Dynamic coupling compensation method for thermal expansion and axial displacement

Abstract

The present application belongs to the field of equipment coupling monitoring, and particularly relates to a dynamic coupling compensation method for thermal expansion and axial displacement, which acquires a thermal expansion parameter and an axial displacement parameter sequence of a machine shell, calculates a first characteristic value representing a dynamic offset of a sensor reference based on a three-dimensional thermal-structure coupling model, calculates a second characteristic value representing a real position change of a rotor based on a rotor-machine shell axial thermodynamic model, establishes a segmented coupling function considering nonlinear effects, working condition self-adaptation and cross interference, eliminates the influence of mechanical thermal inertia and measurement system lag through a dynamic delay compensation mechanism, generates an accurate axial displacement measurement total error compensation index, and intelligently triggers a graded compensation action according to the error level; the present application effectively solves the measurement distortion problem caused by the dynamic coupling of thermal expansion and axial displacement, and significantly improves the accuracy and reliability of rotating machinery state monitoring.

Description

Technical Field

[0001] This invention belongs to the field of equipment coupling monitoring, and particularly relates to a dynamic coupling compensation method for thermal expansion and axial displacement. Background Technology

[0002] In critical industrial sectors such as thermal power and chemical engineering, large and medium-sized target equipment like steam turbines and fans are core components ensuring continuous production. The stability of their operational status directly impacts the safety and efficiency of the overall production system. During operation, thermal expansion and axial displacement are key parameters reflecting the health status of such equipment. Thermal expansion includes casing thermal expansion and differential expansion between the rotor and casing, while axial displacement refers to the change in the rotor's position relative to a fixed reference point. These two factors exhibit significant dynamic coupling during operation. This dynamic coupling is triggered by temperature; casing thermal expansion causes a dynamic shift in the fixed reference point upon which the axial displacement sensor relies, and changes in the expansion difference between the rotor and casing alter the rotor's actual axial operating space. This results in a deviation between the measured and actual axial displacement values, fluctuating with real-time operating conditions. Current monitoring technologies for target equipment lack effective mechanisms to address this dynamic coupling between thermal expansion and axial displacement. This leads to issues such as false triggering of shutdown protection, missed reporting of excessive axial displacement, and distorted fault diagnosis results, making it difficult to meet the actual needs of industrial production for accurate monitoring and reliable protection of target equipment. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a dynamic coupling compensation method for thermal expansion and axial displacement. This method acquires the thermal expansion parameters and axial displacement parameter sequences of the casing, calculates the first characteristic value representing the dynamic offset of the sensor reference based on a three-dimensional thermo-structural coupling model, and calculates the second characteristic value representing the change in the true position of the rotor using a rotor-casing axial thermodynamic model. A piecewise coupling function considering nonlinear effects, adaptive operating conditions, and cross-interference is established. A dynamic delay compensation mechanism eliminates the influence of mechanical thermal inertia and measurement system hysteresis, generating an accurate total error compensation index for axial displacement measurement. Furthermore, it intelligently triggers graded compensation actions based on the error level. This invention effectively solves the measurement distortion problem caused by the dynamic coupling of thermal expansion and axial displacement, significantly improving the accuracy and reliability of rotating machinery condition monitoring.

[0004] To achieve the above objectives, the present invention provides the following technical solution:

[0005] Dynamic coupling compensation methods for thermal expansion and axial displacement include:

[0006] The real-time thermal expansion parameter sequence and the real-time axial displacement parameter sequence of the target device are obtained. The real-time thermal expansion parameter sequence includes the thermal expansion amount of the housing, which characterizes the thermal expansion state of the housing, and the differential expansion value, which characterizes the relative expansion state of the rotor and the housing. The real-time axial displacement parameter sequence includes the original measurement values ​​of the axial displacement sensor.

[0007] Based on the thermal expansion of the housing, which characterizes the thermal expansion state of the housing, a first characteristic value characterizing the dynamic offset of the fixed reference of the axial displacement sensor is calculated.

[0008] Based on the differential expansion value that characterizes the relative expansion state of the rotor and the housing, a second characteristic value characterizing the actual axial position change of the rotor is calculated. The second characteristic value is directly determined by the differential expansion value. The actual axial position change of the rotor is related to the thermal expansion difference between the rotor and the housing.

[0009] Based on the first feature value, the second feature value, and the real-time axial displacement parameter, a real-time coupling compensation index characterizing the total error of axial displacement measurement is generated.

[0010] In response to the absolute value of the real-time coupling compensation index exceeding a preset error trigger condition, a compensation action corresponding to the error trigger condition is selected from a set of actions including at least two compensation actions.

[0011] Specifically, the calculation of the first characteristic value characterizing the dynamic offset of the fixed reference of the axial displacement sensor includes:

[0012] A three-dimensional thermo-structural coupling model of the target equipment housing structure is established. The three-dimensional thermo-structural coupling model is constructed based on the geometric parameters of the housing, the thermophysical properties of the material, and the boundary constraints, combined with the finite element analysis algorithm. It is used to characterize the mapping relationship between the housing temperature distribution and the thermal deformation of the axial displacement sensor mounting base.

[0013] When the target equipment is running under multiple different steady-state temperature conditions, the three-dimensional thermal-structural coupling model calibration step is performed to obtain the calibrated three-dimensional thermal-structural coupling model; the multiple different steady-state temperature conditions cover the operating temperature range of the target equipment from cold state to rated load;

[0014] The first feature value is obtained by multiplying the real-time monitored thermal expansion of the casing by the dynamic offset correction coefficient determined through the calibration step of the three-dimensional thermal-structural coupling model; the dynamic offset correction coefficient is characterized by the slope of the linear relationship obtained by fitting the predicted value of the thermal expansion of the casing with the actual thermal expansion using the least squares method.

[0015] Specifically, the calibration steps for the three-dimensional thermal-structural coupling model include:

[0016] Collect real-time temperature values ​​from at least two temperature measuring points located at different positions on the casing body;

[0017] The real-time temperature value is input into the three-dimensional thermal-structural coupling model to obtain the corresponding predicted values ​​of thermal expansion of the casing and thermal deformation of the mounting base.

[0018] Simultaneously, the actual thermal expansion of the axial displacement sensor mounting base under the corresponding working conditions is measured using a reference measuring device.

[0019] Based on the difference between the predicted value of the thermal deformation of the mounting base and the actual thermal expansion, the error between the predicted value of the thermal deformation of the mounting base and the actual thermal expansion is minimized by adjusting the material thermal expansion coefficient or boundary constraints in the model, thereby obtaining a calibrated three-dimensional thermal-structural coupling model.

[0020] Specifically, the calculation of the second eigenvalue, which characterizes the actual axial position change of the rotor, includes:

[0021] The calibrated three-dimensional thermo-structure coupling model is fine-tuned and trained based on the geometric parameters of the rotor and the casing, the thermophysical properties of the materials, and the thermal boundary conditions to obtain a rotor-casing axial thermodynamic model for simulating the thermal expansion behavior of the rotor and its relative motion behavior with the casing under different operating conditions.

[0022] Based on the rotor-casing axial thermodynamic model, the correspondence between the temperature of the casing differential expansion sensor mounting base and the differential expansion measurement reference drift is established, and a reference drift compensation table is obtained.

[0023] Simultaneously, based on the rotor-casing axial thermodynamic model, the correspondence between the rotor thrust disk region temperature and the rotor three-dimensional thermal deformation axial equivalent quantity is established, and a thermal deformation compensation table is obtained.

[0024] Specifically, calculating the second eigenvalue, which characterizes the actual axial position change of the rotor, also includes:

[0025] The system collects the raw measurement values ​​of the differential expansion sensor, the temperature measurement values ​​of the rotor thrust disk area, and the temperature measurement values ​​of the housing differential expansion sensor mounting base in real time, and performs standardized processing.

[0026] Based on the processed temperature measurement value of the housing differential expansion sensor mounting base, the corresponding reference drift compensation amount is obtained by querying the reference drift compensation table.

[0027] Based on the temperature measurement value of the standardized rotor thrust disk area, the corresponding three-dimensional thermal deformation compensation amount is obtained by consulting the thermal deformation compensation table.

[0028] Based on the original measurement value of the differential expansion sensor, the reference drift compensation amount, and the three-dimensional thermal deformation compensation amount, the second characteristic value is obtained through compensation calculation, wherein the compensation calculation includes subtracting the reference drift compensation amount from the original measurement value of the differential expansion sensor and adding the three-dimensional thermal deformation compensation amount.

[0029] Specifically, coupling is performed based on the first eigenvalue, the second eigenvalue, and the real-time axial displacement parameters, including:

[0030] The thermal expansion coefficient of the material and the deformation of the casing under continuous temperature change rate are obtained, and the boundary of the temperature range is determined by combining the correlation analysis algorithm.

[0031] Based on the historical calibration data output by the calibrated three-dimensional thermo-structure coupling model and the rotor-casing axial thermodynamic model, and combined with the temperature range division boundary, a piecewise coupling function is established. Specifically, in the preset low temperature range, a linear coupling function is established by combining a univariate regression equation; in the medium or high temperature range, a nonlinear function relationship containing quadratic terms and temperature correction terms is established by combining a support vector machine.

[0032] Specifically, the coupling based on the first eigenvalue, the second eigenvalue, and the real-time axial displacement parameter further includes:

[0033] Based on real-time monitoring of temperature change rate and equipment load fluctuation, the current operating condition type is divided by a preset operating condition identification model, and the preset coupling coefficient matrix corresponding to the operating condition type is called to obtain the operating condition adaptive coupling coefficient; the operating condition type includes at least startup operating condition, steady-state operating condition or shutdown operating condition.

[0034] Based on the piecewise coupling function and the adaptive coupling coefficient of the working condition, a cross-interference compensation term constructed by combining the product of the first eigenvalue and the second eigenvalue, and a dynamic correction term constructed by the ratio of the first eigenvalue to the shell expansion rate, a compensation calculation model for eliminating the correlation of eigenvalues ​​is obtained.

[0035] Specifically, the coupling based on the first eigenvalue, the second eigenvalue, and the real-time axial displacement parameter further includes:

[0036] Based on the time difference between the predicted value of thermal deformation of the mounting base output by the three-dimensional thermal-structural coupling model and the actual thermal expansion, a dynamic delay compensation mechanism is established to obtain the real-time feature value sequence after delay compensation.

[0037] Based on the real-time feature value sequence after delay compensation, a real-time coupled compensation index characterizing the total error of axial displacement measurement is obtained through the compensation calculation model.

[0038] Specifically, the process of establishing a dynamic delay compensation mechanism includes:

[0039] During multiple complete thermal cycles, the predicted value sequence of thermal deformation of the mounting base output by the three-dimensional thermal-structure coupling model and the actual thermal expansion value sequence measured by the benchmark measuring device are recorded simultaneously. The time difference from the start of the change of the predicted value to the actual measured value reaching the same change amplitude in each set of data is calculated, and the arithmetic mean of all time differences is taken as the thermal hysteresis time constant of the system.

[0040] Based on the obtained thermal hysteresis time constant, a dynamic delay compensation function in the form of a first-order inertial element is constructed, and the first feature value is input into the dynamic delay compensation function for phase hysteresis processing to obtain a first feature value that keeps time synchronized with the actual thermal deformation state of the mechanical system.

[0041] Based on the dynamic response characteristics of the axial displacement sensor and signal acquisition system, the equivalent filtering time constant of the signal acquisition system is obtained by applying a standard step excitation signal and measuring the time when the system response reaches a preset stable value.

[0042] Specifically, the process of establishing a dynamic delay compensation mechanism also includes:

[0043] Based on the equivalent filtering time constant combined with the pre-trained advance correction algorithm, the axial displacement measurement value is obtained in time synchronized with the actual axial position of the rotor.

[0044] Based on the first feature value processed by the dynamic delay compensation function, the axial displacement measurement value sequence processed by the advance correction algorithm, and the second feature value, a real-time feature value sequence synchronized with time is obtained through unified timestamp alignment and resampling.

[0045] Compared with the prior art, the beneficial effects of the present invention are:

[0046] This invention addresses the shortcomings of existing technologies by establishing a three-dimensional thermo-structural coupling model of the target equipment's casing structure and a rotor-casing axial thermodynamic model. Based on real-time acquired thermal expansion parameter sequences and axial displacement parameter sequences, it calculates a first characteristic value representing the dynamic offset of the fixed reference of the axial displacement sensor and a second characteristic value representing the change in the actual axial position of the rotor. A piecewise coupling function considering nonlinear effects and adaptive operating conditions is employed, combined with a dynamic delay compensation mechanism, to perform time synchronization processing on the characteristic value sequences, generating a precise real-time coupling compensation index representing the total error in axial displacement measurement. When the coupling compensation index exceeds a preset error trigger condition, the invention intelligently selects and executes corresponding compensation actions from a set of graded compensation actions. This effectively solves the measurement distortion problem caused by the dynamic coupling of thermal expansion and axial displacement in rotating machinery, significantly improving the accuracy and operational reliability of equipment condition monitoring. Attached Figure Description

[0047] Figure 1 This is a flowchart of the dynamic coupling compensation method for thermal expansion and axial displacement in Embodiment 1 of the present invention;

[0048] Figure 2 This is a diagram showing the trigger condition response logic result of Embodiment 1 of the present invention. Detailed Implementation

[0049] Example 1

[0050] Please see Figure 1 The present invention provides an embodiment of a dynamic coupling compensation method for thermal expansion and axial displacement, comprising the following steps:

[0051] S1. Obtain the real-time thermal expansion parameter sequence and the real-time axial displacement parameter sequence of the target device. The real-time thermal expansion parameter sequence includes the thermal expansion amount of the casing, which characterizes the thermal expansion state of the casing, and the differential expansion value, which characterizes the relative expansion state between the rotor and the casing. The real-time axial displacement parameter sequence includes the original measurement values ​​of the axial displacement sensor.

[0052] S2. Based on the thermal expansion of the housing, which characterizes the thermal expansion state of the housing, calculate the first characteristic value characterizing the dynamic offset of the fixed reference of the axial displacement sensor.

[0053] S3. Based on the differential expansion value that characterizes the relative expansion state of the rotor and the housing, calculate a second characteristic value that characterizes the actual axial position change of the rotor. The second characteristic value is directly determined by the differential expansion value. The actual axial position change of the rotor is related to the thermal expansion difference between the rotor and the housing.

[0054] S4. Based on the first feature value, the second feature value and the real-time axial displacement parameter, a real-time coupling compensation index characterizing the total error of axial displacement measurement is generated.

[0055] S5. In response to the absolute value of the real-time coupling compensation index exceeding the preset error trigger condition, select the compensation action corresponding to the error trigger condition from the action set including at least two compensation actions.

[0056] Traditional methods directly use the raw measurements from the differential expansion sensor as the basis for rotor position changes, but ignore two key error sources: the measurement reference drift caused by the thermal deformation of the differential expansion sensor mounting base, and the axial projection component of the rotor's three-dimensional thermal deformation. This results in the differential expansion measurement values ​​under hot conditions containing both the actual relative displacement of the rotor and housing, and the axial coupling of sensor reference drift error and rotor spatial deformation. This leads to severely distorted rotor position information, failing to accurately reflect the actual operating state of the equipment, and consequently affecting the reliability of axial displacement protection and the accuracy of fault diagnosis. Therefore, this embodiment calibrates the collected raw data using a three-dimensional thermal-structural coupling model and a rotor-housing axial thermodynamic model.

[0057] It should be further explained that the first characteristic value for calculating the dynamic offset of the fixed reference of the axial displacement sensor in this embodiment includes:

[0058] A three-dimensional thermo-structural coupling model of the target equipment housing structure is established. The three-dimensional thermo-structural coupling model is constructed based on the geometric parameters of the housing, the thermophysical properties of the material, and the boundary constraints, combined with the finite element analysis algorithm. It is used to characterize the mapping relationship between the housing temperature distribution and the thermal deformation of the axial displacement sensor mounting base.

[0059] It should be further explained that the more detailed implementation process of constructing the three-dimensional thermal-structural coupling model in this embodiment includes:

[0060] Based on the design drawings and 3D point cloud scanning data of the target equipment housing, the overall geometric contour of the housing body and the local structural features of the axial displacement sensor mounting base are extracted by the Poisson surface reconstruction algorithm to obtain a housing geometric parameter model containing complete dimensional information and relative positional relationships.

[0061] Based on the material composition spectral analysis data and the material thermophysical property database, the thermal conductivity, specific heat capacity, density and thermal expansion coefficient parameters of the casing material are obtained. At the same time, the performance data of the casing material under multiple temperature gradients are measured by a high-temperature thermodynamic performance testing device. The least squares method is used to establish a continuous functional relationship between thermophysical properties and temperature, and a temperature-dependent material property model is obtained.

[0062] Based on the equipment operation process specifications and on-site thermal monitoring data, the fuzzy C-means clustering algorithm is used to intelligently identify and classify the types of heat sources received by the casing, including heat conduction, radiation and convection. At the same time, the constraint relationship between the casing and the equipment base is determined by the contact mechanics analysis method, and a thermal-mechanical boundary condition dataset containing parameters such as heat flux density, heat transfer coefficient and constraint reaction force is established.

[0063] Based on the geometric parameter model of the casing and the finite element mesh quality standard, the Delaunay triangulation algorithm with the front-end propulsion is used to generate the casing mesh model. For key areas such as the axial displacement sensor mounting base, the size function control method is applied to implement local mesh refinement to ensure the calculation accuracy of thermal-structural coupling analysis.

[0064] Based on a temperature-dependent material property model and a thermo-mechanical boundary condition dataset, steady-state and transient thermal load parameters are applied in a finite element analysis environment. The heat conduction control equation is solved by the Galerkin weighted residual method to obtain the three-dimensional temperature field distribution of the casing under typical working conditions.

[0065] The calculated temperature field distribution is applied as a body load to the casing structure model. Combined with complete boundary constraints, the updated Lagrange algorithm is used to solve the thermo-elastic mechanical equations of the casing structure model to obtain the overall structural deformation field of the casing and the local deformation vector of the mounting base.

[0066] Based on the overall structural deformation field of the casing and the local deformation vector of the mounting base, the feedback effect of geometric deformation on thermal boundary conditions is determined by the Newton-Raphson iterative algorithm. When a change in contact state or gap size is detected based on the deformation field, the heat transfer coefficient is automatically updated and the solution process is restarted from the thermal field calculation until the relative residual between the temperature field and the displacement field is less than the convergence criterion of 0.5%.

[0067] Based on the measured database and combined with the comprehensive fuzzy algorithm, a comprehensive error evaluation model including temperature field error and displacement field error is obtained; the measured database includes temperature data collected by a distributed temperature sensor network and base deformation data measured by a laser tracker.

[0068] In the process of automatically updating the heat transfer coefficient and restarting the solution process from the thermal field calculation, the temperature field error and displacement field error in each update process are analyzed and evaluated. At the same time, based on the error evaluation results, the Levenberg-Marquardt optimization algorithm is applied to automatically adjust the material property parameters and boundary condition parameters. Through multiple rounds of iterative calculations, the model prediction performance is continuously optimized until the comprehensive error index reaches the engineering application standard, and finally a validated three-dimensional thermal-structure coupling model is obtained.

[0069] When the target equipment operates under multiple different steady-state temperature conditions, the three-dimensional thermal-structural coupling model calibration step is performed to obtain a calibrated three-dimensional thermal-structural coupling model; the multiple different steady-state temperature conditions cover the operating temperature range of the target equipment from cold state to rated load; wherein, the specific method for determining the operating temperature range from cold state to rated load includes:

[0070] Based on the equipment design specifications and operating procedures, the upper and lower limits of the temperature range are determined. The temperature range is divided into several intervals using an equal interval division method. At the same time, key temperature points in the typical operating records of the equipment are added to ensure that the temperature points are evenly distributed and cover all characteristic operating conditions.

[0071] The equipment control system stabilizes the equipment at selected temperature points according to the preset heating rate. The holding time at each temperature point is determined based on the equipment's heat capacity calculation to ensure a sufficient thermal balance. During this period, the temperature at each measuring point is monitored by a temperature monitoring instrument to confirm that the temperature fluctuation meets the steady-state requirements.

[0072] Under each steady-state temperature condition, the collected temperature data were grouped and analyzed using the K-means clustering method. Abnormal operating condition data were removed, and the dataset that met the steady-state requirements was retained to ensure the validity and representativeness of the data at each operating condition point.

[0073] The number and distribution of temperature operating points are optimized based on the golden section search method in statistics. The density of operating points is increased in temperature-sensitive areas and the number of operating points is reduced in linearly changing areas to achieve the optimal distribution of temperature operating points.

[0074] The analysis of variance method is used to verify whether the selected temperature operating points fully cover the equipment operating range, and the confidence interval of the data at each operating point is calculated to ensure that the selection of temperature operating points meets the accuracy requirements of model calibration, and finally a complete temperature operating point sequence is formed.

[0075] It should be further explained that the calibration step of the three-dimensional thermal-structural coupling model in this embodiment includes:

[0076] Collect real-time temperature values ​​from at least two temperature measuring points located at different positions on the casing body;

[0077] The real-time temperature value is input into the three-dimensional thermal-structural coupling model to obtain the corresponding predicted values ​​of thermal expansion of the casing and thermal deformation of the mounting base.

[0078] Simultaneously, the actual thermal expansion of the axial displacement sensor mounting base under the corresponding working conditions is measured using a reference measuring device.

[0079] Based on the difference between the predicted value of the thermal deformation of the mounting base and the actual thermal expansion, the error between the predicted value of the thermal deformation of the mounting base and the actual thermal expansion is minimized by adjusting the material thermal expansion coefficient or boundary constraints in the model, thereby obtaining a calibrated three-dimensional thermal-structure coupling model; the material thermal expansion coefficient in this embodiment is set by those skilled in the art according to the specific material properties.

[0080] It should be further explained that, in this embodiment, the step of minimizing the error between the predicted value of the thermal deformation of the mounting base and the actual thermal expansion by adjusting the material thermal expansion coefficient or boundary constraints in the model includes:

[0081] Based on the difference dataset between the predicted value sequence of thermal deformation of the mounting base and the measured value sequence of actual thermal expansion, the objective function of residual sum of squares is established by the least squares method, and the gradient of the objective function is calculated by the normal equation solution method to obtain the value of the error evaluation index that needs to be minimized.

[0082] Based on the error evaluation index and its Jacobian matrix, the Levenberg-Marquardt optimization algorithm is adopted. By adjusting the damping factor, the convergence characteristics of gradient descent and Gauss-Newton method are balanced. The direction of model parameter adjustment is calculated, and the preliminary correction values ​​of material thermal expansion coefficient parameters and boundary constraint condition parameters are obtained.

[0083] Based on the range of values ​​and variation of the material thermal expansion coefficient parameter and boundary constraint condition parameter, the Morris sensitivity analysis method is used to calculate the influence weight coefficient of each parameter on the predicted value of thermal deformation of the mounting base. The single-parameter perturbation method is used to evaluate the degree of influence of parameter changes on the output and obtain the adjustment priority sequence of each parameter.

[0084] Based on the parameter adjustment priority sequence and parameter constraints, a sequential quadratic programming algorithm is adopted. The constraints are handled by the Lagrange multiplier method, and the Hessian matrix is ​​approximated by the quasi-Newton method to determine the parameter adjustment order and obtain a phased parameter optimization implementation plan.

[0085] Based on the phased parameter optimization implementation scheme, firstly, for highly sensitive parameters, the conjugate gradient method is used for iterative calculation, the conjugate direction is calculated using the Fletcher-Reeves formula, the optimal step size is determined by linear search, and the material thermal expansion coefficient parameter value after the first stage of optimization is obtained.

[0086] Based on the material thermal expansion coefficient parameters optimized in the first stage, we continue to calculate the low-sensitivity parameters using the quasi-Newton method iteratively, update the Hessian matrix approximation using the BFGS formula, and ensure the effectiveness of the search direction through the Wolfe condition to obtain the boundary constraint parameters optimized in the second stage.

[0087] Based on the optimized values ​​of the material thermal expansion coefficient and boundary constraint parameters, the finite element thermal field calculation and structural thermal deformation analysis are re-executed. The temperature field and displacement field distribution are updated through the coupled field solver to obtain the updated predicted value of the thermal deformation of the mounting base.

[0088] Based on the comparison between the updated predicted thermal deformation data of the mounting base and the actual measured thermal expansion data, the optimization effect is evaluated by the convergence judgment criterion. The dual standards of relative error change rate and absolute error threshold are adopted. If the convergence criterion is not met, the above optimization process is repeated until the prediction error meets the engineering accuracy requirements.

[0089] Based on the final optimization results, the parameter output module generates a calibrated dataset of material thermal expansion coefficient parameters and a dataset of boundary constraint condition parameters. The data verification process is used to confirm the rationality of the parameters, and a three-dimensional thermal structure coupling model that meets the engineering accuracy requirements is obtained.

[0090] The first feature value is obtained by multiplying the real-time monitored thermal expansion of the casing by the dynamic offset correction coefficient determined through the calibration step of the three-dimensional thermal-structural coupling model; the dynamic offset correction coefficient is characterized by the slope of the linear relationship obtained by fitting the predicted value of the thermal expansion of the casing with the actual thermal expansion using the least squares method.

[0091] This process achieves precise compensation for the coupling error between thermal expansion and axial displacement of rotating machinery by constructing a high-precision three-dimensional thermo-structural coupling model and establishing a complete calibration system. Its beneficial effects are as follows: Based on multi-source data fusion and iterative optimization algorithms, it significantly improves the accuracy of axial displacement measurement, effectively solving the measurement distortion problem caused by neglecting the dynamic characteristics of the temperature field and the coupling effect of structural deformation in traditional methods. By establishing a temperature-dependent material property model and a thermo-mechanical boundary condition parameter set, the prediction accuracy of the model under complex working conditions is ensured; a hierarchical optimization strategy is adopted to collaboratively calibrate the material's thermal expansion coefficient and boundary constraints, minimizing the prediction error of the thermal deformation of the mounting base; and a dynamic offset correction coefficient is innovatively introduced, transforming the model output into the characteristic values ​​required for real-time compensation, significantly improving the reliability of rotating machinery condition monitoring.

[0092] It should be further explained that the second characteristic value, which characterizes the actual axial position change of the rotor, in this embodiment includes:

[0093] The calibrated three-dimensional thermo-structure coupling model is fine-tuned and trained based on the geometric parameters of the rotor and the casing, the thermophysical properties of the materials, and the thermal boundary conditions to obtain a rotor-casing axial thermodynamic model for simulating the thermal expansion behavior of the rotor and its relative motion behavior with the casing under different operating conditions.

[0094] The process of obtaining the rotor-casing axial thermodynamic model includes:

[0095] Based on rotor design drawings and 3D scanning data, the geometric contours and structural dimensions of the rotor body, journal and thrust disk are extracted. Combined with material composition analysis reports and thermophysical property databases, the thermal conductivity, specific heat capacity, thermal expansion coefficient and elastic modulus parameters of the rotor material are obtained. An initial finite element model of the rotor is established through solid modeling and mesh generation.

[0096] Based on the finite element mesh data of the housing in the calibrated three-dimensional thermal-structural coupling model, considering the bearing fit clearance and sealing device clearance characteristics between the rotor and the housing, the interaction relationship between the rotor and the housing is established by the contact interface coupling method, and the initial coupling model of the rotor-housing system is obtained.

[0097] Based on the equipment's operating process parameters and measured rotor surface temperature data, a thermal boundary condition mapping relationship is adopted to assign the heat exchange parameters between the rotor and the working medium, and the heat conduction parameters between the rotor and the bearing assembly, to the corresponding elements of the initial coupled model of the rotor-casing system, thus establishing complete thermal boundary conditions. In this embodiment, the thermal boundary condition mapping relationship mainly includes: establishing a convective heat transfer boundary mapping based on the spatial correspondence between the rotor geometric model and the fluid domain, used to convert process parameters such as the temperature and flow rate of the working medium into the convective heat transfer coefficient of the rotor surface; establishing a heat conduction boundary mapping based on the topological relationship of the rotor-bearing contact surface, used to determine the interface thermal resistance and heat conduction flux according to the bearing temperature and contact state; and establishing a temperature boundary mapping based on the positional relationship between the rotor surface temperature measurement points and the finite element mesh, used to directly apply the measured temperature data as thermal boundary conditions to the corresponding mesh nodes.

[0098] Based on the casing temperature field data provided by the calibrated three-dimensional thermal-structural coupling model, the sequential thermal-structural coupling calculation method is adopted. First, the steady-state and transient thermal field analysis of the system is performed to obtain the rotor temperature distribution. Then, the temperature field is used as a load to calculate the structural deformation, and the predicted data of rotor thermal expansion and rotor-casing relative displacement are obtained.

[0099] Based on the measured rotor thermal expansion and rotor-casing relative displacement data, a model training sample set was constructed. Regression analysis was used to optimize the material thermal expansion coefficient and contact interface stiffness parameters in the coupled model with the goal of minimizing the error between the predicted and measured values, and a preliminary optimized coupled model was obtained.

[0100] Based on measured data of multiple steady-state operating conditions of the equipment from cold state to rated load, the training dataset is divided into training subset and validation subset using cross-validation method. The optimized coupled model is then validated under multiple operating conditions to evaluate the prediction accuracy of rotor thermal expansion and relative displacement.

[0101] Based on the prediction error analysis results obtained from cross-validation, the thermal boundary parameters and structural constraint parameters in the coupled model are adjusted using a parameter optimization algorithm. The thermal-structural coupling calculation and verification process is repeated until the prediction error under each working condition meets the engineering accuracy requirements, and finally an accurate and reliable rotor-casing axial thermodynamic model is obtained.

[0102] Based on the rotor-casing axial thermodynamic model, the correspondence between the temperature of the casing differential expansion sensor mounting base and the differential expansion measurement reference drift is established, and a reference drift compensation table is obtained.

[0103] It should be further explained that the process of establishing the correspondence between the temperature of the housing differential expansion sensor mounting base and the drift of the differential expansion measurement reference in this embodiment includes:

[0104] Based on the rotor-casing axial thermodynamic model, by setting multiple steady-state temperature conditions covering the target equipment from cold state to rated load, the model is run to obtain temperature data of the casing differential expansion sensor mounting base position under each condition. At the same time, laser displacement sensing technology is used to measure the actual thermal deformation of the mounting base under the corresponding conditions to obtain the initial correspondence dataset between temperature and reference drift.

[0105] The time series smoothing method based on the moving average algorithm smooths the temperature series and drift series in the initial dataset to eliminate the interference of instantaneous fluctuations during the measurement process. The outlier detection method based on the Z-score algorithm is used to identify and remove abnormal data points in the dataset that deviate from the normal distribution range, so as to obtain a purified temperature-drift correspondence dataset.

[0106] Based on the purified temperature-drift correlation dataset, a multiple linear regression method using the least squares approach was adopted, with the installation base temperature as the input variable and the differential expansion measurement benchmark drift as the output variable, to establish an initial temperature-drift correlation model. Furthermore, the K-fold cross-validation method was used to divide the dataset into a training subset and a validation subset, and the model coefficients were optimized through iterative calculation to obtain a temperature-drift correlation model with satisfactory prediction accuracy.

[0107] Based on other steady-state temperature data of the target equipment that were not involved in the model training, the temperature data of the mounting base was obtained through the rotor-casing axial thermodynamic model, and then input into the optimized correlation model to obtain the predicted value of the baseline drift.

[0108] Simultaneously, a grating length measuring instrument is used to measure the actual value of the reference drift under this working condition, and the relative error between the predicted value and the actual value is calculated. When the relative error exceeds the preset accuracy range, the model parameters are readjusted and optimized until the prediction error meets the accuracy requirements, and the final temperature-drift correlation model is obtained.

[0109] Based on the finalized temperature-drift correlation model, temperature sampling points are set at fixed intervals according to the equipment operating temperature range, and the predicted baseline drift value corresponding to each temperature point is calculated. The temperature values ​​and the corresponding predicted baseline drift values ​​are arranged in ascending order of temperature to construct a structured query table, thereby obtaining the baseline drift compensation table for real-time compensation.

[0110] Simultaneously, based on the rotor-casing axial thermodynamic model, the correspondence between the rotor thrust disk region temperature and the rotor three-dimensional thermal deformation axial equivalent quantity is established, and a thermal deformation compensation table is obtained.

[0111] It should be further explained that the process of obtaining the thermal deformation compensation scale in this embodiment includes:

[0112] Based on the design drawings and 3D point cloud scan dataset of the rotor thrust disk, the geometric contour features, structural dimension parameters, and thickness distribution characteristics of the thrust disk are extracted using the Poisson surface reconstruction algorithm. Combined with the connection structure recognition algorithm, the connection structure form between the thrust disk and the rotor spindle is determined. Simultaneously, based on the rotor material composition test report and material thermophysical property database, the thermal conductivity, specific heat capacity, coefficient of thermal expansion, and elastic modulus parameters of the material are obtained through data query and extraction algorithms. A complete dataset of rotor thrust disk geometric parameters and material thermophysical properties is established through data fusion processing.

[0113] The boundary condition configuration specification document based on the rotor-casing axial thermodynamic model allows the complete input of the obtained rotor thrust disk geometric parameters and material thermophysical property datasets into the rotor-casing axial thermodynamic model via a data interface.

[0114] Simultaneously, based on the target equipment's operating process parameter document, the heat source type distribution in the rotor thrust disk area is set through a heat source configuration algorithm, the heat source intensity parameters are determined using a heat source intensity calculation algorithm, and the heat dissipation condition characteristics are configured through a heat dissipation condition analysis algorithm, thus completing the comprehensive configuration of the rotor-casing axial thermodynamic model.

[0115] Based on the configured rotor-casing axial thermodynamic model, the temperature field distribution characteristics of the rotor thrust disk region under multiple steady-state temperature conditions are simulated using the finite element thermal analysis algorithm.

[0116] The node temperature extraction algorithm is used to extract the temperature values ​​of key structural parts of the thrust disk under various working conditions, including the thrust working surface and the hub connection surface, from the finite element result file. A complete temperature field dataset of the rotor thrust disk region is obtained through data processing and archiving.

[0117] Based on the obtained temperature field datasets under various operating conditions, the temperature data is applied as a thermal load to the rotor thrust disk analysis unit of the rotor-casing axial thermodynamic model using a load mapping algorithm. Combined with the thermoelastic finite element analysis algorithm, the three-dimensional thermal deformation vector distribution of the rotor thrust disk under various operating conditions is calculated using an iterative solution method. This includes obtaining the radial deformation component, axial deformation component, and circumferential deformation component through a displacement extraction module, thus obtaining a detailed three-dimensional thermal deformation dataset of the rotor thrust disk.

[0118] Based on the obtained three-dimensional thermal deformation vector dataset, the three-dimensional thermal deformation vector data is projected and transformed according to the axial reference direction during equipment operation by using a vector projection calculation algorithm and dot product operation. The equivalent projection value of the three-dimensional thermal deformation of the rotor thrust disk region in the axial direction under various working conditions is calculated by the projection calculation module. A complete dataset of the correspondence between temperature and axial equivalent quantity is established by using a data association algorithm.

[0119] Based on the obtained dataset of the correspondence between temperature and axial equivalent quantities, regression analysis was performed using the least squares fitting algorithm. A mathematical relationship model between the temperature of the rotor thrust disk region and the axial equivalent quantity of three-dimensional thermal deformation was established using both linear regression and polynomial regression methods. The optimal model form was selected through model evaluation indicators to obtain a preliminary model of the correspondence between temperature and axial equivalent quantities.

[0120] Based on the dataset of the correspondence between temperature and axial equivalent quantities, the dataset is divided into a training subset and a validation subset using the K-fold cross-validation algorithm. The parameters of the mathematical relationship model are optimized using the gradient descent algorithm on the training subset, and the prediction accuracy of the model is tested using the root mean square error index on the validation subset. When the prediction error exceeds the preset threshold, the fitting algorithm parameters are readjusted using the parameter adjustment algorithm and the optimization process is repeated until the model prediction accuracy fully meets the requirements, thus obtaining the final temperature and axial equivalent quantity correspondence model.

[0121] Based on the final determined model of the correspondence between temperature and axial equivalent quantity, according to the preset temperature range division rule document, the temperature sampling point generation algorithm system determines each temperature sampling point, the table lookup calculation method is used to obtain the matching data of the corresponding axial equivalent quantity, and the table construction algorithm is used to construct a structured thermal deformation compensation data query table to form a complete thermal deformation compensation table.

[0122] Based on the real-time acquired raw measurement sequence of differential expansion sensor, the temperature measurement sequence of rotor thrust disk area and the temperature measurement sequence of housing differential expansion sensor mounting base, the data is standardized using the Z-score standardization algorithm to obtain a standardized sensor dataset.

[0123] Based on the processed temperature measurement value of the housing differential expansion sensor mounting base, the reference drift compensation table is looked up by a lookup table algorithm, and the corresponding reference drift compensation amount is obtained by linear interpolation method.

[0124] Based on the standardized temperature measurement values ​​of the rotor thrust disk area, the thermal deformation compensation table is looked up by a lookup algorithm, and the corresponding three-dimensional thermal deformation compensation is obtained by linear interpolation.

[0125] Based on the original measurement value of the differential expansion sensor, the reference drift compensation amount, and the three-dimensional thermal deformation compensation amount, the compensation calculation is performed through algebraic operation methods. Specifically, this includes the calculation process of subtracting the reference drift compensation amount from the original measurement value of the differential expansion sensor and adding the three-dimensional thermal deformation compensation amount to obtain accurate second characteristic value data.

[0126] It should be further explained that the coupling based on the first feature value, the second feature value, and the real-time axial displacement parameter in this embodiment includes:

[0127] The thermal expansion coefficient of the material and the deformation of the casing under continuous temperature change rate are obtained, and the boundary of the temperature range is determined by combining the correlation analysis algorithm.

[0128] It should be further explained that the process of determining the boundaries of the temperature range in this embodiment includes:

[0129] Based on the continuous temperature change rate data, material thermal expansion coefficient data and shell deformation data in the three-dimensional original dataset, the temperature change rate data is convolved and smoothed by the Savitzky-Golay filtering algorithm, and high-frequency noise interference is eliminated by second-order polynomial fitting and eleven-term window width.

[0130] Simultaneously, based on the material thermal expansion coefficient data and the casing deformation data, the standard deviation multiple of each data point from the corresponding sequence mean is calculated using the Z-score normalization algorithm to obtain a standardized thermophysical parameter dataset.

[0131] Based on the standardized temperature change rate data and thermophysical parameter dataset, the linear correlation between temperature change rate and material thermal expansion coefficient, temperature change rate and casing deformation, and material thermal expansion coefficient and casing deformation were calculated using the Pearson correlation coefficient algorithm. A ternary correlation evaluation matrix was constructed to obtain a complete quantitative index of parameter correlation.

[0132] Based on the correlation coefficient sequence in the correlation evaluation matrix, the sliding window analysis method is used to set a window width of thirty data points and perform traversal calculations with a step size of five data points. The arithmetic mean and standard deviation of the correlation coefficients in each window are calculated to obtain the mean sequence and variance sequence that reflect the local correlation characteristics.

[0133] Based on the correlation coefficient mean sequence, the Canny edge detection algorithm is used to identify abrupt change feature points using a double threshold method. The high threshold is set to 0.6 and the low threshold is set to 0.3. Combined with fluctuation points in the variance sequence that exceed 0.1, false boundary points are eliminated to obtain a set of candidate temperature range boundary points.

[0134] Based on the phase transition temperature data measured by differential scanning calorimetry of materials, the Euclidean distance between candidate boundary points and material property temperatures is calculated by the nearest neighbor matching algorithm. The matching tolerance is set to five degrees Celsius, and the corresponding point pairs with the smallest distance are selected to obtain the temperature boundary point set verified by material properties.

[0135] Based on a standardized thermophysical parameter dataset, three cluster centers were set using the K-means clustering algorithm. The elbow rule was used to determine the optimal number of clusters. Stable clustering results were obtained after twenty iterations. Boundary temperature values ​​of each category were extracted to form a cluster boundary temperature set.

[0136] Based on the verified temperature boundary point set and cluster boundary temperature set, a cost matrix is ​​constructed using the Hungarian matching algorithm, the optimal allocation scheme with minimum matching cost is calculated, and the matching threshold is set to one degree Celsius to obtain a consistent final temperature range partition boundary set.

[0137] Based on historical calibration data and temperature range boundary sets, a linear mapping relationship between the thermal expansion coefficient and deformation of the material is established in the low temperature range using a univariate linear regression algorithm, and the slope and intercept parameters are calculated and determined. In the medium and high temperature range, a radial basis kernel function is used with a support vector machine algorithm and a penalty factor of 10 to establish a nonlinear function relationship containing quadratic terms and temperature correction terms, thus obtaining a complete piecewise coupled function model.

[0138] Based on real-time temperature change rate data and equipment load fluctuation data, three cluster centers were set up using the K-means clustering algorithm to correspond to startup, steady state and shutdown conditions respectively. Using Euclidean distance as a metric, the accurate classification of the current operating condition type was obtained after fifteen iterations.

[0139] Based on the operating condition classification results and the preset coupling coefficient matrix, a mapping relationship between operating condition types and matrix row and column numbers is established through a matrix query algorithm. The corresponding coupling coefficient vector is dynamically extracted according to the real-time operating conditions to achieve accurate matching and output of adaptive coupling coefficients for operating conditions. The operating condition types include at least startup operating conditions, steady-state operating conditions, or shutdown operating conditions.

[0140] It should be further explained that the process of obtaining the coupling coefficient matrix in this embodiment includes:

[0141] Based on the temperature change rate sequence and equipment load fluctuation sequence in the historical operation database, the operating conditions are classified by the K-means clustering algorithm to obtain typical operating condition classification results including start-up conditions, steady-state conditions and shutdown conditions.

[0142] Based on the classification results of typical working conditions, principal component analysis is used to extract the main characteristic components of temperature change rate and load fluctuation under each working condition, and to obtain a set of feature vectors that characterize the features of different working conditions.

[0143] Based on simulation data of the rotor casing axial thermodynamic model under different working conditions, the mapping relationship between temperature change rate, load fluctuation and coupling coefficient is calculated by multiple linear regression algorithm to obtain the initial coupling coefficient mapping model.

[0144] Based on the axial displacement sensor data and thermal expansion parameter data measured on site, the parameters of the initial coupling coefficient mapping model are optimized using the least squares method to obtain the calibrated coupling coefficient mapping relationship.

[0145] Based on the calibrated coupling coefficient mapping relationship, a coefficient matrix containing the temperature change rate weight coefficient and the load fluctuation weight coefficient is constructed for each typical working condition to obtain a preliminary working condition coupling coefficient matrix.

[0146] Based on the model prediction error analysis results, the ridge regression algorithm is used to regularize the weight coefficients in the working condition coupling coefficient matrix to obtain the optimized coupling coefficient matrix.

[0147] The optimized coupling coefficient matrix is ​​validated based on real-time monitoring data. The cross-validation method is used to evaluate the adaptability of the matrix under different working conditions, and the validated coupling coefficient matrix is ​​obtained.

[0148] Based on equipment operation status monitoring data, a coupling coefficient matrix update mechanism is established. The sliding window learning method is used to update the matrix parameters periodically to obtain a preset coupling coefficient matrix that can be adaptively adjusted.

[0149] Based on the piecewise coupling function and the adaptive coupling coefficient of the working condition, the cross-interference compensation term constructed by combining the product of the first eigenvalue and the second eigenvalue, and the dynamic correction term constructed by the ratio of the first eigenvalue to the shell expansion rate, a compensation calculation model to eliminate the correlation of eigenvalues ​​is obtained.

[0150] It should be further explained that one implementation of the compensation calculation model for eliminating eigenvalue correlation in this embodiment is as follows:

[0151] Based on the basic expression of the piecewise coupling function and the working condition adaptive coupling coefficient matrix, the degree of mutual influence between the first eigenvalue and the second eigenvalue is calculated by Pearson correlation coefficient analysis to obtain a quantitative index of correlation between eigenvalues.

[0152] Based on the quantitative index of correlation between eigenvalues, a mathematical model of the product term of the first eigenvalue and the second eigenvalue is established using the multiple regression analysis method to obtain the basic expression of the compensation term characterizing the intensity of cross-interference.

[0153] Based on the real-time acquired shell expansion data sequence, the instantaneous value of the shell expansion rate of change is calculated using the sliding window difference method to obtain continuous shell expansion rate of change time series data;

[0154] Based on the correspondence between the time series data of the shell expansion rate and the first characteristic value, the ratio analysis method is used to construct a mathematical model of the dynamic correction term and obtain the expression of the correction term considering the dynamic characteristics of thermal expansion.

[0155] Based on the least squares support vector machine algorithm, the cross-interference compensation term and the dynamic correction term are simultaneously introduced into the piecewise coupling function. The basic architecture of the compensation calculation model is established through nonlinear mapping, and a preliminary compensation calculation model is obtained.

[0156] Based on the sample characteristics of historical running datasets, a regularization optimization method is used to constrain the coefficients in the compensation calculation model, thereby obtaining an optimized compensation calculation model with good generalization ability.

[0157] Based on the K-fold cross-validation method, the optimized compensation calculation model is validated and tested on multiple working condition datasets to obtain a model prediction accuracy evaluation report;

[0158] Based on the model prediction accuracy evaluation report, the gradient descent optimization algorithm is used to iteratively adjust the parameter settings of the compensation calculation model until the model output error meets the preset accuracy requirements, thus obtaining the final compensation calculation model that eliminates the correlation of eigenvalues.

[0159] Based on the time difference between the predicted value of thermal deformation of the mounting base output by the three-dimensional thermal-structural coupling model and the actual thermal expansion, a dynamic delay compensation mechanism is established to obtain the real-time feature value sequence after delay compensation.

[0160] Based on the real-time feature value sequence after delay compensation, a real-time coupled compensation index characterizing the total error of axial displacement measurement is obtained through the compensation calculation model.

[0161] During the actual operation of rotating machinery, the significant thermal inertia of the mechanical system causes the changes in characteristic parameters calculated based on temperature models to precede the actual physical deformation. Simultaneously, the inherent signal acquisition, transmission, and processing stages of the measurement system introduce a non-negligible time delay, resulting in sensor measurements lagging behind the actual mechanical state. This timing mismatch between the leading and lagging predicted signals means that characteristic data from different sources exist in different time reference frames, severely impacting the accuracy and timeliness of axial displacement compensation. If this timing inconsistency is not addressed, the condition monitoring system will perform compensation calculations based on asynchronous data, resulting in significant phase errors and amplitude deviations, ultimately affecting the reliability of the equipment's safe operation.

[0162] It should be further explained that the establishment process of the dynamic delay compensation mechanism in this embodiment includes:

[0163] During multiple complete thermal cycles, the predicted value sequence of thermal deformation of the mounting base output by the three-dimensional thermal-structure coupling model and the actual thermal expansion value sequence measured by the benchmark measuring device are recorded simultaneously. The time difference from the start of the change of the predicted value to the actual measured value reaching the same change amplitude in each set of data is calculated, and the arithmetic mean of all time differences is taken as the thermal hysteresis time constant of the system.

[0164] Based on the obtained thermal hysteresis time constant, a dynamic delay compensation function in the form of a first-order inertial element is constructed, and the first feature value is input into the dynamic delay compensation function for phase hysteresis processing to obtain a first feature value that keeps time synchronized with the actual thermal deformation state of the mechanical system.

[0165] It should be further explained that the specific process of obtaining the first characteristic value that is synchronized with the actual thermal deformation state of the mechanical system in this embodiment includes:

[0166] Based on the obtained thermal hysteresis time constant parameters, the difference equation form of the first-order inertial element is constructed using the continuous system discretization method, and the mathematical expression of the dynamic delay compensation function in the discrete time domain is obtained.

[0167] Based on the mathematical expression of the dynamic delay compensation function, the backward difference method is used to transform the continuous differential equation into a discrete difference equation, thereby obtaining a recursive calculation formula suitable for digital system implementation.

[0168] Based on the real-time acquired first feature value data, a sliding window data caching technique is used to store feature value data at multiple consecutive sampling times to obtain a data input sequence that meets the requirements of recursive calculation.

[0169] Based on the recursive calculation formula and the data input sequence, the first feature value is input into the dynamic delay compensation function one by one using the iterative calculation method to obtain the output sequence after phase lag processing;

[0170] Based on the temporal characteristics of the actual thermal deformation state of the mechanical system, a time series alignment method is used to match the processed output sequence with the actual state time axis of the mechanical system to obtain the first feature value data of time synchronization.

[0171] Based on the requirements of real-time data processing, a circular buffer management technique is adopted to update the input data sequence, ensuring that the dynamic delay compensation function continuously receives the latest first feature value data and obtains continuously updated phase lag processing results.

[0172] Based on the stability requirements of the processing results, an amplitude preservation algorithm is used to normalize the output sequence to ensure that the first feature value after phase lag processing retains its original dimensions and physical meaning, thus obtaining the first feature value that is time-synchronized with the actual thermal deformation state of the mechanical system.

[0173] Based on the dynamic response characteristics of the axial displacement sensor and signal acquisition system, the equivalent filtering time constant of the signal acquisition system is obtained by applying a standard step excitation signal and measuring the time when the system response reaches a preset proportion of the stable value.

[0174] It should be further explained that the process of obtaining the equivalent filtering time constant of the signal acquisition system in this embodiment includes:

[0175] Based on the range parameters of the axial displacement sensor and the input characteristic parameters of the signal acquisition system, combined with the technical specifications of the standard step excitation source, the step amplitude parameters and rise time parameters of the standard step excitation signal are determined. According to the calibration specifications of geometric measurement equipment, the output amplitude of the standard step excitation source is accurately calibrated using a standard displacement calibration device. At the same time, according to the waveform measurement standard specifications, the sampling frequency parameters and amplitude measurement accuracy of the signal acquisition system are systematically calibrated using a high-precision oscilloscope, resulting in a fully calibrated test system.

[0176] Based on the calibrated test system, the axial displacement sensor is fixedly installed at the displacement output end of the standard step excitation source, ensuring that the sensor detection end is in close contact with the displacement surface of the excitation source; the sensor output end is connected to the input end of the signal acquisition system through a signal transmission cable, and the trigger port of the standard step excitation source is connected to the external trigger port of the signal acquisition system through a time synchronization cable. A precise time synchronization protocol is used to achieve time synchronization control of the excitation signal and the acquisition signal, thus obtaining a time-synchronized test connection system.

[0177] The time-synchronized test connection system sends a trigger command through the control unit of the standard step excitation source to apply a standard step excitation signal with preset parameters. At the same time as the excitation signal is applied, the trigger signal acquisition system starts the data acquisition process according to the preset sampling frequency, continuously acquiring the response signal output by the sensor until the amplitude of the response signal remains stable within multiple consecutive sampling periods. The data recording system records the timestamp data and response signal amplitude data corresponding to each sampling moment to obtain a complete time and amplitude response data sequence.

[0178] Based on the obtained time and amplitude response data sequence, a moving average filtering algorithm is used to smooth the data in the later stable segment of the data sequence, and the arithmetic mean of the stable segment data is calculated. This arithmetic mean is determined as the stable value of the system response. Based on the stable value of the system response and a preset scaling factor, the target amplitude that the system response needs to achieve is calculated.

[0179] Based on the time and amplitude response data sequence and the calculated target amplitude, a linear interpolation algorithm is used to accurately find the moment when the response signal amplitude first reaches the target amplitude in the data sequence; the timestamp data corresponding to this moment is extracted, the time difference between this timestamp and the moment when the excitation signal is applied is calculated, and this time difference is determined as the time required for the system response to reach a preset proportion of the stable value;

[0180] Based on the dynamic response theory model of a first-order system, when the preset ratio is the characteristic ratio of the step response of a first-order system, the obtained time difference value is directly determined as the equivalent filtering time constant of the signal acquisition system; when the preset ratio is other values, the equivalent filtering time constant of the signal acquisition system is calculated using the first-order system response formula.

[0181] Based on the above test procedure, the complete operation of applying standard step excitation, acquiring response data, and calculating equivalent filter time constant is repeated multiple times. The equivalent filter time constant obtained multiple times is statistically analyzed using the coefficient of variation calculation method. When the coefficient of variation is less than the preset reliability threshold, the validity of the equivalent filter time constant is confirmed. When the coefficient of variation does not meet the requirements, the connection status and calibration accuracy of the test system are rechecked, and the complete test procedure is repeated until an equivalent filter time constant that meets the reliability requirements is obtained.

[0182] Based on the equivalent filtering time constant combined with the pre-trained advance correction algorithm, the axial displacement measurement value is obtained in time synchronized with the actual axial position of the rotor.

[0183] It should be further explained that the process of obtaining the axial displacement measurement value that is synchronized with the actual axial position of the rotor in this embodiment includes:

[0184] Based on the step response dataset collected historically by the axial displacement sensor and the corresponding equivalent filter time constant sequence, a training sample set is constructed using time series analysis to obtain algorithm training data containing the correspondence between input and output.

[0185] Based on the theory of autoregressive moving average model, a mathematical model framework for the lead correction algorithm is established, the autoregressive order and moving average order parameters of the model are determined, and the basic model structure of the algorithm is obtained.

[0186] Based on the model training data, the initial values ​​of the model parameters are calculated using the least squares estimation method to obtain a preliminary set of model parameters.

[0187] The Levinson-Durbin recursive algorithm is used to optimize the model parameters and obtain the optimized solution of the model parameters that satisfies the stability condition.

[0188] Based on the criterion of minimizing model prediction error, the gradient descent algorithm is used to iteratively adjust the model parameters to obtain the final model parameters that bring the prediction error to converge.

[0189] Based on the independent validation dataset, the root mean square error index is used to evaluate the model prediction accuracy and obtain a model performance validation report.

[0190] Based on the model performance verification results, when the prediction accuracy does not meet the requirements, the model order parameter is readjusted and the training process is repeated until the model prediction accuracy reaches the preset standard, and the trained advance correction algorithm model is obtained.

[0191] Based on the real-time acquired axial displacement sensor measurement sequence, a trained advance correction algorithm is used for signal processing to obtain axial displacement measurement data that is synchronized with the rotor's actual axial position in time.

[0192] Based on the first feature value processed by the dynamic delay compensation function, the axial displacement measurement value sequence processed by the advance correction algorithm, and the second feature value, a real-time feature value sequence synchronized with time is obtained through unified timestamp alignment and resampling.

[0193] Further explanation is needed; please refer to [link / reference]. Figure 2 In this embodiment, the specific process of responding to the absolute value of the real-time coupling compensation index exceeding the preset error trigger condition includes:

[0194] Based on the safety operation procedures and allowable error range of axial displacement of the target equipment, and combined with the statistical data of real-time coupling compensation index in the historical operation database, the threshold range of the preset error triggering condition is divided by percentile method to obtain the threshold range of mild error and the threshold range of severe error. The threshold range of mild error corresponds to the lower range of the absolute value of the real-time coupling compensation index, and the threshold range of severe error corresponds to the higher range of the absolute value of the real-time coupling compensation index.

[0195] Based on the real-time coupling compensation index that characterizes the total error of axial displacement measurement obtained through real-time calculation, the real-time coupling compensation index is compared with the preset mild error threshold interval and severe error threshold interval through the interval matching algorithm to determine the error level to which the real-time coupling compensation index belongs.

[0196] Based on the determined error level, the corresponding compensation action is called from a preset set of compensation actions, which includes basic compensation actions and enhanced compensation actions. When the error level is within the mild error threshold range, the axial displacement sensor zero-point reference is updated through the configuration software, and the relay module is simultaneously linked to adjust the alarm threshold to obtain the basic compensation result. When the error level is within the severe error threshold range, in addition to the basic compensation action, the steam inlet valve opening or motor load output is adjusted through the equipment adjustment system. The adjustment amount is determined based on the predicted output of the rotor-casing axial thermodynamic model to obtain the enhanced compensation result.

[0197] Based on real-time monitoring data after the compensation action is executed, new real-time coupled compensation indicators are collected. The ratio of the difference between the real-time coupled compensation indicators before and after compensation to the indicator before compensation is calculated by the error change rate algorithm to evaluate the effectiveness of the compensation action. If the ratio is less than the preset effectiveness threshold, it is determined that the compensation action has not achieved the expected effect. The execution intensity of the compensation action is increased based on the iterative optimization algorithm, such as expanding the alarm threshold adjustment range or increasing the valve opening adjustment amount. The corresponding compensation action is repeated until the ratio reaches the preset effectiveness threshold.

[0198] Based on the execution records of compensation actions, the type, execution parameters, error level, and real-time coupled compensation index change curves before and after compensation are stored in the equipment operation and maintenance database through a data archiving algorithm, forming a historical dataset of compensation actions. This provides data support for subsequent optimization of the threshold range of preset error triggering conditions and the intensity of compensation actions.

[0199] The beneficial effects of this application are reflected in the construction of a complete error compensation system for axial displacement measurement of rotating machinery, achieving full-process optimization from error source control to real-time compensation through multi-level technological innovation. At the model construction level, a high-precision thermal structure coupling modeling method based on geometric reconstruction and parameter optimization is adopted, solving the prediction deviation problem caused by the simplification of material temperature characteristics and boundary conditions in traditional models, and providing a reliable theoretical basis for the calculation of reference dynamic offset. At the feature extraction level, by establishing a dual compensation mechanism to handle sensor reference drift and rotor thermal deformation effects respectively, the calculation accuracy of the rotor's true position change is significantly improved, overcoming the limitations of traditional methods that rely on a single measurement value. At the coupling analysis level, an innovative adaptive coupling algorithm based on operating condition identification and temperature range division is proposed, effectively solving the technical problem that linear models cannot adapt to complex operating states and nonlinear thermal characteristics. At the time synchronization level, by integrating inertial delay compensation and signal lead processing technology, the timing error caused by mechanical thermal inertia and measurement system lag is eliminated, ensuring real-time matching of feature data with the actual state. At the compensation execution level, the graded response mechanism based on error levels enables precise responses from parameter adjustment to system intervention, solving the problem of insufficient adaptability of traditional single compensation strategies. The entire technical solution, through its interconnected error control logic, forms a complete technical closed loop from theoretical modeling to engineering application. This not only significantly improves the accuracy and reliability of axial displacement measurement but also provides solid technical support for the safe operation and intelligent maintenance of rotating machinery, demonstrating significant engineering application value and industry promotion significance.

[0200] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments under the guidance of the present invention without departing from the spirit and scope of the present invention. All of these variations are within the protection scope of the present invention.

Claims

1. Method for dynamic coupling compensation of thermal expansion and axial displacement, characterized in that, The method comprises the following steps: obtaining a real-time thermal expansion parameter sequence and a real-time axial displacement parameter sequence of a target device, the real-time thermal expansion parameter sequence comprising a casing thermal expansion amount representing a thermal expansion state of a casing and a differential expansion value representing a relative expansion state of a rotor and the casing, and the real-time axial displacement parameter sequence comprising original measurement values of an axial displacement sensor; calculating a first characteristic value representing a dynamic offset amount of a fixed reference of the axial displacement sensor based on the casing thermal expansion amount representing the thermal expansion state of the casing; calculating a second characteristic value representing a real axial position change amount of the rotor based on the differential expansion value representing the relative expansion state of the rotor and the casing, the real axial position change amount being related to a thermal expansion difference between the rotor and the casing; coupling the first characteristic value, the second characteristic value, and the real-time axial displacement parameter to generate a real-time coupling compensation index representing a total error of the axial displacement measurement; in response to an absolute value of the real-time coupling compensation index exceeding a preset error trigger condition, selecting a compensation action corresponding to the error trigger condition from an action set comprising at least two compensation actions; calculating the first characteristic value representing the dynamic offset amount of the fixed reference of the axial displacement sensor comprises: establishing a three-dimensional thermal-structure coupling model of a casing structure of the target device, the three-dimensional thermal-structure coupling model being constructed based on geometric parameters, material thermal physical properties, and boundary constraint conditions of the casing in combination with a finite element analysis algorithm, and being used to represent a mapping relationship between a temperature distribution of the casing and a thermal deformation of an installation base of the axial displacement sensor; performing a three-dimensional thermal-structure coupling model calibration step when the target device is operated under a plurality of different steady-state temperature conditions to obtain a calibrated three-dimensional thermal-structure coupling model; the plurality of different steady-state temperature conditions cover a temperature range of the target device from a cold state to a rated load; multiplying a real-time monitored casing thermal expansion amount by a dynamic offset correction coefficient determined through the three-dimensional thermal-structure coupling model calibration step to obtain the first characteristic value; wherein the dynamic offset correction coefficient is determined by: synchronously obtaining a predicted value of the casing thermal expansion amount output by the three-dimensional thermal-structure coupling model and an actual thermal expansion amount of the installation base measured by a reference measurement device under the plurality of different steady-state temperature conditions of the model calibration step; fitting a linear relationship between the predicted value of the casing thermal expansion amount and the actual thermal expansion amount by a least squares method, and a slope of the obtained linear relationship is the dynamic offset correction coefficient.

2. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 1, characterized in that, performing the three-dimensional thermal-structure coupling model calibration step comprises: collecting real-time temperature values of at least two temperature measurement points distributed at different positions on a casing body; inputting the real-time temperature values into the three-dimensional thermal-structure coupling model to obtain a predicted value of a thermal deformation amount of the installation base; synchronously measuring an actual thermal expansion amount of the installation base of the axial displacement sensor under a corresponding condition by a reference measurement device; Based on the difference between the installation base thermal deformation prediction value and the actual thermal expansion, by adjusting the material thermal expansion coefficient or boundary constraint condition in the model, the error between the installation base thermal deformation prediction value and the actual thermal expansion is minimized, and a calibrated three-dimensional thermal-structure coupling model is obtained.

3. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 2, wherein, The second characteristic value representing the real axial position change of the rotor includes: Based on the geometric parameters, material thermal physical properties and thermal boundary conditions of the rotor and the casing, fine tuning training is performed on the calibrated three-dimensional thermal-structure coupling model to obtain a rotor-casing axial thermodynamic model for simulating the thermal expansion behavior of the rotor and the relative motion behavior of the rotor and the casing under different working conditions; Based on the rotor-casing axial thermodynamic model, a corresponding relationship between the casing differential expansion sensor installation base temperature and the differential expansion measurement reference drift is established to obtain a reference drift compensation amount table; Meanwhile, based on the rotor-casing axial thermodynamic model, a corresponding relationship between the rotor thrust disc region temperature and the axial equivalent amount of three-dimensional thermal deformation of the rotor is established to obtain a thermal deformation compensation amount table.

4. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 3, c h a r a c t e r i z e d b y that The second characteristic value representing the real axial position change of the rotor also includes: Real-time acquisition of differential expansion sensor original measurement value, temperature measurement value of rotor thrust disc region, and temperature measurement value of casing differential expansion sensor installation base, and standardization processing; Based on the processed casing differential expansion sensor installation base temperature measurement value, the reference drift compensation amount table is queried to obtain the corresponding reference drift compensation amount; According to the standardized temperature measurement value of the rotor thrust disc region, the thermal deformation compensation amount table is queried to obtain the corresponding three-dimensional thermal deformation compensation amount; Based on the differential expansion sensor original measurement value, the reference drift compensation amount and the three-dimensional thermal deformation compensation amount, the second characteristic value is obtained by compensation calculation, wherein the compensation calculation includes subtracting the reference drift compensation amount from the differential expansion sensor original measurement value and adding the three-dimensional thermal deformation compensation amount.

5. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 4, c h a r a c t e r i z e d b y that The coupling based on the first characteristic value, the second characteristic value and the real-time axial displacement parameter includes: Obtain the material thermal expansion coefficient and the casing deformation under the continuous temperature change rate, and determine the division boundary of the temperature interval combined with the correlation analysis algorithm; Based on the calibrated three-dimensional thermal-structure coupling model and the rotor-casing axial thermodynamic model output historical calibration data combined with the division boundary of the temperature interval, a segmented coupling function is established, specifically: in a preset low temperature interval, a linear coupling function is established combined with a unary regression equation, and in a medium or high temperature interval, a nonlinear function relationship containing a quadratic term and a temperature correction term is established combined with a support vector machine.

6. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 5, wherein, The coupling based on the first characteristic value, the second characteristic value and the real-time axial displacement parameter also includes: Based on the real-time monitored temperature change rate and the equipment load fluctuation, the current operating condition type is divided through a preset operating condition recognition model, and the operating condition adaptive coupling coefficient is obtained by calling the preset coupling coefficient matrix corresponding to the operating condition type; the operating condition type at least includes start-up condition, steady-state condition or shutdown condition; Based on the segmented coupling function and the working condition adaptive coupling coefficient, the cross interference compensation term constructed by the product of the first characteristic value and the second characteristic value, and the dynamic correction term constructed by the ratio of the first characteristic value and the shell expansion rate, a compensation calculation model for eliminating the correlation of characteristic values is obtained.

7. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 6, wherein, Based on the first characteristic value, the second characteristic value and the real-time axial displacement parameter, coupling is performed, and the method further includes: Based on the time difference between the predicted value of the thermal deformation amount of the mounting base output by the three-dimensional thermal-structure coupling model and the actual thermal expansion amount, a dynamic delay compensation mechanism is established, and a real-time characteristic value sequence subjected to delay compensation is obtained; Based on the real-time characteristic value sequence subjected to delay compensation, a real-time coupling compensation index representing the total error of the axial displacement measurement is obtained through the compensation calculation model.

8. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 7, wherein, The establishment process of the dynamic delay compensation mechanism includes: During a plurality of complete thermal cycles, the predicted value sequence of the thermal deformation amount of the mounting base output by the three-dimensional thermal-structure coupling model and the actual thermal expansion value sequence measured by the reference measurement device are recorded synchronously, and the time difference value from the change of the predicted value to the same change amplitude of the actual measurement value in each group of data is calculated, and the arithmetic mean of all time difference values is taken as the thermal hysteresis time constant of the system; Based on the obtained thermal hysteresis time constant, a dynamic delay compensation function in the form of a first-order inertial link is constructed, and the first characteristic value is input into the dynamic delay compensation function for phase lag processing, to obtain the first characteristic value synchronized with the actual thermal deformation state of the mechanical system in time; Based on the dynamic response characteristics of the axial displacement sensor and the signal acquisition system, the equivalent filter time constant of the signal acquisition system is obtained by applying a standard step excitation signal and measuring the time when the system response reaches a preset proportion of the stable value.

9. The method of dynamic coupling compensation of thermal expansion and axial displacement according to claim 8, wherein, The establishment process of the dynamic delay compensation mechanism further includes: Based on the equivalent filter time constant and the pre-trained lead correction algorithm, the axial displacement measurement value synchronized with the real axial position of the rotor in time is obtained; Based on the first characteristic value processed by the dynamic delay compensation function, the axial displacement measurement value sequence processed by the lead correction algorithm, and the second characteristic value, the time-synchronized real-time characteristic value sequence is obtained through uniform timestamp alignment and resampling processing.

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