and buoyancy ratio, respectively. A0, l0 and h0 are the values ​​of cross-sectional area, characteristic width and height of the pipe body. All of the above values ​​should be reasonably selected according to the design requirements of the suspended tunnel.

[0015] S3: Determine the optimization objective

[0016] The optimization objective is to determine the weighted sum of the maximum horizontal and vertical displacements at the control location under wave loads with different wave numbers k. The range of wave number k is denoted as [N]. a N b ], N a N b The value of can be determined based on actual wave observation statistics, and the optimization objective is expressed as:

[0017]

[0018] Where C is the optimization coefficient, S hi ,S vi (i = 2, 4, 8) represent the horizontal and vertical displacements of the pipe at half-span, quarter-span, and eighth-span locations under wave load, respectively. w h wv w is the weighting coefficient. h w v Both are positive numbers and their sum is 1.

[0019] S4: Optimize parameters for the optimization objective.

[0020] The optimization objective is expressed as:

[0021] min f(d s ,α,β,R bw ,X)

[0022]

[0023] The optimization objective is a constrained optimization problem. First, the equality constraints are processed into inequality constraints. Then, based on the calculation method of the dynamic response of the suspended tunnel, either the gradient descent algorithm or the one-dimensional cyclic search algorithm is selected for solving.

[0024] The beneficial effects of this invention are as follows: Using the maximum displacement of critical structural control positions as the optimization target is more practical, considering both structural safety and functionality / comfort. Furthermore, the proposed method comprehensively considers multiple structural parameters, allowing for flexible selection of critical structural positions based on actual design requirements. Therefore, the proposed method has good applicability to different structural design requirements.

[0025] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0026] To make the objectives, technical solutions, and advantages of the present invention clearer, the preferred embodiments of the present invention will be described in detail below with reference to the accompanying drawings, wherein:

[0027] Figure 1 A schematic diagram of a typical suspended tunnel structure is provided.

[0028] Figure 2 Schematic diagram of optimized parameters for a suspended tunnel with an elliptical cross-section;

[0029] Figure 3 To optimize the target value change graph;

[0030] Figure 4 Comparison of structural dynamic response before and after optimization. Detailed Implementation

[0031] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Unless otherwise specified, the following embodiments and features can be combined with each other.

[0032] The accompanying drawings are for illustrative purposes only and are schematic diagrams, not actual pictures. They should not be construed as limiting the invention. To better illustrate the embodiments of the invention, some parts in the drawings may be omitted, enlarged, or reduced, and do not represent the actual product dimensions. It is understandable to those skilled in the art that some well-known structures and their descriptions may be omitted in the drawings.

[0033] In the accompanying drawings of the embodiments of the present invention, the same or similar reference numerals correspond to the same or similar components. In the description of the present invention, it should be understood that if terms such as "upper," "lower," "left," "right," "front," and "rear" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, they are only for the convenience of describing the present invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, the terms used to describe positional relationships in the drawings are only for illustrative purposes and should not be construed as limiting the present invention. For those skilled in the art, the specific meaning of the above terms can be understood according to the specific circumstances.

[0034] Figure 1 This is a schematic diagram and coordinate system of a typical suspended tunnel structure. This method, based on existing methods for calculating the dynamic response of suspended tunnels under wave loads, uses the maximum horizontal and vertical displacements of key control positions of the suspended tunnel under different wave loads as optimization objectives. It is a multi-parameter optimization method for suspended tunnel structures under wave conditions, comprising the following steps:

[0035] S1: Calculate the dynamic response of the structure under wave load.

[0036] Based on existing structural dynamic response calculation methods, such as potential flow theory, computational fluid dynamics (CFD), finite element method, and traditional dynamics, the dynamic response of key locations in a suspended tunnel under wave load is calculated. The proposed method selects the 1 / 2 span, 1 / 4 span, and 1 / 8 span locations of the tunnel as the control positions of the structure, and the maximum horizontal and vertical displacements are denoted as S. hi ,S vi(i = 2, 4, 8; representing 1 / 2 span, 1 / 4 span, and 1 / 8 span respectively).

[0037] S2: Determine the optimization parameters and their feasible range

[0038] Based on previous research, the main parameters that should be considered in the design of suspended tunnel segments include: submerged water depth (d). s ), buoyancy ratio (R) bw ), installation angle (α), tilt angle (β), cross-sectional parameters (X={x1,x2,…,x) n})

[0039] The feasible range of the above parameters can be determined according to the actual design requirements. For cross-sectional parameters, in addition to the requirements for their value range, the basic functional requirements of the suspended tunnel must also be ensured during the optimization process. For example, the spatial size of the tunnel must remain unchanged (the cross-sectional area of ​​the tube (S)). A (The area remains constant), ensuring sufficient lane width (a certain characteristic width (L) of the cross-section is greater than a certain fixed value), and ensuring sufficient tunnel clearance (a certain characteristic height (H) of the cross-section is greater than a certain specific value). In summary, the optimization parameters and feasible region can be expressed as:

[0040]

[0041] S3: Determine the optimization objective

[0042] This method uses the control position at different wave numbers (k), where the wave number variation range is denoted as [N]. a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N b ])(k, the wavenumber variation range is denoted as [N a N bThe optimization objective is to take the weighted sum of the maximum horizontal and vertical displacements under wave load as the optimization objective, which can be expressed as:

[0043]

[0044] Where C is the optimization coefficient, w h w v These are the weighting coefficients.

[0045] S4: Optimize parameters for the optimization objective.

[0046] The above optimization problem can be expressed as:

[0047] min f(d s ,α,β,R bw ,X)

[0048]

[0049] This optimization problem is a constrained optimization problem. The equality constraints can be converted into inequality constraints first. Then, based on the calculation method of the dynamic response of the suspended tunnel, an appropriate numerical solution method can be selected for the solution, such as gradient descent algorithm, one-dimensional cyclic search algorithm, etc.

[0050] To verify the feasibility of the proposed optimization method, this example will perform multi-parameter optimization on an elliptical suspended tunnel cross-section. Figure 2 A schematic diagram of optimized parameters for an elliptical cross-section suspended tunnel is provided. First, according to step S1, this example selects traditional dynamics theory combined with potential flow theory to calculate the dynamic response of the suspended tunnel under wave load. According to step S2, the optimized parameters selected in this example, based on existing research data, are: submerged water depth (d... s ), buoyancy ratio (R) bw Installation angle (α), tilt angle (β), cross-sectional parameters (X = {x1, x2}) T (where x1 represents the length of the major axis of the ellipse and x2 represents the length of the minor axis of the ellipse) and simultaneously determine its feasible region (values ​​are shown in Formula 5). Finally, based on steps 3 and 4, the range of variation of the incident wave number (k) is selected as [0.005-0.05]. The final optimization problem can be expressed as:

[0051]

[0052] min f(d s ,α,β,R bw (x1, x2)

[0053]

[0054] In this example, a one-dimensional iterative search algorithm is used to solve the optimization problem in Equation 5. Table 1 lists the changes of each optimization parameter during the iteration process. From the optimization results, except for the installation angle and tilt angle of the anchor cable, the optimal solutions for the other parameters are all obtained on the boundary of the feasible region. Furthermore, Figure 3 The evolution of the optimization objective value during the iteration process is presented. The objective value continuously decreases with each iteration, implying that the dynamic response at the control position of the pipe is continuously decreasing. Figure 4 A comparison of the dynamic response of the structure before and after parameter optimization is presented. It can be seen that the dynamic response characteristics of the structure after parameter optimization are significantly better than those before parameter optimization. This result shows that the proposed method can effectively optimize multiple parameters of suspended tunnel structures in wave environments.

[0055] Table 1. Iterative process of multi-parameter optimization

[0056]

[0057]

[0058] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A multi-parameter optimization method for a suspended tunnel structure under wave conditions, characterized in that: The method includes the following steps: S1: Calculate the dynamic response of the structure under wave load. Based on existing structural dynamic response calculation methods, including potential flow theory, computational fluid dynamics (CFD), finite element method, and traditional dynamics, the dynamic response of key locations in a suspended tunnel under wave loads is calculated. The 1 / 2 span, 1 / 4 span, and 1 / 8 span locations of the tunnel are selected as the control positions of the structure, and their maximum horizontal and vertical displacements are denoted as: S hi ,S vi , i = 2, 4, 8; representing 1 / 2 span, 1 / 4 span and 1 / 8 span respectively; S2: Determine the optimization parameters and their feasible range The parameters considered in the design of suspended tunnel segments include: submerged water depth d. s buoyancy ratio R bw Installation angle α, tilt angle β, cross-sectional parameters X = {x1, x2, ..., x n }, where x1, x2, ..., x n This refers to a single decision variable to be optimized, determined based on actual needs, including cross-sectional height, cross-sectional width, and wall thickness. The feasible range of the above parameters is determined based on actual design requirements. For cross-sectional parameters, the spatial size of the tunnel remains constant, and the cross-sectional area S of the pipe body is guaranteed. A The area remains constant, ensuring sufficient lane width, ensuring that a certain characteristic width L of the cross section is greater than a certain fixed value, ensuring that the tunnel meets a certain clearance height, and ensuring that a certain characteristic height H of the cross section is greater than a certain specific value. The optimization parameters and feasible region are represented as follows: Where a1, b1, a2, b2, a3, b3 and a4, b4 represent the left and right endpoints of the range of values ​​for submerged water depth, tilt angle, installation angle and buoyancy ratio, respectively. A0, l0 and h0 are the values ​​of cross-sectional area, characteristic width and height of the pipe body. The above values ​​are selected according to the design requirements of the suspended tunnel. S3: Determine the optimization objective The optimization objective is to determine the weighted sum of the maximum horizontal and vertical displacements at the control location under wave loads with different wave numbers k. The range of wave number k is denoted as [N]. a N b ], N a N b The value of can be determined based on actual wave observation statistics, and the optimization objective is expressed as: Where C is the optimization coefficient, S hi ,S vi i = 2, 4, 8, representing the horizontal and vertical displacements of the pipe at half span, quarter span, and eighth span respectively under wave load. w h w v w is the weighting coefficient. h w v Both are positive numbers and their sum is 1; S4: Optimize parameters for the optimization objective. The optimization objective is expressed as: The optimization objective is a constrained optimization problem. First, the equality constraints are processed into inequality constraints. Then, based on the calculation method of the dynamic response of the suspended tunnel, either the gradient descent algorithm or the one-dimensional cyclic search algorithm is selected for solving.

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