A Thermo-Coupling Super-Decrease Prediction Method and System for Multi-Component Assembled Nonlinear Systems

Abstract

This invention relates to a method and system for predicting the thermo-mechanical coupling of a multi-component assembled nonlinear system using a super-reduced order prediction method. The method includes: acquiring multi-scale physical field data; constructing an intrinsic orthogonal decomposition basis function space for the temperature and stress fields, and establishing dual-field coupling constraint equations; using a domain-specific discrete empirical interpolation method to construct a parameterized surrogate model for the contact thermal resistance of the cylinder contact area, bolt area, and free deformation area; constructing a parameterized intrinsic modal tensor network to obtain a reduced-order model, which is used in the online stage to achieve real-time reconstruction of modal basis functions through tensor slices; based on the modal basis function reconstruction results, performing dynamic inversion to output the predicted transient displacement field, temperature gradient field, and contact stress field; acquiring real-time parameters and calculating residuals with the corresponding prediction results to dynamically update the basis functions and interpolation point distribution. Compared with existing technologies, this invention achieves real-time prediction of transient thermo-mechanical coupling in multi-component contact systems while ensuring accuracy.

Description

Technical Field

[0001] This invention relates to the field of multiphysics coupling simulation of high-temperature power equipment, and in particular to a method and system for predicting super-degraded order of thermo-mechanical coupling in nonlinear systems with multiple components. Background Technology

[0002] Currently, thermo-mechanical coupling analysis of high-temperature components mainly relies on high-fidelity numerical models such as the finite element method (FEM) and the finite volume method (FVM). While these methods accurately characterize the coupling between temperature and stress fields by discretizing and solving the Navier-Stokes equations and thermoelasticity equations, they face significant challenges in practical engineering. For example, to capture the microscale heat transfer effect at the interface between the cooling airflow and the blade, a full-order model with over 5 million mesh elements is required, resulting in a single transient simulation taking over 48 hours. Furthermore, when the temperature rise rate is high, the failure rate of traditional contact algorithms (such as the penalty function method) increases due to abrupt changes in thermal resistance, leading to a higher rate of convergence failure. Although the academic community has proposed acceleration strategies such as adaptive mesh refinement and parallel computing, their computational resource consumption still cannot meet the demands of online condition monitoring for second-level response times.

[0003] To overcome efficiency bottlenecks, model reduction model (ROM) techniques have become a research hotspot. Based on intrinsic orthogonal decomposition (POD), reduced-order models can construct a low-dimensional approximation space by extracting the dominant modes of the temperature and stress fields, thus compressing the computational scale to 1%-5% of that of full-order models. However, existing ROM methods have significant limitations in multi-component contact systems of gas turbines: First, traditional POD independently reduces the order of the temperature and stress fields, ignoring the cross-scale energy transfer effect of the dual-field coupling terms, resulting in excessive displacement prediction errors under transient conditions; Second, non-smooth mechanical responses generated at the contact interface (such as fretting wear of the sealing surface and loosening of bolt preload) violate the linear superposition assumption of POD. Although the existing global discrete empirical interpolation method (DEIM) can reduce the dimension of nonlinear terms, it does not consider the physical heterogeneity of local contact features such as sealing grooves and film pores, resulting in excessive contact thermal resistance reconstruction errors; Third, fixed modal basis functions are difficult to adapt to dynamic changes in a wide range of temperature rise rates (0-600℃). When the actual operating conditions deviate from the training set, time-consuming offline modal updates need to be re-executed, resulting in the loss of real-time prediction capabilities.

[0004] In recent years, the integration of deep learning (DL) and physics-driven models has provided new ideas for computational acceleration. Some studies have attempted to combine neural networks with physical displacement analysis (POD) to quickly predict temperature field distribution using the meshless nature of the model. However, such methods have inherent drawbacks: First, data-driven models require tens of thousands of sets of high-fidelity simulation data for training, while the cost of acquiring experimental data for multi-component contact systems in gas turbines is extremely high; second, the black-box nature of neural networks leads to a lack of physical interpretability in the prediction results, making it difficult to meet the stringent safety certification requirements in fields such as aviation and nuclear power; third, existing algorithms are slow to respond to sudden changes in contact stress under transient thermal shock, and experimental results show that their prediction results lag behind the actual displacement by 3-5 seconds, failing to support fault early warning.

[0005] The essence of the aforementioned technical bottleneck lies in the fact that existing methods fail to effectively reconcile the contradictions between multi-component contact nonlinearity, transient thermo-mechanical coupling, and dynamic adaptation under wide operating conditions. The chain-like contact constraints of the turbine rotor blade-disc flange-cylinder bolt system, and the transient interaction between cooling airflow and high-temperature combustion gas, require simulation models to possess physical accuracy, computational efficiency, and robustness under operating conditions. However, traditional ROMs oversimplify the contact mechanism during order reduction, and data-driven models deviate from the physical essence, neither of which can meet practical engineering needs. Therefore, there is an urgent need to develop a super-order reduction technology that integrates physical mechanisms and intelligent algorithms to achieve real-time prediction of transient thermo-mechanical coupling in multi-component contact systems while ensuring accuracy, providing a core tool for online health monitoring and life assessment of high-temperature power equipment. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of the prior art in the analysis of nonlinear contact transient thermo-mechanical coupling of high-temperature multi-component systems, such as low efficiency and poor temperature rise adaptability, and to provide a super-decrease-order prediction method and system for nonlinear systems with multi-component assembly, so as to achieve high-precision prediction at the second level and meet the online monitoring requirements of equipment such as aero-engines and nuclear reactors.

[0007] The objective of this invention can be achieved through the following technical solutions:

[0008] A thermo-mechanically coupled super-order reduction prediction method for a multi-component assembled nonlinear system includes the following steps:

[0009] Collect multi-scale physical field data of nonlinear systems, including temperature field data, stress field data, and contact thermal resistance data;

[0010] Based on the temperature field data and stress field data, an eigenorthogonal decomposition basis function space of the temperature field and stress field is constructed, and a dual-field coupling constraint equation is established.

[0011] Based on the contact thermal resistance data, a parameterized proxy model of the contact thermal resistance of the cylinder contact area, bolt area and free deformation area is constructed by using the domain discrete empirical interpolation method.

[0012] Based on the intrinsic orthogonal decomposition basis function space of temperature field and stress field, and the discretized parameter values ​​of contact thermal resistance data, a parametric intrinsic mode tensor network for 0-600℃ working conditions is constructed to obtain a price reduction model. This model is used in the online stage to realize real-time reconstruction of modal basis functions by acquiring tensor slices, and to determine the intrinsic orthogonal decomposition modal basis and the domain discrete empirical interpolation operator.

[0013] Based on the modal basis function reconstruction results in the online stage, dynamic inversion of thermo-mechanical dual-field generalized coordinates is performed, and contact constraints based on the contact parameter prediction results are added to output the predicted transient displacement field, temperature gradient field and contact stress field.

[0014] The system acquires real-time parameters from multi-scale physical field data and calculates residuals with the corresponding prediction results to dynamically update the basis functions of the temperature and stress fields and the interpolation point distribution of the contact thermal resistance data.

[0015] Furthermore, the method of using domain-discrete empirical interpolation to construct a parameterized proxy model for the contact thermal resistance of the cylinder contact area, bolt area, and free deformation area is as follows:

[0016] For the cylinder contact area, Hermite polynomial interpolation is used to construct the contact thermal resistance gradient response surface, and the corresponding calculation expression is:

[0017]

[0018] In the formula, The sealing contact thermal resistance at the cylinder contact interface. Let m be the Hermite polynomial basis functions, with pressure gradient as the basis. and gap δ g H is the input variable. m γ is the polynomial truncation order, M is the total order, and γ m The weighting coefficients are the polynomial expansion coefficients.

[0019] For the bolt zone, stress gradient clustering is used to select DEIM interpolation points, and the corresponding calculation expression is:

[0020]

[0021] In the formula, Let x be the set of locations in the bolt area selected as DEIM interpolation points. i These are the coordinates of a discrete point in space. For x iThe von Mises stress spatial gradient at a point, where η is a threshold coefficient used to control the range of interpolation points. This represents the maximum value of the stress gradient norm across the entire computational domain.

[0022] For the free deformation region, a thermal resistance probability density response model is constructed using Latin hypercube sampling.

[0023] Furthermore, the basis function sets of the temperature field and the stress field satisfy the orthogonality condition, which is expressed as follows:

[0024]

[0025] In the formula, Let x be the i-th order POD basis function of the temperature field at position x. Let δ be the j-th order POD basis function of the temperature field at position x. ij Let be the Kronecker delta function, indicating that the basis functions are mutually orthogonal and normalized in the spatial domain Ω; Let x be the i-th order POD basis function of the stress field at position x. Let be the j-th order POD basis function of the stress field at position x.

[0026] Furthermore, the expression for the dual-field coupling constraint equation is as follows:

[0027]

[0028] In the formula, Let α(T′) = tanh(βT′) be the two-field coupling matrix for the thermal stress change caused by temperature rise, and let C be the dynamic coupling factor. σT This represents the two-field coupling matrix for temperature field perturbation caused by stress variation. Let L be the rate of change of the generalized coordinate vectors of the temperature and stress fields with time. T and L σ Let C represent the linear evolution operator matrices of the temperature field and the stress field, respectively. Tσ and C σT This represents the dynamic coupling effect between the two fields.

[0029] Furthermore, the construction process of the parametric intrinsic mode tensor network includes:

[0030] The fourth-order parametric eigenmode tensor is constructed, and the corresponding computational expression is as follows:

[0031]

[0032] In the formula, For the fourth-order parametric eigenmode tensor, n T and n σLet n be the number of POD basis function modes for the temperature and stress fields. R and n v Let the radius of curvature be R. c The number of sampling points for the discretization parameter of the temperature rise rate v, Let be the i-th order POD basis function of the temperature field. Let J be the j-th order POD basis function of the stress field. For the k-th discretized geometric parameter value, This is the value of the temperature rise rate parameter for the l-th discretized parameter.

[0033] Tucker decomposition is used for tensor compression to transform the fourth-order parametric eigenmode tensor. Decomposed into a core tensor The product of the four factor matrices is calculated using the following expression:

[0034]

[0035] In the formula, Includes tensors The main coupling characteristics, The rank of U is determined by optimization using alternating least squares method. T U σ U R U v These are low-dimensional projection matrices corresponding to the temperature field, stress field, geometric parameters, and temperature rise rate, respectively.

[0036] Furthermore, the dynamic inversion process includes constructing a reduced-order Lyapunov function with contact constraints and performing modal coefficient evolution. The expression for the reduced-order Lyapunov function with contact constraints is as follows:

[0037]

[0038] In the formula, V(a) is a reduced-order Lyapunov function with contact constraints, Q is the two-field energy weight matrix, and a T The generalized coordinate vector after order reduction represents the modal coefficients of the temperature or stress field; R is the energy stability term. c The actual contact parameters include contact thermal resistance and geometric radius of curvature. P represents the contact parameters predicted by the reduced-order model. DEIM Let λ be the projection matrix, and λ be the regularization coefficient used to balance the weights of energy stability and contact constraints. For contact constraints, these are used to force the predicted contact parameters in the reduced-order model. Approximating the true value R at key interpolation points c .

[0039] Furthermore, the nonlinear system is a cylinder system or a nuclear reactor system.

[0040] The present invention also provides a super-order reduction prediction system for implementing the above-described thermo-mechanical coupling super-order reduction prediction method for multi-component assembled nonlinear systems, comprising:

[0041] The multi-physics data acquisition unit is used to integrate temperature sensors, strain gauges and contact thermal resistance measurement devices to acquire multi-scale physical field data of nonlinear systems, including temperature field data, stress field data and contact thermal resistance data.

[0042] The intrinsic mode decoupling engine is used to construct the intrinsic orthogonal decomposition basis function space of the temperature field and stress field based on the temperature field data and stress field data, establish the dual-field coupling constraint equation, and manage the dynamic weighting factor.

[0043] The contact nonlinear modeling module is used to construct a parameterized proxy model of the contact thermal resistance of the cylinder contact area, bolt area and free deformation area based on the contact thermal resistance data and using the domain discrete empirical interpolation method.

[0044] A thermal shock rate adaptive controller is used to construct a parametric intrinsic mode tensor network for operating conditions from 0 to 600℃ based on the intrinsic orthogonal decomposition of the basis function space of the temperature field and stress field, as well as the discretized parameter values ​​of the contact thermal resistance data, to obtain a price reduction model. This price reduction model includes a multi-condition mode library and tensor mapping relationships.

[0045] The online prediction and verification unit includes a real-time parameter synchronizer, a transient response solver, and a residual feedback module. The real-time parameter synchronizer reconstructs modal basis functions in real time based on the acquired tensor slices, determining the intrinsic orthogonal decomposition modal basis and the domain-specific discrete empirical interpolation operator. The transient response solver performs dynamic inversion of the thermo-mechanical dual-field generalized coordinates based on the modal basis function reconstruction results from the online stage, adding contact constraints based on the contact parameter prediction results, and outputting the predicted transient displacement field, temperature gradient field, and contact stress field. The residual feedback module performs dynamic correction.

[0046] Furthermore, the online prediction and verification unit is deployed on an industrial edge computing node and connected to a multiphysics data acquisition unit via a high-speed data bus.

[0047] Furthermore, the residual feedback module adaptively adjusts the interpolation point distribution of the contact thermal resistance data and the modal weighting coefficients of the temperature field and stress field based on the deviation between the measured data and the predicted results.

[0048] Compared with the prior art, the present invention has the following advantages:

[0049] (1) This invention addresses the nonlinear problem of multi-component contact by dividing the contact interface into a sealing groove area, a bolt preload area, and a free deformation area using the Domain Discrete Empirical Interpolation (DEIM) method. Feature sampling points are selected for each area, and a functional response surface model of the contact thermal resistance is constructed to achieve differentiated sampling modeling, thereby compressing the contact thermal resistance reconstruction error to below 5%. Compared with the traditional global dimensionality reduction method, the accuracy can be improved by 6.1 times. Furthermore, by combining the dual-field dynamic weight factor coordination technology, high-fidelity cross-field coupling and transmission of temperature gradient and mechanical deformation are achieved, with flange displacement prediction error ≤1.9mm and contact stress deviation ≤0.15MPa, reaching industrial-grade accuracy standards.

[0050] (2) This invention achieves significant breakthroughs in computational efficiency, modeling accuracy, working condition adaptability and engineering practicality by innovatively integrating thermo-mechanical dual-field intrinsic mode decoupling, domain-specific contact nonlinear modeling and parameterized mode library construction technologies. Compared with the traditional finite element method, the time for single transient thermo-mechanical coupling prediction is reduced from tens of hours to less than one or two hours, the computational efficiency is improved by more than 11 times, and the memory usage is reduced by 90%. It meets the real-time requirements of second-level online monitoring of high-temperature equipment and provides core technical means with high efficiency, accuracy and robustness for the intelligent operation and maintenance of high-end equipment such as aero-engines and nuclear reactors.

[0051] (3) The present invention realizes matrix compression optimization of the super-reduced order model of nonlinear system, requiring only ≤100MB of storage space, and can be efficiently deployed on embedded edge computing nodes (such as industrial GPU / FPGA), supporting real-time status perception and fault warning of high temperature components under complex working conditions. Attached Figure Description

[0052] Figure 1 This is a flowchart illustrating a thermo-mechanical coupling super-order reduction prediction method for a multi-component assembled nonlinear system provided in an embodiment of the present invention.

[0053] Figure 2 This is a schematic diagram of a steam turbine intermediate pressure cylinder component provided in an embodiment of the present invention;

[0054] Figure 3 This is a cylinder bolt sensor arrangement diagram provided in an embodiment of the present invention;

[0055] Figure 4 This is a schematic diagram comparing sensor data and super-order reduction calculation results under a certain working condition, provided in an embodiment of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0057] Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the invention.

[0058] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0059] Example 1

[0060] like Figure 1 As shown, this embodiment provides a thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system, including the following steps:

[0061] S1: Collect multi-scale physical field data of the nonlinear system, including temperature field data, stress field data and contact thermal resistance data;

[0062] S2: Based on temperature field data and stress field data, construct the eigenorthogonal decomposition (POD) basis function space of temperature field and stress field, and establish the dual-field coupling constraint equation;

[0063] S3: Based on contact thermal resistance data, a parameterized proxy model of contact thermal resistance for the cylinder contact area, bolt area and free deformation area is constructed using the domain discrete empirical interpolation method (DEIM).

[0064] S4: Based on the intrinsic orthogonal decomposition basis function space of temperature field and stress field, and the discretized parameter values ​​of contact thermal resistance data, construct a parametric intrinsic mode tensor network for 0-600℃ working conditions to obtain a price reduction model. This model is used in the online stage to realize real-time reconstruction of modal basis functions by acquiring tensor slices, and to determine the intrinsic orthogonal decomposition modal basis and the domain discrete empirical interpolation operator.

[0065] S5: Based on the modal basis function reconstruction results in the online stage, perform dynamic inversion of thermo-mechanical dual-field generalized coordinates, and add contact constraints based on the contact parameter prediction results to output the predicted transient displacement field, temperature gradient field and contact stress field.

[0066] S6: Obtain real-time parameters of multi-scale physical field data, calculate residuals with corresponding prediction results, and dynamically update the basis functions of temperature and stress fields and the interpolation point distribution of contact thermal resistance data.

[0067] In step S1, multi-fidelity data of microscale thermal resistance distribution at the contact interface (obtained through experimental measurement) and macroscopic temperature-stress field (obtained through numerical simulation) are acquired during the multi-scale physical field data processing.

[0068] In step S2, the two-field decoupling and order reduction includes constructing the temperature field POD basis function set {Φ T} and the stress field POD basis function set {Φ σ}, satisfying the orthogonality condition:

[0069]

[0070] In the formula, Let x be the i-th order POD basis function of the temperature field at position x. Let δ be the j-th order POD basis function of the temperature field at position x. ij Let be the Kronecker delta function, indicating that the basis functions are mutually orthogonal and normalized in the spatial domain Ω; Let x be the i-th order POD basis function of the stress field at position x. Let be the j-th order POD basis function of the stress field at position x.

[0071] The expression for the dual-field coupling constraint equation is:

[0072]

[0073] In the formula, Let α(T′) = tanh(βT′) be the two-field coupling matrix for the thermal stress change caused by temperature rise, and let C be the dynamic coupling factor. σT This represents the two-field coupling matrix for temperature field perturbation caused by stress variation. Let L be the rate of change of the generalized coordinate vectors of the temperature and stress fields (i.e., the reduced-order low-dimensional modal coefficients) with time. T and L σ Let C represent the linear evolution operator matrices of the temperature field and stress field, respectively, containing the physical processes within their respective fields (such as heat conduction, stress relaxation, etc.). Tσ and C σT This refers to the dynamic coupling effect between two fields, such as thermal stress (C) caused by temperature rise. Tσ or temperature field disturbances caused by stress changes (C) σT Its specific form includes nonlinear functions (such as the coupling strength of hyperbolic tangent function constraints).

[0074] In step S3, a parameterized proxy model for the contact thermal resistance of the cylinder contact area, bolt area, and free deformation area is constructed using the domain-discrete empirical interpolation method, specifically as follows:

[0075] For the cylinder contact area, Hermite polynomial interpolation is used to construct the contact thermal resistance gradient response surface, and the corresponding calculation expression is:

[0076]

[0077] In the formula, The sealing contact thermal resistance characterizes the reduction in heat conduction efficiency at the cylinder contact interface due to microscopic gaps or surface roughness; its value is related to the contact pressure gradient. and interface gap δ g Related. Let m be the Hermite polynomial basis functions, with pressure gradient as the basis. and gap δ g γ is the input variable. m The weighting coefficients of the polynomial expansion are calibrated using experimental data or high-fidelity simulations to reflect the contribution of each order of basis functions to the thermal resistance. H m The order of the polynomial truncation determines the balance between model complexity and computational efficiency; higher-order terms capture details, while lower-order terms ensure stability.

[0078] For the bolt zone, stress gradient clustering is used to select DEIM interpolation points, and the corresponding calculation expression is:

[0079]

[0080] In the formula, Let x be the set of locations in the bolt area selected as DEIM interpolation points. i These are the coordinates of a discrete point in space. Let be the spatial gradient of the von Mises stress, representing the rate of change of stress in space. η is a threshold coefficient (0 < η ≤ 1), used to control the range of interpolation points. The maximum value of the stress gradient norm in the entire computational domain.

[0081] For the free deformation region, a thermal resistance probability density response model is constructed using Latin hypercube sampling.

[0082] In step S4, the construction process of the parametric intrinsic mode tensor network includes:

[0083] The fourth-order parametric eigenmode tensor is constructed, and the corresponding computational expression is as follows:

[0084]

[0085] In the formula, For the fourth-order parametric eigenmode tensor, n T and n σ For the temperature field (Φ T ) and stress field (Φ σ The number of modes of the POD basis functions, i.e., the dimension after order reduction. R and n v Geometric parameters (such as radius of curvature R) c The number of sampling points for the discretization parameter of the temperature rise rate v. and Let i and j be the i-th and j-th order POD basis functions of the temperature and stress fields. and These are the values ​​of the kth and lth discretized geometric parameters and the temperature rise rate parameter.

[0086] Tucker decomposition is used for tensor compression to transform the fourth-order parametric eigenmode tensor. Decomposed into a core tensor The product of the four factor matrices is calculated using the following expression:

[0087]

[0088] In the formula, Includes tensors The main coupling feature, its dimension r T <<n T r σ <<n σ r R <<n R r v <<n v This represents the compressed low-rank structure. The rank of U is determined by optimization using alternating least squares (ALS) method. T U σ U R U v These are low-dimensional projection matrices corresponding to the temperature field, stress field, geometric parameters, and temperature rise rate, respectively.

[0089] In step S5, the dynamic inversion process includes constructing a reduced-order Lyapunov function with contact constraints and performing the evolution of the modal coefficients. The expression for the reduced-order Lyapunov function with contact constraints is:

[0090]

[0091] Where Q is the dual-field energy weight matrix, which is solved by... Determine the stable evolution step size. T The generalized coordinate vector after order reduction represents the modal coefficients of the temperature or stress field. This is the energy stabilization term, ensuring the stability of the system's dynamic evolution process through a quadratic energy function, which is the standard form of the classical Lyapunov function. R c Actual contact parameters, such as contact thermal resistance and geometric radius of curvature, must meet physical constraints. P represents the contact parameters predicted by the reduced-order model. DEIM λ is the projection matrix, used to select key interpolation points from the high-dimensional parameter space. λ is the regularization coefficient, balancing the weights of energy stability and contact constraints. This is a contact constraint term, its function is to force the contact parameters predicted by the reduced-order model. Approximating the true value R at key interpolation points c This avoids physical distortion caused by model order reduction.

[0092] Alternatively, the nonlinear system can be a cylinder system or a nuclear reactor system.

[0093] The following provides a specific implementation process for the above solution, including:

[0094] First, in the data acquisition phase, a distributed fiber optic grating sensor array is deployed circumferentially along the cylinder flange, and thermocouple sensors are simultaneously placed on each bolt to monitor the temperature gradient field in real time. Simultaneously, a microelectromechanical contact pressure sensor array is used to acquire the contact pressure distribution in the sealing groove area. Combined with a high-speed industrial camera, digital image correlation analysis (DIC) is performed to capture the sub-pixel-level micro-displacement field of the flange sealing surface, constructing a multiphysics spatiotemporal synchronous training dataset. In the offline modeling phase, intrinsic orthogonal decomposition (POD) is performed on the temperature and stress fields respectively, retaining the first 30 modal basis functions with an energy percentage ≥99.99%. For the nonlinear distribution of contact thermal resistance in the cylinder sealing groove area, the domain discrete empirical interpolation (DEIM) method is used to select 100 feature sampling points in the contact pressure gradient abrupt change region, constructing a Hermite polynomial response surface model. Simultaneously, in the bolt preload area... Based on the dynamic tracking of 12 key points according to the preload decay gradient, the contact thermal resistance dimension in the free deformation zone is reduced from 10,000 levels to 500 levels through Latin hypercube sampling (LHS). In the online prediction stage, the turbine outlet temperature signal is received in real time, and the optimal POD mode basis and DEIM operator are generated by interpolation from the pre-built parameterized mode library according to the current temperature rise rate. The temperature-stress dual-field transient response reconstruction is completed within 1 second using a GPU-accelerated matrix compression algorithm, and the flange radial displacement, sealing surface contact stress and temperature gradient distribution are output. In the closed-loop correction stage, the flange deformation is measured by a laser displacement meter and compared with the prediction results to generate a residual spectrum. When the residual exceeds the 1.9mm threshold, the DEIM sampling point adaptive migration algorithm is triggered to dynamically optimize the feature point distribution in the sealing groove area, and at the same time adjust the dual-field dynamic weight factor to ensure that the long-term prediction accuracy fluctuation of the model is ≤±0.1mm.

[0095] See Figure 2 It can be observed that the turbine cylinder consists of two parts, upper and lower, containing a large number of complex curved surfaces. In actual operation, due to excessive temperature and pressure, it is necessary to consider the nonlinearity of materials and contact. Therefore, it is very suitable for verifying the reliability of the present invention.

[0096] See Figure 3 It can be observed that sensors are evenly distributed on the split surface of the cylinder flange and at the contact point of the bolts and nuts, and high-frequency sampling is used to ensure that a large amount of real-time data is available for comparison with the prediction system of this invention.

[0097] See Figure 4 This is a comparison curve of the temperature data measured by a sensor in the cylinder system under a certain working condition and the calculation by the super-decrease system. It can be seen that the accuracy of the prediction system proposed in this patent fully meets the requirements of industrial grade.

[0098] Example 2

[0099] This embodiment provides a super-order reduction prediction system that implements the thermo-mechanical coupling super-order reduction prediction method for a multi-component assembled nonlinear system as described in Embodiment 1, comprising:

[0100] The multi-physics data acquisition unit is used to integrate temperature sensors, strain gauges and contact thermal resistance measurement devices to acquire multi-scale physical field data of nonlinear systems, including temperature field data, stress field data and contact thermal resistance data.

[0101] The intrinsic mode decoupling engine is used to construct the intrinsic orthogonal decomposition basis function space of temperature field and stress field based on temperature field data and stress field data, establish the dual-field coupling constraint equation, perform POD order reduction processing of thermal field and force field and manage dynamic weight factor;

[0102] The contact nonlinear modeling module is used to construct a parameterized proxy model of the contact thermal resistance of the cylinder contact area, bolt area and free deformation area based on contact thermal resistance data and using the domain discrete empirical interpolation method to achieve dimensionality reduction representation.

[0103] A thermal shock rate adaptive controller is used to construct a parametric intrinsic mode tensor network for operating conditions from 0 to 600℃ based on the intrinsic orthogonal decomposition of the basis function space of the temperature field and stress field, as well as the discretized parameter values ​​of the contact thermal resistance data, to obtain a price reduction model. This price reduction model includes a multi-condition mode library and tensor mapping relationships.

[0104] The online prediction and verification unit includes a real-time parameter synchronizer, a transient response solver, and a residual feedback module. The real-time parameter synchronizer reconstructs modal basis functions in real time based on the acquired tensor slices, determining the intrinsic orthogonal decomposition modal basis and the domain-specific discrete empirical interpolation operator. The transient response solver performs dynamic inversion of the thermo-mechanical dual-field generalized coordinates based on the modal basis function reconstruction results from the online stage, adding contact constraints based on the contact parameter prediction results, and outputting the predicted transient displacement field, temperature gradient field, and contact stress field. The residual feedback module performs dynamic correction.

[0105] Specifically, the residual feedback module adaptively adjusts the interpolation point distribution of the contact thermal resistance data and the modal weighting coefficients of the temperature field and stress field based on the deviation between the measured data and the prediction results, ensuring that the prediction error is ≤1.9mm.

[0106] Preferably, the online prediction and verification unit is deployed on an industrial edge computing node and connected to a multiphysics data acquisition unit via a high-speed data bus.

[0107] The preferred embodiments of the present invention have been described in detail above. It should be understood that those skilled in the art can make numerous modifications and variations based on the concept of the present invention without creative effort. Therefore, all technical solutions that can be obtained by those skilled in the art based on the concept of the present invention through logical analysis, reasoning, or limited experimentation on the basis of existing technology should be within the scope of protection defined by the claims.

Claims

1. A method for thermal coupling reduced order prediction of multi-component assembled nonlinear systems, characterized in that, Includes the following steps: Collect multi-scale physical field data of nonlinear systems, including temperature field data, stress field data, and contact thermal resistance data; Based on the temperature field data and stress field data, an eigenorthogonal decomposition basis function space of the temperature field and stress field is constructed, and a dual-field coupling constraint equation is established. Based on the contact thermal resistance data, a parameterized proxy model of the contact thermal resistance of the cylinder contact area, bolt area and free deformation area is constructed by using the domain discrete empirical interpolation method. Based on the intrinsic orthogonal decomposition basis function space of temperature field and stress field, and the discretized parameter values ​​of contact thermal resistance data, a parametric intrinsic mode tensor network for 0-600℃ working conditions is constructed to obtain a reduced-order model. This model is used in the online stage to realize real-time reconstruction of modal basis functions by acquiring tensor slices, and to determine the intrinsic orthogonal decomposition modal basis and the domain discrete empirical interpolation operator. Based on the modal basis function reconstruction results in the online stage, dynamic inversion of thermo-mechanical dual-field generalized coordinates is performed, and contact constraints based on the contact parameter prediction results are added to output the predicted transient displacement field, temperature gradient field and contact stress field. The system acquires real-time parameters from multi-scale physical field data and calculates residuals with the corresponding prediction results to dynamically update the basis functions of the temperature and stress fields and the interpolation point distribution of the contact thermal resistance data.

2. The thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system according to claim 1, characterized in that, The method employs a domain-discrete empirical interpolation to construct a parameterized proxy model for the contact thermal resistance of the cylinder contact area, bolt area, and free deformation area. Specifically: For the cylinder contact area, Hermite polynomial interpolation is used to construct the contact thermal resistance gradient response surface, and the corresponding calculation expression is: In the formula, The sealing contact thermal resistance at the cylinder contact interface. Let m be the Hermite polynomial basis functions, with pressure gradient as the basis. and gap δ g H is the input variable. m γ is the polynomial truncation order, M is the total order, and γ m The weighting coefficients are the polynomial expansion coefficients. For the bolt zone, stress gradient clustering is used to select DEIM interpolation points, and the corresponding calculation expression is: In the formula, Let x be the set of locations in the bolt area selected as DEIM interpolation points. i These are the coordinates of a discrete point in space. For x i The von Mises stress spatial gradient at a point, where η is a threshold coefficient used to control the range of interpolation points. This represents the maximum value of the stress gradient norm across the entire computational domain. For the free deformation region, a thermal resistance probability density response model is constructed using Latin hypercube sampling.

3. The thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system according to claim 1, characterized in that, The basis function sets of the temperature field and stress field satisfy the orthogonality condition, which is expressed as follows: In the formula, Let x be the i-th order POD basis function of the temperature field at position x. Let δ be the j-th order POD basis function of the temperature field at position x. ij Let be the Kronecker delta function, indicating that the basis functions are mutually orthogonal and normalized in the spatial domain Ω; Let x be the i-th order POD basis function of the stress field at position x. Let be the j-th order POD basis function of the stress field at position x.

4. The thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system according to claim 1, characterized in that, The expression for the dual-field coupling constraint equation is as follows: In the formula, Let α(T′) = tanh(βT′) be the two-field coupling matrix for the thermal stress change caused by temperature rise, and let C be the dynamic coupling factor. σT This represents the two-field coupling matrix for temperature field perturbation caused by stress variation. Let L be the rate of change of the generalized coordinate vectors of the temperature and stress fields with time. T and L σ Let C represent the linear evolution operator matrices of the temperature field and the stress field, respectively. Tσ and C σT This represents the dynamic coupling effect between the two fields.

5. The thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system according to claim 1, characterized in that, The construction process of the parametric intrinsic mode tensor network includes: The fourth-order parametric eigenmode tensor is constructed, and the corresponding computational expression is as follows: In the formula, For the fourth-order parametric eigenmode tensor, n T and n σ Let n be the number of POD basis function modes for the temperature and stress fields. R and n v Let the radius of curvature be R. c The number of sampling points for the discretization parameter of the temperature rise rate v, Let be the i-th order POD basis function of the temperature field. Let J be the j-th order POD basis function of the stress field. Let v be the value of the k-th discretized geometric parameter. (l) This is the value of the temperature rise rate parameter for the l-th discretized parameter. Tucker decomposition is used for tensor compression to transform the fourth-order parametric eigenmode tensor. Decomposed into a core tensor The product of the four factor matrices is calculated using the following expression: In the formula, Includes tensors The main coupling characteristics, The rank of U is determined by optimization using alternating least squares method. T U σ U R U v These are low-dimensional projection matrices corresponding to the temperature field, stress field, geometric parameters, and temperature rise rate, respectively.

6. The thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system according to claim 1, characterized in that, The dynamic inversion process includes constructing a reduced-order Lyapunov function with contact constraints and performing modal coefficient evolution. The expression for the reduced-order Lyapunov function with contact constraints is as follows: In the formula, V(a) is a reduced-order Lyapunov function with contact constraints, Q is the two-field energy weight matrix, and a T The generalized coordinate vector after order reduction represents the modal coefficients of the temperature or stress field; R is the energy stability term. c The actual contact parameters include contact thermal resistance and geometric radius of curvature. P represents the contact parameters predicted by the reduced-order model. DEIM Let λ be the projection matrix, and λ be the regularization coefficient used to balance the weights of energy stability and contact constraints. For contact constraints, these are used to force the predicted contact parameters in the reduced-order model. Approximating the true value R at key interpolation points c .

7. The thermo-mechanical coupling super-decrease prediction method for a multi-component assembled nonlinear system according to claim 1, characterized in that, The nonlinear system is a cylinder system or a nuclear reactor system.

8. A super-order reduction prediction system for implementing the thermo-mechanical coupling super-order reduction prediction method for a multi-component assembled nonlinear system as described in any one of claims 1-7, characterized in that, include: The multi-physics data acquisition unit is used to integrate temperature sensors, strain gauges and contact thermal resistance measurement devices to acquire multi-scale physical field data of nonlinear systems, including temperature field data, stress field data and contact thermal resistance data. The intrinsic mode decoupling engine is used to construct the intrinsic orthogonal decomposition basis function space of the temperature field and stress field based on the temperature field data and stress field data, establish the dual-field coupling constraint equation, and manage the dynamic weighting factor. The contact nonlinear modeling module is used to construct a parameterized proxy model of the contact thermal resistance of the cylinder contact area, bolt area and free deformation area based on the contact thermal resistance data and using the domain discrete empirical interpolation method. A thermal shock rate adaptive controller is used to construct a parametric intrinsic mode tensor network for 0-600℃ operating conditions based on the intrinsic orthogonal decomposition basis function space of temperature field and stress field, and the discretized parameter values ​​of contact thermal resistance data, to obtain a reduced-order model. This reduced-order model includes a multi-condition mode library and tensor mapping relationship. The online prediction and verification unit includes a real-time parameter synchronizer, a transient response solver, and a residual feedback module. The real-time parameter synchronizer reconstructs the modal basis functions in real time based on the acquired tensor slices, and determines the intrinsic orthogonal decomposition modal basis and the domain discrete empirical interpolation operator. The transient response solver performs dynamic inversion of the thermo-mechanical dual-field generalized coordinates based on the modal basis function reconstruction results in the online stage, and adds contact constraints based on the contact parameter prediction results to output the predicted transient displacement field, temperature gradient field and contact stress field; dynamic correction is performed through the residual feedback module.

9. The system according to claim 8, characterized in that, The online prediction and verification unit is located at an industrial edge computing node and is connected to a multiphysics data acquisition unit via a high-speed data bus.

10. The system according to claim 8, characterized in that, The residual feedback module adaptively adjusts the interpolation point distribution of the contact thermal resistance data and the modal weighting coefficients of the temperature field and stress field based on the deviation between the measured data and the predicted results.

Images