A shock absorption control method for long-span continuous bridges with long spans

Abstract

The present invention discloses a shock absorption control method for a long-span continuous bridge with long spans, including: S1, constructing a dynamic finite element analysis model of the long-span continuous bridge, taking the magnetorheological damper as the shock absorption control device of the continuous bridge and constructing a controller dynamic model, which together serve as the shock absorption control system; S2, for the shock absorption control system, adopting a semi-active control scheme considering fault tolerance to control the output force of the continuous bridge; S3, conducting seismic reliability analysis on the continuous bridge structure under random seismic excitation, and determining the optimal output force control scheme to control the shock absorption of the continuous bridge. In view of the situation that the magnetorheological damper at the control part may fail during operation and affect the normal output force control, the present invention analyzes the fault modes of the actuator, and based on this, incorporates fault tolerance control into the semi-active control scheme, and achieves the purpose of maintaining the expected shock absorption effect of the semi-active control scheme by making a boost compensation for the fault output force.

Description

Technical Field

[0001] The present invention belongs to the technical field of bridge shock absorption control, and particularly relates to a shock absorption control method for long-span continuous bridges with long continuous spans. Background Art

[0002] A bridge is a structure erected on special terrain to ensure passage. It is an important part of the modern transportation system and also an important infrastructure for the development of the country and society. The continuous beam bridge has the advantages of large self-structure stiffness, good integrity, material saving, large overloading capacity, good dynamic performance, etc., and is one of the most widely used bridge types in China at present. China is one of the countries with frequent earthquakes in the world, and the characteristics of large self-weight and special structural system of the continuous beam bridge are not conducive to earthquake resistance. Therefore, applying a shock absorption control scheme to the continuous beam bridge to reduce the damage suffered by the structure under earthquake action has positive significance.

[0003] In the prior art, a lot of research has been done on the shock absorption of bridge engineering. However, the structural elements as control devices are often relatively delicate, and bridge engineering usually serves in an open-air environment. The control device may be affected by external factors or its own aging during long-term operation, especially sudden high-intensity factors such as earthquakes will have a negative impact on the control device, and after a major earthquake, aftershocks often occur many times, making the control device lose stability and unable to achieve the expected control effect. At present, the research on countermeasures for the loss of stability of control devices is still relatively few, which limits the application effect of control devices on bridge seismic isolation. After some control devices fail, how to make the entire shock absorption control system still operate stably to ensure the safety of the bridge before the maintenance measures arrive has become a problem that needs further research at present. Summary of the Invention

[0004] Aiming at the above deficiencies in the prior art, the shock absorption control method for long-span continuous bridges provided by the present invention solves the problem that the loss of stability of the control device is not considered in the existing bridge shock absorption control system.

[0005] In order to achieve the above invention purpose, the technical solution adopted by the present invention is: a shock absorption control method for long-span continuous bridges with long continuous spans, including the following steps:

[0006] S1. Construct a dynamic finite element analysis model of the long-span continuous bridge with long continuous spans, use the magnetorheological damper as the shock absorption control device of the continuous bridge and construct a controller dynamic model, and jointly use them as the shock absorption control system;

[0007] S2. For the shock absorption control system, adopt a semi-active control scheme considering fault tolerance to control the output force of the continuous bridge;

[0008] S3. Conduct seismic reliability analysis on the continuous bridge structure under random seismic excitation, and determine the optimal output force control scheme to control the shock absorption of the continuous bridge.

[0009] Furthermore, the dynamic finite element analysis model in step S1 includes the superstructure model of the bridge, the substructure model, and the modeling and layout model of the bearings;

[0010] The controller dynamic model includes a forward model and a reverse model. Based on the controller dynamic model, the magnetorheological damper controls the output force of the continuous bridge structure by adjusting the voltage.

[0011] Furthermore, the forward model is the Bingham model, the Bouc-Wen model, or the Spencer model;

[0012] The reverse model is the reverse model trained based on the SSA-BP neural network.

[0013] Furthermore, in step S2, the semi-active control scheme considering fault tolerance means that when a fault occurs in the system, the system can automatically adjust the parameters of the control device in a timely manner according to the dynamic response of the structure or the change of the external load, so that the system maintains stability and continuity within an acceptable range. The expression of the fault tolerance control is:

[0014]

[0015] In the formula, f d is the adjustable semi-active control force of the damper, δ is the fault compensation coefficient, f dmax is the maximum value of the control force that the damper can output, is the step function, u is the active optimal control force, is the relative velocity of the damper piston, f dmin is the minimum value of the control force that the damper can output.

[0016] Furthermore, in step S2, when using the semi-active control scheme considering fault tolerance to control the output force of the continuous bridge, when the faulty magnetorheological damper is isolated, it will no longer participate in the system control before its repair and recovery function, and other non-faulty magnetorheological dampers at the same control part will be adjusted to compensate the output force of the control part;

[0017] Among them, the expression of the output force compensation is:

[0018]

[0019] In the formula, is the output force after compensation at the next moment, δ is the fault gain coefficient, u(t + 1) is the expected output force when the system is normal, u f (t + 1) is the output force of the control part at the next moment, and μ is the failure factor of the magnetorheological damper, and μ is expressed as [μ1, μ2,..., μ i ,..., μ n 1×n , where n is the total number of magnetorheological dampers installed at the control part, is the expected output force of each magnetorheological damper at the same control part,

[0020] Further, the step S3 is specifically as follows:

[0021] S3-1. Construct a random earthquake physical model;

[0022] S3-2. Generate random seismic waves of the continuous bridge structure according to the random earthquake physical model;

[0023] S3-3. Based on the generated random seismic waves, use the probability density evolution method to solve the random seismic response information of the continuous bridge structure, and obtain the probability density evolution information of the structural response quantity of the continuous bridge structure;

[0024] S3-4. Based on the probability density evolution information and combined with the absorption boundary conditions, calculate the dynamic reliability of the continuous bridge structure under different output force control schemes;

[0025] S3-5. Based on the calculated dynamic possibility, determine the optimal output force control scheme and perform seismic reduction control on the continuous bridge.

[0026] Further, the random earthquake physical model in the step S3-1 is modeled according to the peak acceleration A0, the dominant period T of the site soil, the damping ratio ξ of the site g and the dominant frequency domain ω of the site soil g , and considering the earthquake source, propagation path and site conditions.

[0027] Further, the step S3-2 is specifically as follows:

[0028] S32-1. Use the GF deviation method to select a discrete representative point set, assign values to the parameters of the random earthquake physical model, and then generate a sample of the seismic acceleration time history with the assigned probability;

[0029] S32-3. Based on the generated sample of the seismic acceleration time history, perform seismic excitation on the constructed dynamic finite element analysis model, and then input random seismic waves along the continuous bridge structure.

[0030] The beneficial effects of the present invention are:

[0031] ​(1) The present invention uses a genetic algorithm to optimize and solve the control force of the classical LQR optimal control algorithm, determines reasonable control parameters, obtains the corresponding weight matrix, and obtains the optimal active control force. The classical LQR optimal active control algorithm is used as the theoretical basis for the semi-active control scheme. In view of the situation that the magnetorheological damper at the control part may fail during operation, affecting the normal output control, the failure mode of the actuator is analyzed, and based on this, fault tolerance control is considered in the semi-active control scheme. By making a pressure boost compensation for the fault output, the purpose of maintaining the expected shock absorption effect of the semi-active control scheme is achieved.

[0032] (2) The present invention uses a numerical analysis method to calculate the dynamic response of a continuous beam bridge structure under multiple working conditions, evaluates the shock absorption control scheme applied to each working condition, and compares the seismic responses of the continuous beam bridge in the states of no control, active control, normal working state of semi-active control, state of taking compensation measures during fault, and state of no compensation measures during fault. The comparison of the shock absorption results shows that the semi-active control scheme considering fault tolerance is effective and necessary.

[0033] (3) The present invention takes the displacement response at the top of the pier of the continuous beam bridge as the comparison basis, and through the comparative analysis of the dynamic reliability of the structure under three working conditions of no control, state of taking compensation measures during fault, and state of no compensation measures during fault under random seismic action, it is concluded that the reliability of the continuous beam bridge decreases rapidly with the decrease of the set failure threshold. Under the same failure threshold index, the dynamic reliability of the semi-active control scheme considering fault tolerance is the highest. Description of the Drawings

[0034] Figure 1 It is the flow chart of the shock absorption control method for a long-span continuous bridge in the embodiment of the present invention.

[0035] Figure 2 It is the schematic diagram of the Bingham model in the embodiment of the present invention.

[0036] Figure 3 It is the schematic diagram of the Bouc-Wen model in the embodiment of the present invention.

[0037] Figure 4 It is the schematic diagram of the Spencer model in the embodiment of the present invention.

[0038] Figure 5 The time history of the displacement of 100 pier positions in the uncontrolled state under the 0.6g earthquake action in the embodiment of the present invention.

[0039] Figure 6 It is the statistical mean and statistical standard deviation of the displacement at the top of the continuous beam bridge pier under the 0.6g earthquake action in the embodiment of the present invention.

[0040] Figure 7It is a comparison chart of the statistical standard deviation of the pier top displacement of the continuous beam under the 0.6g earthquake action in the embodiment of the present invention.

[0041] Figure 8 It is the probability density surface of the typical time period (10s - 16s) in the embodiment of the present invention.

[0042] Figure 9 It is the probability density contour line of the typical time period (10s - 16s) in the embodiment of the present invention.

[0043] Figure 10 It is the seismic reliability curve of the long - span continuous beam bridge structure under different failure threshold indexes in the embodiment of the present invention; among them, (a) uncontrolled state; (b) actuator failure state; (c) fault - tolerant control state.

[0044] Figure 11 It is the change trend of the reliability with the failure threshold in the embodiment of the present invention. Specific Embodiment

[0045] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the concept of the present invention are within the scope of protection.

[0046] Embodiment 1:

[0047] The embodiment of the present invention provides a shock - absorption control method for a long - span continuous multi - span bridge, as Figure 1 shown, including the following steps:

[0048] S1. Construct a dynamic finite - element analysis model of the long - span continuous multi - span bridge, take the magnetorheological damper as the shock - absorption control device of the continuous bridge and construct a controller dynamic model, and jointly use them as the shock - absorption control system;

[0049] S2. For the shock - absorption control system, adopt a semi - active control scheme considering fault tolerance to control the output force of the continuous bridge;

[0050] S3. Conduct seismic reliability analysis on the continuous bridge structure under random seismic excitation, and determine the optimal output force control scheme to control the shock absorption of the continuous bridge.

[0051] In step S1 of the embodiment of the present invention, the basic idea of constructing the dynamic finite element analysis model is as follows: First, the continuous solution region of the structure is discretized into an assembly of finite elements connected together in a certain way; appropriate interpolation or displacement modes are selected within each element; the kinetic energy and strain energy of each element and the entire structure are calculated. Due to the complex structural form and constitutive relationship of the bridge, there are too many computational subdivision elements and the solution scale is large, which brings many inconveniences to the computational research. Bridges are usually slender structures. To simplify the computational difficulty and shorten the analysis time, the beam segment finite element method is used in this embodiment for the spatial dynamic calculation of the bridge structure. In this embodiment, according to the dynamic equilibrium equation of the continuous beam bridge structure, the element mass matrix, element stiffness matrix, and element damping matrix of each part of the bridge are first derived, and on this basis, the coordinate transformation matrix is further derived; therefore, the dynamic finite element analysis model in step S1 of this embodiment includes the upper structure model, lower structure model of the bridge, and the modeling and layout model of the bearings.

[0052] In step S1 of the embodiment of the present invention, the controller dynamic model constructed based on the magnetorheological damper includes a forward model and a reverse model. Based on the controller dynamic model, the magnetorheological damper controls the output force on the continuous bridge structure by adjusting the voltage.

[0053] In this embodiment, the forward model is the Bingham model, Bouc-Wen model, or Spencer model; among them, the Bingham model library is composed of a Coulomb friction element and a damping element in parallel, and its structure is as Figure 2 shown; the Bouc-Wen model is composed of a Bouc-Wen hysteresis loop, a damping element, and an elastic element in parallel, and its structure is as Figure 3 shown; the Spencer model is a further modification of the Bouc-Wen model, and its model structure is as Figure 4 shown. In this embodiment, it is preferred that the Bouc-Wen model improved by Spencer can more accurately reflect the mechanical characteristic effect of the damper and is more suitable for application in large-scale projects.

[0054] The reverse model in this embodiment is a reverse model trained based on the SSA-BP neural network, which is used to describe the relationship between the output damping force, the relative displacement and velocity of the internal piston, and the input electrical signal. The input layer, hidden layer, and output layer of the SSA-BP neural network are all 1 layer, and the input variables of the SSA-BP neural network are the input voltage U(t - 1) at the previous moment, the relative displacement x(t - 1) of the piston at the previous moment, the relative velocity of the piston at the previous moment the output force F(t - 1) at the previous moment, the relative displacement x(t) of the piston at the current moment, and the relative velocity of the piston at the current moment Output force F(t) at the current moment. Seven nodes are set in the input layer. The output variable is selected as: input voltage U(t) at the current moment. One node is set in the output layer. According to the number of nodes in the input layer and the output layer:

[0055]

[0056] In the formula, n is the number of nodes in the input layer, taking 7; m is the number of nodes in the output layer, taking 1; μ is a constant ranging from 1 to 10, and its value can be determined according to the debugging results. In this embodiment, q values from 2 to 13 are taken for experiments respectively. The transfer function in the hidden layer is set as the tangent sigmoid function tan-sig, and the transfer function in the output layer is set as the linear purelin function. The training algorithm uses the Levenberg-Marquardt algorithm trainlm with a relatively fast convergence speed. In order to prevent the problem of local minimum, the learning function uses the learngdm function.

[0057] In step S2 of the embodiment of the present invention, to prevent the continuous beam bridge structure from being damaged, a feasible method is to apply control measures to the structure to reduce its dynamic response under dynamic loads. The structural shock absorption control relies on the collaborative system composed of the control devices arranged at reasonable positions of the structure and the structure itself to jointly resist external excitations. Conducting shock absorption control on the continuous beam bridge structure can effectively improve the seismic capacity of the structure, which is an active and effective countermeasure in the field of engineering disaster prevention and mitigation. According to the relationship between the control system and the external input energy and the structural vibration feedback information, the shock absorption control of the structure can be divided into passive control, active control, and semi-active control.

[0058] In the semi-active control with fault tolerance adopted in this embodiment, the bridge faces a complex environment during actual operation. Therefore, in the practical application of MR dampers for seismic reduction control of continuous girder bridges, they are often affected by various external factors (such as changes in external temperature, sudden changes in loads caused by traffic or earthquakes, etc.) or various internal factors of the dampers (such as oil leakage in the cavity, precipitation or aggregation of magnetic particles, etc.). This may lead to failures of MR dampers. Fault-tolerant control refers to a type of control that can handle itself after a system failure and maintain stability and continuity within an acceptable range. After adding fault-tolerant consideration to the control system, the failure of one or more components within the system will not cause the entire system to collapse. The principle of fault-tolerant control is to isolate the faulty components and reconstruct the system based on hardware redundancy or software redundancy, thereby solving or alleviating the fault problem. Hardware redundancy uses parallel components with the same function as the faulty components to replace the original components to work; software redundancy analyzes the parsing relationship of the faulty components and reconstructs the system by calculating and generating signals. In fault-tolerant control strategies, generally both software redundancy and hardware redundancy are involved. For the seismic reduction control of long-span continuous girder bridges with large self-weights, a higher control output is required. The control system arranged at specific positions on the bridge needs multiple MR dampers to operate together to complete the output task. When some of the dampers are faulty, the remaining non-faulty dampers do not reach the output upper limit, which creates conditions for fault-tolerant control using the hardware redundancy of other non-faulty dampers.

[0059] Therefore, the semi-active control with fault tolerance means that after a system failure, the system can automatically adjust the parameters of the control device in a timely manner according to the dynamic response of the structure or the change of external loads, so that the system can maintain stability and continuity within an acceptable range of fault-tolerant control.

[0060] The expression of fault-tolerant control is:

[0061]

[0062] In the formula, f d is the adjustable semi-active control force of the damper, δ is the fault compensation coefficient, f dmax is the maximum value of the control force that the damper can output, is the step function, u is the active optimal control force, is the relative velocity of the damper piston, f dmin is the minimum value of the control force that the damper can output.

[0063] In order to facilitate the adoption of corresponding countermeasures after the MR damper fails, it is necessary to define the failure modes of the damper. A large deviation between the expected output and the actual output is the most typical failure manifestation of the MR damper. Generally speaking, the failure modes of the MR damper can be divided into three types: gain change failure, jamming failure, and deviation change failure. According to different failure modes, the failure model of the MR damper can be expressed in the following form:

[0064]

[0065] In the formula, f(t) is the actual output of the magnetorheological damper measured by the force sensor, is the expected output of the magnetorheological damper, a is the degree of gain failure, and b is the value of the deviation failure that occurs in the magnetorheological damper;

[0066] When a deviation change failure occurs, the value of a is 1, and the value of b represents the value of the deviation failure that occurs in the magnetorheological damper; when a gain change failure occurs, the value of b is 0, and the value of a ranges from 0 to 1, and the value of a characterizes the degree of gain failure; when a jamming failure occurs, the value of a is 0.

[0067] The output task of the control system is jointly completed by multiple MR dampers in the same control part. When some of the dampers suffer a complete gain loss failure due to a fault, the adjustable range of the total control force output by the control part where the faulty damper is located will be reduced. If the other normal dampers in this control part still input the corresponding voltage or current according to the calculated expected output at this time, the existence of the failed damper will cause the actual output to not meet the requirements of the calculated output, thereby affecting the structural shock absorption control effect. For a single damper with a gain change failure or a deviation change failure, if the failure is lower than a certain threshold and the ratio of the failed output force to the expected output force is small, it has little impact on the normal operation of the bridge. At this time, the faulty damper can still be regarded as a normal damper to participate in the work due to the small deviation. If the failure is higher than a certain threshold, it is considered that the damper has a failure fault, which may affect the normal operation of the bridge.

[0068] When the damper fails, the following failure model is established: Combining the actual engineering situation, the actual output f(t) of the damper is measured by the force sensor and compared with the expected output for comparison. The output range of the MR damper model used in this embodiment is 0 - 1000 KN after parameter amplification. Considering and at this time, it is considered that the magnetorheological damper has a failure fault. The failure factor μ of the i-th magnetorheological damper in a certain control part is introduced i ;

[0069]

[0070] The failure factor μ of each damper i is input into the fault-tolerant control section in the matrix form [μ1, μ2,..., μ i ,..., μ n , 1×n where n is the total number of magnetorheological dampers installed in this control section. This matrix can be regarded as the fault factor μ of the control section to which this failed magnetorheological damper belongs. When the i-th damper fails, the matrix form of the fault factor μ is [1, 1,..., 0,..., 1] 1×n . The expected output forces of each MR damper in the same control section are also assembled and represented in the form of a matrix: Assume that when a damper fails, the output force of the control section is u f (t), then u f (t) can be expressed as:

[0071]

[0072] The failed damper is isolated and no longer participates in the system control before its function is restored after maintenance.

[0073] The occurrence of a fault will make the traditional method of using MR dampers for vibration reduction control lose stability and fail to achieve the optimal vibration reduction purpose. In order to enable the bridge to still operate safely within a short time after a fault occurs, this embodiment adds the consideration of fault tolerance to the existing traditional semi-active control algorithm, and the output force of the non-failed dampers can be adjusted to compensate for the output force of the entire control section. The following formula expresses the relationship between the fault output force and the non-fault output force of the control section:

[0074] u f (t) = δu(t)

[0075] In the formula, u(t) is the total output force of the control section when the damper is fault-free. In the ideal case, that is, when all dampers are in normal state and the failure factor μ i are all 1, u(t) is equal to the actual output force u f (t) of the control section; δl is the fault gain coefficient, representing the ratio of the fault output force and the expected output force of the control section.

[0076] For the convenience of fault analysis of the damper, let the fault F a (t) = (1 - δ)u(t), then the actual output u f (t) of the fault control section is u(t) - F a (t). When there is a damper failure in the control section, the system control output is abnormal. The fault gain coefficient δ < 1, and at this time u f(t) The output force value of u(t) fails to reach the expected force value of the control system, so the performance of the control system will be affected to a certain extent.

[0077] Therefore, in the embodiment of the present invention, when using the semi-active control scheme considering fault tolerance to control the output of a continuous bridge, when a faulty magnetorheological damper is isolated, it will no longer participate in the system control before its repair and recovery function, and other non-faulty magnetorheological dampers at the same control part are adjusted to compensate for the output of the control part; wherein, the expression of the output compensation is:

[0078]

[0079] In the formula, is the output force after compensation at the next moment, δ is the fault gain coefficient, u(t + 1) is the expected output force when the system is normal, u f (t + 1) is the output force of the control part at the next moment, and μ is the failure factor of the magnetorheological damper, and μ is expressed as [μ1, μ2,..., μ i ,..., μ n 1×n , n is the total number of magnetorheological dampers installed at the control part, is the expected output force of each magnetorheological damper at the same control part,

[0080] The actual output damping force is compensated by other non-faulty dampers at the same control part, and the voltage or current input of the non-faulty damper is adjusted so that the output damping force after compensation at the next moment of the control system is equal to the expected damping force u(t + 1) when the system is normal, thereby eliminating the influence of the damper failure on the system performance.

[0081] Step S3 of step S3 in the embodiment of the present invention is specifically:

[0082] S3-1. Construct a random seismic physical model;

[0083] S3-2. Generate random seismic waves of the continuous bridge structure according to the random seismic physical model;

[0084] S3-3. Based on the generated random seismic waves, use the probability density evolution method to solve the random seismic response information of the continuous bridge structure, and obtain the probability density evolution information of the structural response quantity of the continuous bridge structure;

[0085] S3-4. Based on the probability density evolution information and combined with the absorbing boundary conditions, calculate the dynamic reliability of the continuous bridge structure under different output control schemes;

[0086] ​S3-5. Determine the optimal output control scheme based on the calculated dynamic possibility and perform shock absorption control on the continuous bridge.

[0087] In the random seismic motion physical model in step S3-1 of this embodiment, it is based on the peak acceleration A0, the dominant period T of the site soil, the damping ratio ξ of the site g and the dominant frequency domain ω of the site soil g , and is modeled by considering the earthquake source, the propagation path, and the site conditions. This random seismic motion physical model characterizes the physical essence of the randomness of the earthquake motion process and enables the basic physical quantities therein to be statistically analyzed and observed. Therefore, this model introducing random source parameters can probabilistically describe the generated earthquake motion samples. Different types of projects have different site conditions, and ξ g and ω g can also be determined through on-site testing to reduce the variation range of random seismic motion.

[0088] In this embodiment, under the earthquake action exceeding the fortification intensity of the structure itself, the safety of the continuous beam bridge structure will inevitably be more severely threatened. It is very important to evaluate whether the continuous beam bridge structure can remain safe in this case, that is, to conduct a reliability assessment on it. Due to the strong randomness of earthquake motion excitation, there is no way to accurately predict its spectrum, amplitude, and duration before an earthquake occurs. This situation will bring great difficulties to the reliability assessment of the continuous beam bridge structure. Considering the safety of the continuous beam bridge structure itself, the present invention proposes the concept of the reliability of the long-span continuous beam bridge structure under random earthquake excitation. Based on this, step S3-2 of the embodiment of the present invention is specifically as follows:

[0089] S32-1. Select a discrete representative point set by using the GF deviation method, assign values to the parameters of the random seismic motion physical model, and then generate earthquake acceleration time history samples with assigned probabilities;

[0090] S32-3. Based on the generated earthquake acceleration time history samples, perform earthquake motion excitation on the constructed dynamic finite element analysis model, and then input random seismic waves along the continuous bridge structure.

[0091] It should be noted that in the above process, the value orders of magnitude of the parameters in the sample space of the random variable parameters are not consistent, and this situation may lead to the error of "big numbers eating small numbers" when calculating the representative volume. Therefore, in order to avoid this error from generating errors, the probability space can be normalized first. The operation method is: Let Θ be the random variable to be investigated, and the mean and standard deviation of the random variable can be respectively expressed as μ Θ and σ Θ , and let:

[0092]

[0093] Wherein, is the normalized random variable. Random sampling is performed on it, and Θ can be obtained again by restoration according to the above formula.

[0094] In step S3-3 of the embodiment of the present invention, the finite difference method controlled by total variation is used to solve the probability density evolution information.

[0095] In embodiments S3-3 to S3-4 of the present invention, on the basis of the probability density evolution method to determine the probability density evolution theory, it is applied to the derivation of the semi-active control and shock absorption analysis method of the bridge structure considering fault tolerance. A series of deterministic analyses are performed on the structure through the point evolution method, and combined with the solution of the probability density evolution equation, so as to reflect the mechanism of the probability density evolution theory. Through numerical simulation, the random dynamic analysis problem is solved by combining the probability density evolution method and the system physical equation, and the probability density function of the key physical response quantity is obtained, and then the reliability of the structure under the absorption boundary condition is obtained.

[0096] Considering the randomness of ground motion, the motion equation of the dynamic system considering randomness is expressed as:

[0097]

[0098] Wherein, M and C are the mass and damping matrices respectively, f(·) and F(·) are the restoring force and the input earthquake vector respectively; Θ = (Θ1, Θ2,..., Θn) represents n random parameters in the system; and U(t) represent acceleration, velocity and displacement respectively.

[0099] Embodiment 2:

[0100] In this embodiment, the displacement at the top of the pier of the long-span continuous girder bridge is selected as the physical response quantity of interest for analysis, and the probability density evolution analysis and the corresponding reliability solution are carried out. After setting the shock-absorbing magnetorheological damper, the seismic resistance level of the bridge has been improved to a certain extent. In order to further test the seismic resistance level of the bridge and the effectiveness of the shock absorption scheme after the bridge encounters ground motion exceeding the seismic fortification intensity of the structure itself, the peak value of the random ground motion acceleration is set to 0.6g, and the random dynamic characteristics of the long-span continuous girder bridge structure are analyzed. In actual engineering, the complete probability distribution information of the structure, such as the probability distribution function of the response, receives more attention.

[0101] Analyze the second pier of the bridge, Figure 5 is the time history of the displacement at the top of the pier of the continuous girder bridge structure in the uncontrolled state under 100 random ground motions with an acceleration of 0.6g. Figures 6-7The statistical mean and statistical standard deviation of the displacement response at the top of the bridge pier are plotted. By comparing the statistical mean and statistical standard deviation in the same figure, it can be intuitively seen that the seismic response of the long-span continuous girder bridge structure has significant variability. The randomness of ground motion excitation can lead to a six-fold variability in structural response. Figure 8 and Figure 9 respectively present the surface plot and contour plot of the probability density of the displacement response at the top of the second pier of the long-span continuous girder bridge under the uncontrolled state evolving with time. These two figures can be vividly called the "mountain peak diagram" and the "river diagram", which extend and fluctuate randomly like mountain peaks and rivers respectively. Through the analysis of the continuous girder bridge structure using probability density evolution, rich probability information of the structural response can be obtained, which can be used to describe the fluctuation of the overall performance of the structure over time and can be more vividly and conveniently applied to the analysis and evaluation of the reliability of the structure.

[0102] Based on the probability density information of the dynamic response of the long-span continuous girder bridge structure obtained previously, on this basis, by applying the absorption boundary condition corresponding to the failure threshold, the dynamic reliability of the continuous girder bridge structure can be obtained through calculation.

[0103] In this embodiment, taking the main bridge of the Yellow River Extra-large Bridge on the Yangxin Expressway as an example of a bridge on expressways and first-class highways with a single-span span not exceeding 150 m and a seismic fortification category of Class B, the allowable displacement of the bridge pier can be calculated according to the following formula:

[0104]

[0105] θ u =L p (φ u -φ y ) / K ds

[0106] In the formula, θ u is the maximum allowable rotation angle, φ y is the equivalent yield curvature of the section (1 / cm), φ u is the curvature capacity at the ultimate failure state (1 / cm). For a bridge with a rectangular pier section, φ y and φ u are related to the section size, the yield strain of the steel bars, and the ultimate compressive strain of the confined concrete. L p is the equivalent plastic hinge length (cm), and K ds is the ductility safety factor, which can be taken as 2.0. Combining the section and material data of the Yellow River Extra-large Bridge on the Yangxin Expressway and calculating according to the specifications, the allowable displacement Δ uThe thresholds are taken as 0.08m, 0.07m, 0.06m, 0.05m, and 0.04m respectively. The corresponding dynamic reliability is calculated for each of the set different thresholds.

[0107] Table 1 gives the reliability of the long-span continuous beam bridge structure corresponding to each failure threshold index under different control schemes. The seismic reliability curves of the continuous beam bridge structure under each control scheme are as Figure 10 shown.

[0108] Table 1: Seismic reliability of continuous beam bridge structure under different control schemes and different failure thresholds

[0109]

[0110] Combined with Table 1 and Figure 10 it can be seen that as the failure threshold index decreases, the seismic reliability of the continuous beam bridge structure decreases step by step, showing great differences. Comparing the seismic reliability data of the continuous beam bridge structure with different failure thresholds under three working conditions. It can be seen that when the fault-tolerant control scheme is adopted, when the failure thresholds are set to 0.08m and 0.07m, the semi-active control scheme considering fault tolerance can maintain 100% dynamic reliability. It shows that when the earthquake action exceeds the fortification intensity of the continuous beam bridge structure itself, the semi-active control scheme considering fault tolerance can still keep the bridge running safely. Under the same failure threshold index, the dynamic reliability of the semi-active control scheme considering fault tolerance is the highest, followed by the control scheme where the actuator fails without taking corresponding measures, and the dynamic reliability in the uncontrolled state is the lowest.

[0111] Figure 11 Figure 20 shows the change trend of the dynamic reliability of the continuous beam bridge structure as the selected failure threshold decreases under three working conditions. It can be seen from the figure that as the failure threshold gradually decreases, the dynamic reliability of the continuous beam bridge under the three working conditions shows an accelerating downward trend. This is because under earthquake action, the time when the displacement at the top of the bridge pier is large or even exceeds the allowable maximum displacement still accounts for a small proportion in the whole earthquake process. The smaller the failure threshold is set, the greater the possibility that the displacement at the top of the bridge pier exceeds the failure threshold in the whole earthquake process, so the dynamic reliability decreases rapidly as the set failure threshold decreases. The downward trend of the dynamic reliability of the three working conditions is the most obvious in the uncontrolled state, and the downward trend of the semi-active control scheme considering fault tolerance is the slowest. When the actuator fails without taking corresponding measures, the dynamic reliability of the structure is always lower than that of the fault-tolerant control scheme. Through the analysis of the seismic reliability of the continuous beam bridge structure under the three working conditions, it shows that the semi-active control scheme considering fault tolerance can effectively control the continuous beam bridge and still achieve the expected control effect after some actuators fail.

[0112] In the description of the present invention, it should be understood that the orientation or positional relationship indicated by terms such as "center", "thickness", "upper", "lower", "horizontal", "top", "bottom", "inner", "outer", "radial", etc. is based on the orientation or positional relationship shown in the drawings. It is only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation. Therefore, it should not be construed as a limitation to the present invention. In addition, the terms "first", "second", and "third" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly specifying the number of technical features. Therefore, the features defined by "first", "second", and "third" may explicitly or implicitly include one or more of such features.

Claims

1. A shock absorption control method for a long-span continuous bridge with long spans, characterized in that, It includes the following steps: S1. Construct a dynamic finite element analysis model of a long-span continuous bridge, use a magnetorheological damper as a shock-absorbing control device for the continuous bridge and construct a controller dynamic model, and jointly use them as a shock-absorbing control system; S2. For the shock-absorbing control system, adopt a semi-active control scheme considering fault tolerance to control the output force of the continuous bridge; S3. Conduct seismic reliability analysis on the continuous bridge structure under random seismic excitation, and determine the optimal output force control scheme to control the shock absorption of the continuous bridge; In step S2, the semi-active control scheme considering fault tolerance means that after a system failure, the system can automatically adjust the parameters of the control device in a timely manner according to the dynamic response of the structure or the change of the external load, so that the system remains stable and continuous within an acceptable range. The expression of fault tolerance control is: where f d is the adjustable semi-active control force of the damper, δ is the fault compensation coefficient, and f dmax is the maximum value of the control force that the damper can output, is the step function, u is the active optimal control force, is the relative velocity of the damper piston, and f dmin is the minimum value of the control force that the damper can output, and u f is the output force of the control part; In step S2, when using the semi-active control scheme considering fault tolerance to control the output force of the continuous bridge, when a faulty magnetorheological damper is isolated, it will no longer participate in the system control before its repair and restoration of functions, and other non-faulty magnetorheological dampers at the same control part will be adjusted to compensate for the output force of the control part; Among them, the expression of output force compensation is: In the formula, is the output after compensation at the next moment, δ is the fault compensation coefficient, u(t + 1) is the expected output when the system is normal, and u f (t + 1) is the output force of the control part at the next moment, and μ is the failure factor of the magnetorheological damper, and μ is expressed as [μ1, μ2,..., μ i ,..., μ n 1×n , where n is the total number of magnetorheological dampers installed at the control part, is the expected output of each magnetorheological damper at the same control part, ​ 2. The shock absorption control method for a long-span continuous bridge with long spans as claimed in claim 1, wherein In step S1, the dynamic finite element analysis model includes the upper structure model, the lower structure model of the bridge, and the modeling and layout model of the bearings; The controller dynamic model includes a forward model and a reverse model. Based on the controller dynamic model, the magnetorheological damper controls the output force of the continuous bridge structure by adjusting the voltage.

3. The shock absorption control method for a long-span continuous bridge with long spans as claimed in claim 2, wherein The forward model is the Bingham model, the Bouc-Wen model or the Spencer model; The reverse model is a reverse model trained based on the SSA-BP neural network.

4. The shock absorption control method for a long-span continuous bridge with long joints according to claim 1, characterized in that Step S3 is specifically: S3-1. Construct a random earthquake physical model; S3-2. Generate random seismic waves of the continuous bridge structure according to the random earthquake physical model; S3-3. Based on the generated random seismic waves, use the probability density evolution method to solve the random seismic response information of the continuous bridge structure and obtain the probability density evolution information of the structural response quantity of the continuous bridge structure; S3-4. Based on the probability density evolution information and combined with the absorbing boundary conditions, calculate the dynamic reliability of the continuous bridge structure under different output force control schemes; S3-5. Based on the calculated dynamic reliability, determine the optimal output force control scheme to control the shock absorption of the continuous bridge.

5. The shock absorption control method for long-span continuous bridges with long spans as claimed in claim 4, wherein The random seismic physical model in the step S3-1 is formed by modeling according to the peak acceleration A0, the predominant period T of the site soil, the damping ratio ξ of the site g and the predominant frequency domain ω of the site soil g , and considering the earthquake source, the propagation path and the site conditions.

6. The shock absorption control method for a long-span continuous bridge with long spans as claimed in claim 5, wherein Step S3-2 is specifically: S32-1. Use the GF deviation method to select a discrete representative point set, assign values to the parameters of the random earthquake physical model, and then generate a sample of the seismic acceleration time history with the assigned probability; S32-3. Based on the generated sample of the seismic acceleration time history, conduct seismic excitation on the constructed dynamic finite element analysis model, and then input random seismic waves along the continuous bridge structure.

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