A series base filter optimization method based on variable fidelity proxy model

Abstract

The application discloses a series base filter optimization method based on a variable fidelity surrogate model and belongs to the technical field of aircraft control. The method of the application is as follows: 1, frequency band determination of an aircraft control system; 2, series trap model construction; 3, combination of design parameters of all candidate base filters into total optimization variables, minimization of a low-frequency phase lag with the introduction of a penalty weight as an optimization objective, and establishment of a series base filter optimization model with the amplitude in a target trap frequency band as a constraint condition; 4, establishment of a variable fidelity surrogate model corresponding to the series base filter optimization model; 5, in two-stage step optimization solving, the method is divided into a base filter enabling state screening stage and a local parameter optimization stage; compared with the prior art, the application realizes the determination of the measurement error of an elastic modal center frequency, the wide target trap frequency band and the pre-determination of the number and structure parameters of the series trap filter in the aircraft aerodynamic servo elasticity problem.

Description

Technical Field

[0001] This invention relates to a series basis filter optimization method based on a variable fidelity surrogate model, belonging to the field of aircraft control technology. Background Technology

[0002] As aircraft evolve towards lighter weight, higher aspect ratios, and greater maneuverability, the frequency of structural elastic vibrations gradually decreases. The coupling between rigid body motion and elastic vibrations becomes more pronounced, easily leading to aerodynamic servo-elastic coupling problems between aerodynamic loads, structural elasticity, flight control systems, and servo actuators. These problems reduce the stability margin of the aircraft control system and, in severe cases, may amplify elastic vibrations or even cause system instability.

[0003] For aerodynamic servo-elasticity problems, notch filters are commonly used in engineering to attenuate signals near the elastic vibration frequency. When the center frequency of the notch filter is close to the actual elastic vibration frequency, it can effectively suppress elastic vibration. However, during flight or experimental measurements, the center frequency of the elastic mode may deviate due to measurement errors, model errors, and changes in flight conditions, causing the notch center to be inconsistent with the actual vibration frequency, thus weakening the suppression effect. To cover the uncertain frequency band caused by the center frequency error, multiple notch filters are usually used in series. However, traditional methods often require pre-determining the number of filters in series; too few filters may not guarantee the suppression effect, while too many filters will increase the system order and introduce additional low-frequency phase lag.

[0004] Therefore, the measurement error of the center frequency of the elastic mode, the wide target notch frequency band, and the pre-determination of the number and structural parameters of the series notch filters in the aerodynamic servo elasticity problem of aircraft have become urgent problems to be solved. Summary of the Invention

[0005] The purpose of this invention is to address the technical problems in aerodynamic servo-elasticity problems of aircraft, such as measurement errors in the center frequency of elastic modes, a wide target notch frequency band, and the difficulty in pre-determining the number of cascaded notch filters. This invention proposes a cascaded basis filter optimization method based on a variable fidelity surrogate model. By optimizing the number and structural parameters of the cascaded notch filters, this method can automatically determine the final number of notch filters and their structural parameters, thereby minimizing phase lag in the low-frequency control band while meeting the elastic vibration suppression requirements of the target frequency band.

[0006] The objective of this invention is achieved through the following technical solution:

[0007] This invention discloses a method for optimizing a series basis filter based on a variable fidelity surrogate model, comprising the following steps:

[0008] Step 1: In determining the frequency band of the aircraft control system, based on the measured value of the center frequency of the aircraft's elastic modes. and measurement error range Determine the target notch band The low-frequency phase lag band for evaluating the low-frequency phase performance of the notch filter on the flight control system is determined based on the operating frequency band of the aircraft control system. ;

[0009] The target notch band is:

[0010]

[0011] Step 2: In the construction of the cascaded notch filter model, set the maximum number of candidate basis filters to [value missing]. The single fundamental filter is a second-order notch filter, and the structure is constructed using... A cascaded notch filter model composed of candidate basis filters; the total transfer function of the cascaded notch filter model. It is the product of the transfer functions of each candidate basis filter;

[0012] The transfer function of the candidate basis filter is expressed as:

[0013]

[0014] In the formula, For complex variables in Laplace transform, For the first The center angular frequency of each base filter For the first The zero-point damping ratio of each base filter, For the first The pole damping ratio of each base filter;

[0015] The overall transfer function of the cascaded notch filter model is:

[0016]

[0017] Step 3: In the construction of the series basis filter optimization model, the design parameters of all candidate basis filters are combined into the total optimization variable. The optimization objective is to minimize the low-frequency phase lag with the introduction of penalty weights, and the amplitude in the target notch band is used as the constraint condition to establish the series basis filter optimization model.

[0018] The design parameters for the candidate basis filter are:

[0019]

[0020] in, For the first The center frequency of each base notch filter satisfies ; For the first The theoretical notch depth parameters at the center frequency of each base notch filter satisfy the amplitude attenuation relationship. ;

[0021] The total optimization variable is:

[0022]

[0023] Where T is the transpose function;

[0024] The optimization objective is:

[0025]

[0026] in, For penalty weighting; This represents the actual number of filters activated. Indicator functions; Used to reduce in Frequency band phase lag, expressed as an objective function, is as follows:

[0027]

[0028] in, This refers to the notch filter weighting coefficient; It is a phase lag function;

[0029] To optimize variables; The phase of the series basis filter;

[0030] The constraint condition is: to impose conditional constraints on the amplitude of the series basis filter model;

[0031]

[0032] in, Preset notch depth; Used to meet the notch band Depth requirements;

[0033] The conditions and constraints include:

[0034] The center frequencies of each fundamental notch filter satisfy: ;in, These are the lower and upper bounds of the center frequency, respectively.

[0035] The pole damping ratios of each base notch filter satisfy: ;in, , These are the lower and upper bounds of the pole damping ratio, respectively.

[0036] The notch depth of each base notch filter satisfies: ;in, , These are the minimum and maximum values ​​of the notch depth of the notch filter, respectively.

[0037] The optimization model for the series basis filter is as follows:

[0038]

[0039] Step 4: In the construction of the variable fidelity proxy model, establish the variable fidelity proxy model corresponding to the series basis filter optimization model; for the target notch band and the low-frequency phase lag band, simultaneously select low-fidelity sparse frequency sampling points for rapid scheme evaluation and high-fidelity dense frequency sampling points for accurate verification, fit the deviation correction term of the high-fidelity and low-fidelity model responses through radial basis functions, and obtain the approximate expression of the high-fidelity objective function and constraint function in the form of additive correction;

[0040] The deviation correction term for the high-fidelity and low-fidelity model responses is:

[0041]

[0042] The objective function and constraint functions calculated by the low-fidelity model are respectively... , The objective function and constraint functions calculated by the high-fidelity model are as follows: , ;

[0043] The approximate expressions for the high-fidelity objective function and constraint function are as follows:

[0044]

[0045] in, , The deviation surrogate model is obtained by constructing the radial basis functions;

[0046] Step 5: The two-stage step-by-step optimization solution is divided into the base filter activation state screening stage and the local parameter optimization stage;

[0047] During the base filter activation state screening phase, based on the variable fidelity surrogate model, a global search is performed on all candidate base filter design variables using a genetic algorithm with penalty factor constraints. In this global search, the base notch depth parameter is used to... Combined basis filter enable threshold Perform base filter enable / delete status determination and filtering;

[0048] In the local parameter optimization stage, the effective branch subset of the base filter is optimized using a sequential quadratic programming algorithm.

[0049] Output the structure and parameters of a cascaded notch filter that meets the amplitude attenuation requirements of the target notch band and achieves a balance between minimizing low-frequency phase lag and optimizing the number of filters in use;

[0050] The activation and deactivation status of the base filter is determined as follows: when... At that time, the judgment of the first Each base filter is enabled; when At that time, the judgment of the first Each base filter is in the deletion state; when hour, That is, the zero-point damping ratio is equal to the pole damping ratio, the transfer function of the base filter is 1, which is equivalent to a bypass path and does not change the amplitude and phase characteristics of the system.

[0051] The genetic algorithm with the penalty factor constraint is as follows:

[0052]

[0053] in, This is the fitness evaluation function for the genetic algorithm. The penalty factor is used to implement a global search for the enabled combination of basis filters and optimize the center frequency, pole damping ratio, and notch depth of each enabled filter.

[0054] The quadratic programming algorithm is as follows: The center frequency of the enabled filter is determined using a sequential quadratic programming algorithm. Pole damping ratio and notch depth Perform continuous optimization; keep parameters fixed for filters that are not enabled;

[0055]

[0056] In the formula, The set of design variables corresponding to enabling the base filter;

[0057] Compared with existing technologies, it has the following beneficial effects:

[0058] 1. This invention solves the problem of changes in the dimension of optimization variables caused by changes in the number of cascaded notch filters by setting several candidate basis filters, and realizes adaptive selection and parameter optimization of cascaded notch filter structure;

[0059] 2. This invention considers both low-frequency phase lag and filter quantity penalty terms in the objective function, which can reduce unnecessary filter quantity and low-frequency phase impact while meeting the amplitude attenuation requirements of the target notch band.

[0060] 3. This invention reduces the number of frequency response calculations by using a variable fidelity proxy model, and combines genetic algorithms and sequential quadratic programming algorithms to balance global search capabilities and continuous parameter local refinement capabilities. Attached Figure Description

[0061] Figure 1 This is a flowchart of the series basis filter optimization method based on the variable fidelity proxy model of the present invention;

[0062] Figure 2 The amplitude and phase frequency response curves of the series base filter in an embodiment of the present invention are shown.

[0063] Figure 3 This is the amplitude characteristic curve of the target notch frequency band of the series base filter in an embodiment of the present invention;

[0064] Figure 4 The image shows the phase frequency response curve of the series base filter in the low-frequency lag band according to an embodiment of the present invention. Detailed Implementation

[0065] To better illustrate the purpose and advantages of this invention, the invention will be further described below with reference to the accompanying drawings and examples. It should be noted that the implementation of this invention is not limited to the following embodiments, and any modifications or alterations made to this invention will fall within the scope of protection of this invention.

[0066] Example

[0067] The workflow of this embodiment is as follows: First, based on the measured center frequency of the aircraft's elastic modes and its potential measurement error range, the target notch frequency band for vibration suppression is determined. Then, several candidate second-order notch filters are pre-set, each with three design parameters: center frequency, pole damping ratio, and notch depth. Next, the notch depth parameter controls whether the corresponding candidate filter actually participates in series filtering, making the unused candidate filter equivalent to a bypass state. This achieves automatic selection of the number of series notch filters without changing the dimensions of the optimization variables. Simultaneously, this invention aims to minimize the phase lag in the low-frequency control band, constrains the amplitude attenuation of the target notch frequency band to meet requirements, and introduces a filter quantity penalty term. It combines a variable fidelity surrogate model, a genetic algorithm, and a sequential quadratic programming algorithm to optimize the filter structure and parameters, improving solution efficiency and optimization accuracy. The workflow of the series basis filter optimization method based on the variable fidelity surrogate model of this invention is as follows: Figure 1 As shown.

[0068] The specific implementation steps of the series basis filter optimization method based on the variable fidelity surrogate model in this embodiment are as follows:

[0069] Step 1: Determine the target notch band and low-frequency phase lag band

[0070] Based on the measured center frequency of the aircraft's elastic modes and the possible range of measurement errors, the target notch band is determined. If the measured center frequency of the elastic modes is... The measurement error range is The target notch band is:

[0071]

[0072] In this embodiment, take , . The frequency band is used to cover frequency shifts caused by measurement errors or model errors in the center frequency of the elastic modality. Simultaneously, based on the operating frequency band of the control system, the low-frequency phase lag frequency band is determined as follows:

[0073]

[0074] This frequency band is used to evaluate the impact of notch filters on the low-frequency phase performance of flight control systems.

[0075] Step 2: Construct a candidate basis filter set and establish a cascaded notch filter model.

[0076] Step 2-1: Construct the basis filter set

[0077] Set the maximum number of candidate basis filters to In this embodiment, we take For a single fundamental filter, a second-order notch filter is selected. The transfer function of the basis filter is:

[0078]

[0079] In the formula, For complex variables in Laplace transform, For the first The center angular frequency of each base filter For the first The zero-point damping ratio of each base filter, For the first The pole damping ratio of each base filter.

[0080] Step 2-2: Establish the cascaded notch filter model

[0081] When setting With one base filter, the total cascaded notch filter transfer function is:

[0082]

[0083] Step 3: Establish the optimization model of the series basis filter

[0084] Step 3-1: Optimize variables for a single basis filter

[0085] In the At the center frequency of the fundamental filter, the amplitude attenuation is:

[0086]

[0087] In the formula, For the first The theoretical notch depth at the center frequency of each fundamental notch filter. Therefore, the design parameters for each fundamental filter are defined as follows:

[0088]

[0089] In the formula, For the first The center frequency of each base notch filter is calculated as follows: .

[0090] Step 3-2: Design variables for the series basis filter model

[0091] for The total design variables are: (1 base filter, 1 total design variable)

[0092]

[0093] Furthermore, the base filter enabling and deleting mechanism is achieved through... Simultaneously implement notch depth design and filter activation judgment. When At that time, the first Individual base filters are enabled; when At that time, it was believed that the first Each base filter is deleted, making ,at this time ,have:

[0094]

[0095] At this point, the filter is completely equivalent to a bypass, without changing the system amplitude and phase, and ensuring that the dimension of the optimization variables remains fixed. .in, The threshold for enabling the base filter is set in this embodiment. .

[0096] Step 3-3: Construct a series notch filter model and optimize the objective function

[0097] Calculate the optimization variables as follows When, the phase of the series basis filter Since negative phase corresponds to phase lag, phase lag is defined as:

[0098]

[0099] In the formula, Let be the maximum value function. Considering the worst-case phase lag in the low-frequency band and the overall average phase lag, the objective function is defined as:

[0100]

[0101] In the formula, Here is the notch weighting coefficient, taken as... , The larger the value, the more attention it indicates. The frequency point with the greatest phase lag; Smaller indicates greater attention The overall average phase lag is present. Furthermore, to prevent the optimizer from unduly enabling too many filters, a filter count penalty term is introduced:

[0102]

[0103] In the formula, To determine the penalty weight, take ; The actual number of filters used is expressed as:

[0104]

[0105] In the formula, The indicator function allows the optimizer to automatically determine the final number of notch filters to use, without requiring a pre-fixed number of filters.

[0106] Steps 3-4: Set constraints for the series basis filter model

[0107] The amplitude response of the cascaded basis filter model is calculated as follows:

[0108]

[0109] The amplitude constraint is:

[0110]

[0111] In the formula, To preset the notch depth, take -40dB

[0112] For the The center frequency of each fundamental notch filter should satisfy:

[0113]

[0114] In the formula, and For the first The lower and upper bounds of the center frequency of the notch filter are taken as follows: and .

[0115] For the The pole damping ratio of a base notch filter should satisfy:

[0116]

[0117] In the formula, and For the first The lower and upper bounds of the pole damping ratio of a notch filter are taken as follows: and .

[0118] For the The notch depth of each base notch filter should satisfy the following:

[0119]

[0120] In the formula, and For the first The minimum and maximum notch depths of each notch filter are taken as... and .

[0121] Steps 3-5: Optimization Model of Series Basis Filter

[0122] Based on steps 3-1 to 3-4, the optimization model for the cascaded basis filter can be written as follows:

[0123]

[0124] Step 4: Construct a series basis filter optimization model and a strain fidelity surrogate model

[0125] Step 4-1: Selection of sampling points for the variable fidelity model

[0126] The low-fidelity model uses fewer frequency sampling points for rapid design evaluation; the high-fidelity model uses denser frequency sampling points for accurate design verification. In this embodiment, the low-fidelity model uses the following frequency grid:

[0127]

[0128] The high-fidelity model uses the following grid frequency:

[0129]

[0130] Step 4-2: Construct a variable fidelity proxy model

[0131] The objective function and constraint functions calculated by the low-fidelity model are as follows: , The objective function and constraint functions calculated by the high-fidelity model are as follows: , Using several sample points, the low-fidelity and high-fidelity responses were calculated separately, and a bias correction term was constructed between the high-fidelity and low-fidelity models.

[0132]

[0133] A deviation surrogate model is constructed using radial basis functions, resulting in... , Thus, we obtain approximate expressions for the high-fidelity objective function and constraint functions:

[0134]

[0135] We prioritize using low-fidelity models and variable-fidelity surrogate models to quickly screen candidate solutions; then, we use high-fidelity models to accurately verify the best candidate solutions. This reduces the number of high-fidelity frequency response calculations and improves optimization efficiency.

[0136] Step 5: Optimize using genetic algorithm and sequential quadratic programming algorithm.

[0137] Step 5-1: Optimization using genetic algorithm

[0138] Genetic algorithms are used to evaluate design variables. A global search is performed. Each individual in the genetic algorithm represents a complete candidate scheme for a cascaded basis filter:

[0139]

[0140] In genetic algorithms, penalty functions are used to handle constraints. The penalty function and fitness evaluation function in a genetic algorithm are defined as follows:

[0141]

[0142] In the formula, It is a function with maximum value. As a penalty factor, take .

[0143] Step 5-2: Determine whether the base filter is enabled based on the notch depth.

[0144] After the genetic algorithm completes the global search, it determines the notch depth parameter based on the optimal individual. Determine whether each base filter is enabled. For those that satisfy... The base filter, let At this point, it is equivalent to a bypass state; for those satisfying The base filter retains its center frequency, pole damping ratio, and notch depth as variables for subsequent local optimization.

[0145] Step 5-3: Perform local training of the basis filter using a sequential quadratic programming algorithm.

[0146] A sequential quadratic programming algorithm is used to locally refine the activated basis filters. At this time, the inactive basis filters remain unchanged, and only the center frequency of the activated filters is adjusted. Pole damping ratio and notch depth Continuous optimization is performed, and the objective and constraint functions are computed using a high-fidelity frequency grid. The local optimization problem can be expressed as:

[0147]

[0148] In the formula, The set of design variables to enable the base filter.

[0149] To verify the adaptive suppression effect of the method for aircraft elastic vibration in this invention, the target notch filter frequency band was set to 28Hz~32Hz, the low-frequency phase lag frequency band to 2Hz~3Hz, and the maximum number of candidate basis filters was [missing information]. After global search using a genetic algorithm and local refinement using sequential quadratic programming, five basis filters are automatically selected for activation based on the method of this invention, while the remaining candidate basis filters are equivalent to bypassed states. The parameters of the five activated notch filters are shown in Table 1.

[0150] Table 1. Enabling Base Filter Structure Parameters

[0151]

[0152] High-fidelity frequency grid verification shows that the maximum phase lag in the 2Hz–3Hz low-frequency band is 4.3262deg, and the average phase lag is 3.5951deg; the maximum amplitude in the target notch band (28Hz–32Hz) is -40.00dB, satisfying the notch constraint. The optimization results show the amplitude and phase frequency characteristics of the cascaded base filter as follows: Figure 2 As shown, the amplitude characteristic curve of the target notch band of the series base filter is as follows: Figure 3 As shown, the phase frequency response curve of the series base filter in the low-frequency lag band is as follows: Figure 4 As shown. Through the above process, a series notch filter that meets the attenuation requirements of the target notch band, has low low-frequency phase lag, and has an optimal number of filters can be obtained.

[0153] The above description is merely a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any equivalent substitutions, modifications, or improvements made within the spirit and principles of the present invention to the number of candidate filters, target notch band, low-frequency phase evaluation band, activation threshold, surrogate model form, or optimization algorithm parameters should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing a series basis filter based on a variable fidelity surrogate model, characterized in that: Includes the following steps, Step 1: In determining the frequency band of the aircraft control system, based on the measured value of the center frequency of the aircraft's elastic modes. and measurement error range Determine the target notch band The low-frequency phase lag band for evaluating the low-frequency phase performance of the notch filter on the flight control system is determined based on the operating frequency band of the aircraft control system. ; Step 2: In the construction of the cascaded notch filter model, set the maximum number of candidate basis filters to [value missing]. The single fundamental filter is a second-order notch filter, and the structure is constructed using... A cascaded notch filter model composed of candidate basis filters; the total transfer function of the cascaded notch filter model. It is the product of the transfer functions of each candidate basis filter; Step 3: In the construction of the series basis filter optimization model, the design parameters of all candidate basis filters are combined into the total optimization variable. The optimization objective is to minimize the low-frequency phase lag with the introduction of penalty weights, and the amplitude in the target notch band is used as the constraint condition to establish the series basis filter optimization model. In step 3, the design parameters of the candidate basis filter are as follows: in, For the first The center frequency of each base notch filter satisfies ; For the first The theoretical notch depth parameters at the center frequency of each base notch filter satisfy the amplitude attenuation relationship. ; The total optimization variable is, Where T is the transpose function; In step 3, the optimization objective is, in, For penalty weighting; This represents the actual number of filters activated. Indicator functions; Used to reduce in Frequency band phase lag, expressed as an objective function, is... in, This refers to the notch filter weighting coefficient; It is a phase lag function; To optimize variables; The phase of the series basis filter; In step 3, the constraint condition is to impose a conditional constraint on the amplitude of the series basis filter model; in, Preset notch depth; Used to meet the notch band Depth requirements; The condition constraints include, The center frequencies of each fundamental notch filter satisfy: ;in, These are the lower and upper bounds of the center frequency, respectively. The pole damping ratios of each base notch filter satisfy: ;in, , These are the lower and upper bounds of the pole damping ratio, respectively. The notch depth of each base notch filter satisfies: ;in, , These are the minimum and maximum values ​​of the notch depth of the notch filter, respectively. The optimization model for the series basis filter is as follows: Step 4: In the construction of the variable fidelity proxy model, establish the variable fidelity proxy model corresponding to the series basis filter optimization model; for the target notch band and the low-frequency phase lag band, simultaneously select low-fidelity sparse frequency sampling points for rapid scheme evaluation and high-fidelity dense frequency sampling points for accurate verification, fit the deviation correction term of the high-fidelity and low-fidelity model responses through radial basis functions, and obtain the approximate expression of the high-fidelity objective function and constraint function in the form of additive correction; Step 5: The two-stage step-by-step optimization solution is divided into a base filter activation state screening stage and a local parameter optimization stage. In the base filter activation state screening stage, based on the variable fidelity surrogate model, a global search is performed on all candidate base filter design variables using a genetic algorithm with penalty factor constraints. During the global search, the base filter notch depth parameter is used to optimize the notch depth. Combined basis filter enable threshold The system performs a screening process to determine the activation and deletion status of base filters; during the local parameter optimization phase, the system uses a sequential quadratic programming algorithm to optimize the effective branch subset of the base filters; and outputs the structure and parameters of the series notch filter that meet the amplitude attenuation requirements of the target notch band, achieve a balance between minimizing low-frequency phase lag and optimizing the number of activated filters.

2. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 1, the target notch band is: .

3. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 2, the transfer function of the candidate basis filter is expressed as follows: In the formula, For complex variables in Laplace transform, For the first The center angular frequency of each base filter For the first The zero-point damping ratio of each base filter, For the first The pole damping ratio of each base filter.

4. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 2, the overall transfer function of the cascaded notch filter model is: .

5. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 4, the deviation correction term for the high-fidelity and low-fidelity model responses is: The objective function and constraint functions calculated by the low-fidelity model are respectively... , The objective function and constraint functions calculated by the high-fidelity model are as follows: , .

6. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 4, the approximate expressions for the high-fidelity objective function and constraint function are as follows: in, , The deviation surrogate model is obtained by constructing the radial basis functions.

7. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 5, the activation and deactivation status of the base filter is determined as follows: when... At that time, the judgment of the first Each base filter is enabled; when At that time, the judgment of the first Each base filter is in the deletion state; when hour, That is, when the zero-point damping ratio is equal to the pole damping ratio, the transfer function of the base filter is 1, which is equivalent to a bypass path and does not change the amplitude and phase characteristics of the system.

8. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 5, the genetic algorithm for the penalty factor constraint is as follows: in, This is the fitness evaluation function for the genetic algorithm. The penalty factor is used to implement a global search for the enabled combination of basis filters and optimize the center frequency, pole damping ratio and notch depth of each enabled filter.

9. The method for optimizing a series basis filter based on a variable fidelity surrogate model as described in claim 1, characterized in that: In step 5, the quadratic programming algorithm is to use a sequential quadratic programming algorithm to determine the center frequency of the enabled filter. Pole damping ratio and notch depth Perform continuous optimization; keep parameters fixed for filters that are not enabled; In the formula, The set of design variables to enable the base filter.

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