Mechanical and electrical equipment shock absorption and noise reduction installation method

Abstract

The application provides a mechanical and electrical equipment shock absorption and noise reduction installation method, and belongs to the technical field of mechanical and electrical equipment installation. A multi-dimensional vibration noise collection system is first constructed to collect comprehensive vibration noise characteristic data. Then, vibration noise characteristics are extracted through wavelet transform and non-negative matrix decomposition. Next, a small-scale model is constructed, and the influence of installation parameters is analyzed by using an orthogonal test method. Singular value decomposition is used to obtain a vibration noise variation matrix. A multi-objective optimization model is constructed based on this, and a particle swarm algorithm is used to solve optimal installation parameters. The rationality of the parameters is verified by using an elastic damping dynamics equation set. A matched shock absorber material and installation position are selected. Actual installation is performed according to the optimal parameters, and the effect is verified. Finally, a parameter correction model is established, a complete knowledge base is formed, and precise optimization of mechanical and electrical equipment shock absorption and noise reduction installation is realized.

Description

Technical Field

[0001] This invention belongs to the field of electromechanical equipment installation technology, and more specifically, relates to a vibration reduction and noise reduction installation method for electromechanical equipment. Background Technology

[0002] Vibration and noise reduction installation of electromechanical equipment is an important technology in industrial production and civil equipment fields. Traditional installation methods mainly rely on experience to select vibration damping materials and installation parameters, or use simple passive vibration damping devices such as spring vibration isolators and rubber pads. These methods are commonly used in engineering practice in scenarios such as elevator machine rooms, central air conditioning systems, industrial pump stations, and large generator sets, achieving basic vibration and noise reduction effects through empirical parameter settings and standardized installation procedures.

[0003] However, traditional technologies have obvious drawbacks: First, the vibration reduction and noise reduction effect is highly dependent on the experience of the installers and lacks a systematic parameter optimization mechanism; second, it is difficult to take into account the vibration and noise characteristics under different load conditions and operating modes at the same time; third, it is impossible to achieve accurate identification and targeted suppression of multi-frequency vibration and noise; and fourth, the selection of installation parameters lacks dynamic adaptability and is difficult to optimize and adjust for changes in operating conditions throughout the entire life cycle of the equipment.

[0004] Faced with modern high-precision, high-speed operating electromechanical equipment, traditional technologies struggle to address the complex coupling of vibration and noise under various operating conditions. In particular, when electromechanical equipment exhibits significantly varying vibration and noise characteristics under different loads, ambient temperatures, and operating frequencies, traditional empirical or single-parameter optimization installation methods cannot achieve optimal vibration and noise reduction across the entire frequency band and operating conditions. This leads to problems such as decreased equipment performance, shortened lifespan, and noise pollution in the surrounding environment. In other words, existing technologies suffer from the inability to simultaneously and accurately analyze and optimize vibration and noise across multiple operating conditions and frequency bands during the installation of electromechanical equipment. Summary of the Invention

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

[0006] This invention is implemented as follows: It provides a vibration and noise reduction installation method for electromechanical equipment, including constructing a multi-dimensional vibration and noise acquisition system to collect vibration and noise spectrum data; performing wavelet transform analysis on the collected vibration and noise spectra and forming feature matrices through non-negative matrix decomposition; constructing a small-scale model of the electromechanical equipment and changing installation parameter values ​​through orthogonal experimental design; calculating the vibration characteristic change matrix and noise characteristic change matrix and decomposing them using singular value decomposition; constructing a multi-objective optimization model and using particle swarm optimization to solve for the optimal combination of installation parameters; applying the elastic damping dynamic equations to analyze the interaction between the electromechanical equipment and the installation structure, predicting the vibration suppression rate and noise reduction value; selecting matching shock absorber materials and structural types; 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 electromechanical equipment, forming a comprehensive vibration and noise characteristic database.

[0008] Nonnegative matrix decomposition decomposes a high-dimensional original data matrix into the product of two nonnegative matrices, one representing the basic pattern and the other representing the weight distribution of the basic pattern. This is used to reduce dimensionality and discover the intrinsic structure of vibration feature vectors and noise feature vectors.

[0009] Among them, the small-scale model is a physical model of electromechanical equipment scaled down according to the principle of geometric similarity. It maintains the similarity between the mechanical and dynamic characteristics of the prototype and the model, and is used to verify and optimize the set of installation parameter variables before actual installation.

[0010] The set of installation parameter variables includes installation height, tilt angle, contact area, fastening torque, and hardness of the damping material.

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

[0012] The mass damping equation describes the dynamic relationship between the mass of 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 parameters obtained from the installation parameter variable set. The output is the system damping response curve.

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

[0014] The heat conduction equation is used to evaluate the efficiency of vibration energy conversion into heat energy and its impact on damping performance. The inputs include the thermal conductivity obtained from the damper 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 damper material, and the temperature gradient obtained from the installation environment. The output is the energy dissipation rate.

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

[0016] This invention constructs a comprehensive vibration and noise characteristic database, extracts key features by combining wavelet transform and nonnegative matrix decomposition techniques, systematically analyzes the influence of installation parameter variables on vibration reduction and noise reduction effects using a small-scale model orthogonal experiment method, and finally uses a particle swarm optimization algorithm to solve for the optimal combination of installation parameters.

[0017] This method effectively addresses the shortcomings of traditional technologies. First, it acquires comprehensive vibration and noise characteristic data through a multi-dimensional vibration and noise acquisition system, breaking the limitations of traditional reliance on experience. Second, it applies singular value decomposition to decompose the characteristic variation matrix into a stable matrix and a variable matrix, achieving accurate identification and targeted suppression of multi-frequency vibration and noise. Third, the application of the elastic damping dynamic equations ensures that the optimization of installation parameters is based on a solid theoretical foundation, guaranteeing the stability of vibration reduction and noise reduction effects under different working conditions. Finally, based on the parameter correction model of actual installation results, the installation method achieves self-improvement and continuous optimization.

[0018] Through the above-mentioned systematic technological innovations, this invention has successfully solved the problem of accurate analysis and optimization of vibration and noise of electromechanical equipment under multiple operating conditions and multiple frequency bands. This makes the vibration reduction and noise reduction effect no longer limited to specific operating conditions or frequency bands, but can be dynamically optimized for various operating states throughout the entire life cycle of the equipment. This significantly improves the operational stability of electromechanical equipment, extends its service life, and improves the noise conditions of the surrounding environment. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

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

[0021] like Figure 1 The diagram shown is a flowchart of a vibration damping and noise reduction installation method for electromechanical equipment provided by the present invention. This method includes the following steps:

[0022] S01. Construct a multi-dimensional vibration and noise acquisition system to collect vibration spectrum and noise spectrum data under different positions, angles and load conditions of electromechanical equipment, and form a comprehensive vibration and noise characteristic database.

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

[0024] S03. Construct a small-scale model of the electromechanical equipment, design a set of installation parameter variables, including installation height, tilt angle, contact area, fastening torque and damping material hardness, change the installation parameter values ​​in the set of installation parameter variables through the orthogonal test method of the small-scale model, and record the changes of the vibration characteristic matrix and the noise characteristic matrix.

[0025] S04. Based on the test data obtained by the small-scale model orthogonal test method, calculate the vibration characteristic change matrix and the noise characteristic change matrix, and use the singular value decomposition method to decompose the vibration characteristic change matrix and the noise characteristic 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 noise reduction value as objective functions, and use the particle swarm optimization algorithm to solve for the optimal combination of installation parameters.

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

[0028] S07. Based on the optimal combination of installation parameters, select matching shock absorber materials and structural types, and determine the installation position and direction of the electromechanical equipment;

[0029] S08. Install the electromechanical equipment according to the optimal installation parameter combination. Optionally, after installation, use the multi-dimensional vibration and noise acquisition system to perform vibration and noise testing to verify the vibration suppression rate and the noise reduction value.

[0030] S09. Optionally, it also includes establishing a parameter correction model based on actual installation results, and associating the parameter correction model with the multi-objective optimization model to form a complete knowledge base of vibration reduction and noise reduction installation methods for electromechanical equipment.

[0031] Specifically, wavelet transform analysis uses wavelet functions to decompose the signal in the time-frequency domain, extracting the energy distribution characteristics of different frequency bands, thereby identifying the main frequency components of the vibration spectrum and the noise spectrum and their amplitude variation patterns.

[0032] Specifically, nonnegative matrix decomposition decomposes the high-dimensional original data matrix into the product of two nonnegative matrices, one representing the basic pattern and the other representing the weight distribution of the basic pattern, which is used to reduce dimensionality and discover the intrinsic structure of the vibration feature vector and the noise feature vector.

[0033] Specifically, the small-scale model is a physical model of the electromechanical equipment that is scaled down according to the principle of geometric similarity, maintaining the similarity between the mechanical and dynamic characteristics of the prototype and the model, and is used to verify and optimize the set of installation parameter variables before actual installation.

[0034] Among them, the orthogonal experimental design method is a highly efficient experimental design method. By arranging the combination of experimental factor levels through orthogonal arrays, it can obtain the most experimental information with the fewest number of experiments, thereby systematically analyzing the influence of multiple factors on the vibration suppression rate and the noise reduction value.

[0035] Specifically, the singular value decomposition method decomposes the vibration feature change matrix and the noise feature change matrix into the product of three matrices: the left singular vector matrix, the singular value diagonal matrix, and the right singular vector matrix transpose. The vibration stability matrix, the vibration variation matrix, the noise stability matrix, and the noise variation matrix are separated by retaining the main singular values.

[0036] Among them, the particle swarm optimization algorithm is a swarm intelligence optimization method that simulates the foraging behavior of bird flocks. It searches for the global optimal solution of the optimal installation parameter combination in the search space by iteratively updating the particle position and velocity.

[0037] The elastic damping dynamics equations include the mass damping equation, stiffness vibration equation, heat conduction equation, and 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 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, which is used to calculate the vibration suppression rate.

[0039] The stiffness vibration equation is used to analyze the influence of 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 ambient temperature coefficient obtained from the installation environment. The output is a 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 vibration energy conversion into heat energy and its impact on damping performance. The inputs include the thermal conductivity obtained from the damper 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 damper 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 damper material.

[0041] The material yield equation is used to predict 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 period number 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 a material life prediction curve, which is used to evaluate the long-term stability of the vibration reduction and noise reduction installation method of the electromechanical equipment.

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

[0043] The specific implementation of step S01 involves constructing a multi-dimensional vibration and noise acquisition system. This system consists of multiple high-precision accelerometers, acoustic sensors, and data acquisition devices. First, at least eight accelerometers are evenly arranged on the surface of the electromechanical equipment. The sensors have a sensitivity of at least 100 mV / g and a frequency response range of 0–10000 Hz. Then, at least four acoustic sensors are installed 1 meter away from the perimeter of the electromechanical equipment. These acoustic sensors have a sensitivity of at least 50 mV / Pa and a frequency response range of 20–20000 Hz. Next, four different load conditions (25%, 50%, 75%, and 100%) are set on the electromechanical equipment. Under each load condition, vibration and noise data in the X, Y, and Z directions are collected. The sampling frequency is at least 44100 Hz, and each sampling duration is at least 60 seconds. Finally, the collected data undergoes preliminary filtering to remove 50 Hz power supply interference and environmental background noise, forming a vibration and noise characteristic database covering all operating conditions. The establishment of this database provides a comprehensive data foundation for subsequent analysis, effectively ensuring the relevance and effectiveness of vibration reduction and noise reduction solutions.

[0044] The specific implementation of step S02 involves using wavelet transform and nonnegative matrix factorization (NMF) techniques to perform in-depth processing and feature extraction on the acquired vibration and noise spectra. First, the db4 wavelet function is used to perform a 5-level decomposition of the vibration and noise signals to obtain approximation and detail coefficients. Based on energy distribution characteristics, frequency bands with an energy contribution rate exceeding 5% in the main frequency components are extracted as feature bands. Then, statistical parameters for each feature band are calculated, including mean, standard deviation, kurtosis, skewness, and peak-to-peak value, forming vibration and noise feature vectors. Next, an original feature matrix is ​​constructed, where rows represent sampling points and columns represent feature parameters. The NMF algorithm is applied, with the decomposition rank set to 30% of the original feature count, at least 1000 iterations, and a convergence threshold set to 10. -4 The original feature matrix is ​​decomposed into a basic pattern matrix and a weight allocation matrix. Finally, based on the decomposition results, a dimensionality-reduced vibration feature matrix and noise feature matrix are formed for subsequent parameter optimization. This step, through joint time-frequency domain analysis, reveals the intrinsic characteristics of vibration and noise, providing a theoretical basis for precise control.

[0045] The specific implementation of step S03 involves constructing a small-scale model of the electromechanical equipment and conducting orthogonal experiments. First, based on similarity theory, a physical model of the electromechanical equipment is constructed at a geometric scale of 1:5, ensuring that the structural, mass, and stiffness ratios between the model and the prototype meet similarity conditions. Then, a set of installation parameter variables is designed, including installation height (10–50 mm), tilt angle (0–15°), contact area (30%–90% of the original equipment's bottom area), tightening torque (50%–150% of the standard torque), and damping material hardness (Shore hardness 30–85A). Next, an L16 (4^5) orthogonal array is created using the orthogonal experimental design method, determining 16 test schemes. Each test scheme is repeated three times under the same environmental conditions to ensure data reliability. In each test, the changes in the vibration characteristic matrix and noise characteristic matrix obtained in step S02 are recorded, and the rate of change of vibration intensity and noise intensity under each test condition is calculated. Finally, the range analysis method is applied to determine the ranking of the influence of each parameter on the vibration reduction and noise reduction effect. This step effectively simulates actual installation conditions using a small-scale model, significantly reducing testing costs and improving the efficiency of parameter optimization.

[0046] The specific implementation of step S04 is based on calculating the characteristic variation matrix and performing singular value decomposition on orthogonal experimental data. First, the vibration characteristic matrix and noise characteristic matrix under different installation parameter combinations in step S03 are compared with the characteristic matrix under the original state to calculate the difference, obtaining the vibration characteristic variation matrix and noise characteristic variation matrix. Then, the singular value decomposition algorithm is applied to these two variation matrices respectively, representing the matrix 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. Next, the distribution of singular values ​​is analyzed, and the contribution rate threshold of the main singular values ​​is determined to be 85%. Singular values ​​whose cumulative contribution rate reaches this threshold and their corresponding singular vectors are retained. The matrices are reconstructed using the retained singular values ​​and singular vectors, separating the vibration stability matrix, vibration variation matrix, noise stability matrix, and noise variation matrix. Finally, the eigenvalues ​​and condition numbers of these four matrices are calculated to evaluate their stability and sensitivity. This step effectively separates the influence of installation parameter changes on vibration and noise characteristics, providing a clear mathematical model for subsequent optimization.

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

[0048] The specific implementation of step S06 involves applying the elastic damping dynamic equations to verify the theoretical rationality of the optimal installation parameter combination. First, a coupled dynamic model of the electromechanical equipment and the installation structure is constructed, treating the equipment as a flexible body and the installation structure as an elastic support with damping characteristics. Then, the system damping response curve is calculated using the mass damping equation. The inputs to this equation include the equipment mass distribution, damping coefficient of the damping material, external excitation frequency, stiffness of the support structure, and contact area parameters. The output damping response curve is used to predict the vibration suppression rate. The vibration transmission characteristics between the equipment and the installation structure are analyzed using the stiffness vibration equation. The inputs to this equation include the stiffness matrix of the support structure, vibration frequency spectrum, equipment natural frequency, connection point distribution, and ambient temperature coefficient. The output vibration transfer function is used to optimize the installation position and orientation. Finally, the efficiency of vibration energy conversion to heat energy is evaluated using the heat conduction equation. The inputs to this equation include the thermal conductivity of the damping material, vibration power density, contact area, material thickness, and temperature gradient. The output energy dissipation rate is used to guide the selection of damping materials. The long-term performance of vibration damping materials is predicted using the material yield equation. This equation takes into account the material's elastic modulus, yield stress, cumulative vibration period, stress amplitude, and environmental factor correction coefficients. 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 values ​​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 results through mechanical theory, enhancing the reliability of the installation scheme.

[0049] The specific implementation of step S07 involves selecting matching damper materials and structural types based on the optimal combination of installation parameters, and determining the installation location and direction of the electromechanical equipment. First, based on the optimal installation height and damping material hardness parameters determined in step S05, the most suitable damping material is selected from materials such as rubber, polyurethane, and elastomer composites. Material selection criteria include frequency matching (matching the equipment's main frequency by no less than 80%), temperature stability (hardness change not exceeding 15% within the operating temperature range), and aging characteristics (performance degradation not exceeding 20% ​​within a 3-year service life). Then, based on the optimal tilt angle and contact area parameters, a suitable damper structural type is selected. Structural types include flat plate, conical, corrugated, and composite types. Selection criteria include load distribution uniformity, directional damping effect, and spatial adaptability. Next, based on the output results of the stiffness vibration equation, the optimal installation location of the electromechanical equipment is determined. The installation location should avoid vibration-sensitive points and acoustic standing wave points of the building structure, while ensuring sufficient space for equipment operation and maintenance. Finally, based on the vibration transfer function analysis results, the installation direction of the equipment is determined, ensuring that the vibration transmission path of the main vibration source is perpendicular to the direction of maximum stiffness of the building structure. This step transforms the theoretical optimization results into specific engineering implementation plans, ensuring the actual realization of vibration reduction and noise reduction effects.

[0050] The specific implementation of step S08 involves actually installing the electromechanical equipment according to the optimal combination of installation parameters and verifying the installation effect. First, prepare the installation site, clean the installation surface, measure and mark the installation position reference points, ensuring that the flatness error of the installation surface does not exceed 2mm / m. Then, adjust the position of the shock absorber according to the optimal installation height and tilt angle, using a level to ensure that the equipment tilt angle deviation does not exceed ±0.5°. Next, according to the optimal tightening torque parameters, use a torque wrench to tighten the connecting bolts sequentially, following a diagonal cross principle, with the tightening torque error controlled within ±5%. Optional steps follow, including, after installation, using the multi-dimensional vibration and noise acquisition system from step S01 to conduct vibration and noise tests. Under the same working conditions and measuring point locations, collect the vibration spectrum and noise spectrum after installation, calculate the actual obtained vibration suppression rate and noise reduction value, and compare them with the theoretical predicted 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 is verified to meet the requirements. This step, through a standardized installation process and rigorous effect verification, ensures the effectiveness of the vibration reduction and noise reduction method in practical applications.

[0051] Step S09 is optional. Its specific implementation involves establishing a parameter correction model based on actual installation results, forming a complete knowledge base for vibration and noise reduction installation methods for electromechanical equipment. First, the differences between the actual measured vibration suppression rate and noise reduction value and the theoretical predicted value are compared, and correction coefficients for each parameter are calculated. The calculation of correction coefficients is based on the ratio of measured values ​​to theoretical values, and least squares regression analysis is used to determine the functional relationship between parameters and correction coefficients. Then, a parameter correction model is constructed. This model can automatically adjust the optimal installation parameter values ​​according to equipment type, installation environment, and expected service life, with a 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. This system can continuously optimize and adjust the theoretical model based on actual installation results. Finally, the theoretical knowledge, algorithm models, and experimental data from all steps are integrated to establish a knowledge base for vibration and noise reduction installation methods for electromechanical equipment. The knowledge base includes four parts: equipment classification directory, parameter optimization module, material selection guide, and installation process standards. The knowledge base supports case retrieval and similarity matching functions, providing reference solutions and expected effect evaluations for the installation of new equipment. This step, through the combination of theory and practice, has enabled continuous optimization of installation methods and accumulation of knowledge, significantly improving the applicability and scalability of vibration reduction and noise reduction methods.

[0052] The mathematical model or calculation process involved in this invention will be described in detail below.

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

[0054]

[0055] In the formula, S vib (f) represents the vibration spectrum; S noise (f) represents the noise spectrum; a i p is the acceleration value at the i-th time point; i Let f be the sound pressure level at time point i; f be the frequency; t be the sound pressure level at time point i. i For the i-th sampling time point; w(t) i ) is the window function, usually the Hanning window is used to reduce spectral leakage; N is the number of sampling points; j is the complex unit.

[0056] The data acquisition method for vibration and noise spectra is as follows: First, accelerometers are uniformly arranged on the surface of the electromechanical equipment, with a sensor sensitivity of not less than 100 mV / g. Then, the raw time-domain signal is acquired through a data acquisition system at a sampling frequency of not less than 44100 Hz. Next, the raw signal is preprocessed, including removing the DC component and applying a window function. Finally, the time-domain signal is converted into a frequency-domain signal using a fast Fourier transform to obtain the vibration and noise spectra. The spectrum calculation adopts the average periodogram method, dividing the long-time signal into segments, each segment with a length of 8192 points and an overlap rate of 50%, to improve the reliability of spectrum estimation.

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

[0058]

[0059] In the formula, C j，k ψ represents the wavelet coefficients; s(t) represents the original signal; ψ represents the wavelet coefficients. j，k (t) represents a scale of 2 j ψ is a wavelet function shifted by k. * (t) represents the complex conjugate of ψ(t); j is the number of decomposition scale layers, ranging from 1 to 5; k is the translation parameter.

[0060] The wavelet transform coefficients are obtained as follows: First, the db4 wavelet function is selected as the basis function; then, the original signal is decomposed into 5 levels to obtain an approximate coefficient and five detail coefficients; next, the energy distribution of the signal at each scale is calculated, and the frequency band with an energy contribution rate of more than 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 nonnegative matrix factorization is shown below:

[0062] V≈W·H;

[0063]

[0064] stW≥0, H≥0;

[0065] In the formula, is the original feature matrix, m is the number of sampling points, and n is the number of features; This is the basic pattern matrix; The weight assignment matrix is ​​used; r is the decomposition rank, set to 30% of the original number of features; ∥·∥ F This represents the Frobenius norm.

[0066] The method for obtaining nonnegative matrix factorization parameters is as follows: First, construct the original feature matrix V, where each row represents a sampling point and each column represents a feature parameter; then, randomly initialize matrices W and H as nonnegative matrices; next, iteratively update W and H using the alternating least squares method, with the update rule as follows:

[0067]

[0068] The number of iterations should be no less than 1000, and the convergence threshold should be set to 10. -4 That is, when the change in the objective function value between two iterations is less than 10. -4 Stop iterating when the time comes.

[0069] The construction process of vibration feature vectors and noise feature vectors is specifically represented 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] In the formula, F vib F is the vibration eigenvector; noise f is the noise feature vector; mean f is the signal mean; std f is the standard deviation of the signal. kurt For signal kurtosis; f skew For signal skewness; f p-p f is the peak-to-peak value of the signal. energy This refers to signal energy.

[0073] The characteristic parameters are calculated as follows:

[0074]

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

[0076]

[0077] In the formula, x i Let be 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 represented as follows:

[0079] ΔM vib =M vib -M vib_0 ;

[0080] ΔM noise =M noise -M noise_0 ;

[0081]

[0082] In the formula, M vib The vibration characteristic matrix under different combinations of installation parameters; M noise The noise characteristic matrix under different combinations of installation parameters; M vib_0 M represents the vibration characteristic matrix in its original state. noise_0 The noise feature matrix in the original state; ΔM vib The vibration characteristic variation matrix; ΔM noise U is the noise feature variation matrix; vib and U noise For a left singular vector matrix; ∑ vib and ∑ noise It is a singular value diagonal matrix; and It is the transpose of the right singular vector matrix.

[0083] After singular value decomposition, the matrix is ​​divided into a stable part and a variable part based on the contribution rate of the singular values:

[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 M is the vibration stability matrix; vib_variable M is the vibration variation matrix; noise_stable M is the noise stability matrix; noise_variable The noise variation matrix; ∑ vib_stable and ∑ noise_stable These are diagonal matrices that retain the principal singular values ​​(those with a cumulative contribution rate of 85%), with all other singular values ​​set to 0; ∑ vib_variable and Σ noise_variable These are diagonal matrices that retain minor singular values, with major singular values ​​set to 0.

[0089] The method for calculating the singular value contribution rate is as follows:

[0090]

[0091] In the formula, C i The contribution rate of the i-th singular value; σ i Let be the i-th singular value; n is the total number of singular values; C cumulative，k This represents 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 represented as follows:

[0093]

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

[0095] F(x) = w1·f1(x) + w2·f2(x);

[0096] maxF(x);

[0097] stg 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 objective function for vibration suppression rate; f2(x) is the objective function for noise reduction; F(x) is the comprehensive objective function; x = [x1, x2, ..., x...]. n [M] is a vector of installation parameters, including installation height, tilt angle, contact area, tightening torque, and damping material hardness; vib_0 M represents the vibration characteristic matrix in its original state. vib(x) is the vibration characteristic matrix when the installation parameter is x; ||·|| F L represents the Frobenius norm; p0 The noise sound pressure level under original conditions, in dB; L p (x) represents the noise sound pressure level (dB) when the installation parameter is x; w1 and w2 are weighting coefficients, set to 0.6 and 0.4 respectively; g j (x) represents the inequality constraints; h k (x) represents the equality constraint; and These are the lower and upper limits of the i-th installation parameter, respectively.

[0101] The constraints specifically include:

[0102] (Stability constraints)

[0103] (Spatial height constraints)

[0104] (Noise Limit Constraints)

[0105] In the formula, K stable is the system stability coefficient; m is the equipment mass; g is the gravitational acceleration; x1 is the installation height; h device h represents the equipment height. max Maximum permissible height; L work Noise level during operation; L limit This is the noise limit.

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

[0107]

[0108] In the formula, Let be the velocity of the i-th particle in the t-th iteration; pbest represents the position of the i-th particle in the t-th iteration. i is the historical best position of the i-th particle; gbest is the global best position; w is the inertia weight, which decreases linearly 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.

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

[0114] Calculation of system damping response curve:

[0115]

[0116] In the formula, H(ω) is the system frequency response function; ω is the angular frequency; j is the complex unit; H0(ω) is the frequency response function under the original state; R vib This represents the vibration suppression rate.

[0117] 2. Stiffness vibration equation:

[0118]

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

[0120]

[0121] In the formula, K total K represents the total stiffness of the system. device For equipment stiffness; K mount For the stiffness of the vibration damping device; K structure To support structural stiffness; K mount0 The stiffness of the damping device at the reference temperature; α T ΔT is the temperature coefficient; f(A, θ) is a function related to the contact area A and the tilt angle θ; t(ω) is the vibration transfer function; ω is the excitation frequency; ω n ζ is the system's natural frequency; ζ is the damping ratio.

[0122] 3. Heat conduction equation:

[0123]

[0124] q v =η·ω·σ·ε;

[0125]

[0126] In the formula, ρ is the material density; c p Specific heat capacity; T is temperature; t is time; k is thermal conductivity; For the Laplace operator; q v For volumetric heat sources, η represents the portion of vibrational energy converted into heat energy; ω is the loss factor; ω is the angular frequency; σ is the stress; ε is the strain; D E E represents the energy dissipation rate. dissipated Energy dissipated; E input The input vibrational energy.

[0127] 4. Material yield equation:

[0128]

[0129] In the formula, σ eq For equivalent stress; σ x , σ y , σ z Principal stress; τ xy , τ xz , τ yz For shear stress; N f σ represents the number of fatigue life cycles. y C1, C2, and C3 are material constants; T is the operating temperature; C4(env) is the environmental factor correction factor; L predicted The predicted service life is expressed in years; f is the dominant vibration frequency; t daily This represents the equipment's daily operating time, expressed in hours.

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

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

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

[0133]

[0134] In the formula, R actual R represents the actual vibration suppression rate. theoretical L represents the theoretical vibration suppression rate. actual This represents the actual noise reduction value; L theoretical This represents the theoretical noise reduction value; r vib and γ noise These are the correction factors for vibration and noise, respectively; x i For the i-th installation parameter; a0, a i aij and b0, b i b ij ε is the regression coefficient; vib and ε noise This is the error term, within ±0.07.

[0135] The regression coefficients are obtained using the least squares method:

[0136]

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

[0138] The construction principles and significance of these equations are as follows: Wavelet transform formulas employ scaling and translation operations, effectively capturing the time-frequency characteristics of signals, making them particularly suitable for analyzing non-stationary signals such as vibration and noise of electromechanical equipment; Non-negative matrix decomposition achieves dimensionality reduction and feature extraction by decomposing high-dimensional data into a product of low-rank matrices, overcoming the limitation of traditional principal component analysis requiring data to follow a Gaussian distribution; Singular value decomposition decomposes a matrix into a product of three matrices, revealing the intrinsic structure of the data and separating the stable and variable parts of vibration and noise by retaining singular values ​​with different contribution rates, providing a mathematical basis for parameter optimization; Multi-objective optimization models combine vibration suppression and noise reduction objectives through weighted coefficients, maximizing the overall effect; Elastic damping dynamic equations comprehensively describe the dynamic behavior of electromechanical equipment and installation structures from four aspects: mass, stiffness, heat conduction, and material yielding, providing a mechanical basis for theoretical verification; Parameter correction models bridge the gap between theoretical predictions and actual effects, capturing the interaction between parameters through a quadratic regression model, improving the applicability and accuracy of the model. These equations take into account the effects of nonlinearity, coupling effects, and environmental factors, making the vibration reduction and noise reduction methods more accurate and adaptable.

[0139] Specifically, the principle of this invention is as follows: The technical principle of this 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," it achieves precise optimization of the installation parameters for vibration reduction and noise reduction of electromechanical equipment. Its core principle can be divided into four levels:

[0140] First, at the feature extraction and pattern recognition level, this invention employs wavelet transform for time-frequency domain decomposition, which can accurately capture the characteristics of vibration noise signals in different frequency bands, overcoming the shortcomings of traditional Fourier transform in processing non-stationary signals. Combined with non-negative matrix factorization technology, the high-dimensional vibration noise data is reduced in dimensionality and its intrinsic structure is extracted, enabling the system to identify the main patterns and contributing factors of vibration noise. This dual feature extraction mechanism allows this invention to specifically identify key vibration noise frequency bands under different operating conditions.

[0141] Secondly, regarding the analysis of parameter influence mechanisms, this invention systematically analyzes the impact of parameters such as installation height, tilt angle, contact area, fastening torque, and damping material hardness on vibration and noise suppression through a small-scale orthogonal experimental method. The application of singular value decomposition further decomposes the vibration and noise characteristic variation matrix into stable and variable parts, enabling the system to accurately grasp the influence of parameter changes on vibration and noise reduction, avoiding the blind selection of parameters in traditional technologies.

[0142] Third, multi-objective optimization decision-making. Based on the vibration variation matrix and noise variation matrix, this invention constructs a multi-objective optimization model with vibration suppression rate and noise reduction as objective functions, and uses particle swarm optimization algorithm to find the global optimum in high-dimensional parameter space. This swarm intelligence-based optimization method avoids the shortcomings of traditional single-objective optimization or empirical parameter selection, which are prone to getting trapped in local optima, and ensures the best vibration reduction and noise reduction effect under complex and variable working conditions.

[0143] Fourth, theoretical verification and dynamic correction. This invention applies the elastic damping dynamic equations, including the mass damping equation, stiffness vibration equation, heat conduction equation, and material yield equation, to theoretically predict and verify the effectiveness of the optimal combination of installation parameters. Simultaneously, a parameter correction model based on actual installation results is established, enabling the self-improvement and continuous optimization of the installation method, thus giving the system the ability to cope with changes in operating conditions throughout the equipment's entire lifecycle.

[0144] The above four levels of technical principles are organically combined to form a complete system of vibration reduction and noise reduction installation methods for electromechanical equipment. This system can fundamentally solve the technical problems of accurate analysis and optimization of vibration and noise in multiple working conditions and multiple frequency bands of electromechanical equipment. It conforms to the basic theories of systems engineering and vibration and noise control, and has a solid scientific foundation and practical application value.

[0145] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0146] The specific implementation of step S01 involves constructing a multi-dimensional vibration and noise acquisition system. This system consists of multiple high-precision accelerometers, acoustic sensors, and data acquisition equipment. First, at least eight accelerometers are evenly arranged on the surface of the electromechanical equipment. The sensors have a sensitivity of at least 100 mV / g and a frequency response range of 0–10000 Hz. Then, at least four acoustic sensors are installed 1 meter away from the perimeter of the electromechanical equipment. These acoustic sensors have a sensitivity of at least 50 mV / Pa and a frequency response range of 20–20000 Hz. Next, four different load conditions (25%, 50%, 75%, and 100%) are set on the electromechanical equipment. Under each load condition, vibration and noise data in the X, Y, and Z directions are collected. The sampling frequency is at least 44100 Hz, and each sampling duration is at least 60 seconds. Finally, the collected data undergoes preliminary filtering to remove 50 Hz power supply interference and environmental background noise, forming a vibration and noise characteristic database covering all operating conditions. The calculation formulas for the collected vibration and noise spectrum data are as follows:

[0147]

[0148] In the formula, S vib (f) represents the vibration spectrum; S noise (f) represents the noise spectrum; a i p is the acceleration value at the i-th time point; i Let f be the sound pressure level at time point i; f be the frequency; t be the sound pressure level at time point i. i For the i-th sampling time point; w(t) i ) represents the window function, typically the Hanning window, to reduce spectral leakage; N is the number of sampling points; and j is the complex unit. The establishment of this database provides a comprehensive data foundation for subsequent analysis, effectively ensuring the relevance and effectiveness of the vibration reduction and noise reduction scheme.

[0149] The specific implementation of step S02 involves using wavelet transform and nonnegative matrix factorization techniques to perform in-depth processing and feature extraction on the acquired vibration and noise spectra. First, the db4 wavelet function is used to perform a 5-level decomposition on the vibration and noise signals 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 tk);

[0152] In the formula, C j，k ψ represents the wavelet coefficients; s(t) represents the original signal; ψ represents the wavelet coefficients. j，k (t) represents a scale of 2 j ψ is a wavelet function shifted by k.* (t) represents the complex conjugate of ψ(t); j is the decomposition scale level, ranging from 1 to 5; k is the translation parameter. Based on the energy distribution characteristics, frequency bands with an energy contribution rate exceeding 5% among the main frequency components are extracted as characteristic frequency bands. Then, the statistical parameters of each characteristic frequency band are calculated to form vibration feature vectors and noise feature vectors, constructed using the following formula:

[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 f is the vibration eigenvector; noise f is the noise feature vector; mean f is the signal mean; std f is the standard deviation of the signal. kurt For signal kurtosis; f skew For signal skewness; f p-p f is the peak-to-peak value of the signal. energy This represents the signal energy. Next, the original feature matrix is ​​constructed, where rows represent sampling points and columns represent feature parameters. The non-negative matrix factorization algorithm is applied, and its calculation formula is as follows:

[0156] V≈W·H;

[0157]

[0158] stW≥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; This is the basic pattern matrix; The weight assignment matrix is ​​used; r is the decomposition rank, set to 30% of the original number of features; ∥·∥ F Let Frobenius norm be used. The decomposition rank is set to 30% of the original feature count, the number of iterations is no less than 1000, and the convergence threshold is set to 10. -4The original feature matrix is ​​decomposed into a basic pattern matrix and a weight allocation matrix. Finally, based on the decomposition results, a dimensionality-reduced vibration feature matrix and noise feature matrix are formed for subsequent parameter optimization. This step, through joint time-frequency domain analysis, reveals the intrinsic characteristics of vibration and noise, providing a theoretical basis for precise control.

[0160] The specific implementation method of step S03 is the same as described above, and will not be repeated in detail here.

[0161] The specific implementation of step S04 is based on calculating the characteristic variation matrix and performing singular value decomposition using orthogonal experimental data. First, the vibration characteristic matrix and noise characteristic matrix under different installation parameter combinations in step S03 are compared with the characteristic matrix under the original state to calculate the difference, resulting in the vibration characteristic variation matrix and noise characteristic variation matrix. The calculation formula is as follows:

[0162] ΔM vib =M vib -M vib_0 ;

[0163] ΔM noise =M noise -M noise_0 ;

[0164] In the formula, M vib The vibration characteristic matrix under different combinations of installation parameters; M noise The noise characteristic matrix under different combinations of installation parameters; M vib_0 M represents the vibration characteristic matrix in its original state. noise_0 The noise feature matrix in the original state; ΔM vib The vibration characteristic variation matrix; ΔM noise Let be the noise feature transformation matrix. Then, apply the singular value decomposition algorithm to both transformation matrices, with the calculation formula as follows:

[0165]

[0166] In the formula, U vib and U noise Σ is a left singular vector matrix; vib and Σ noise It is a singular value diagonal matrix; and This is the transpose of the right singular vector matrix. Next, the singular value distribution is analyzed, and the contribution rate threshold of the principal singular values ​​is determined to be 85%. Singular values ​​whose cumulative contribution rate reaches this threshold and their corresponding singular vectors are retained. The formula for calculating the singular value contribution rate is:

[0167]

[0168] In the formula, C iThe contribution rate of the i-th singular value; σ i Let be the i-th singular value; n is the total number of singular values; C cumulative，k This represents the cumulative contribution rate of the first k singular values. Using the retained singular values ​​and singular vectors, the matrix is ​​reconstructed, separating the vibration stability matrix, vibration variation matrix, noise stability matrix, and noise variation matrix. 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 M is the vibration stability matrix; vib_variable M is the vibration variation matrix; noise_stable M is the noise stability matrix; noise_variable The noise variation matrix; ∑ vib_stable and ∑ noise_stable These are diagonal matrices that retain the principal singular values, with all other singular values ​​set to 0; ∑ vib_variable and ∑ noise_variable These are diagonal matrices that retain minor singular values, while the major singular values ​​are set to 0. Finally, the eigenvalues ​​and condition numbers of these four matrices are calculated to evaluate their stability and sensitivity. This step effectively isolates the impact of installation parameter variations on vibration and noise characteristics, providing a clear mathematical model for subsequent optimization.

[0173] The specific implementation of step S05 involves constructing a multi-objective optimization model and using a particle swarm optimization algorithm to solve for the optimal combination of installation parameters. First, based on the vibration variation matrix and noise variation matrix obtained in step S04, the objective functions for vibration suppression rate and noise reduction value are defined, and 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 objective function for vibration suppression rate; f2(x) is the objective function for noise reduction; F(x) is the comprehensive objective function; x = [x1, x2, ..., x...]. n[M] is a vector of installation parameters, including installation height, tilt angle, contact area, tightening torque, and damping material hardness; vib_0 M represents the vibration characteristic matrix in its original state. vib (x) is the vibration characteristic matrix when the installation parameter is x; ||·|| F L represents the Frobenius norm; p0 The noise sound pressure level under original conditions, in dB; L p (x) represents the noise sound pressure level (dB) when the installation parameter is x; w1 and w2 are weighting coefficients, set to 0.6 and 0.4 respectively. Then, a comprehensive objective function F(x) is constructed, with weighting coefficients w1 and w2 set to 0.6 and 0.4 respectively to balance vibration reduction and noise reduction effects. Next, constraints on the installation parameters are set, including equipment stability constraints, space limitation constraints, and material performance constraints. An improved particle swarm optimization algorithm is applied to solve the problem, with the iterative update formula as follows:

[0178]

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

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

[0181]

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

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

[0184]

[0185] In the formula, H(ω) is the system frequency response function; ω is the angular frequency; j is the complex unit; H0(ω) is the frequency response function under the original state; R vib Let be the vibration suppression rate. The vibration transmission characteristics between the equipment and the mounting structure are analyzed using the stiffness vibration equation, which is:

[0186]

[0187] In the formula, K total K represents the total stiffness of the system. device For equipment stiffness; K mount For the stiffness of the vibration damping device; K structure To support structural stiffness; K mount0 The stiffness of the damping device at the reference temperature; α T ΔT is the temperature coefficient; f(A, θ) is a function related to the contact area A and the tilt angle θ; t(ω) is the vibration transfer function; ω is the excitation frequency; ω n Let be the system's natural frequency; ζ be the damping ratio. The efficiency of the conversion of vibrational energy into thermal energy is evaluated using the heat conduction equation, which is:

[0188]

[0189] In the formula, ρ is the material density; c p Specific heat capacity; T is temperature; t is time; k is thermal conductivity; For the Laplace operator; q v For volumetric heat source; η is the loss factor; ω is the angular frequency; σ is the stress; ε is the strain; D E E represents the energy dissipation rate. dissipated Energy dissipated; E input Let be the input vibration energy. The long-term performance of the damping material is predicted using the material yield equation, which is:

[0190]

[0191] In the formula, σ eq For equivalent stress; σ x , σy , σ z Principal stress; τ xy , τ xz , τ yz For shear stress; N f σ represents the number of fatigue life cycles. y C1, C2, and C3 are material constants; T is the operating temperature; C4(env) is the environmental factor correction factor; L predicted The predicted service life is expressed in years; f is the dominant vibration frequency; t daily This represents the daily operating time of the equipment, expressed in hours. Finally, the theoretically predicted vibration suppression rate and noise reduction values ​​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 results through mechanical theory, enhancing the reliability of the installation scheme.

[0192] The specific implementation methods for steps S07-S08 are the same as those described above, and will not be repeated in detail here.

[0193] Step S09 is optional. Its specific implementation involves establishing a parameter correction model based on actual installation results, forming a complete knowledge base of vibration reduction and noise reduction installation methods for electromechanical equipment. First, the differences between the actually measured vibration suppression rate and noise reduction value and the theoretical predicted value are compared. Correction coefficients for each parameter are calculated. The calculation of the correction coefficients is based on the ratio of the measured value to the theoretical value. Least squares regression analysis is used to determine the functional relationship between the parameters and the correction coefficients. The calculation formula for 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 R represents the actual vibration suppression rate. theoretical L represents the theoretical vibration suppression rate. actual This represents the actual noise reduction value; L theoretical This represents the theoretical noise reduction value; γ vib and γ noise These are the correction factors for vibration and noise, respectively; x i For the i-th installation parameter; a0, a i a ij and b0, b i b ij ε is the regression coefficient;vib and ε noise This represents the error term, within ±0.07. The regression coefficients are obtained using the least squares method.

[0198]

[0199] In the formula, y k This is the actual correction factor; The model prediction correction coefficients are defined as follows: m represents the sample size. A parameter correction model is then constructed, which automatically adjusts the optimal installation parameter values ​​based on equipment type, installation environment, and expected service life, with a correction accuracy controlled within ±7%. Next, the parameter correction model is linked to the multi-objective optimization model in step S05 to form a closed-loop optimization system. This system continuously optimizes and adjusts the theoretical model based on actual installation results. Finally, the theoretical knowledge, algorithm models, and experimental data from all steps are integrated to establish a knowledge base for vibration reduction and noise reduction installation methods for electromechanical equipment. The knowledge base includes four parts: equipment classification directory, parameter optimization module, material selection guide, and installation process standards. It supports case retrieval and similarity matching functions, providing reference solutions and expected effect evaluations for new equipment installations. This step, through the combination of theory and practice, achieves continuous optimization and knowledge accumulation of installation methods, significantly improving the applicability and scalability of vibration reduction and noise reduction methods.

[0200] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: Researchers discovered in the cooling system of a large data center that the vibration and noise generated by the equipped refrigeration compressor unit during operation severely affected the surrounding office environment and the normal operation of precision equipment. To address this problem, the research team adopted the electromechanical equipment vibration reduction and noise reduction installation method of this invention. First, the researchers constructed a multi-dimensional vibration and noise acquisition system, setting 12 accelerometers and 6 acoustic sensors at different locations to comprehensively collect the vibration and noise characteristics of the compressor unit under four load conditions: 25%, 50%, 75%, and 100%, with the acquisition frequency set at 48000Hz. Specifically, the accelerometers were installed at different parts of the compressor body (such as the top, sides, and base), the motor section, pipe connection points, support structures, and the connection between the unit and the ground to capture multi-directional vibration transmission paths. The acoustic sensors were arranged at points at different distances and directions around the compressor, near inlet and outlet pipes, at locations with significant radiated noise from the unit casing, in the personnel activity area of ​​the work area, and near adjacent precision equipment to comprehensively assess the spatial distribution characteristics of the noise. The collected raw data is shown in Table 1:

[0201] Table 1. Raw data of vibration and noise under different load conditions.

[0202]

[0203] Then, wavelet transform analysis was performed on the collected vibration and noise spectra. A 5-level decomposition using the db4 wavelet function was employed to extract vibration and noise feature vectors. These were then transformed into a dimension-reduced feature matrix through non-negative matrix decomposition. Feature extraction analysis identified the main vibration frequencies of the compressor unit as being in the range of 48–75 Hz, and the main noise frequency band as being concentrated in the range of 250–2000 Hz. The key extracted feature parameters are shown in Table 2.

[0204] Table 2 Vibration and noise characteristic parameters of refrigeration compressor units

[0205] Feature parameters Vibration characteristic value Noise characteristics mean 7.48 80.8 Standard deviation 3.92 5.85 Kudo 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 1:5 scale and designed a set of installation parameter variables. These parameters included installation height (15–45 mm), tilt angle (0–12°), contact area (40%–85% of the equipment's bottom area), tightening torque (60%–140% of the standard torque), and damping material hardness (Shore hardness 35–75A). Sixteen test schemes were designed using an L16(4^5) orthogonal array, with each scheme tested three times. The changes in the vibration characteristic matrix and noise characteristic matrix under different combinations of installation parameters were recorded. The results of the orthogonal experiments are shown in Table 3.

[0207] Table 3. Partial Results of the Orthogonal Experiment

[0208]

[0209] Based on orthogonal experimental data, the vibration characteristic variation matrix and noise characteristic variation matrix were calculated using the singular value decomposition method, and then 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 three singular values ​​reached 87.3%, and matrix reconstruction was performed accordingly.

[0210] Next, the research team constructed a multi-objective optimization model with vibration suppression rate and noise reduction as objective functions, and weight coefficients set to 0.6 and 0.4, respectively. The particle swarm optimization algorithm was used to solve for the optimal combination of installation parameters. 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. The optimal combination of installation parameters obtained after optimization is shown in Table 4.

[0211] Table 4 Optimal Installation Parameter Combinations

[0212] Installation parameters optimal value Installation height 32.5mm inclination 5.8° Contact area 65% of the equipment's base area Tightening torque 110% of standard torque Vibration damping material hardness 48 Shaw Brothers A

[0213] Then, the research team applied the elastic damping dynamic equations to analyze the interaction between the compressor unit and the installation structure, predicting the vibration suppression rate and noise reduction under the optimal combination of installation parameters. The calculated theoretical prediction results are shown in Table 5:

[0214] Table 5. Theoretical Prediction Data

[0215]

[0216] Based on the optimal combination of installation parameters, researchers selected a polyurethane composite damping material with a Shore hardness of 48A and adopted a corrugated damper structure. When determining the installation location, vibration-sensitive points of the building structure were avoided, and floor slab support points with high stiffness were selected. The installation direction was designed so that the compressor's main vibration direction forms a 75° angle with the direction of maximum stiffness of the building structure to reduce vibration transmission.

[0217] After the actual installation was completed, researchers conducted verification tests using a multi-dimensional vibration and noise acquisition system. Table 6 shows a comparison between the actual installation results and theoretical predictions.

[0218] Table 6 Comparison of Actual Installation Results and Theoretical Predictions

[0219] Evaluation indicators Theoretical prediction value Actual measured value Relative error (%) Vibration suppression rate (%) 58.7 54.2 -7.7 Noise reduction (dB) 8.5 7.8 -8.2 System resonant 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 results, calculated the correction coefficients for vibration and noise to be 0.92 and 0.91, respectively, and linked the correction model with the multi-objective optimization model to form a complete knowledge base.

[0221] Traditional vibration and noise reduction installation methods for refrigeration compressors mainly rely on empirical or single-experiment approaches, typically considering only simple vibration damping pads or soundproof enclosures, lacking systematic optimization and theoretical guidance. These methods offer limited vibration and noise reduction effects and are difficult to adapt to different equipment and environmental conditions, usually achieving only 25%-35% vibration suppression and 3-5 dB noise reduction. In contrast, the method employed in this invention utilizes multi-dimensional data acquisition, wavelet analysis, non-negative matrix decomposition, singular value decomposition, and multi-objective optimization algorithms to construct a complete theoretical and practical system for vibration and noise reduction. Implementation results show that, compared to traditional methods, this invention achieves a 54.2% vibration suppression rate and a 7.8 dB noise reduction, representing improvements of approximately 70% and 60% respectively. This significantly improves the working environment of data centers, extends equipment lifespan, and the established parameter correction model gives the method good transferability and adaptability, making it widely applicable to vibration and noise reduction installations for various electromechanical equipment.

[0222] It should be noted that the variables involved in this invention are explained in detail in Tables 7, 8, and 9 below.

[0223] Table 7. Variable Explanation Table (Part 1)

[0224]

[0225]

[0226] Table 8. Variable Explanation Table (Part Two)

[0227]

[0228] Table 9. Variable Explanation Table (Part 3)

[0229]

[0230]

[0231] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for vibration damping and noise reduction installation of electromechanical equipment, characterized in that, include: S01. Construct a multi-dimensional vibration and noise acquisition system to collect vibration spectrum and noise spectrum data under different positions, angles and load conditions of electromechanical equipment, and form a comprehensive vibration and noise characteristic database. S02. Perform wavelet transform analysis on the collected vibration spectrum and noise spectrum to extract vibration feature vectors and noise feature vectors, and form vibration feature matrix and noise feature matrix through non-negative matrix decomposition. S03. Construct a small-scale model of the electromechanical equipment, design a set of installation parameter variables, including installation height, tilt angle, contact area, fastening torque and damping material hardness, change the installation parameter values ​​in the set of installation parameter variables through the orthogonal test method of the small-scale model, and record the changes of the vibration characteristic matrix and the noise characteristic matrix. S04. Based on the test data obtained by the small-scale model orthogonal test method, calculate the vibration characteristic change matrix and the noise characteristic change matrix, and use the singular value decomposition method to decompose the vibration characteristic change matrix and the noise characteristic change matrix into a vibration stability matrix, a vibration variation matrix, a noise stability matrix and a noise variation matrix. S05. Construct a multi-objective optimization model. Based on the vibration variation matrix and the noise variation matrix, set the vibration suppression rate and noise reduction value as objective functions, and use the particle swarm optimization algorithm to solve for the optimal combination of installation parameters. S06. Apply the elastic damping dynamic equations to analyze the interaction between the electromechanical equipment and the installation structure, predict the vibration suppression rate and noise reduction value generated under the optimal installation parameter combination, and verify the theoretical rationality of the optimal installation parameter combination. S07. Based on the optimal combination of installation parameters, select matching shock absorber materials and structural types, and determine the installation position and direction of the electromechanical equipment; S08. Perform the actual installation of the electromechanical equipment according to the optimal installation parameter combination; The calculation process of singular value decomposition is shown below: ； ； ； ； In the formula, Vibration characteristic matrix under different combinations of installation parameters; The noise characteristic matrix under different combinations of installation parameters; This represents the vibration characteristic matrix in its original state. This represents the noise feature matrix in its original state. This is the vibration characteristic variation matrix; This is the noise feature variation matrix; and It is a left singular vector matrix; and It is a singular value diagonal matrix; and It is the transpose of the right singular vector matrix; After singular value decomposition, the matrix is ​​divided into a stable part and a variable part based on the contribution rate of the singular values: ； ； ； ； ； ； In the formula, The vibration stability matrix; The vibration variation matrix; This is the noise stability matrix; This is the noise variation matrix; and These are diagonal matrices that retain the principal singular values, with the remaining singular values ​​set to 0; and These are diagonal matrices that retain minor singular values, with major singular values ​​set to 0; The calculation process of the multi-objective optimization model is specifically represented as follows: ； ； ； ； ； ； ； In the formula, The objective function is the vibration suppression rate. The objective function is the noise reduction value; The overall objective function; This is a vector of installation parameters, including installation height, tilt angle, contact area, tightening torque, and damping material hardness. This represents the vibration characteristic matrix in its original state. The installation parameters are The vibration characteristic matrix at that time; Denotes the Frobenius norm; The noise sound pressure level under the original conditions, in dB; The installation parameters are The noise sound pressure level at that time, in dB; and These are the weighting coefficients, set to 0.6 and 0.4 respectively; These are inequality constraints. These are equality constraints; and The first The lower and upper limits of each installation parameter; The constraints specifically include: Stability constraints: ; Space height constraints: ; Noise limit constraints: ; In the formula, The system stability coefficient; For equipment quality; It is the acceleration due to gravity; Installation height; For equipment height; Maximum allowable height; Noise level during operation; Noise limits; The elastic damping dynamics equations include the mass damping equation, stiffness vibration equation, heat conduction equation, and material yield equation. The mass damping equation describes the dynamic relationship between the mass of the electromechanical equipment and the damping coefficient. Inputs include the equipment mass distribution obtained from the vibration characteristic matrix, the damping coefficient obtained from the damper material, the external excitation frequency obtained from the vibration spectrum, the support structure stiffness obtained from the installation structure, and the contact area parameters obtained from the installation parameter variable set. The output is the system damping response curve. The stiffness vibration equation analyzes the influence of stiffness matching between the electromechanical equipment and the installation structure on vibration transmission. Inputs include the support structure stiffness matrix obtained from the installation structure, the vibration frequency spectrum obtained from the vibration spectrum, the equipment natural frequencies obtained from the electromechanical equipment, and the connection point distribution obtained from the installation parameter variable set. The ambient temperature coefficient obtained from the installation environment is used as the output of the vibration transfer function. The heat conduction equation is used to evaluate the efficiency of vibration energy conversion into heat energy and its impact on damping performance. The inputs include the thermal conductivity obtained from the damper material, the vibration power density obtained from the vibration characteristic matrix, the contact area obtained from the installation parameter variable set, the material thickness obtained from the damper material, and the temperature gradient obtained from the installation environment. The output is the energy dissipation rate. The material yield equation is used to predict the change of the yield characteristics of the damper material under long-term vibration. The inputs include the elastic modulus obtained from the damper material, the yield stress obtained from the damper material, the cumulative vibration period number 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.

2. The method for vibration damping and noise reduction installation of electromechanical equipment according to claim 1, characterized in that, The multi-dimensional vibration and noise acquisition system collects vibration and noise spectrum data from electromechanical equipment at different locations, angles, and under different load conditions, forming a comprehensive vibration and noise characteristic database.

3. The method for vibration damping and noise reduction installation of electromechanical equipment according to claim 2, characterized in that, Nonnegative matrix factorization decomposes a high-dimensional original data matrix into the product of two nonnegative matrices, one representing the basic pattern and the other representing the weight distribution of the basic pattern. It is used to reduce dimensionality and discover the intrinsic structure of vibration feature vectors and noise feature vectors.

4. The vibration damping and noise reduction installation method for electromechanical equipment according to claim 3, characterized in that, Small-scale models are physical models of electromechanical equipment scaled down according to the principle of geometric similarity. They maintain the similarity between the mechanical and dynamic properties of the prototype and the model, and are used to verify and optimize the set of installation parameter variables before actual installation.

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