Damping and noise-reducing mounting method for electromechanical equipment

Abstract

The invention provides a damping and noise-reducing installation method for electromechanical equipment, and belongs to the technical field of electromechanical equipment installing.The damping and noise-reducing installation method comprises the steps that firstly, a multi-dimensional vibration noise collection system is constructed, and comprehensive vibration noise characteristic data is collected; then extracting vibration noise features through wavelet transform and non-negative matrix factorization; constructing a small-scale model, and analyzing the influence of the installation parameters by adopting an orthogonal test method; obtaining a vibration noise variation matrix by using a singular value decomposition method; constructing a multi-objective optimization model based on the optimal installation parameters, and solving the optimal installation parameters by adopting a particle swarm algorithm; the parameter rationality is verified by applying an elastic damping dynamics equation set; matched damper materials and installation positions are selected; actual installation is carried out according to the optimal parameters, and the effect is verified; and finally, a parameter correction model is established, a complete knowledge base is formed, and accurate optimization of damping and noise reduction installation of the electromechanical equipment is realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of installation of electromechanical equipment, and more specifically, relates to a method for installing electromechanical equipment with shock absorption and noise reduction. Background Art

[0002] The shock absorption and noise reduction installation of electromechanical equipment is an important technology in the fields of industrial production and civil equipment. Traditional installation methods mainly rely on experience to select shock-absorbing materials and installation parameters, or use simple passive shock-absorbing devices such as spring shock absorbers and rubber pads. These methods are usually applied in engineering practice to scenarios such as elevator machine rooms, central air-conditioning systems, industrial pump stations, and large generator sets, and achieve basic shock absorption and noise reduction effects through empirical parameter setting and standardized installation processes.

[0003] However, traditional technologies have obvious defects: First, the shock absorption and noise reduction effects highly depend on the experience of installers and lack a systematic parameter optimization mechanism; second, it is difficult to simultaneously take into account the vibration and noise characteristics under different load conditions and operating modes; third, it is impossible to accurately identify and directionally suppress multi-frequency vibrations and noises; fourth, the selection of installation parameters lacks dynamic adaptability and it is difficult to optimize and adjust according to the changes in working conditions during the entire life cycle of the equipment.

[0004] In the face of modern high-precision and high-speed rotating electromechanical equipment, traditional technologies are difficult to solve the complex coupling problems of vibration and noise under multiple working conditions. Especially when electromechanical equipment exhibits significantly varying vibration and noise characteristics under different loads, different ambient temperatures, and different operating frequencies, traditional empirical or single-parameter optimized installation methods cannot achieve the optimization of shock absorption and noise reduction effects in the full frequency band and full working conditions, resulting in problems such as reduced equipment performance, shortened service life, and noise pollution in the surrounding environment. That is to say, there is a technical problem in the prior art that it is impossible to accurately analyze and optimize the vibration and noise in multiple working conditions and multiple frequency bands during the installation process of electromechanical equipment. Summary of the Invention

[0005] In view of this, the present invention provides a method for installing electromechanical equipment with shock absorption and noise reduction, which can solve the technical problem in the prior art that it is impossible to accurately analyze and optimize the vibration and noise in multiple working conditions and multiple frequency bands during the installation process of electromechanical equipment.

[0006] The present invention is implemented as follows: The present invention provides a method for installing an electromechanical device to reduce vibration and noise, which includes constructing a multi-dimensional vibration and noise acquisition system to collect vibration spectrum and noise spectrum data; performing wavelet transform analysis on the collected vibration spectrum and noise spectrum and forming a feature matrix through non-negative matrix factorization; constructing a small-scale model of the electromechanical device and changing the installation parameter values through the orthogonal test method; calculating the vibration feature change matrix and the noise feature change matrix and decomposing them using the singular value decomposition method; constructing a multi-objective optimization model and using the particle swarm optimization algorithm to solve the optimal installation parameter combination; applying the elastic damping dynamics equations to analyze the interaction between the electromechanical device and the installation structure, predicting the vibration suppression rate and the noise reduction value; selecting a matching shock absorber material and structure type; and performing actual installation.

[0007] Among them, the multi-dimensional vibration and noise acquisition system collects vibration spectrum and noise spectrum data at different positions, angles, and load conditions of the electromechanical device, forming a comprehensive vibration and noise characteristic database.

[0008] Among them, non-negative matrix factorization decomposes the high-dimensional original data matrix into the product of two non-negative matrices, one representing the basic mode and the other representing the weight distribution of the basic mode, which is used for dimensionality reduction and discovering the internal structure of the vibration feature vector and the noise feature vector.

[0009] Among them, the small-scale model is a physical model of the electromechanical device scaled down according to the principle of geometric similarity, maintaining the similarity relationship of mechanical characteristics and dynamic characteristics between the prototype and the model, which is used for verifying and optimizing the installation parameter variable set before actual installation.

[0010] Among them, the installation parameter variable set includes installation height, inclination angle, contact area, fastening torque, and shock absorber material hardness.

[0011] Among them, the elastic damping dynamics equations include the mass damping equation, the stiffness vibration equation, the heat conduction equation, and the material yield equation.

[0012] Among them, the mass damping equation is used to describe the dynamic relationship between the mass of the electromechanical device and the damping coefficient. The inputs include the device mass distribution obtained from the vibration feature matrix, the damping coefficient obtained from the shock absorber material, the external excitation frequency obtained from the vibration spectrum, the support structure stiffness obtained from the installation structure, and the contact area parameter obtained from the installation parameter variable set. The output is the system damping response curve.

[0013] Among them, the stiffness vibration equation is used to analyze the influence of the stiffness matching between the electromechanical device and the installation structure on vibration transmission. The inputs include the support structure stiffness matrix obtained from the installation structure, the vibration frequency spectrum obtained from the vibration spectrum, the device natural frequency obtained from the electromechanical device, the connection point distribution obtained from the installation parameter variable set, and the environmental temperature coefficient obtained from the installation environment. The output is the vibration transfer function.

[0014] Among them, the heat conduction equation is used to evaluate the efficiency of the conversion of vibration energy into heat energy and its impact on the shock absorption performance. The inputs include the thermal conductivity obtained from the shock absorber material, the vibration power density obtained from the vibration characteristic matrix, the contact area obtained from the set of installation parameter variables, the material thickness obtained from the shock absorber material, and the temperature gradient obtained from the installation environment. The output is the energy dissipation rate.

[0015] Among them, the material yield equation is used to predict the change in the yield characteristics of the shock absorber material under long-term vibration. The inputs include the elastic modulus obtained from the shock absorber material, the yield stress obtained from the shock absorber material, the cumulative number of vibration cycles predicted by the vibration spectrum, the stress amplitude obtained from the vibration characteristic matrix, and the environmental factor correction coefficient obtained from the installation environment. The output is the material life prediction curve.

[0016] The present invention constructs a comprehensive vibration and noise characteristic database, extracts key features by combining wavelet transform and non-negative matrix factorization techniques, systematically analyzes the influence of installation parameter variables on the shock absorption and noise reduction effects using the small-scale model orthogonal test method, and finally uses the particle swarm optimization algorithm to solve the optimal installation parameter combination.

[0017] This method effectively solves the defects of the traditional technology. First, it obtains comprehensive vibration and noise characteristic data through a multi-dimensional vibration and noise acquisition system, breaking the limitation of relying on traditional experience. Second, the singular value decomposition method is applied to decompose the feature change matrix into a stable matrix and a variable matrix, achieving precise identification and targeted suppression of multi-band vibrations and noises. Third, the application of the elastic damping dynamics equations enables the optimization of installation parameters to be based on a solid theoretical foundation, ensuring the stability of the shock absorption and noise reduction effects under different working conditions. Finally, based on the parameter correction model of the actual installation effect, the self-improvement and continuous optimization of the installation method are realized.

[0018] Through the above systematic technological innovation, the present invention successfully solves the problem of precise analysis and optimization of multi-condition and multi-band vibration and noise of electromechanical equipment, enabling the shock absorption and noise reduction effects to no longer be limited to specific working conditions or frequency bands, but to be able to dynamically optimize for various operating states throughout the life cycle of the equipment, significantly improving the operating stability of electromechanical equipment, extending the service life, and improving the noise condition of the surrounding environment. Brief Description of the Drawings

[0019] Figure 1 It is a flowchart of the method of the present invention. Detailed Embodiments

[0020] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention.

[0021] Such asFigure 1 As shown, it is a flowchart of a method for reducing vibration and noise in the installation of a mechatronic device provided by the present invention. This method includes the following steps:

[0022] S01. Construct a multi-dimensional vibration and noise acquisition system, collect vibration spectrum and noise spectrum data at different positions, angles, and load conditions of the mechatronic device, and form a comprehensive vibration and noise characteristic database;

[0023] S02. Perform wavelet transform analysis on the collected vibration spectrum and noise spectrum, extract vibration feature vectors and noise feature vectors, and form a vibration feature matrix and a noise feature matrix through non-negative matrix factorization;

[0024] S03. Construct a small-scale model of the mechatronic device, design a set of installation parameter variables, including installation height, inclination angle, contact area, fastening torque, and the hardness of the damping material. Change the installation parameter values in the set of installation parameter variables by the orthogonal test method of the small-scale model, and record the changes in the vibration feature matrix and the noise feature matrix;

[0025] S04. Based on the test data obtained by the orthogonal test method of the small-scale model, calculate the vibration feature change matrix and the noise feature change matrix, and use the singular value decomposition method to decompose the vibration feature change matrix and the noise feature change matrix into a vibration stability matrix, a vibration variation matrix, a noise stability matrix, and a noise variation matrix;

[0026] S05. Construct a multi-objective optimization model, based on the vibration variation matrix and the noise variation matrix, set the vibration suppression rate and the noise reduction value as the objective functions, and use the particle swarm optimization algorithm to solve the optimal installation parameter combination;

[0027] S06. Apply the elastic damping dynamic equations to analyze the interaction between the mechatronic device and the installation structure, predict the vibration suppression rate and the noise reduction value generated under the optimal installation parameter combination, and verify the theoretical rationality of the optimal installation parameter combination;

[0028] S07. According to the optimal installation parameter combination, select a matching shock absorber material and structure type, and determine the installation position and installation direction of the mechatronic device;

[0029] S08. Perform the actual installation of the mechatronic device according to the optimal installation parameter combination. Optionally, after the installation is completed, use the multi-dimensional vibration and noise acquisition system to conduct vibration and noise tests to verify the vibration suppression rate and the noise reduction value;

[0030] S09. Optionally, it further includes establishing a parameter correction model based on the actual installation effect, associating the parameter correction model with the multi-objective optimization model, and forming a complete knowledge base for the method of reducing vibration and noise in the installation of mechatronic devices.

[0031] Among them, the wavelet transform analysis specifically uses wavelet functions to decompose the signal in the time-frequency domain, extract the energy distribution characteristics of different frequency bands, so as to identify the main frequency components of the vibration spectrum and the noise spectrum and their amplitude change laws;

[0032] Among them, non-negative matrix factorization specifically decomposes a high-dimensional original data matrix into the product of two non-negative matrices, one representing the basic pattern and the other representing the weight distribution of the basic pattern, for dimensionality reduction and discovering the internal structure of the vibration eigenvector and the noise eigenvector;

[0033] Among them, the small-scale model is specifically a physical model of the electromechanical equipment scaled down according to the principle of geometric similarity, maintaining the similarity relationship of mechanical characteristics and dynamic characteristics between the prototype and the model, and is used to verify and optimize the installation parameter variable set before actual installation;

[0034] Among them, the orthogonal test method is specifically an efficient experimental design method. By arranging the experimental factor level combinations through an orthogonal table, it is possible to obtain the most experimental information with the least number of experiments, so as to systematically analyze the influence degree of multiple factors on the vibration suppression rate and the noise reduction value;

[0035] Among them, the singular value decomposition method specifically decomposes the vibration characteristic change matrix and the noise characteristic change matrix into the product of three matrices, namely the left singular vector matrix, the singular value diagonal matrix, and the transpose of the right singular vector matrix, and separates the vibration stable matrix, the vibration variation matrix, the noise stable matrix, and the noise variation matrix by retaining the main singular values;

[0036] Among them, the particle swarm optimization algorithm is specifically a swarm intelligence optimization method that simulates the foraging behavior of bird flocks. By iteratively updating the particle positions and velocities, it searches for the global optimal solution of the optimal installation parameter combination in the search space;

[0037] Among them, the elastic damping dynamic equations include the mass damping equation, the stiffness vibration equation, the heat conduction equation, and the material yield equation;

[0038] The mass damping equation is used to describe the dynamic relationship between the mass of the electromechanical equipment and the damping coefficient. The inputs include the equipment mass distribution obtained from the vibration characteristic matrix, the damping coefficient obtained from the shock absorber material, the external excitation frequency obtained from the vibration spectrum, the support structure stiffness obtained from the installation structure, and the contact area parameter obtained from the installation parameter variable set. The output is the system damping response curve, and the system damping response curve is used to calculate the vibration suppression rate;

[0039] The stiffness vibration equation is used to analyze the influence of the stiffness matching between the electromechanical device and the installation structure on vibration transmission. The inputs include the support structure stiffness matrix obtained from the installation structure, the vibration frequency spectrum obtained from the vibration spectrum, the natural frequency of the device obtained from the electromechanical device, the distribution of connection points obtained from the set of installation parameter variables, and the environmental temperature coefficient obtained from the installation environment. The output is the vibration transfer function, which is used to optimize the installation position and installation direction in the optimal installation parameter combination;

[0040] The heat conduction equation is used to evaluate the efficiency of the conversion of vibration energy into heat energy and its influence on the shock absorption performance. The inputs include the thermal conductivity obtained from the shock absorber material, the vibration power density obtained from the vibration characteristic matrix, the contact area obtained from the set of installation parameter variables, the material thickness obtained from the shock absorber material, and the temperature gradient obtained from the installation environment. The output is the energy dissipation rate, which is used to guide the selection of the shock absorber material;

[0041] The material yield equation is used to predict the change in the yield characteristics of the shock absorber material under long-term vibration. The inputs include the elastic modulus obtained from the shock absorber material, the yield stress obtained from the shock absorber material, the cumulative number of vibration cycles predicted from the vibration spectrum, the stress amplitude obtained from the vibration characteristic matrix, and the environmental factor correction coefficient obtained from the installation environment. The output is the material life prediction curve, which is used to evaluate the long-term stability of the shock absorption and noise reduction installation method for the electromechanical device.

[0042] The specific implementation manners of the above steps are described in detail below.

[0043] The specific implementation manner of step S01 is to construct a multi-dimensional vibration and noise acquisition system, which consists of multiple high-precision acceleration sensors, acoustic sensors, and data acquisition devices. First, at least 8 acceleration sensors are evenly arranged on the surface of the electromechanical device, and the sensor sensitivity is not less than 100 mV / g, and the frequency response range is 0 - 10000 Hz. Then, at least 4 acoustic sensors are set at a distance of 1 m from the periphery of the electromechanical device, and the acoustic sensor sensitivity is not less than 50 mV / Pa, and the frequency response range is 20 - 20000 Hz. Next, four different load conditions of 25%, 50%, 75%, and 100% are set for the electromechanical device. Under each load condition, the vibration data and noise data in the X, Y, and Z directions are collected respectively, the sampling frequency is not less than 44100 Hz, and the sampling duration each time is not less than 60 s. Finally, the collected data is subjected to preliminary filtering to remove 50 Hz power interference and environmental background noise, and a vibration and noise characteristic database covering the full working conditions is formed. The establishment of this database provides a comprehensive data basis for subsequent analysis and effectively ensures the pertinence and effectiveness of the shock absorption and noise reduction scheme.

[0044] The specific implementation of step S02 is to use wavelet transform and non - negative matrix factorization techniques to deeply process and extract features from the collected vibration spectrum and noise spectrum. First, the db4 wavelet function is used to decompose the vibration signal and noise signal into 5 layers to obtain approximation coefficients and detail coefficients. According to the energy distribution characteristics, the frequency bands with an energy contribution rate exceeding 5% in the main frequency components are extracted as characteristic frequency bands. Then, the statistical parameters of each characteristic frequency band are calculated, including mean, standard deviation, kurtosis, skewness, and peak - to - peak value, to form a vibration feature vector and a noise feature vector. Next, an original feature matrix is constructed, where the rows of the matrix represent sampling points and the columns represent feature parameters. The non - negative matrix factorization algorithm is applied, setting the decomposition rank to 30% of the original feature quantity, the number of iterations to be no less than 1000 times, and the convergence threshold to 10 -4 , and the original feature matrix is decomposed into a basic mode matrix and a weight assignment matrix. Finally, the vibration feature matrix and noise feature matrix after dimensionality reduction are formed according to the decomposition results for use in the subsequent parameter optimization process. This step reveals the internal characteristics of vibration noise through joint time - frequency domain analysis and provides a theoretical basis for precise control.

[0045] The specific implementation of step S03 is to construct a small - scale model of the electromechanical equipment and conduct orthogonal experiments. First, according to the similarity theory, a physical model of the electromechanical equipment is constructed according to a geometric ratio of 1:5 to ensure that the structural ratio, mass ratio, and stiffness ratio between the model and the prototype meet the similarity conditions. Then, a set of installation parameter variables is designed, including installation height (10 - 50 mm), inclination angle (0 - 15°), contact area (30% - 90% of the bottom area of the original equipment), fastening torque (50% - 150% of the standard torque), and the hardness of the damping material (Shore hardness 30 - 85A). Next, an L16(4^5) orthogonal table is created according to the orthogonal experimental design method to determine 16 groups of experimental schemes, and each group of experiments is repeated 3 times under the same environmental conditions to ensure data reliability. In each experiment, the changes in the vibration feature matrix and noise feature matrix obtained in step S02 are recorded, and the vibration intensity change rate and noise intensity change rate under each experimental condition are calculated. Finally, the range analysis method is applied to determine the ranking of the influence degree of each parameter on the vibration and noise reduction effect. This step effectively simulates the actual installation conditions through a small - scale model, greatly reducing the experimental cost and improving the efficiency of parameter optimization.

[0046] The specific implementation of step S04 is to calculate the feature change matrix based on the orthogonal experimental data and perform singular value decomposition. First, the vibration feature matrix and noise feature matrix under different installation parameter combinations in step S03 are used to calculate the difference with the feature matrix in the original state to obtain a vibration feature change matrix and a noise feature change matrix. Then, the singular value decomposition algorithm is applied to these two change matrices respectively, and the matrix is expressed as U·Σ·V T形式，其中U为左奇异向量矩阵，Σ为奇异值对角矩阵，VT is the transpose of the right singular vector matrix. Then, the singular value distribution is analyzed, and the contribution rate threshold of the main singular values is determined to be 85%. The singular values and the corresponding singular vectors whose cumulative contribution rates reach this threshold are retained. The matrix is reconstructed using the retained singular values and singular vectors to separate the vibration stability matrix, the vibration variation matrix, the noise stability matrix, and the noise variation matrix. Finally, the eigenvalues and condition numbers of these four matrices are calculated to evaluate the stability and sensitivity of the matrices. This step effectively separates the influence of the installation parameter changes on the vibration and noise characteristics, providing a clear mathematical model for subsequent optimization.

[0047] The specific implementation of step S05 is to construct a multi-objective optimization model and use the particle swarm optimization algorithm to solve for the optimal installation parameter combination. First, based on the vibration variation matrix and the noise variation matrix obtained in step S04, the vibration suppression rate objective function f1 and the noise reduction value objective function f2 are defined. Here, f1 represents the percentage reduction value of the vibration intensity after installation relative to the original state, and f2 represents the decibel reduction value of the noise sound pressure level after installation relative to the original state. Then, the comprehensive objective function F = w1·f1 + w2·f2 is constructed, and the weight coefficients w1 and w2 are set to 0.6 and 0.4 respectively to balance the vibration damping and noise reduction effects. Next, the constraint conditions of the installation parameters are set, including equipment stability constraints, space limitation constraints, and material property constraints. The improved particle swarm optimization algorithm is applied for solution, with the population size set to 50, the maximum number of iterations set to 200, the inertia weight linearly decreasing from 0.9 to 0.4, the learning factors c1 = c2 = 2.0, and the convergence criterion being that the change rate of the optimal solution is less than 0.1% for 20 consecutive iterations. Finally, by running the algorithm independently multiple times, the parameter combination with the best and stable performance is selected as the final optimal installation parameter combination. This step efficiently finds the optimal solution in the complex parameter space through the intelligent optimization algorithm, achieving the maximization of the vibration damping and noise reduction effects.

[0048] The specific implementation of step S06 is to verify the theoretical rationality of the optimal installation parameter combination by applying the elastic damping dynamics equations. First, a coupled dynamics model of the electromechanical equipment and the installation structure is constructed, with the equipment regarded as a flexible body and the installation structure regarded as an elastic support with damping characteristics. Then, the mass damping equation is used to calculate the system damping response curve. The inputs of this equation include the equipment mass distribution, the damping coefficient of the shock-absorbing material, the external excitation frequency, the stiffness of the support structure, and the contact area parameters. The output damping response curve is used to predict the vibration suppression rate. The stiffness vibration equation is used to analyze the vibration transfer characteristics between the equipment and the installation structure. The inputs of this equation include the stiffness matrix of the support structure, the vibration frequency spectrum, the natural frequency of the equipment, the distribution of connection points, and the environmental temperature coefficient. The output vibration transfer function is used to optimize the installation position and direction. The heat conduction equation is used to evaluate the conversion efficiency of vibration energy into heat energy. The inputs of this equation include the thermal conductivity of the shock-absorbing material, the vibration power density, the contact area, the material thickness, and the temperature gradient. The output energy dissipation rate is used to guide the selection of the shock-absorbing material. The material yield equation is used to predict the long-term performance of the shock-absorbing material. The inputs of this equation include the elastic modulus of the material, the yield stress, the cumulative vibration period, the stress amplitude, and the environmental factor correction coefficient. The output material life prediction curve is used to evaluate the long-term stability of the installation method. Finally, the theoretically predicted vibration suppression rate and noise reduction value are compared with the target values to verify the theoretical rationality of the optimal installation parameter combination. This step verifies the physical feasibility of the optimization result through mechanical theory and enhances the reliability of the installation plan.

[0049] The specific implementation of step S07 is to select the matching shock-absorber material and structure type according to the optimal installation parameter combination, and determine the installation position and installation direction of the electromechanical equipment. First, based on the optimal installation height and the hardness parameter of the shock-absorbing material determined in step S05, the most matching shock-absorbing material is selected from materials such as rubber, polyurethane, and elastomer composites. The material selection criteria include frequency matching (the matching degree with the main frequency of the equipment is not less than 80%), temperature stability (the hardness change within the working temperature range does not exceed 15%), and aging characteristics (the performance decay within 3 years of use does not exceed 20%). Then, according to the optimal inclination angle and contact area parameters, the appropriate shock-absorber structure type is selected. The structure types include flat type, cone type, corrugated type, and composite type. The selection criteria include the uniformity of load distribution, the directional shock-absorbing effect, and the space adaptability. Next, according to the output result of the stiffness vibration equation, the optimal installation position of the electromechanical equipment is determined. The installation position should avoid the vibration-sensitive points and acoustic standing wave points of the building structure, and at the same time ensure the operation and maintenance space of the equipment. Finally, according to the analysis result of the vibration transfer function, the installation direction of the equipment is determined to make the vibration transfer path of the main vibration source perpendicular to the direction with the maximum stiffness of the building structure. This step transforms the theoretical optimization result into a specific engineering implementation plan, ensuring the actual realization of the shock-absorbing and noise-reducing effect.

[0050] The specific implementation of step S08 is to actually install the electromechanical equipment according to the optimal installation parameter combination and verify the installation effect. First, prepare the installation site, clean the installation surface, measure and mark the installation position reference points to ensure that the flatness error of the installation surface does not exceed 2 mm / m. Then adjust the position of the shock absorber according to the optimal installation height and inclination angle, and use a level to ensure that the inclination deviation of the equipment does not exceed ±0.5°. Next, according to the optimal tightening torque parameters, use a torque wrench to tighten the connecting bolts in sequence, and the tightening sequence follows the diagonal cross principle, and the tightening torque error is controlled within ±5%. After that is an optional step, including after the installation is completed, use the multi-dimensional vibration and noise acquisition system in step S01 to conduct vibration and noise tests, collect the vibration spectrum and noise spectrum after installation under the same working conditions and measuring point positions, calculate the actually obtained vibration suppression rate and noise reduction value, and compare them with the theoretical prediction values. If the actual vibration suppression rate is not less than 90% of the theoretical value and the noise reduction value is not less than 85% of the theoretical value, then the installation effect meets the requirements. This step ensures the effectiveness of the shock and noise reduction method in practical applications through a standardized installation process and strict effect verification.

[0051] Step S09 is an optional step, and its specific implementation is to establish a parameter correction model based on the actual installation effect to form a complete knowledge base of the shock and noise reduction installation method for electromechanical equipment. First, compare the differences between the actually measured vibration suppression rate and noise reduction value and the theoretical prediction values, calculate the correction coefficients of each parameter, and the calculation of the correction coefficients is based on the ratio of the measured value to the theoretical value, and use the least squares regression analysis to determine the functional relationship between the parameters and the correction coefficients. Then construct a parameter correction model, which can automatically adjust the optimal installation parameter values according to the equipment type, installation environment and expected service life, and the correction accuracy is controlled within ±7%. Next, associate the parameter correction model with the multi-objective optimization model in step S05 to form a closed-loop optimization system, which can continuously optimize and adjust the theoretical model according to the actual installation effect. Finally, integrate the theoretical knowledge, algorithm models and experimental data of all steps to establish a knowledge base of the shock and noise reduction installation method for electromechanical equipment. The knowledge base includes four parts: equipment classification directory, parameter optimization module, material selection guide and installation process standard. The knowledge base supports case retrieval and similarity matching functions, and can provide reference solutions and expected effect evaluations for the installation of new equipment. This step realizes the continuous optimization and knowledge accumulation of the installation method through the combination of theory and practice, and greatly improves the applicability and popularization of the shock and noise reduction method.

[0052] The following details the mathematical models or calculation processes involved in the present invention.

[0053] In step S01, the calculation process of collecting vibration spectrum and noise spectrum data at different positions, angles and load conditions of the electromechanical equipment is specifically expressed as follows:

[0054]

[0055] Wherein, S vib (f) is the vibration spectrum; S noise (f) is the noise spectrum; a i is the acceleration value at the i-th time point; p i is the sound pressure value at the i-th time point; f is the frequency; t i is the i-th sampling time point; w(t i ) is the window function, usually a Hanning window is adopted to reduce spectral leakage; N is the number of sampling points; j is the imaginary unit.

[0056] The method for collecting vibration spectrum and noise spectrum data is as follows: First, acceleration sensors are evenly arranged on the surface of the electromechanical equipment, and the sensitivity of the sensors is not less than 100 mV / g; then the original time-domain signal is collected through the data acquisition system at a sampling frequency not less than 44100 Hz; then the original signal is preprocessed, including removing the DC component and applying the window function; finally, the time-domain signal is converted into a frequency-domain signal through fast Fourier transform to obtain the vibration spectrum and the noise spectrum. The spectrum calculation adopts the average periodogram method, and the long-time signal is segmented, each segment having a length of 8192 points and an overlap rate of 50%, to improve the reliability of the spectrum estimation.

[0057] In step S02, the calculation process of wavelet transform analysis is specifically expressed as follows:

[0058]

[0059] Wherein, C j，k is the wavelet coefficient; s(t) is the original signal; ψ j，k (t) is the wavelet function with a scale of 2 j and a translation of k; ψ * (t) represents the complex conjugate of ψ(t); j is the decomposition scale level, and the value range is from 1 to 5; k is the translation parameter.

[0060] The method for obtaining wavelet transform coefficients is as follows: First, the db4 wavelet function is selected as the basis function; then the original signal is decomposed into 5 layers to obtain an approximation coefficient and five detail coefficients; then the energy distribution of the signal at each scale is calculated, and the frequency band with an energy contribution rate exceeding 5% is selected as the characteristic frequency band; finally, the statistical characteristic parameters of each characteristic frequency band are extracted.

[0061] The calculation process of non-negative matrix factorization is specifically expressed as follows:

[0062] V≈W·H;

[0063]

[0064] s.t. W ≥ 0, H ≥ 0;

[0065] Wherein, is the original feature matrix, m is the number of sampling points, and n is the number of features; is the basic mode matrix; is the weight assignment matrix; r is the decomposition rank, set to 30% of the original number of features; ∥·∥ F represents the Frobenius norm.

[0066] The method for obtaining non - negative matrix factorization parameters is as follows: First, construct the original feature matrix V, where each row of the matrix represents a sampling point and each column represents a feature parameter; then randomly initialize the matrices W and H as non - negative matrices; then iteratively update W and H by the alternating least - squares method, and the update rules are:

[0067]

[0068] The number of iterations is not less than 1000 times, and the convergence threshold is set to 10 -4 , that is, when the change in the objective function value between two iterations is less than 10 -4 stop the iteration.

[0069] The construction process of the vibration feature vector and the noise feature vector is specifically expressed as follows:

[0070] F vib = [f mean , f std , f kurt , f skew , f p-p , f energy ;

[0071] F noise = [f mean , f std , f kurt , f skew , f p-p , f energy ;

[0072] Wherein, F vib is the vibration feature vector; F noise is the noise feature vector; f mean is the signal mean value; f std is the signal standard deviation; f kurt is the signal kurtosis; f skew is the signal skewness; f p-p is the signal peak - to - peak value; f energy is the signal energy.

[0073] The calculation method of the feature parameters is:

[0074]

[0075] f p-p = max(x) - min(x);

[0076]

[0077] where x i is the value of the signal at time point i; N is the signal length.

[0078] In step S04, the calculation process of the singular value decomposition method is specifically expressed as follows:

[0079] ΔM vib = M vib - M vib_0 ;

[0080] ΔM noise = M noise - M noise_0 ;

[0081]

[0082] where M vib is the vibration characteristic matrix under different combinations of installation parameters; M noise is the noise characteristic matrix under different combinations of installation parameters; M vib_0 is the vibration characteristic matrix in the original state; M noise_0 is the noise characteristic matrix in the original state; ΔM vib is the vibration characteristic change matrix; ΔM noise is the noise characteristic change matrix; U vib and U noise are the left singular vector matrices; ∑ vib and ∑ noise are the singular value diagonal matrices; and are the transposes of the right singular vector matrices.

[0083] After singular value decomposition, according to the contribution rate of the singular values, the matrix is decomposed into a stable part and a variable part:

[0084] ΔM vib = M vib_stable + M vib_varibale ;

[0085] ΔM noise = M noise_stable + M noise_variable ;

[0086]

[0087]

[0088] In the formula, M vib_stable is the vibration stability matrix; M vib_variable is the vibration variation matrix; M noise_stable is the noise stability matrix; M noise_variable is the noise variation matrix; ∑ vib_stable and ∑ noise_stable are respectively diagonal matrices retaining the main singular values (cumulative contribution rate reaching 85%), and the remaining singular values are set to 0; ∑ vib_variable and Σ noise_variable are respectively diagonal matrices retaining the minor singular values, and the main singular values are set to 0.

[0089] The calculation method of the singular value contribution rate is as follows:

[0090]

[0091] In the formula, C i is the contribution rate of the i-th singular value; σ i is the i-th singular value; n is the total number of singular values; C cumulative，k is the cumulative contribution rate of the first k singular values.

[0092] In step S05, the calculation process of the multi-objective optimization model is specifically expressed as follows:

[0093]

[0094] f2(x) = L p0 -L p (x);

[0095] F(x) = w1·f1(x) + w2·f2(x);

[0096] maxF(x);

[0097] s.t. g j (x) ≤ 0, j = 1, 2,..., m;

[0098] h k (x) = 0, k = 1, 2,..., p;

[0099]

[0100] In the formula, f1(x) is the vibration suppression rate objective function; f2(x) is the noise reduction value objective function; F(x) is the comprehensive objective function; x = [x1, x2,..., x n is the installation parameter vector, including installation height, inclination angle, contact area, fastening torque, and shock-absorbing material hardness; M vib_0 is the vibration characteristic matrix in the original state; M vib$\mathbf{V}(x)$ is the vibration characteristic matrix when the installation parameter is $x$; $\|\cdot\|$ F represents the Frobenius norm; $L$ p0 is the noise sound pressure level in the original state, with the unit of dB; $L$ p $\mathbf{G}(x)$ is the noise sound pressure level when the installation parameter is $x$, with the unit of dB; $w_1$ and $w_2$ are weight coefficients, set to 0.6 and 0.4 respectively; $g$ j $\mathbf{h}(x)$ is the inequality constraint condition; $h$ k $\mathbf{e}(x)$ is the equality constraint condition; and are the lower and upper limits of the $i$-th installation parameter respectively.

[0101] The constraint conditions specifically include:

[0102] (Stability constraint)

[0103] (Space height constraint)

[0104] (Noise limit constraint)

[0105] In the formula, $K$ stable is the system stability coefficient; $m$ is the mass of the device; $g$ is the acceleration due to gravity; $x_1$ is the installation height; $h$ device is the height of the device; $h$ max is the maximum allowable height; $L$ work is the noise level in the working state; $L$ limit is the noise limit.

[0106] The iterative update formula of the particle swarm optimization algorithm is:

[0107]

[0108] In the formula, is the velocity of the $i$-th particle at the $t$-th iteration; is the position of the $i$-th particle at the $t$-th iteration; $pbest$ i is the historical optimal position of the $i$-th particle; $gbest$ is the global optimal position; $w$ is the inertia weight, linearly decreasing from 0.9 to 0.4; $c_1$ and $c_2$ are learning factors, both set to 2.0; $r_1$ and $r_2$ are random numbers between 0 and 1.

[0109] In step S06, the calculation process of the elastic damping dynamic equations is specifically expressed as follows:

[0110] 1. Mass damping equation:

[0111]

[0112] C = αM + βK + C material (A, h, E, η);

[0113] Where M is the mass matrix; C is the damping matrix; K is the stiffness matrix; x is the displacement vector; is the velocity vector; is the acceleration vector; F(t) is the external excitation force vector; α and β are the proportional damping coefficients; C material is the material damping contribution; A is the contact area; h is the material thickness; E is the elastic modulus; η is the loss factor.

[0114] Calculation of the system damping response curve:

[0115]

[0116] Where H(ω) is the system frequency response function; ω is the angular frequency; j is the imaginary unit; H0(ω) is the frequency response function in the original state; R vib is the vibration suppression rate.

[0117] 2. Stiffness vibration equation:

[0118]

[0119] K mount = K mount0 ·(1 + α T ·ΔT)·f(A, θ);

[0120]

[0121] Where K total is the total stiffness of the system; K device is the stiffness of the equipment; K mount is the stiffness of the shock absorber; K structure is the stiffness of the support structure; K mount0 is the stiffness of the shock absorber at the reference temperature; α T is the temperature coefficient; ΔT is the temperature change; f(A, θ) is a function related to the contact area A and the inclination angle θ; t(ω) is the vibration transfer function; ω is the excitation frequency; ω n is the natural frequency of the system; ζ is the damping ratio.

[0122] 3. Heat conduction equation:

[0123]

[0124] q v = η·ω·σ·ε;

[0125]

[0126] where ρ is the material density; c p is the specific heat capacity; T is the temperature; t is the time; k is the thermal conductivity; is the Laplace operator; q v is the volume heat source, representing the part where vibration energy is converted into heat energy; η is the loss factor; ω is the angular frequency; σ is the stress; ε is the strain; D E is the energy dissipation rate; E dissipated is the dissipated energy; E input is the input vibration energy.

[0127] 4. Material yield equation:

[0128]

[0129] where σ eq is the equivalent stress; σ x , σ y , σ z are the principal stresses; τ xy , τ xz , τ yz are the shear stresses; N f is the number of fatigue life cycles; σ y is the material yield stress; C1, C2, C3 are material constants; T is the operating temperature; C4(env) is the environmental factor correction coefficient; L predicted is the predicted service life, in years; f is the main vibration frequency; t daily is the daily operating time of the equipment, in hours.

[0130] In step S09, the calculation process of the parameter correction model is specifically expressed as follows:

[0131] R actual = γ vib ·R theoretical ;

[0132] L actual = γ noise ·L theoretical ;

[0133]

[0134] where R actual is the actual vibration suppression rate; R theoretical is the theoretical vibration suppression rate; L actual is the actual noise reduction value; L theoretical is the theoretical noise reduction value; r vib and γ noise are the correction coefficients for vibration and noise respectively; x i is the i-th installation parameter; a0, a i , aij and b0, b i , b ij are regression coefficients; ε vib and ε noise are error terms, with a range within ±0.07.

[0135] The regression coefficients are solved by the least squares method:

[0136]

[0137] In the formula, y k is the actual correction coefficient; is the model predicted correction coefficient; m is the number of samples.

[0138] The construction principles and meanings of these equations are as follows: The wavelet transform formula adopts scale transformation and translation operations, which can effectively capture the time-frequency characteristics of signals and is particularly suitable for analyzing non-stationary signals such as the vibration and noise of electromechanical equipment; non-negative matrix factorization realizes dimensionality reduction and feature extraction by decomposing high-dimensional data into the product of low-rank matrices, overcoming the limitation that traditional principal component analysis requires data to follow a Gaussian distribution; singular value decomposition decomposes a matrix into the product of three matrices, which can reveal the internal structure of the data, and by retaining singular values with different contribution rates, separates the stable part and the varying part of vibration and noise, providing a mathematical basis for parameter optimization; the multi-objective optimization model combines the two objectives of vibration suppression and noise reduction through weight coefficients to maximize the comprehensive effect; the elastic damping dynamic equations comprehensively describe the dynamic behavior of electromechanical equipment and the installation structure from four aspects: mass, stiffness, heat conduction, and material yield, providing a mechanical basis for theoretical verification; the parameter correction model builds a bridge between theoretical prediction and actual effect, captures the interaction between parameters through a quadratic regression model, and improves the applicability and accuracy of the model. These equations consider the effects of nonlinearity, coupling effects, and environmental factors, making the shock and noise reduction method more accurate and adaptable.

[0139] Specifically, the principle of the present invention is: The technical principle of the present invention is based on the deep integration of systems engineering and vibration and noise control theory. By constructing a closed-loop system of "acquisition - analysis - optimization - verification - correction", precise optimization of the shock and noise reduction installation parameters of electromechanical equipment is achieved. Its core principle can be divided into four levels:

[0140] First, at the level of feature extraction and pattern recognition. The present invention uses wavelet transform for time-frequency domain decomposition, which can accurately capture the vibration noise signal characteristics in different frequency bands, making up for the deficiencies of traditional Fourier transform in dealing with non-stationary signals. Combining with non-negative matrix factorization technology, the high-dimensional vibration noise data is reduced in dimension and the internal structure is extracted, enabling the system to identify the main patterns and contributing factors of vibration noise. This dual feature extraction mechanism enables the present invention to specifically identify the key vibration noise frequency bands under different working conditions.

[0141] Second, at the level of analyzing the parameter influence mechanism. Through the orthogonal test method of small-scale models, the present invention systematically analyzes the influence of parameters such as installation height, inclination angle, contact area, fastening torque, and the hardness of damping materials on the vibration noise suppression effect. The application of singular value decomposition method further decomposes the vibration noise feature change matrix into a stable part and a variable part, enabling the system to accurately grasp the influence law of parameter changes on the damping and noise reduction effect, and avoiding the blindness of parameter selection in traditional technologies.

[0142] Third, at the level of multi-objective optimization decision-making. Based on the vibration change matrix and the noise change matrix, the present invention constructs a multi-objective optimization model with the vibration suppression rate and the noise reduction value as the objective functions, and searches for the global optimal solution in the high-dimensional parameter space through the particle swarm optimization algorithm. This optimization method based on swarm intelligence avoids the defect that traditional single-objective optimization or empirical parameter selection is prone to fall into local optimum, ensuring the best damping and noise reduction effect under complex and changeable working conditions.

[0143] Fourth, at the level of theoretical verification and dynamic correction. The present invention applies elastic damping dynamic equations, including mass damping equation, stiffness vibration equation, heat conduction equation, and material yield equation, to theoretically predict and verify the effectiveness of the optimal installation parameter combination. At the same time, a parameter correction model based on the actual installation effect is established, realizing the self-improvement and continuous optimization of the installation method, and enabling the system to have the ability to cope with the working condition changes during the entire life cycle of the equipment.

[0144] The technical principles of the above four levels are organically combined to form a complete installation method system for reducing vibration and noise of electromechanical equipment. This system can fundamentally solve the technical problems of accurate analysis and optimization of multi-condition and multi-frequency band vibration and noise of electromechanical equipment, conforms to the basic theories of systems engineering and vibration noise control, and has a solid scientific basis and practical application value.

[0145] Next, a specific Embodiment 1 of the present invention is provided, and the specific implementation manners of each step in this Embodiment 1 are described in detail as follows.

[0146] The specific implementation of step S01 is to construct a multi-dimensional vibration and noise acquisition system, which consists of multiple high-precision acceleration sensors, acoustic sensors, and data acquisition devices. First, at least 8 acceleration sensors are evenly arranged on the surface of the electromechanical equipment, with a sensor sensitivity of not less than 100 mV / g and a frequency response range of 0 to 10,000 Hz. Then, at least 4 acoustic sensors are set 1 m away from the periphery of the electromechanical equipment, with an acoustic sensor sensitivity of not less than 50 mV / Pa and a frequency response range of 20 to 20,000 Hz. Next, four different load conditions of 25%, 50%, 75%, and 100% are set for the electromechanical equipment. Under each load condition, vibration data and noise data in the X, Y, and Z directions are collected respectively, with a sampling frequency of not less than 44,100 Hz and a sampling duration of not less than 60 s each time. Finally, the collected data is subjected to preliminary filtering to remove 50 Hz power interference and environmental background noise, forming a vibration and noise characteristic database covering the full operating conditions. The calculation formulas for the collected vibration spectrum and noise spectrum data are as follows:

[0147]

[0148] In the formula, S vib (f) is the vibration spectrum; S noise (f) is the noise spectrum; a i is the acceleration value at the i-th time point; p i is the sound pressure value at the i-th time point; f is the frequency; t i is the i-th sampling time point; w(t i ) is the window function, usually a Hanning window is used to reduce spectral leakage; N is the number of sampling points; j is the imaginary unit. The establishment of this database provides a comprehensive data basis for subsequent analysis, effectively ensuring the pertinence and effectiveness of the vibration and noise reduction solutions.

[0149] The specific implementation of step S02 is to use wavelet transform and non-negative matrix factorization techniques to deeply process and extract features from the collected vibration spectrum and noise spectrum. First, the db4 wavelet function is used to decompose the vibration signal and noise signal into 5 layers to obtain approximation coefficients and detail coefficients. The calculation formula for wavelet transform analysis is as follows:

[0150]

[0151] ψ j，k (t) = 2 -j / 2 ·ψ(2 -j t - k);

[0152] In the formula, C j，k is the wavelet coefficient; s(t) is the original signal; ψ j，k (t) is the wavelet function with a scale of 2 j and a translation of k; ψ* (t) represents the complex conjugate of ψ(t); j is the number of decomposition scale levels, with a value range of 1 to 5; k is the translation parameter. According to the energy distribution characteristics, the frequency bands with an energy contribution rate exceeding 5% in the main frequency components are extracted as the characteristic frequency bands. Then, the statistical parameters of each characteristic frequency band are calculated to form the vibration feature vector and the noise feature vector, and their construction formulas are as follows:

[0153] F vib = [f mean , f std , f kurt , f skew , f p-p , f energy ;

[0154] F noise = [f mean , f std , f kurt , f skew , f p-p , f energy ;

[0155] In the formula, F vib is the vibration feature vector; f noise is the noise feature vector; f mean is the signal mean; f std is the signal standard deviation; f kurt is the signal kurtosis; f skew is the signal skewness; f p-p is the signal peak-to-peak value; f energy is the signal energy. Then, the original feature matrix is constructed, where the rows of the matrix represent the sampling points and the columns represent the feature parameters. The non-negative matrix factorization algorithm is applied, and its calculation formula is:

[0156] V ≈ W·H;

[0157]

[0158] s.t. W ≥ 0, H ≥ 0;

[0159] In the formula, is the original feature matrix, m is the number of sampling points, and n is the number of features; is the basic mode matrix; is the weight distribution matrix; r is the decomposition rank, set to 30% of the original number of features; ∥·∥ F represents the Frobenius norm. The decomposition rank is set to 30% of the original number of features, the number of iterations is not less than 1000 times, and the convergence threshold is set to 10 -4, the original feature matrix is decomposed into a basic mode matrix and a weight assignment matrix. Finally, based on the decomposition results, a vibration feature matrix and a noise feature matrix after dimensionality reduction are formed for the subsequent parameter optimization process. This step reveals the internal characteristics of vibration noise through joint time-frequency domain analysis, providing a theoretical basis for precise control.

[0160] The specific implementation of step S03 is the same as the foregoing, and will not be elaborated in detail here.

[0161] The specific implementation of step S04 is to calculate the feature change matrix based on orthogonal test data and perform singular value decomposition. First, the vibration feature matrix and the noise feature matrix under different installation parameter combinations in step S03 are subtracted from the feature matrix in the original state to obtain the vibration feature change matrix and the noise feature change matrix. The calculation formulas are as follows:

[0162] ΔM vib =M vib -M vib_0 ;

[0163] ΔM noise =M noise -M noise_0 ;

[0164] In the formula, M vib is the vibration feature matrix under different installation parameter combinations; M noise is the noise feature matrix under different installation parameter combinations; M vib_0 is the vibration feature matrix in the original state; M noise_0 is the noise feature matrix in the original state; ΔM vib is the vibration feature change matrix; ΔM noise is the noise feature change matrix. Then, the singular value decomposition algorithm is applied to these two change matrices respectively. The calculation formula is as follows:

[0165]

[0166] In the formula, U vib and U noise are left singular vector matrices; Σ vib and Σ noise are singular value diagonal matrices; and are the transposes of the right singular vector matrices. Then, the singular value distribution is analyzed, and the contribution rate threshold of the main singular values is determined to be 85%. The singular values and the corresponding singular vectors whose cumulative contribution rates reach this threshold are retained. The singular value contribution rate calculation formula is as follows:

[0167]

[0168] In the formula, C iis the contribution rate of the i-th singular value; σ i is the i-th singular value; n is the total number of singular values; C cumulative，k is the cumulative contribution rate of the first k singular values. The matrix is reconstructed using the retained singular values and singular vectors, and the vibration stable matrix, vibration variation matrix, noise stable matrix, and noise variation matrix are separated. Their calculation formulas are as follows:

[0169] ΔM vib = M vib_stable + M vib_variable ;

[0170] ΔM noise = M noise_stable + M noise_variable ;

[0171]

[0172] In the formula, M vib_stable is the vibration stable matrix; M vib_variable is the vibration variation matrix; M noise_stable is the noise stable matrix; M noise_variable is the noise variation matrix; ∑ vib_stable and ∑ noise_stable are respectively the diagonal matrices retaining the main singular values, and the remaining singular values are set to 0; ∑ vib_variable and ∑ noise_variable are respectively the diagonal matrices retaining the secondary singular values, and the main singular values are set to 0. Finally, the eigenvalues and condition numbers of these four matrices are calculated to evaluate the stability and sensitivity of the matrix. This step effectively separates the influence of installation parameter changes on vibration and noise characteristics, providing a clear mathematical model for subsequent optimization.

[0173] The specific implementation of step S05 is to construct a multi-objective optimization model and use the particle swarm optimization algorithm to solve the optimal installation parameter combination. First, based on the vibration variation matrix and noise variation matrix obtained in step S04, the vibration suppression rate objective function and noise reduction value objective function are defined. Their calculation formulas are as follows:

[0174]

[0175] f2(x) = L p0 - L p (x);

[0176] F(x) = w1·f1(x) + w2·f2(x);

[0177] In the formula, f1(x) is the vibration suppression rate objective function; f2(x) is the noise reduction value objective function; F(x) is the comprehensive objective function; x = [x1, x2,..., x nis the installation parameter vector, including installation height, inclination angle, contact area, fastening torque, and hardness of the damping material; M vib_0 is the vibration characteristic matrix in the original state; M vib (x) is the vibration characteristic matrix when the installation parameter is x; ||·|| F represents the Frobenius norm; L p0 is the noise sound pressure level in the original state, with the unit of db; L p (x) is the noise sound pressure level when the installation parameter is x, with the unit of db; w1 and w2 are weight coefficients, which are set to 0.6 and 0.4 respectively. Then, the comprehensive objective function F(x) is constructed, and the weight coefficients w1 and w2 are set to 0.6 and 0.4 respectively to balance the damping and noise reduction effects. Next, the constraint conditions of the installation parameters are set, including equipment stability constraint, space limitation constraint, and material property constraint. The improved particle swarm optimization algorithm is applied for solution, and its iterative update formula is:

[0178]

[0179] In the formula, is the velocity of the i-th particle at the t-th iteration; is the position of the i-th particle at the t-th iteration; pbest i is the historical optimal position of the i-th particle; gbest is the global optimal position; w is the inertia weight, which linearly decreases from 0.9 to 0.4; c1 and c2 are learning factors, both set to 2.0; r1 and r2 are random numbers between 0 and 1. The population size is set to 50, the maximum number of iterations is 200, the inertia weight linearly decreases from 0.9 to 0.4, the learning factors c1 = c2 = 2.0, and the convergence criterion is that the change rate of the optimal solution is less than 0.1% for 20 consecutive iterations. Finally, by running the algorithm independently for multiple times, the parameter combination with the optimal and stable performance is selected as the final optimal installation parameter combination. This step efficiently finds the optimal solution in the complex parameter space through the intelligent optimization algorithm, achieving the maximization of the damping and noise reduction effects.

[0180] The specific implementation of step S06 is to verify the theoretical rationality of the optimal installation parameter combination by applying the elastic damping dynamics equations. First, a coupled dynamics model of the electromechanical equipment and the installation structure is constructed, with the equipment regarded as a flexible body and the installation structure regarded as an elastic support with damping characteristics. Then, the system damping response curve is calculated using the mass damping equation, and its equation is:

[0181]

[0182] C = αM + βK + C material (A, h, E, η);

[0183] Wherein, M is the mass matrix; C is the damping matrix; K is the stiffness matrix; x is the displacement vector; is the velocity vector; is the acceleration vector; F(t) is the external excitation force vector; α and β are the proportional damping coefficients; C material is the material damping contribution; A is the contact area; h is the material thickness; E is the elastic modulus; η is the loss factor. The calculation formula for the system damping response curve is:

[0184]

[0185] Wherein, H(ω) is the system frequency response function; ω is the angular frequency; j is the imaginary unit; H0(ω) is the frequency response function in the original state; R vib is the vibration suppression rate. Analyze the vibration transfer characteristics between the equipment and the installation structure using the stiffness vibration equation, and its equation is:

[0186]

[0187] Wherein, K total is the total system stiffness; K device is the equipment stiffness; K mount is the shock absorber stiffness; K structure is the support structure stiffness; K mount0 is the shock absorber stiffness at the reference temperature; α T is the temperature coefficient; ΔT is the temperature change; f(A, θ) is a function related to the contact area A and the inclination angle θ; t(ω) is the vibration transfer function; ω is the excitation frequency; ω n is the system natural frequency; ζ is the damping ratio. Evaluate the conversion efficiency of vibration energy into heat energy using the heat conduction equation, and its equation is:

[0188]

[0189] Wherein, ρ is the material density; c p is the specific heat capacity; T is the temperature; t is the time; k is the thermal conductivity; is the Laplace operator; q v is the volume heat source; η is the loss factor; ω is the angular frequency; σ is the stress; ε is the strain; D E is the energy dissipation rate; E dissipated is the dissipated energy; E input is the input vibration energy. Predict the long-term performance of the shock-absorbing material using the material yield equation, and its equation is:

[0190]

[0191] Wherein, σ eq is the equivalent stress; σ x , σy , σ z is the principal stress; τ xy , τ xz , τ yz is the shear stress; N f is the number of fatigue life cycles; σ y is the yield stress of the material; C1, C2, C3 are material constants; T is the working temperature; C4(env) is the environmental factor correction coefficient; L predicted is the predicted service life, in years; f is the main vibration frequency; t daily is the daily operating time of the equipment, in hours. Finally, compare the theoretically predicted vibration suppression rate and noise reduction value with the target values to verify the theoretical rationality of the optimal installation parameter combination. This step verifies the physical feasibility of the optimization results through mechanical theory and enhances the reliability of the installation plan.

[0192] The specific implementation manners of steps S07 - S08 are the same as those described above and will not be elaborated here in detail.

[0193] Step S09 is an optional step, and its specific implementation manner is to establish a parameter correction model based on the actual installation effect to form a complete knowledge base for the shock and noise reduction installation method of electromechanical equipment. First, compare the differences between the actually measured vibration suppression rate and noise reduction value and the theoretically predicted values, calculate the correction coefficients of each parameter. The calculation of the correction coefficient is based on the ratio of the measured value to the theoretical value, and the least - squares regression analysis is used to determine the functional relationship between the parameters and the correction coefficients. The calculation formula of the parameter correction model is:

[0194] R actual = γ vib ·R theoretical ;

[0195] L actual = γ noise ·L theoretical ;

[0196]

[0197] In the formula, R actual is the actual vibration suppression rate; R theoretical is the theoretical vibration suppression rate; L actual is the actual noise reduction value; L theoretical is the theoretical noise reduction value; γ vib and γ noise are the correction coefficients of vibration and noise respectively; x i is the i - th installation parameter; a0, a i , a ij and b0, b i , b ij are the regression coefficients; εvib and ε noise are error terms, with a range within ±0.07. The regression coefficients are solved by the least squares method:

[0198]

[0199] In the formula, y k is the actual correction coefficient; is the model-predicted correction coefficient; m is the number of samples. Then, a parameter correction model is constructed, which can automatically adjust the optimal installation parameter values according to the equipment type, installation environment, and expected service life, with the correction accuracy controlled within ±7%. Next, the parameter correction model is associated with the multi-objective optimization model in step S05 to form a closed-loop optimization system, which can continuously optimize and adjust the theoretical model according to the actual installation effect. Finally, the theoretical knowledge, algorithm models, and experimental data of all steps are integrated to establish a knowledge base for the shock and noise reduction installation method of electromechanical equipment. The knowledge base includes four parts: equipment classification catalog, parameter optimization module, material selection guide, and installation process standard. The knowledge base supports case retrieval and similarity matching functions, and can provide reference solutions and expected effect evaluations for the installation of new equipment. This step realizes the continuous optimization and knowledge accumulation of the installation method through the combination of theory and practice, and greatly improves the applicability and popularization of the shock and noise reduction method.

[0200] To better understand and implement the present invention, Example 2 of a specific application scenario of the present invention is provided below: Researchers found in the refrigeration system of a large data center that the vibration and noise generated by the equipped refrigeration compressor unit during operation seriously affected the normal operation of the surrounding office environment and precision equipment. To solve this problem, the research team adopted the shock and noise reduction installation method of electromechanical equipment of the present invention. First, the researchers constructed a multi-dimensional vibration and noise acquisition system, and set 12 acceleration sensors and 6 acoustic sensors at different positions to comprehensively collect the vibration and noise characteristics of the compressor unit under four load conditions of 25%, 50%, 75%, and 100%, with the acquisition frequency set at 48000 Hz. Specifically, the acceleration sensors were installed at different parts of the compressor body (such as the top, side, and base), the motor part, the pipeline connection points, the support structure, the connection between the unit and the ground, etc. to capture the vibration transmission paths in multiple directions. The acoustic sensors were arranged at points at different distances and directions around the compressor, near the inlet and outlet pipes, at significant positions of the radiation noise of the unit housing, in the personnel activity area of the working area, and near the adjacent precision equipment, etc. to comprehensively evaluate the spatial distribution characteristics of the noise. The original data collected is shown in Table 1:

[0201] Table 1 Original vibration and noise data under different load conditions

[0202]

[0203] Then, wavelet transform analysis was performed on the collected vibration spectrum and noise spectrum. The db4 wavelet function was used for 5-layer decomposition to extract the vibration feature vector and noise feature vector, and a dimensionality-reduced feature matrix was formed through non-negative matrix factorization. Through feature extraction and analysis, it was identified that the main vibration frequency of the compressor unit was in the range of 48 - 75 Hz, and the main noise frequency band was concentrated in the range of 250 - 2000 Hz. The key feature parameters extracted are shown in Table 2:

[0204] Table 2 Vibration and Noise Feature Parameters of Refrigeration Compressor Unit

[0205] Characteristic parameter Vibration eigenvalue Noise eigenvalue Mean value 7.48 80.8 Standard deviation 3.92 5.85 Kurtosis 2.38 1.87 Skewness 0.76 0.43 Peak-to-peak value 13.62 15.82 Energy 324.58 6553.24

[0206] Subsequently, the researchers constructed a small-scale model of the compressor unit at a ratio of 1:5, designed a set of installation parameter variables, and the parameter ranges included installation height (15 - 45 mm), inclination angle (0 - 12°), contact area (40% - 85% of the equipment bottom area), fastening torque (60% - 140% of the standard torque), and the hardness of the damping material (Shore hardness 35 - 75A). The L16(4^5) orthogonal array was used to design 16 groups of test schemes, and each group was tested 3 times repeatedly. The changes in the vibration feature matrix and noise feature matrix under different installation parameter combinations were recorded. Partial results of the orthogonal experiment are shown in Table 3:

[0207] Table 3 Partial Result Data of Orthogonal Experiment

[0208]

[0209] Based on the orthogonal experiment data, the vibration feature change matrix and noise feature change matrix were calculated by the singular value decomposition method and decomposed into a vibration stability matrix, a vibration variation matrix, a noise stability matrix, and a noise variation matrix. The singular value decomposition results showed that the cumulative contribution rate of the first 3 singular values reached 87.3%, and matrix reconstruction was performed accordingly.

[0210] Next, the research team constructed a multi-objective optimization model with the vibration suppression rate and noise reduction value as the objective functions, and the weight coefficients were set to 0.6 and 0.4 respectively. The particle swarm optimization algorithm was used to solve the optimal installation parameter combination. The algorithm parameters were set as follows: population size 50, maximum number of iterations 200, inertia weight linearly decreasing from 0.9 to 0.4, and learning factors c1 = c2 = 2.0. Through optimization calculation, the optimal installation parameter combination obtained is shown in Table 4:

[0211] Table 4 Optimal Installation Parameter Combination

[0212] Installation parameter Optimal value Installation height 32.5 mm Inclination angle 5.8° Contact area 65% of the bottom area of the device Tightening torque 110% of the standard torque Hardness of damping material 48 Shore A

[0213] Then, the research team applied the elastic damping dynamics equations to analyze the interaction between the compressor unit and the installation structure, and predicted the vibration suppression rate and noise reduction value under the optimal installation parameter combination. The theoretical prediction results are shown in Table 5 as follows:

[0214] Table 5 Theoretical prediction result data

[0215]

[0216] According to the optimal installation parameter combination, the researchers selected a polyurethane composite damping material with a Shore hardness of 48A and adopted a corrugated shock absorber structure. When determining the installation position, the vibration-sensitive points of the building structure were avoided, and the floor support points with greater stiffness were selected. The installation direction was designed so that the main vibration direction of the compressor formed a 75° angle with the direction of the maximum stiffness of the building structure to reduce vibration transmission.

[0217] After the actual installation was completed, the researchers conducted verification tests using a multi-dimensional vibration and noise acquisition system. The comparison between the actual installation effect and the theoretical prediction is shown in Table 6 as follows:

[0218] Table 6 Comparison between the actual installation effect and the theoretical prediction

[0219] Evaluation index Theoretical predicted value Actual measured value Relative error (%) Vibration suppression rate (%) 58.7 54.2 -7.7 Noise reduction value (dB) 8.5 7.8 -8.2 System resonance frequency (Hz) 16.9 18.3 8.3 Energy dissipation rate (%) 44.5 41.2 -7.4

[0220] Finally, the researchers established a parameter correction model based on the actual installation effect, calculated the correction coefficients for vibration and noise to be 0.92 and 0.91 respectively, and associated the correction model with the multi-objective optimization model to form a complete knowledge base.

[0221] Traditional shock absorption and noise reduction installations for refrigeration compressors mainly use empirical methods or single experimental methods, usually only considering simple shock pads or sound insulation covers, lacking systematic optimization and theoretical guidance. The shock absorption and noise reduction effects of these methods are limited, and it is difficult to adapt to different equipment and environmental conditions. Usually, only 25%-35% of vibration suppression and 3-5 dB of noise reduction can be achieved. However, the method adopted in the present invention constructs a complete theoretical and practical system for shock absorption and noise reduction through algorithms such as multi-dimensional data acquisition, wavelet analysis, non-negative matrix factorization, singular value decomposition, and multi-objective optimization. The implementation results show that compared with traditional methods, the present invention achieves a vibration suppression rate of 54.2% and a noise reduction value of 7.8 dB, which are increased by approximately 70% and 60% respectively, greatly improving the working environment of the data center, extending the service life of the equipment. At the same time, the established parameter correction model makes the method have good migration and adaptability, and can be widely applied to the shock absorption and noise reduction installations of various electromechanical equipment.

[0222] It should be noted that the detailed explanations of the variables involved in the present invention are shown in Tables 7, 8, and 9 as follows.

[0223] Table 7 Variable explanation table (the first part)

[0224]

[0225]

[0226] Table 8 Variable Explanation Table (Second Part)

[0227]

[0228] Table 9 Variable Explanation Table (Third Part)

[0229]

[0230]

[0231] As described above, it is only the specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or substitutions, which should all be covered within the protection scope of the present invention.

Claims

1. A method for installing an electromechanical device to reduce vibration and noise, characterized in that, It includes constructing a multi-dimensional vibration and noise acquisition system to collect vibration spectrum and noise spectrum data; performing wavelet transform analysis on the collected vibration spectrum and noise spectrum and forming a feature matrix through non-negative matrix factorization; constructing a small-scale model of the electromechanical equipment and changing the installation parameter values by the orthogonal test method; calculating the vibration feature change matrix and the noise feature change matrix and decomposing them using the singular value decomposition method; constructing a multi-objective optimization model and using the particle swarm optimization algorithm to solve the optimal installation parameter combination; applying the elastic damping dynamic equations to analyze the interaction between the electromechanical equipment and the installation structure, and predicting the vibration suppression rate and the noise reduction value; selecting a matching shock absorber material and structure type; performing actual installation.

2. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 1, wherein, The multi-dimensional vibration and noise acquisition system collects vibration spectrum and noise spectrum data at different positions, angles, and load conditions of the electromechanical equipment to form a comprehensive vibration and noise characteristic database.

3. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 2, characterized in that, Non-negative matrix factorization decomposes the high-dimensional original data matrix into the product of two non-negative matrices. One represents the basic mode, and the other represents the weight distribution of the basic mode, which is used for dimensionality reduction and discovering the internal structure of the vibration feature vector and the noise feature vector.

4. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 3, characterized in that, The small-scale model is a physical model of the electromechanical equipment scaled down according to a certain ratio in accordance with the principle of geometric similarity, maintaining the similarity relationship of mechanical and dynamic characteristics between the prototype and the model, and is used for verifying and optimizing the installation parameter variable set before actual installation.

5. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 4, characterized in that, The installation parameter variable set includes installation height, inclination angle, contact area, fastening torque, and shock absorber material hardness.

6. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 5, characterized in that, The elastic damping dynamic equations include the mass damping equation, the stiffness vibration equation, the heat conduction equation, and the material yield equation.

7. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 6, characterized in that, The mass damping equation is used to describe the dynamic relationship between the mass of the electromechanical equipment and the damping coefficient. The inputs include the equipment mass distribution obtained from the vibration feature matrix, the damping coefficient obtained from the shock absorber material, the external excitation frequency obtained from the vibration spectrum, the support structure stiffness obtained from the installation structure, and the contact area parameter obtained from the installation parameter variable set. The output is the system damping response curve.

8. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 7, wherein, The stiffness vibration equation is used to analyze the influence of the stiffness matching between the electromechanical equipment and the installation structure on vibration transmission. The inputs include the support structure stiffness matrix obtained from the installation structure, the vibration frequency spectrum obtained from the vibration spectrum, the equipment natural frequency obtained from the electromechanical equipment, the connection point distribution obtained from the installation parameter variable set, and the environmental temperature coefficient obtained from the installation environment. The output is the vibration transfer function.

9. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 8, characterized in that, The heat conduction equation is used to evaluate the efficiency of the conversion of vibration energy into heat energy and its influence on the shock absorption performance. The inputs include the thermal conductivity obtained from the shock absorber material, the vibration power density obtained from the vibration feature matrix, the contact area obtained from the installation parameter variable set, the material thickness obtained from the shock absorber material, and the temperature gradient obtained from the installation environment. The output is the energy dissipation rate.

10. The installation method for shock absorption and noise reduction of the electromechanical equipment according to claim 9, characterized in that, The material yield equation is used to predict the change of the yield characteristics of the shock absorber material under long-term vibration. The inputs include the elastic modulus obtained from the shock absorber material, the yield stress obtained from the shock absorber material, the cumulative vibration cycle number predicted by the vibration spectrum, the stress amplitude obtained from the vibration feature matrix, and the environmental factor correction coefficient obtained from the installation environment. The output is the material life prediction curve.

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