An overall blade disc active mistuning optimization method based on agent model optimization

Abstract

This invention discloses an active detuning optimization method for integral bladed disks based on a surrogate model, belonging to the field of aero-engine and turbomachinery structural dynamics. First, a high-fidelity finite element model of the integral bladed disk is established. For vibration problems caused by random detuning, four active detuning stiffness distribution methods—alternating, continuous gradient, periodic step, and spatial harmonic—are selected for study. Under the same random detuning condition, the area difference between the curves formed by active detuning and the 95% amplitude amplification factor of random detuning is used as an indicator to evaluate the vibration reduction effect. Based on this, initial samples are obtained using Latin hypercube sampling, and a Kriging surrogate model is constructed to optimize the results. This invention can find the optimal combination of active detuning parameters for different excitation orders, reduce the amplitude amplification factor of the system, and improve the fatigue life and operational safety of the integral bladed disk structure.

Description

Technical Field

[0001] This invention relates to the field of structural vibration control, and more specifically to an active detuning method for an integral bladed disk based on surrogate model optimization. Background Technology

[0002] Aero engines and gas turbines are core power plants in modern industry. Integral bladed disks (IBDs) are widely used as key rotor components in next-generation compressors and turbines. IBDs integrate the blades and disk into a single unit, completely eliminating the tenon-mortise connection interface. While this integrated manufacturing significantly reduces rotor weight and improves aerodynamic efficiency, it also leads to a significant reduction in the system's structural friction damping. In an ideal design, IBDs exhibit perfect cyclic symmetry, with external excitation energy evenly distributed across all sectors. However, in actual manufacturing, factors such as machining tolerances, material micro-inhomogeneities, and operational wear inevitably cause slight random differences in the physical parameters of each blade, known as "random detuning." Due to the extremely low damping and extremely high modal density of IBDs, even minute random detuning can trigger drastic changes in the system's dynamic characteristics, causing vibration energy to concentrate highly on individual blades, leading to "vibration localization." This can easily cause high-cycle fatigue cracks and ultimately fracture failure, seriously threatening the operational safety of aircraft.

[0003] To overcome the harm of vibration localization caused by random mistuning, the engineering community has proposed active mistuning technology. This technology artificially and systematically introduces specific structural parameter differences within the design tolerances to construct a deterministic asymmetric field in the circumferential space of the entire bladed disk. This artificially introduced macroscopic mistuning can disrupt the malignant localization modes excited by random mistuning, sever the vibration energy coupling channels between adjacent blades, and force a redistribution of vibration energy.

[0004] Despite the significant vibration reduction potential of active mistuning, its design and optimization still face numerous technical bottlenecks in practical engineering. Existing active mistuning design methods largely rely on empirical trial and error, often limited to extremely simple modes such as alternating mistuning, lacking a systematic comparison scheme encompassing multi-dimensional continuous and discrete spaces. This makes it difficult to match the optimal topology to the complex excitation order of the engine. Furthermore, existing vibration reduction effect evaluations are mostly based on calculating the amplitude amplification factor limit value based on a given random mistuning intensity. However, actual manufacturing errors span a wide statistical range, and single-point limit evaluations cannot reflect the global robustness of the scheme across the entire error tolerance band, easily leading to overfitting of the optimization results to specific errors. In addition, the integral bladed disk system has a large degree of freedom, requiring repeated solutions to the system dynamics equations when using the Monte Carlo method to evaluate the statistical characteristics of mistuning. Therefore, it is necessary to propose an efficient method for optimizing the active mistuning parameters of integral bladed disks. Summary of the Invention

[0005] To avoid the problems existing in the prior art, this invention provides an active detuning optimization method for integral bladed disks based on surrogate model optimization. This method finds the optimal combination of active detuning parameters for different excitation orders, reduces the amplitude amplification factor of the system, and improves the fatigue life and operational safety of the integral bladed disk structure.

[0006] To achieve its objectives, the present invention employs the following technical solution: The present invention features an active mistuning optimization method for integral bladed disks based on a surrogate model. It establishes a high-fidelity finite element model of the integral bladed disk and analyzes the vibration problem caused by random mistuning using four active mistuning stiffness distribution methods: alternating type, continuous gradient type, periodic step type, and spatial harmonic type. Under the same random mistuning condition, initial samples are obtained by Latin hypercube sampling of active and random mistuning, and a Kriging surrogate model is constructed to optimize the results, thereby achieving optimization of the active mistuning mode of the integral bladed disk based on the surrogate model.

[0007] The present invention provides an active mistuning optimization method for the overall bladed disk based on a surrogate model, comprising the following steps: Step 1: Construct a high-fidelity finite element model and select the active mistuning mode: To address the random detuning problem in integral bladed disk (IBD) structures, active detuning is introduced into the blades to suppress vibration localization caused by random detuning. For the optimization of active detuning modes, two high-fidelity finite element (FEM) models of the IBD structure are constructed. The first FEM model integrates the random detuning mode solely in the form of equivalent elastic modulus, while the second FEM model integrates both active and random detuning modes simultaneously in the form of equivalent elastic modulus. For the active detuning modes, four modes are selected: alternating, continuous gradient, periodic step, and harmonic modes. This completes the construction of the high-fidelity finite element model and the selection of the active detuning modes. Step 2: Select the optimization objective and optimization variables: A mathematical model for optimizing the active mistuning mode of the overall bladed disk is constructed, and the standard deviation in the mathematical model is defined. The statistical interval is: ,in The upper limit of the standard deviation statistical interval is defined as the standard deviation used to characterize the overall dispersion of blade manufacturing errors. The standard deviation is selected within this statistical interval. A discrete standard deviation evaluation point, At each standard deviation evaluation point, random detuning samples are generated using the Monte Carlo method. These random detuning samples are then substituted into two high-fidelity models for dynamic solution to obtain two maximum response values. These two maximum response values ​​are: the maximum response value under the pure random detuning condition and the maximum response value under the combined effect of random detuning and active detuning. For each of these two maximum response values, the ratio of their values ​​to the maximum harmonic response value is calculated to obtain two amplitude amplification factors. The dynamic solution process is set as follows: input the random detuning sample into the first high-fidelity finite element model and solve for the amplitude amplification factor under the pure random detuning condition; input the same random detuning sample and the current active detuning quantity into the second high-fidelity finite element model and solve for the amplitude amplification factor under the combined action of random detuning and active detuning. Arrange the two amplitude amplification factors in ascending order and select 95. The values ​​at the quantiles are plotted to obtain the 95% pure random detuning. Amplitude amplification factor curve and active mistuning 95 Amplitude amplification factor curve ; Selecting area difference As the optimization objective, the area difference It is the integral bounded by the two curves obtained by equation (1), and the active mistuning of each blade is selected as the optimization variable: (1); This completes the selection of the optimization objective and optimization variables; Step 3: Construct the initial Kriging agent model For the optimization objective and optimization variables determined in step 2, the Latin hypercube sampling algorithm is used to generate... Given an initial sample set, each sample is substituted into the dynamic solution process described in step 2 for calculation to obtain the optimization objective value corresponding to each sample point. From the above Selecting from the initial sample set Construct a training sample set from the samples, and then use the remaining samples... A test sample set is constructed using a set of training samples; an initial Kriging surrogate model is constructed using the training sample set, which employs an adaptive sampling criterion combined with a surrogate model minimization prediction criterion; the initial Kriging surrogate model is used to construct the mapping relationship between the optimization variables and the optimization objective, and the variation range of the optimization variables is limited to a certain value. Thus, the initial Kriging proxy model for the optimization of the overall bladed disk active mistuning mode was constructed. Step 4: Train and update the Kriging agent model to complete the optimization of the overall bladed disk active detuning mode.

[0008] The characteristic of the overall bladed disk active detuning optimization method based on the surrogate model optimization of this invention is that step 4 involves training and updating the Kriging surrogate model in the following manner to complete the optimization of the overall bladed disk active detuning mode: The initial Kriging proxy model described in step 3 is trained, a maximum number of iterations is set, and the coefficient of determination is calculated. Only when detected Output the current initial Kriging proxy model; then, substitute the four active detuning modes selected in step 1 into the current initial Kriging proxy model for synchronous evaluation and horizontal comparison; on the high-density continuous grid generated by the initial Kriging proxy model, search for the candidate optimal active detuning parameters that maximize the optimization objective value. To improve prediction accuracy, the candidate optimal active mistuning parameters are substituted into the dynamic solution process described in step 2 for high-fidelity calculation to obtain the accurate value of the optimization target. The accurate value of the optimization target is then added to the training sample set as a new sample point to reconstruct and update the Kriging surrogate model. Optimization iterations are performed until the difference between the optimal values ​​obtained from two adjacent iterations reaches the set minimum convergence boundary. Finally, the optimal active mistuning mode after comparison and selection of the four active mistuning modes is output, along with the optimal active mistuning parameter combination for each active mistuning mode under different excitation orders. This completes the optimization of the overall bladed disk active mistuning mode.

[0009] The active detuning modes in the overall bladed disk active detuning optimization method based on the surrogate model in this invention are as follows: Mode 1: Alternating active detuning: The natural frequencies of the odd and even blades exhibit a step distribution, characterized by equation (2): (2); In formula (2): To introduce the natural frequency after active detuning; This is the original inherent frequency; , The detuning coefficient; Number the blades. The total number of blades, of which ; Mode 2: Continuous gradient active detuning: The blade's natural frequency exhibits a gradient distribution, characterized by equation (3): (3); In formula (3): To introduce the natural frequency after active detuning; The minimum detuning coefficient is set. The maximum detuning coefficient is set. ; Mode 3: Periodic Step-Type Active Detuning: with One blade constitutes one cycle, and in each cycle... One design variable, Dimensional design variables Assign values ​​to each cycle respectively One leaf; for Each blade has a corresponding detuning coefficient; Mode 4: Harmonic-type active detuning: The blade's natural frequency exhibits spatial sinusoidal fluctuations, characterized by equation (4): (4); In equation (4): To introduce the natural frequency after active detuning; This is the original inherent frequency; This is the detuning coefficient.

[0010] The principle of active detuning vibration reduction is to artificially introduce regular stiffness differences within the overall bladed disk, actively disrupting structural symmetry and redistributing the energy generated by vibration. This avoids energy concentration in a single blade, thereby reducing the maximum amplitude of the blade. To achieve the best vibration reduction effect, this invention combines a surrogate model to systematically optimize the active detuning mode and its parameters. Compared with existing technologies, this invention has at least the following beneficial effects: 1. This invention addresses the problem of vibration localization caused by random detuning in integral bladed disks (IBDs). It introduces a regular active detuning stiffness distribution within the blades and optimizes and compares alternating, continuous gradient, periodic step, and spatial harmonic active detuning modes to obtain the optimal active detuning parameter combination for different excitation orders. By actively controlling the circumferential stiffness distribution of the IBD, vibration energy is redistributed among the blades, reducing the peak response and amplitude amplification factor of individual blades under random detuning conditions. This weakens vibration localization and improves the fatigue life and operational safety of the IBD structure. 2. This invention uses the area difference between the pure random detuning 95 amplitude amplification factor curve and the active detuning 95 amplitude amplification factor curve as the optimization target, instead of using only the extreme response under a single random detuning intensity as the evaluation basis. This area difference can reflect the overall vibration reduction effect of the active detuning scheme within the entire random detuning standard deviation statistical interval, avoiding the optimization results being effective only for a specific random detuning level, and is more in line with actual processing conditions; 3. This invention employs Latin hypercube sampling to construct an initial sample set and utilizes a Kriging surrogate model to establish a mapping relationship between active mistuning design variables and optimization objectives. Active mistuning parameter optimization and horizontal comparison of various active mistuning modes are then performed on the surrogate model. This method reduces the number of times high-fidelity finite element models and Monte Carlo methods are used for iterative dynamic solutions, lowers the computational cost of the overall bladed disk active mistuning optimization process, improves parameter search efficiency, and facilitates the rapid acquisition of feasible active mistuning design schemes under different excitation orders and active mistuning modes. Attached Figure Description

[0011] Figure 1 This is an overall flowchart of the method for optimizing the active mistuning mode of an integral bladed disk according to the present invention.

[0012] Figure 2 This invention relates to 95% random detuning and active detuning. Comparison of amplitude amplification factor curves.

[0013] Figure 3 This is the high-fidelity response surface output by the Kriging model optimization of the alternating active detuning in this invention.

[0014] Figure 4 This is a high-altitude line optimization positioning diagram for the present invention. Detailed Implementation

[0015] like Figure 1 The diagram shows the flowchart of the active detuning optimization method for the overall bladed disk based on the surrogate model of the present invention.

[0016] To address the random detuning problem in integral bladed disk (IBD) structures caused by factors such as manufacturing tolerances, material micro-inhomogeneities, or operational wear, active detuning is introduced into the blades to suppress vibration localization. Random detuning refers to the random differences between blades in an IBD structure. Active detuning involves artificially introducing regular active detuning during the design and manufacturing of the IBD. By actively disrupting the cyclic symmetry of the IBD structure, the energy generated by vibration is redistributed, preventing energy concentration in a single blade and thus reducing the maximum amplitude of the blade. The active detuning mode is crucial to the vibration reduction effect; among a vast number of active detuning modes, optimization is necessary to obtain the optimal active detuning mode.

[0017] In this embodiment, the active detuning optimization method for the integral bladed disk based on the surrogate model is to establish a high-fidelity finite element model of the integral bladed disk. For the vibration problem caused by random detuning, four active detuning stiffness distribution methods—alternating, continuous gradient, periodic step, and spatial harmonic—are selected for analysis. Under the same random detuning condition, the area difference between the 95% amplitude amplification factor curves of active and random detuning is used as the optimization objective to evaluate the vibration reduction effect. Initial samples are obtained using Latin hypercube sampling, and a Kriging surrogate model is constructed to optimize the results, thereby achieving optimization of the active detuning mode of the integral bladed disk based on the surrogate model. This method, considering the statistical characteristics of random detuning, provides a unified evaluation and horizontal comparison of different active detuning modes, and obtains active detuning parameter combinations suitable for different excitation orders while reducing the cost of repetitive high-fidelity dynamic calculations.

[0018] The active mistuning optimization method for the overall bladed disk based on the surrogate model in this embodiment includes the following steps: Step 1: Construct a high-fidelity finite element model and select the active mistuning mode: To address the random detuning problem in integral bladed disk (IBD) structures, active detuning is introduced into the blades to suppress vibration localization caused by random detuning. For the optimization of the active detuning mode, two high-fidelity finite element (FEM) models of the IBD structure are constructed. The first FEM model integrates the random detuning mode separately using the equivalent elastic modulus, while the second FEM model integrates both the active and random detuning modes simultaneously using the equivalent elastic modulus. Both models use the same random detuning samples for calculation, ensuring comparability of results before and after active detuning.

[0019] The equivalent elastic modulus is used to characterize detuning because the changes in the blade's natural frequency and stiffness can be equivalently described by changes in the elastic modulus. In the finite element model, by changing the equivalent elastic modulus of different blades, the stiffness or natural frequency of each blade can be differentiated, thereby simulating the effects of random and active detuning on the overall bladed disk dynamic response. This approach facilitates the introduction of different detuning modes into high-fidelity finite element models while maintaining consistency in model structure and solution process.

[0020] To cover different forms of circumferential stiffness distribution, this embodiment presupposes four active mistuning modes: alternating, continuous gradient, periodic step, and spatial harmonic. Alternating active mistuning creates an alternating distribution of stiffness differences between odd and even blades; continuous gradient active mistuning creates a gradually changing stiffness difference along the circumference; periodic step active mistuning creates a periodically repeating step-like stiffness distribution; and spatial harmonic active mistuning creates a stiffness distribution that varies according to spatial harmonic laws. By simultaneously examining all four active mistuning modes, the design space limitations caused by relying on a single active mistuning law can be avoided, which is beneficial for obtaining more suitable combinations of active mistuning parameters under different excitation orders.

[0021] Step 2: Select the optimization objective and optimization variables: Construct a mathematical model for optimizing the active mistuning mode of the overall bladed disk, and define the standard deviation in the mathematical model. The statistical interval is: ,in The upper limit of the standard deviation statistical interval is used to characterize the overall dispersion of blade manufacturing errors. The standard deviation is selected within the statistical interval. A discrete standard deviation evaluation point, Considering the highly random nature of the detuning mode, at each standard deviation evaluation point, a random detuning sample is generated using the Monte Carlo method. The random detuning sample is then substituted into two high-fidelity models for dynamic solution to obtain two maximum response values. These two maximum response values ​​are: the maximum response value under the pure random detuning condition and the maximum response value under the combined effect of random detuning and active detuning. For each of the two maximum response values, the ratio of its value to the maximum harmonic response value is calculated to obtain two amplitude amplification factors.

[0022] The dynamic solution process is set as follows: input the random detuning sample into the first high-fidelity finite element model and solve for the amplitude amplification factor under the pure random detuning condition; input the same random detuning sample and the current active detuning quantity into the second high-fidelity finite element model and solve for the amplitude amplification factor under the combined action of random detuning and active detuning.

[0023] In practice, the standard deviation is used to describe the overall dispersion of blade manufacturing errors or structural parameter deviations. A larger standard deviation indicates more significant random differences between blades, and a higher risk of vibration localization in the overall bladed disk. To ensure that the optimization results are applicable not only to a fixed random mistuning intensity but also to a range of manufacturing errors, this embodiment sets multiple discrete evaluation points within the standard deviation statistical interval. For each standard deviation evaluation point, a Monte Carlo method is used to generate multiple random mistuning samples to simulate various random error distributions that may occur during actual manufacturing.

[0024] For each random detuning sample, two types of dynamic solutions are performed. The first type is for the pure random detuning case, which only considers random detuning caused by manufacturing errors, and is used to obtain the system vibration response without the introduction of active detuning. The second type is for the combined effect of random and active detuning, which superimposes the current active detuning parameters on the same random detuning sample, and is used to obtain the system vibration response after the active detuning. For both types of cases, the ratio of the maximum response value to the maximum harmonic response value is calculated, and this ratio is defined as the amplitude amplification factor. The larger the amplitude amplification factor, the more significant the response amplification caused by random detuning; the smaller the amplitude amplification factor, the better the suppression effect of active detuning on vibration localization.

[0025] Arrange the two amplitude amplification factors in ascending order and select 95. The value at the quantile, such as Figure 2 As shown, the quantile values ​​of each evaluation point are connected sequentially to plot the pure random detuning 95. Amplitude amplification factor curve and active mistuning 95 Amplitude amplification factor curve .

[0026] Using 95 Quantiles, used as statistical evaluation values, aim to reflect the high response levels of most randomly mistuned samples while avoiding the excessive influence of a single extreme sample on the evaluation results. If only the maximum sample response is used as the evaluation criterion, the optimization results may be controlled by extreme random samples; if the average value is used, the fatigue risk brought by high-response samples may be underestimated. Therefore, 95%... The amplitude amplification factor can effectively characterize the degree of vibration amplification with a high confidence level under random detuning conditions.

[0027] Selecting area difference As the optimization objective, the area difference It is the integral bounded by the two curves obtained by equation (1), and the active mistuning of each blade is selected as the optimization variable: (1); This completes the selection of the optimization objective and optimization variables; Area difference refers to 95% of purely random detuning. Amplitude amplification factor curve and active detuning 95 The area difference between the amplitude amplification factor curves. The area difference characterizes the overall vibration reduction benefit of the active detuning scheme compared to the purely random detuning condition over the entire standard deviation statistical interval. If the amplitude amplification factor curve of 95% active detuning is generally lower than that of 95% pure random detuning... The amplitude amplification factor curve shows a large area difference, indicating that the active detuning scheme has a good vibration reduction effect under multiple manufacturing error levels. Compared with evaluating the amplitude amplification factor only at a single standard deviation point, using the area difference as the optimization target can more fully reflect the robustness of the active detuning scheme and avoid the optimization results being effective only for a specific random detuning intensity.

[0028] In this embodiment, the optimization variable is the active detuning amount of each blade. Depending on the active detuning mode, the optimization variable can be represented as the detuning coefficients of odd and even blades in alternating active detuning, the minimum and maximum detuning coefficients in continuous gradient active detuning, the detuning coefficients of each blade within a period in periodic step-type active detuning, or the harmonic amplitude and detuning coefficients in spatial harmonic active detuning. By changing the optimization variable, the overall circumferential stiffness distribution of the bladed disk can be altered, thereby affecting the distribution of vibration energy among the blades.

[0029] Step 3: Construct the initial Kriging agent model For the optimization objective and optimization variables determined in step 2, the Latin hypercube sampling algorithm is used to generate... Given an initial sample set, each sample is substituted into the dynamic solution process of step 2 for calculation to obtain the optimization objective value corresponding to each sample point. ;from Selecting from the initial sample set Construct a training sample set from the samples, and then use the remaining samples... A test sample set is constructed using a set of training samples. An initial Kriging surrogate model is then built using this training sample set. This initial Kriging surrogate model employs an adaptive sampling criterion combined with a surrogate model minimization prediction criterion. The initial Kriging surrogate model is used to construct the mapping relationship between the optimization variables and the optimization objective, and the variation range of the optimization variables is limited. Thus, the initial Kriging agent model for optimizing the overall bladed disk active mistuning mode was constructed.

[0030] In practice, if a high-fidelity finite element model combined with the Monte Carlo method is directly used for global optimization, a large number of random detuning samples need to be generated for each set of active detuning parameters at multiple standard deviation evaluation points, and the dynamics solution needs to be repeatedly performed, resulting in high computational costs. Therefore, this embodiment uses Latin hypercube sampling to generate an initial sample set, so that the samples are evenly distributed in the design variable space, thereby covering the main design area with a limited number of samples.

[0031] Limiting the range of variation of optimization variables ensures that the active detuning parameters remain within a reasonable range that is manufacturable, achievable, and does not compromise the basic structural performance. If the active detuning is too small, it will be difficult to effectively change the circumferential stiffness distribution, resulting in insignificant vibration reduction; if the active detuning is too large, it may cause the structural performance to deviate from design requirements and even introduce new dynamic risks. Therefore, setting a range for the variation of the active detuning during the surrogate model optimization process can improve the engineering feasibility of the optimization results.

[0032] Step 4: Train and update the Kriging agent model to complete the optimization of the overall bladed disk active detuning mode: Train the initial Kriging proxy model from step 3, set the maximum number of iterations, and calculate the coefficient of determination. Only when detected The initial Kriging surrogate model is output; subsequently, the four active detuning modes selected in step 1 are substituted into the initial Kriging surrogate model for simultaneous evaluation and cross-sectional comparison; for example... Figure 3 As shown, this is the high-fidelity spatial response surface output of the alternating active detuning after optimization using the aforementioned Kriging model. On the high-density continuous grid generated by the initial Kriging surrogate model, candidate optimal active detuning parameters that maximize the optimization objective value are searched; on the high-density continuous grid generated by the surrogate model, combined with... Figure 4 The contour line optimization positioning map shown is used to search for the optimal active detuning parameters that maximize the optimization target value.

[0033] To improve prediction accuracy, the candidate optimal active mistuning parameters are substituted into the dynamic solution process in step 2 for high-fidelity calculation to obtain the accurate value of the optimization target. The accurate value of the optimization target is added to the training sample set as a new sample point to reconstruct and update the Kriging surrogate model. The optimization iteration is carried out until the difference between the optimal values ​​obtained in two adjacent iterations reaches the set minimum convergence boundary. Finally, the optimal active mistuning mode after comparison and selection of four active mistuning modes is output, as well as the optimal active mistuning parameter combination of each active mistuning mode under different excitation orders. This completes the optimization of the overall bladed disk active mistuning mode.

[0034] The coefficient of determination is used to evaluate the fit and prediction accuracy of the Kriging surrogate model to the sample data. When the coefficient of determination meets the set requirements, it indicates that the current surrogate model can reflect the relationship between the active detuning design variables and the optimization objective well, and can be used for subsequent parameter search. Due to the limited number of initial sample points, the initial Kriging surrogate model may still have prediction errors near the optimal region. Therefore, in this embodiment, the candidate optimal active detuning parameters are re-substituted into the dynamic solution process described in step 2 for high-fidelity calculation to obtain the accurate value of the optimization objective, and this accurate value is added to the training sample set as a new sample point. By continuously supplementing high-fidelity samples near the optimal region, the prediction accuracy of the Kriging surrogate model in the key design region can be improved. The above training, search, high-fidelity correction, and model update process continues until the difference between the optimal values ​​obtained in two adjacent iterations reaches the set convergence boundary, thereby outputting a stable and reliable optimal combination of active detuning parameters.

[0035] In practical implementation, for the optimization problem of active mistuning mode, firstly, based on the specific model of the integral bladed disk, a high-fidelity finite element model of the integral bladed disk structure is constructed to obtain the total mass matrix of the system. and overall stiffness matrix Introducing the overall structural damping coefficient Excitation load The frequency domain vibration equation of the harmonic system is established as follows: ; in: The excitation angular frequency; Let be the system response vector. It is the imaginary unit.

[0036] The vibration response of the integral bladed disk in harmonic mode can be obtained using the frequency domain vibration equation expressed in the above formula. When designing for active detuning, it should be considered that in actual manufacturing, factors such as machining tolerances, material micro-inhomogeneity, or operational wear can affect the detuning modes and degrees of even integral bladed disks from the same batch. To obtain satisfactory results, this embodiment pre-sets four stiffness adjustment modes, namely: Mode 1: Alternating active detuning: The natural frequencies of the odd and even blades exhibit a step distribution, characterized by equation (2): (2); In formula (2): To introduce the natural frequency after active detuning; This is the original inherent frequency; , The detuning coefficient; Number the blades. The total number of blades, of which ; Mode 2: Continuous gradient active detuning: The blade's natural frequency exhibits a gradient distribution, characterized by equation (3): (3); In formula (3): To introduce the natural frequency after active detuning; The minimum detuning coefficient is set. The maximum detuning coefficient is set. ; Mode 3: Periodic Step-Type Active Detuning: with One blade constitutes one cycle, and in each cycle... One design variable, Dimensional design variables Assign values ​​to each cycle respectively One leaf; for Each blade has a corresponding detuning coefficient; Mode 4: Harmonic-type active detuning: The blade's natural frequency exhibits spatial sinusoidal fluctuations, characterized by equation (4): (4); In equation (4): To introduce the natural frequency after active detuning; This is the original inherent frequency; This is the detuning coefficient.

[0037] The invention ultimately outputs the optimal active detuning parameter combination for each of the four active detuning modes under different excitation orders, after comparison and selection. This robust optimization method effectively improves the vibration reduction performance of the overall bladed disk through active detuning.

Claims

1. A method for active mistuning optimization of a global bladed disk based on a surrogate model, characterized by establishing... A high-fidelity finite element model of the integral bladed disk is used to analyze the vibration problem caused by random detuning. Four active detuning stiffness distribution methods are selected: alternating type, continuous gradient type, periodic step type, and spatial harmonic type. Under the same random detuning condition, the initial samples are obtained by Latin hypercube sampling of active detuning and random detuning. A Kriging surrogate model is constructed to optimize the results, thereby realizing the optimization of the active detuning mode of the integral bladed disk based on the surrogate model.

2. The active mistuning optimization method for the overall bladed disk based on the surrogate model optimization according to claim 1, characterized in that, The method includes the following steps: Step 1: Construct a high-fidelity finite element model and select the active mistuning mode: To address the random detuning problem in integral bladed disk (IBD) structures, active detuning is introduced into the blades to suppress vibration localization caused by random detuning. For the optimization of active detuning modes, two high-fidelity finite element (FEM) models of the IBD structure are constructed. The first FEM model integrates the random detuning mode solely in the form of equivalent elastic modulus, while the second FEM model integrates both active and random detuning modes simultaneously in the form of equivalent elastic modulus. For the active detuning modes, four modes are selected: alternating, continuous gradient, periodic step, and harmonic modes. This completes the construction of the high-fidelity finite element model and the selection of the active detuning modes. Step 2: Select the optimization objective and optimization variables: A mathematical model for optimizing the active mistuning mode of the overall bladed disk is constructed, and the standard deviation in the mathematical model is defined. The statistical interval is: ,in The upper limit of the standard deviation statistical interval is defined as the standard deviation used to characterize the overall dispersion of blade manufacturing errors. The standard deviation is selected within this statistical interval. A discrete standard deviation evaluation point At each standard deviation evaluation point, random detuning samples are generated using the Monte Carlo method. These random detuning samples are then substituted into two high-fidelity models for dynamic solution to obtain two maximum response values. These two maximum response values ​​are: the maximum response value under the pure random detuning condition and the maximum response value under the combined effect of random detuning and active detuning. For each of these two maximum response values, the ratio of their values ​​to the maximum harmonic response value is calculated to obtain two amplitude amplification factors. The dynamic solution process is set as follows: input the random detuning sample into the first high-fidelity finite element model and solve for the amplitude amplification factor under the pure random detuning condition; input the same random detuning sample and the current active detuning quantity into the second high-fidelity finite element model and solve for the amplitude amplification factor under the combined action of random detuning and active detuning. Arrange the two amplitude amplification factors in ascending order and select 95. The values ​​at the quantiles are plotted to obtain the 95% pure random detuning. Amplitude amplification factor curve and active mistuning 95 Amplitude amplification factor curve ; Selecting area difference As the optimization objective, the area difference It is the integral bounded by the two curves obtained by equation (1), and the active mistuning of each blade is selected as the optimization variable: （1）； This completes the selection of the optimization objective and optimization variables; Step 3: Construct the initial Kriging agent model For the optimization objective and optimization variables determined in step 2, the Latin hypercube sampling algorithm is used to generate... Given an initial sample set, each sample is substituted into the dynamic solution process described in step 2 for calculation to obtain the optimization objective value corresponding to each sample point. From the above Selecting from the initial sample set Construct a training sample set from the samples, and then use the remaining samples... A test sample set is constructed using a set of training samples; an initial Kriging surrogate model is constructed using the training sample set, which employs an adaptive sampling criterion combined with a surrogate model minimization prediction criterion; the initial Kriging surrogate model is used to construct the mapping relationship between the optimization variables and the optimization objective, and the variation range of the optimization variables is limited to a certain value. Thus, the initial Kriging proxy model for the optimization of the overall bladed disk active mistuning mode was constructed. Step 4: Train and update the Kriging agent model to complete the optimization of the overall bladed disk active detuning mode.

3. The active mistuning optimization method for the overall bladed disk based on the surrogate model optimization according to claim 2, characterized in that: Step 4 involves training and updating the Kriging agent model as follows to optimize the overall bladed disk active detuning mode: The initial Kriging proxy model described in step 3 is trained, a maximum number of iterations is set, and the coefficient of determination is calculated. Only when detected Output the current initial Kriging proxy model; then, substitute the four active detuning modes selected in step 1 into the current initial Kriging proxy model for synchronous evaluation and horizontal comparison; on the high-density continuous grid generated by the initial Kriging proxy model, search for the candidate optimal active detuning parameters that maximize the optimization objective value. To improve prediction accuracy, the candidate optimal active mistuning parameters are substituted into the dynamic solution process described in step 2 for high-fidelity calculation to obtain the accurate value of the optimization target. The accurate value of the optimization target is then added to the training sample set as a new sample point to reconstruct and update the Kriging surrogate model. Optimization iterations are performed until the difference between the optimal values ​​obtained from two adjacent iterations reaches the set minimum convergence boundary. Finally, the optimal active mistuning mode after comparison and selection of the four active mistuning modes is output, along with the optimal active mistuning parameter combination for each active mistuning mode under different excitation orders. This completes the optimization of the overall bladed disk active mistuning mode.

4. The active mistuning optimization method for the overall bladed disk based on the surrogate model optimization according to claim 1, characterized in that... The active detuning modes are as follows: Mode 1: Alternating active detuning: The natural frequencies of odd and even blades exhibit a step distribution, characterized by equation (2): （2）； In formula (2): To introduce the natural frequency after active detuning; This is the original inherent frequency; , The detuning coefficient; Number the blades. The total number of blades, of which ; Mode 2: Continuous gradient active detuning: The blade's natural frequency exhibits a gradient distribution, characterized by equation (3): （3）； In formula (3): To introduce the natural frequency after active detuning; The minimum detuning coefficient is set. The maximum detuning coefficient is set. ; Mode 3: Periodic Step-Type Active Detuning: with One blade constitutes one cycle, and in each cycle... One design variable, Dimensional design variables Assign values ​​to each cycle respectively One leaf; for Each blade has a corresponding detuning coefficient; Mode 4: Harmonic-type active detuning: The blade's natural frequency exhibits spatial sinusoidal fluctuations, characterized by equation (4): （4）； In equation (4): To introduce the natural frequency after active detuning; This is the original inherent frequency; This is the detuning coefficient.

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