A pipeline hanger stiffness parameter identification method and related device

Abstract

This application discloses a method and related device for identifying the stiffness and resistance parameters of pipeline hangers, relating to the field of pipeline system dynamics analysis technology. The method includes acquiring the geometric and material parameters of the pipeline system and establishing a transfer matrix dynamic model; constructing a frequency response function based on vibration response and extracting experimental frequency response data; constructing a forward calculation model of the frequency response function, calculating theoretical frequency response data, and extracting characteristic parameters; comparing experimental and theoretical frequency response characteristic parameters to obtain frequency response error data; searching for Pareto optimal solutions within the feasible search range of stiffness and damping based on the frequency response error data and the NSGA-II algorithm, and selecting optimal stiffness and damping parameters from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion. This application eliminates the need for direct contact measurement of the hangers; parameter identification can be achieved simply by collecting the vibration response on the pipeline, solving the technical problem of accurately measuring the dynamic parameters of hangers under complex working conditions.

Description

Technical Field

[0001] This application relates to the field of pipeline system dynamics analysis technology, and in particular to a method and related device for identifying the stiffness and resistance parameters of pipeline hangers. Background Technology

[0002] In industrial applications, various piping systems, such as cooling water pipelines and oil pump pipelines, are crucial for the normal operation of equipment. Among these, flexible pipe supports not only support and fix the pipes but also serve as a primary channel for the transmission of vibration and noise energy from the piping system to the ship's hull. However, due to limitations imposed by actual engineering conditions, the stiffness parameters of pipe supports are difficult to measure accurately. Flexible supports are a type of support, and this application selects them as a representative of this category for discussion.

[0003] The stiffness characteristics of pipe supports and hangers have a significant impact on the dynamic analysis of pipe systems. When stiffness parameters deviate from actual values, the natural frequencies, mode shapes, and other characteristics calculated by the dynamic model based on these parameters will not match the actual situation, leading to distorted vibration and noise prediction results. This not only affects the design optimization of the pipe system but may also cause vibration reduction and noise reduction measures to fail. Currently, the stiffness and damping of pipe supports and hangers are usually obtained through experimental determination or finite element simulation, which is time-consuming and costly, making it difficult to meet the needs of rapid engineering analysis. Although some scholars have attempted to use optimization algorithms for parameter inversion, the iterative process still requires repeated calls to finite element calculations, resulting in low computational efficiency. Summary of the Invention

[0004] The purpose of this application is to provide a method and related device for identifying the stiffness and resistance parameters of pipeline hangers. This method eliminates the need for direct contact measurement of the hangers and supports, and only requires collecting the vibration response on the pipeline to achieve parameter identification. This solves the technical problem of accurately measuring the dynamic parameters of hangers and supports under complex working conditions.

[0005] To achieve the above objectives, this application provides the following solution: In a first aspect, this application provides a method for identifying the rigidity and resistance parameters of pipe hangers, comprising the following steps: Obtain the geometric and material parameters of the pipeline system, and establish a transfer matrix dynamic model of the pipeline system based on the geometric and material parameters.

[0006] Obtain the vibration response in the constraint direction of the elastic hanger, and obtain experimental frequency response data based on the vibration response.

[0007] Based on the aforementioned transfer matrix dynamics model, a forward calculation model for the frequency response function is constructed to obtain theoretical frequency response data. The error between the theoretical frequency response data and the experimental frequency response data is then calculated to obtain frequency response error data.

[0008] Using the NSGA-II algorithm, a multi-objective optimization function is constructed based on the frequency response error data. The Pareto optimal solution set is searched within the feasible search range of stiffness and damping parameters, and the optimal stiffness and damping parameters are selected from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion.

[0009] Secondly, this application provides a computer device, including: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the pipe hanger stiffness parameter identification method described above.

[0010] Thirdly, this application provides a computer program product, including a computer program that, when executed by a processor, is used to implement the steps of the pipe hanger stiffness parameter identification method described above.

[0011] According to the specific embodiments provided in this application, this application has the following technical effects: This application provides a method and related apparatus for identifying the stiffness and resistance parameters of pipeline hangers. By acquiring the geometric and material parameters of the pipeline system and establishing a transfer matrix dynamic model of the pipeline system based on these parameters, a complex continuum problem can be transformed into a computable algebraic problem, providing a core tool for subsequent optimization algorithms to invert the parameters of elastic hangers. Based on the transfer matrix dynamic model, a forward calculation model of the frequency response function is constructed, thereby obtaining theoretical frequency response data. This constructs a verifiable forward calculation tool, transforming the parameterized model into a numerical calculation tool capable of quickly outputting theoretical frequency response characteristics. The system provides reliable theoretical values ​​for subsequent parameter inversion. By obtaining resonance frequency error, peak amplitude error, and half-power bandwidth error from experimental and theoretical frequency response data, a quantitative evaluation of the inversion accuracy is achieved. A multi-objective optimization function is constructed using these errors as indicators, solving the problem of simultaneously optimizing multiple error indicators under conflicting objectives. The search range for stiffness and resistance parameters is preset using engineering prior conditions, effectively reducing the optimization domain. Compared to traditional single-objective weighted methods, this application effectively avoids optimization bias caused by improper allocation of objective weights, and can simultaneously ensure accurate matching of resonance peak position, peak height, and bandwidth characteristics. Combining the elite retention and crowding distance mechanism of the NSGA-II algorithm, it effectively balances global exploration and local exploitation capabilities. The algorithm can achieve a rapid transition from large-amplitude oscillation exploration to high-precision convergence around generation 30, with the average objective function value eventually stabilizing at an extremely low level. This application introduces a normalized weighted Euclidean distance criterion to automatically select the unique solution with the best overall performance from the Pareto optimal solution set, eliminating the influence of differences in the dimensions of different objectives and ensuring that the final selected parameter combination has excellent fitting effect across the entire frequency band. Attached Figure Description

[0012] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0013] Figure 1 This is an application environment diagram of a pipe hanger stiffness parameter identification method according to an embodiment of this application; Figure 2 A flowchart illustrating a method for identifying the rigidity and resistance parameters of a pipe hanger according to an embodiment of this application; Figure 3 This is a schematic diagram of the installation of a flexible hanger provided in one embodiment of this application; Figure 4 The curve showing the change of the average objective function value of the Pareto front with the number of generations is provided in another embodiment of this application; Figure 5 This application provides a curve showing the change in Pareto front distribution degree with the number of generations, as described in another embodiment of the present application. Figure 6 This is a distribution map of the Pareto optimal solution set finally obtained by a pipeline hanger stiffness parameter identification method in another embodiment of this application in the three-dimensional target space; Figure 7 A comparison diagram of the theoretical frequency response function curves and the response data of the finite element (FEM) reference measurement points for three examples provided in another embodiment of this application in the direction of elastic hanger constraint; Figure 8 This is a schematic diagram of the structure of a computer device provided in an embodiment of this application. Detailed Implementation

[0014] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0015] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, the application will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0016] The pipe hanger stiffness parameter identification method provided in this application embodiment can be applied to, for example... Figure 1In the application environment shown, terminal 102 communicates with server 104 via a network. A data storage system can store the data that server 104 needs to process. The data storage system can be set up independently, integrated into server 104, or placed in the cloud or on another server. Terminal 102 can send the acquired geometric and material parameters of the pipeline system to server 104. After receiving the geometric and material parameters, server 104 establishes a transfer matrix dynamic model of the pipeline system based on the acquired geometric and material parameters. The vibration response in the constraint direction of the elastic hanger is acquired, and experimental frequency response data is obtained based on the vibration response. Based on the transfer matrix dynamic model, a forward calculation model of the frequency response function is constructed to obtain theoretical frequency response data, and the error between the theoretical frequency response data and the experimental frequency response data is calculated to obtain frequency response error data. Using the NSGA-II algorithm, a multi-objective optimization function is constructed based on the frequency response error data. Within the feasible search range of stiffness and damping parameters, a Pareto optimal solution set is searched, and the optimal stiffness and damping parameters are selected from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion. The server 104 can feed back the obtained optimal stiffness and damping parameters to the terminal 102. Furthermore, in some embodiments, the pipe hanger stiffness and damping parameter identification method can also be implemented separately by the server 104 or the terminal 102. For example, the terminal 102 can directly process the acquired geometric and material parameters of the pipe system, or the server 104 can obtain the geometric and material parameters of the pipe system from the data storage system and process them accordingly.

[0017] The terminal 102 can be, but is not limited to, various desktop computers, laptops, smartphones, tablets, IoT devices, and portable wearable devices. IoT devices can include smart speakers, smart TVs, smart air conditioners, and smart in-vehicle devices. Portable wearable devices can include smartwatches, smart bracelets, and head-mounted devices. The server 104 can be implemented using a standalone server or a server cluster composed of multiple servers, or it can be a cloud server.

[0018] In one exemplary embodiment, such as Figure 2 As shown, a method for identifying the rigidity and resistance parameters of pipe hangers is provided. This method is executed by a computer device, specifically by a terminal or server alone, or by both a terminal and a server. In this embodiment, the method is applied to... Figure 1 Taking server 104 as an example, the explanation includes the following steps A1 to A4.

[0019] Step A1: Obtain the geometric and material parameters of the pipeline system, and establish the transfer matrix dynamic model of the pipeline system based on the geometric and material parameters of the pipeline system.

[0020] In this embodiment, the transfer matrix dynamics model is used to perform forward calculations and fitness evaluations of each parameter combination within a feasible search range for stiffness and damping. The specific geometric parameters of the pipeline system are: nominal diameter 100mm, outer diameter 108mm, wall thickness 5mm, total length 1m, and straight pipe material Q235B; the specific material parameters are: density... The Young's modulus is 210 GPa, and the Poisson's ratio is 0.3; the pipe damping ratio is 0.05. (See below.) Figure 3 As shown, three flexible hangers are installed at the starting point (0m from the beginning), the midpoint (0.5m from the beginning), and the end point (1m from the beginning) of the pipeline. In practice, the actual geometric parameters of the pipeline system (such as pipe length) are first determined. , outer diameter Wall thickness ) and material parameters (such as Young's modulus) ,density Poisson's ratio The pipeline is discretized into several pipe segment elements. For each pipe segment element, a 12×12 order field transfer matrix is ​​established based on the Timoshenko Beam Theory. This matrix comprehensively considers the effects of axial tension and compression, lateral bending, torsional vibration, shear deformation, and rotational inertia on the pipeline.

[0021] Next, a point transfer matrix is ​​introduced at the installation locations of the flexible hangers (such as the start, middle, and end points of the pipeline). The elastic hanger is equivalent to a unidirectional linear spring-damped system, where the stiffness parameter to be inverted is... and damping parameters As unknown decision variables, they are embedded in the point matrix. By performing matrix multiplication, the field matrices of each pipe segment and the point matrices of the supports are sequentially combined to construct a global transfer matrix equation describing the input-output relationship of the entire pipeline system: ; in, and These are the state vectors at the beginning and end of the pipeline (containing 12 state variables such as displacement, rotation angle, bending moment, and shear force). For global transfer matrix, For the first n The field matrix of each pipe segment For the first nThe point matrix of each support and hanger. Combined with specific boundary conditions (such as both ends being free, simply supported, or fixed, and both ends being elastically supported), the system transfer equations can be constructed.

[0022] Step A2: Obtain the vibration response in the constraint direction of the elastic hanger, and obtain the experimental frequency response data based on the vibration response.

[0023] Step A3: Based on the transfer matrix dynamics model, construct a forward calculation model for the frequency response function to obtain theoretical frequency response data, and calculate the error between the theoretical frequency response data and the experimental frequency response data to obtain frequency response error data.

[0024] In this embodiment, the theoretical frequency response data includes the theoretical resonant frequency, the theoretical peak amplitude, and the theoretical half-power bandwidth; the frequency response error data includes the resonant frequency error, the peak amplitude error, and the half-power bandwidth error; the resonant frequency error is expressed in the root mean square form of the relative error, and the peak amplitude error and the half-power bandwidth error are expressed in the root mean square form of the logarithmic error.

[0025] Step A4: Using the NSGA-II algorithm, a multi-objective optimization function is constructed based on the frequency response error data. The Pareto optimal solution set is searched within the feasible search range of stiffness and damping. The optimal stiffness and damping parameters are selected from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion.

[0026] In this embodiment, the frequency response error data includes resonant frequency error, peak amplitude error, and half-power bandwidth error. The feasible search range for stiffness and damping is predetermined by the implementer based on prior engineering conditions such as support type, product specifications, or reasonable physical magnitude, and serves as a boundary constraint for the optimization variables; in this embodiment, the stiffness search range is taken as... N / m, damping search range is taken N·s / m (logarithmic scale uniform sampling / initialization).

[0027] Implementing steps A1 to A4 above can effectively and accurately identify the stiffness and resistance parameters of pipeline hangers. This method combines experimental data with theoretical models, constructing a frequency response function, calculating errors, and employing a multi-objective optimization algorithm to ensure high accuracy and reliability in parameter identification. In practical applications, this method is of great significance for the design, operation, and maintenance of pipeline systems. This vibration response prediction method based on inversion parameters can provide important theoretical basis and data support for the vibration characteristic analysis, vibration reduction optimization design, and fault diagnosis of pipeline systems. This method can also be extended to parameter identification and dynamic modeling of various engineering pipeline systems, providing an efficient and reliable technical means for the vibration characteristic analysis and response prediction of pipeline systems.

[0028] In another exemplary embodiment of this application, in order to verify the accuracy and reliability of the transfer matrix dynamics model, after step A4 above, the following may be included: measuring the actual vibration response in the constraint direction of the elastic hanger, substituting the optimal stiffness and damping parameters into the transfer matrix dynamics model, calculating the theoretical vibration response in the constraint direction of the elastic hanger, and comparing and verifying the theoretical vibration response with the actual vibration response.

[0029] In another exemplary embodiment of this application, in order to transform the real continuous pipeline system into an algebraic model computable by the transfer matrix method, thereby improving the iteration efficiency, step A1 above is replaced by steps B1 to B3: Step B1: Discretize the pipeline system into several pipe segment units based on the geometric and material parameters of the pipeline system; the pipeline system is equipped with elastic hangers; the geometric parameters include pipe length, inner and outer diameters, and wall thickness; the material parameters include Young's modulus, density, and Poisson's ratio.

[0030] Step B2: Install flexible hangers at the start, middle and end of each pipe unit.

[0031] Step B3: Establish a pipeline unit transfer matrix for each pipeline unit, introduce a point transfer matrix at the location of the elastic hanger, and treat the elastic hanger as an equivalent spring-damped support. Introduce the stiffness parameter and damping parameter as unknowns to be identified into the model to obtain the transfer matrix dynamic model of the pipeline system.

[0032] In another exemplary embodiment of this application, in order to obtain experimental frequency response data, step A2 above is replaced by steps C1 to C4: Step C1: Apply impact excitation at a designated location in the pipeline using the force hammer excitation method, and use an acceleration sensor to measure the vibration response in the constraint direction of the elastic hanger to obtain the vibration acceleration or velocity response signal in the constraint direction of the elastic hanger.

[0033] In this embodiment, a hammer excitation method is used, applying impact excitation at a distance of 0.25 meters from the beginning of the pipeline, and using an accelerometer at a distance of 0.75 meters from the beginning along the constraint direction of the elastic hanger. Figure 3 The vibration response was measured in the y-direction (with a sampling frequency of 800 Hz and a sampling time of 10 s) to obtain the acceleration or force frequency response function (i.e., acceleration admittance) at the measuring point, which was used as the frequency response curve for subsequent analysis.

[0034] Step C2: Calculate the frequency response function using a fast Fourier transform based on the vibration acceleration or velocity response signal in the constraint direction of the elastic hanger.

[0035] Step C3 involves using a peak detection algorithm to identify resonance peaks in the frequency response function, extracting the experimental resonance frequencies, and extracting the experimental peak amplitude at each resonance peak.

[0036] Step C4: Using the half-power bandwidth method, determine the left and right boundary frequencies at the point where the experimental peak amplitude drops by 3dB, and calculate the experimental half-power bandwidth.

[0037] In another exemplary embodiment of this application, in order to construct a forward calculation model of the frequency response function, obtain theoretical frequency response data, and calculate the error between the theoretical frequency response data and the experimental frequency response data to obtain frequency response error data, step A3 above is replaced by steps D1 to D7: Step D1: Based on the aforementioned transfer matrix dynamics model, construct a forward calculation model for the frequency response function.

[0038] Step D2: Select stiffness and damping parameters from the feasible search range of the stiffness and damping parameters, and substitute the stiffness and damping parameters into the forward calculation model to calculate the theoretical frequency response function of the elastic hanger in the constraint direction.

[0039] Step D3: Use a peak detection algorithm to identify the resonance peaks in the theoretical frequency response function, extract the theoretical resonance frequency, and extract the theoretical peak amplitude at each resonance peak.

[0040] Step D4: Using the half-power bandwidth method, determine the left and right boundary frequencies at the point where the theoretical peak amplitude drops by 3dB, and calculate the theoretical half-power bandwidth.

[0041] Step D5: Calculate the error between the theoretical resonance frequency and the experimental resonance frequency to obtain the resonance frequency error.

[0042] Step D6: Calculate the error between the theoretical peak amplitude and the experimental peak amplitude to obtain the peak amplitude error.

[0043] Step D7: Calculate the error between the theoretical half-power bandwidth and the experimental half-power bandwidth to obtain the half-power bandwidth error.

[0044] In this embodiment, the resonant frequency error is calculated using the following formula: ; in, For the first The relative error between the theoretical resonance frequency calculated from the solution and the experimental resonance frequency. Calculate the frequency for the k-th order. For the k-th order target frequency, =1~3 represents the number of peaks to be matched, in this application Take 3.

[0045] The peak amplitude error is calculated using the following formula: ; in, Let the logarithmic relative error between the theoretical peak amplitude calculated for the i-th solution and the experimental peak amplitude be denoted as . , The first The calculated amplitude and target amplitude of the order. =1~3 represents the number of peaks to be matched, in this application Take 3.

[0046] The half-power bandwidth error is calculated using the following formula: ; in, Let the logarithmic relative error between the theoretical half-power bandwidth calculated for the i-th solution and the experimental half-power bandwidth be denoted as . , These are the calculated half-power bandwidth and the target half-power bandwidth at the k-th order, respectively. =1~3 represents the number of peaks to be matched, in this application Take 3.

[0047] After constructing the forward calculation model of the frequency response function based on the transfer matrix dynamics model in step A3 above, the method may further include the following steps E1 to E2.

[0048] Step E1: From the feasible search range of stiffness and damping parameters, several sets of stiffness and damping parameter examples are arbitrarily selected. The reference frequency response data is calculated using the finite element method (FEM), and the theoretical frequency response data is calculated using the forward calculation model. In this embodiment, to verify the correctness of the forward calculation model, several sets of stiffness and damping parameter examples are arbitrarily selected for forward calculation, and the results are compared with those obtained using the finite element method (FEM). The verification cases and comparison results are shown in Table 1. Table 1 Validation Table of Forward Computation Model

[0049] Step E2 involves comparing and verifying the reference frequency response data obtained by the finite element method and the theoretical frequency response data obtained by the forward calculation model for each group using the error formula.

[0050] The error formula is: ; in, for These represent three objectives: resonant frequency, amplitude, and half-power bandwidth. The theoretical frequency response data is obtained from the forward calculation model. This is the reference frequency response data obtained by the finite element method.

[0051] Before step A4 above, the method may further include: setting parameters and initializing the population for the NSGA-II algorithm, specifically including: setting the population size to 200, the maximum number of iterations to 50 generations, the crossover probability to 0.8, and the Pareto front retention ratio to 0.35; the initial population is randomly generated using a logarithmic scale within the feasible search range of stiffness and damping parameters.

[0052] In another exemplary embodiment of this application, in order to search for the Pareto optimal solution set within the feasible search range of stiffness and damping parameters, step A4 above is replaced by steps F1 to F10: Step F1: Based on the resonant frequency error, peak amplitude error, and half-power bandwidth error, obtain the three-target fitness error vector.

[0053] Step F2 involves stratifying the population based on the three-objective fitness error vector and Pareto dominance relation, and then selecting non-dominated solutions that are at the Pareto front.

[0054] Step F3: Calculate the crowding distance between individuals in the same layer and prioritize retaining individuals in sparsely distributed areas.

[0055] In this embodiment, the population is first ranked according to the dominance relationship between individuals. Individuals in the first rank do not dominate each other and are superior to those in other ranks. Then, the crowding distance between individuals in the same rank is calculated to maintain the diversity of the solution set and avoid getting trapped in local optima.

[0056] Step F4 generates a progeny population based on the current population through tournament selection, simulated binary crossover, and polynomial mutation.

[0057] Step F5: Merge the current population with the offspring population, and select the next generation of the current population through non-dominated sorting and crowding selection.

[0058] Step F6: Determine whether the number of iterations completed is greater than or equal to the preset number of iterations to obtain the first determination result.

[0059] In step F7, if the first judgment result is yes, then the non-dominated solutions in the current population of the new generation are taken as the Pareto optimal solution set.

[0060] In step F8, if the first judgment result is negative, then determine whether the convergence condition is met to obtain the second judgment result.

[0061] In this embodiment, the convergence condition is: within a consecutive preset stagnation algebra, the geometric mean of the relative changes in the Pareto front scatter is less than a preset function tolerance; wherein, the consecutive preset stagnation algebra is 50, and the preset function tolerance is... .

[0062] In step F9, if the second judgment result is yes, then the non-dominated solutions in the current population of the new generation are taken as the Pareto optimal solution set.

[0063] In step F10, if the second judgment result is negative, the new generation of the current population is taken as the current population, and the process jumps to step F2.

[0064] In another exemplary embodiment of this application, the step A4 above, "selecting the optimal stiffness and damping parameters from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion," is replaced by the following steps G1 to G2: Step G1: Normalize the objective function values ​​in the Pareto optimal solution set to the interval [0,1], and calculate the weighted distance from each function value to the ideal point; the ideal point is the point where all objectives are minimized.

[0065] Step G2: Select the stiffness and damping parameters corresponding to the solution with the smallest weighted distance score as the inversion result.

[0066] Calculate the weighted distance from each function value to the ideal point using the following formula: ; Where j=1,2,3 represent three targets: resonant frequency, amplitude, and half-power bandwidth, respectively. For the first The weighted distance scores of each solution; For the first The weights for each target are set as follows: frequency, amplitude, and bandwidth are set to 1, 0.5, and 0.2, respectively. For the first The solution is at the th solution. Function values ​​on each target; and These are the first solutions in the current solution set. The minimum and maximum values ​​of each target are determined; in this application, N is set to 3, and the first three resonant frequencies, peak amplitudes, and half-power bandwidths are matched to ensure that the inversion parameters can accurately describe the dynamic characteristics of the elastic hanger over a wide frequency range.

[0067] In another exemplary embodiment of this application, in order to verify the convergence speed and global optimization capability of the pipeline hanger stiffness parameter identification method proposed in this application, Example 2 was selected, and the performance indicators in the optimization iteration process were statistically analyzed.

[0068] Suppose that at the end of the t-th generation of evolution, the algorithm finds a set of non-dominated solutions (i.e., the Pareto front), denoted as set . .set up There are M individuals (i.e., M sets of currently optimal parameter combinations), and each individual i has N objective function values. In this application, N=3, corresponding to: frequency error (j=1), amplitude error (j=2), and bandwidth error (j=3). Let... Let be the function value of the i-th solution on the j-th objective.

[0069] Figure 4 Pareto Front Average Objective Function Value Defined as: ; Where M is the number of individuals in a non-dominated solution set found by the algorithm at the end of the t-th generation of evolution, i is each individual, and N is the objective function value of each individual. In this application, N=3, corresponding to: frequency error (j=1), amplitude error (j=2), and bandwidth error (j=3), respectively. Let be the function value of the i-th solution on the j-th objective. This index sums up the errors of all current optimal solutions on all objectives and then divides by the total number of objectives, reflecting the "total average error" level of all optimal solutions.

[0070] Figure 5 The Pareto front distribution S is defined as the sum of the standard deviations of the objective function values: ; Where N is the objective function value of each individual in the set of non-dominated solutions found by the algorithm at the end of the t-th generation of evolution. In this application, N=3, corresponding to: frequency error (j=1), amplitude error (j=2), and bandwidth error (j=3), respectively. It is the standard deviation of the j-th target value, expressed as: ; Where M is the number of individuals in a non-dominated solution set found by the algorithm at the end of the t-th generation of evolution, i is each individual, and N is the objective function value of each individual. In this application, N=3, corresponding to: j=1: frequency error, j=2: amplitude error, and j=3: bandwidth error, respectively. Let i be the function value of the i-th solution on the j-th objective. Let the mean of the j-th objective over all Pareto optimal solutions be expressed as: ; Where M is the number of individuals in a non-dominated solution set found by the algorithm at the end of the t-th generation of evolution, i is each individual, and N is the objective function value of each individual. In this application, N=3, corresponding to: j=1: frequency error, j=2: amplitude error, and j=3: bandwidth error, respectively. Let S be the function value of the i-th solution on the j-th objective. The smaller the distribution degree S, the more concentrated the solutions are on the Pareto front, and the higher the degree of convergence of the algorithm.

[0071] Figure 4 The curve shows the change in the average objective function value of the Pareto front with the number of generations. In the first 30 generations, the average objective function value oscillates significantly within the range of 20 to 60, indicating that the algorithm performs extensive global exploration within the parameter space. After the 30th generation, the objective value decreases sharply and converges to around 0.01731. This "oscillating exploration-rapid convergence" characteristic demonstrates that this application possesses excellent global optimization capabilities, and the extremely low convergence value proves that the inverted parameters achieve a high-precision match with the true values.

[0072] Figure 5 The curve shows the Pareto front distribution degree as a function of generations. For the first 30 generations, the distribution degree remained at a relatively high level of 150-220, indicating that the population maintained sufficient diversity and effectively avoided premature convergence of the algorithm. Subsequently, the distribution degree rapidly decreased, eventually stabilizing at 0.05729. This convergence of the distribution degree indicates that the Pareto optimal solution set has converged to a stable region, concentrated near a relatively optimal parameter combination. This demonstrates that this application possesses extremely high determinism and accuracy in identifying stiffness and damping parameters, rather than remaining in a state of multiple solution trade-offs.

[0073] In another exemplary embodiment of this application, by Figure 6 The figure shows the distribution of the Pareto optimal solution set obtained by a method for identifying the stiffness and resistance parameters of pipe hangers in a three-dimensional target space. The coordinate axes in the figure are shown below. , , These represent frequency error, amplitude error, and half-power bandwidth error, respectively. From... Figure 6 It can be seen that all Pareto optimal solutions are closely distributed near the origin. Within a narrow region. Among them, frequency error The amplitude error should be controlled within 0.02 (i.e., 2%). and bandwidth error The accuracy is controlled within 0.2 (i.e., 20%). This distribution characteristic close to the origin intuitively demonstrates that the parameter inversion method proposed in this application has high inversion accuracy. Furthermore, the discrete point distribution of the solution set reveals a typical Pareto trade-off characteristic in multi-objective optimization problems: since the stiffness parameter dominates the resonant frequency location, while the damping parameter simultaneously affects the peak amplitude and half-power bandwidth, a single parameter combination is unlikely to simultaneously achieve the global optimum for all three objectives. This distribution characteristic of the non-dominated solution provides a flexible decision space for engineering applications. In practical engineering, the most suitable parameter combination can be selected from the Pareto optimal solution set according to requirements—for example, prioritizing the solution with the smallest frequency error in cases requiring high accuracy in resonant frequency prediction, or prioritizing the solution with the smallest amplitude error in cases requiring strict vibration amplitude control.

[0074] In another exemplary embodiment of this application, to verify the validity and accuracy of this application, three sets of elastic hanger examples with different combinations of stiffness and damping parameters were selected for parameter inversion tests. The comparison and analysis of the inversion results with the set true values ​​are shown in Table 2: Table 2 Comparison Analysis of Inverted Stiffness and Actual Value

[0075] As shown in Table 2, the inversion errors of stiffness parameters in all three sets of examples are controlled at a low level, mostly within 5%, indicating that this application has high inversion accuracy for stiffness parameters. The inversion error of damping parameters is relatively large. This is because stiffness directly determines the location of the resonant frequency, and its influence is concentrated and obvious, while damping mainly affects the peak height and bandwidth, but this influence is relatively gradual. Moreover, there is a coupling effect between multiple damping parameters—dampening changes of different hangers may produce similar frequency response curve changes, resulting in low parameter identification during inversion.

[0076] In another exemplary embodiment of this application, by Figure 7 This paper presents a comparison between the theoretical frequency response curves in the elastic hanger constraint direction of three instances calculated by substituting the optimal stiffness and damping parameters selected from the Pareto optimal solution set in step A4 into the transfer matrix dynamic model, and the response data from the finite element method (FEM) benchmark points. Figure 7 As can be seen, the theoretically calculated curves and the reference curves highly overlap across the entire frequency band (especially in terms of resonance peak positions and amplitudes), verifying the accuracy and reliability of the inversion parameters. Table 3 shows a comparison between the theoretical frequency response functions and the finite element method (FEM) reference point response data for the three examples above. Table 3 Verification Results of Inversion Parameters

[0077] Note: TMM calculations are based on inversion results; data in the table are rounded to two significant figures. This application also provides an application scenario in which the above-mentioned method for identifying the stiffness and resistance parameters of pipe hangers is applied. Specifically, the method for identifying the stiffness and resistance parameters of pipe hangers provided in this embodiment can be applied to the dynamic design and vibration control of various pipeline systems, such as cooling water pipelines and oil pump pipelines, in the industrial field. In this scenario, the elastic pipe hanger not only supports and fixes the pipeline, but also serves as one of the main channels for the transmission of vibration and noise energy from the pipeline system to the hull. The stiffness and damping parameters of the elastic hanger directly affect the vibration transmission characteristics and operational stability of the system. Specifically, during the design or operation and maintenance phase of a pipeline system, a parametric dynamic model based on the transfer matrix method is established by acquiring the geometric and material parameters of the pipeline system. Vibration response test data in the constraint direction of the elastic hanger is used to extract characteristic parameters such as the resonant frequency, peak amplitude, and half-power bandwidth of the frequency response function. Based on this, the NSGA-II multi-objective optimization algorithm is used to search for the Pareto optimal solution set within the feasible search range of stiffness and damping. The optimal stiffness and damping parameters are automatically selected from the solution set based on the normalized weighted Euclidean distance criterion. Finally, the identified optimal parameters are substituted into the transfer matrix model to achieve accurate prediction of the pipeline system's vibration response and precise inversion of hanger parameters. This method enables efficient inversion of equivalent stiffness and damping using limited vibration test data, even in the absence of precise hanger parameters. It provides reliable data support for vibration assessment, hanger selection, and vibration reduction design of pipeline systems, significantly reducing the design uncertainty caused by traditional trial-and-error or empirical methods.

[0078] In one exemplary embodiment, a computer device is provided, which may be a server or a terminal, and its internal structure diagram may be as follows. Figure 8 As shown, the computer device includes a processor, memory, input / output (I / O) interfaces, and a communication interface. The processor, memory, and I / O interfaces are connected via a system bus, and the communication interface is also connected to the system bus via the I / O interfaces. The processor provides computational and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system, computer programs, and a database. The internal memory provides the environment for the operating system and computer programs in the non-volatile storage media to run. The database stores the acquired geometric and material parameters of the piping system. The I / O interfaces are used for information exchange between the processor and external devices. The communication interface is used for communication with external terminals via a network connection. When executed by the processor, the computer program implements a method for identifying the stiffness and resistance parameters of pipe hangers.

[0079] Those skilled in the art will understand that Figure 8 The structures shown are merely block diagrams of some structures related to the present application and do not constitute a limitation on the computer device to which the present application is applied. Specific computer devices may include more or fewer components than shown in the figures, or combine certain components, or have different component arrangements. In an exemplary embodiment, a computer device is provided, including a memory and a processor. The memory stores a computer program, and the processor executes the computer program to implement the steps in the above-described method embodiments.

[0080] In one exemplary embodiment, a computer-readable storage medium is provided storing a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0081] In one exemplary embodiment, a computer program product is provided, including a computer program that, when executed by a processor, implements the steps in the above-described method embodiments.

[0082] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties, and the collection, use and processing of the relevant data must comply with relevant regulations.

[0083] Those skilled in the art will understand that all or part of the processes in the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments described above. Any references to memory, databases, or other media used in the embodiments provided in this application can include at least one of non-volatile and volatile memory. Non-volatile memory can include read-only memory (ROM), magnetic tape, floppy disk, flash memory, optical memory, high-density embedded non-volatile memory, resistive random access memory (ReRAM), magnetic random access memory (MRAM), ferroelectric random access memory (FRAM), phase change memory (PCM), graphene memory, etc. Volatile memory can include random access memory (RAM) or external cache memory, etc. By way of illustration and not limitation, RAM can take many forms, such as Static Random Access Memory (SRAM) or Dynamic Random Access Memory (DRAM).

[0084] The databases involved in the embodiments provided in this application may include at least one type of relational database and non-relational database. Non-relational databases may include, but are not limited to, blockchain-based distributed databases. The processors involved in the embodiments provided in this application may be general-purpose processors, central processing units, graphics processing units, digital signal processors, programmable logic devices, quantum computing-based data processing logic devices, etc., and are not limited to these.

[0085] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0086] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. Furthermore, those skilled in the art will recognize that, based on the ideas of this application, there will be changes in the specific implementation methods and application scope. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for identifying the rigidity and resistance parameters of pipe hangers, characterized in that, include: Obtain the geometric and material parameters of the pipeline system, and establish a transfer matrix dynamic model of the pipeline system based on the geometric and material parameters of the pipeline system; Obtain the vibration response in the constraint direction of the elastic hanger, and obtain experimental frequency response data based on the vibration response; Based on the aforementioned transfer matrix dynamics model, a forward calculation model for the frequency response function is constructed to obtain theoretical frequency response data. The error between the theoretical frequency response data and the experimental frequency response data is then calculated to obtain frequency response error data. Using the NSGA-II algorithm, a multi-objective optimization function is constructed based on the frequency response error data. The Pareto optimal solution set is searched within the feasible search range of stiffness and damping parameters, and the optimal stiffness and damping parameters are selected from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion.

2. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1, characterized in that, A transfer matrix dynamic model of the pipeline system is established based on its geometric and material parameters, specifically including: The pipeline system is discretized into several pipe segment units based on its geometric and material parameters; elastic hangers are installed on the pipeline system; the geometric parameters include pipe length, inner and outer diameters, and wall thickness; the material parameters include Young's modulus, density, and Poisson's ratio. Flexible hangers are installed at the beginning, middle and end of each pipe unit; A pipeline unit transfer matrix is ​​established for each pipeline unit, and a point transfer matrix is ​​introduced at the location of the elastic hanger. The elastic hanger is equivalent to a spring-damped support. The stiffness parameter and damping parameter are introduced into the model as unknowns to be identified, and the transfer matrix dynamic model of the pipeline system is obtained.

3. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1, characterized in that, Obtain the vibration response in the constraint direction of the elastic hanger, and derive experimental frequency response data based on the vibration response, specifically including: Impact excitation is applied at a designated location in the pipeline using the force hammer excitation method. An accelerometer is used to measure the vibration response in the constraint direction of the elastic hanger, and the vibration acceleration or velocity response signal in the constraint direction of the elastic hanger is obtained. The frequency response function is obtained by performing a fast Fourier transform on the vibration acceleration or velocity response signal in the direction of the elastic hanger constraint. A peak detection algorithm is used to identify the resonance peaks in the frequency response function, extract the experimental resonance frequency, and extract the experimental peak amplitude at each resonance peak. The half-power bandwidth method is used to determine the left and right boundary frequencies at the point where the experimental peak amplitude drops by 3dB, and then calculate the experimental half-power bandwidth.

4. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1 or 3, characterized in that, Based on the aforementioned transfer matrix dynamics model, a forward calculation model for the frequency response function is constructed to obtain theoretical frequency response data. The error between the theoretical and experimental frequency response data is then calculated to obtain frequency response error data, specifically including: Based on the aforementioned transfer matrix dynamics model, a forward calculation model for the frequency response function is constructed. Stiffness and damping parameters are selected from the feasible search range of the stiffness and damping parameters, and the stiffness and damping parameters are substituted into the forward calculation model to calculate the theoretical frequency response function of the elastic hanger in the constraint direction. A peak detection algorithm is used to identify the resonance peaks in the theoretical frequency response function, extract the theoretical resonance frequency, and extract the theoretical peak amplitude at each resonance peak. Using the half-power bandwidth method, the left and right boundary frequencies are determined at a 3dB drop in the theoretical peak amplitude, and the theoretical half-power bandwidth is calculated. The error between the theoretical resonance frequency and the experimental resonance frequency is calculated to obtain the resonance frequency error. The error between the theoretical peak amplitude and the experimental peak amplitude is calculated to obtain the peak amplitude error; The error between the theoretical half-power bandwidth and the experimental half-power bandwidth is calculated to obtain the half-power bandwidth error.

5. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1, characterized in that, After constructing the forward calculation model of the frequency response function based on the aforementioned transfer matrix dynamics model, the method further includes: Within the feasible search range of stiffness and damping parameters, several sets of stiffness and damping parameter instances are arbitrarily selected. The reference frequency response data is obtained by calculating using the finite element method, and the theoretical frequency response data is obtained by calculating using the forward calculation model. The reference frequency response data obtained by the finite element method and the theoretical frequency response data obtained by the forward calculation model for each group are compared and verified by the error formula. The error formula is: ； in, for These represent three objectives: resonant frequency, amplitude, and half-power bandwidth. The theoretical frequency response data is obtained from the forward calculation model. This is the reference frequency response data obtained from the finite element method.

6. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1, characterized in that, The frequency response error data includes resonant frequency error, peak amplitude error, and half-power bandwidth error. The resonant frequency error is calculated using the following formula: ； in, For the first The relative error between the theoretical resonance frequency calculated from the solution and the experimental resonance frequency. Calculate the frequency for the k-th order. For the k-th order target frequency, =1~3 indicates the number of peaks to be matched; The peak amplitude error is calculated using the following formula: ； in, Let the logarithmic relative error between the theoretical peak amplitude calculated for the i-th solution and the experimental peak amplitude be denoted as . , The first The calculated amplitude and target amplitude of the order. =1~3 indicates the number of peaks to be matched; The half-power bandwidth error is calculated using the following formula: ； in, The logarithmic relative error between the theoretical half-power bandwidth calculated for the i-th solution and the experimental half-power bandwidth is given by [the relevant parameter]. , These are the calculated half-power bandwidth and the target half-power bandwidth at the k-th order, respectively. =1~3 indicates the number of peaks to be matched.

7. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1, characterized in that, Using the NSGA-II algorithm, with the frequency response error data as the multi-objective optimization function, the search for the Pareto optimal solution set within the feasible search range of stiffness and damping parameters specifically includes: The three-target fitness error vector is obtained based on the resonant frequency error, peak amplitude error, and half-power bandwidth error. The population is stratified based on the three-objective fitness error vector and Pareto dominance relation, and non-dominated solutions at the Pareto front are selected. Calculate the crowding distance between individuals in the same layer, and prioritize retaining individuals in sparsely distributed areas; A progeny population is generated based on the current population through tournament selection, simulated binary crossover, and polynomial mutation. The current population is merged with the offspring population, and a new generation of the current population is selected from them by non-dominant sorting and crowding selection. Determine whether the current number of iterations completed is greater than or equal to the preset number of iterations to obtain the first determination result; If the first judgment result is yes, then the non-dominated solutions in the current population of the new generation are taken as the Pareto optimal solution set; If the first judgment result is negative, then it is determined whether the convergence condition is met, and the second judgment result is obtained. If the second judgment result is yes, then the non-dominated solutions in the current population of the new generation are taken as the Pareto optimal solution set; If the second judgment result is negative, then the current population of the new generation is taken as the current population, and the process jumps to the step "stratify the population based on the three-objective fitness error vector and Pareto dominance relationship, and screen out the non-dominated solutions at the Pareto front".

8. The method for identifying the rigidity and resistance parameters of pipe hangers according to claim 1, characterized in that, The optimal stiffness and damping parameters are selected from the Pareto optimal solution set based on the normalized weighted Euclidean distance criterion, specifically including: Normalize the objective function values ​​in the Pareto optimal solution set to the interval [0,1], and calculate the weighted distance from each function value to the ideal point; the ideal point is the point where all objectives are minimized. The stiffness and damping parameters corresponding to the solution with the smallest weighted distance score are selected as the inversion result; the weighted distance from each function value to the ideal point is calculated according to the following formula: ； Where j=1,2,3 represent three targets: resonant frequency, amplitude, and half-power bandwidth, respectively. For the first The weighted distance scores of each solution; For the first The weights for each target are set as follows: frequency, amplitude, and bandwidth are set to 1, 0.5, and 0.2, respectively. For the first The solution is at the th solution. Function values ​​on each target; and These are the first solutions in the current solution set. The minimum and maximum values ​​of each objective.

9. A computer device, comprising: A memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that the processor executes the computer program to implement the pipe hanger stiffness parameter identification method according to any one of claims 1-8.

10. A computer program product, comprising a computer program, characterized in that, When executed by a processor, the computer program implements the pipe hanger stiffness parameter identification method according to any one of claims 1-8.

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