Air suspension fan predictive maintenance method and system based on digital twinning

Abstract

The invention provides a predictive maintenance method and system for an air suspension fan based on digital twinning, and the method comprises the steps: collecting an air flow abrupt change characteristic when high-temperature dust-containing waste gas flows into the air suspension fan, transmitting the air flow abrupt change characteristic to a digital twinning system, and determining the air flow abrupt change characteristic; extracting a local clearance reduction trend of the foil and the bearing from the non-uniform expansion amount of the foil, and calculating space distribution after clearance reduction to obtain a target gas film thickness value; the target gas film thickness value is compared with a preset collision and abrasion threshold value, and if the target gas film thickness value is smaller than the threshold value, the collision and abrasion risk probability is evaluated through a Monte Carlo method; if the collision and abrasion risk probability exceeds a preset safety range, calculating a gas film rigidity fluctuation range based on a gas dynamics theory; and extracting a vibration amplitude analysis result from the dynamic response parameters of the foil bearing of the air suspension fan, and calculating a stability prediction index.

Description

Technical Field

[0001] This invention relates to the field of information technology, and in particular to a predictive maintenance method and system for air-suspended fans based on digital twins. Background Technology

[0002] As a core component of industrial waste heat recovery systems, the stable operation of air-suspended fans is crucial for efficient energy utilization and environmental protection. Foil bearings, due to their advantages such as oil-free lubrication and high-speed adaptability, are key components supporting the efficient operation of these fans. However, under extreme conditions of sudden influx of high-temperature, dust-laden exhaust gas, the stability of the bearings faces severe challenges. Therefore, researching thermal shock protection technology based on digital twins has become an important direction for improving system reliability. Currently, the industrial sector generally relies on traditional simulation and empirical design to optimize bearing performance. However, these methods are insufficient in handling dynamic responses under abrupt changes, often neglecting the real-time impact of transient thermo-mechanical coupling and gas property changes, leading to decreased prediction accuracy and difficulty in effectively preventing the risk of impact wear. Existing solutions mostly focus on bearing design and optimization under static conditions, with few systematic studies addressing dynamic disturbances such as sudden changes in inlet airflow temperature and composition. This limitation makes it impossible for traditional methods to accurately capture transient phenomena such as non-uniform thermal expansion of the foil, fluctuations in gas film stiffness damping, and minimum gas film thickness approaching the impact-abrasion threshold. Especially in high-temperature, dusty environments, gas viscosity fluctuates significantly due to changes in temperature and impurity content, further exacerbating the complexity of prediction. The core challenge lies in how to accurately characterize the rapid reduction in local gaps caused by foil thermal expansion under abrupt changes, the dynamic imbalance of gas film properties due to changes in physical properties, and the transient evolution process when the minimum gas film thickness approaches the impact-abrasion threshold. If these technical factors are not properly addressed, they will directly induce bearing instability or even failure, threatening the safe operation of the entire waste heat recovery system. Therefore, how to combine digital twin system technology, integrate the thermo-mechanical coupling effect of materials with changes in gas physical properties through transient simulation models, and assess the probability of impact-abrasion risk in real time has become a key issue in ensuring the effectiveness of the bearing stability prediction mechanism. Summary of the Invention

[0003] This invention provides a predictive maintenance method for air-suspended fans based on digital twins, mainly including:

[0004] The characteristics of airflow abrupt change when high-temperature dust-laden exhaust gas enters the air suspension fan are collected and transmitted to the digital twin system to determine the characteristics of airflow abrupt change.

[0005] The transient thermal expansion distribution of the foil is calculated based on the characteristics of sudden airflow changes. The non-uniform expansion amount in each region of the foil is obtained by combining the interaction between the temperature field and the stress-strain field of the material.

[0006] The shrinkage trend of the local gap between the foil and the bearing is extracted from the non-uniform expansion of the foil, and the spatial distribution after the gap shrinkage is calculated to obtain the target air film thickness value.

[0007] The target air film thickness is compared with a preset impact threshold. If it is less than the threshold, the probability of impact risk is assessed using the Monte Carlo method.

[0008] If the probability of collision and abrasion exceeds the preset safety range, the range of air film stiffness fluctuation is calculated based on gas dynamics theory.

[0009] Based on the fluctuation range of air film stiffness, combined with the real-time acquisition of the operating conditions and bearing structure of the air suspension fan, the dynamic response parameters of the foil bearing of the air suspension fan are calculated using a fluid-structure interaction algorithm.

[0010] Vibration amplitude analysis results are extracted from the dynamic response parameters of the foil bearing of the air suspension fan, and stability prediction index is calculated.

[0011] An adaptive filtering algorithm is used to optimize the real-time evaluation logic of the preset digital twin system, and the bearing wear monitoring data is updated based on the stability prediction index to determine the failure probability evaluation result.

[0012] Based on the failure probability assessment results, control commands are generated and transmitted to the thermal shock protection module of the air suspension fan to generate a dynamic adjustment scheme for bearing stability.

[0013] Furthermore, the characteristics of airflow abrupt changes when high-temperature dust-laden exhaust gas enters the air suspension fan are collected and transmitted to the digital twin system to determine the characteristics of airflow abrupt changes. This includes: collecting airflow pressure data at five measuring points deployed in the gas flow channel using piezoelectric pressure sensors; calculating the airflow pressure change rate by dividing the pressure difference between adjacent measuring points by the sampling time interval; dynamically adjusting the sampling frequency according to the airflow turbulence intensity to generate an airflow pressure abrupt change dataset. Dust concentration data in the exhaust gas is obtained from a dust concentration sensor. Based on the dust particle size range, the concentration data is divided into three levels: less than 10 micrometers, 10 to 50 micrometers, and greater than 50 micrometers, for counting and statistical analysis. This data is then combined with the airflow pressure abrupt change dataset from step one to calculate the gas-solid two-phase flow velocity field distribution. Based on the exhaust gas temperature data measured by a thermocouple temperature sensor and combined with the gas-solid two-phase flow velocity field distribution obtained in step two, a temperature field distribution parameter set including temperature gradient, heat flux, and convective heat transfer coefficient is established for each measuring point. A data acquisition device is used to synchronize the data sets of abrupt changes in airflow pressure, velocity field distribution, and temperature field distribution in gas-solid two-phase flow with time, generating a multi-dimensional airflow characteristic data set. An airflow state space is constructed based on this multi-dimensional airflow characteristic data set, and the mapping relationship between the four parameters—airflow pressure, flow rate, dust concentration, and temperature—is calculated using the least squares method to obtain the airflow abrupt change characteristic parameter matrix.

[0014] Furthermore, the transient thermal expansion distribution of the foil is calculated based on the characteristics of abrupt airflow changes. Combining the interaction between the material's temperature field and stress-strain field, the non-uniform expansion of each region of the foil is obtained. This includes: dividing the foil's computational grid based on temperature field data from abrupt airflow changes; using adaptive quadrilateral grid cells to subdivide the foil's geometric region; determining that the grid density satisfies the convergence condition when the temperature gradient difference between adjacent grid cells is less than a preset threshold, thus constructing the initial temperature field distribution of the foil. The thermal stress coefficient matrix is ​​calculated based on the material's thermal expansion coefficient and elastic modulus; the stress field distribution at each grid cell node is solved using Lagrange interpolation; and the initial values ​​of the foil's stress-strain field are generated by combining the temperature field distribution obtained in step one. For the obtained initial values ​​of the foil's stress-strain field, the displacement increment of each grid cell node is calculated using the linear elastic constitutive equation; and the local deformation of the foil is solved by combining the temperature field distribution, obtaining the transient deformation field data of the foil. A set of heat conduction equations is established based on the transient deformation field data of the foil; the thermal conductivity distribution of the foil is calculated using the least squares method; and the temperature-stress coupling coefficient of the foil is obtained by combining the stress field distribution. The thermal strain increment is calculated based on the foil temperature-stress coupling coefficient. The thermal displacement vector of each grid element node is solved using the finite difference method to obtain the non-uniform thermal expansion distribution data of the foil. For this non-uniform thermal expansion distribution data, nodal strain interpolation is used to calculate the thermal deformation gradient of each region of the foil. Combined with the stress field distribution, the non-uniform expansion amount of each grid element of the foil is determined. Further, the shrinkage trend of the local gap between the foil and the bearing is extracted from the non-uniform expansion amount of the foil. The spatial distribution of the reduced gap is calculated to obtain the target gas film thickness value. This includes: constructing a foil deformation grid matrix based on the non-uniform expansion amount of the foil; calculating the displacement distribution of the foil deformation on the bearing surface using Lagrange interpolation; correcting the grid point coordinates for the bearing surface roughness parameters to obtain the initial contact gap field. A contact stress distribution matrix is ​​constructed based on the initial contact gap field data. Bézier curves are used to fit the feature points of the foil and bearing surface contours. Combined with the surface normal vector, the contact deformation amount is calculated to obtain the local contact pressure field. The gap change rate is calculated for the local contact pressure field. The least squares method is used to fit the geometric surface equation of the contact area. Combined with the elastic deformation amount of the foil, the real-time gap distribution function is determined. The air film pressure field equation is established based on the real-time gap distribution function. The air film pressure gradient distribution is solved using the Reynolds equation to obtain the air film pressure distribution matrix. The air film bearing capacity is calculated based on the air film pressure distribution matrix. The air film thickness response function is established using the spatial mapping method, and the target air film thickness is calculated by combining the air film compression characteristic curve.

[0015] Furthermore, the target air film thickness is compared with a preset impact threshold. If it is less than the threshold, the probability of impact risk is assessed using the Monte Carlo method. This includes: establishing a gridded spatial distribution function based on the target air film thickness; comparing the values ​​with the preset impact threshold; if the value is less than the threshold, calculating the probability of local impact point locations using Bernoulli distribution random sampling; constructing the bearing load stress distribution based on the probability of local impact point locations; establishing a local stress concentration factor based on material surface finish parameters; and calculating the impact contact stress field in conjunction with the friction coefficient. The radial displacement distribution is calculated for the impact contact stress field. Multiple random operating conditions are generated using Monte Carlo sampling, and the impact contact duration distribution is determined in conjunction with the material loss rate. A frictional heat power field is established based on the impact contact duration distribution, and the dynamic stress evolution curve is predicted using a random forest algorithm to obtain the foil vibration amplitude distribution. The air film thickness attenuation law is calculated based on the foil vibration amplitude distribution, and an impact damage accumulation function is constructed in conjunction with the collision impact force data. A probability density distribution is constructed for the cumulative function of impact and wear damage. The parameters of the probability distribution of impact and wear risk are determined by maximum likelihood estimation, and the probability value of impact and wear risk is obtained.

[0016] Furthermore, if the probability of impact wear exceeds the preset safety range, the gas film stiffness fluctuation range is calculated based on gas dynamics theory. This includes: if the probability of foil bearing impact wear exceeds the preset safety range, waste gas temperature data is collected using thermocouple sensors, and the temperature gradient distribution is measured using a thermistor array. The gas temperature field function is then fitted using the least squares method. The waste gas impurity concentration distribution is measured using a laser particle size sensor, and the gas density change rate is calculated based on the gas state equation. The gas-solid two-phase flow velocity field is solved using the Navier-Stokes equations. Gas film pressure distribution data is acquired using a pressure sensor array, and a gas film stress distribution function is established for the pressure fluctuation amplitude. The gas film deformation response characteristics are calculated using the finite difference method. A gas film stiffness calculation model is constructed based on the gas film deformation response characteristics, and the aerodynamic load distribution is calculated using gas dynamic viscosity and Reynolds number. The gas film support stiffness coefficient is solved based on the aerodynamic load distribution, and the upper and lower limits of gas film stiffness fluctuation are calculated using the gas film damping characteristic equation. A gas film stability criterion is established for the upper and lower limits of gas film stiffness fluctuation, and Bayesian regression is used to predict the dynamic change range of gas film stiffness.

[0017] Furthermore, based on the fluctuation range of the air film stiffness and combined with the real-time acquisition of the operating conditions and bearing structure of the air-suspended fan, a fluid-structure interaction algorithm is used to calculate the dynamic response parameters of the foil bearing of the air-suspended fan. This includes: constructing a computational grid for the air film flow field based on the fluctuation range of the air film stiffness; collecting real-time data on the fan speed fluctuation rate and dynamic balance from sensors; and establishing an aerodynamic load distribution function based on the bearing clearance ratio and bearing preload. The stress field of the foil structure is solved based on the aerodynamic load distribution function, and the foil deformation is calculated using the elasticity equations. The air film pressure distribution field is constructed based on the finite volume method. The interaction between the air film pressure and foil deformation is calculated using a fluid-structure interaction iterative solver, and the shaft offset is calculated using the Newton-Raphson iteration method. The transient flow field distribution is obtained by combining the air film compression ratio. A set of control equations for foil vibration is established for the transient flow field distribution. The vibration acceleration and axial displacement are calculated using the Runge-Kutta method to obtain the shaft trajectory curve of the foil bearing. A harmonic analysis function is constructed based on the shaft trajectory curve, and the vibration amplitude spectrum is calculated using the fast Fourier transform. The dominant vibration frequency is determined by combining the vibration frequency ratio parameter. Based on the dominant vibration frequency, an air film thickness distribution function is constructed. The air film pressure fluctuation curve is fitted using the least squares method, and the minimum air film thickness is solved using the aerodynamic balance equation. Furthermore, vibration amplitude analysis results are extracted from the dynamic response parameters of the air-suspended fan foil bearing to calculate stability prediction indices. This includes: extracting the vibration time-domain signal from the dynamic response parameters of the air-suspended fan foil bearing, decomposing the frequency components of the vibration signal using wavelet transform, and constructing the vibration amplitude envelope spectrum using Hilbert transform. The amplitude ratio of two adjacent vibration cycles is calculated based on the vibration amplitude envelope spectrum. A vibration response equation is established based on the amplitude decay law, and the logarithmic decay rate is calculated using the damping coefficient. A bearing stability evaluation matrix is ​​constructed based on the logarithmic decay rate and the dynamic stiffness ratio. The eddy component in the vibration signal is extracted using fast Fourier transform to obtain eddy angular velocity data. The eddy motion trajectory characteristics are calculated based on the eddy angular velocity data. The dominant eddy frequency signal is obtained using discrete Fourier transform, and the eddy frequency ratio is calculated using the critical speed. A bearing stability discrimination criterion is established based on the eddy frequency ratio, and the vibration response function is calculated using spectral analysis to obtain stability prediction indices. A dynamic characteristic evaluation function is constructed based on stability prediction indices, and an autoregressive model is used to predict the changing trends of logarithmic decay rate and eddy frequency ratio.

[0018] Furthermore, an adaptive filtering algorithm is employed to optimize the pre-defined real-time evaluation logic of the digital twin system. Bearing wear monitoring data is updated based on stability prediction indices to determine the failure probability assessment results. This includes: constructing an adaptive filtering parameter matrix based on stability prediction indices; using a state observation equation to describe the characteristics of the bearing wear data; and dynamically adjusting the filtering gain coefficient by measuring the noise variance. The digital twin evaluator parameters are optimized based on the filtering gain coefficient. A state transition equation is established for the bearing wear monitoring data, and a state estimation function is constructed by combining real-time response characteristics. The bearing wear rate is calculated using the state estimation function, and a deep neural network is used to predict the wear development trend. A life degradation curve is established by combining historical failure data. A failure probability transition matrix is ​​constructed based on the life degradation curve, and the remaining bearing life distribution is calculated using a Markov chain to obtain the failure probability threshold range. An adaptive evaluation criterion is established for the failure probability threshold range, and the evaluation parameter correction amount is calculated based on the data update cycle to achieve dynamic optimization of the evaluation logic. The bearing wear monitoring parameters are updated based on the optimized evaluation logic results, and the failure probability is calculated multiple times using the Monte Carlo method to obtain the failure probability assessment results.

[0019] Furthermore, joint time-domain and frequency-domain indices are extracted from bearing wear monitoring data, input into a preset stability prediction model, and output as a prediction residual sequence. A covariance matrix is ​​calculated based on the prediction residual sequence, and this covariance matrix is ​​used to update the noise suppression coefficient of the adaptive filtering algorithm. The bearing wear monitoring data is reconstructed based on the updated noise suppression coefficient to generate a wear time-series curve. The prediction residual sequence and the wear time-series curve are fused to calculate the cumulative failure probability value, including: extracting the root mean square value and spectral kurtosis value from the bearing wear monitoring data; calculating the envelope spectrum features using Hilbert transform; establishing a time-frequency joint prediction function using a long short-term memory network to obtain the prediction residual sequence. A sample matrix is ​​constructed based on the prediction residual sequence, and singular value decomposition is used to calculate the noise subspace eigenvalues. A noise covariance matrix is ​​established by combining the residual convergence. The optimal filtering gain is calculated based on the noise covariance matrix, and the noise suppression coefficient is updated using recursive least squares. The filtering parameters are optimized for data reconstruction accuracy. The wear monitoring data is reconstructed based on the optimized filtering parameters, and wavelet transform is used to extract wear feature coefficients to establish a wear evolution equation. A time-series state matrix is ​​generated based on the wear amount evolution equation. State transition probabilities are calculated using a Markov chain, and the wear amount time-series curve is obtained by combining this with a failure threshold. Data fusion is performed between the wear amount time-series curve and the predicted residual sequence. A Wiener filter is used to eliminate data redundancy, and a failure probability density function is established. The state transition matrix is ​​calculated based on the failure probability density function, and the cumulative failure probability value is solved using a Bernoulli distribution.

[0020] Furthermore, control commands are generated based on the failure probability assessment results and transmitted to the thermal shock protection module of the air-suspended fan to generate a dynamic adjustment scheme for bearing stability. This includes: constructing a thermal shock protection parameter set based on the failure probability assessment results; generating a temperature control curve for the temperature regulation ratio and cooling power value; and calculating a dynamic temperature regulation sequence using an adaptive controller. Digital control commands are generated based on the dynamic temperature regulation sequence and transmitted to the thermal shock protection device via a serial communication interface, with signal transmission delay compensation used to optimize the command execution timing. A bearing operating state parameter set is constructed based on the command execution timing; a bearing dynamic characteristic monitoring function is established for the stability range threshold; and support vector regression is used to predict the bearing regulation gain curve. The dynamic heat power allocation ratio is calculated based on the bearing regulation gain curve; a cooling power control sequence is generated based on the bearing temperature change rate; and the thermal shock response characteristics are optimized using dynamic programming. Bearing stability assessment criteria are established based on the thermal shock response characteristics; the adjustment parameter correction amount is calculated for the temperature fluctuation amplitude; and the control parameters are updated using recursive least squares. A bearing thermal protection control strategy is generated based on the updated control parameters; and the adjustment execution commands are calculated using a fuzzy controller to realize the dynamic adjustment scheme for bearing stability.

[0021] This invention provides a predictive maintenance system for air-suspended fans based on digital twins, mainly comprising:

[0022] The airflow change feature acquisition module is used to collect the airflow change features when high-temperature dusty exhaust gas rushes into the air suspension fan, and transmit it to the digital twin system to determine the airflow change features.

[0023] The foil transient thermal expansion calculation module is used to calculate the transient thermal expansion distribution of the foil based on the characteristics of sudden airflow changes. It combines the interaction between the temperature field and stress-strain field of the material to obtain the non-uniform expansion amount in each region of the foil.

[0024] The gap reduction trend extraction module is used to extract the local gap reduction trend between the foil and the bearing from the non-uniform expansion of the foil, calculate the spatial distribution after the gap reduction, and obtain the target air film thickness value.

[0025] The collision and abrasion risk assessment module is used to compare the target air film thickness value with the preset collision and abrasion threshold. If it is less than the threshold, the probability of collision and abrasion risk is assessed by the Monte Carlo method.

[0026] The air film stiffness fluctuation calculation module is used to calculate the air film stiffness fluctuation range based on gas dynamics theory if the probability of collision and abrasion exceeds the preset safety range.

[0027] The dynamic response parameter calculation module is used to calculate the dynamic response parameters of the foil bearing of the air suspension fan based on the air film stiffness fluctuation range, combined with the real-time acquisition of the operating conditions and bearing structure of the air suspension fan, and using a fluid-structure interaction algorithm.

[0028] The stability prediction index calculation module is used to extract vibration amplitude analysis results from the dynamic response parameters of the foil bearing of the air suspension fan and calculate the stability prediction index.

[0029] The real-time evaluation logic optimization module is used to optimize the preset real-time evaluation logic of the digital twin system using an adaptive filtering algorithm, update the bearing wear monitoring data based on stability prediction indicators, and determine the failure probability evaluation results.

[0030] The dynamic adjustment scheme generation module is used to generate control commands based on the failure probability assessment results, which are then transmitted to the thermal shock protection module of the air suspension fan to generate a dynamic adjustment scheme for bearing stability.

[0031] The technical solutions provided by the embodiments of the present invention may include the following beneficial effects:

[0032] This invention discloses a predictive maintenance method for air-suspended fans based on digital twins. It collects real-time data on abrupt airflow changes during the influx of high-temperature, dust-laden exhaust gas, calculates the non-uniform thermal expansion distribution of the bearing foil, assesses the trend of local bearing clearance reduction, and compares this assessment with a preset wear threshold. If wear risk exists, the method calculates the air film stiffness fluctuation range based on gas dynamics theory, analyzes the bearing's dynamic response using a fluid-structure interaction algorithm, extracts vibration characteristics, and calculates stability indices. Finally, the invention utilizes an adaptive filtering algorithm to optimize the evaluation logic, update bearing wear monitoring data, determine the failure probability, and generate a dynamic adjustment scheme for bearing stability. This method can effectively predict and prevent bearing wear risk in air-suspended fans under harsh operating conditions, improving equipment reliability and service life. Attached Figure Description

[0033] Figure 1 This is a flowchart of a predictive maintenance method for air-suspended fans based on digital twins according to the present invention.

[0034] Figure 2 This is a schematic diagram of the structure of a predictive maintenance system for air-suspended fans based on digital twins according to the present invention. Detailed Implementation

[0035] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0036] like Figure 1-2 This embodiment of a predictive maintenance method for air-suspended fans based on digital twins may specifically include:

[0037] S101. Real-time airflow change characteristics when high-temperature dusty exhaust gas enters the air suspension fan are collected by sensors and transmitted to the digital twin system to determine the airflow change characteristic parameters.

[0038] The operating environment of air-suspended fans is complex, and sudden changes in high-temperature, dusty exhaust gas can cause bearing stability issues. Therefore, it is necessary to collect airflow characteristic data in real time using sensors and transmit it to a digital twin system for analysis. The collected airflow characteristics include pressure, flow rate, dust concentration, and temperature, and the specific operation is completed collaboratively by multiple sensors. The data acquisition process must ensure data synchronization and accuracy to support subsequent transient simulations and risk assessments.

[0039] S1011. Collect airflow pressure data using a piezoelectric pressure sensor, calculate the pressure change rate, and generate an airflow pressure abrupt change dataset.

[0040] Piezoelectric pressure sensors are deployed at multiple measuring points within the airflow channel to collect airflow pressure data in real time. Based on the pressure difference between adjacent measuring points and the sampling time interval, the pressure change rate is calculated, forming a dataset of sudden airflow pressure changes. The sampling frequency can be dynamically adjusted according to the airflow turbulence intensity to improve data accuracy. For example, with five measuring points set up in the airflow channel, with an adjacent spacing of 2 meters, pressure values ​​of 98 kPa, 97 kPa, 95 kPa, 92 kPa, and 88 kPa, and a sampling interval of 0.1 seconds, the calculated pressure change rate reflects the trend of airflow energy loss.

[0041] S1012. Collect dust concentration data through a dust concentration sensor, and calculate the velocity field distribution of the gas-solid two-phase flow by combining the data with the airflow pressure change dataset.

[0042] Dust concentration sensors are used to acquire dust concentration data in exhaust gas and classify it according to particle size range, for example, into three categories: less than 10 micrometers, 10 to 50 micrometers, and greater than 50 micrometers, with concentrations of 280 mg / m³. 3 150mg / m 3 and 70mg / m 3 By combining a dataset of abrupt changes in airflow pressure, a numerical calculation method is used to generate the velocity field distribution of the gas-solid two-phase flow, characterizing the following characteristics of small-diameter dust particles and the inertial hysteresis characteristics of large-diameter dust particles.

[0043] S1013. Collect exhaust gas temperature data through thermocouple temperature sensors, and generate a temperature field distribution parameter set by combining the gas-solid two-phase flow velocity field distribution.

[0044] Thermocouple temperature sensors measure the exhaust gas temperature, with an inlet temperature of 650 degrees Celsius and an outlet temperature of 580 degrees Celsius, exhibiting a non-linear decay along the flow path. Combined with the gas-solid two-phase flow velocity field distribution, the temperature gradient, heat flux, and convective heat transfer coefficient are calculated for each measuring point, forming a temperature field distribution parameter set. For example, the heat flux in the inlet region is 4200 W / m². 2 The convective heat transfer coefficient is 85 W / (m·K), which is used for thermal expansion analysis.

[0045] S1014. Time synchronization processing is performed on the data set of sudden changes in airflow pressure, the velocity field distribution of gas-solid two-phase flow, and the temperature field distribution parameter set to construct the airflow state space and calculate the characteristic parameter matrix of sudden changes in airflow.

[0046] The aforementioned dataset was time-synchronized using a data acquisition device to generate a multi-dimensional airflow characteristic data set. Based on this data set, an airflow state space was constructed, and the mapping relationship between pressure, flow rate, dust concentration, and temperature was fitted using the least squares method to generate an airflow abrupt change characteristic parameter matrix. This matrix reflects the coupling relationship between parameters; for example, a 10 kPa decrease in pressure corresponds to a 20% decrease in flow rate, a 35% increase in dust concentration, and a 60-degree Celsius increase in temperature. When the monitored parameters exceed a preset threshold range, such as a pressure fluctuation of ±15 kPa, an alarm signal is output.

[0047] Through multi-sensor collaborative data acquisition and synchronous data processing, the abrupt changes in high-temperature dust-laden exhaust gas can be accurately characterized, providing reliable input for the analysis of foil thermal expansion and gas film thickness. In practical applications, the airflow abrupt change characteristic parameter matrix supports online monitoring and early warning, significantly improving the real-time performance and accuracy of bearing stability prediction and reducing the risk of rubbing caused by airflow disturbances.

[0048] S102. Based on the characteristic parameters of airflow sudden change, the transient thermal expansion distribution of the foil bearing of the air suspension fan is calculated by finite element analysis method. Combined with the thermo-mechanical coupling characteristics of the material, the non-uniform expansion amount of each region of the foil is determined.

[0049] The characteristic parameters of sudden airflow changes provide key inputs for the thermal expansion analysis of the foil, covering the dynamic changes in temperature, pressure, and dust concentration. Finite element analysis, by constructing a geometric model of the foil and combining it with the thermodynamic properties of the material, accurately simulates the transient thermal expansion behavior under the influence of high-temperature dusty exhaust gas. The calculation process must consider the interaction of the temperature field, stress field, and strain field to ensure the accuracy of the non-uniform expansion. This application does not impose excessive limitations on the specific mesh generation algorithm, which can be adjusted by technicians according to the actual scenario.

[0050] S1021. Based on the temperature data in the characteristic parameters of airflow sudden change, the initial temperature field distribution of the foil is generated by using adaptive grid partitioning technology.

[0051] Temperature data from the airflow abrupt change characteristic parameters is used to initialize the foil temperature field. An adaptive quadrilateral mesh is used to partition the foil geometry, with the mesh density dynamically adjusted according to the temperature gradient. For example, when the airflow temperature fluctuates between 350°C and 650°C, areas with larger temperature gradients on the foil surface require finer meshing, with a mesh size of approximately 0.5 mm at the edges and approximately 2 mm in the center. When the temperature gradient difference between adjacent mesh cells is less than a preset threshold of 5°C / mm, mesh convergence is determined, generating the initial temperature field distribution of the foil, providing a basis for stress analysis.

[0052] S1022. Combining the thermal expansion coefficient and elastic modulus of the material, the stress field distribution of the foil is calculated using the Lagrange interpolation method to generate the initial values ​​of the stress-strain field.

[0053] The coefficient of thermal expansion and the modulus of elasticity of foil materials are key parameters for calculating thermal stress. Taking stainless steel foil as an example, the coefficient of thermal expansion is 16.5 × 10⁻⁶. -6 The temperature is / degrees Celsius, and the elastic modulus is 193 GPa. Based on the initial temperature field distribution, the stress field distribution of each grid element node is calculated using the Lagrange interpolation method to generate initial values ​​for the stress and strain field. For example, when the temperature in the central region of the foil increases by 100 degrees Celsius, the main diagonal element of the thermal stress coefficient matrix is ​​approximately 320 MPa, and the stress value in the central region can reach 275 MPa, reflecting the significant tensile stress caused by the temperature change.

[0054] S1023. Calculate the displacement increment of the grid element nodes using the linear elastic constitutive equation, and generate transient deformation field data of the foil by combining the temperature field distribution.

[0055] The linear elastic constitutive equation is used to quantify the deformation of the foil under the combined effects of temperature and stress. Based on the initial values ​​of the stress-strain field, the displacement increment of each grid element node is calculated. For example, when the stress in the central region is 275 MPa and the temperature increases by 100 degrees Celsius, the node displacement increment is approximately 0.18 mm, mainly distributed radially. Combined with the temperature field distribution, the local deformation of the foil is solved, generating transient deformation field data that reflects the nonlinear deformation characteristics of the foil under high-temperature conditions.

[0056] S1024. The thermal conductivity distribution of the foil is fitted using the least squares method, and the nodal thermal displacement vector is calculated by combining the temperature stress coupling coefficient and the finite difference method.

[0057] The thermal conductivity of the foil dynamically adjusts with temperature, for example, it is 15 W / (m·K) at 350°C and decreases to 12 W / (m·K) at 650°C. The thermal conductivity distribution is fitted using the least squares method, and the temperature-stress coupling coefficient is calculated using stress field data. When the stress exceeds 200 MPa, the coupling coefficient is approximately 0.85. Based on the heat conduction equations, the thermal displacement vector of each grid element node is solved using the finite difference method. The maximum radial thermal expansion is approximately 0.45 mm, and the circumferential expansion is approximately 0.15 mm, reflecting the regional differences in non-uniform thermal expansion.

[0058] S1025. Based on the transient deformation field data of the foil, the thermal deformation gradient is calculated using the nodal strain interpolation method to determine the non-uniform expansion amount in each region of the foil.

[0059] Nodal strain interpolation was used to analyze the spatial distribution of the thermal deformation gradient of the foil. In the transition region with large temperature and stress gradients, the thermal deformation gradient can reach 0.12 mm / mm, while in the uniform region it is only 0.03 mm / mm. Combined with the stress field distribution, the non-uniform expansion of each grid cell of the foil was calculated, with larger expansion in the central region and smaller expansion in the edge region. This non-uniform expansion characteristic directly affects the gas film thickness and needs to provide accurate input for subsequent impact and abrasion risk assessment.

[0060] Through multi-level finite element analysis and thermo-mechanical coupling calculations, the transient thermal expansion behavior of foils under sudden airflow changes can be accurately characterized. Compared with traditional static analysis, this application dynamically adjusts the mesh density and incorporates the temperature-stress coupling effect, significantly improving the calculation accuracy. In practical applications, the accurate quantification of non-uniform expansion supports air film thickness analysis and stability prediction, reduces the risk of impact and abrasion caused by thermal expansion, and improves the operational reliability of air-suspended fans.

[0061] S103. Based on the non-uniform thermal expansion distribution data of the foil, extract the trend of local gap change between the foil and the bearing of the air suspension fan, and calculate the target air film thickness distribution.

[0062] Non-uniform thermal expansion of the foil directly affects the bearing clearance, thus determining the gas film thickness and stability. Based on the aforementioned thermal expansion data, this step precisely quantifies the impact of clearance changes on the gas film thickness by constructing a foil deformation mesh, calculating the contact stress distribution and gas film pressure field. A geometric mapping algorithm combined with fluid dynamics theory ensures the accuracy of the gas film thickness calculation and the reliability of the stability verification. This method, through multi-level analysis, dynamically responds to clearance changes caused by high-temperature dusty exhaust gas, providing crucial input for subsequent impact risk assessment.

[0063] S1031. Based on the non-uniform thermal expansion data of the foil, construct the foil deformation mesh matrix, use the Lagrange interpolation method to calculate the bearing surface displacement distribution, and correct for the influence of surface roughness.

[0064] Non-uniform thermal expansion data of the foil was used to generate a deformable mesh matrix. Taking a circular foil with a diameter of 200 mm as an example, 50×50 mesh points were arranged radially and circumferentially to discretize the deformation. Thermal expansion caused the mesh point coordinates to shift, with a maximum radial displacement of approximately 0.45 mm and a circumferential displacement of approximately 0.15 mm. The displacement distribution on the bearing surface was calculated using Lagrange interpolation to generate a continuous displacement field. Considering the variation of bearing surface roughness from 0.8 μm to 1.2 μm, coordinate correction was used to eliminate the interference of roughness on the clearance calculation, ensuring the accuracy of the initial contact clearance field.

[0065] S1032. Based on the bearing surface displacement distribution, a contact stress distribution matrix is ​​constructed, and the surface profile features are fitted using Bézier curves to calculate the local contact pressure field.

[0066] The bearing surface displacement distribution is used to construct the contact stress distribution matrix, reflecting the mechanical interaction between the foil and the bearing. Bézier curves are used to fit the surface profile feature points, with a control point spacing of 5 mm to ensure the smoothness and accuracy of the fitted curve. Contact deformation is calculated using the surface normal vector; the normal inclination angle fluctuates within ±15 degrees, and the local contact pressure is distributed between 2 MPa and 5 MPa. The generation of the contact pressure field is based on contact mechanics principles, accurately characterizing the gap reduction trend and providing a foundation for film pressure analysis.

[0067] S1033. Based on the local contact pressure field, the Reynolds equation is used to solve the air film pressure field, construct the air film pressure distribution matrix, and calculate the air film bearing capacity.

[0068] The local contact pressure field was used to establish the air film pressure field equation, which follows the fluid dynamics described by the Reynolds equation. Numerical solutions generated the air film pressure distribution matrix, showing that the pressure peak is located in the foil inlet region, at approximately 0.8 MPa. The circumferential pressure gradient exhibits periodic variation, with the maximum gradient occurring at the minimum gap, at approximately 0.5 MPa / mm. Based on the pressure distribution matrix, the air film bearing capacity was calculated; under typical operating conditions, the bearing capacity per unit area is approximately 0.4 MPa, providing a mechanical basis for the air film thickness response analysis.

[0069] S1034. Based on the air film pressure distribution matrix, the air film thickness response function is established using the spatial mapping method. Combined with the air film compression characteristic curve, the target air film thickness distribution is calculated.

[0070] The spatial mapping method is used to construct the film thickness response function, quantifying the impact of pressure changes on the thickness. The film compression characteristic curve is nonlinear, with a compression ratio between 1.2 and 1.5. When the pressure increases by 0.1 MPa, the film thickness decreases by approximately 0.01 mm. Combined with the pressure distribution matrix, the target film thickness is calculated. Under stable operating conditions, the thickness is between 15 and 25 micrometers, with a circumferential deviation of less than 5 micrometers, ensuring the uniformity and stability of the thickness distribution.

[0071] The rationality of the gas film thickness distribution is verified by the aerodynamic balance equation, and the final gas film thickness field is generated.

[0072] Aerodynamic equilibrium equations were used to verify the stability of the film thickness field. The thickness field tends to stabilize when the film bearing capacity is balanced with the external load. Calculation results show that the circumferential uniformity of the film thickness field is good, with a maximum deviation of no more than 5 micrometers. This uniform distribution effectively reduces the risk of film misalignment caused by uneven gaps. In practical applications, an accurate film thickness field provides reliable data for bearing stability assessment and supports the reliable operation of air-suspended fans in high-temperature, dusty environments.

[0073] S104. The target air film thickness of the foil bearing of the air suspension fan is compared with the preset abrasion threshold. If it is lower than the threshold, the Monte Carlo method is used to assess the probability of abrasion risk.

[0074] The spatial distribution of the target gas film thickness directly affects the stability of the bearing, especially in high-temperature, dusty exhaust gas environments, where excessively small local clearances may lead to rubbing failure. By comparing with preset thresholds, high-risk areas are identified, and probability analysis and dynamic stress evolution are combined to quantify the likelihood and severity of rubbing failure. The Monte Carlo method improves the robustness of risk assessment by simulating various stochastic operating conditions, providing data support for subsequent maintenance strategy optimization. This method does not strictly limit the specific probability distribution model and can be adjusted according to actual needs.

[0075] S1041. Based on the target air film thickness value, construct a gridded spatial distribution function and use Bernoulli distribution random sampling to calculate the probability of local collision point locations.

[0076] The target air film thickness is generated into a spatial distribution function through meshing to characterize the thickness variation in different regions of the bearing surface. For example, the air film thickness is sampled every 10 degrees within a 360-degree circumferential range to construct a discretized distribution model. When the local thickness is below a preset abrasion threshold of 15 micrometers, random sampling is performed using a Bernoulli distribution to calculate the probability of abrasion point locations. Sampling results show that when the thickness drops to 12 micrometers, the probability of abrasion in a local area can reach 0.35. This probability distribution reflects the direct impact of air film thickness non-uniformity on abrasion risk, providing a location basis for stress analysis.

[0077] S1042. Based on the probability of local contact point locations, construct the bearing load stress distribution, and calculate the contact stress field by combining the material surface finish parameters.

[0078] The probability of local contact point locations is used to generate the bearing's stress distribution under load, and the stress concentration effect is quantified by combining the material surface finish parameters. Taking a surface finish of 0.8 micrometers as an example, the local stress concentration factor is approximately 1.8, and the maximum local stress can reach 9 MPa under a nominal contact stress of 5 MPa. Considering a friction coefficient of 0.15, the calculated tangential stress component is approximately 1.35 MPa, forming a complete contact stress field. This stress field reflects the mechanical properties of the contact area, laying the foundation for frictional heat and vibration analysis.

[0079] S1043. Based on the contact stress field of friction, a frictional heat power field is constructed, and the dynamic stress evolution curve is predicted by the random forest algorithm to generate the vibration amplitude distribution of the foil.

[0080] The contact stress field of the frictional contact is used to calculate the frictional heat power field, characterizing the energy conversion during the frictional contact process. When the frictional contact duration exceeds 0.1 seconds, the local frictional heat power can reach 250 W / cm², leading to a rapid temperature increase. A random forest algorithm is used, ensembled from multiple decision trees, to predict the dynamic stress evolution curve. Input features include stress amplitude, contact duration, and temperature change. The prediction results show that stress fluctuations range from 0.5 MPa to 2 MPa, with the foil vibration amplitude reaching a maximum of 0.15 mm, reflecting the dynamic response characteristics induced by the frictional contact.

[0081] Based on the vibration amplitude distribution of the foil, the attenuation law of the air film thickness is calculated. Combined with the impact force data, the cumulative function of impact damage is constructed, and the probability of impact risk is determined by maximum likelihood estimation.

[0082] The vibration amplitude distribution of the foil is used to analyze the attenuation law of the gas film thickness. For example, when the peak impact force of a single collision is 15N, the attenuation rate of the gas film thickness is approximately 0.5 μm / s. A cumulative damage function for impact-wearing is constructed using a Weibull distribution to quantify the trend of damage accumulation over time. Maximum likelihood estimation is used to fit the parameters of a log-normal distribution, resulting in an impact-wearing risk probability distribution with a mean of -1.2 and a standard deviation of 0.4. At a 95% confidence level, the impact-wearing risk probability is approximately 0.28, indicating a 28% probability of significant damage. In practical applications, this probability prediction supports dynamic maintenance decisions and extends bearing life.

[0083] S105. If the probability of rubbing against the foil bearing of the air suspension fan exceeds the preset safety range, the temperature and impurity content data of the high-temperature dusty exhaust gas are collected in real time by the sensor, and the air film stiffness fluctuation range is calculated based on the gas dynamics theory.

[0084] When the probability of wear and tear exceeds a preset safety threshold, it indicates that the bearing may face instability risk. Therefore, exhaust gas characteristic data is collected collaboratively by multiple sensors, and the impact of gas film stiffness fluctuations on bearing stability is analyzed using gas dynamics theory. The calculation process integrates temperature field, impurity concentration, and pressure distribution to construct a dynamic model of gas film stiffness, ensuring the accuracy and reliability of the evaluation results. This method supports dynamic adjustment of maintenance strategies to extend bearing life.

[0085] S1051. The exhaust gas temperature and gradient distribution are collected by thermocouple sensors and thermistor arrays, and the gas temperature field function is fitted by the least squares method.

[0086] In this application embodiment, eight thermocouple sensors are arranged along the circumference of the bearing, with a sampling frequency of 100Hz, to monitor the exhaust gas temperature in real time, ranging from 350°C to 650°C. A thermistor array measures the temperature gradient, with a maximum value of 15°C / mm. The least squares method is used to fit the temperature field function, generating a continuous spatial distribution model that reflects the non-uniform characteristics of the exhaust gas temperature. The fitting process uses polynomial regression to optimize the sum of squared residuals, ensuring function accuracy and providing reliable input for gas density calculation.

[0087] S1052. Based on the measurement of the concentration distribution of impurities in exhaust gas using a laser particle size sensor, and combined with the gas state equation and Navier-Stokes equation, calculate the rate of change of gas density and the velocity field of the gas-solid two-phase flow.

[0088] Laser particle size analyzers were used to analyze the concentration of impurities in the exhaust gas. The particle distribution was as follows: 65% were smaller than 10 micrometers, 25% were between 10 and 50 micrometers, and 10% were larger than 50 micrometers. Based on the gas law, the gas density was calculated as a function of temperature; for example, the density was 0.55 kg / m³ at 350°C, decreasing to 0.35 kg / m³ at 650°C. Using the Navier-Stokes equations, the velocity field of the gas-solid two-phase flow was numerically solved. The airflow velocity fluctuated between 15 m / s and 25 m / s, characterizing the following behavior of small particles and the inertial hysteresis of large particles, providing flow field data for film pressure analysis.

[0089] S1053. Collect the air film pressure distribution through a pressure sensor array, construct the air film stress distribution function, and solve the air film deformation response characteristics using the finite difference method.

[0090] A pressure sensor array with 12 measuring points arranged circumferentially measured the peak pressure of the air film at 0.8 MPa and the fluctuation amplitude at 0.2 MPa. Based on the pressure data, an air film stress distribution function was constructed, with the maximum tangential stress of 1.5 MPa appearing in the region of maximum pressure gradient. Using the finite difference method and discretizing the Reynolds equation, the air film deformation response was calculated, with a thickness change rate reaching 0.5 μm / ms. This dynamic response characteristic reflects the deformation behavior of the air film under pressure disturbance, providing a mechanical basis for stiffness calculation.

[0091] S105. Based on the gas film deformation response characteristics, combined with gas dynamic viscosity and Reynolds number, the aerodynamic load distribution is calculated. The gas film damping characteristic equation and Bayesian regression are used to determine the gas film stiffness fluctuation range and stability.

[0092] The gas film deformation response characteristics were used to construct a stiffness calculation model. The gas dynamic viscosity varies with temperature, reaching 2.3 × 10⁻⁶ at 350°C. -5 Pascal-second (Pa·s) increases to 3.1 × 10⁻⁶ at 650 degrees Celsius. -5 Pa·s. A Reynolds number between 8000 and 12000 indicates turbulent flow. Calculate the aerodynamic load; the bearing capacity per unit area is approximately 0.4 MPa. Based on the air film damping characteristic equation, the radial stiffness coefficient is calculated to be 1.2 × 10⁻⁶. 5 Up to 1.8×10 5 The bearing has a stiffness of approximately 0.6 times its nominal value (N / m) and a damping ratio of 0.15 to 0.25. Using Bayesian regression to fuse stiffness and damping data, the predicted stiffness fluctuation range is ±20% of the nominal value. When the fluctuation exceeds this range, stability decreases, and operating parameters need to be adjusted to maintain reliable bearing operation.

[0093] S106. Based on the air film stiffness fluctuation range, combined with the real-time collected operating conditions of the air suspension fan and bearing structure data, the dynamic response parameters of the foil bearing are calculated using a fluid-structure interaction algorithm, including the shaft center trajectory, vibration amplitude, and minimum air film thickness.

[0094] The fluctuation range of the air film stiffness reflects the disturbance effect of high-temperature dusty exhaust gas on the dynamic behavior of the bearing. By acquiring real-time fan operating data through sensors and combining it with a fluid-structure interaction algorithm, the interaction between the air film and the foil structure is accurately simulated, quantifying the dynamic response characteristics of the bearing. The calculation process comprehensively considers speed fluctuations, load distribution, and material mechanical properties to ensure the reliability and accuracy of the results. This method supports dynamic optimization of operating parameters, improving the stability of the fan in complex environments.

[0095] S1061. Collect fan speed fluctuation rate and dynamic balance data through sensors, and construct aerodynamic load distribution function by combining bearing clearance ratio and preload parameters.

[0096] Sensors monitor the fan's operating status in real time, with a speed fluctuation rate of approximately 5% and a dynamic balance rating of G2.5. The bearing clearance ratio is set at 2.5‰, and the preload is 0.15. These parameters are used to generate an aerodynamic load distribution function through numerical mapping, characterizing the spatial distribution of the load. The function is constructed based on polynomial interpolation, considering the nonlinear effects of speed and clearance to ensure that the load distribution reflects the actual operating conditions and provides mechanical input for subsequent stress field calculations.

[0097] S1062. Based on the aerodynamic load distribution function, the stress field and deformation of the foil structure are calculated using the elasticity equations, and the air film pressure distribution field is generated by the finite volume method.

[0098] Aerodynamic load distribution functions were used to solve the stress field of the foil structure. Using the equations of elasticity, combined with Young's modulus and Poisson's ratio of the foil material, the stress distribution was calculated, with a maximum deformation of approximately 0.08 mm. The air film space was discretized using the finite volume method, with 120 grid points in the circumferential direction and 60 in the axial direction, generating the air film pressure distribution field. The results show that the pressure peak of 0.8 MPa occurs in the minimum gap region, and the circumferential pressure fluctuation amplitude is 0.2 MPa, reflecting the periodic mechanical characteristics of the air film.

[0099] The interaction between film pressure and foil deformation is calculated using a fluid-structure interaction iterative solver. Combined with the film compressibility ratio, the transient flow field distribution is generated and the axis offset is analyzed.

[0100] The fluid-structure interaction iterative solver calculates the dynamic equilibrium between film pressure and foil deformation using Newton's iteration method, achieving a convergence accuracy of 0.001 mm. The film compressibility ratio fluctuates between 1.2 and 1.5, reflecting the gas compressibility characteristics. The transient flow field distribution reveals the unsteady nature of the gas flow, with the axis offset varying between 0.15 mm and 0.25 mm. The ratio of the major axis to the minor axis of the elliptical axis trajectory is approximately 1.8, indicating the influence of bearing anisotropy on the dynamic response and providing data support for vibration analysis.

[0101] S1063. Based on the transient flow field distribution, a set of control equations for foil vibration is constructed. The Runge-Kutta method is used to calculate the vibration acceleration and axial displacement. The main vibration frequency is determined by fast Fourier transform.

[0102] The transient flow field distribution was used to establish the vibration control equations, describing the dynamic behavior of the foil under film disturbance. The Runge-Kutta method was used to solve the differential equations, calculating a peak vibration acceleration of 50 m / s² and a maximum axial displacement of 0.12 mm. Fast Fourier Transform analysis of the vibration signal revealed a dominant vibration frequency of 0.47 times the rotational frequency, accompanied by second and third harmonic components with amplitudes of 0.35 and 0.15 times the fundamental frequency, respectively. This frequency distribution reveals the multiharmonic characteristics of the vibration, supporting stability assessment.

[0103] S1064. Based on the vibration characteristics, construct the air film thickness distribution function, fit the air film pressure fluctuation curve using the least squares method, and calculate the minimum air film thickness using the aerodynamic balance equation.

[0104] Vibration characteristics were used to generate the film thickness distribution function, characterizing the periodic variation of thickness over time and space. The least squares method was employed to fit the film pressure fluctuation curve, with the fluctuation frequency synchronized with the rotational speed and the amplitude approximately 25% of the average pressure. Using the aerodynamic balance equations, the minimum film thickness was calculated to be approximately 15 micrometers, located within the load-bearing region. The calculation error was controlled within 5%, validating the rationality of the thickness distribution and providing accurate data for optimizing the bearing's dynamic response.

[0105] S107. Extract vibration amplitude analysis results from the dynamic response parameters of the foil bearing of the air suspension fan, and calculate stability prediction indicators, including logarithmic decay rate and eddy frequency ratio.

[0106] The dynamic response parameters of foil bearings provide the basis for vibration characteristic analysis. Through time-frequency domain signal processing and stability modeling, the dynamic behavior of the bearings in high-temperature, dusty exhaust gas environments is quantified. The calculation process comprehensively considers vibration attenuation and eddy current characteristics, employing multi-scale signal decomposition and spectral analysis to ensure the accuracy of stability indicators. This method provides a crucial basis for optimizing dynamic maintenance strategies and supports reliable wind turbine operation.

[0107] S1071. Obtain the vibration time-domain signal in the dynamic response parameters of the foil bearing, decompose the frequency components using wavelet transform, and construct the vibration amplitude envelope spectrum.

[0108] The vibration time-domain signal was acquired by a sensor at a sampling frequency of 10 kHz for a duration of 10 seconds, exhibiting periodic fluctuations. Multi-scale decomposition was performed using wavelet transform to identify the fundamental frequency (120 Hz) and its harmonics (240 Hz and 360 Hz). Wavelet transform, through discrete wavelet basis functions, decomposed the signal into different frequency sub-bands, preserving local time-frequency characteristics. Based on the decomposition results, Hilbert transform was used to generate the vibration amplitude envelope spectrum, with amplitude ranging from 0.15 mm to 0.25 mm, reflecting the dynamic changes in vibration intensity and providing a data foundation for attenuation analysis.

[0109] S1072. Based on the vibration amplitude envelope spectrum, calculate the amplitude ratio of adjacent vibration periods, and combine it with the damping coefficient to calculate the logarithmic decay rate using the vibration response equation.

[0110] The vibration amplitude envelope spectrum is used to quantify the vibration decay characteristics. By comparing the amplitudes of adjacent periods, a ratio of approximately 1.12 is obtained, indicating a decay of approximately 10.7% per period. Combined with a damping coefficient of 0.18, a vibration response equation is constructed. Based on an exponential decay model, the logarithmic decay rate is calculated to be approximately 0.113. The equation considers the coupling effect of mass, stiffness, and damping, reflecting the bearing's vibration suppression capability and ensuring the physical consistency of the decay rate calculation.

[0111] Based on the logarithmic decay rate and dynamic stiffness ratio, a bearing stability evaluation matrix is ​​constructed. Whirl components are extracted by fast Fourier transform, and the whirl frequency ratio is calculated.

[0112] The bearing stability assessment matrix integrates logarithmic decay rate and dynamic stiffness ratio, with a stiffness ratio ranging from 1.5 to 2.0. Vibration signals are processed using Fast Fourier Transform (FFT) to extract eddy current components, with amplitudes approximately 0.35 times the fundamental frequency and angular velocities reaching 0.47 times the rotational speed. The dominant eddy current frequency of 56Hz is obtained through Discrete Fourier Transform (DFT), and compared to the critical speed of 32,000 rpm, the eddy current frequency ratio is 0.105. Matrix analysis combined with spectral analysis generates a vibration response function, revealing resonance peaks at 120Hz, 240Hz, and 360Hz, with amplitude ratios of 1:0.35:0.15, reflecting the system's frequency characteristics.

[0113] S1073. Based on the eddy frequency ratio and vibration response function, construct a dynamic characteristic evaluation function and use an autoregressive model to predict the trend of logarithmic decay rate and eddy frequency ratio.

[0114] In this application embodiment, the whirl frequency ratio and vibration response function are used to construct a dynamic characteristic evaluation function, quantifying the system stability margin to approximately 0.28. An autoregressive model is employed, fitted with historical vibration data, to predict trends over the next 1000 rotor cycles. Based on time series data and considering autocorrelation, the model predicts logarithmic decay rate fluctuations between 0.105 and 0.125, and whirl frequency ratios between 0.095 and 0.115. This prediction supports long-term stability assessment, optimizes maintenance decisions, and improves bearing reliability under complex operating conditions.

[0115] S108. Adaptive filtering algorithm is used to optimize the real-time evaluation logic of the digital twin system. The wear monitoring data of the air suspension fan foil bearing is updated based on the stability prediction index to generate failure probability evaluation results.

[0116] Wear monitoring data from foil bearings is processed using an adaptive filtering algorithm, combined with stability prediction indices, to dynamically optimize the evaluation logic of the digital twin system. The algorithm integrates time-domain and frequency-domain features to construct a wear state model and accurately predict failure probabilities. The processing comprehensively considers noise suppression, state estimation, and probabilistic analysis to ensure the robustness and real-time performance of the evaluation results. This method supports optimized maintenance strategies and extended bearing life in high-temperature, dusty exhaust gas environments.

[0117] S1081. Extract bearing wear data features through state observation equations, calculate measurement noise variance, optimize filter gain coefficients, and construct state transition equations.

[0118] The state observation equation describes the dynamic characteristics of bearing wear data, with vibration signals and wear measurements as inputs. The measurement noise variance is adjusted from an initial 0.01 to 0.05 to reflect changes in operating conditions. Based on the noise variance, the filter gain coefficient is calculated, decreasing from 0.8 to 0.4, and the state estimation is optimized using the Kalman filter principle. The state transition equation is based on the system noise covariance, which converges from 0.02 to 0.008, generating real-time response characteristics with a delay time of less than 100 milliseconds, providing high-precision input for wear rate analysis.

[0119] S1082. Based on the real-time response characteristics, a state estimation function is constructed, and a deep neural network is used to predict the wear rate and generate a life degradation curve.

[0120] The state estimation function is generated through the state transition equation, with the root mean square error controlled within 3%. The wear rate is predicted using a deep neural network with three fully connected layers and ReLU activation. Input features include vibration amplitude, temperature, and load. Prediction results show a wear rate of 0.5 μm / hour under normal operating conditions, increasing to 0.8 μm / hour with a 20% increase in load. Based on the predicted data, a life degradation curve is constructed, conforming to a Weibull distribution, with a characteristic life of approximately 5000 hours, reflecting the bearing degradation trend.

[0121] By integrating wear rate and stability prediction indices, a failure probability transition matrix is ​​constructed. Then, using Markov chains and Monte Carlo methods, the remaining life distribution and failure probability of the bearing are calculated.

[0122] The failure probability transition matrix is ​​constructed based on wear rate and stability indices. Matrix elements represent state transition probabilities; for example, the probability of transitioning from normal to sub-healthy state is 0.15, and the probability of transitioning from sub-healthy to failure is 0.25. Markov chain analysis is used to analyze state evolution, combined with Monte Carlo methods for 10,000 iterations to generate the remaining lifetime distribution, with a failure probability threshold range of 0.1 to 0.3. At a 95% confidence level, the probability of early failure is 0.12, the probability of failure within normal lifetime is 0.75, and the probability of ultra-long lifetime is 0.13. The evaluation logic adjusts parameters according to a 1-hour update cycle, with a correction amount of 15% of the original value, optimizing prediction accuracy.

[0123] S1083. Extract the time-domain and frequency-domain features of bearing wear monitoring data, use a long short-time memory network to generate a prediction residual sequence, optimize the filtering parameters, and reconstruct the wear data.

[0124] Wear monitoring data were characterized by a root mean square value of 0.35 mm / s and a spectral kurtosis of 3.8. Hilbert transform was used to generate the envelope spectrum, with the fault characteristic frequency being 0.47 times the shaft frequency and sideband frequencies ranging from 120 Hz to 360 Hz. A long short-time memory network, combined with time-frequency joint features, was used to generate a predictive residual sequence. Singular value decomposition was used to extract the noise subspace, with eigenvalues ​​of 2.5, 1.8, and 0.9, a residual convergence of 0.95, and a noise covariance matrix trace of 0.15. Recursive least squares optimization improved the noise suppression coefficient to 0.82, and the reconstructed data correlation coefficient reached 0.96, significantly improving the signal-to-noise ratio.

[0125] S1084. Based on the reconstructed data, wavelet transform is used to extract wear characteristic coefficients, and wear amount evolution equation is constructed. Wear amount time series curve and cumulative failure probability are generated through data fusion.

[0126] Wavelet transform extracts 250Hz frequency band feature coefficients of 0.28 at level 4 decomposition, consistent with the fault frequency. The wear evolution equation has eigenvalues ​​of -0.15±0.08j, reflecting stable attenuation characteristics. A time-series state matrix is ​​generated based on the evolution equation, and a Markov chain calculates the probability of normal to mild wear (0.15) and mild to moderate wear (0.25). A Wiener filter with a bandwidth of 100Hz fuses residual and time-series data, showing a steady-state wear growth rate of 0.02 mm / h and an overload rate of 0.05 mm / h. The failure probability density function exhibits a right-skewed distribution, and the state transition matrix predicts a failure probability of 0.28 within 1000 hours with a goodness of fit of 92%, providing a reliable basis for maintenance decisions.

[0127] S109. Based on the failure probability assessment results, control commands are generated and transmitted to the thermal shock protection module of the air suspension fan to dynamically optimize the bearing stability adjustment scheme.

[0128] Failure probability assessment results provide crucial input for thermal shock protection, generating precise control commands to dynamically adjust bearing operating conditions. The solution comprehensively considers temperature control, cooling power distribution, and stability monitoring, employing adaptive control and intelligent algorithms to optimize response characteristics and ensure reliable bearing operation under extreme conditions. This method reduces failure risk and extends equipment life through real-time feedback and dynamic optimization.

[0129] S1091. Based on the failure probability assessment results, construct a thermal shock protection parameter set, generate a temperature control curve, and calculate the dynamic temperature adjustment sequence through an adaptive controller.

[0130] The thermal shock protection parameter set is triggered based on failure probability. When the probability exceeds 0.35, the temperature regulation ratio is set to 1.5 and the cooling power to 2.5 kW. Using these parameters, a temperature control curve is generated through polynomial interpolation to characterize the change of the target temperature over time. The adaptive controller, based on real-time temperature feedback, uses a proportional-integral-derivative algorithm to generate a dynamic temperature adjustment sequence, with a response time controlled within 100 milliseconds to ensure rapid adaptation to temperature fluctuations and provide a basis for command generation.

[0131] S1092. Convert the dynamic temperature adjustment sequence into digital control instructions, transmit them to the thermal shock protection device through the serial communication interface, and optimize the instruction execution timing.

[0132] The dynamic temperature control sequence is encoded into digital control commands, which are transmitted to the thermal shock protection device via an RS485 interface at a rate of 115,200 bits / second. Considering a 5-millisecond signal transmission delay, a feedforward compensation algorithm is used to optimize the command execution timing, keeping the delay within 10 milliseconds. The optimization process involves predicting signal propagation time and adjusting the transmission interval to ensure accurate command execution and improve the real-time performance of the thermal shock protection.

[0133] Based on the instruction execution timing, a set of bearing operating state parameters is constructed, a dynamic characteristic monitoring function is generated, and the gain curve is predicted and adjusted to optimize heat power distribution.

[0134] The instruction execution timing is used to generate a set of bearing operating status parameters, including a vibration amplitude of 0.15 mm and a temperature fluctuation of ±15 degrees Celsius. Based on the parameter set, a dynamic characteristic monitoring function is constructed, and the gain curve is adjusted by support vector regression prediction. The gain is 0.8 under normal operating conditions and decreases to 0.5 under overload conditions. Combined with a temperature change rate of 5 degrees Celsius / minute, the dynamic heat power distribution ratio is calculated. When the fast response mode is triggered, the cooling power reaches 85% of the rated value within 0.5 seconds, effectively suppressing temperature overshoot.

[0135] S1093. Dynamic programming is used to optimize the thermal shock response characteristics, and a fuzzy controller is used to generate a bearing thermal protection control strategy to dynamically adjust the stability parameters.

[0136] Dynamic programming optimizes thermal shock response by minimizing temperature fluctuation amplitude, controlling fluctuations within ±8 degrees Celsius. The fuzzy controller employs a three-layer structure, taking temperature deviation, rate of change, and vibration amplitude as inputs, and outputting the intensity and duration of adjustment commands. After membership function optimization, it responds rapidly to rapid fluctuations and adjusts smoothly to slow changes. When the temperature rises sharply, the controller increases cooling power and reduces preload; after stabilization, it restores parameters, reducing the failure probability by 45% and significantly improving bearing life.

[0137] This invention provides a predictive maintenance system for air-suspended fans based on digital twins, mainly comprising:

[0138] The airflow change feature acquisition module is used to collect the airflow change features when high-temperature dusty exhaust gas rushes into the air suspension fan, and transmit it to the digital twin system to determine the airflow change features.

[0139] The foil transient thermal expansion calculation module is used to calculate the transient thermal expansion distribution of the foil based on the characteristics of sudden airflow changes. It combines the interaction between the temperature field and stress-strain field of the material to obtain the non-uniform expansion amount in each region of the foil.

[0140] The gap reduction trend extraction module is used to extract the local gap reduction trend between the foil and the bearing from the non-uniform expansion of the foil, calculate the spatial distribution after the gap reduction, and obtain the target air film thickness value.

[0141] The collision and abrasion risk assessment module is used to compare the target air film thickness value with the preset collision and abrasion threshold. If it is less than the threshold, the probability of collision and abrasion risk is assessed by the Monte Carlo method.

[0142] The air film stiffness fluctuation calculation module is used to calculate the air film stiffness fluctuation range based on gas dynamics theory if the probability of collision and abrasion exceeds the preset safety range.

[0143] The dynamic response parameter calculation module is used to calculate the dynamic response parameters of the foil bearing of the air suspension fan based on the air film stiffness fluctuation range, combined with the real-time acquisition of the operating conditions and bearing structure of the air suspension fan, and using a fluid-structure interaction algorithm.

[0144] The stability prediction index calculation module is used to extract vibration amplitude analysis results from the dynamic response parameters of the foil bearing of the air suspension fan and calculate the stability prediction index.

[0145] The real-time evaluation logic optimization module is used to optimize the preset real-time evaluation logic of the digital twin system using an adaptive filtering algorithm, update the bearing wear monitoring data based on stability prediction indicators, and determine the failure probability evaluation results.

[0146] The dynamic adjustment scheme generation module is used to generate control commands based on the failure probability assessment results, which are then transmitted to the thermal shock protection module of the air suspension fan to generate a dynamic adjustment scheme for bearing stability.

[0147] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A predictive maintenance method for air-suspended fans based on digital twins, characterized in that, The method includes: The characteristics of airflow abrupt change when high-temperature dust-laden exhaust gas enters the air suspension fan are collected and transmitted to the digital twin system to determine the characteristics of airflow abrupt change. The transient thermal expansion distribution of the foil is calculated based on the characteristics of sudden airflow changes. The non-uniform expansion amount in each region of the foil is obtained by combining the interaction between the temperature field and the stress-strain field of the material. The shrinkage trend of the local gap between the foil and the bearing is extracted from the non-uniform expansion of the foil, and the spatial distribution after the gap shrinkage is calculated to obtain the target air film thickness value. The target air film thickness is compared with a preset impact threshold. If it is less than the threshold, the probability of impact risk is assessed using the Monte Carlo method. If the probability of collision and abrasion exceeds the preset safety range, the range of air film stiffness fluctuation is calculated based on gas dynamics theory. Based on the fluctuation range of air film stiffness, combined with the real-time acquisition of the operating conditions and bearing structure of the air suspension fan, the dynamic response parameters of the foil bearing of the air suspension fan are calculated using a fluid-structure interaction algorithm. Vibration amplitude analysis results are extracted from the dynamic response parameters of the foil bearing of the air suspension fan, and stability prediction index is calculated. An adaptive filtering algorithm is used to optimize the real-time evaluation logic of the preset digital twin system, and the bearing wear monitoring data is updated based on the stability prediction index to determine the failure probability evaluation result. Based on the failure probability assessment results, control commands are generated and transmitted to the thermal shock protection module of the air suspension fan to generate a dynamic adjustment scheme for bearing stability.

2. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The characteristics of airflow abrupt changes when high-temperature dust-laden exhaust gas enters the air suspension fan are collected and transmitted to the digital twin system to determine the characteristics of airflow abrupt changes, including: Airflow pressure data is acquired in the gas flow channel by a piezoelectric pressure sensor, and the pressure change rate of adjacent measuring points is calculated based on the airflow pressure data to obtain a data set of sudden airflow pressure changes. Based on the airflow pressure change dataset and the dust concentration data obtained from the dust concentration sensor, the dust concentration data is classified and statistically analyzed according to the dust particle size range, and the velocity field distribution of the gas-solid two-phase flow is calculated. Based on the velocity field distribution of the gas-solid two-phase flow and the exhaust gas temperature data obtained from the thermocouple temperature sensor, a temperature field distribution parameter set including temperature gradient, heat flux and convective heat transfer coefficient is established. The airflow pressure change dataset, the gas-solid two-phase flow velocity field distribution, and the temperature field distribution parameter set are time-synchronized to construct an airflow state space, and the airflow change characteristics are calculated by the least squares method.

3. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The transient thermal expansion distribution of the foil is calculated based on the characteristics of sudden airflow changes. Combining the interaction between the material's temperature field and stress-strain field, the non-uniform expansion amount in each region of the foil is obtained, including: An adaptive quadrilateral grid cell is obtained based on the foil temperature field data. When the temperature gradient difference between adjacent grid cells is less than a preset threshold, the initial temperature field distribution of the foil is obtained. The stress field distribution at the nodes of the foil mesh element was calculated using the Lagrange interpolation method. The initial values ​​of the stress-strain field of the foil were obtained based on the initial temperature field distribution and the thermal stress coefficient matrix. The displacement increment of the grid element nodes is calculated by using the linear elastic constitutive equation, and the local deformation of the foil is solved based on the initial temperature field distribution of the foil to obtain the transient deformation field data of the foil. The thermal conductivity distribution of the foil is calculated using the least squares method. The temperature-stress coupling coefficient is obtained based on the transient deformation field data and stress field distribution of the foil. The thermal displacement vector of the grid unit node is solved by the finite difference method, and the non-uniform expansion of each region of the foil is obtained by solving the thermal displacement vector of each grid unit node by the finite difference method.

4. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The process of extracting the trend of local gap reduction between the foil and the bearing from the non-uniform expansion of the foil, calculating the spatial distribution after the gap reduction, and obtaining the target air film thickness value includes: The foil deformation mesh matrix is ​​obtained based on the non-uniform expansion of the foil, and the bearing surface displacement distribution data is calculated by Lagrange interpolation using the foil deformation mesh matrix. A contact stress distribution matrix is ​​constructed based on the bearing surface displacement distribution data. The bearing surface contour feature points are fitted using a Bezier curve, and the local contact pressure field data is calculated using the surface normal vector. Based on the local contact pressure field data, an air film pressure field equation is established, and the air film pressure distribution matrix is ​​obtained by solving the air film pressure field equation using the Reynolds equation. A spatial mapping method is used to establish the air film thickness response function for the air film pressure distribution matrix, and the target air film thickness value is calculated through the air film compression characteristic curve.

5. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The target air film thickness value is compared with a preset impact threshold. If it is less than the threshold, the probability of impact risk is assessed using the Monte Carlo method, including: A gridded spatial distribution function is established based on the target air film thickness value. If the air film thickness is less than the preset collision threshold, the probability value of the local collision point location is obtained by random sampling using Bernoulli distribution. The bearing load stress distribution is constructed based on the probability values ​​of the local rubbing point locations, and the local stress concentration coefficient is obtained through the material surface finish parameters to obtain the rubbing contact stress field. A frictional heat power field is established based on the friction contact stress field, the dynamic stress evolution curve is predicted, and the vibration amplitude distribution data of the foil is obtained. The attenuation law of air film thickness is calculated based on the vibration amplitude distribution data of the foil. The cumulative function of impact damage is constructed through the impact force data. The probability distribution parameters of impact risk are determined by maximum likelihood estimation, and the probability value of impact risk is obtained.

6. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, If the probability of impact and wear exceeds the preset safety range, the air film stiffness fluctuation range is calculated based on gas dynamics theory, including: By collecting exhaust gas temperature data and combining it with thermistor array measurements of temperature gradient distribution, the temperature field distribution function is obtained. Based on the temperature field distribution function and the concentration distribution of impurities in the exhaust gas measured by the laser particle size sensor, the gas density change rate is calculated using the gas state equation. The air film pressure distribution data is acquired by a pressure sensor array, an air film stress distribution function is established based on the air film pressure distribution data, and the air film deformation response characteristics are solved by the finite difference method. The aerodynamic load distribution is calculated based on the gas film deformation response characteristics and gas dynamic viscosity, and the upper and lower limits of gas film stiffness fluctuation are solved using the gas film damping characteristic equation.

7. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The process involves calculating the dynamic response parameters of the foil bearings of the air-suspended fan based on the air film stiffness fluctuation range, combined with real-time acquisition of the air-suspended fan's operating conditions and bearing structure, using a fluid-structure interaction algorithm. This includes: Collect the fan speed fluctuation rate signal and dynamic balance signal, and establish the aerodynamic load distribution function based on the bearing clearance ratio parameter and bearing preload parameter; The stress field of the foil structure is solved based on the aerodynamic load distribution function, the deformation of the foil is calculated using the elasticity equations, and the air film pressure distribution field is obtained by the finite volume method. Based on the air film pressure distribution field and the foil deformation, the axis offset is calculated using a fluid-structure interaction iterative solver, and the transient flow field distribution is obtained through the air film compressibility ratio parameter. Based on the transient flow field distribution, a set of control equations for foil vibration was established. The vibration acceleration and axial displacement were calculated using the Runge-Kutta method, and the main vibration frequency was obtained through fast Fourier transform.

8. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The process of extracting vibration amplitude analysis results from the dynamic response parameters of the foil bearings of the air-suspended fan and calculating stability prediction indices includes: The vibration time-domain signal in the dynamic response parameters of the foil bearing of the air suspension fan is obtained, and the vibration time-domain signal is decomposed by wavelet transform to obtain the frequency component of the vibration signal; The vibration amplitude envelope spectrum is constructed using Hilbert transform based on the frequency components of the vibration signal. The amplitude attenuation data is obtained by calculating the amplitude ratio of adjacent vibration periods in the vibration amplitude envelope spectrum. A bearing stability evaluation matrix is ​​constructed based on the amplitude attenuation data and dynamic stiffness ratio. Whirlwind signal data is obtained by extracting whirlwind components from the bearing stability evaluation matrix. If the eddy signal data meets the sampling theorem requirements, then the discrete Fourier transform is used to obtain the eddy dominant frequency signal, and the eddy frequency ratio is calculated based on the eddy dominant frequency signal and the critical speed.

9. The predictive maintenance method for air-suspended fans based on digital twins according to claim 1, characterized in that, The real-time evaluation logic of the preset digital twin system, which employs an adaptive filtering algorithm to optimize the system, updates bearing wear monitoring data based on stability prediction indices and determines the failure probability assessment result, includes: The bearing wear data characteristics are obtained by using the state observation equation, the measurement noise variance is calculated based on the bearing wear data characteristics, and the filter gain coefficient is obtained through the measurement noise variance. A state transition equation is constructed based on the filter gain coefficients, and the real-time response characteristics are obtained through the state transition equation. A state estimation function is then constructed based on the real-time response characteristics. The wear rate data is obtained based on the state estimation function, the wear rate data is processed by a deep neural network, and a lifetime degradation curve is established based on the wear rate data. A failure probability transition matrix is ​​constructed based on the life degradation curve. A Markov chain is used to process the failure probability transition matrix, and an adaptive evaluation criterion is established to optimize the evaluation logic. The bearing wear monitoring parameters are updated based on the optimization results of the evaluation logic. The failure probability is calculated by sampling multiple times using the Monte Carlo method to obtain the failure probability evaluation result.

10. A predictive maintenance system for air-suspended fans based on digital twins, characterized in that, The system includes: The airflow change feature acquisition module is used to collect the airflow change features when high-temperature dusty exhaust gas rushes into the air suspension fan, and transmit it to the digital twin system to determine the airflow change features. The foil transient thermal expansion calculation module is used to calculate the transient thermal expansion distribution of the foil based on the characteristics of sudden airflow changes. It combines the interaction between the temperature field and stress-strain field of the material to obtain the non-uniform expansion amount in each region of the foil. The gap reduction trend extraction module is used to extract the local gap reduction trend between the foil and the bearing from the non-uniform expansion of the foil, calculate the spatial distribution after the gap reduction, and obtain the target air film thickness value. The collision and abrasion risk assessment module is used to compare the target air film thickness value with the preset collision and abrasion threshold. If it is less than the threshold, the probability of collision and abrasion risk is assessed by the Monte Carlo method. The air film stiffness fluctuation calculation module is used to calculate the air film stiffness fluctuation range based on gas dynamics theory if the probability of collision and abrasion exceeds the preset safety range. The dynamic response parameter calculation module is used to calculate the dynamic response parameters of the foil bearing of the air suspension fan based on the air film stiffness fluctuation range, combined with the real-time acquisition of the operating conditions and bearing structure of the air suspension fan, and using a fluid-structure interaction algorithm. The stability prediction index calculation module is used to extract vibration amplitude analysis results from the dynamic response parameters of the foil bearing of the air suspension fan and calculate the stability prediction index. The real-time evaluation logic optimization module is used to optimize the preset real-time evaluation logic of the digital twin system using an adaptive filtering algorithm, update the bearing wear monitoring data based on stability prediction indicators, and determine the failure probability evaluation results. The dynamic adjustment scheme generation module is used to generate control commands based on the failure probability assessment results, which are then transmitted to the thermal shock protection module of the air suspension fan to generate a dynamic adjustment scheme for bearing stability.

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