A wheel disc reliability optimization method considering correlation of multiple failure modes

Abstract

The application discloses a wheel disc reliability optimization method considering multiple failure mode correlations, and belongs to the field of aerospace. The method comprises three steps: a pair-copula method is used to analyze correlations between failure modes; a reliability distribution method is used to distribute wheel disc reliability to the failure modes; and an improved multi-objective particle swarm optimization algorithm is used to realize wheel disc reliability optimization design. The application establishes a reliability analysis and distribution model based on a cost function from the perspective of system reliability, and realizes a low-cost reliability optimization method considering failure correlations.

Description

Technical Field

[0001] This invention belongs to the field of aerospace engine technology, specifically relating to a disk reliability optimization method that considers the correlation of multiple failure modes. Background Technology

[0002] As a critical and life-limiting component of aero-engines, the wheel disk's life reliability directly affects the operational safety of the engine and aircraft. Developing a high-confidence wheel disk life reliability design method is particularly urgent and important for ensuring engine flight safety. The wheel disk has a complex structure and endures complex loads during service, with different parts exhibiting different failure modes. The same input variables lead to correlations among various failure modes; ignoring these correlations will reduce the accuracy of reliability predictions. Therefore, it is necessary to conduct multi-failure mode correlation studies, clarify the impact of failure correlations on wheel disk life, and establish a reliability assessment method that considers multiple failure modes and their correlations.

[0003] On the other hand, for wheel structures with multiple failure modes, the structural design needs to simultaneously satisfy multiple design parameters. Optimizing these parameters is a typical multi-objective optimization problem. In the multi-objective reliability optimization design problem of wheel structures, different design objectives may conflict with each other. It is necessary to search for suitable design objectives among these conflicting objectives to achieve the optimal design result. Therefore, it is necessary to develop high-precision and high-efficiency multi-objective optimization strategies to optimize the wheel design, and to consider the influence of failure correlations during optimization, thereby improving the reliability of the wheel structure. Summary of the Invention

[0004] To address the aforementioned technical problems, this invention provides a roulette wheel reliability optimization method considering the correlation of multiple failure modes. It utilizes a pair-copula model to establish a complex correlation model among multiple failure modes, and establishes a reliability analysis and allocation model based on a cost function from a system reliability perspective. Furthermore, it implements a low-cost reliability allocation method that considers failure correlation. By assigning structural reliability indices to each failure mode, the computational complexity of roulette wheel reliability analysis and optimization is reduced, serving as the model foundation for subsequent roulette wheel reliability optimization. The invention also conducts research on reliability-based optimization methods for roulette wheel structures from a multi-objective perspective, determining constraint functions by combining the reliability allocation model, and developing an improved multi-objective particle swarm optimization algorithm as an optimization tool. Finally, it achieves the reliability optimization design of the roulette wheel structure.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A reliability optimization method for a roulette wheel that considers the correlation of multiple failure modes is proposed, and the specific implementation steps are as follows:

[0007] The first step is multi-failure mode correlation analysis. The pair-copula method is introduced to characterize the correlation of multiple variables. First, a lifetime model for each failure mode of the roulette wheel is established, random input variables are determined, and lifetime sample points for each failure mode are obtained using joint sampling. Then, the parameters of the pair-copula model are simulated using the maximum likelihood estimation method, and a joint probability distribution model describing the correlation of each failure mode is established.

[0008] The second step involves performing a reliability allocation algorithm that considers failure correlation, assigning the structural reliability requirements to each failure mode according to certain rules. This transforms the reliability allocation problem into an optimization problem, expressed as:

[0009]

[0010] Where min represents taking the minimum value, C is the sum of the cost functions of each failure mode, and st represents making R s It is the reliability estimate of the structure obtained through reliability estimation of each failure mode, and it is the reliability R under each failure mode. i The functions H, R d It refers to design reliability, i.e., the reliability index to be assigned, where n represents the number of failure modes and c i The cost function for each failure mode has an exponential form:

[0011]

[0012] Among them, R i,min and R i,max and represent the current reliability result and the maximum achievable reliability for the i-th failure mode, respectively. The maximum achievable reliability is usually less than 100%, affecting the change of the cost function, and is also known as the proportional parameter of the cost function. i ∈[0,1] is the probability index for improving reliability, f i The higher the value, the easier it is to improve reliability.

[0013] Among them, the reliability estimate R s The specific calculation method is as follows:

[0014] In the fatigue failure of a roulette wheel, the failure modes are interconnected, and the structural life is determined by the life of each failure mode. Assuming that the life of each failure mode is described using a surrogate model, it can be expressed as:

[0015] N f,i =G i (x) (3)

[0016] Where, N f,i Let 'output' represent the lifetime of the i-th failure mode, 'x' represent the input variable, and 'G' represent the surrogate model.

[0017] First, N failure modes and m groups of lifetime samples are obtained through collaborative sampling. ij The values ​​i = 1, ..., n, j = 1, ..., m are used as input data for correlation analysis. Since the failure modes are interconnected, the structural lifetime can be calculated as:

[0018] t s,j =min{t 1j ,t 2j ,...,t nj}=min{N f,ij ·t i0 ,i=1,...,n} (4)

[0019] Among them, t ij t represents the lifetime calculated from the j-th sampling of the i-th failure mode. i0 N is the cycle time of the i-th failure mode. f,ij This represents the j-th sample of the i-th failure mode.

[0020] The specific calculation method for the probability index is as follows:

[0021] First, a hazard analysis is conducted to assess the overall effect of each failure mode, quantified using a risk priority number (RPN). The risk priority number (RPN) for the i-th failure mode is... i It can be calculated as:

[0022]

[0023] Among them, s i Indicates the severity level, o i Indicates the degree of occurrence, α ik The coefficient represents the degree of influence of the i-th failure mode on the k-th failure mode, expressed here as a linear correlation coefficient. The risk priority number measures the combined effect of severity and incidence, where severity and incidence are both rated on a scale of 1-10.

[0024] After normalizing the risk priority numbers, the reliability allocation weights are calculated as follows:

[0025]

[0026] Where, r i w represents the risk priority number of the i-th failure mode. i Given their weights, the probability index f for each failure mode is... i Set its assigned weight, that is:

[0027] f i =w i ,i=1,...,n (7)

[0028] The third step involves conducting reliability optimization design for the wheel. By optimizing the wheel's geometry, the lifespan of the wheel is increased while meeting reliability requirements. With the maximum equivalent stress as the objective, key geometric dimensions of the wheel are obtained as design variables through sensitivity analysis. The optimization objective is to maximize the wheel's lifespan under various failure modes. After determining the design variables and optimization objectives, an improved multi-objective particle swarm optimization algorithm is used to complete the multi-objective reliability optimization design of the wheel.

[0029] The improved multi-objective particle swarm optimization algorithm is as follows:

[0030] In the optimization process of particle swarm optimization, the position and velocity of a single particle i in the (t+1)th iteration satisfy the governing equation:

[0031] x i (t+1)=x i (t)+v i (t+1) (8)

[0032]

[0033] Where x and v represent the particle's position and velocity, respectively; the superscripts p and g represent the particle's individual optimality and global optimality, respectively; c1 and c2 are the individual and global acceleration factors, respectively; r1 and r2 are random numbers between [0,1]; and ω is the inertia weight, controlling the degree to which the velocity at the current moment inherits the velocity from the previous moment. To accelerate the global search capability in the initial stage of iteration and simultaneously promote the local search capability in the later stages, it is assumed that the inertia weight has dynamic characteristics, decreasing linearly and differentially with the number of iterations, resulting in the following expression:

[0034]

[0035] Where, ω st and ω ed Let T be the initial and final values ​​of the inertia weight ω. max This represents the maximum number of iterations.

[0036] The optimal update rule for an individual is:

[0037]

[0038] The globally optimal update rule is:

[0039]

[0040] Where Fit represents the fitness function, and arg represents the value of x corresponding to the function Fit(x).

[0041] To improve the computational efficiency of the multi-objective particle swarm optimization algorithm, the Pareto optimal solution is stored in a high-fitness elite set to guide the iterative process of other particles. The fitness of particles in the elite set is solved using a niche strategy; the higher the particle clustering, the lower the fitness. There is an upper limit to the number of particles in the elite set. When the number exceeds this predefined limit, particles with low fitness are removed and replaced by examples with higher fitness. The fitness function Fit(i) of the i-th particle is defined using the niche strategy and calculated as follows:

[0042] Fit(i) = 1 / e i i = 1, ..., N e (13)

[0043] Where, N e e represents the number of particles. i The niche number of the i-th particle is represented by:

[0044]

[0045] Where d(i,j) represents the Euclidean distance between particles i and j, and sh is the shared function, expressed as:

[0046]

[0047] Where, σ sh Let be the niche radius, and α control the shape of the shared function sh, typically taking the value 1 or 2. The niche strategy reduces the fitness of particles in similar positions, thereby decreasing the likelihood of finding the same local optimum.

[0048] In multi-objective particle swarm optimization (PSO), the extrema of the population guide the iterative update of the position and velocity of each particle. To ensure that the optimization solution converges to the global optimum, a roulette wheel selection method is used to select the global optimum based on the particle's fitness. The probability p(i) of a particle being selected is proportional to the fitness function, i.e.:

[0049]

[0050] Furthermore, the improved multi-objective particle swarm optimization algorithm is described in the following steps:

[0051] (a) Initialize the random position x0 and velocity v0 of the particle; configure the iteration count t = 0, and the elite set N. e =0;

[0052] (b) Calculate the objective function of the particles and store the non-dominated solutions in the elite set;

[0053] (c) Calculate the fitness function of the particle using formula (13) and determine the individual and global extreme values ​​by roulette wheel method;

[0054] (d) Update the particle position and order using formulas (8) and (9), where the dynamic inertia weight is calculated using formula (10);

[0055] (e) Update Elite Collection N e Determine whether the number of particles in the elite set exceeds the swarm capacity T. max If the number exceeds the limit, remove low-fitness particles; otherwise, proceed to step (f).

[0056] (f) Repeat steps (c) to (e) until the iteration termination condition is met. Output the best optimization result in the elite set.

[0057] Beneficial effects:

[0058] This invention proposes a multi-failure mode correlation analysis method based on the pair-copula model, which reduces the complexity of multi-failure mode correlation analysis while ensuring fitting accuracy. It quantifies the cost required to improve the reliability of each failure mode through probability index and establishes a structural reliability allocation method based on cost function, realizing reliability analysis that considers correlation. On this basis, it proposes an improved multi-objective particle swarm optimization algorithm to realize multi-objective reliability optimization design of roulette structure, which significantly improves computational efficiency while ensuring accuracy. Attached Figure Description

[0059] Figure 1 A schematic diagram of the improved multi-objective particle swarm optimization algorithm;

[0060] Figure 2 This is a fault tree model diagram for the roulette wheel failure.

[0061] Figure 3 This is a D-vine structure diagram (ternary variables);

[0062] Figure 4 This is a logic diagram of a disk reliability optimization method that considers the correlation of multiple failure modes according to the present invention. Detailed Implementation

[0063] The present invention will be further described below with reference to specific embodiments, but is not limited to the specific embodiments.

[0064] The following example, using a high-pressure compressor disk of an aero-engine, further illustrates the reliability optimization method of this invention that considers the correlation of multiple failure modes. Figure 4 As shown, the specific steps are as follows:

[0065] The first step is to conduct a failure correlation analysis. First, three failure modes are identified: low-cycle fatigue failure at the disk center, creep-fatigue failure at the disk rim, and high-low cycle fatigue failure at the tenon joint. For the low-cycle fatigue failure mode at the disk center, the maximum stress at the disk center is used as the test stress, and the low-cycle fatigue life is described using the SWT (Smith-Watson-Topper) model. For creep-fatigue failure at the disk rim, the low-cycle fatigue life is described using the SWT model, the creep life is described using the Larsen-Miller parameter method, and then the creep-fatigue failure life is obtained through linear cumulative theory. For high-low cycle fatigue failure at the tenon joint, the low-cycle fatigue life is described using the SWT model, the high-cycle fatigue life is described using the stress-life (SN) model, and then the high-low cycle fatigue life is obtained through linear cumulative theory.

[0066] Then, the uncertainties in the load, geometry, and life model are described using probability distributions. Assuming that the failure of each part during the wheel's failure process is controlled by a primary failure mode, a wheel failure fault tree model is established as follows: Figure 2 As shown, considering that the three failure modes are interconnected, a joint sampling method is used to obtain lifetime sample points for the three failure modes, and correlation analysis is carried out using the data of the upper bound of the lifetime.

[0067] The pair-copula method was used to characterize the correlation of multivariate variables. The D-vine structure of the ternary variables is as follows: Figure 3 T i Represents a tree, u i Representing variables, C ij Let c represent the copula distribution function. ij Let C represent the copula density function. ij|k Let c represent the bivariate copula distribution function. ij|k The bivariate copula density function and the joint probability density function are expressed as follows:

[0068]

[0069] First, the parameters of the marginal distribution function are estimated using the marginal function inference estimation method, and based on this, the relevant parameters of the copula function are estimated. When estimating the relevant parameters of the copula function, the structure of the pair-copula model is considered, and the relevant parameters of the copula function in each layer of the tree are estimated sequentially using a sequential estimation method. During the sequential estimation process, the Akaike information content criterion is used to select the copula model with the highest good fit. The optimal model for all three pair-copula models is a Gaussian copula function.

[0070] The second step is to carry out a reliability allocation of the wheel that takes into account the correlation of failures.

[0071] First, reliability estimates are obtained. Load spectrum analysis is used to obtain the cycle times for three failure modes: low-cycle fatigue failure, creep-fatigue failure, and high-low-cycle fatigue failure. In this invention, the cycle times are taken as 4 min, 45 min, and 5.63 min, respectively. This invention assumes a design life of 1E+05 min for the wheel and uses a pair-copula model to simulate the wheel's life. The predicted reliability range for the wheel structure under the design life is between 79.61% and 89.64%. Further, the predicted reliability ranges are: low-cycle fatigue failure (79.52%–91.16%), creep-fatigue failure (99.51%–99.99%), and high-low-cycle fatigue failure (81.13%–92.17%).

[0072] Then, the probability index of each failure mode is obtained. A hazard analysis is conducted to evaluate the comprehensive effect of each failure mode, quantified by risk priority numbers, as shown in formula (5). Severity and incidence are scored on a scale of 1-10. The severity of low-cycle fatigue failure, creep-fatigue failure, and high-low-cycle fatigue failure is determined by expert experience. In this invention, the severity is set to 9, 5, and 8, and the incidence to 6, 4, and 9, respectively. The calculated risk priority numbers are 192.8, 153.5, and 212.0, respectively. The risk priority numbers are normalized, and the reliability allocation weights for the three failure modes are calculated to be 0.3453, 0.2750, and 0.3797, respectively. The probability index of each failure mode is then set to its allocated weight, i.e., the probability indices for low-cycle fatigue failure, creep-fatigue failure, and high-low-cycle fatigue failure are 0.3453, 0.2750, and 0.3797, respectively.

[0073] After obtaining the reliability estimate and probability index, the reliability allocation problem is transformed into an optimization problem. According to formula (1), when the reliability index is 99%, the actual reliability of the wheel is 99.01%, and the reliability of low-cycle fatigue failure, creep-fatigue failure and high-low cycle fatigue failure is 99.05%, 99.53% and 99.21%, respectively.

[0074] After assigning the structural reliability indicators to each failure mode, the third step, multi-objective reliability optimization, is carried out to meet the reliability indicators.

[0075] The third step is to conduct reliability optimization design of the roulette wheel. In this invention, the design life of the roulette wheel is taken as 1E+05min, and the confidence interval of the mean life is selected as (1-ε). c ) = 1 - 10 -5 =99.999%, and the minimum reliability requirement for the wheel is 99.0%. The goal of reliability optimization design is to improve the wheel's lifespan while meeting reliability requirements by optimizing the wheel's geometry.

[0076] In reliability optimization, the design variables are 5 types of key geometric dimensions x. d =(r1,r2,r a7 (w1, w7) T The range of variation was obtained through sensitivity analysis (with the maximum equivalent stress as the objective). The optimization objective was to maximize the life of the disk under three failure modes: low-cycle fatigue, creep-fatigue, and high-low-cycle fatigue. This was considered because the life model under all three failure modes is related to the maximum equivalent stress σ. max and maximum equivalent strain ε max The damage parameter is related, and the optimization objective is equivalent to minimizing the maximum equivalent stress σ. max and maximum equivalent strain ε max .

[0077] Optimization is performed using an improved multi-objective particle swarm optimization algorithm, such as... Figure 1 As shown, the specific steps are as follows:

[0078] (a) Initialize the random position x0 and velocity v0 of the particle; configure the iteration count t = 0, and the elite set N. e =0;

[0079] (b) Calculate the objective function of the particles and store the non-dominated solutions in the elite set;

[0080] (c) Calculate the fitness function of the particle using formula (13) and determine the individual and global extreme values ​​by roulette wheel method;

[0081] Formula (13) is as follows: The fitness function of the i-th particle is defined using the niche strategy and calculated as follows:

[0082] Fit(i) = 1 / e i i = 1, ..., N e (13)

[0083] (d) Update the particle position and order using formulas (8) and (9), where the dynamic inertia weight is calculated using formula (10);

[0084] Formulas (8) and (9) are as follows:

[0085] In the optimization process of particle swarm optimization, the position and velocity of a single particle i in the (t+1)th iteration satisfy the governing equation:

[0086] x i (t+1)=x i (t)+v i (t+1) (8)

[0087]

[0088] Where x and v represent the particle's position and velocity, respectively; the superscripts p and g represent the particle's individual optimality and global optimality, respectively; c1 and c2 are the individual and global acceleration factors, respectively; r1 and r2 are random numbers between [0,1]; and ω is the inertia weight, which controls the degree to which the velocity at the current moment inherits the velocity at the previous moment.

[0089] Formula (10) is as follows: In order to accelerate the global search capability in the initial stage of iteration and promote the local search capability in the later stage of iteration, it is assumed that the inertia weight has dynamic characteristics and decreases linearly with the number of iterations, and the expression is:

[0090]

[0091] (e) Update Elite Collection N e Determine whether the number of elite particles t exceeds the swarm size T. max If the number exceeds the limit, remove low-fitness particles; otherwise, proceed to step (f).

[0092] (f) Repeat steps (c) to (e) until the iteration termination condition is met. Output the best optimization result in the elite set.

[0093] This invention utilizes both a traditional and an improved multi-objective particle swarm optimization (MPS) algorithm for multi-objective reliability optimization design analysis of a roulette wheel. The results show that the improved MPS algorithm yields a more uniform Pareto front distribution. The maximum equivalent stress of the roulette wheel is reduced by 1.63% and 1.73% respectively, and the maximum equivalent strain is reduced by 5.93% and 6.74% respectively. Comparing the computation time of the two algorithms, the traditional MPS algorithm takes 95 minutes, while the improved MPS algorithm only takes 43 minutes, a 71% reduction in computation time. These results demonstrate that the improved MPS algorithm can improve the optimization efficiency of multi-objective reliability optimization design problems. Furthermore, the reliability results for each failure mode and the roulette wheel obtained using the improved MPS algorithm meet the design requirements, proving the optimization accuracy of the improved MPS algorithm.

[0094] The above embodiments are provided merely for the purpose of describing the present invention and are not intended to limit the scope of the invention. The scope of the invention is defined by the appended claims. Various equivalent substitutions and modifications made without departing from the spirit and principles of the invention should be covered within the scope of the invention.

Claims

1. A method for optimizing the reliability of a rotary disk considering the correlation of multiple failure modes, characterized in that, Includes the following steps: The first step is to conduct multi-failure mode correlation analysis: the pair-copula method is introduced to characterize the correlation of multivariate variables. First, the lifetime model of each failure mode of the roulette wheel is established, the random input variables are determined, the lifetime sample points of each failure mode are obtained by joint sampling method, and the parameters of the pair-copula model are simulated by the maximum likelihood estimation method to establish a joint probability distribution model describing the correlation of each failure mode. The second step is to perform multi-failure-mode reliability allocation: This involves conducting a reliability allocation of the wheel considering failure correlations, assigning the structural reliability requirements to each failure mode according to certain rules. First, the probability index for each failure mode is obtained. Given that the reliability index of the wheel structure is no less than a specified value under the design life, reliability allocation considering correlations is performed, assigning the structural reliability index to each failure mode, including: The probability index is determined by weighting factors in reliability allocation, and the specific calculation method is as follows: First, a hazard analysis is conducted to assess the overall effect of each failure mode, quantified using a risk priority number (RPN); the risk priority number (RPN) for the i-th failure mode is... i It can be calculated as: (1) Among them, s i Indicates the severity level, o i Indicates the degree of occurrence, α ik This represents the degree of influence of the i-th failure mode on the k-th failure mode, expressed here by the linear correlation coefficient; After normalizing the risk priority numbers, the reliability allocation weights are calculated as follows: (2) in, This represents the risk priority number of the i-th failure mode, and n represents the number of failure modes. Given their weights, the probability index f for each failure mode is... i Set its assigned weight, that is: (3) The reliability requirements of the structure are assigned to each failure mode according to certain rules, specifically: The reliability allocation problem is transformed into an optimization problem, expressed as: (4) Where min represents taking the minimum value, C is the sum of the cost functions of each failure mode, and st represents making R s It is the structural reliability estimated through the reliability of each failure mode, and it is the reliability R under each failure mode. i The functions H, R d It refers to design reliability, i.e., the reliability metric to be assigned, c i The cost function for each failure mode has an exponential form: (5) Among them, R i,min and R i,max Let represent the current reliability result and the maximum achievable reliability for the i-th failure mode, respectively. It is an indicator of the potential for improving reliability; The third step is to perform multi-objective reliability optimization design of the wheel: by optimizing the wheel's geometry, the wheel's lifespan is improved while meeting reliability requirements; with the maximum equivalent stress as the objective, the key geometric dimensions of the wheel are obtained as design variables through sensitivity analysis. These key geometric dimensions include the wheel's inner diameter, outer diameter, width, tenon width, and tenon thickness. The optimization objective is to maximize the wheel's lifespan under each failure mode; after determining the design variables and optimization objectives, the multi-objective particle swarm optimization algorithm is used to complete the multi-objective reliability optimization design of the wheel.

2. The disk reliability optimization method considering the correlation of multiple failure modes according to claim 1, characterized in that, In the third step, the multi-objective reliability optimization design of the roulette wheel is completed using a multi-objective particle swarm optimization algorithm based on dynamic weights. During the optimization process of the particle swarm optimization algorithm: In the (t+1)th iteration, the position and velocity of a single particle i satisfy the governing equations: (6) (7) in, and The positions and velocities of the particles are represented by p and g, respectively. The superscripts p and g represent the individual optimality and global optimality of the particles, respectively. c1 and c2 are the individual and global acceleration factors, r1 and r2 are random numbers between [0,1], and ω is the inertia weight, which controls the degree to which the velocity at the current moment inherits the velocity at the previous moment. To accelerate the global search capability in the initial stage of iteration and improve the local search capability in the later stage, it is assumed that the inertia weight has dynamic characteristics and decreases linearly with the number of iterations, resulting in the following expression: (8) Where, ω st and ω ed Let T be the initial and final values ​​of the inertia weight ω. max This represents the maximum number of iterations.

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