Method and system for optimizing the inclination angle of oblique rotary jet grouting piles in heavy haul railway transition section based on multi-body coupled dynamics

Abstract

This invention relates to the field of construction optimization technology, and specifically discloses a method and system for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics. The method includes: constructing a multi-body coupled dynamics model; calculating the vibration response calculation error and adjusting the multi-body coupled dynamics model based on vibration acceleration data and vertical compression deformation data of the multi-body coupled dynamics model and a scaled model under different inclined jet grouting pile inclination angles; performing dynamic simulations on multiple working conditions based on the validated multi-body coupled dynamics model, extracting key dynamic response indicators of the transition section under each working condition and their variation with the inclined jet grouting pile inclination angle; fitting a correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement based on this law; and obtaining the optimal inclined jet grouting pile inclination angle by combining the target transition section type determined by actual engineering needs with the corresponding train load level and preset optimization targets; thereby reducing the vibration and settlement impact of the transition section.

Description

Technical Field

[0001] This invention relates to the field of construction optimization technology, and in particular to a method and system for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics. Background Technology

[0002] Currently, in heavy-haul railway construction, the transition section, as a key area connecting different structures, plays a crucial role in the safe operation of the railway due to its stability. As a commonly used reinforcement method, the rational setting of the inclination angle of inclined jet grouting piles is of great significance for improving the load-bearing capacity of the transition section and reducing vibration and settlement. With the continuous growth of heavy-haul railway transportation demand, the performance requirements for transition sections are also increasing. With the continuous expansion of heavy-haul railway construction scale, the method and system for optimizing the inclination angle of inclined jet grouting piles based on multibody coupled dynamics is expected to be more widely applied in the field of railway engineering, promoting the development of heavy-haul railway construction technology towards a more refined and scientific direction.

[0003] In the design of inclined jet grouting pile reinforcement for transition sections of heavy-haul railways, existing technologies have significant shortcomings. Currently, the design of the inclination angle of inclined jet grouting pile reinforcement severely lacks dynamic basis. Engineers lack scientific dynamic theoretical support when determining the inclination angle, making it difficult to accurately design an inclination angle that meets actual needs. Simultaneously, the vibration suppression effect of different inclination angles is unclear, making it impossible to clearly understand the vibration changes in the transition section under different inclination angle settings, thus making it difficult to assess its impact on railway operational stability. Furthermore, existing methods cannot effectively integrate multi-body coupled dynamics theory to comprehensively consider the complex interaction relationships between trains, tracks, and subgrades in the design. This makes it difficult for the design scheme to meet the high stability requirements of heavy-haul railways for transition sections, and it is impossible to achieve accurate design of the inclination angle of inclined jet grouting piles, affecting the long-term stable operation of heavy-haul railway transition sections.

[0004] Therefore, this invention proposes a method and system for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics. Summary of the Invention

[0005] This invention provides a method and system for optimizing the inclination angle of inclined jet grouting piles in heavy-haul railway transition sections based on multibody coupled dynamics. It comprehensively considers the complex interactions between trains, tracks, roadbeds, and the inclined jet grouting piles, and accurately determines the optimal inclination angle of the piles through scientific modeling, experimentation, and analysis. This not only helps improve the stability and durability of heavy-haul railway transition sections, reducing maintenance costs and safety hazards, but also provides a more scientific and reliable basis for railway engineering design and construction.

[0006] This invention provides a method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics, comprising:

[0007] Based on the basic parameters of the transition section of heavy-haul railway, a multi-body coupled dynamic model including train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles is constructed.

[0008] Vibration acceleration data and vertical compression deformation data of a scaled model in the inclined jet grouting pile reinforcement room of the transition section of heavy-haul railway under different inclined jet grouting pile inclination angles were collected.

[0009] Based on the vibration acceleration data and vertical compression deformation data of the multibody coupled dynamics model and the scaled model under different inclined jet grouting pile inclination angles, the vibration response calculation error was calculated, and the multibody coupled dynamics model was adjusted based on the vibration response calculation error to obtain a fully validated multibody coupled dynamics model.

[0010] Based on the validated multibody coupled dynamics model, dynamic simulations were performed on multiple working conditions. Key dynamic response indicators of the transition section under each working condition were extracted, and the variation of key dynamic response indicators under each working condition with the inclination angle of the inclined jet grouting pile was analyzed.

[0011] Based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting pile under each working condition, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is fitted.

[0012] The target transition section type, corresponding train load level, and preset optimization target, determined according to actual engineering needs, are input into the inclined jet grouting pile inclination angle-vibration suppression rate-settlement correlation model to obtain the target inclination angle range. Based on the target inclination angle range, the optimal inclined jet grouting pile inclination angle is determined.

[0013] Preferred basic parameters include:

[0014] The transition section type, axle load of heavy-haul trains, train speed, elastic modulus of subgrade soil, pile material parameters of inclined jet grouting piles, and initial design inclination angle of inclined jet grouting piles.

[0015] Preferably, in the multi-body coupled dynamics model, wheel-rail contact units are set between the train wheelset and the rail to simulate wheel-rail interaction forces, elastic cushion layer units are set between the rail and the sleeper to simulate rail support, contact units are set between the sleeper and the roadbed to transfer loads, and inclined jet grouting pile units are embedded inside the roadbed and given preset pile material parameters and the initial design inclined jet grouting pile inclination angle.

[0016] Preferably, the scaled-down model includes the same subgrade structure, sleeper arrangement, and inclined jet grouting piles as the actual transition section;

[0017] Vibration acceleration sensors and settlement observation markers were installed on the roadbed surface, slope toe, and inclined jet grouting piles of the scaled model to simulate the static and dynamic loads of heavy-load trains.

[0018] Preferably, each working condition maintains consistent axle load of heavy-duty trains, train speed, subgrade soil parameters, and horizontal pile spacing of inclined jet grouting piles.

[0019] Preferred key dynamic response indicators include: roadbed dynamic displacement, vibration acceleration, vertical stress of inclined jet grouting piles, and cumulative settlement of the roadbed.

[0020] Preferably, a correlation model between the inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is fitted based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting pile under each working condition, including:

[0021] Based on the key dynamic response indicators under all working conditions, a dynamic response spatiotemporal matrix is ​​constructed. The row vectors of the dynamic response spatiotemporal matrix represent the inclination angle of the inclined jet grouting pile under different working conditions, and the column vectors represent the dynamic response data arranged according to the time series or spatial measurement point location.

[0022] Based on the dynamic response spatiotemporal matrix, the time-domain and frequency-domain characteristics of each working condition are calculated, and a dimension-reduced key dynamic response feature matrix is ​​constructed based on the time-domain and frequency-domain characteristics of each working condition.

[0023] Based on the variation of key dynamic response indicators with the inclination angle of inclined jet grouting piles under each working condition, the vibration suppression rate and normalized cumulative subgrade settlement under each working condition are determined.

[0024] Based on the vibration suppression rate and the normalized cumulative settlement of the subgrade under each working condition, an optimization target vector set is constructed, which includes the vibration suppression rate target vector and the normalized settlement target vector.

[0025] Based on the tilt angle optimization knowledge graph, the main control dynamic response index is selected from all key dynamic response indices.

[0026] Based on the inclination angle of the inclined jet grouting pile under all working conditions, all main control dynamic response indicators, and the optimized target vector set, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is constructed.

[0027] Preferably, based on the tilt angle optimization knowledge graph, the main control dynamic response indicators are selected from all key dynamic response indicators, including:

[0028] Using design parameters, dynamic response characteristics, and optimization objectives as nodes, the numerical values ​​and trends of corresponding nodes as node attributes, and the correlation strength between nodes as edges, and combining the edge weights calculated based on grey relational analysis or transfer entropy of key dynamic response feature matrices and optimization objective vector sets, a knowledge graph for tilt angle optimization is constructed.

[0029] In the knowledge graph of tilt angle optimization, the tilt angle of the inclined jet grouting pile is used as the starting node, and the vibration suppression rate and the cumulative settlement of the subgrade are used as the ending nodes respectively. Multi-path reasoning is carried out to select the top K influence paths with the highest correlation weight.

[0030] The key dynamic response indicators corresponding to the nodes in the top K influence paths with the highest correlation weights are taken as the main control dynamic response indicators.

[0031] Preferably, based on the inclination angle of the inclined jet grouting pile under all working conditions, all main control dynamic response indicators, and the optimized target vector set, a correlation model of inclination angle-vibration suppression rate-settlement of the inclined jet grouting pile is constructed, including:

[0032] A spatial matrix is ​​constructed based on all the main control dynamic response indices under each set of working conditions, and the corresponding orthogonal complementary spatial representation is calculated.

[0033] Based on the spatial matrix, a projection matrix is ​​constructed. Based on the projection matrix, the projection distance of each optimized target vector in the optimized target vector set in the subspace spanned by all main control dynamic response indices is calculated. Combined with the corresponding orthogonal complement space representation, the vertical distance of each optimized target vector in the optimized target vector set in the corresponding orthogonal complement space is calculated as the projection residual distance.

[0034] For similar optimization target elements in the optimization target vector set, the projected distances in the subspace spanned by all master dynamic response indices are weighted and corrected to obtain the estimated optimization target values;

[0035] A dual-output response surface model is established, with the inclination angle of the inclined jet grouting pile as input and the optimized target estimate and the projected residual distance as joint outputs.

[0036] Partial least squares regression was used to fit the parameters of the dual-output response surface model. The bias terms of the dual-output response surface model were calibrated by introducing the transition section type correction coefficient and the train load level correction coefficient, thus obtaining the correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement.

[0037] This invention provides a system for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics, comprising:

[0038] The dynamic model construction module is used to construct a multi-body coupled dynamic model, including train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles, based on the basic parameters of the transition section of heavy-haul railway.

[0039] The vibration deformation data acquisition module is used to collect vibration acceleration data and vertical compression deformation data of a scaled model in the inclined jet grouting pile reinforcement chamber of the transition section of heavy-haul railway under different inclined jet grouting pile inclination angles.

[0040] The dynamic model verification module is used to calculate the vibration response calculation error based on the vibration acceleration data and vertical compression deformation data of the multi-body coupled dynamic model and the scaled model under different inclined jet grouting pile inclination angles, and to adjust the multi-body coupled dynamic model based on the vibration response calculation error to obtain a verified multi-body coupled dynamic model.

[0041] The dynamic simulation analysis module is used to perform dynamic simulations on multiple working conditions based on the validated multibody coupled dynamic model, extract the key dynamic response indicators of the transition section under each working condition, and analyze the variation of the key dynamic response indicators under each working condition with the inclination angle of the inclined jet grouting pile.

[0042] The correlation model fitting module is used to fit the correlation model of inclination angle, vibration suppression rate and settlement of inclined jet grouting piles based on the law of the key dynamic response indexes changing with the inclination angle of the inclined jet grouting piles under each working condition.

[0043] The tilt angle optimization calculation module is used to input the target transition section type, corresponding train load level and preset optimization target determined according to actual engineering needs into the inclined jet grouting pile tilt angle-vibration suppression rate-settlement correlation model to obtain the target tilt angle range, and determine the optimal inclined jet grouting pile tilt angle based on the target tilt angle range.

[0044] The beneficial effects of this invention compared to existing technologies are as follows: It constructs a multi-body coupled dynamic model encompassing train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles, comprehensively covering all key elements of the transition section and providing a basic framework for subsequent analysis. Vibration acceleration and vertical compression deformation data of the inclined jet grouting pile reinforcement indoor scale model at different inclination angles are collected to obtain key data for actual working conditions. The multi-body coupled dynamic model is adjusted by calculating vibration response errors to ensure its accuracy and reliability. Based on the validated model, dynamic simulations are performed on multiple working conditions to analyze the variation of key dynamic response indicators with inclination angle, deeply exploring the impact of different inclination angles on the performance of the transition section. A correlation model of inclined jet grouting pile inclination angle, vibration suppression rate, and settlement is fitted to establish a quantitative relationship between inclination angle and key performance indicators. By inputting the target transition section type, train load level, and preset optimization target determined by actual engineering needs, the target inclination angle range is obtained and the optimal inclination angle is determined, providing a scientific and accurate inclination angle optimization scheme for actual engineering, effectively improving the stability and reliability of heavy-haul railway transition sections and reducing the impact of vibration and settlement.

[0045] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in this application.

[0046] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0047] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings:

[0048] Figure 1 This invention relates to a method and system for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics.

[0049] Figure 2 This is a flowchart illustrating the construction process of the association model in this embodiment of the invention;

[0050] Figure 3 This is a flowchart of the weighted correction and model fitting process in an embodiment of the present invention. Detailed Implementation

[0051] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0052] like Figure 1 As shown, this invention provides an implementation method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics, including:

[0053] Based on the basic parameters of the transition section of heavy-haul railway, a multi-body coupled dynamic model including train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles is constructed.

[0054] Vibration acceleration data and vertical compression deformation data of a scaled model in the inclined jet grouting pile reinforcement room of the transition section of heavy-haul railway under different inclined jet grouting pile inclination angles were collected.

[0055] Based on the vibration acceleration data and vertical compression deformation data of the multibody coupled dynamics model and the scaled model under different inclined jet grouting pile inclination angles, the vibration response calculation error was calculated, and the multibody coupled dynamics model was adjusted based on the vibration response calculation error to obtain a fully validated multibody coupled dynamics model.

[0056] Based on the validated multibody coupled dynamics model, dynamic simulations were performed on multiple working conditions. Key dynamic response indicators of the transition section under each working condition were extracted, and the variation of key dynamic response indicators under each working condition with the inclination angle of the inclined jet grouting pile was analyzed.

[0057] Based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting pile under each working condition, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is fitted.

[0058] The target transition section type, corresponding train load level, and preset optimization target, determined according to actual engineering needs, are input into the inclined jet grouting pile inclination angle-vibration suppression rate-settlement correlation model to obtain the target inclination angle range. Based on the target inclination angle range, the optimal inclined jet grouting pile inclination angle is determined.

[0059] In this embodiment, the heavy-haul railway transition section refers to the part where different structures connect in a heavy-haul railway line, such as the road-bridge transition section (the part where the railway connects to the bridge) and the road-culvert transition section (the part where the railway connects to the culvert). Due to structural differences, this part of the area is prone to uneven settlement and other problems when trains are running, so it requires special treatment.

[0060] In this embodiment, the train wheelset is the part of the train that directly contacts the rail, responsible for bearing the weight of the train and transmitting power; the rail is the track on which the train travels, guiding the direction of the train's movement and bearing the train's load; the sleeper serves to support the rail, fix the position of the rail, and distribute the train load to the roadbed; the roadbed, as the foundation of the railway line, bears the load transmitted from the sleeper; and the inclined jet grouting pile is a pile structure used to reinforce the roadbed, which is set inside the roadbed at a certain inclination angle to enhance the stability of the roadbed.

[0061] In this embodiment, the multi-body coupled dynamics model is constructed based on the fundamental parameters of the transition section of a heavy-haul railway, and includes multiple components such as train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles. The model simulates the interaction between these components by setting different units. For example, wheel-rail contact units are set between the train wheelsets and rails to simulate wheel-rail forces, elastic cushion layer units are set between the rails and sleepers to simulate rail support, and contact units are set between the sleepers and roadbed to transfer loads, thereby analyzing the dynamic response of the transition section during train operation.

[0062] In this embodiment, the scaled-down model of the inclined jet grouting pile reinforcement room in the heavy-haul railway transition section is an indoor model built at a certain scale (e.g., 1:10). It reproduces the actual roadbed structure, sleeper arrangement, and inclined jet grouting pile installation of the transition section. The model uses scaled-down soil with the same physical and mechanical properties as the actual roadbed soil to fill the roadbed, prefabricates scaled-down piles with material properties matching the actual inclined jet grouting piles, and embeds them according to the actual initial design inclination angle of the inclined jet grouting piles. This is used to simulate the situation of the heavy-haul railway transition section under train load and to collect relevant data.

[0063] In this embodiment, the inclination angle of the inclined jet grouting pile refers to the angle between the inclined jet grouting pile and the vertical direction. Different design angles exist in actual engineering projects, such as 15°, 30°, and 45°. Different inclination angles have different effects on the reinforcement effect of the roadbed and the dynamic response of the transition section, making them an important parameter studied in this optimization method.

[0064] In this embodiment, the vibration acceleration data is collected by deploying vibration acceleration sensors at locations such as the roadbed surface, slope toe, and inclined jet grouting piles of the scaled-down model. It reflects the severity of vibration at these locations under simulated static and dynamic loads from a heavy-load train and is one of the important indicators for evaluating the stability and safety of the transition section.

[0065] In this embodiment, the vertical compression deformation data is obtained using settlement observation markers placed at locations such as the roadbed surface on the scaled-down model. It reflects the amount of compression deformation of the roadbed in the vertical direction under train loads, which is of great significance for studying roadbed settlement and evaluating the reinforcement effect of inclined jet grouting piles.

[0066] In this embodiment, the vibration acceleration data and vertical compression deformation data of the grouting piles at different inclination angles are used to calculate the vibration response calculation error based on the multi-body coupled dynamics model and the scaled model. This involves comparing the vibration acceleration and vertical compression deformation data obtained from the multi-body coupled dynamics model simulation with the corresponding data collected from the scaled model experiment. According to… The formula is used to calculate the error between the model simulation data and the experimental data, thereby evaluating the accuracy of the model.

[0067] In this embodiment, adjusting the multibody coupled dynamics model based on the vibration response calculation error to obtain a validated multibody coupled dynamics model means that when the calculated vibration response error is greater than 6%, parameters such as wheel-rail contact stiffness (fine-tuned by ±5%) and subgrade soil elastic modulus (fine-tuned by ±10%) in the multibody coupled dynamics model are adjusted. After adjustment, simulation is performed again and the error is calculated. This process is repeated until the error is ≤6%. At this point, the model can more accurately reflect the dynamic response characteristics of the transition section, which is the validated multibody coupled dynamics model.

[0068] In this embodiment, dynamic simulations of multiple working conditions are performed based on a validated multi-body coupled dynamics model. Key dynamic response indicators of the transition section under each working condition are extracted. This involves using the validated model to set multiple working conditions for different inclined jet grouting pile inclination angles (e.g., 15°, 30°, and 45° inclination angles), ensuring that the axle load of the heavy-load train, train speed, subgrade soil parameters, and horizontal pile spacing of the inclined jet grouting piles remain consistent across all working conditions. During the simulation, the train is set to pass through the transition section at a preset constant speed, and the calculation time step is set to 10. -4 The simulation duration is set to 1.5 times the time required for the train to completely pass through the transition section. Key dynamic response indicators of the transition section under each working condition are extracted in real time, such as roadbed dynamic displacement, vibration acceleration, vertical stress of inclined jet grouting piles, and cumulative settlement of the roadbed.

[0069] In this embodiment, the key dynamic response indicators under each working condition are analyzed in relation to the inclination angle of the inclined jet grouting piles. This involves a comparative analysis of the extracted key dynamic response indicators under different working conditions. For example, the numerical changes of indicators such as subgrade dynamic displacement, vibration acceleration, vertical stress of the inclined jet grouting pile body, and cumulative subgrade settlement are observed at different inclination angles of the inclined jet grouting piles (e.g., 15°, 30°, 45°). This reveals patterns such as a 28% increase in vibration acceleration attenuation rate at an inclination angle of 30° compared to 15° and a 15% increase compared to 45°, providing a basis for the subsequent construction of a correlation model.

[0070] In this embodiment, a correlation model of inclined jet grouting pile inclination angle, vibration suppression rate, and settlement is fitted based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting pile under each working condition. First, a spatiotemporal matrix of dynamic response is constructed, time-domain and frequency-domain features are calculated, and a dimension-reduced key dynamic response feature matrix is ​​constructed. The vibration suppression rate and normalized cumulative subgrade settlement under each working condition are determined, and an optimization target vector set is constructed. Then, the main controlling dynamic response indicators are selected based on the inclination angle optimization knowledge graph. Finally, by constructing a spatial matrix, calculating the projection distance and vertical distance, weighted correcting the projection distance, establishing a dual-output response surface model, and using partial least squares regression to fit the parameters, a transition section type correction coefficient and a train load level correction coefficient are introduced to calibrate the bias term, resulting in the correlation model of inclined jet grouting pile inclination angle, vibration suppression rate, and settlement.

[0071] In this embodiment, the target transition section type and corresponding train load level determined according to actual engineering needs refer to the determination of whether it is a road-bridge transition section or a road-culvert transition section based on the specific line conditions in actual heavy-haul railway construction or maintenance projects. At the same time, the train load level (such as axle load of 27t, 30t, 35t, etc.) is determined according to the train design requirements. These parameters will affect the optimization results of the inclined jet grouting pile inclination angle.

[0072] In this embodiment, the preset optimization target is a set of target conditions to determine the optimal inclination angle of the inclined jet grouting piles. For example, the vibration suppression rate is set to be ≥20%, and the cumulative settlement of the roadbed is ≤10mm. By meeting these target conditions, the transition section achieves better stability and safety during train operation.

[0073] In this embodiment, when new engineering requirements arise, the user determines the target transition section type and selects the corresponding transition section type correction coefficient, as well as the target train load level and selects the corresponding train load level correction coefficient. These values, along with preset optimization targets (such as "vibration suppression rate > 85%, settlement < 10mm"), are input into the established correlation model. Based on the transition section type correction coefficient and the train load level correction coefficient, the model calculates the curves of vibration suppression rate and settlement as a function of tilt angle under the new conditions, thereby identifying the target tilt angle range that simultaneously meets the preset optimization targets, and ultimately determining the optimal tilt angle.

[0074] In this embodiment, the optimal inclined jet grouting pile inclination angle is determined based on the target inclination angle range. This means determining the final optimal inclined jet grouting pile inclination angle within the obtained target inclination angle range. If the target inclination angle range is a continuous interval, the midpoint of the interval is usually taken as the optimal inclination angle; if it is a discrete interval, the inclination angle with the maximum vibration suppression rate and the minimum settlement is taken. For example, in a road-culvert transition section with a train axle load of 30t, if the output target inclination angle range is 25°-30°, then 27.5° is taken as the optimal inclination angle; if it is a road-bridge transition section with a train axle load of 35t, after adjusting the target inclination angle range according to the model calculation results, the inclination angle that reduces the cumulative settlement of the transition section by more than 30% is taken as the optimal inclination angle.

[0075] To clarify the fundamental parameters required for constructing a multibody coupled dynamics model, covering transition section type, train-related parameters, subgrade soil and inclined jet grouting pile parameters, etc., and to provide a comprehensive and accurate basis for model construction, the following fundamental parameters are proposed:

[0076] The transition section type, axle load of heavy-haul trains, train speed, elastic modulus of subgrade soil, pile material parameters of inclined jet grouting piles, and initial design inclination angle of inclined jet grouting piles.

[0077] In this embodiment, the transition section type refers to the category of different structural connections in heavy-haul railways, divided into road-bridge transition sections (the connection between railway and bridge) and road-culvert transition sections (the connection between railway and culvert). Different types of transition sections have different impacts on railway operation due to differences in structural characteristics, which is an important factor that needs to be considered in the optimization method.

[0078] The axle load of a heavy-haul train refers to the weight borne by each axle of the train, ranging from 27 to 35 tons. The axle load directly affects the load that railway infrastructure can withstand. The greater the axle load, the greater the pressure on the roadbed, track, and other structures. When studying the optimization of the inclination angle of inclined jet grouting piles, the effect of axle load on the mechanical response of the transition section must be considered.

[0079] Train speed refers to the speed at which a heavy-haul train travels on a railway, ranging from 60 to 120 km / h. Changes in speed alter the dynamic action of the train on the track and roadbed, such as generating varying degrees of vibration and impact, which in turn affects the stability of the transition section. Therefore, it is a key parameter to consider during the optimization process.

[0080] The elastic modulus of subgrade soil reflects the ease with which it undergoes elastic deformation under stress. Its value range is determined based on actual geological survey data of the transition section, generally between 20-50 MPa. It embodies the mechanical properties of the subgrade soil; different elastic moduli result in different deformations and stress distributions of the subgrade under train loads, significantly impacting the reinforcement effect of inclined jet grouting piles and the overall performance of the transition section.

[0081] The material parameters of inclined jet grouting piles include elastic modulus (30-35 GPa) and Poisson's ratio (0.2-0.25). The elastic modulus determines the pile's ability to resist deformation, while Poisson's ratio reflects the relationship between the pile's lateral and longitudinal deformation. These parameters affect the reinforcement effect and stress characteristics of inclined jet grouting piles in roadbeds.

[0082] The initial design inclination angle of the inclined jet grouting pile refers to the angle between the inclined jet grouting pile and the vertical direction set during the initial design. Generally, 15°, 30°, and 45° are selected. These angles cover the commonly used inclination angle range of inclined jet grouting piles in existing projects. Different inclination angles have different effects on subgrade reinforcement and dynamic response of transition sections, and are the key variables studied in this optimization method.

[0083] To clearly define the connection units and parameter settings between the various parts in the multi-body coupled dynamics model, accurately simulate the interaction between components such as wheel-rail, sleeper, and roadbed, and make the model more in line with actual conditions, it is proposed that wheel-rail contact units be set between the train wheelset and the rail to simulate wheel-rail forces, elastic cushion layer units be set between the rail and the sleeper to simulate rail support, contact units be set between the sleeper and the roadbed to transfer loads, and inclined jet grouting pile units be embedded inside the roadbed and given preset pile material parameters and initial design inclined jet grouting pile inclination angle.

[0084] In this embodiment, the multibody coupled dynamics model employs different element configurations to accurately simulate the interactions between components in the transition section of a heavy-haul railway. Wheel-rail contact elements are installed between the train wheelsets and the rails to simulate the forces generated during train operation, such as friction and vertical forces. This is crucial for studying train stability and track stress conditions. For example, different forces of varying directions and magnitudes are generated between the wheels and rails during train acceleration, deceleration, or turning; the wheel-rail contact elements effectively simulate these situations.

[0085] An elastic padding unit is installed between the rail and the sleeper to simulate rail support. In reality, elastic materials are laid under the rail to buffer vibrations and distribute loads; the elastic padding unit mimics this characteristic. By setting appropriate parameters, the supporting effect of the elastic padding on the rail can be demonstrated, such as absorbing some of the vibration energy from train travel and reducing the impact on the sleepers and roadbed.

[0086] Contact units are installed between the sleepers and the roadbed to transfer loads. The train transfers the load to the sleepers via the rails, and the sleepers then transfer these loads to the roadbed through the contact units. These contact units simulate the mechanical transfer characteristics of the contact area between the sleeper and the roadbed, allowing the model to accurately reflect the load transfer process between these two components, such as the uniformity and magnitude variation of load transfer when sleepers of different materials and shapes contact the roadbed.

[0087] Inclined jet grouting pile units are embedded within the roadbed, and preset pile material parameters (such as elastic modulus 30-35 GPa, Poisson's ratio 0.2-0.25) and initial design inclination angles (such as 15°, 30°, 45°) are assigned. This is done to demonstrate the reinforcing effect of inclined jet grouting piles on the roadbed in the model. The pile material parameters determine the mechanical properties of the pile itself, while the inclination angle affects its reinforcing effect on the roadbed and the direction of force transmission. For example, inclined jet grouting piles with different inclination angles have different effects on the lateral and vertical stability of the roadbed. Through these settings, the model can analyze the reinforcing effectiveness of inclined jet grouting piles on the roadbed under different conditions.

[0088] In order to make the scaled model realistically simulate the actual transition section, the same structure, layout and piles are set up, and sensors are deployed to simulate train loads to obtain accurate vibration acceleration and vertical compression deformation data. It is proposed that the scaled model includes the same roadbed structure, sleeper layout and inclined jet grouting piles as the actual transition section.

[0089] Vibration acceleration sensors and settlement observation markers were installed on the roadbed surface, slope toe, and inclined jet grouting piles of the scaled model to simulate the static and dynamic loads of heavy-load trains.

[0090] In this embodiment, the scaled-down model is constructed at a certain scale (e.g., 1:10), and its subgrade structure, sleeper arrangement, and inclined jet grouting piles are consistent with the actual transition section. This means that the scaled-down model realistically reproduces the actual heavy-haul railway transition section in terms of structural layout. For example, the subgrade cross-sectional dimensions (subgrade surface width, 1:1.5 slope) and sleeper spacing (600mm) correspond proportionally to the actual situation, and the number, location, and initial design inclination angle of the inclined jet grouting piles are also the same as the actual ones. Through this reproduction, the condition of the actual transition section under train load can be simulated in an indoor environment, providing a reliable physical model foundation for research.

[0091] In this embodiment, vibration acceleration sensors and settlement monitoring markers are installed on the roadbed surface, slope toe, and inclined jet grouting piles of the scaled model, simulating the static and dynamic loads of a heavy-load train. Sensors are placed at these key locations to accurately collect relevant data. The vibration acceleration sensors measure the vibration acceleration of various parts of the scaled model under simulated loads, reflecting the vibration caused by the train load, such as the intensity of vibration on the roadbed surface, slope toe, and inclined jet grouting piles when a train passes. The settlement monitoring markers are used to monitor vertical compression deformation data, i.e., the settlement of the scaled model under load, such as the settlement at 2m intervals on the roadbed surface and at the junction of the transition section and the structure. By simulating the static and dynamic loads of heavy-haul trains, the static load is simulated by applying a uniformly distributed load to the rail of a scaled-down model, while the dynamic load is simulated by applying a sinusoidal excitation force to the rail end using a vibrator. The excitation frequency is determined by converting the train speed and the wheel-rail contact frequency, and the excitation force amplitude is determined by scaling down the actual wheel-rail action force. This simulates the effect of the train on the transition section under actual working conditions, thereby obtaining the data required for the study and providing a basis for analyzing the reinforcement effect of the inclined jet grouting piles on the transition section and the dynamic response of the transition section.

[0092] To ensure the comparability and effectiveness of each working condition, the dynamic simulation analysis is made more scientific by maintaining consistency in the axle load of the heavy-load train, the train speed, the subgrade soil parameters, and the horizontal pile spacing of the inclined jet grouting piles.

[0093] In this embodiment, the axle load of the heavy-load train, the train speed, the subgrade soil parameters, and the horizontal pile spacing of the inclined jet grouting piles were kept constant for each working condition. This was done to follow the single variable principle when studying the influence of the inclined jet grouting pile inclination angle on the dynamic response of the transition section. Only by keeping other factors constant can the influence of the inclined jet grouting pile inclination angle on the dynamic response of the transition section be accurately analyzed.

[0094] For example, a change in the axle load of a heavy-haul train directly affects the load on the entire system, thus influencing the dynamic response of the transition section. If the axle load also changes when studying the effect of the tilt angle, it becomes impossible to determine whether the change in axle load or the tilt angle causes the change in dynamic response. Similarly, different train speeds result in different impact forces and vibration frequencies on the track and subgrade; subgrade soil parameters (such as elastic modulus) affect the mechanical properties of the subgrade; and the horizontal spacing of the inclined jet grouting piles affects the reinforcement distribution effect of the piles on the subgrade. Only by keeping these factors consistent in each set of working conditions can we examine how the key dynamic response indicators of the transition section (such as subgrade dynamic displacement, vibration acceleration, vertical stress of the inclined jet grouting pile, and cumulative subgrade settlement) change when the tilt angle of the inclined jet grouting piles changes, thereby accurately determining the relationship between the tilt angle of the inclined jet grouting piles and the dynamic response of the transition section.

[0095] To determine key dynamic response indicators that can effectively reflect the performance of the transition section, including subgrade dynamic displacement and vibration acceleration, and to provide a quantitative basis for subsequent analysis of the influence of the inclination angle of the inclined jet grouting pile on the performance of the transition section, key dynamic response indicators are proposed, including: subgrade dynamic displacement, vibration acceleration, vertical stress of the inclined jet grouting pile body, and cumulative subgrade settlement.

[0096] In this embodiment, the subgrade dynamic displacement, vibration acceleration, vertical stress of the inclined jet grouting pile, and cumulative subgrade settlement are key dynamic response indicators for evaluating the performance of the transition section of a heavy-haul railway.

[0097] Roadbed dynamic displacement refers to the movement and changes of the roadbed under train load, and is divided into vertical displacement and horizontal displacement. Vertical displacement reflects the settlement or heave of the roadbed in the vertical direction. Excessive vertical displacement may lead to uneven track, affecting the stability and safety of train operation. Horizontal displacement reflects the deformation of the roadbed in the horizontal direction, which may cause lateral deformation of the track and threaten the safety of train operation. For example, when a train passes, the roadbed may experience local vertical or horizontal displacement due to uneven stress.

[0098] Vibration acceleration indicates the severity of roadbed vibration under train loads, including vertical and horizontal acceleration. Peak vibration acceleration is used to calculate the vibration suppression rate and evaluate the vibration suppression effect of inclined jet grouting piles; the root mean square value can measure the vibration comfort of the transition section. Excessive vibration acceleration can affect the lifespan of train components, passenger comfort, and may also cause vibration disturbance to the surrounding environment. For example, when a train passes at high speed, it will cause relatively strong vibration of the roadbed, and the vibration situation can be understood by measuring vibration acceleration.

[0099] The vertical stress in an inclined jet grouting pile refers to the force borne by the pile in the vertical direction. It is necessary to monitor the stress at three sections: the pile top, the midpoint of the pile, and the pile bottom. By analyzing the stress at these locations, we can understand the stress transmission pattern within the pile and assess the bearing capacity and reinforcement effect of the inclined jet grouting pile. For example, excessive stress at the pile top may indicate stress concentration at the top of the pile, requiring optimization of the pile design or construction process.

[0100] Subgrade cumulative settlement is the sum of the vertical displacement of the subgrade at each time step throughout the simulation period, directly reflecting the long-term settlement risk of the transition section. Excessive subgrade cumulative settlement over a long period can cause changes in track elevation, increase track maintenance costs, and even affect train operation safety. For example, as trains continue to pass through, subgrade cumulative settlement may gradually increase, requiring monitoring of its changing trend and corresponding measures.

[0101] like Figure 2As shown, in order to construct the dynamic response spatiotemporal matrix, reduce dimensions, and determine the vibration suppression rate and settlement, a correlation model of inclination angle, vibration suppression rate, and settlement of inclined jet grouting piles is fitted based on the variation law of key dynamic response indicators with inclination angle, establishing a quantitative relationship among the three. A correlation model of inclination angle, vibration suppression rate, and settlement of inclined jet grouting piles is proposed based on the variation law of key dynamic response indicators with the inclination angle of inclined jet grouting piles under each working condition, including:

[0102] Based on the key dynamic response indicators under all working conditions, a dynamic response spatiotemporal matrix is ​​constructed. The row vectors of the dynamic response spatiotemporal matrix represent the inclination angle of the inclined jet grouting pile under different working conditions, and the column vectors represent the dynamic response data arranged according to the time series or spatial measurement point location.

[0103] Based on the dynamic response spatiotemporal matrix, the time-domain and frequency-domain characteristics of each working condition are calculated, and a dimension-reduced key dynamic response feature matrix is ​​constructed based on the time-domain and frequency-domain characteristics of each working condition.

[0104] Based on the variation of key dynamic response indicators with the inclination angle of inclined jet grouting piles under each working condition, the vibration suppression rate and normalized cumulative subgrade settlement under each working condition are determined.

[0105] Based on the vibration suppression rate and the normalized cumulative settlement of the subgrade under each working condition, an optimization target vector set is constructed, which includes the vibration suppression rate target vector and the normalized settlement target vector.

[0106] Based on the tilt angle optimization knowledge graph, the main control dynamic response index is selected from all key dynamic response indices.

[0107] Based on the inclination angle of the inclined jet grouting pile under all working conditions, all main control dynamic response indicators, and the optimized target vector set, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is constructed.

[0108] In this embodiment, a spatiotemporal matrix of dynamic response is constructed based on key dynamic response indicators under all working conditions. This involves arranging key dynamic response indicators such as subgrade dynamic displacement, vibration acceleration, vertical stress of inclined jet grouting piles, and cumulative subgrade settlement in a matrix format according to a specific order, using different working conditions as dimensions. The row vectors of the matrix represent different working conditions, while the column vectors arrange the dynamic response data according to a specific order, such as time series or spatial measurement point locations, thereby comprehensively recording and presenting the changes in the dynamic response of the transition section over time or space under each working condition.

[0109] In this embodiment, the inclination angle of the inclined jet grouting piles under different working conditions refers to the angle values ​​between the inclined jet grouting piles and the vertical direction set during the research process, such as the common 15°, 30°, and 45°. By setting different inclination angle working conditions, the variation law of key dynamic response indicators with these angles is observed and analyzed, thereby studying the impact of the inclination angle of the inclined jet grouting piles on the performance of the transition section of heavy-haul railway.

[0110] In this embodiment, the dynamic response data arranged by time series or spatial measurement point location refers to organizing and arranging the collected key dynamic response index data according to the chronological order (time series) or the spatial order of different measurement points on structures such as the roadbed and inclined jet grouting piles (spatial measurement point location). For example, arranging it by time series can reflect the dynamic changes of each index over time during the train's passage; arranging it by spatial measurement point location can reflect the differences in dynamic response at different locations.

[0111] In this embodiment, based on the dynamic response spatiotemporal matrix, the time-domain and frequency-domain characteristics of each working condition are calculated, and a dimensionality-reduced key dynamic response feature matrix is ​​constructed based on these characteristics. Specifically, the time-domain features reflect the changing characteristics of dynamic response indicators over time, such as mean, variance, and peak value; the frequency-domain features show the distribution of data across different frequency components, which can be obtained through methods such as Fourier transform. After calculating these features, to simplify the data while retaining key information, a dimensionality reduction method (such as principal component analysis) is used to remove redundant information, converting the high-dimensional time-domain and frequency-domain feature data into a low-dimensional key dynamic response feature matrix, facilitating subsequent analysis and processing.

[0112] In this embodiment, based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting piles under each working condition, the vibration suppression rate and the normalized cumulative subgrade settlement under each working condition are determined. The vibration suppression rate is calculated by comparing the changes in vibration acceleration at different inclination angles, such as… The cumulative settlement of the roadbed is the sum of the vertical displacement of the roadbed under the train load in each working condition. Since the cumulative settlement of the roadbed under different working conditions may vary greatly, it is normalized to a specific interval (such as [0,1]) for easy comparison and analysis.

[0113] In this embodiment, constructing the optimization target vector set refers to creating a structured dataset to systematically characterize the comprehensive performance of all test conditions. Specifically, the system first calculates two core performance indicators for all tested inclination conditions: vibration suppression rate (evaluating vibration reduction effect) and normalized cumulative subgrade settlement (evaluating long-term stability). Then, the system organizes these data into two specialized mathematical vectors: one called the vibration suppression rate target vector, which lists the vibration suppression rate values ​​for all conditions in sequence; the other called the normalized settlement target vector, which lists the normalized settlement values ​​for all conditions in the same order. The combination of these two vectors constitutes the optimization target vector set.

[0114] In this embodiment, the vibration suppression rate target vector is the part of the optimization target vector set that specifically reflects the vibration suppression effect. It consists of the vibration suppression rate calculated under each working condition. This vector reflects the degree of vibration suppression under different inclined jet grouting pile inclination angles and can be used to analyze the relationship between the vibration suppression effect and the inclined jet grouting pile inclination angle.

[0115] In this embodiment, the normalized settlement target vector is the part of the optimization target vector that characterizes the cumulative settlement of the subgrade, and it consists of the normalized cumulative settlement of the subgrade under each working condition. It is used to study the correlation between subgrade settlement and the inclination angle of the inclined jet grouting pile. During the optimization process, it is combined with the vibration suppression rate target vector to jointly determine the optimal inclination angle of the inclined jet grouting pile.

[0116] In this embodiment, the tilt angle optimization knowledge graph is constructed using design parameters (such as the tilt angle of inclined jet grouting piles), dynamic response characteristics (such as subgrade dynamic displacement, vibration acceleration, etc.), and optimization objectives (vibration suppression rate, settlement) as nodes. Node attributes include their numerical values, physical units, and trends. Edges in the graph represent causal or strong correlations between nodes, and edge weights are obtained through grey relational analysis or transfer entropy calculation of the key dynamic response feature matrix and the optimization objective vector set. This knowledge graph visually displays the relationships between various factors, aiding in the selection of factors that play a crucial role in vibration suppression and settlement control.

[0117] In this embodiment, the dominant dynamic response index is obtained through analysis of the tilt angle optimization knowledge graph. Starting with the tilt angle of the inclined jet grouting pile as the starting node, and using vibration suppression rate and cumulative subgrade settlement as the ending nodes, multi-path reasoning is performed to select the top K influencing paths with the highest correlation weights. The key dynamic response indices corresponding to the dynamic response characteristic nodes traversed by these paths are the dominant dynamic response indices. They play a leading role in vibration suppression and settlement control and are key factors in constructing the correlation model of inclined jet grouting pile tilt angle-vibration suppression rate-settlement.

[0118] In this embodiment, the inclined jet grouting pile inclination angle-vibration suppression rate-settlement correlation model is constructed based on the relationship between the inclined jet grouting pile inclination angle, the main control dynamic response index, the vibration suppression rate, and the cumulative settlement of the roadbed under each working condition. By integrating path weights and projection residuals, a model is established with the inclined jet grouting pile inclination angle as input and the vibration suppression rate and settlement as outputs. Partial least squares regression is used to fit the model parameters, and a calibration bias term is introduced with transition section type and train load level correction coefficients to accurately describe the influence of the inclined jet grouting pile inclination angle on the vibration suppression rate and settlement, thereby determining the optimal inclined jet grouting pile inclination angle to meet actual engineering requirements.

[0119] like Figure 2 As shown, in order to construct a knowledge graph for tilt angle optimization, multi-path reasoning is performed starting with the tilt angle of the inclined jet grouting pile and ending with the vibration suppression rate and settlement. The key dynamic response indicators corresponding to the path with the highest association weight are selected as the main controlling dynamic response indicators to determine key factors for constructing the association model. Based on the tilt angle optimization knowledge graph, the main controlling dynamic response indicators are selected from all key dynamic response indicators, including:

[0120] Using design parameters, dynamic response characteristics, and optimization objectives as nodes, the numerical values ​​and trends of corresponding nodes as node attributes, and the correlation strength between nodes as edges, and combining the edge weights calculated based on grey relational analysis or transfer entropy of key dynamic response feature matrices and optimization objective vector sets, a knowledge graph for tilt angle optimization is constructed.

[0121] In the knowledge graph of tilt angle optimization, the tilt angle of the inclined jet grouting pile is used as the starting node, and the vibration suppression rate and the cumulative settlement of the subgrade are used as the ending nodes respectively. Multi-path reasoning is carried out to select the top K influence paths with the highest correlation weight.

[0122] The key dynamic response indicators corresponding to the nodes in the top K influence paths with the highest correlation weights are taken as the main control dynamic response indicators.

[0123] In this embodiment, the design parameters refer to the parameters that are set and adjustable by humans during the optimization of the inclination angle of the inclined jet grouting piles in the transition section of the heavy-haul railway. The main parameter is the inclination angle of the inclined jet grouting piles, and it may also include the pile material parameters (such as elastic modulus and Poisson's ratio), horizontal pile spacing, etc. The setting of these parameters will affect the performance of the entire system and are the control variables in the optimization study.

[0124] In this embodiment, dynamic response characteristics refer to the dynamic properties exhibited by various parts of the transition section of a heavy-haul railway (such as the roadbed and inclined jet grouting piles) under train load. Specifically, these are reflected in key dynamic response indicators such as roadbed dynamic displacement (including vertical and horizontal displacement), vibration acceleration (vertical and horizontal acceleration), and vertical stress of the inclined jet grouting piles (stress at the pile top, pile body, and pile bottom). These characteristics reflect the actual mechanical response of the transition section during train operation and are important bases for evaluating the performance of the transition section.

[0125] In this embodiment, the optimization objective is the desired outcome during the optimization of the inclined jet grouting pile inclination angle, primarily including maximizing vibration suppression rate and minimizing cumulative subgrade settlement. By adjusting the inclined jet grouting pile inclination angle and related design parameters, vibration of the transition section during train operation is effectively suppressed, while controlling cumulative subgrade settlement within a reasonable range to ensure the safe and stable operation of the railway.

[0126] In this embodiment, the values ​​and trends of the corresponding nodes are represented in the tilt angle optimization knowledge graph. Each node (such as a node representing design parameters, dynamic response characteristics, or optimization objectives) has a specific value, such as the specific degree of the tilt angle of the inclined jet grouting pile, the specific percentage value of the vibration suppression rate, and the specific displacement value of the roadbed dynamic displacement. The trend describes the direction of these values ​​as a function of certain factors (such as changes in the tilt angle of the inclined jet grouting pile, changes in train load, etc.). For example, as the tilt angle of the inclined jet grouting pile increases, does the vibration suppression rate increase or decrease, and does the cumulative settlement of the roadbed increase or decrease?

[0127] In this embodiment, the correlation strength between nodes represents the degree of interconnection between nodes in the tilt angle optimization knowledge graph. For example, the degree of influence of changes in design parameters (such as the tilt angle of inclined jet grouting piles) on dynamic response characteristics (such as vibration acceleration), or the magnitude of the effect of changes in dynamic response characteristics on optimization objectives (such as vibration suppression rate). This correlation strength reflects the interaction between different factors and helps to understand the operating mechanism of the entire system.

[0128] In this embodiment, the edge weights calculated based on grey relational analysis or transfer entropy of the key dynamic response feature matrix and the optimization target vector set are numerical values ​​that quantify the strength of the association between nodes. Grey relational analysis calculates the association degree by measuring the similarity of different data sequences in terms of geometric shape and development trend, while transfer entropy quantifies, from an information theory perspective, the extent to which the uncertainty of one node's state can be explained by the historical information of another node. Through these two methods, the complex physical influence relationships between nodes are transformed into specific, comparable numerical weights, thus objectively reflecting the tightness of the interaction in the causal chain from design parameters to dynamic response and finally to the optimization target. Higher weights indicate a stronger association between the two nodes and a more significant mutual influence during the optimization process.

[0129] In this embodiment, the vibration suppression rate is an indicator that measures the vibration suppression effect of the inclined jet grouting pile on the transition section. It is calculated by comparing the changes in vibration acceleration under different inclination angles of the inclined jet grouting piles. The formula is as follows:

[0130] ".

[0131] It reflects the degree of attenuation of vibration acceleration in the transition section as the inclination angle of the inclined jet grouting pile changes. The higher the vibration suppression rate, the better the vibration suppression effect of the inclined jet grouting pile.

[0132] In this embodiment, the cumulative settlement of the roadbed refers to the cumulative displacement of the roadbed in the vertical direction under continuous train load. It is an important indicator for assessing the long-term stability of the roadbed. Excessive cumulative settlement may lead to track deformation and affect the safe operation of trains. In this study, this value is obtained by summing the vertical displacement of the roadbed at each time step under each working condition, and may be normalized or otherwise processed according to actual needs to better analyze and compare the settlement under different working conditions.

[0133] In this embodiment, in the tilt angle optimization knowledge graph, the tilt angle of the inclined jet grouting pile is used as the starting node, and vibration suppression rate and cumulative subgrade settlement are used as the ending nodes, respectively. Multi-path reasoning is performed to select the top K influencing paths with the highest association weights. Since the nodes in the knowledge graph are interconnected, there may be multiple paths from the tilt angle of the inclined jet grouting pile to the vibration suppression rate or the cumulative subgrade settlement, and each path has a weighted edge. Multi-path reasoning involves analyzing all possible paths to find the top K paths with the highest sum of association weights in the two relationships: from the tilt angle of the inclined jet grouting pile to the vibration suppression rate, and from the tilt angle of the inclined jet grouting pile to the cumulative subgrade settlement. These paths demonstrate the factors and their effects that have the most significant impact on vibration suppression and cumulative subgrade settlement, helping to determine the main controlling dynamic response indicators and thus optimize the tilt angle of the inclined jet grouting pile.

[0134] like Figure 3As shown, in order to establish and calibrate a dual-output response surface model with the inclined jet grouting pile inclination angle as input and the optimized target estimate and projection residual distance as outputs through steps such as constructing a spatial matrix, calculating projection and residual distance, and weighted correcting the projection distance, a precise correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement is obtained. Based on the inclined jet grouting pile inclination angle under all working conditions, all main control dynamic response indices, and the optimized target vector set, a correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement is constructed, including:

[0135] A spatial matrix is ​​constructed based on all the main control dynamic response indices under each set of working conditions, and the corresponding orthogonal complementary spatial representation is calculated.

[0136] Based on the spatial matrix, a projection matrix is ​​constructed. Based on the projection matrix, the projection distance of each optimized target vector in the optimized target vector set in the subspace spanned by all main control dynamic response indices is calculated. Combined with the corresponding orthogonal complement space representation, the vertical distance of each optimized target vector in the optimized target vector set in the corresponding orthogonal complement space is calculated as the projection residual distance.

[0137] For similar optimization target elements in the optimization target vector set, the projected distances in the subspace spanned by all master dynamic response indices are weighted and corrected to obtain the estimated optimization target values;

[0138] A dual-output response surface model is established, with the inclination angle of the inclined jet grouting pile as input and the optimized target estimate and the projected residual distance as joint outputs.

[0139] Partial least squares regression was used to fit the parameters of the dual-output response surface model. The bias terms of the dual-output response surface model were calibrated by introducing the transition section type correction coefficient and the train load level correction coefficient, thus obtaining the correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement.

[0140] In this embodiment, a spatial matrix is ​​constructed based on all the main control dynamic response indices under each working condition, and the corresponding orthogonal complementary spatial representation is calculated. After determining the main control dynamic response indices for each working condition, these indices are used as vectors to construct a matrix, which is called the spatial matrix. For example, if the main control dynamic response indices are roadbed dynamic displacement, vibration acceleration, and vertical stress of inclined jet grouting piles, and there are n working conditions, then each column of the spatial matrix corresponds to an index, and each row corresponds to the data of a working condition. Subsequently, the system calculates the "orthogonal complementary spatial representation" of the spatial matrix through linear algebraic operations (such as singular value decomposition). The orthogonal complementary spatial representation refers to finding another space orthogonal (perpendicular) to the space spanned by this spatial matrix. Calculating the orthogonal complementary spatial representation helps to analyze data from different perspectives and understand the relationship between the optimization target vector and the main control dynamic response index space. For example, it can be known which parts of the optimization target cannot be fully explained by the main control dynamic response indices.

[0141] For example, define a subspace spanned by the main control parameters in the operating condition space. This subspace is spanned by two vectors:

[0142] Vector A (subgrade dynamic displacement): ;

[0143] Vector B (vertical stress in the pile): .

[0144] Let the space matrix be... The column consists of these two vectors: ;

[0145] The projection matrix P is: This is a 4x4 matrix used to project any vector in 4-dimensional space onto a 2-dimensional subspace spanned by A and B.

[0146] Vibration suppression rate vector Projection on subspace for:

[0147] = ;

[0148] It is a new 4-dimensional vector, for example, it could be ;

[0149] and The best approximation in the subspace spanned by the dynamic response index. This means that a relationship has been found that can almost completely explain the vibration suppression rate using the two main controlling indices: subgrade dynamic displacement and pile vertical stress.

[0150] Projection distance The smaller the value, the stronger the explanatory power of the main control index for the optimization objective, and the more reliable the established correlation model.

[0151] In this embodiment, a projection matrix is ​​constructed based on the spatial matrix: the projection matrix is ​​used to project vectors onto a subspace spanned by the master dynamic response index. The process of constructing the projection matrix involves linear algebra operations, utilizing the spatial matrix and its transpose. Through this projection matrix, vectors in the optimization target vector set can be projected onto the subspace formed by the master dynamic response index, thereby analyzing the projection characteristics of the optimization target vectors in this subspace. For example, the correlation between the optimization target and the master dynamic response index can be quantified through the projection distance.

[0152] In this embodiment, the projection distance of each optimized target vector in the optimized target vector set is calculated based on the projection matrix in the subspace spanned by all master dynamic response indices. Combined with the corresponding orthogonal complement space representation, the vertical distance of each optimized target vector in the optimized target vector set in the corresponding orthogonal complement space is calculated: For each vector in the optimized target vector set under each working condition (such as the vibration suppression rate target vector or the normalized settlement target vector), it is projected onto the subspace spanned by the master dynamic response indices using the projection matrix, and the distance between this vector and its projection vector is calculated, i.e., the projection distance. The projection distance can be understood as a certain norm of the projection component itself, or its representation in the subspace, reflecting the extent to which the optimized target vector can be explained by the master dynamic response indices. Simultaneously, combined with the previously calculated orthogonal complement space representation, the vertical distance from the optimized target vector to the orthogonal complement space is calculated. This vertical distance represents the portion of the optimized target vector that cannot be explained by the master dynamic response index subspace, i.e., the projection residual distance, used to measure the incompleteness of the model's explanation of the optimized target.

[0153] In this embodiment, the system performs weighted correction on the projection distances of similar optimization target elements (such as vibration suppression rate data sequences for all operating conditions) in the subspace spanned by the main control dynamic response indices within the optimization target vector set, thereby obtaining an estimated value for the optimization target. Specifically, the system first obtains the initial projection representation of the target data sequence in the subspace through projection calculation; then, it introduces path weights obtained from multi-path reasoning in the knowledge graph, which quantifies the degree of influence of different main control indices on the optimization target; based on these weights, a weighted matrix is ​​constructed to correct the initial projection result, so that the more important main control indices occupy a greater weight in the projection calculation; finally, the corrected estimated value for the optimization target is obtained through weighted projection calculation.

[0154] In this embodiment, a dual-output response surface model is established, using the inclination angle of the inclined jet grouting pile as input and the optimized target estimate and the projected residual distance as joint outputs. The inclination angle of the inclined jet grouting pile is used as the independent variable, and the optimized target estimate obtained through weighted correction and the calculated projected residual distance are used as dependent variables to construct a dual-output model. The geometry of this model resembles a curved surface, hence the name dual-output response surface model. It can visually demonstrate how the inclination angle of the inclined jet grouting pile affects the optimized target estimate and the projected residual distance; for example, how the optimized target estimate changes and the projected residual distance changes with the inclination angle of the inclined jet grouting pile, thus providing a visual tool for analysis and optimization.

[0155] In this embodiment, partial least squares regression is used to fit the parameters of the dual-output response surface model. A transition section type correction coefficient and a train load level correction coefficient are introduced to calibrate the bias terms of the dual-output response surface model, resulting in a correlation model between the inclined jet grouting pile inclination angle, vibration suppression rate, and settlement. Partial least squares regression is a method suitable for multivariate data analysis, especially when there is multicollinearity among independent variables. In this embodiment, using partial least squares regression to fit the parameters in the dual-output response surface model effectively handles the potential correlations between the main control dynamic response indicators, finds the most suitable model parameters, and allows the model to better fit the data. Simultaneously, considering the influence of transition section type (road-bridge transition section or road-culvert transition section) and train load level (e.g., axle load 27t, 30t, 35t, etc.) on the relationship between the inclined jet grouting pile inclination angle, vibration suppression rate, and settlement, a transition section type correction coefficient and a train load level correction coefficient are introduced to calibrate the bias terms of the dual-output response surface model. In this way, a correlation model of inclined jet grouting pile inclination angle, vibration suppression rate, and settlement is finally obtained. This model can more accurately reflect the complex relationship between the inclination angle of inclined jet grouting pile and vibration suppression rate and settlement under different conditions, and provides a basis for determining the optimal inclination angle of inclined jet grouting pile in actual engineering.

[0156] The final mathematical form of the "correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement" is: ;

[0157] in, It refers to the inclination angle of the inclined jet grouting pile. This is the transition section type correction coefficient. It is a discrete variable, for example: road-bridge transition section = 1.0, road-tunnel transition section = 1.2, embankment transition section = 0.9. These values ​​are derived from previous finite element analyses or code comparisons of different transition sections. This is the train load rating correction factor. It can be a continuous or discrete variable, for example: 25-ton axle load = 0.8, 30-ton axle load = 1.0, 35-ton axle load = 1.3. These values ​​are derived from the calculation results of changing the axle load in dynamic simulation.

[0158] In this embodiment, the transition section type correction coefficient is used because the transition sections between road-bridge and road-culvert sections differ in structural stiffness, etc. This difference affects the effect of the inclined jet grouting pile inclination angle on vibration suppression rate and settlement. The transition section type correction coefficient is a parameter introduced to calibrate this difference. For example, the transition section type correction coefficient for road-bridge transition sections is specified as 1.0, and the transition section type correction coefficient for road-culvert transition sections is specified as 0.95. This coefficient is used to adjust the bias term of the dual-output response surface model, enabling the model to more accurately reflect the relationship between the inclined jet grouting pile inclination angle and the optimization target under different transition section types.

[0159] In this embodiment, the train load level correction factor is used because different train load levels (such as different axle loads) have different effects on the transition section of heavy-haul railways, thus affecting the relationship between the inclination angle of the inclined jet grouting pile and the vibration suppression rate and settlement. The train load level correction factor is a parameter derived based on the relationship between axle load and load effect. For example, the train load level correction factor is 0.9 when the axle load is 27t, 1.0 when it is 30t, and 1.1 when it is 35t. When constructing the correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement, this factor is used to calibrate the bias term of the model, enabling the model to take into account the impact of different train load levels on the optimization objective, thereby improving the accuracy and practicality of the model.

[0160] This invention provides an implementation method for an inclined jet grouting pile inclination angle optimization system based on multibody coupled dynamics in the transition section of heavy-haul railways, comprising:

[0161] The dynamic model construction module is used to construct a multi-body coupled dynamic model, including train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles, based on the basic parameters of the transition section of heavy-haul railway.

[0162] The vibration deformation data acquisition module is used to collect vibration acceleration data and vertical compression deformation data of a scaled model in the inclined jet grouting pile reinforcement chamber of the transition section of heavy-haul railway under different inclined jet grouting pile inclination angles.

[0163] The dynamic model verification module is used to calculate the vibration response calculation error based on the vibration acceleration data and vertical compression deformation data of the multi-body coupled dynamic model and the scaled model under different inclined jet grouting pile inclination angles, and to adjust the multi-body coupled dynamic model based on the vibration response calculation error to obtain a verified multi-body coupled dynamic model.

[0164] The dynamic simulation analysis module is used to perform dynamic simulations on multiple working conditions based on the validated multibody coupled dynamic model, extract the key dynamic response indicators of the transition section under each working condition, and analyze the variation of the key dynamic response indicators under each working condition with the inclination angle of the inclined jet grouting pile.

[0165] The correlation model fitting module is used to fit the correlation model of inclination angle, vibration suppression rate and settlement of inclined jet grouting piles based on the law of the key dynamic response indexes changing with the inclination angle of the inclined jet grouting piles under each working condition.

[0166] The tilt angle optimization calculation module is used to input the target transition section type, corresponding train load level and preset optimization target determined according to actual engineering needs into the inclined jet grouting pile tilt angle-vibration suppression rate-settlement correlation model to obtain the target tilt angle range, and determine the optimal inclined jet grouting pile tilt angle based on the target tilt angle range.

[0167] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of this invention and its equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics, characterized in that, include: Based on the basic parameters of the transition section of heavy-haul railway, a multi-body coupled dynamic model including train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles is constructed. Vibration acceleration data and vertical compression deformation data of a scaled model in the inclined jet grouting pile reinforcement room of the transition section of heavy-haul railway under different inclined jet grouting pile inclination angles were collected. Based on the vibration acceleration data and vertical compression deformation data of the multibody coupled dynamics model and the scaled model under different inclined jet grouting pile inclination angles, the vibration response calculation error was calculated, and the multibody coupled dynamics model was adjusted based on the vibration response calculation error to obtain a fully validated multibody coupled dynamics model. Based on the validated multibody coupled dynamics model, dynamic simulations were performed on multiple working conditions. Key dynamic response indicators of the transition section under each working condition were extracted, and the variation of key dynamic response indicators under each working condition with the inclination angle of the inclined jet grouting pile was analyzed. Based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting pile under each working condition, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is fitted. The target transition section type, corresponding train load level, and preset optimization target, determined according to actual engineering needs, are input into the inclined jet grouting pile inclination angle-vibration suppression rate-settlement correlation model to obtain the target inclination angle range. Based on the target inclination angle range, the optimal inclined jet grouting pile inclination angle is determined.

2. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics as described in claim 1, is characterized in that... Basic parameters, including: The transition section type, axle load of heavy-haul trains, train speed, elastic modulus of subgrade soil, pile material parameters of inclined jet grouting piles, and initial design inclination angle of inclined jet grouting piles.

3. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics as described in claim 1, is characterized in that... In the multibody coupled dynamics model, wheel-rail contact units are set between the train wheelset and the rail to simulate wheel-rail forces, elastic cushion layer units are set between the rail and the sleeper to simulate rail support, contact units are set between the sleeper and the roadbed to transfer loads, and inclined jet grouting pile units are embedded inside the roadbed and given preset pile material parameters and the initial design inclined jet grouting pile inclination angle.

4. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics as described in claim 1, characterized in that, The scaled-down model includes the same subgrade structure, sleeper arrangement, and inclined jet grouting piles as the actual transition section. Vibration acceleration sensors and settlement observation markers were installed on the roadbed surface, slope toe, and inclined jet grouting piles of the scaled model to simulate the static and dynamic loads of heavy-load trains.

5. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics as described in claim 1, characterized in that, For each working condition, the axle load of the heavy-load train, the train speed, the subgrade soil parameters, and the horizontal pile spacing of the inclined jet grouting piles are kept consistent.

6. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics as described in claim 1, is characterized in that... Key dynamic response indicators include: roadbed dynamic displacement, vibration acceleration, vertical stress of inclined jet grouting piles, and cumulative settlement of the roadbed.

7. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics as described in claim 1, is characterized in that... Based on the variation of key dynamic response indicators with the inclination angle of the inclined jet grouting pile under each working condition, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is fitted, including: Based on the key dynamic response indicators under all working conditions, a dynamic response spatiotemporal matrix is ​​constructed. The row vectors of the dynamic response spatiotemporal matrix represent the inclination angle of the inclined jet grouting pile under different working conditions, and the column vectors represent the dynamic response data arranged according to the time series or spatial measurement point location. Based on the dynamic response spatiotemporal matrix, the time-domain and frequency-domain characteristics of each working condition are calculated, and a dimension-reduced key dynamic response feature matrix is ​​constructed based on the time-domain and frequency-domain characteristics of each working condition. Based on the variation of key dynamic response indicators with the inclination angle of inclined jet grouting piles under each working condition, the vibration suppression rate and normalized cumulative subgrade settlement under each working condition are determined. Based on the vibration suppression rate and the normalized cumulative settlement of the subgrade under each working condition, an optimization target vector set is constructed, which includes the vibration suppression rate target vector and the normalized settlement target vector. Based on the tilt angle optimization knowledge graph, the main control dynamic response index is selected from all key dynamic response indices. Based on the inclination angle of the inclined jet grouting pile under all working conditions, all main control dynamic response indicators, and the optimized target vector set, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is constructed.

8. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics as described in claim 7, is characterized in that... Based on the tilt angle optimization knowledge graph, the main control dynamic response indicators were selected from all key dynamic response indicators, including: Using design parameters, dynamic response characteristics, and optimization objectives as nodes, the numerical values ​​and trends of corresponding nodes as node attributes, and the correlation strength between nodes as edges, and combining the edge weights calculated based on grey relational analysis or transfer entropy of key dynamic response feature matrices and optimization objective vector sets, a knowledge graph for tilt angle optimization is constructed. In the knowledge graph of tilt angle optimization, the tilt angle of the inclined jet grouting pile is used as the starting node, and the vibration suppression rate and the cumulative settlement of the subgrade are used as the ending nodes respectively. Multi-path reasoning is carried out to select the top K influence paths with the highest correlation weight. The key dynamic response indicators corresponding to the nodes in the top K influence paths with the highest correlation weights are taken as the main control dynamic response indicators.

9. The method for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multi-body coupled dynamics as described in claim 7, is characterized in that... Based on the inclination angle of the inclined jet grouting pile under all working conditions, all main control dynamic response indices, and the optimized target vector set, a correlation model of inclination angle, vibration suppression rate, and settlement of the inclined jet grouting pile is constructed, including: A spatial matrix is ​​constructed based on all the main control dynamic response indices under each set of working conditions, and the corresponding orthogonal complementary spatial representation is calculated. Based on the spatial matrix, a projection matrix is ​​constructed. Based on the projection matrix, the projection distance of each optimized target vector in the optimized target vector set in the subspace spanned by all main control dynamic response indices is calculated. Combined with the corresponding orthogonal complement space representation, the vertical distance of each optimized target vector in the optimized target vector set in the corresponding orthogonal complement space is calculated as the projection residual distance. For similar optimization target elements in the optimization target vector set, the projected distances in the subspace spanned by all master dynamic response indices are weighted and corrected to obtain the estimated optimization target values; A dual-output response surface model is established, with the inclination angle of the inclined jet grouting pile as input and the optimized target estimate and the projected residual distance as joint outputs. Partial least squares regression was used to fit the parameters of the dual-output response surface model. The bias terms of the dual-output response surface model were calibrated by introducing the transition section type correction coefficient and the train load level correction coefficient, thus obtaining the correlation model of inclined jet grouting pile inclination angle-vibration suppression rate-settlement.

10. A system for optimizing the inclination angle of inclined jet grouting piles in the transition section of heavy-haul railways based on multibody coupled dynamics, characterized in that, include: The dynamic model construction module is used to construct a multi-body coupled dynamic model, including train wheelsets, rails, sleepers, roadbed, and inclined jet grouting piles, based on the basic parameters of the transition section of heavy-haul railway. The vibration deformation data acquisition module is used to collect vibration acceleration data and vertical compression deformation data of a scaled model in the inclined jet grouting pile reinforcement chamber of the transition section of heavy-haul railway under different inclined jet grouting pile inclination angles. The dynamic model verification module is used to calculate the vibration response calculation error based on the vibration acceleration data and vertical compression deformation data of the multi-body coupled dynamic model and the scaled model under different inclined jet grouting pile inclination angles, and to adjust the multi-body coupled dynamic model based on the vibration response calculation error to obtain a verified multi-body coupled dynamic model. The dynamic simulation analysis module is used to perform dynamic simulations on multiple working conditions based on the validated multibody coupled dynamic model, extract the key dynamic response indicators of the transition section under each working condition, and analyze the variation of the key dynamic response indicators under each working condition with the inclination angle of the inclined jet grouting pile. The correlation model fitting module is used to fit the correlation model of inclination angle, vibration suppression rate and settlement of inclined jet grouting piles based on the law of the key dynamic response indexes changing with the inclination angle of the inclined jet grouting piles under each working condition. The tilt angle optimization calculation module is used to input the target transition section type, corresponding train load level and preset optimization target determined according to actual engineering needs into the inclined jet grouting pile tilt angle-vibration suppression rate-settlement correlation model to obtain the target tilt angle range, and determine the optimal inclined jet grouting pile tilt angle based on the target tilt angle range.

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