Parametric modeling and multi-objective optimization design method for composite propeller laminate

Abstract

The present application provides a composite propeller layup parameterized modeling and multi-objective optimization design method, relates to the layup optimization design technical field, and establishes a geometric parameterized model of the composite propeller, sets initial layup parameters under the satisfaction of load boundary conditions and manufacturing constraint conditions; extracts the total thickness of each layup area and the layup angle distribution from the initial layup parameters, calculates the feasible region boundary of the continuous variable vector according to the manufacturing constraint conditions; performs constraint-oriented gradient sampling on the continuous variable vector according to the feasible region boundary, and outputs a performance response data set; performs a directional discretization operation on the performance response data set based on the manufacturing constraint conditions, and outputs a multi-objective optimal solution set; performs weighted evaluation on the candidate layup schemes in the multi-objective optimal solution set, inversely analyzes the optimal layup parameters according to the optimal layup scheme, and improves the calculation efficiency, comprehensive performance and process adaptability of the layup optimization.

Description

Technical Field

[0001] This invention relates to the field of ply optimization design technology, specifically to a parametric modeling and multi-objective optimization design method for composite material propeller ply layups. Background Technology

[0002] Composite material propellers, with their high specific strength, excellent fatigue resistance, and designability, have become key components in electric aviation propulsion systems, tiltrotor aircraft, and high-performance unmanned surface vessels. Their ply structure directly determines the static strength, bending stiffness, first-order natural frequency, and dynamic response characteristics of the blades, having a decisive impact on propulsion efficiency and service safety. Current composite material propeller design is transitioning from "experience-based trial and error + single-condition verification" to "parametric modeling-driven + multi-objective collaborative optimization," with the core objective being to simultaneously achieve lightweight, high strength, high stiffness, and frequency vibration damping while meeting manufacturing constraints.

[0003] In existing technologies, conventional composite propeller ply optimization methods often use integer encoding to discretize the ply angles into a finite number of fixed engineering angles, using the ply sequence or ply ratio as design variables. They combine non-dominated sorting genetic algorithms or multi-island genetic algorithms for multi-objective evolutionary search, and embed fluid-structure interaction analysis or orthogonal experimental preprocessing during the optimization process to evaluate individual performance. Some methods further introduce radial basis function surrogate models to reduce the number of finite element calculations, or use optimal deformation field quantization combined with Pareto solution set verification to improve convergence efficiency. These methods directly use the ply angle distribution as a discrete variable to participate in the evolutionary iteration, and the dimension of the design variable increases in a combinatorial manner with the number of ply layers.

[0004] The aforementioned conventional methods use discrete ply angles as direct optimization variables, leading to a combinatorial explosion in the design space with the number of ply layers, a sharp increase in the number of finite element solutions, and difficulty in converging to the global optimal neighborhood within a reasonable time. While radial basis function surrogate models can reduce the number of calls, their point addition criteria lack mathematical construction for the feasible region of the stack parameters, limiting sample filling efficiency. Existing methods do not establish an effective mapping bridge between continuous and discrete spaces, and continuous optimal solutions cannot be directly back-derived into manufacturable discrete ply schemes. In addition, optimization objectives often focus on Pareto tradeoffs for a few indicators such as quality and frequency, without systematically incorporating probabilistic weighted evaluations and manufacturing constraint filtering for various working conditions in the actual task profile, resulting in the final scheme's comprehensive performance and process feasibility failing to meet engineering requirements.

[0005] The information disclosed in the background section is only intended to enhance the understanding of the background of this disclosure, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0006] The purpose of this invention is to provide a parametric modeling and multi-objective optimization design method for composite material propeller layup, so as to solve the problems mentioned in the background art.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A parametric modeling and multi-objective optimization design method for composite material propeller layup, comprising the following steps: S1. Establish a geometric parameterized model of the composite propeller. Based on the geometric parameterized model, divide the composite propeller into multiple ply regions along the blade span. Extract the ply orientation data of each ply region and set the initial ply parameters under the conditions of satisfying the load boundary conditions and manufacturing constraints. S2. Extract the total ply thickness and ply angle distribution of each ply region from the initial ply parameters, map the ply angle distribution to continuous ply angles, arrange the continuous ply angles and total ply thickness in order, output the continuous variable vector, and calculate the feasible domain boundary of the continuous variable vector based on the manufacturing constraints. S3. Based on the feasible domain boundary, perform constraint-guided gradient sampling on the continuous variable vector to generate multiple sets of candidate continuous variable vectors with performance optimization tendency. Input the candidate continuous variable vectors, ply orientation data and load boundary conditions into the pre-trained parameterized finite element model for simulation and output the performance response dataset. S4. Based on manufacturing constraints, perform directional discretization on the performance response dataset to generate a candidate sequence set. Calculate the constraint matching degree between the candidate sequence set and the candidate continuous variable vectors in the performance response dataset. Combine the performance evaluation values ​​of the performance response dataset to sort and filter the candidate sequence set according to multiple indicators, and output the multi-objective optimal solution set. S5. Perform weighted evaluation on the candidate plying schemes in the multi-objective optimal solution set, select the optimal plying scheme from the multi-objective optimal solution set, and back-analyze the optimal plying parameters based on the optimal plying scheme to complete the propeller plying design.

[0008] Furthermore, a geometric parameterized model of the composite propeller is established. Based on the geometric parameterized model, the composite propeller is divided into multiple ply regions along the blade span, and the ply orientation data of each ply region is extracted. The specific steps are as follows: The blade length, maximum chord length, twist angle distribution, and thickness variation from blade root to blade tip of the composite material propeller are defined as control parameters. Based on the control parameters, the composite material propeller is parametrically geometrically constructed to generate a geometric parametric model of the composite material propeller. Based on the geometric parameterization model, the composite propeller is divided into multiple layup regions along the blade span of the composite propeller. Extract the local coordinate system, reference line direction, and load transfer path of each ply region, and summarize them into ply orientation data.

[0009] Furthermore, the ply angle distribution is mapped to continuous ply angles, and the continuous ply angles and total ply thickness are arranged sequentially to output a continuous variable vector. The specific steps are as follows: Based on the ply angle distribution of each ply region, the fixed ply angle is read layer by layer according to the ply stacking order, and the position coordinates of each layer in the normalized thickness direction of the ply region are recorded to form an angle-position correspondence. Trigonometric function calculations are performed on the fixed ply angles of each ply region according to the angle-position correspondence to obtain the trigonometric function values ​​for each layer. The trigonometric function values ​​of each ply region are integrated according to the position coordinates to output the continuous ply angle; Arrange the continuous ply angles and total ply thicknesses of each ply region in the order of their ply numbers, and output a continuous variable vector.

[0010] Furthermore, the feasible region boundary of the continuous variable vector is calculated based on the manufacturing constraints. The specific steps are as follows: Extract the types of fixed engineering angles and the quantity limits of consecutive identical ply angles from the manufacturing constraints; Based on the fixed types of engineering angles and the number of consecutive identical ply angles, calculate the upper and lower limits of the consecutive ply angles in each ply region; Based on the limitation on the number of consecutive ply angles with the same angle, the upper and lower limits of the total ply thickness in each ply region are determined; The upper and lower limits of the continuous ply angle and the upper and lower limits of the total ply thickness are combined according to the arrangement order of the continuous variable vectors to generate the feasible domain boundary of the continuous variable vectors.

[0011] Furthermore, constrained guided gradient sampling is performed on the continuous variable vectors based on the feasible region boundary to generate multiple sets of candidate continuous variable vectors with performance optimization tendencies. The specific steps are as follows: Based on the feasible region boundary of the continuous variable vector, a restricted sampling space is constructed with the continuous variable vector as the sampling origin; Extract the minimum laying limit from the manufacturing constraints, divide the restricted sampling space into grids according to the minimum laying limit, and output a compliant sampling grid; Based on the load boundary conditions, a sampling bias is assigned to the compliant sampling grid to form performance optimization trend information; Based on the continuous variable vector, grid nodes are extracted in the compliant sampling grid along the performance optimization trend information, and multiple sets of discrete sampling points are output. The grid node parameters within each discrete sampling point set are arranged sequentially to output multiple sets of candidate continuous variable vectors with performance optimization tendencies.

[0012] Furthermore, in step S4, the optimal solution set for the multi-objective objective is output. The specific steps are as follows: Using the continuous ply angles corresponding to each group of candidate continuous variable vectors in the performance response dataset as matching templates, under the premise of satisfying manufacturing constraints, the continuous ply angles are matched and filtered, and discrete ply sequences that conform to engineering laying rules are generated in a directional manner to form a candidate sequence set. According to the numbering order of each ply region, the normalized deviation value between each discrete ply sequence in the candidate sequence set and the continuous ply angle of the corresponding matching template is calculated, and the normalized deviation value is used as the constraint matching degree. Retrieve each performance evaluation value in the performance response dataset that corresponds one-to-one with the matching template; Among them, the performance evaluation values ​​include blade mass, first-order bending frequency, maximum principal strain and maximum tip displacement. The candidate sequence set is initially screened based on a preset constraint matching threshold to obtain an initial candidate sequence set; By combining the constraint matching degree and performance evaluation values ​​of each candidate sequence, the initial candidate sequence set is sorted by multiple indicators to obtain the optimal solution set for multiple objectives.

[0013] Furthermore, a weighted evaluation is performed on the candidate plying schemes in the multi-objective optimal solution set to select the optimal plying scheme. The specific steps are as follows: The preset performance weight coefficients are weighted and calculated with the performance evaluation values ​​of each candidate ply scheme in the multi-objective optimal solution set to obtain the comprehensive evaluation value of each candidate ply scheme. Compare the comprehensive evaluation values ​​of each candidate ply scheme, and select the candidate ply scheme with the highest comprehensive evaluation value as the optimal ply scheme.

[0014] Furthermore, the optimal ply parameters are derived through back-analysis based on the optimal ply scheme, thus completing the propeller ply design. The specific steps are as follows: Extract the continuous ply angle and total ply thickness of each ply region from the optimal ply scheme; Using manufacturing constraints as boundaries, the continuous ply angles of each ply region are inversely analyzed into the ply angle distribution of each ply region, which is arranged in order of fixed engineering angles; The ply angle distribution of each ply region and the corresponding total ply thickness are summarized as the optimal ply parameters for the composite propeller ply, thus completing the propeller ply design.

[0015] Compared with the prior art, the beneficial effects of the present invention are: This invention maps the ply angle distribution to a continuous ply angle, sequentially arranges the continuous ply angle and the total ply thickness to output a continuous variable vector, and calculates the feasible domain boundary of the vector based on manufacturing constraints. This realizes the transformation from discrete ply design space to continuous differentiable design space, allowing the optimization process to be carried out in a clearly defined continuous space, thereby fundamentally alleviating the search efficiency bottleneck caused by the explosion of discrete ply variable combinations. Meanwhile, this invention performs constraint-guided gradient sampling on continuous variable vectors based on the feasible domain boundary, generates candidate continuous variable vectors with performance optimization tendencies in batches, and outputs a performance response dataset through simulation. This enables the acquisition of performance quantification results for multiple candidate schemes at once, reducing the computational cost of the optimization process. The performance response dataset simultaneously provides a directly reusable continuous matching benchmark and performance verification basis for subsequent directional discretization steps, allowing subsequent steps to quickly filter out discrete sequences that deviate from the performance target without additional simulation. This further connects the information link between continuous space optimization and discrete space manufacturability screening, ultimately providing high-value data support for obtaining the optimal layup scheme that simultaneously meets performance requirements and process feasibility within an acceptable computation cycle. Furthermore, this invention performs directional discretization on the performance response dataset based on manufacturing constraints. By calculating the constraint matching degree between the candidate sequence set and the candidate continuous variable vector, and combining the performance evaluation values, it completes the sorting and screening of multiple indicators. Since the performance response dataset has been acquired in batches during the continuous space optimization stage, the directional discretization step can directly reuse this dataset as the continuous matching benchmark and performance verification basis. There is no need to re-initiate finite element simulation for each discrete candidate sequence. This allows the continuous space optimization and the discrete space manufacturable screening to form a unidirectional data flow closed loop, ensuring that the output multi-objective optimal solution set satisfies both manufacturing constraints and conforms to the performance orientation of continuous space optimization. Finally, through weighted evaluation and inverse analysis, the optimal layup parameters that can be directly implemented are obtained, completing the propeller layup design that takes into account both performance requirements and process feasibility. Attached Figure Description

[0016] Figure 1 A flowchart illustrating the parametric modeling and multi-objective optimization design method for composite material propeller layups; Figure 2 This is the bending moment distribution curve for the ply unit. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments.

[0018] It should be noted that, unless otherwise defined, the technical or scientific terms used in this invention should have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0019] Example: Please see Figures 1-2 The present invention provides a technical solution: A parametric modeling and multi-objective optimization design method for composite material propeller layups, comprising the following steps: S1. Establish a geometric parameterized model of the composite propeller. Based on the geometric parameterized model, divide the composite propeller into multiple ply regions along the blade span. Extract the ply orientation data of each ply region and set the initial ply parameters under the conditions of satisfying the load boundary conditions and manufacturing constraints.

[0020] In this embodiment, the blade length, maximum chord length, twist angle distribution, and thickness variation from blade root to blade tip of the composite material propeller are defined as control parameters. The blade length and maximum chord length are determined by the overall design input of the composite material propeller, the twist angle distribution is determined by the aerodynamic shape design requirements, and the thickness variation from blade root to blade tip is determined by the structural load distribution and initial ply design. The blade length determines the overall spanwise dimension of the blade, the maximum chord length determines the maximum chordwise dimension of the blade, the twist angle distribution determines the installation angle of the blade section at each spanwise position, and the thickness variation from blade root to blade tip determines the unidirectional bending stiffness distribution of the blade.

[0021] Based on control parameters, a parametric geometry model of the composite propeller is generated. The specific process of parametric geometry construction is as follows: a global cylindrical coordinate system is established with the hub center as the origin. The blade length is used as the overall spanwise dimension, and the blade is discretized into multiple cross-sections along the spanwise direction. For each cross-section: the chord length is determined based on the maximum chord length and the current relative position along the spanwise direction, ensuring a gradual distribution of chord length from the blade root to the blade tip; the installation twist angle of the current cross-section is determined based on the twist angle distribution, and the cross-section is rotated around the spanwise axis by the corresponding angle; again, the installation twist angle is determined based on the blade root to tip distribution. The thickness variation at the blade tip determines the blade thickness of the current profile, resulting in a decreasing blade thickness distribution along the spanwise direction from thicker at the blade root to thinner at the blade tip. Each profile section is spatially positioned according to its spanwise location, and the leading and trailing edge points of each section are sequentially connected along the spanwise direction. The pressure and suction surfaces of the blade are then swept to generate the complete three-dimensional solid geometry of the blade. This three-dimensional solid geometry of the blade is combined with the hub geometry according to the assembly relationship to generate the geometric parameterized model of the composite propeller. When any parameter in the control parameters changes, the geometric parameterized model is reconstructed according to the parameterized geometry construction process, realizing parameterized driving.

[0022] In this embodiment, based on a geometric parameterization model, the composite propeller is divided into multiple ply regions along the blade span. According to the attenuation law of blade bending moment along the span, the span is divided into multiple independent ply units, namely the ply regions mentioned above. The blade root section corresponds to the high load region, the blade tip section corresponds to the low load region, and the middle section is arranged in sequence according to the load decreasing gradient. Each ply unit serves as a basic unit for independent optimization of ply parameters. The initial total ply thickness of each unit is determined based on the control parameters of the thickness change from the blade root to the blade tip, specifically, it is a linear transition from the blade root thickness to the blade tip thickness according to the span position.

[0023] The local coordinate system, reference line direction, and load transfer path of each ply region are extracted and summarized into ply orientation data. The reference line direction is the main load-bearing direction of each ply unit along the spanwise generatrix from the blade root to the blade tip, and aligned with the profile installation twist angle. It is directly extracted from the profile spatial positioning results and twist angle distribution control parameters of the geometric parameterization model. The load transfer path is the trajectory of the load from each unit on the blade tip side along the spanwise direction to the blade root and then to the rotor hub.

[0024] Simultaneously acquire load boundary conditions and manufacturing constraints. The load boundary conditions are the equivalent bending moments at the root of each ply unit, obtained by integrating the hydrodynamic pressure and centrifugal force on the blade surface under cruise conditions. The equivalent bending moments at the root of each ply unit are obtained by integrating from the current ply unit towards the blade tip, and the calculation formula is as follows: In the formula, The element index representing the layup element. ; Indicates the first The equivalent bending moment of each ply unit; This represents the total number of ply units; Indicates the summation index of the ply unit. , Indicates the first The surface load borne by each ply unit; Indicates the first chord length of each ply unit; Indicates the first span of each unit; Indicates the first The radial distance from the center of each ply unit to the hub; Indicates the first The radial distance from the center of each ply unit to the hub.

[0025] It should be noted that the equivalent bending moment calculation formula is derived based on classical beam theory and the principle of the infinitesimal element method. This formula accurately characterizes the moment transfer behavior along the span of a composite material propeller under complex loads. In the ply element summation index, the formula... Representing the The first ply unit and the first The difference in radial distance between each ply element (starting element) in the global cylindrical coordinate system, i.e., the lever arm of the load line of that element to the calculated section, reflects the vertical distance at which the load produces a rotational effect. The product represents the action on the first... The total normal force of the micro-segments on each ply unit, of which Indicates the first The surface load borne by each ply unit; Indicates the first chord length of each ply unit; Indicates the first The spanwise length of each element, multiplied together, transforms the distributed surface load into a concentrated force along the spanwise direction; this concentrated force is then multiplied by the lever arm. That is, to obtain the first The load of the first ply element on the first The micro bending moment generated at the section where the ply unit is located; from the first The number of layup units to the first The summation of all micro-bending moments of each ply element essentially completes the integral operation of the continuously distributed load, thereby obtaining the total equivalent bending moment of the load transmitted to the section along the spanwise direction. This calculation process strictly follows the moment balance theorem in theoretical mechanics, providing a reliable mechanical input for subsequent ply parameterization modeling and optimization.

[0026] The chord length of the ply unit is obtained by directly extracting the chord length of the cross section at the spanwise position of the current unit, which is determined by the maximum chord length and the relative spanwise position. The spanwise length of the ply unit is obtained by taking the spanwise division spacing of the adjacent cross sections at both ends of the current unit, which is determined by the spanwise discretization rule. The radial distance from the center of each ply unit to the hub is obtained by directly reading the radial coordinate of the center of the corresponding cross section of the current unit in the global cylindrical coordinate system. The surface load borne by the ply unit is the total load of the blade hydrodynamic pressure and rotational centrifugal force acting on the corresponding blade area of ​​the current unit under the cruise condition, which is calculated by dividing by the product of the chord length and the spanwise length of the current unit.

[0027] Among them, the manufacturing constraints limit the available ply angles to 0°, +45°, -45°, and 90°. The minimum thickness of a single layer is determined based on the process capability. The number of consecutive layers laid at the same angle does not exceed the upper limit of the process. The upper and lower limits of the total thickness of each unit are determined based on the thickness variation from the blade root to the blade tip and the manufacturing constraints.

[0028] Under the conditions of satisfying the load boundary conditions and manufacturing constraints, the initial ply parameters are set as follows: the initial total ply thickness of each unit obtained by linearly transitioning from the thickness at the blade root to the thickness at the blade tip along the spanwise position is used as the thickness reference. This thickness is divided by the minimum single-layer thickness in the process and rounded up to obtain the initial total number of layers in each unit. At the same time, based on the spanwise distribution law of the equivalent bending moment at the root of each ply unit, the principle of prioritizing the arrangement of the 0° main load layer in the high load area of ​​the blade root and adapting the ±45° shear load layer in the low load area of ​​the blade tip is followed. Combined with the manufacturing constraints that the available ply angles are only 0°, +45°, -45°, and 90° and the number of consecutive ply layers at the same angle does not exceed the upper limit of the process, the ply angle sequence matching the initial total number of layers is determined for each unit, and finally the complete initial ply parameters of each ply unit including the ply angle distribution and the total ply thickness are formed.

[0029] Table 1: Distribution of equivalent bending moment in the spanwise direction Based on the 16 sets of data shown in Table 1, combined with Figure 2 It can be seen that as the ply unit number increases and the position extends from the blade root to the blade tip, the normalized equivalent bending moment continuously decreases from 1.00 to 0.12, with a smooth transition throughout. When the number is 1, the position is 0.20 and the bending moment is 1.00, corresponding to the blade root bearing the entire load; when the number is 8, the position is 0.55 and the bending moment is 0.50, the load is reduced to half, matching the transition requirements in the middle; when the number is 16, the position is 0.95 and the bending moment is 0.12, with only a small amount of load remaining at the blade tip. The above data conforms to the mechanical law of blade bending moment decaying along the span, verifying the rationality of the load boundary condition definition, providing an accurate basis for subsequent allocation of ply thickness according to load, ensuring that the ply design is not redundant and does not have insufficient strength, and improving optimization efficiency.

[0030] The spanwise normalized position is defined based on the global cylindrical coordinate system established in step S1 with the hub center as the origin. The direction from the blade root to the blade tip is taken as the spanwise reference. The radial distance from the center of the profile corresponding to the last ply unit at the blade tip to the center of the hub is taken as the total spanwise reference value. The radial distance from the center of the profile corresponding to each ply unit to the center of the hub is divided by the total spanwise reference value. The resulting dimensionless value is the spanwise normalized position of the unit. Its value gradually increases as the unit extends from the blade root to the blade tip, which intuitively represents the relative arrangement position of each ply unit in the blade span.

[0031] S2. Extract the total ply thickness and ply angle distribution of each ply region from the initial ply parameters, map the ply angle distribution to continuous ply angles, arrange the continuous ply angles and total ply thickness in sequence, output the continuous variable vector, and calculate the feasible domain boundary of the continuous variable vector based on the manufacturing constraints.

[0032] In this embodiment, based on the ply angle distribution of each ply region, the fixed ply angle is read layer by layer according to the ply stacking order, and the position coordinates of each layer in the normalized thickness direction of the ply region are recorded to form an angle-position correspondence.

[0033] Furthermore, with the side of the region closest to the leaf surface as 0 and the side closest to the leaf back as 1, the total number of layers is obtained by dividing the initial total thickness of the region by the minimum single-layer thickness of the process and rounding it up. The thickness direction is divided into corresponding parts from 0 to 1. The midpoint of the thickness interval occupied by each corresponding single-layer layup in the normalized thickness direction is taken as the normalized position coordinate of the corresponding layup.

[0034] Based on the angle-position correspondence, trigonometric function calculations are performed on the fixed ply angles of each ply region to obtain layer-by-layer trigonometric function values; that is, for each layer of fixed engineering angle, take twice the angle value, convert it to radians, and then calculate the cosine and sine values ​​respectively. The calculation formula is as follows: In the formula, The trigonometric function values ​​for the cosine term are given at each level. This indicates the fixed ply angle corresponding to each layer of the project; These are the trigonometric function values ​​for the sine term.

[0035] In this embodiment, the trigonometric function values ​​of each ply region are integrated according to the position coordinates to output the continuous ply angle. Specifically, the operation is as follows: the thickness proportion of each layer in the normalized thickness direction is used as the weight, and the cosine and sine values ​​of all layers are weighted and accumulated to obtain two cumulative values ​​corresponding to the overall tensile and compressive and shear stiffness orientation of the ply. The two cumulative values ​​are arctangented in four quadrants to obtain the radian value representing twice the engineering angle of the ply in that region. This radian value is divided by 2 (divided by 2 because the aforementioned trigonometric function calculation used twice the angle for the fixed engineering ply angle to adapt to the calculation rules of the equivalent stiffness of the laminate, and the arctangent gives the radian result of twice the orientation angle, and dividing by 2 restores it to the continuous angle of the angle between the corresponding real fiber and the reference line) to convert it into the continuous ply angle of that ply region. The layer position information is taken into account when weighting and accumulating. The same angle will correspond to different results at different thickness positions. This value is only used as a continuous optimization variable and is not directly used for manufacturing.

[0036] The continuous ply angles and total ply thicknesses of each ply region are arranged sequentially according to their ply region numbers, and a continuous variable vector is output. The ply region numbers are derived from the physical positional order when dividing the ply regions along the spanwise direction in S1: starting from the blade root near the hub, the ply regions are sequentially numbered along the spanwise direction towards the blade tip, with number 1 corresponding to the high-load area at the blade root, and so on. Corresponding to the low-load area at the blade tip, the numbering sequence corresponds exactly to the spanwise position and the load transfer path.

[0037] In this embodiment, the types of fixed engineering angles and the quantity limits of consecutive identical ply angles are extracted from the manufacturing constraints. Based on the types of fixed engineering angles and the quantity limits of consecutive identical ply angles, the upper and lower limits of the consecutive ply angles in each ply region are calculated. Specifically, based on the types of fixed engineering angles, the values ​​of the consecutive ply angles in each region cover the full range from -45° to 90°. Therefore, the lower limit of the consecutive ply angles in each region is uniformly set to -45° and the upper limit is uniformly set to 90° to ensure that the consecutive values ​​generated by subsequent optimization can be back-mapped to a compliant fixed engineering angle sequence.

[0038] It should be noted that the lower limit of the continuous layup angle in each layup region is uniformly set to -45° and the upper limit is uniformly set to 90° because the manufacturing constraints clearly limit the fixed engineering angles that can be used in actual production to only four types: -45°, 0°, +45°, and 90°. The continuous layup angle in this step is a continuous variable that represents the actual angle between the layup fiber and the reference line after inverse calculation using trigonometric functions. Its value directly corresponds one-to-one with the process layup angle. Therefore, the legal range of values ​​for this continuous variable is naturally completely covered by the minimum angle of -45° and the maximum angle of 90° allowed by the process. This ensures that any continuous angle generated by subsequent optimization can be back-mapped to the above four types of compliant fixed engineering angles through subsequent matching rules, thus avoiding the problem of angles exceeding process constraints from the source of variables. In this embodiment, the fixed engineering angles are set to -45°, 0°, +45°, and 90° because this combination of four angles constitutes the recognized benchmark layup system in composite laminate design. It can effectively cover complex stress conditions such as axial tension and compression, lateral support, and shear torsion. It is also highly compatible with existing mainstream automatic tape laying and manual layup manufacturing processes and can be directly used as discrete manufacturing constraint output.

[0039] Based on the limitation on the number of consecutive identical ply angles, the upper and lower limits of the total ply thickness of each ply region are determined. That is, under the process constraint that the consecutive identical ply angles do not exceed 4 layers, the minimum total ply thickness of each region is 0.5 times the initial total thickness and the maximum is 2 times the initial total thickness. Then, the upper and lower limits are rounded down and up to integer multiples of the minimum single-layer thickness of the process, respectively, to obtain the upper and lower limits of the thickness of each region, which satisfies the process requirements and retains the optimization margin.

[0040] It should be noted that setting the maximum number of consecutive identical ply angles to no more than 4 layers and the total ply thickness of each region to be 0.5 to 2 times the initial total thickness is because 4 consecutive layers at the same angle is a common upper limit in the hot pressing of composite prepregs to avoid interlayer thermal stress concentration and ensure curing quality. This limit, combined with the minimum single-layer thickness of the process, has already limited the range of thickness increments that a single angle can contribute. 0.5 times the initial thickness is the minimum allowable value to match the lightweight requirements of the low-load area at the blade tip while meeting the allowable strain safety margin under cruise conditions. 2 times the initial thickness is the maximum allowable value to reserve bending reinforcement space for the high-load area at the blade root while avoiding the overall mass from exceeding the design limit. Rounding the upper and lower limits down and up to integer multiples of the minimum single-layer thickness of the process, respectively, is to ensure that the thickness variable naturally conforms to the manufacturing rule of layer-by-layer laying. Finally, the upper and lower limits of angle and thickness are combined in the spanwise numbering order to form the feasible domain boundary of the continuous variable vector, ensuring that all subsequent sampling points simultaneously meet process compliance and performance baselines.

[0041] The upper and lower limits of the continuous ply angle and the upper and lower limits of the total ply thickness are combined according to the arrangement order of the continuous variable vectors to generate the feasible domain boundary of the continuous variable vectors.

[0042] S3. Based on the feasible domain boundary, perform constraint-guided gradient sampling on the continuous variable vector to generate multiple sets of candidate continuous variable vectors with performance optimization tendency. Input the candidate continuous variable vectors, ply orientation data and load boundary conditions into the pre-trained parametric finite element model for simulation and output the performance response dataset.

[0043] In this embodiment, a restricted sampling space is constructed based on the feasible domain boundary of the continuous variable vector, with the continuous variable vector as the sampling origin. The restricted sampling space is a multi-dimensional cube centered on the initial continuous variable vector, with each dimension boundary truncated by the upper and lower limits of the feasible domain. The coordinates of any point in the space naturally satisfy the manufacturing constraints, eliminating the need for subsequent secondary compliance verification.

[0044] The minimum laying limit is extracted from the manufacturing constraints, and the restricted sampling space is meshed according to the minimum laying limit to output a compliant sampling mesh. The minimum laying limit is the collective term for the minimum thickness increment and the minimum angle mapping step specified in the manufacturing constraints. During the segmentation, the continuous interval is discretized into nodes along each dimension of the sampling space according to the corresponding constraints. The thickness dimension nodes are all integer multiples of the single-layer thickness allowed by the process, and the angle dimension nodes can be back-mapped to a fixed engineering angle. All nodes together constitute a compliant sampling mesh.

[0045] Based on the load boundary conditions, a sampling bias is assigned to the compliant sampling grid to form performance optimization trend information. Specifically, in combination with the goals of reducing blade mass, increasing first-order bending frequency, and controlling maximum principal strain under cruise conditions, a directional bias is applied to the grid: the thickness dimension is shifted in the direction of reducing the total ply thickness, corresponding to the exploration of reducing blade mass; the angle dimension is shifted in the direction of the spanwise load transfer path in the matching ply azimuth data (i.e., the continuous ply angle value corresponding to the fixed engineering angle), corresponding to the exploration of increasing the spanwise bending stiffness and thus increasing the first-order bending frequency.

[0046] Based on the continuous variable vector, grid nodes are extracted within the compliant sampling grid along the performance optimization trend information, and multiple sets of discrete sampling points are output.

[0047] The grid node parameters within each discrete sampling point set are arranged sequentially to output multiple sets of candidate continuous variable vectors with performance optimization tendencies. Specifically, each set of sampling points is converted into a candidate continuous variable vector with the same dimension as the initial vector by using a fixed arrangement rule of ply region numbering order, continuous ply angle first and ply total thickness second.

[0048] In this embodiment, candidate continuous variable vectors, ply orientation data, and load boundary conditions are input into a pre-trained parametric finite element model for simulation, and the performance response dataset is output. The pre-trained parametric finite element model is a fully automated parametric solution process developed based on a general finite element solver script interface. Essentially, it solidifies the standard steps of manually conducting finite element analysis of composite propellers into code logic. It has four built-in functional modules: input adaptation, ply inversion, load application and solution, and performance extraction. Each module initially uses the general mapping rules of composite mechanics as the processing operator and can respond to any compliant continuous variable input and automatically output the corresponding structural performance. The parametric finite element model is used for engineering calibration and accuracy solidification of mapping rules: First, based on the variable rules defined in S1~S2, several sets of typical input samples covering the entire feasible domain of continuous ply angles and ply thicknesses are generated. Each set of samples includes candidate continuous variable vectors, ply orientation data, and load boundary conditions. The initial version of the solution process is driven to automatically complete finite element modeling, ply definition, load application, and solution. The output blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement are compared with the calculation results of the manually constructed standard finite element model. Fine-tuning is performed on mapping links with excessive deviations (such as the layer allocation logic of restoring continuous angles to fixed engineering angles, and the radial weighting coefficient of equivalent bending moment to nodal loads). The specific fine-tuning strategy is as follows: for the layer allocation logic of restoring continuous angles to fixed engineering angles, a layer interchange and redistribution strategy based on local stiffness deviation feedback is used for correction; for the radial weighting coefficient of equivalent bending moment to nodal loads, a linear scaling strategy based on the relative error of bending moment is used for correction. The judgment criterion is: the output blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement are compared with the calculation results of the manually constructed standard finite element model. The relative deviations of blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement from the calculation results of the manually constructed standard finite element model are compared with preset engineering accuracy thresholds (preset engineering accuracy thresholds are based on the general engineering allowable error standards in the field of composite propeller finite element analysis and the design tolerance requirements of specific projects). When the relative deviations of the four properties of all verification samples are less than or equal to the preset engineering accuracy thresholds, it is determined that the engineering accuracy requirements are met. The termination condition is: when the performance deviations of all verification samples meet the above judgment criteria, or when the number of iterations reaches the preset maximum number of iterations (the preset maximum number of iterations is based on the calculation time of finite element solution, engineering calibration efficiency requirements, and conventional numerical iteration convergence experience), the calibration process is terminated. After the above termination conditions are met, the final mapping rules are locked as permanent processing operators of each module. This process is only for the verification and shaping of mechanical mapping rules and does not involve any data-driven learning algorithms, which is completely in line with the engineering logic of traditional finite element simulation.

[0049] After pre-construction, the parameterized finite element model can be used directly as the simulation execution end: all candidate continuous variable vectors obtained by gradient sampling are input into the model in sequence, the input adaptation layer completes the parameter format alignment, the layup inversion layer converts the continuous layup angles of each region into standard layup sequences of 0°, +45°, -45°, and 90° according to the solidified rules and assigns element attributes, the load application and solution layer maps the root equivalent bending moment into finite element node distributed loads according to the solidified weighted logic and calls the solver to complete static and modal calculations, and the performance extraction layer automatically captures the four target performance outputs.

[0050] S4. Based on manufacturing constraints, perform directional discretization on the performance response dataset to generate a candidate sequence set. Calculate the constraint matching degree between the candidate sequence set and the candidate continuous variable vectors in the performance response dataset. Combine the performance evaluation values ​​of the performance response dataset to sort and filter the candidate sequence set according to multiple indicators, and output the multi-objective optimal solution set.

[0051] In this embodiment, the continuous ply angles corresponding to each group of candidate continuous variable vectors in the performance response dataset are used as matching templates. Under the premise of meeting manufacturing constraints, the continuous ply angles are matched with the nearest fixed engineering angles, and the number of layers is determined according to the total thickness of the corresponding units. Discrete ply sequences that conform to the engineering laying rules are generated in a directional manner, and all unit sequences are combined to form a candidate sequence set.

[0052] According to the numbering order of each ply region, the normalized deviation value between the continuous ply angles of each discrete ply sequence in the candidate sequence set and the corresponding matching template is calculated. The calculation logic of the normalized deviation value is as follows: first, take the difference between the continuous angle of the matching template and the continuous angle corresponding to the discrete ply sequence in each ply unit; then divide this difference by the total span of the process-allowed ply angles to obtain the relative deviation ratio of a single unit; finally, average the relative deviations of all ply units; use this normalized deviation value as the constraint matching degree, and the formula for calculating the constraint matching degree is: In the formula, To constrain the matching degree; Indicates the first The continuous ply angle of each ply unit matches the template; Indicates the first The continuous ply angles corresponding to each discrete ply sequence in a ply unit; The feasible span for continuous ply angle is a feasible span from -45° to 90°.

[0053] In this embodiment, the performance evaluation values ​​that correspond one-to-one with the matching template in the performance response dataset are retrieved; each performance evaluation value includes blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement.

[0054] The candidate sequence set is initially screened based on the preset constraint matching degree threshold. Candidate sequences with constraint matching degree lower than the matching degree threshold are removed, as are candidate sequences whose structural performance does not meet the load boundary condition limit. The initial candidate sequence set is obtained. Specifically, the matching degree threshold is set based on the manufacturing allowable layup restoration error (corresponding to the process tolerance of ±3° of continuous layup angle), and the operating condition limit is set based on the overall design requirements of the allowable principal strain of composite material, the vibration damping requirements of the first-order bending frequency, and the upper limit of blade mass under cruise conditions.

[0055] By combining the constraint matching degree and performance evaluation values ​​of each candidate sequence, the initial candidate sequence set is sorted by multiple indicators to obtain the multi-objective optimal solution set. Specifically, the constraint matching degree, blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement of each candidate are normalized. The sorting criteria are: the smaller the constraint matching degree, the higher the process compliance; the higher the first-order bending frequency, the better the stiffness; and the other performances do not exceed the operating condition limits. The initial candidate sequence set is sorted from high to low to form the multi-objective optimal solution set.

[0056] S5. Perform weighted evaluation on the candidate plying schemes in the multi-objective optimal solution set, select the optimal plying scheme from the multi-objective optimal solution set, and back-analyze the optimal plying parameters based on the optimal plying scheme to complete the propeller plying design.

[0057] In this embodiment, the preset performance weighting coefficients are weighted and calculated with the performance evaluation values ​​of each candidate ply scheme in the multi-objective optimal solution set to obtain the comprehensive evaluation value of each candidate ply scheme. The performance weighting coefficients are set according to the probability of occurrence of each working condition in the actual service mission profile, and the corresponding performance evaluation values ​​are four categories: blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement. The formula for calculating the comprehensive evaluation value is as follows: In the formula, This represents the overall evaluation value; These represent the performance weighting coefficients, namely the first-order bending frequency weighting coefficient, the blade mass weighting coefficient, the maximum principal strain weighting coefficient, and the maximum tip displacement weighting coefficient. This represents the positively normalized value of the first-order bending frequency. This represents the negative normalized value of the blade mass; This represents the negative normalized value of the maximum principal strain; This represents the negative normalized value of the maximum displacement of the propeller tip.

[0058] It should be noted that the comprehensive evaluation value is a comprehensive evaluation index used to quantitatively integrate and weigh multiple performance indicators of candidate propeller layup schemes. The comprehensive evaluation index linearly sums four physically independent core performance parameters—blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement—through engineering weighting coefficients, and uses a single value to macroscopically characterize the overall comprehensive performance of the layup scheme under actual service missions. The larger the value, the better the scheme meets the pre-set service mission preferences while satisfying structural strength, stiffness, and geometric constraints.

[0059] In this embodiment, the blade mass directly determines the propeller's overall inertia and cruise drag. The lighter the mass, the lower the load pressure on the aircraft or ship, and the higher the cruise efficiency. Therefore, the blade mass is negatively correlated with the comprehensive evaluation value. In the quantitative logic of the comprehensive evaluation value, the blade mass is a key negative indicator. The smaller its actual value, the more beneficial the contribution of the normalized evaluation value to the sum, thereby guiding the optimization process towards lightweight design.

[0060] The first-order bending frequency is a core stiffness indicator that ensures the propeller avoids the resonance zone and maintains the dynamic stability of the structure. The higher the frequency, the stronger the overall bending stiffness of the blade, and the more effectively it can suppress the risk of harmful resonance in complex flow fields. Therefore, the first-order bending frequency is positively correlated with the comprehensive evaluation value. It is included in the calculation as a positive indicator. The larger the value, the better the structural dynamic performance and the stronger the positive pulling effect on the comprehensive evaluation value.

[0061] Maximum principal strain is an important parameter for measuring the stress level and structural safety margin of a blade under ultimate load, and is directly related to the allowable strength limit of the material. The smaller the maximum principal strain, the more reasonable the stress distribution inside the structure, and the further away from the safety boundary where plastic deformation or fatigue failure occurs. Therefore, the maximum principal strain is negatively correlated with the comprehensive evaluation value, and is defined as a negative index to penalize high-strain design schemes and ensure that the final optimal scheme has sufficient structural safety.

[0062] Tip displacement reflects the degree of elastic deformation of the propeller under high-speed rotation and aerodynamic load coupling. Excessive deformation will damage the aerodynamic shape of the blade, leading to a sharp drop in efficiency or even flutter instability. Therefore, the maximum tip displacement is negatively correlated with the comprehensive evaluation value. This index also serves as a negative constraint. The smaller the value, the better the stiffness performance of the blade and the stronger its geometric conformity, which is more conducive to maintaining the efficient and reliable operation of the propeller and thus obtaining a higher score in the comprehensive evaluation.

[0063] Based on this, to ensure the mathematical rigor and engineering adaptability of the linear weighted calculation, the four indicators have been preprocessed by normalization and homogenization before the calculation: For the positive indicator of first-order bending frequency, which is "the larger the value, the better the performance", the relative deviation between its simulated value and the preset ideal target value is taken as the positive normalization input; For the three negative indicators of blade mass, maximum principal strain, and maximum tip displacement, which are "the smaller the value, the better the performance", the relative deviation between the preset ideal target value and the simulated value is taken as the positive normalization input, so that all the sub-items participating in the weighting are unified as dimensionless "equivalent positive contribution" - that is, regardless of the orientation of the original indicators, the standardized values ​​that enter the weighted summation formula are "the larger the value, the better the performance of the corresponding dimension". Then, they are multiplied and accumulated with the preset engineering weight coefficients of cruise energy efficiency, structural safety, aerodynamic holding, etc. The final output comprehensive evaluation value is the single quantitative result after the homogeneous fusion of each independent performance dimension. Its value directly corresponds to the comprehensive service performance of the candidate layup scheme under the consideration of manufacturing constraints.

[0064] The four indicators—blade mass, first-order bending frequency, maximum principal strain, and maximum tip displacement—characterize the comprehensive performance of the plywood design from four non-overlapping core dimensions: inertial load, dynamic stiffness, material strength, and geometric accuracy. Mass relates to the system's energy consumption and inertia; frequency relates to the structure's dynamic safety boundary; strain relates to the material's failure threshold; and displacement relates to the ability to maintain the aerodynamic shape. The effects of changing plywood parameters on these four dimensions are independent and decoupled, each contributing to different aspects of the propeller's overall performance without any physical linear substitution or dimensional overlap. Based on the principle of multi-objective independent action in engineering mechanics, the comprehensive influence of these four independent performance factors can be quantified by linear superposition. Therefore, a weighted sum function is used to describe the intrinsic relationship between the comprehensive evaluation value and each sub-indicator.

[0065] Among them, the sum of the weighting coefficients for the first-order bending frequency, blade mass, maximum principal strain, and maximum tip displacement is 1, and their order of magnitude is: maximum principal strain weighting coefficient > first-order bending frequency weighting coefficient > maximum tip displacement weighting coefficient > blade mass weighting coefficient. This conforms to the general design principle of propellers: "safety red line first, performance bottom line second, and energy efficiency optimization last." The maximum principal strain corresponds to the static strength limit of the material and is an inviolable red line to prevent structural fracture and failure, hence it has the highest weight. The first-order bending frequency determines whether the resonance range can be avoided and is the core guarantee for long-term dynamic service safety, hence it has the second highest weight. The maximum tip displacement directly affects aerodynamic efficiency and flutter boundary and belongs to the performance bottom line that must be met, hence it has the third highest weight. Blade mass only relates to cruise load and energy consumption and is a lightweight optimization goal after all safety and performance requirements have been met, hence it has the lowest weight.

[0066] Compare the comprehensive evaluation values ​​of each candidate ply scheme, and select the candidate ply scheme with the highest comprehensive evaluation value as the optimal ply scheme.

[0067] Extract the continuous ply angle and total ply thickness of each ply region from the optimal ply scheme.

[0068] Using manufacturing constraints as boundaries, the continuous ply angles of each ply region are inversely analyzed into a ply angle distribution in each ply region arranged in order of fixed engineering angles. The inverse analysis follows the inverse rule of thickness-weighted integral in step S2: the total number of layers is calculated based on the total ply thickness, and under the constraint of the number of consecutive ply angles of the same type, fixed engineering angles are arranged layer by layer from near the blade surface to near the blade back, with the main angles aligned with the reference line direction of the ply orientation data, to generate a ply angle distribution with a clear stacking order.

[0069] The ply angle distribution of each ply region and the corresponding total ply thickness are summarized as the optimal ply parameters for the composite propeller ply, thus completing the propeller ply design.

[0070] The above formulas are all dimensionless calculations. The formulas are derived from software simulations based on a large amount of collected data to obtain the most recent real-world results. The preset parameters in the formulas are set by those skilled in the art according to the actual situation.

[0071] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented in software, the above embodiments can be implemented, in whole or in part, as a computer program product. Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution.

[0072] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0073] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application.

Claims

1. A parametric modeling and multi-objective optimization design method for composite material propeller layup, characterized in that, The specific steps include: S1. Establish a geometric parameterized model of the composite propeller. Based on the geometric parameterized model, divide the composite propeller into multiple ply regions along the blade span. Extract the ply orientation data of each ply region and set the initial ply parameters under the conditions of satisfying the load boundary conditions and manufacturing constraints. S2. Extract the total ply thickness and ply angle distribution of each ply region from the initial ply parameters, map the ply angle distribution to continuous ply angles, arrange the continuous ply angles and total ply thickness in order, output the continuous variable vector, and calculate the feasible domain boundary of the continuous variable vector based on the manufacturing constraints. S3. Perform constraint-guided gradient sampling on the continuous variable vectors based on the feasible region boundary to generate multiple sets of candidate continuous variable vectors with performance optimization tendencies. The specific steps are as follows: Based on the feasible domain boundary, a restricted sampling space is constructed with the continuous variable vector as the sampling origin, and the minimum laying limit is extracted from the manufacturing constraints to divide the space into grids to obtain a compliant sampling grid. Based on the load boundary conditions, a sampling bias is assigned to the compliant sampling grid to form performance optimization trend information. Grid nodes are extracted within the compliant sampling grid along this trend information, and multiple sets of discrete sampling points are output. The parameters of each discrete sampling point set are arranged sequentially to generate multiple sets of candidate continuous variable vectors with performance optimization tendencies; The candidate continuous variable vector, ply orientation data and load boundary conditions are input into the pre-trained parametric finite element model for simulation, and the performance response dataset is output. S4. Based on manufacturing constraints, perform directional discretization on the performance response dataset to generate a candidate sequence set. Calculate the constraint matching degree between the candidate sequence set and the candidate continuous variable vectors in the performance response dataset. Combine the performance evaluation values ​​of the performance response dataset to perform multi-index ranking and screening of the candidate sequence set, and output the multi-objective optimal solution set. The specific steps are as follows: Using the continuous ply angles corresponding to each group of candidate continuous variable vectors in the performance response dataset as matching templates, under the premise of satisfying manufacturing constraints, the discrete ply sequences that conform to the engineering laying rules are matched, filtered, and generated in a directional manner to form a candidate sequence set. According to the numbering order of each ply region, the normalized deviation value between each discrete ply sequence in the candidate sequence set and the continuous ply angle of the corresponding matching template is calculated, and the normalized deviation value is used as the constraint matching degree. The candidate sequence set is initially screened based on the preset constraint matching degree threshold, and the constraint matching degree of each candidate sequence and the corresponding performance evaluation values ​​in the performance response dataset are combined to perform multi-index priority ranking and output the multi-objective optimal solution set. S5. Perform weighted evaluation on the candidate plying schemes in the multi-objective optimal solution set, select the optimal plying scheme from the multi-objective optimal solution set, and back-analyze the optimal plying parameters based on the optimal plying scheme to complete the propeller plying design.

2. The parametric modeling and multi-objective optimization design method for composite material propeller layup according to claim 1, characterized in that: A geometric parameterized model of the composite propeller is established. Based on the geometric parameterized model, the composite propeller is divided into multiple ply regions along the blade span, and the ply orientation data of each ply region is extracted. The specific steps are as follows: The blade length, maximum chord length, twist angle distribution, and thickness variation from blade root to blade tip of the composite material propeller are defined as control parameters. Based on the control parameters, the composite material propeller is parametrically geometrically constructed to generate a geometric parametric model of the composite material propeller. Based on the geometric parameterization model, the composite propeller is divided into multiple layup regions along the blade span of the composite propeller. Extract the local coordinate system, reference line direction, and load transfer path of each ply region, and summarize them into ply orientation data.

3. The parametric modeling and multi-objective optimization design method for composite material propeller layup according to claim 1, characterized in that: The ply angle distribution is mapped to continuous ply angles. The continuous ply angles and total ply thickness are arranged sequentially, and a continuous variable vector is output. The specific steps are as follows: Based on the ply angle distribution of each ply region, the fixed ply angle is read layer by layer according to the ply stacking order, and the position coordinates of each layer in the normalized thickness direction of the ply region are recorded to form an angle-position correspondence. Trigonometric function calculations are performed on the fixed ply angles of each ply region according to the angle-position correspondence to obtain the trigonometric function values ​​for each layer. The trigonometric function values ​​of each ply region are integrated according to the position coordinates to output the continuous ply angle; Arrange the continuous ply angles and total ply thicknesses of each ply region in the order of their ply numbers, and output a continuous variable vector.

4. The parametric modeling and multi-objective optimization design method for composite material propeller layup according to claim 3, characterized in that: The specific steps for calculating the feasible region boundary of a continuous variable vector based on manufacturing constraints are as follows: Extract the types of fixed engineering angles and the quantity limits of consecutive identical ply angles from the manufacturing constraints; Based on the fixed types of engineering angles and the number of consecutive identical ply angles, calculate the upper and lower limits of the consecutive ply angles in each ply region; Based on the limitation on the number of consecutive ply angles with the same angle, the upper and lower limits of the total ply thickness in each ply region are determined; The upper and lower limits of the continuous ply angle and the upper and lower limits of the total ply thickness are combined according to the arrangement order of the continuous variable vectors to generate the feasible domain boundary of the continuous variable vectors.

5. The parametric modeling and multi-objective optimization design method for composite material propeller layup according to claim 1, characterized in that: The candidate plying schemes in the multi-objective optimal solution set are evaluated using a weighted average, and the optimal plying scheme is selected from the multi-objective optimal solution set. The specific steps are as follows: The preset performance weight coefficients are weighted and calculated with the performance evaluation values ​​of each candidate ply scheme in the multi-objective optimal solution set to obtain the comprehensive evaluation value of each candidate ply scheme. Compare the comprehensive evaluation values ​​of each candidate ply scheme, and select the candidate ply scheme with the highest comprehensive evaluation value as the optimal ply scheme.

6. The parametric modeling and multi-objective optimization design method for composite material propeller layup according to claim 1, characterized in that: The optimal ply parameters are derived through back-analysis of the optimal ply scheme to complete the propeller ply design. The specific steps are as follows: Extract the continuous ply angle and total ply thickness of each ply region from the optimal ply scheme; Using manufacturing constraints as boundaries, the continuous ply angles of each ply region are inversely analyzed into the ply angle distribution of each ply region, which is arranged in order of fixed engineering angles; The ply angle distribution of each ply region and the corresponding total ply thickness are summarized as the optimal ply parameters for the composite propeller ply, thus completing the propeller ply design.

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