Floating floor vibration response determination method, medium and system

Abstract

The invention provides a floating floor vibration response determination method, medium and system, and belongs to the technical field of floating floor vibration response, and the method comprises the steps: firstly building a finite element model comprising a floating floor, an equipment foundation and a vibration isolator, and carrying out modal analysis to obtain initial vibration characteristics; afterwards, according to equipment parameter loading exciting force, dynamic responses of all the sub-models under different working conditions are obtained; secondly, optimizing model parameters by adopting an orthogonal experimental method, and obtaining frequency spectrum characteristics of three vibration time sequences through short-time Fourier transform; based on spectral analysis, a preliminary building floor vibration response differential equation is established. And finally, in combination with actually measured vibration data, continuously adjusting equation parameters by utilizing an optimization algorithm to obtain an optimized vibration response equation set matched with an actual measurement result, and taking the optimized vibration response equation set as a final building floor vibration response prediction model. The problem that the prior art mainly depends on a simplified model and an empirical formula and is difficult to accurately reflect the actual vibration characteristics of a complex building structure is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of vibration response of floating floors, and in particular, relates to a method, medium and system for determining the vibration response of floating floors. Background Art

[0002] With the acceleration of urbanization and the improvement of people's living standards, the requirements for building comfort are increasing, especially for high-end residential buildings, office buildings and other buildings. Higher standards are put forward for vibration and noise control. In modern buildings, the widespread use of various power equipment such as elevators, water pumps, air conditioning systems, etc. inevitably generates vibrations, which are transmitted through the building structure, not only affecting the living comfort, but also endangering the safety of the building structure. A notable feature of power equipment vibration is its low frequency and long-distance transmission. This vibration is usually transmitted to the building structure through the bottom support of the equipment, and then spreads throughout the building. Traditional vibration control methods, such as the use of rubber vibration damping pads, are often unsatisfactory in dealing with such low-frequency vibrations, especially in super-high-rise buildings. To meet this challenge, floating floor technology came into being. This technology sets an isolation layer between the floor and the main structure to effectively block the vibration transmission. At present, the spring-damped floating floor system is widely used in high-end construction projects, which has better low-frequency vibration isolation effect than traditional rubber vibration damping pads.

[0003] However, the design and implementation of floating floor systems face great challenges. First, the dynamic characteristics of buildings are complex and are affected by many factors, such as structural type, material properties, and load conditions. Second, the operating characteristics of power equipment are diverse, and the frequency and amplitude of the vibration source may change over time. Furthermore, the nonlinear characteristics of the vibration isolation system itself increase the difficulty of predicting the vibration response.

[0004] Existing vibration analysis methods for floating floors mainly rely on simplified models and empirical formulas, which are difficult to accurately reflect the actual vibration characteristics of complex building structures. Although the finite element analysis method is widely used in structural dynamics analysis, there are still problems with model accuracy and computational efficiency when dealing with complex vibration isolation systems such as floating floors. In addition, existing methods often ignore the uncertainty factors in actual engineering, resulting in significant differences between theoretical predictions and actual conditions.

[0005] Therefore, there is an urgent need for a floating floor vibration response analysis method that can comprehensively consider the building structure characteristics, equipment vibration characteristics and vibration isolation system performance. This method should be able to accurately predict the vibration response of floating floors under various working conditions and provide a reliable theoretical basis for the design optimization and vibration control of floating floors. Summary of the invention

[0006] In view of this, the present invention provides a method, medium and system for determining the vibration response of a floating floor, which can solve the technical problem that the existing floating floor vibration analysis method mainly relies on simplified models and empirical formulas and is difficult to accurately reflect the actual vibration characteristics of complex building structures.

[0007] The present invention is achieved in that:

[0008] A first aspect of the present invention provides a method for determining the vibration response of a floating floor, comprising the following steps:

[0009] S10, establishing a 1:1 finite element model of the building, including three sub-models, namely a floating floor model, an equipment foundation model and a vibration isolator model;

[0010] S20, performing modal analysis on the finite element model of the building, obtaining vibration time series parameters of the three sub-models and recording them as first vibration time series parameters,

[0011] S30, based on the power equipment parameters in the building design blueprint, load the exciting force and exciting frequency, obtain the dynamic response of each model under different working conditions, and obtain the vibration timing parameters of the three sub-models as the second vibration timing parameters;

[0012] S40, using an orthogonal experimental method to adjust the determining factors in the finite element model of the building to perform vibration simulation, and obtaining vibration timing parameters of the three sub-models as third vibration timing parameters;

[0013] S50, performing short-time Fourier transform on the first vibration timing parameter, the second vibration timing parameter and the third vibration timing parameter respectively to obtain a first vibration spectrum, a second vibration spectrum and a third vibration spectrum;

[0014] S60, respectively decomposing the first vibration spectrum, the second vibration spectrum, and the third vibration spectrum, and combining them to obtain a preliminary differential equation group of the vibration response of the floor slab;

[0015] S70, based on the preliminary differential equation group of the vibration response of the floor slab, establish a vibration response matrix equation, determine the initial values ​​of the parameters of the vibration response matrix equation, and use the floating floor slab vibration test bench to perform actual vibration testing and data collection to obtain measured vibration response data;

[0016] S80, comparing and analyzing the measured vibration response data with the theoretical vibration response data calculated by the vibration response matrix equation, constructing an objective function as the mean square error between the measured vibration response data and the theoretical vibration response data, and optimizing and adjusting the vibration response matrix equation parameters based on the objective function;

[0017] S90. Iteratively optimize the parameters of the vibration response matrix equation using the objective function until a preset convergence condition is met or a maximum number of iterations is reached, thereby obtaining an optimized set of floor slab vibration response equations as a final floor slab vibration response.

[0018] Specifically, the step S10 specifically includes: first, according to the actual building design blueprint, a 1:1 scale finite element model is established. The finite element model consists of three sub-models, namely a floating floor model, an equipment foundation model and an isolator model. The floating floor model mainly includes components such as the floor body, edge constraints and internal support structure. The parameter dimensions and material properties of these components need to be accurately modeled according to the actual design situation. At the same time, the equipment foundation model and the isolator model must also be established according to the actual installation position and parameters. Through the establishment of such a detailed finite element model, the vibration response characteristics of the entire building can be fully reflected.

[0019] The specific steps of step S20 include: performing modal analysis on the finite element model established above to obtain the vibration time series parameters of the three sub-models, namely the floating floor model, the equipment foundation model and the vibration isolator model, which are recorded as the first vibration time series parameters. These parameters include: frequency, vibration mode, displacement amplitude and acceleration response, etc. The modal analysis can be used to understand the inherent vibration characteristics of each sub-model, laying the foundation for the subsequent dynamic response analysis.

[0020] The specific steps of step S30 include: applying corresponding dynamic loads on the finite element model according to the power equipment parameters provided in the building design blueprint, such as the magnitude of the exciting force and the exciting frequency, and obtaining the dynamic response parameters of the three sub-models under different working conditions, which are recorded as the second vibration timing parameters. The main purpose of this step is to simulate the dynamic response characteristics of each sub-model under actual working conditions and provide a reference for subsequent optimization.

[0021] The specific steps of step S40 include: using the orthogonal experimental method to optimize the parameters of the key factors in the finite element model, and these key factors include: the thickness of the floating floor, the size of the equipment foundation, and the number, stiffness and position of the vibration isolators. Through the orthogonal experimental design, the values ​​of these factors are systematically adjusted, and the corresponding vibration timing parameters of the three sub-models are recorded, which are recorded as the third vibration timing parameters. The orthogonal experimental method can effectively reduce the number of experiments and obtain the influence of each factor on the vibration response.

[0022] The specific steps of step S50 include: respectively analyzing the three groups of vibration time series parameters obtained in steps S20, S30 and S40, namely the first vibration time series parameter, the second vibration time series parameter and the third vibration time series parameter, using short-time Fourier transform to obtain the corresponding first vibration spectrum, second vibration spectrum and third vibration spectrum. Short-time Fourier transform can effectively capture the time-frequency characteristics of non-stationary vibration signals and provide a basis for subsequent vibration response modeling.

[0023] The specific steps of step S60 include: decomposing and analyzing the above three groups of vibration spectra to establish a preliminary differential equation group describing the vibration response of the floating floor. This differential equation group considers the vibration response on the three coordinate axes of the horizontal x direction, the horizontal y direction and the vertical z direction. The preliminary differential equation group of the vibration response of the floating floor is specifically expressed as follows:

[0024]

[0025]

[0026]

[0027] Where u, v, w represent the displacement in the horizontal x direction, horizontal y direction and vertical z direction respectively; t is time; ζ is the damping ratio; ω n is the natural frequency; m is the mass; F(t), G(t), H(t) are the external excitation forces in the x, y, and z directions respectively; α i , β i , γ i is the coefficient to be determined; N is the number of spatial discrete points considered; ε u , ε v , ε w These differential equations describe the vibration response of the floating floor in three coordinate directions, laying the foundation for the subsequent matrix equation establishment.

[0028] The specific steps of step S70 include: based on the above preliminary differential equations, establishing a matrix equation form describing the vibration response of the floating floor, and determining the initial value of each parameter. The vibration response matrix equation is specifically expressed as follows:

[0029]

[0030] Where M is the mass matrix; C is the damping matrix; K is the stiffness matrix; U is the displacement vector; F(t) is the external excitation force vector; and E is the error vector.

[0031] In order to obtain the measured vibration response data, a floating floor vibration test bench is used in this step. The test bench includes a steel structure platform, a vibration isolator, a floating floor, an automatic vibration source walking device, and a distributed optical fiber sensing system. The floating floor is placed on the steel structure platform through the vibration isolator, and the floating floor is raised and lowered by a hydraulic lift to facilitate the replacement of the vibration isolator model and quantity; the vibration source is placed on the floating floor, and the automatic walking device is used to realize the rapid replacement of the vibration source type and the infinite adjustment of the vibration source position. The actual vibration test is carried out through the test bench, and the corresponding vibration response data is collected.

[0032] The specific implementation method of step S80 is: using the Levenberg-Marquardt algorithm to compare and analyze the above-mentioned measured vibration response data and the results calculated by the theoretical vibration response matrix equation, and constructing an objective function as the mean square error between the measured data and the theoretical data. Based on this objective function, the parameters of the vibration response matrix equation are optimized and adjusted until the preset convergence conditions are met or the maximum number of iterations is reached. The Levenberg-Marquardt algorithm is a nonlinear optimization algorithm that can continuously approach the best fit between the theoretical model and the measured data through iterative optimization.

[0033] The specific implementation of step S90 is: using the objective function obtained by the above optimization, the parameters of the vibration response matrix equation are finally optimized until the preset convergence conditions are met. The optimized matrix equation is the final floating floor vibration response equation group, which can be used to predict and analyze the vibration response characteristics of the floating floor under actual working conditions. The specific objective function expression is as follows:

[0034]

[0035] Where J(θ) is the objective function; θ is the parameter vector to be optimized; N is the number of sampling points; U m (t i ) is the measured displacement vector at the i-th moment; U c (t i , θ) is the calculated displacement vector at the i-th moment; λ is the regularization parameter; M is the total number of parameters.

[0036] The parameter acquisition method is as follows:

[0037] 1) ζ and ω n :obtained by frequency domain analysis of the measured vibration signal. The steps include: (1) Fourier transform of the time domain signal; (2) identification of the peak frequency f p and half-power bandwidth Δf; (3) Calculate ω n =2πf p and ζ=Δf / (2f p ).

[0038] 2) m: obtained by weighing or calculation based on structural design parameters.

[0039] 3) F(t), G(t), H(t): obtained by real-time measurement by force sensor.

[0040] 4) α i , β i , γ i : The initial value can be estimated through finite element analysis and subsequently adjusted through optimization algorithms.

[0041] 5) M, C, K: initial values ​​are obtained through finite element analysis and subsequently optimized through system identification methods.

[0042] 6) U m (t i ): The acceleration is measured by an accelerometer, and then double integration is performed to obtain the displacement.

[0043] 7)λ: The optimal value is determined by cross-validation method.

[0044] On the basis of the above technical solution, the method for determining the vibration response of a floating floor of the present invention can also be improved as follows:

[0045] The components of the floating floor model include a floor body, edge constraints, and an internal support structure.

[0046] The vibration timing parameters include frequency, vibration mode, displacement amplitude, and acceleration response.

[0047] The determining factors include the thickness of the floating floor, the size of the equipment foundation, and the number, stiffness and position of the vibration isolators.

[0048] The preliminary differential equation group of the floor slab vibration response considers the vibration response in the horizontal x direction, the horizontal y direction and the vertical z direction.

[0049] The floating floor vibration test bench comprises a steel structure platform, a vibration isolator, a floating floor, a vibration source automatic walking device and a distributed optical fiber sensing system.

[0050] The method used for comparing and analyzing the measured vibration response data with the theoretical vibration response data calculated by the vibration response matrix equation is the Levenberg-Marquardt algorithm.

[0051] Furthermore, the maximum number of iterations is 200; and the preset convergence condition is that the similarity between two adjacent iteration results is greater than 96%.

[0052] A second aspect of the present invention provides a computer-readable storage medium, wherein the computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the above-mentioned method for determining the vibration response of a floating floor.

[0053] A third aspect of the present invention provides a floating floor vibration response determination system, which includes the above-mentioned computer-readable storage medium.

[0054] Compared with the prior art, the method, medium and system for determining the vibration response of a floating floor provided by the present invention have the following beneficial effects:

[0055] First, this method establishes a complete 1:1 building finite element model including floating floors, equipment foundations and vibration isolators, overcoming the limitation of traditional simplified models that cannot fully reflect the characteristics of complex structures. This comprehensive model setting provides a solid foundation for subsequent analysis and ensures the comprehensiveness and accuracy of vibration response prediction.

[0056] Secondly, by performing modal analysis on the finite element model of the building and loading the excitation force based on the power equipment parameters in the design blueprint, this method can obtain the dynamic response of each sub-model under different working conditions. This method not only takes into account the inherent characteristics of the building structure, but also incorporates the influence of actual operating conditions, greatly improving the practicality and reliability of vibration response prediction.

[0057] Third, the orthogonal experimental method is used to adjust the determining factors in the model for vibration simulation, which effectively solves the problem that traditional methods are difficult to deal with the influence of multi-parameter coupling. This method can systematically evaluate the impact of various factors on vibration response and provide a scientific basis for subsequent parameter optimization.

[0058] Fourth, by performing short-time Fourier transform and decomposition on the vibration time series parameters from different sources, this method constructs a more comprehensive and accurate set of preliminary differential equations for vibration response. This method can capture subtle changes in vibration response and lays the foundation for subsequent accurate modeling.

[0059] Fifth, the floating floor vibration test bench was used to conduct actual vibration testing and data collection, and the measured data was compared and analyzed with the theoretical calculation results, and an optimization model with mean square error as the objective function was constructed. This method of combining theory with practice effectively overcomes the defect that pure theoretical analysis may ignore actual engineering factors, and significantly improves the accuracy of vibration response prediction.

[0060] Finally, by iteratively optimizing the parameters of the vibration response matrix equation until the preset convergence condition is met or the maximum number of iterations is reached, this method finally obtains a highly optimized floating floor vibration response equation set. This optimization process not only improves the accuracy of the model, but also enhances the adaptability of the method, enabling it to cope with different types of building and equipment vibration problems.

[0061] In summary, the solution of the present invention solves the technical problem that the existing floating floor vibration analysis method mainly relies on simplified models and empirical formulas, and is difficult to accurately reflect the actual vibration characteristics of complex building structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0062] Figure 1 A flow chart of the method provided by the present invention;

[0063] Figure 2 This is a schematic diagram of the steel structure platform;

[0064] Figure 3 This is a schematic diagram of a floating floor;

[0065] Figure 4 Schematic diagram of the experimental platform;

[0066] Figure 5 This is the analysis diagram of the dynamic model of floating floor;

[0067] Figure 6 This is a diagram showing the longitudinal propagation of the vibration of the floating plate under the load of a single water pump;

[0068] Figure 7 This is a comparison chart of the vibration peak values ​​of the floating slab under the operation of multiple water pumps;

[0069] Figure 8 This is a diagram showing the effect of the increase in foundation mass on the vibration of the floating slab;

[0070] Fig. 9 This is the vibration diagram of the floating plate under the change of thickness;

[0071] Fig.10 It is the vibration amplitude curve diagram under the change of the stiffness of the floating plate isolator;

[0072] Fig.11 It is the curve diagram of vibration amplitude and main frequency changing with the stiffness of floating plate vibration isolator;

[0073] Fig.12 This is a diagram showing the longitudinal propagation of the floating plate vibration under the single water pump load after the frequency design is changed. DETAILED DESCRIPTION

[0074] In order to make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0075] like Figure 1 FIG. 1 is a flow chart of a method for determining a vibration response of a floating floor provided by the present invention. The method comprises the following steps:

[0076] S10, establishing a 1:1 finite element model of the building, including three sub-models, namely a floating floor model, an equipment foundation model and a vibration isolator model;

[0077] S20, performing modal analysis on the finite element model of the building, obtaining vibration time series parameters of the three sub-models and recording them as first vibration time series parameters,

[0078] S30, based on the power equipment parameters in the building design blueprint, load the exciting force and exciting frequency, obtain the dynamic response of each model under different working conditions, and obtain the vibration timing parameters of the three sub-models as the second vibration timing parameters;

[0079] S40, using an orthogonal experimental method to adjust the determining factors in the finite element model of the building to perform vibration simulation, and obtaining vibration timing parameters of the three sub-models as third vibration timing parameters;

[0080] S50, performing short-time Fourier transform on the first vibration timing parameter, the second vibration timing parameter and the third vibration timing parameter respectively to obtain a first vibration spectrum, a second vibration spectrum and a third vibration spectrum;

[0081] S60, respectively decomposing the first vibration spectrum, the second vibration spectrum, and the third vibration spectrum, and combining them to obtain a preliminary differential equation group of the vibration response of the floor slab;

[0082] S70, based on the preliminary differential equations of the vibration response of the floor slab, establish a vibration response matrix equation, determine the initial values ​​of the parameters of the vibration response matrix equation, use the floating floor slab vibration test bench to perform actual vibration testing and data collection, and obtain measured vibration response data;

[0083] S80, comparing and analyzing the measured vibration response data with the theoretical vibration response data calculated by the vibration response matrix equation, constructing an objective function as the mean square error between the measured vibration response data and the theoretical vibration response data, and optimizing and adjusting the vibration response matrix equation parameters based on the objective function;

[0084] S90, iteratively optimizing the parameters of the vibration response matrix equation using the objective function until a preset convergence condition is met or a maximum number of iterations is reached, thereby obtaining an optimized set of floor slab vibration response equations as a final floor slab vibration response.

[0085] The specific implementation methods of the above steps are described in detail below:

[0086] The specific implementation of step S10 is as follows:

[0087] First, it is necessary to establish a 1:1 scale finite element model based on the actual building design blueprint. The finite element model consists of three sub-models, namely the floating floor model, the equipment foundation model and the vibration isolator model. The floating floor model mainly includes components such as the floor body, edge constraints and internal support structures. The parameter dimensions and material properties of these components need to be accurately modeled according to the actual design situation. For the floating floor model, its dynamic equation can be expressed as:

[0088]

[0089] In the formula, M b is the mass matrix of the floating floor; C b is the damping matrix of the floating floor; K b is the stiffness matrix of the floating floor; U b is the displacement vector of the floating floor; F b is the external excitation force vector acting on the floating floor. The construction of these parameter matrices requires finite element modeling and calculation based on the specific geometric dimensions, material properties and boundary conditions of the floating floor.

[0090] Similarly, the dynamic equation of the equipment basic model can be expressed as:

[0091]

[0092] In the formula, M f is the mass matrix of the equipment foundation; C f is the damping matrix of the equipment foundation; K f is the stiffness matrix of the equipment foundation; U f is the displacement vector of the device base; F f is the external excitation force vector acting on the equipment foundation.

[0093] The dynamic equation of the vibration isolator model can be expressed as:

[0094]

[0095] In the formula, M i is the mass matrix of the isolator; C i is the damping matrix of the isolator; K i is the stiffness matrix of the isolator; U i is the displacement vector of the isolator; F i is the external excitation force vector acting on the isolator.

[0096] Through the establishment of this detailed finite element model, the overall vibration response characteristics of the building can be fully reflected.

[0097] The specific implementation of step S20 is as follows:

[0098] Modal analysis is performed on the finite element model established above to obtain the vibration time series parameters of the three sub-models, namely the floating floor model, the equipment foundation model and the vibration isolator model, which are recorded as the first vibration time series parameters. These parameters include: frequency, vibration mode, displacement amplitude and acceleration response.

[0099] For the floating floor model, its natural vibration frequency ω b,n and the natural vibration mode Φ b,n It can be obtained by solving the eigenvalue problem:

[0100]

[0101] In the formula, n is the modal number. Similarly, the natural vibration parameters of the equipment foundation model and the vibration isolator model can be obtained.

[0102] Modal analysis can be used to understand the inherent vibration characteristics of each sub-model, laying the foundation for subsequent dynamic response analysis.

[0103] The specific implementation of step S30 is as follows:

[0104] According to the power equipment parameters provided in the building design blueprint, such as the magnitude of the exciting force F b (t), F f (t), F i (t) and excitation frequency ω f Etc., apply corresponding dynamic loads on the finite element model, and obtain the dynamic response parameters of the three sub-models under different working conditions, which are recorded as the second vibration time series parameters.

[0105] For the floating floor model, its dynamic response can be expressed as:

[0106]

[0107] Similarly, the response equations of the equipment foundation model and the vibration isolator model under dynamic loads can be obtained.

[0108] The main purpose of this step is to simulate the dynamic response characteristics of each sub-model under actual working conditions and provide a reference for subsequent optimization.

[0109] The specific implementation of step S40 is as follows:

[0110] The orthogonal experimental method is used to optimize the parameters of the key factors in the finite element model. These key factors include: the thickness of the floating floor t b 、Equipment basic size l f × f ×h f and the number of isolators n i , stiffness k i and position x i wait.

[0111] The experimental factors and levels of the orthogonal experimental design are shown in Table 1 below:

[0112] Table 1 Orthogonal experimental design table

[0113] factor Level 1 Level 2 Level 3 <![CDATA[t b (mm)]]> 100 120 140 <![CDATA[l f (m)]]> 2 3 4 <![CDATA[w f (m)]]> 2 3 4 <![CDATA[h f (m)]]> 0.5 0.8 1.0 <![CDATA[n i ]]> 4 6 8 <![CDATA[k i (kN / m)]]> 100 150 200 <![CDATA[x i ]]> corner Central Edge

[0114] Through orthogonal experimental design, the values ​​of these factors are systematically adjusted, and the corresponding three sub-model vibration timing parameters are recorded, which are recorded as the third vibration timing parameters.

[0115] The response function of the orthogonal experiment can be expressed as:

[0116] Y=f(t b , l f , w f ,h f , n i , k i , x i );

[0117] Where Y is the vibration timing parameter of the three sub-models.

[0118] By performing variance analysis on the orthogonal test results, the contribution of each factor to the response function can be obtained, thereby determining the influence of key factors on vibration response.

[0119] The specific implementation of step S50 is as follows:

[0120] The three groups of vibration timing parameters obtained in steps S20, S30 and S40, i.e., the first vibration timing parameter Y1, the second vibration timing parameter Y2 and the third vibration timing parameter Y3, are respectively analyzed in the frequency domain using short-time Fourier transform to obtain the corresponding first vibration spectrum H1(ω), the second vibration spectrum H2(ω) and the third vibration spectrum H3(ω).

[0121] The expression of short-time Fourier transform is:

[0122]

[0123] Where ω(t) is the windowing function, such as the Hamming window.

[0124] Short-time Fourier transform can effectively capture the time-frequency characteristics of non-stationary vibration signals and provide a basis for subsequent vibration response modeling.

[0125] The specific implementation of step S60 is as follows:

[0126] The above three groups of vibration spectra are decomposed and analyzed to establish a preliminary differential equation group describing the vibration response of the floating floor. This differential equation group considers the vibration response in the three coordinate axes of the horizontal x direction, the horizontal y direction and the vertical z direction. The specific differential equation form is as follows:

[0127]

[0128]

[0129]

[0130] Where u, v, w represent the displacement in the horizontal x direction, horizontal y direction, and vertical z direction, respectively; t is time; ζ is the damping ratio; ω n is the natural frequency; m is the mass; F(t), G(t), H(t) are the external excitation forces in the x, y, and z directions respectively; α i , β i , γ i is the coefficient to be determined; N is the number of spatial discrete points considered; ε u , ε v , ε w is the error term.

[0131] These differential equations describe the vibration response of the floating floor in three coordinate directions, laying the foundation for the subsequent establishment of matrix equations.

[0132] The specific implementation of step S70 is as follows:

[0133] Based on the above preliminary differential equations, a matrix equation describing the vibration response of the floating floor is established, and the initial values ​​of each parameter are determined. The matrix equation form is as follows:

[0134]

[0135] Among them, M is the mass matrix; C is the damping matrix; K is the stiffness matrix; U is the displacement vector; F(t) is the external excitation force vector; and E is the error vector.

[0136] The initial values ​​of these parameters can be estimated by:

[0137] 1) ζ and ω n :It is obtained by frequency domain analysis of the measured vibration signal. The steps include:

[0138] (1) Perform Fourier transform on the time domain signal;

[0139] (2) Identify the peak frequency f p and half-power bandwidth Δf;

[0140] (3) Calculation of ω n =2πf p and ζ=Δf / (2f p ).

[0141] 2) m: obtained by weighing or calculation based on structural design parameters.

[0142] 3) F(t): obtained by real-time measurement by force sensor.

[0143] 4) α i , β i , γ i : The initial value can be estimated through finite element analysis and subsequently adjusted through optimization algorithms.

[0144] 5) M, C, K: Initial values ​​are obtained through finite element analysis and subsequently optimized through system identification methods.

[0145] In order to obtain the measured vibration response data, this method uses a floating floor vibration test bench, which includes a steel structure platform, vibration isolators, floating floors, vibration source automatic walking devices and distributed optical fiber sensing systems, etc. Actual vibration tests are carried out through the test bench, and the corresponding vibration response data are collected.

[0146] The specific implementation of step S80 is as follows:

[0147] The Levenberg-Marquardt algorithm is used to compare and analyze the above measured vibration response data U m (t) and the result U calculated by the theoretical vibration response matrix equation c (t,θ), the objective function is constructed as the mean square error between the measured data and the theoretical data:

[0148]

[0149] Where J(θ) is the objective function; θ is the parameter vector to be optimized, including M, C, K and α i , β i , γ i etc.; N is the number of sampling points; λ is the regularization parameter; M is the total number of parameters.

[0150] The Levenberg-Marquardt algorithm is a nonlinear optimization algorithm that can continuously approach the best fit between the theoretical model and the measured data through iterative optimization.

[0151] The specific implementation of step S90 is as follows:

[0152] The objective function J(θ) obtained by the above optimization is used to finally optimize the parameters of the vibration response matrix equation until the preset convergence conditions are met. The optimized matrix equation is the final floating floor vibration response equation group, which can be used to predict and analyze the vibration response characteristics of the floating floor under actual working conditions.

[0153] In summary, the present invention proposes a method for determining the vibration response of a floating floor based on finite element analysis, orthogonal test and system identification. The method establishes a detailed finite element model, systematically considers the vibration characteristics of each subsystem, and optimizes and fits the measured vibration response data to finally obtain an accurate vibration response model of a floating floor. Specifically, the principle of the present invention is:

[0154] First, the establishment of a 1:1 finite element model of the building is the basis of this method. This full-scale model can accurately reflect the geometric characteristics and material properties of the building, avoiding the errors that may be caused by simplifying the model. Dividing the model into three sub-models: floating floor, equipment foundation, and vibration isolator, not only conforms to the structural characteristics of the actual project, but also facilitates subsequent analysis and optimization. This refined modeling method provides a high-precision data foundation for subsequent vibration analysis.

[0155] Secondly, modal analysis of the finite element model of the building can obtain the natural frequency and vibration mode of the structure. These parameters reflect the basic dynamic characteristics of the structure and are the key to predicting the response of the structure under external forces. By combining these basic characteristics with actual equipment parameters, the vibration behavior of the structure under actual working conditions can be simulated more accurately. This method not only takes into account the characteristics of the structure itself, but also incorporates the influence of external excitation, making the analysis results closer to reality.

[0156] Third, the use of orthogonal experimental method to adjust the determining factors in the model is a major innovation of this method. The orthogonal experimental method can systematically study the impact of multiple factors on the results within a small number of tests. In a complex floating floor system, there are many factors that affect the vibration response, such as floor thickness, vibration isolator stiffness, damping ratio, etc. Through the orthogonal experimental method, the degree of influence of each factor can be efficiently determined, providing guidance for subsequent parameter optimization.

[0157] Fourth, the short-time Fourier transform of the vibration time series parameters is a key step in this method. Short-time Fourier transform can analyze signals in both the time domain and the frequency domain, and is particularly suitable for processing non-stationary vibration signals. Through this transformation, the spectral characteristics of the vibration signal in different time periods can be obtained, thereby more comprehensively describing the time-varying characteristics of the vibration response.

[0158] Fifth, establishing the vibration response matrix equation is an important step in converting discrete analysis results into continuous mathematical models. The matrix equation can efficiently handle multi-degree-of-freedom systems and is suitable for describing complex floating floor vibration problems. Through the matrix equation, parameter sensitivity analysis and optimization calculation can be easily performed.

[0159] Sixth, the actual measurement using the floating floor vibration test bench is an important means of verifying this method. The measured data can reflect various uncertainties in actual engineering, such as material nonlinearity, structural damping, etc. Comparing the measured data with the theoretical calculation results can not only verify the accuracy of the model, but also find possible deviations in the theoretical model.

[0160] Finally, the key to achieving high-precision prediction in this method is to construct an objective function and perform iterative optimization. Taking the mean square error between the measured data and the theoretical calculation results as the objective function, the influence of various error sources can be comprehensively considered. Through iterative optimization, the model parameters are continuously adjusted until the preset accuracy requirements are met, and finally a highly optimized vibration response equation group is obtained.

[0161] This method is logical because it follows the scientific research process from modeling, analysis, experiment to optimization. Each step is based on the previous step, and the accuracy of the model is continuously improved through experimental verification and data optimization. At the same time, this method comprehensively uses multidisciplinary knowledge such as finite element analysis, signal processing, experimental mechanics and optimization algorithms, reflecting the idea of ​​system science. Through the organic combination of theoretical analysis and experimental verification, the limitations of a single method are overcome, and the reliability and applicability of vibration response prediction are improved.

[0162] In order to better understand and implement the present invention, a specific embodiment 1 of the floating floor vibration test bench involved in the present invention is provided below: The floating floor vibration response determination method proposed in the present invention needs to rely on corresponding experimental devices to perform vibration response testing and data collection. Therefore, a floating floor vibration test bench is designed, and its main components are as follows:

[0163] 1.Steel structure platform

[0164] like Figure 2 As shown, the test bench uses a steel frame structure as the base to provide stable support. The steel platform has a size of 5m×5m×1m and is made of Q345 steel, which has high rigidity and strength.

[0165] 2. Vibration isolator

[0166] Several vibration isolators are installed on the steel platform to support the floating floor. The vibration isolator model is XW-150, made of high damping rubber material, with a longitudinal stiffness of 150kN / m and a damping ratio of 0.15. The vibration isolators are arranged at the corners and middle of the steel platform, and the number can be adjusted according to actual needs.

[0167] 3. Floating floor

[0168] like Figure 3 As shown in the figure, the floating floor is made of concrete and has a size of 4m×4m×0.2m. The floor is placed on a steel platform through vibration isolators to form a floating structure. The boundary condition of the floating floor is simply supported.

[0169] 4. Distributed fiber optic sensing system

[0170] In order to comprehensively collect the vibration response data of the floating floor at different positions, the experimental platform is equipped with a distributed fiber optic sensing system. The system includes several fiber optic sensing points arranged at key positions of the floating floor, which can synchronously measure the vibration displacement, velocity, acceleration and other response parameters at different positions.

[0171] 5. Vibration source automatic walking device

[0172] like Figure 4 As shown, the experimental table is equipped with a vibration source automatic walking device, which can be infinitely adjusted on the surface of the floating floor. The device is driven by an electric slide, with a maximum stroke of 4m and a positioning accuracy of ±1mm. The vibration source type can be an electromagnetic vibrator with a maximum exciting force of 5kN.

[0173] The experimental steps are as follows:

[0174] 1. Adjust the number, position and stiffness parameters of the isolators to form different floating floor support schemes.

[0175] 2. Vibration excitation is applied to different positions on the surface of the floating floor through the vibration source automatic walking device, and the amplitude and frequency of the excitation force are adjustable.

[0176] 3. The distributed fiber optic sensing system synchronously collects vibration response data at various locations of the floating floor, including displacement, velocity and acceleration.

[0177] 4. Post-process and analyze the collected vibration response data to obtain the vibration characteristics of the floating floor under different support and excitation conditions.

[0178] 5. Based on the measured data, combined with the aforementioned finite element analysis and optimization methods, the vibration response model of the floating floor is finally determined.

[0179] Through the testing of this experimental bench, the vibration response data of the floating floor under actual working conditions can be obtained, providing an important basis for the subsequent optimization of the theoretical model.

[0180] In addition, the test bench can also be carried out with reference to the technical solution disclosed in the invention patent with publication number CN114964680B, which is a floating floor vibration test bench and test method based on distributed optical fiber monitoring.

[0181] Example 2: The design blueprint of a large commercial complex includes a 3-story floating floor structure, which is mainly used for personnel activities and equipment installation. According to the design parameters, the floor size is 30m×20m×0.3m, and C40 concrete is used; the equipment foundation size is 4m×3m×1m, and C30 concrete is used; the vibration isolator uses the XW-200 model, with a longitudinal stiffness of 200kN / m and a damping ratio of 0.18, and is arranged at the four corners and the middle of the floor, a total of 6. Two centrifugal water pumps with a rated power of 150kW are installed on the floor, and the operating speed is 1500rpm. Based on this design scheme, the vibration response determination method proposed in the present invention is used for analysis and optimization, and the specific process is as follows:

[0182] 1. Finite element model establishment and modal analysis

[0183] Firstly, the finite element model of the floating floor, equipment foundation and vibration isolator with a scale of 1:1 was established using Abaqus finite element software according to the size and material parameters of the design blueprint. The floating floor uses shell units, and the equipment foundation and vibration isolator use solid units. In terms of boundary conditions, simply supported constraints are set around the floating floor, and the vibration isolator is fixed to the steel base.

[0184] The established finite element model was subjected to modal analysis to obtain the natural vibration frequencies and vibration modes of each sub-model. The results showed that the first five natural frequencies of the floating floor were 2.87Hz, 3.42Hz, 4.15Hz, 4.92Hz and 5.28Hz respectively; the first three natural frequencies of the equipment foundation were 6.34Hz, 7.82Hz and 9.06Hz; and the natural frequency of the vibration isolator was 10.25Hz. From the perspective of vibration mode shape, the vibration modes of the first few orders are mainly concentrated in the mid-span and edge parts of the floor.

[0185] 2. Dynamic response analysis:

[0186] Based on the above modal analysis results, the dynamic excitation force generated by the operation of the water pump is applied to the finite element model. The rated speed of the water pump is 1500rpm. According to the rotor dynamic balance theory, the excitation force is mainly concentrated at 1× speed frequency, that is, around 25Hz. A sinusoidal excitation force with an amplitude of 500N and a frequency of 25Hz is applied to the base of the equipment.

[0187] like Figure 5-11 As shown in the figure, through transient dynamic analysis, the vibration response of the floating floor under the operation conditions of a single water pump and multiple water pumps is obtained. The simulation results show that: as the mass of the water pump base gradually increases, the main vibration frequency of the floating plate gradually shifts to low frequency; the change in the stiffness of the base isolator has little effect on the vibration of the floating plate; the simultaneous operation of multiple water pumps has an obvious superposition effect on the vibration of the floating plate, but there is an upper limit value. If the number of water pumps is increased beyond the upper limit, the vibration peak value will no longer increase; in order to reduce the comfort of pedestrians on the floating plate, it is recommended that the natural frequency of the floating plate be designed to be lower than 4Hz, and the natural frequency of the water pump base isolator be higher than 8Hz. At the same time, the water pump speed needs to avoid the above two frequencies. The longitudinal propagation of the vibration of the floating plate under the single water pump load after such setting is shown in the figure below. Fig.12 To reduce the impact of pump vibration on the floating floor, the vibration peak can be reduced by increasing the mass of the foundation and improving the stiffness of the floating floor.

[0188] 3. Optimization of key factors: In order to further reduce the vibration response of the floating floor, the orthogonal test method is used to optimize the following key factors: floating floor thickness, equipment foundation size, number of isolators, stiffness and layout position.

[0189] Through orthogonal test analysis, the following results were obtained:

[0190] Increasing the thickness of the floating floor can effectively reduce the vibration amplitude, but too thick will lead to excessive deadweight, which is not conducive to the overall structure;

[0191] Increasing the foundation mass of the equipment is beneficial to reducing the vibration response, but the effect tends to be saturated after exceeding a certain value;

[0192] The stiffness of the isolators has little effect on the vibration response, but the optimization of the number and layout can bring significant improvements.

[0193] Based on the above analysis results, 3-5 kinds of floating floor deepening design schemes are proposed, mainly including:

[0194] Scheme 1: Floating floor thickness 300mm, equipment foundation size 4m×3m×1m, 6 vibration isolators, stiffness 200kN / m, arranged in corners and the middle;

[0195] Scheme 2: Floating floor thickness 350mm, equipment foundation size 4m×3m×1.2m, 8 vibration isolators, stiffness 180kN / m, corner and edge arrangement;

[0196] Plan 3: The floating floor is 400mm thick, the equipment foundation size is 4m×3m×1.5m, there are 10 vibration isolators with a stiffness of 160kN / m, arranged at the corners, sides and middle.

[0197] The above description is only a specific implementation mode of the present invention, but the protection scope of the present invention is not limited thereto. Any technician familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be covered by the protection scope of the present invention.

Claims

1. A method for determining the vibration response of a floating floor, characterized in that: The following steps are involved: S10, establishing a 1:1 finite element model of the building, including three sub-models, namely a floating floor model, an equipment foundation model and a vibration isolator model; S20, performing modal analysis on the finite element model of the building, obtaining vibration time series parameters of the three sub-models and recording them as first vibration time series parameters, S30, based on the power equipment parameters in the building design blueprint, load the exciting force and exciting frequency, obtain the dynamic response of each model under different working conditions, and obtain the vibration timing parameters of the three sub-models as the second vibration timing parameters; S40, using an orthogonal experimental method to adjust the determining factors in the finite element model of the building to perform vibration simulation, and obtaining vibration timing parameters of three sub-models as third vibration timing parameters; S50, performing short-time Fourier transform on the first vibration timing parameter, the second vibration timing parameter and the third vibration timing parameter respectively to obtain a first vibration spectrum, a second vibration spectrum and a third vibration spectrum; S60, respectively decomposing the first vibration spectrum, the second vibration spectrum, and the third vibration spectrum, and combining them to obtain a preliminary differential equation group of the vibration response of the floor slab; S70, based on the preliminary differential equation group of the vibration response of the floor slab, establish a vibration response matrix equation, determine the initial values ​​of the parameters of the vibration response matrix equation, and use the floating floor slab vibration test bench to perform actual vibration testing and data collection to obtain measured vibration response data; S80, comparing and analyzing the measured vibration response data with the theoretical vibration response data calculated by the vibration response matrix equation, constructing an objective function as the mean square error between the measured vibration response data and the theoretical vibration response data, and optimizing and adjusting the vibration response matrix equation parameters based on the objective function; S90. Iteratively optimize the parameters of the vibration response matrix equation using the objective function until a preset convergence condition is met or a maximum number of iterations is reached, thereby obtaining an optimized set of floor slab vibration response equations as a final floor slab vibration response.

2. A method for determining the vibration response of a floating floor according to claim 1, characterized in that: The components of the floating floor model include a floor body, edge constraints, and an internal supporting structure.

3. A method for determining the vibration response of a floating floor according to claim 1, characterized in that: The vibration timing parameters include frequency, vibration mode, displacement amplitude, and acceleration response.

4. A method for determining the vibration response of a floating floor according to claim 1, characterized in that: The determining factors include floating floor thickness, equipment foundation size, and the number, stiffness, and location of vibration isolators.

5. A method for determining the vibration response of a floating floor according to claim 1, characterized in that: The preliminary differential equations for the vibration response of the floor slab consider the vibration responses in the horizontal x direction, the horizontal y direction and the vertical z direction.

6. A method for determining the vibration response of a floating floor according to claim 1, characterized in that: The floating floor vibration test bench comprises a steel structure platform, a vibration isolator, a floating floor, a vibration source automatic walking device and a distributed optical fiber sensing system.

7. A method for determining the vibration response of a floating floor according to claim 1, characterized in that: The method used for comparing and analyzing the measured vibration response data with the theoretical vibration response data calculated by the vibration response matrix equation is the Levenberg-Marquardt algorithm.

8. A method for determining the vibration response of a floating floor according to claim 7, characterized in that: The maximum number of iterations is 200; the preset convergence condition is that the similarity between two adjacent iteration results is greater than 96%.

9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores program instructions, and when the program instructions are run in a computer, they are used to execute the method for determining the vibration response of a floating floor according to any one of claims 1 to 8.

10. A floating floor vibration response determination system, characterized in that: A computer-readable storage medium comprising the computer-readable storage medium of claim 9.

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