A reliability test method and system for track damping measures

Abstract

The application discloses a kind of reliability test method and system of track vibration reduction measures, it is related to track traffic vibration reduction technical field, specifically for: determine indirect control target point and vibration limit value;Build vibration transmission full-link model, and utilize vibration limit value to deduce tunnel wall vibration control target quantity;Define track vibration reduction measure target vibration reduction quantity;The uncertainty of vibration source under wheel-rail interaction is quantified by probability density function, and the probabilistic vibration source parameter under given guarantee rate is generated;Based on track vibration reduction measure target vibration reduction quantity, the probabilistic track vibration reduction measure target vibration reduction quantity is calculated using probabilistic vibration source parameter;Improved Markov chain Monte Carlo method is used to optimize loading sequence, and reliability test loading strategy is generated;Based on reliability test loading strategy, test is carried out, and the probability parameter of track vibration reduction measure meeting the demand is obtained.The application establishes full-link attenuation model and vibration reduction measure test method based on probability reliability, and improves the accuracy of vibration reduction effect evaluation.

Description

Technical Field

[0001] This invention relates to the field of vibration reduction technology for rail transit, and more specifically to a reliability testing method and system for rail vibration reduction measures. Background Technology

[0002] Currently, with the deepening of urbanization, the population continues to concentrate in the core areas of large cities, leading to a surge in demand for residential land resources and exacerbating the tight supply situation. Simultaneously, urban residents' strong demand for efficient and convenient transportation has driven the increasing popularity of "station-city integration" planning and implementation. The combination of these two factors has resulted in the distance between urban core area rail transit lines or stations and residential buildings continuously decreasing, even to the point of near-zero-distance underpasses. With the significant improvement in people's living standards, economic conditions, and awareness of their rights, the public's pursuit of a quiet and harmonious vibration environment is growing, making the environmental vibration and noise pollution issues caused by close-range train operation a major concern in urban core area station-city integration projects.

[0003] Vibration and noise from rail transit originate from complex wheel-rail interactions. Accurate prediction and evaluation, as well as the development of cost-effective vibration reduction products and control measures, remain technical challenges. Therefore, improving the level of vibration and noise pollution control is key to overcoming the bottleneck of surrounding property development. Vibration propagation in the rail transit environment is typically divided into three subsystems: the vibration source (vehicle track and supporting structure system), the propagation path (soil and rock), and the vibrating body (buildings). When a train runs, the wheel-rail impact excites system vibration, which is transmitted through the track, roadbed / tunnel / bridge to the ground, and then propagates through the soil and rock media, ultimately inducing vibration in nearby buildings and the environment. To mitigate the impact, vibration control research is mainly (or comprehensively) conducted from the three subsystems: the vibration source, the propagation path, and the vibrating body. Practice shows that track vibration reduction is the most direct and widely used measure. Common methods include seamless rail construction, various vibration-damping track beds, vibration-damping fasteners, and movable-point turnouts for turnout areas.

[0004] However, existing technologies have significant limitations in the application and evaluation of track vibration reduction measures, mainly reflected in:

[0005] The evaluation system is imperfect: traditional methods often take tunnel wall vibration as the direct control target, ignoring the attenuation characteristics of vibration during transmission to the building foundation, which leads to a distortion in the evaluation of vibration reduction effect.

[0006] The testing methods are limited: existing laboratory performance tests mostly use static loading or single-frequency excitation, which cannot effectively simulate the complex random vibration spectrum (including broadband, random, and dynamic loads) of trains in actual operation. This huge difference between the test conditions and the actual operating conditions results in a serious discrepancy between the excellent performance of vibration reduction products in the laboratory and their performance in real service environments.

[0007] Lack of reliability mechanism: Existing technologies do not quantify the impact of uncertainties in vibration source characteristics, building parameters, etc., on the probability of achieving vibration reduction targets.

[0008] Therefore, how to solve the above problems is a key issue that urgently needs to be addressed by those skilled in the art. Summary of the Invention

[0009] In view of this, the present invention provides a reliability testing method and system for track vibration reduction measures, overcoming the above-mentioned defects.

[0010] To achieve the above objectives, the present invention adopts the following technical solution:

[0011] A reliability testing method for track vibration reduction measures, comprising the following steps:

[0012] Indirect control target points and vibration limits VL0 are determined based on the building foundation or the ground surface of the building base;

[0013] A full-link model of vibration transmission is constructed, and the vibration limit VL0 is used to inversely deduce the target quantity VL for tunnel wall vibration control. T ;

[0014] Obtaining rail vibration level VL R The attenuation of rail vibration to tunnel wall vibration when there are no track vibration reduction measures C B Based on the rail vibration level VL R The attenuation C of rail vibration to tunnel wall vibration when there are no track vibration reduction measures. B and the target quantity VL for tunnel wall vibration control T Define the target vibration reduction amount C for track vibration reduction measures R ;

[0015] Collect rail vibration level (VL) under multiple vehicle types and working conditions R and superior frequency F R The time-varying data is used to quantify the uncertainty of the vibration source under the wheel-rail interaction through the probability density function, and the probabilistic vibration source parameters under a given guarantee rate are generated.

[0016] Based on the target vibration reduction C of the aforementioned track vibration reduction measures R The target vibration reduction amount of the probabilistic track vibration reduction measures is calculated using the probabilistic vibration source parameters. ;

[0017] Based on the target vibration reduction amount of the probabilistic track vibration reduction measures A multi-factor coupled loading spectrum is generated, and the loading sequence is optimized using an improved Markov chain Monte Carlo method to generate a reliability test loading strategy. Based on the reliability test loading strategy, tests are conducted to obtain the probability parameters of track vibration reduction measures that meet the requirements.

[0018] Optionally, the target quantity VL for tunnel wall vibration control T The expression is:

[0019] VL T =VL0+C D ;

[0020] In the formula, VL0 is the vibration limit; C D This is the site vibration level attenuation correction term.

[0021] Optionally, the expression for the site vibration level attenuation correction term is:

[0022] ;

[0023] in, ;

[0024] In the formula, L is the straight-line distance from the prediction point to the top of the rail; f is the frequency; Vs is the equivalent shear wave velocity of the soil layer; R is the horizontal distance from the prediction point to the centerline of the adjacent track; and H is the vertical distance from the prediction point to the top of the rail. The height of the source strength measurement point.

[0025] Optionally, the attenuation C of rail vibration to tunnel wall vibration when the track-free vibration reduction measures are not implemented. B The steps to obtain it are as follows:

[0026] The baseline value of vibration attenuation from the track bed to the tunnel wall for known tunnel structure types is obtained through numerical simulation or statistical regression of measured data.

[0027] The target tunnel structure type is determined. Based on the correspondence between the known tunnel structure types and the target tunnel structure type, the vibration attenuation benchmark value is corrected according to a preset correction table to obtain the vibration attenuation C of rail vibration to tunnel wall without track vibration reduction measures. B .

[0028] Optionally, the target vibration reduction amount of the probabilistic track vibration reduction measures The expression is:

[0029] ;

[0030] In the formula, VL R For rail vibration level; σ V For guarantee rate; VL T C is the target quantity for controlling tunnel wall vibration. D C is the site vibration level attenuation correction term; B VL represents the attenuation of rail vibration to tunnel wall vibration without track vibration reduction measures; L is the vibration evaluation point; L is the straight-line distance from the prediction point to the top of the rail; f is the frequency; and Vs is the equivalent shear wave velocity of the soil layer.

[0031] Optionally, the steps for obtaining the probability parameter of the track vibration reduction measure are as follows:

[0032] Taking the exceedance probability P(A < a) that the maximum Z vibration level VL = A of the indirect control target point does not exceed the vibration limit VL0 = a as the reliability index of the vibration reduction effect;

[0033] Attributing the uncertainty of the target vibration reduction amount of the probabilistic track vibration reduction measure to M vibration source uncertainty factors, where the vibration source uncertainty factors include differences in train models, time-varying track irregularities, differences in train speeds, and differences in train weights;

[0034] Converting the M vibration source uncertainty factors into the loading conditions of the test system, where the loading conditions include dynamically varying loading amplitudes F and loading frequencies f;

[0035] Obtaining the loading sequence of the test system, constructing a multi-factor coupled loading spectrum based on the reliability index of the vibration reduction effect and the loading conditions, and generating a loading sequence in the probability space M based on the improved Markov chain Monte Carlo method;

[0036] Performing a loading test based on the loading sequence and outputting the probability density function of the influencing factors of the vibration reduction effect to characterize the reliability of the vibration reduction effect under the full life cycle conditions.

[0037] Optionally, the loading sequence is: static preloading, random vibration loading, train speed change sweep frequency loading, temperature change coupled variable stiffness loading, and temperature change variable damping loading.

[0038] Optionally, the expression of the reliability index of the vibration reduction effect is:

[0039] ;

[0040] In the formula, is the probability of the occurrence of the influencing factor M, is the probability under the condition of the occurrence of the Mth influencing factor.

[0041] A reliability test system for track vibration reduction measures includes:

[0042] An indirect target point selection module for determining an indirect control target point and a vibration limit VL0 based on the building foundation or the ground surface of the building foundation;

[0043] A vibration control target back-calculation module for constructing a full-link vibration transfer model and using the vibration limit VL0 to back-calculate the tunnel wall vibration control target amount VL T ;

[0044] A track measure vibration reduction amount definition module for obtaining the rail vibration level VLR and the vibration attenuation amount C from the rail vibration to the tunnel wall without track damping measures B , based on the rail vibration level VL R and the vibration attenuation amount C from the rail vibration to the tunnel wall without track damping measures B and the tunnel wall vibration control target amount VL T define the target damping amount C of the track damping measures R ;

[0045] The vibration source uncertainty quantification module is used to collect the time-varying data of the rail vibration level VL R and the dominant frequency F R under multiple vehicle types and multiple working conditions, and quantify the uncertainty of the vibration source under the wheel-rail interaction through the probability density function to generate the probabilistic vibration source parameters under a given assurance rate;

[0046] The probabilistic track measure damping amount calculation module is used to calculate the probabilistic track measure damping amount according to the target damping amount C of the track damping measures R using the probabilistic vibration source parameters and the tunnel wall vibration control target amount VL T ; ;

[0047] The reliability test loading module is used to generate a multi-factor coupling loading spectrum based on the probabilistic track measure damping amount and optimize the loading sequence using the improved Markov chain Monte Carlo method to generate a reliability test loading strategy; perform tests based on the reliability test loading strategy to obtain the probability parameters of the track damping measures that meet the requirements.

[0048] Optionally, the reliability test loading module includes:

[0049] The reliability index definition sub-module is used to use the exceeding probability P(A < a) that the maximum Z vibration level VL = A of the indirect control target point does not exceed the vibration limit VL0 = a as the damping effect reliability index;

[0050] The uncertainty factor identification sub-module is used to attribute the uncertainty of the probabilistic track measure damping amount to M vibration source uncertainty factors, and the vibration source uncertainty factors include train type differences, track irregularity time-variation, train speed differences, and train weight differences;

[0051] The loading condition conversion sub-module is used to convert the M vibration source uncertainty factors into the loading conditions of the test system, and the loading conditions include the dynamically changing loading amplitude F and loading frequency f;

[0052] The loading sequence generation submodule is used to obtain the loading order of the test system, construct a multi-factor coupled loading spectrum based on the vibration reduction effect reliability index and the loading conditions, and generate the loading sequence in probability space M based on the improved Markov chain Monte Carlo method.

[0053] The test execution submodule is used to perform load tests based on the loading sequence and output the probability density function of the factors affecting the vibration reduction effect to characterize the reliability of the vibration reduction effect under the full life cycle working conditions.

[0054] As can be seen from the above technical solution, the present invention provides a reliability testing method and system for track vibration reduction measures, which has the following advantages compared with the prior art:

[0055] 1. Indirect control target points are determined by the building foundation or the ground surface of the building foundation. Based on the vibration limit, the vibration control target of the tunnel wall is inferred. This breaks through the limitation of the traditional method that only takes the tunnel wall as the direct control target. By establishing a full-link attenuation model of "vibration source → tunnel wall → building foundation", the accuracy of vibration reduction effect assessment is improved.

[0056] 2. A probability density quantization method is introduced to characterize the randomness of the time-domain / frequency-domain differences in rail vibration levels, and to obtain the quantified value of rail vibration under a given guarantee rate. By integrating uncertain factors, the target vibration reduction amount of track vibration reduction measures is optimized from a fixed value to a probabilistic reliable value, thereby improving the scientificity and adaptability of the vibration reduction target setting.

[0057] 3. Using the probability of indirectly controlling the vibration of the target point to meet the standard as the core reliability indicator, the generation of track vibration reduction measures is driven. It quantifies the reliability of the entire link from vibration source excitation to building response, ensuring that the vibration reduction measures can still meet the building vibration control requirements under complex operating conditions (such as load randomness, geological variability, and equipment aging) during the operation period, and providing probabilistic assurance for the design, inspection and service performance of vibration reduction products. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the provided drawings without creative effort.

[0059] Figure 1 This is a schematic diagram of the method flow provided by the present invention. Detailed Implementation

[0060] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0061] One embodiment of the present invention discloses a reliability testing method for track vibration reduction measures, such as... Figure 1 As shown, the specific steps are as follows:

[0062] Step 1: Determine the indirect control target points and vibration limit VL0 based on the building foundation or the ground surface of the building base;

[0063] Step 2: Construct a full-link model of vibration transmission, and use the vibration limit VL0 to infer the target quantity VL for tunnel wall vibration control. T ;

[0064] Step 3: Obtain the rail vibration level VL R The attenuation of rail vibration to tunnel wall vibration when there are no track vibration reduction measures C B Based on rail vibration level VL R When there are no track vibration reduction measures, the vibration attenuation C of the rail vibration to the tunnel wall B and the target quantity VL for tunnel wall vibration control T Define the target vibration reduction amount C for track vibration reduction measures R ;

[0065] Step 4: Collect rail vibration level (VL) data under multiple vehicle types and working conditions. R and superior frequency F R The time-varying data is used to quantify the uncertainty of the vibration source under the wheel-rail interaction through the probability density function, and the probabilistic vibration source parameters under a given guarantee rate are generated.

[0066] Step 5: Target vibration reduction C based on track vibration reduction measures R Calculating the target vibration reduction amount of probabilistic track vibration reduction measures using probabilistic vibration source parameters ;

[0067] Step 6: Target vibration reduction amount based on probabilistic track vibration reduction measures A multi-factor coupled loading spectrum is generated, and the loading sequence is optimized using an improved Markov chain Monte Carlo method to generate a reliability test loading strategy. Based on the reliability test loading strategy, tests are conducted to obtain the probability parameters of track vibration reduction measures that meet the requirements.

[0068] Furthermore, in step 1, the indirect control target point is selected within 0.5m outside the ground surface of the proposed building foundation or building base as the vibration evaluation point, and information related to the evaluation project, such as tunnel type, site type, or shear wave velocity, is collected (or a dataset is established).

[0069] In this embodiment, the vibration limit VL0 = 67dB.

[0070] In one embodiment, step 2 is used to back-calculate the direct control target value. Specifically, it adopts a full-link vibration transmission model to back-calculate the vibration value of the rail under the given source strong vibration reduction measures, tunnel and site type from the vibration limit of the selected site or foundation, and uses this as the target value for vibration control design.

[0071] In one embodiment, the target quantity VL for tunnel wall vibration control is obtained. T Its expression is: VL T =VL0+C D ;

[0072] Among them, the site vibration level attenuation correction term C D The method used to correct for composite distance attenuation characteristics includes two terms: soil damping attenuation term and geometric attenuation term of direct body wave from the line source. The specific expression is as follows:

[0073] ;

[0074] ;

[0075] In the formula, L is the straight-line distance from the predicted point to the top of the rail, in meters (m); f is the frequency, in Hz, generally taken as the dominant frequency of the reference vibration source; Vs is the equivalent shear wave velocity of the soil layer, in m / s; R is the horizontal distance from the predicted point to the centerline of the adjacent track, in meters (m); and H is the vertical distance from the predicted point to the top of the rail, in meters (m). The height of the source strength measuring point is generally taken as 1.25m.

[0076] In one embodiment, the attenuation C of rail vibration to tunnel wall vibration when there are no track vibration reduction measures B The steps to obtain it are as follows:

[0077] The baseline value of vibration attenuation from the track bed to the tunnel wall for known tunnel structure types is obtained through numerical simulation or statistical regression of measured data.

[0078] The target tunnel structure type is determined. Based on the correspondence between known tunnel structure types and the target tunnel structure type, the vibration attenuation benchmark value is corrected according to a preset correction table to obtain the vibration attenuation C of rail vibration to tunnel wall without track vibration reduction measures. B .

[0079] Furthermore, the amount of vibration attenuation from rail vibration to tunnel wall vibration when there are no track vibration reduction measures is denoted as C. B The vibration attenuation of track vibration reduction measures (including vibration-damping fasteners, vibration-damping sleepers, or vibration-damping track beds and their combinations) is denoted as C. R C R The target vibration reduction amount for track vibration reduction measures; when the rail vibration level is denoted as VL R At that time, C R The expression can be represented as:

[0080] ;

[0081] The vibration level VL at the selected vibration evaluation point (building foundation or base or soil within 0.5m of the foundation), VL = VL R -C B -C D -C R And VL≤VL0 (VL0=67dB);

[0082] In the formula, VL R C B C D C R The vibration levels of the rails, the vibration attenuation from the rails to the tunnel wall without track vibration reduction measures, the site vibration level attenuation correction item from the tunnel wall to the vibration evaluation point, and the target vibration reduction amount of track vibration reduction measures are all considered separately. D It can be obtained through calculation using a formula; C B The value can be obtained through numerical simulation or statistical regression of measured vibration data of rails, track bed, and tunnel walls. It should be noted that different tunnel types, different vibration source characteristics, and different vibration reduction measures will result in different values ​​for C. B The results will also differ. If the vibration transmission relationship between the track bed and tunnel wall in single-track tunnels, double-track tunnels (including double-bore double-track tunnels), stations, and rock tunnels (including single-track and double-track tunnels) under the same vibration reduction measures is collected, empirical formulas can be used to estimate the vibration amount in another type of tunnel structure. The relative correction amounts are 0, -3, -5, and -6 dB, respectively. That is, if the vibration attenuation from the track bed to the tunnel wall in a single-track tunnel is known, the vibration attenuation from the track bed to the tunnel wall in a double-track tunnel should be increased by 3 dB on this basis, and so on.

[0083] In one embodiment, the rail vibration level VL under wheel-rail interaction was investigated. R Uncertainty arises, for example, in the case of a subway line, the train models passing through a uniform cross-section may differ due to operational arrangements, resulting in variations in vibration amplitude and frequency. Probability density is used to quantify the time-domain and frequency-domain differences of these vibration sources. The specific quantization method is as follows:

[0084] Suppose there are two trains, Train 1 and Train 2 produced by different manufacturers, running on the same track. The rail vibration levels caused by them at the same running speed are VL R1 and VL R2 , and the dominant frequencies of the rail vibration levels caused by them are F R1 and F R2 . If VL R1 <VL R2 、F R1 <F R2 , then through statistical regression, the differences in vibration level and frequency VL V and σ F under a certain confidence level σ R2 -VL R1 、F R2 -F R1 are obtained, that is, VL R2 =VL R1 +σ V 、F R2 =F R1 +σ F . Then the uncertainty of the rail vibration level VL R and the dominant frequency F R can be expressed by the vibration level VL R +σ V and the frequency F R +σ F under a given confidence level (such as 95%).

[0085] The target vibration reduction amount of the track vibration reduction measure introducing the probability quantification of the rail vibration level is expressed as:

[0086] ;

[0087] In an embodiment, the steps for obtaining the probability parameters of the track vibration reduction measure are as follows:

[0088] Taking the exceedance probability P(A < a) that the maximum Z vibration level VL = A of the indirectly controlled target point does not exceed the vibration limit VL0 = a as the reliability index of the vibration reduction effect;

[0089] Attributing the uncertainty of the probabilistic track vibration reduction measure target vibration reduction amount to M vibration source uncertainty factors, and the vibration source uncertainty factors include train model differences, time-varying track irregularities, train speed differences, and train weight differences;

[0090] Converting the M vibration source uncertainty factors into the loading conditions of the test system, and the loading conditions include the dynamically changing loading amplitude F and the loading frequency f;

[0091] Obtain the loading sequence of the test system, construct a multi-factor coupled loading spectrum based on the reliability index of the vibration damping effect and the loading conditions, and generate a loading sequence in the probability space M based on the improved Markov chain Monte Carlo method;

[0092] Perform a loading test based on the loading sequence, and output the probability density function of the influencing factors of the vibration damping effect to characterize the reliability of the vibration damping effect under the full life cycle conditions.

[0093] Furthermore, introduce a reliability index to probabilistically quantify the target quantity of the vibration damping effect, and give the target quantity of the vibration damping effect based on time-varying and deterioration effects. The specific operation is as follows:

[0094] The reliability of the track vibration damping effect is expressed by the probability of exceeding. Assume that the single-value vibration evaluation quantity of the target vibration control point on the building foundation or the ground surface of the site after implementing the track vibration damping measures is represented by VL0, and its control standard is VL0 = a = 67 dB. Then, considering the site attenuation C D and the vibration attenuation amount C from the rail vibration without track vibration damping measures to the tunnel wall vibration B After that, the target vibration damping amount of the probabilistic track vibration damping measure after meeting the vibration control standard VL0 is Then, the probability value of P(A < a) can be calculated, and this probability value is the reliability that the maximum Z vibration level VL = A of the target control point meets the vibration control standard VL0 = a after implementing the vibration damping effect. The larger this value is, the easier it is to meet the standard.

[0095] In the reliability design and test method of the vibration damping effect of track vibration damping measures, the uncertainties of C D and C B are not considered, and only the uncertainty of is considered. That is, the probability of the evaluation point vibration meeting the standard P(A < a) mainly depends on the uncertainty of . Assume that there are M factors affecting the uncertainty of . That is, the factors affecting the design target value of the track vibration damping effect are summarized as differences in train models, time-varying track irregularities, differences in train speeds, differences in train weights, etc. That is, the uncertainty factors of the vibration source are used to replace the M influencing factors affecting the uncertainty of . The probability of the evaluation point vibration meeting the standard under a single (the mth) influencing factor is denoted as , that is, the probability that the vibration level A of its target control point is less than or equal to the vibration control standard a under the action of the mth track vibration damping effect influencing factor, that is, the non-exceeding probability value. In order to consider the probability of vibration meeting the standard under the combined action of K influencing factors when multiple trains pass (or multiple test conditions), using the conditional probability and total probability formula, the probability that the maximum Z vibration level A of the target control point is less than or equal to the vibration control standard a is obtained as

[0096] ;

[0097] In the formula, Let M be the probability of the influencing factor occurring. Let be the probability given the occurrence of the Mth influencing factor.

[0098] Regarding track vibration on-site, the M factors influencing the track vibration reduction effect mainly include the uncertainty of the vibration source caused by the vehicle, which is also the main factor in the positive design of track vibration reduction measures. Regarding the testing of the track vibration reduction effect, these M factors can be equivalently replaced by test conditions and summarized as the loading conditions of the test system, mainly including changes in the loading amplitude F or loading frequency f of the test system. The target vibration reduction amount of probabilistic track vibration reduction measures is... The structural dynamic parameters mainly include the stiffness K and damping C of the vibration reduction system. Therefore, under the test method of the vibration reduction effect of track vibration reduction measures, the test target is mainly the law of the stiffness K and damping C of the vibration reduction system under uncertain input (change of loading amplitude F or loading frequency f), that is, to give the stiffness K and damping C of the vibration reduction system a probabilistic connotation.

[0099] The stiffness and damping of the elastic pads in vibration damping fasteners are chosen as the target components for design or testing because: the selection of the stiffness and damping of the elastic pads has a major impact on the vibration damping performance of the vibration damping fasteners. Specifically: the stiffness of the elastic pads determines the response speed of the vibration damping system to vibration. Generally, the greater the pad stiffness, the weaker the ability to transmit vibration to the structure. Therefore, selecting appropriate elastic pad stiffness can ensure that the vibration damping system provides effective vibration damping for vibrations in different frequency ranges. The damping of the elastic pads refers to the vibration damping system's ability to dissipate vibration energy. It can reduce the duration and amplitude of structural vibration. Reasonable selection of elastic pad damping can enable the vibration damping system to maintain effective energy absorption capacity within the vibration frequency range, thereby further achieving better vibration damping effects.

[0100] Secondly, the reliability testing scheme and time-varying life prediction model for track vibration reduction measures that conform to the actual operating conditions throughout the entire life cycle need to address the following issues:

[0101] The loading strategy for the experimental system should fully consider the probability-quantified target amount of vibration reduction effect.

[0102] Achieving Target 1 - Stiffness K: ;

[0103] Achieving Target 2 - Damping C: ;

[0104] Achieve both Objective 1 and Objective 2 simultaneously:

[0105] ;

[0106] Among them, M is the probability space of the loading system.

[0107] On the other hand, this embodiment discloses a reliability test system for track vibration reduction measures, including:

[0108] An indirect target point selection module, configured to determine an indirect control target point and a vibration limit value VL0 based on the building foundation or the surface site of the building foundation;

[0109] A vibration control target back-calculation module, configured to construct a full-link vibration transfer model and use the vibration limit value VL0 to back-calculate the tunnel wall vibration control target quantity VL T ;

[0110] A track measure vibration reduction quantity definition module, configured to obtain the rail vibration level VL R and the attenuation quantity C from the rail vibration to the tunnel wall vibration without track vibration reduction measures B , and define the target vibration reduction quantity C of the track vibration reduction measure based on the rail vibration level VL R , the attenuation quantity C from the rail vibration to the tunnel wall vibration without track vibration reduction measures B and the tunnel wall vibration control target quantity VL T ; R ;

[0111] A vibration source uncertainty quantification module, configured to collect the time-varying data of the rail vibration level VL R and the dominant frequency F R under multiple vehicle types and multiple working conditions, and quantify the uncertainty of the vibration source under the wheel-rail interaction through the probability density function to generate probabilistic vibration source parameters under a given confidence level;

[0112] A probabilistic track measure vibration reduction quantity calculation module, configured to calculate the probabilistic target vibration reduction quantity of the track vibration reduction measure R using the probabilistic vibration source parameters and the tunnel wall vibration control target quantity VL T ; ;

[0113] A reliability test loading module, configured to generate a multi-factor coupled loading spectrum based on the probabilistic target vibration reduction quantity of the track vibration reduction measure , and optimize the loading sequence by using the improved Markov chain Monte Carlo method to generate a reliability test loading strategy; perform tests based on the reliability test loading strategy to obtain the probability parameters of the track vibration reduction measure that meet the requirements.

[0114] In one embodiment, the reliability test loading module includes:

[0115] A reliability index definition sub-module, configured to use the exceedance probability P(A < a) that the maximum Z vibration level VL = A of the indirect control target point does not exceed the vibration limit value VL0 = a as the vibration reduction effect reliability index;

[0116] The uncertainty factor identification submodule is used to identify the target vibration reduction amount of probabilistic track vibration reduction measures. The uncertainty is attributed to M source uncertainty factors, which include differences in train type, time-varying track irregularities, differences in train speed, and differences in train weight.

[0117] The loading condition conversion submodule is used to convert the uncertainties of M vibration sources into loading conditions of the test system. The loading conditions include dynamically changing loading amplitude F and loading frequency f.

[0118] The loading sequence generation submodule is used to obtain the loading order of the test system, construct a multi-factor coupled loading spectrum based on the vibration reduction effect reliability index and loading conditions, and generate the loading sequence in probability space M based on the improved Markov chain Monte Carlo method.

[0119] The test execution submodule is used to perform load tests based on the loading sequence and output the probability density function of the factors affecting the vibration reduction effect to characterize the reliability of the vibration reduction effect under the full life cycle working conditions.

[0120] Furthermore, laboratory testing needs to consider static preload → random vibration loading → train speed change frequency sweep loading → temperature-coupled variable stiffness loading → temperature-variable damping loading.

[0121] Based on the above influencing conditions and loading sequence, a multi-factor coupled loading spectrum is designed based on the probability density function. An improved Markov chain Monte Carlo (MCMC) method can be used to generate the loading sequence, which can shorten the test time while ensuring the coverage of the working conditions.

[0122] In summary, by using a reliability-based test method for track vibration reduction measures, we can obtain a design or test method for track vibration reduction measures that takes into account the uncertainty of the vibration source, with tunnel wall vibration or track bed vibration as the target design value, under the condition that the vibration of the building foundation or site reaches the standard limit.

[0123] The various embodiments in this specification are described in a progressive manner, with each embodiment focusing on its differences from other embodiments. Similar or identical parts between embodiments can be referred to interchangeably. For the apparatus disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the description is relatively simple; relevant parts can be referred to the method section.

[0124] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for testing the reliability of a track damping measure, characterized in that The specific steps are: Determine an indirect control target point and a vibration limit value VL0 based on a building base or a building foundation ground surface site; A vibration transmission full-link model is constructed, and the vibration limit value VL0 is used to deduce a tunnel wall vibration control target value VL T ; Obtaining rail vibration level VL R The attenuation of rail vibration to tunnel wall vibration when there are no track vibration reduction measures C B Based on the rail vibration level VL R The attenuation C of rail vibration to tunnel wall vibration when there are no track vibration reduction measures. B and the target quantity VL for tunnel wall vibration control T Define the target vibration reduction amount C for track vibration reduction measures R ; Collecting time-varying data of rail vibration level VL R and dominant frequency F R under multi-vehicle types and multi-working conditions, quantifying the uncertainty of vibration source under wheel-rail interaction by probability density function, and generating probabilistic vibration source parameters under given assurance rate; based on the track damping measure target damping amount C R a probabilistic track damping measure target damping amount is calculated using the probabilistic vibration source parameter ; a target damping amount of the probabilistic track damping measure A multi-factor coupled loading spectrum is generated, and an improved Markov chain Monte Carlo method is used to optimize the loading sequence to generate a reliability test loading strategy. Test based on the reliability test loading strategy to obtain a probability parameter of a track vibration reduction measure meeting a demand; The tunnel wall vibration control target quantity VL T The expression is: VL T = VL0+ C D ; In the formula, VL0 is the vibration limit value; C D is the site vibration level attenuation correction term; The expression of the ground vibration level decay correction term is: ； wherein ; wherein, L is the straight-line distance from the prediction point to the rail top; f is the frequency; Vs is the equivalent shear wave velocity of the soil layer; R is the horizontal distance from the prediction point to the adjacent line centerline; H is the vertical distance from the prediction point to the rail top; is the source strength measurement point height; The probabilistic track damping measure target damping amount The expression is: ； wherein VL R is the rail vibration level; σ V is the assurance rate; VL T is the tunnel wall vibration control target quantity; C D is the site vibration level attenuation correction term; C B is the rail vibration to tunnel wall vibration attenuation quantity when there is no track vibration reduction measure; VL L is the straight line distance from the prediction point to the rail top; f is the frequency; Vs is the soil layer equivalent shear wave velocity.

2. A method of testing the reliability of a track vibration mitigation measure according to claim 1, characterized in that The trackless damping measure is a damping amount C of rail vibration to tunnel wall vibration B The acquisition step is: Obtain a reference value of vibration decay from a track bed to a tunnel wall of a known tunnel structure type through numerical simulation or measured data statistical regression; Determine the target tunnel structure type, according to the correspondence between the known tunnel structure type and the target tunnel structure type, modify the vibration attenuation amount reference value by a preset correction table, and obtain the rail vibration to tunnel wall vibration attenuation amount C without track vibration reduction measures B .

3. A method of testing the reliability of a track vibration mitigation measure according to claim 1, characterized in that, The probability parameter of the track vibration reduction measure is obtained by: Taking an exceeding probability P(A a target damping amount of the probabilistic track damping measure attributed to M vibration source uncertainty factors, including train type difference, track irregularity time variation, train speed difference and train weight difference; Convert M vibration source uncertainty factors into loading conditions of a test system, the loading conditions including a dynamically changed loading amplitude F and a loading frequency f; Obtain a test system loading sequence, and based on the vibration reduction effect reliability index and the loading conditions, construct a multi-factor coupled loading spectrum, and generate a loading sequence under a probability space M based on an improved Markov chain Monte Carlo method; Based on the loading sequence, perform loading test, and output a probability density function of a vibration reduction effect influencing factor to represent a vibration reduction effect reliability under a full life cycle working condition.

4. A method of testing the reliability of a track vibration mitigation measure according to claim 3, characterized in that, The loading sequence is: static preloading, random vibration loading, train speed change sweep frequency loading, temperature change coupled stiffness loading, and temperature change damping loading.

5. A method of testing the reliability of a track vibration mitigation measure according to claim 3, characterized in that, The expression of the vibration reduction effect reliability index is: ； wherein is the probability of the occurrence of the influencing factor M, is the probability under the condition of the occurrence of the Mth influencing factor.

6. A system for testing the reliability of a track damping measure, characterized in that It comprises: An indirect target point selection module for determining an indirect control target point and a vibration limit value VL0 based on a building base or a building foundation ground surface site; a vibration control target backstepping module, configured to construct a vibration transmission full-link model, and backstep a tunnel wall vibration control target quantity VL by using the vibration limit value VL0 T ; a track measure damping amount defining module configured to obtain a rail vibration level VL R and a tunnel wall vibration damping amount C from rail vibration to tunnel wall vibration without a track damping measure B , based on the rail vibration level VL R , the tunnel wall vibration damping amount C from rail vibration to tunnel wall vibration without a track damping measure B and the tunnel wall vibration control target amount VL T define a track damping measure target damping amount C R ; A vibration source uncertainty quantification module is configured to collect time-varying data of rail vibration level VL under multiple vehicle types and multiple working conditions, and quantifies the uncertainty of the vibration source under wheel-rail interaction through a probability density function to generate probabilistic vibration source parameters under a given assurance rate. R and a dominant frequency F R . a probabilistic track measure damping amount calculation module configured to calculate a target damping amount C of the track damping measure based on the track damping measure target damping amount C R using the probabilistic vibration source parameter and the tunnel wall vibration control target amount VL T calculating a probabilistic track damping measure target damping amount ; A reliability test loading module is configured to determine a target damping amount of the probabilistic track damping measure based on the probability distribution A multi-factor coupled loading spectrum is generated, and an improved Markov chain Monte Carlo method is used to optimize the loading sequence to generate a reliability test loading strategy. Test based on the reliability test loading strategy to obtain a probability parameter of a track vibration reduction measure meeting a demand; The tunnel wall vibration control target quantity VL T The expression is: VL T = VL0+ C D ; In the formula, VL0 is the vibration limit value; C D is the site vibration level attenuation correction term; The expression of the ground vibration level decay correction term is: ； wherein ; wherein, L is the straight-line distance from the prediction point to the rail top; f is the frequency; Vs is the equivalent shear wave velocity of the soil layer; R is the horizontal distance from the prediction point to the adjacent track centerline; H is the vertical distance from the prediction point to the rail top; is the source strength measurement point height; The probabilistic track damping measure target damping amount The expression is: ； VL R σ V C T VL D C B VL L L f f Vs V 7. A system for testing the reliability of a track vibration mitigation measure according to claim 6, characterized in that The reliability test loading module comprises: A reliability index definition submodule for taking an exceeding probability P(A An uncertainty factor identification sub-module is configured to determine the target vibration reduction amount of the probabilistic track vibration reduction measure The uncertainty is attributed to M vibration source uncertainty factors, including train type difference, track irregularity time variation, train speed difference, and train weight difference. A loading condition conversion submodule for converting M vibration source uncertainty factors into loading conditions of a test system, the loading conditions including a dynamically changed loading amplitude F and a loading frequency f; A loading sequence generation submodule for obtaining a test system loading sequence, and based on the vibration reduction effect reliability index and the loading conditions, constructing a multi-factor coupled loading spectrum, and generating a loading sequence under a probability space M based on an improved Markov chain Monte Carlo method; A test execution submodule for performing loading test based on the loading sequence, and outputting a probability density function of a vibration reduction effect influencing factor to represent a vibration reduction effect reliability under a full life cycle working condition.

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