Complex network-based aero-engine assembly quality optimization method

Abstract

The invention discloses an aero-engine assembly quality optimization method based on a complex network. The method comprises the steps that assembly data and test run data are acquired for an aero-engine, and assembly indexes and test run indexes are screened; taking the monitoring indexes as nodes, and constructing an observation network of the aero-engine by utilizing a complex network theory and combining with the maximum information coefficient; indirect correlation among the monitoring indexes is eliminated by using a network deconvolution method, so that a direct correlation network of the aero-engine is constructed; using information geometric causal reasoning to identify the edge connection direction between the monitoring indexes in the direct association network, establishing an assembly process error transmission network of the aero-engine, and extracting a local sub-assembly process error transmission network related to the test run index; constructing an assembly process error transfer model of the aero-engine; and based on each local sub-assembly process error transfer network, determining a steady-state value of a test run index by using the assembly process error transfer model to predict the assembly quality of the aero-engine.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft engine assembly quality optimization, and in particular to an aircraft engine assembly quality optimization method based on a complex network. Background Art

[0002] Aircraft engines are often called the "heart of the aircraft," the "flower of industry," and the "crown jewel of industry." Their high precision and complexity make them one of the most advanced industrial products in the global manufacturing industry. The development of aircraft engines involves multiple cutting-edge disciplines, including mechanical engineering, automation, and electronic information technology. The technical requirements are extremely high and highly integrated. Therefore, every link, from design and development to production and subsequent maintenance, presents severe challenges.

[0003] Assembly is a core step in aircraft engine manufacturing, and its quality directly impacts overall engine performance. Aircraft engines are extremely complex structures, and assembly accounts for over 50% of the total manufacturing workload, while the overall assembly cost accounts for over one-third of the total manufacturing cost. Aircraft engines are composed of numerous parts and components, and the sheer number and complexity of these parts make the assembly process complex and cumbersome, with a low degree of automation. Therefore, improving assembly quality, production efficiency, shortening assembly cycles, reducing error rates, and effectively controlling the entire assembly process have become key challenges that require urgent solutions.

[0004] In the field of aero-engine assembly, accurately characterizing error transmission paths and intensities is a core challenge in improving assembly quality. Aero-engines are characterized by complex structures, high precision, and multi-stage coupling. Their assembly process involves hundreds of steps and thousands of parts. The coupling of geometric errors and assembly stresses between multiple steps can lead to cumulative errors. This chain-like propagation of errors can cause key assembly characteristic parameters, such as rotor coaxiality misalignment and rotor-stator clearance anomalies, to deviate from their design values, leading to risks such as increased vibration of the entire machine and decreased aerodynamic performance. Complex network theory provides a new paradigm for addressing this challenge. On the one hand, its network topology can map the error propagation relationships between parts in the assembly system. At the same time, the cascade effect quantification method based on a dynamic model can simulate the transmission process of assembly errors in the network, providing an effective solution for optimizing aero-engine assembly quality.

[0005] Existing assembly quality optimization technologies are primarily based on tolerance transfer modeling (error flow theory). For example, patent application CN118035299A describes a method and device for characterizing and optimizing assembly quality for complex products. This method establishes a three-dimensional dimensional deviation transfer model, a manufacturing cost function, and an objective function by acquiring basic process plan information. This method utilizes a genetic algorithm to solve the optimal process plan. This approach primarily relies on tolerance transfer modeling, analyzing the assembly process, and providing a theoretical basis for error modeling and quality control. However, this approach presents significant challenges for complex products like aircraft engines, which have large scale and complex assembly structures. Summary of the Invention

[0006] The purpose of the present invention is to provide an aero-engine assembly quality optimization method based on a complex network, so as to overcome the problem that the existing methods are difficult to adapt to the aero-engine quality optimization analysis.

[0007] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0008] The complex network-based aircraft engine assembly quality optimization method includes:

[0009] For multiple aircraft engines of the same model, assembly data and test data are obtained and assembly and test indicators are screened. The screened assembly and test indicators are used as monitoring indicators.

[0010] Using monitoring indicators as nodes, the observation network of aircraft engines is constructed using complex network theory combined with the maximum information coefficient;

[0011] For the observation network of aircraft engines, the network deconvolution method is used to eliminate the indirect correlation between monitoring indicators, thereby constructing a direct correlation network of aircraft engines;

[0012] Information geometry causal reasoning is used to identify the direction of the edges between monitoring indicators in a directly associated network. An assembly process error transmission network for aircraft engines is established, and local sub-assembly process error transmission networks related to test run indicators are extracted. An assembly process error transmission model for aircraft engines is constructed. Based on the error transmission networks of each local sub-assembly process, the assembly process error transmission model is used to determine the steady-state value of the test run indicator for predicting the assembly quality of aircraft engines.

[0013] Furthermore, the method further comprises:

[0014] For the error propagation network of the assembly process of aircraft engines, combined with the maximum matching theory of complex networks, the minimum driving point set is determined, and each minimum driving point set is used to form a node control scheme;

[0015] A cost model of assembly error is established, and each node control scheme is solved based on the genetic algorithm. The assembly quality optimization strategy corresponding to each node control scheme is obtained and optimized, thereby minimizing the assembly cost.

[0016] Furthermore, using monitoring indicators as nodes, the observation network of aircraft engines is constructed using complex network theory combined with the maximum information coefficient, including:

[0017] The correlation between monitoring indicators is abstracted into edges between nodes to construct an observation network for aircraft engines. The correlation between monitoring indicators is represented by the maximum information coefficient.

[0018] The adjacency matrix of the observation network is constructed using the correlation between monitoring indicators, and a construction threshold is set to limit the value of the correlation.

[0019] Furthermore, for the observation network of aircraft engines, the network deconvolution method is used to eliminate the indirect correlation between monitoring indicators, thereby constructing a direct correlation network of aircraft engines, including:

[0020] The adjacency matrix of the observation network is defined as G obs , the part of the observation network formed by the transmission coupling effect is an indirect correlation network, and its adjacency matrix is ​​defined as G indir ; After the observation network removes the indirect association network, the remaining part is the direct association network, and its adjacency matrix is ​​defined as G dir , then the relationship between the three is:

[0021] G obs =G dir +G indir

[0022] The adjacency matrix G of the indirect connection network indir Using the adjacency matrix G dir Characterize and use the infinite geometric series summation formula to calculate the adjacency matrix G of the observation network obs :

[0023] G obs =G dir (IG dir ) -1

[0024] To G obs With G dir Eigenvalue decomposition can be performed to obtain the eigenvalue matrix and eigenvector matrix:

[0025]

[0026] Where U is the decomposed eigenvector matrix, U -1 is the inverse matrix of U, Σobs and Σ dir is the adjacency matrix G obs With G dir The corresponding eigenvalue matrix;

[0027] Combine the eigenvalue decomposition results and the adjacency matrix G obs The expression of eigenvalue matrix ∑ obs and ∑ dir The relationship between the eigenvalues ​​in , based on the adjacency matrix G of the observation network obs Get the adjacency matrix G of the directly connected network dir , achieving the elimination of indirect associations.

[0028] Furthermore, information geometry causal reasoning is used to identify the direction of the edges between monitoring indicators in the direct association network, and an error propagation network for the assembly process of aircraft engines is established, including:

[0029] By determining the causal relationship between the monitoring indicators in the direct correlation network, the direct correlation network is converted into a directed network, that is, the assembly process error transmission network is obtained;

[0030] Directly associated with monitoring indicators x in the network i and x j Causal relationship It is expressed as follows:

[0031]

[0032] when When the edge direction is inferred as the monitoring indicator x i Pointing monitoring indicator x j ;when When is the monitoring indicator x j Pointing monitoring indicator x i Where and Represents the monitoring index x i and monitoring indicators x j The exponential family of "smooth" reference distributions, and Represents monitoring indicator x i and monitoring indicators x j The probability density of , D(·) represents the relative entropy distance or Kullback Leibler divergence;

[0033] The adjacency matrix A of the assembly process error propagation network is expressed as follows:

[0034]

[0035] Among them A ijRepresents the element in row i and column j in the adjacency matrix A.

[0036] Furthermore, the error propagation network of the local sub-assembly process related to the test run index is extracted, including:

[0037] In the assembly process error propagation network, the test run indicator node in the most downstream node of the assembly process error propagation network is found as the target node; starting from each target node, the breadth-first search algorithm is used to trace back along the direction of the edges of each node to determine all reachable assembly indicator nodes; finally, the target node and all its reachable assembly indicator nodes, as well as all the edges between them, are extracted from the assembly process error propagation network to form a local sub-assembly process error propagation network corresponding to each target node and the corresponding adjacency matrix.

[0038] Furthermore, an error propagation model for the assembly process of an aircraft engine is constructed. Based on the error propagation networks of each local sub-assembly process, the assembly process error propagation model is used to determine the steady-state values ​​of the test run indicators for predicting the assembly quality of the aircraft engine, including:

[0039] The error propagation model of the aircraft engine assembly process is as follows:

[0040]

[0041] Where t is the time parameter, x i 、x j They represent the i-th and j-th monitoring indicators in the error transmission network of the local sub-assembly process, I i is the initial state of the i-th monitoring indicator, B i represents the rate of change of the monitoring indicator itself, β represents the transmission rate between adjacent monitoring indicators, and A′ ij The adjacency matrix representing the error propagation network of the local subassembly process;

[0042] By giving a given time t, the specific values ​​of each monitoring indicator are brought into the local sub-assembly process error transfer network to obtain the corresponding adjacency matrix A′ ij , the steady-state value of each test index is calculated through the error propagation model of the aircraft engine assembly process; the lower the steady-state value, the better the assembly quality of the aircraft engine.

[0043] Furthermore, for the error propagation network of the assembly process of aircraft engines, combined with the maximum matching theory of complex networks, the minimum driving point set is determined. Each minimum driving point set is used to form a node control scheme, including:

[0044] Among all the nodes in the assembly process error propagation network, the test run indicator is designated as the target node, and the remaining test run indicators are the source nodes. The Hungarian algorithm is first used to obtain an initial maximum matching set and minimum driving node set of the assembly process error propagation network from all source nodes. The matching reversal theorem is then used to continuously replace one of the nodes with an in-degree greater than 0 to obtain a new minimum driving node set. The nodes are updated, and the incoming and outgoing edges corresponding to the two nodes involved in the matching reversal are deleted from the network respectively. The above process is repeated until the in-degree of all nodes in the minimum driving node set is 0. All minimum driving node sets are summarized. The assembly indicators corresponding to the nodes contained in each minimum driving node set constitute a node control scheme that can be adopted to achieve global assembly quality control.

[0045] Furthermore, a cost model for assembly error is established. Based on the genetic algorithm, each node control scheme is solved to obtain the assembly quality optimization strategy corresponding to each node control scheme and select the optimal one, thereby minimizing the assembly cost, including:

[0046] The cost model of assembly error is constructed using the level of assembly index;

[0047] The assembly indicators are divided into multiple assembly levels. For each assembly indicator included in the node control scheme, an initial assembly level is first assigned to each assembly indicator. The initial assembly level of each assembly indicator is used as the input of the genetic algorithm, and the parameters of the genetic algorithm are set. The assembly cost of the node control scheme is calculated as the fitness based on the cost model, and the global optimal solution is updated based on the fitness. After the number of iterations is reached, the final global optimal solution is output, which is a set of optimal assembly indicator levels as the assembly quality optimization strategy obtained by optimizing the node control scheme.

[0048] Determine the assembly quality optimization strategies corresponding to different node control schemes, bring the levels of assembly indicators contained in the assembly quality optimization strategies into the cost model formula, compare the assembly costs of all assembly quality optimization strategies, and select the assembly quality optimization strategy with the lowest assembly cost as the optimal strategy.

[0049] Furthermore, when there are multiple minimum assembly costs, the structural controllability theory is used to calculate and compare the average control centrality of all nodes in each minimum driving node set. At this time, the assembly quality optimization strategy with the minimum assembly cost and the maximum node average control centrality is selected as the optimal strategy.

[0050] A terminal device comprises a processor, a memory and a computer program stored in the memory; when the processor executes the computer program, the complex network-based aircraft engine assembly quality optimization method is implemented.

[0051] A computer-readable storage medium stores a computer program; when the computer program is executed by a processor, the complex network-based aircraft engine assembly quality optimization method is implemented.

[0052] Compared with the prior art, the present invention has the following technical features:

[0053] 1. The present invention constructs an error propagation model of the assembly process of an aero-engine based on real aero-engine assembly-test data and complex networks, which can reveal the error propagation relationship in the highly complex aero-engine assembly process.

[0054] 2. The aircraft engine assembly error transmission model constructed by the present invention can better simulate the error transmission process between aircraft engine assembly processes, achieve better prediction of assembly quality, and quantitatively analyze the error transmission behavior in aircraft engine assembly processes.

[0055] 3. The aircraft engine assembly quality optimization method proposed in the present invention can effectively optimize assembly data, ensuring that costs are minimized while meeting assembly quality requirements, and provide theoretical support and practical guidance for the manufacturing process of aircraft engines. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 Schematic diagram of the process of the present invention;

[0057] Figure 2 : This is the error propagation network of the local sub-assembly process of each test index of the aircraft engine in the embodiment of the present invention; (a) to (f) are the error propagation networks of the local sub-assembly process of test index 1 to test index 6 respectively;

[0058] Figure 3 Comparison of predicted and actual values ​​of test indicators reflecting assembly quality of aircraft engines according to an embodiment of the present invention; (a) to (f) are comparisons of six different test indicators (actual vibration values ​​1 to 6).

[0059] Figure 4 The control centrality distribution of different nodes of the aircraft engine in the embodiment of the present invention;

[0060] Figure 5 The figure shows a comparison of the aircraft engine assembly quality control effects of the optimization algorithm obtained in the embodiment of the present invention and the original data. DETAILED DESCRIPTION

[0061] Based on aircraft engine assembly and test run data, the present invention proposes an aircraft engine assembly quality optimization method in combination with complex networks. By establishing an aircraft engine assembly error transmission model and a quality optimization model, the fault propagation behavior in the aircraft engine assembly process can be numerically and quantitatively analyzed, providing an effective assembly quality optimization method, providing theoretical support and practical guidance for the aircraft engine manufacturing process, thereby improving product quality and production efficiency and reducing manufacturing costs.

[0062] See attached Figure 1 The present invention provides a complex network-based aircraft engine assembly quality optimization method, comprising the following steps:

[0063] Step 1: Obtain assembly data and performance-related test data for the aircraft engine and screen assembly indicators and test indicators, and use the screened assembly indicators and test indicators as monitoring indicators.

[0064] To effectively ensure the final assembly quality of the product, sensors are installed at assembly stations in key aircraft engine assembly processes to collect and acquire aircraft engine assembly indicators. The locations where the sensors are installed serve as inspection points for assembly quality. The assembly data of each aircraft engine consists of multiple assembly indicators, and the test data consists of multiple performance-related test indicators. This solution, for the same model of aircraft engines, collects assembly indicators for key units (fan, compressor, high-pressure turbine, low-pressure turbine) and all links involved in their assembly into aircraft engines, as well as multiple vibration-related test indicators that reflect errors generated during the assembly process and evaluate the operational stability of the aircraft engine.

[0065] Afterwards, the assembly indicators and test indicators were used as monitoring indicators, and variance analysis was performed on all monitoring indicators. Based on statistical principles, monitoring indicators with zero variance were eliminated, thereby achieving scientific screening of aircraft engine assembly indicators and test indicators.

[0066] Step 2: Using monitoring indicators as nodes, the observation network of aircraft engines is constructed using complex network theory combined with the maximum information coefficient.

[0067] All monitoring indicators of the aircraft engine screened in step 1, namely the assembly indicators and test indicators, are abstracted as nodes, and the correlations between the monitoring indicators are abstracted as edges between the nodes to construct an observation network for the aircraft engine. The correlations between the monitoring indicators are represented by the maximum information coefficient, which is expressed as follows:

[0068]

[0069] In the above formula, x i 、x jrepresents the i-th and j-th monitoring indicators in the observation network, MIC(x i ,x j ) represents the monitoring indicator x i 、x j The maximum information coefficient between them, that is, the correlation between them; i 、x j Construct a two-dimensional scatter plot and divide the grid; first, i 、x j Divide the interval into grids; then a and b are respectively i Dimension and x j The number of grids divided in the dimension; B is the preset value, which is generally taken to be about 0.6 power of the total amount of monitoring indicators; max(·) and min(·) are the maximum and minimum value operations respectively; I(x i ,x j ) represents the monitoring indicator x i 、x j The relative entropy between can be calculated by the following formula:

[0070]

[0071] Among them, p(x i ',x' j ) is the joint probability density function, x i 'Indicates the monitoring index x i The value in the divided interval, x' j Indicates the monitoring indicator x j The value in the divided interval; p(x' i )、p(x' j ) are x i 'and x' j The marginal probability density function, I(x i ,x j ) is larger, indicating that the monitoring index x i with x j The greater the degree of correlation between them.

[0072] The maximum information coefficient is more inclusive of the direct correlation calculation of the data, so it is necessary to set a correlation threshold to ensure that the calculated correlation coefficient actually exists in reality:

[0073]

[0074] Among them, MIC i,j is the element in row i and column j of the adjacency matrix of the observation network, representing the monitoring indicator x i and x jThe observation correlation between them; σ is the threshold for constructing the network model, which is 0.2 in this embodiment; when MIC(x i ,x j )≥σ, then the monitoring index x i and x j There exists an edge between them; otherwise, there does not exist.

[0075] Step 3: For the observation network of aircraft engines, the network deconvolution method is used to eliminate the indirect correlation between monitoring indicators, thereby constructing a direct correlation network of aircraft engines.

[0076] Due to the transfer coupling effect between aircraft engine assembly processes, correlations are calculated between many unrelated assembly processes. Therefore, in the observation network obtained by calculating the maximum information coefficient in step 2, there are usually various false connections, that is, indirect associations. In order to filter out these indirect associations, the network deconvolution algorithm is used to extract the direct correlation network.

[0077] Specifically, the adjacency matrix of the observation network constructed in step 2 is defined as G obs , the part of the observation network formed by the transmission coupling effect is an indirect correlation network, and its adjacency matrix is ​​defined as G indir ; After the observation network removes the indirect association network, the remaining part is the direct association network, and its adjacency matrix is ​​defined as G dir , then the relationship between the three can be expressed as:

[0078] G obs =G dir +G indir (4)

[0079] Adjacency matrix G of indirect connection network indir is the sum of all noises generated by the transfer coupling effects within the system:

[0080]

[0081] Among them, the noise generated by the transmission coupling effect of the second-order path between any two adjacent monitoring indicators is represented by the adjacency matrix G dir The square representation of the noise generated by the third-order path is represented by the adjacency matrix G dir The cubic representation of , and so on.

[0082] The matrix elements in formula (4) can be linearly scaled to limit the value range to the interval (0,1). Then, formula (5) is substituted into formula (4) to calculate the adjacency matrix G of the observation network using the infinite geometric series summation formula. obs :

[0083]

[0084] Where I is the unit matrix, and the dimension is the number of nodes in the directly connected network; the superscript -1 indicates the inversion operation; the adjacency matrix G of the directly connected network can be calculated from formula (6): dir Adjacency matrix G of the observation network obs The relationship is specifically expressed as follows:

[0085] G dir =G obs (I+G obs ) -1 (7)

[0086] For symmetric input matrices, G obs With G dir Eigenvalue decomposition can be performed to obtain the eigenvalue matrix and eigenvector matrix:

[0087]

[0088] Where U is the decomposed eigenvector matrix, U -1 is the inverse matrix of U, ∑ obs and ∑ dir is the adjacency matrix G obs With G dir The corresponding eigenvalue matrix is ​​specifically formed by the eigenvalue λ obs and λ dir The diagonal matrix is ​​composed of:

[0089]

[0090] in, and The adjacency matrix G is obs and the adjacency matrix G dir The i-th eigenvalue of , i = 1, 2..., N, N is the number of eigenvalues; Substituting equations (9) and (8) into equation (6) yields:

[0091]

[0092] From this we can get the eigenvalue matrix ∑ obs and ∑ dir The relationship between the eigenvalues ​​in :

[0093]

[0094] Therefore, the adjacency matrix G of the observation network can be obs The eigenvalue of Transformed into the adjacency matrix G of the direct association network through formula (11) dir The eigenvalue of Since the adjacency matrix G of the observation network obsIt has been constructed in step 2 and is known; then the adjacency matrix G of the directly connected network can be obtained dir , achieving the elimination of indirect associations.

[0095] Step 4: Use information geometry causal reasoning to identify the direction of the edges between monitoring indicators in the direct association network, establish the aircraft engine assembly process error propagation network, and extract the local sub-assembly process error propagation network related to the test indicators;

[0096] An error propagation model for the assembly process of an aero-engine is constructed. Based on the error propagation networks of each local sub-assembly process, the steady-state values ​​of the test run indicators are determined using the assembly process error propagation model to predict the assembly quality of the aero-engine.

[0097] 4.1 Information geometry causal reasoning.

[0098] Based on the direct correlation network obtained in step 3, the monitoring index x in the direct correlation network is determined using information-geometric causal inference (IGCI). i and x j The causal relationship between them, that is, the direction of error transmission It is expressed as follows:

[0099]

[0100] when When the monitoring indicator x i 、x j The direction of the edge between them is the monitoring indicator x i Pointing monitoring indicator x j ;when When is the monitoring indicator x j Pointing monitoring indicator x i Where and Represents the monitoring index x i and monitoring indicators x j The exponential family of "smooth" reference distributions, and Represents monitoring indicator x i and monitoring indicators x j The probability density of express and The relative entropy distance or Kullback Leibler divergence between express and The relative entropy distance or Kullback Leibler divergence between them; where a "smooth" reference distribution refers to a continuous, differentiable, and non-peaked approximate distribution used to compare with the true distribution when computing the relative entropy distance or Kullback Leibler divergence.

[0101] 4.2 Assembly process error transmission network.

[0102] Therefore, based on the direct association network constructed in step 3, the direct association network is converted into a directed network by determining the causal relationship between the monitoring indicators in the direct association network, that is, the assembly process error transmission network is obtained; the causal relationship between the monitoring indicators characterizes the error transmission direction in the network; and the influence of the assembly condition on the error transmission is introduced to construct the adjacency matrix A of the assembly process error transmission network, which is specifically expressed as follows:

[0103]

[0104] Among them A ij Represents the element in row i and column j in the adjacency matrix A.

[0105] 4.3 Error propagation network of local sub-assembly process.

[0106] Finally, the error propagation network of the local sub-assembly process is extracted based on the directed propagation characteristics of the error in the assembly process error propagation network:

[0107] First, the target node is determined; in the assembly process error transmission network, the test run indicator is located at the downstream of the network and inherits the transmission results of the upstream error; therefore, the test run indicator node in the downstream node of the assembly process error transmission network is found as the target node. The target node is specified by the user, for example, the test run indicator node of interest; then, starting from each target node, the breadth-first search algorithm is used to trace back along the direction of the edges of each node to determine all reachable assembly indicator nodes; finally, the target node and all its reachable assembly indicator nodes, as well as all the edges between them, are extracted from the assembly process error transmission network to form a local sub-assembly process error transmission network corresponding to each target node and the corresponding adjacency matrix (the corresponding part is extracted from the adjacency matrix A).

[0108] 4.4 Error transfer model of aircraft engine assembly process.

[0109] Aiming at the error propagation network of each local sub-assembly process, the infectious disease model is used to construct the error propagation model of the assembly process of aircraft engines.

[0110] During the assembly process, errors in assembly indicators themselves are transmitted to other assembly indicators through closely related processes, thus forming a chain reaction of errors. This is similar to the infectious disease model. Therefore, based on the dynamics of infectious diseases, the assembly indicators and test indicators of aircraft engines are introduced to construct an error propagation model for aircraft engine assembly processes:

[0111]

[0112] In the formula represents the differential, t is the time parameter, x i 、x j They represent the i-th and j-th monitoring indicators in the error transmission network of the local sub-assembly process, I i is the initial state of the i-th monitoring indicator, B i represents the rate of change of the monitoring indicator itself, β represents the transmission rate between adjacent monitoring indicators, and A′ ij Adjacency matrix representing the error propagation network of the local subassembly process.

[0113] Finally, for the assembly process error transmission model corresponding to each target node, the steady-state value of each monitoring indicator is calculated. Specifically:

[0114] By giving a given time t, the specific values ​​of each monitoring indicator are brought into the local sub-assembly process error transfer network to obtain the corresponding adjacency matrix A′ ij , the steady-state values ​​of each test index are calculated by formula (14) (the left side of the equation is set to 0), which is used to predict the assembly quality of the aircraft engine.

[0115] Among all monitoring indicators, the steady-state value of the test indicator can be used to predict the assembly quality of the aircraft engine; in an example of the present invention, the steady-state value of each test indicator calculated is as follows: Figure 3 shown; from Figure 3 The steady-state value (predicted value) of the test index shows a relatively obvious linear positive correlation with the actual value (the vibration amount measured during the actual test process), which shows that the assembly process error transmission model in the present invention can effectively predict the assembly quality of aircraft engines; the lower the steady-state value, the better the assembly quality.

[0116] Step 5: For the error transmission network of the assembly process of the aircraft engine, combined with the maximum matching theory of complex networks, the minimum driving point set is determined, and each minimum driving point set is used to form a node control scheme.

[0117] Among all the nodes in the assembly process error transmission network, the test run indicator is designated as the target node, and the remaining assembly indicators are the source nodes; the Hungarian algorithm is first used to obtain an initial maximum matching set and minimum driving node set of the assembly process error transmission network from all source nodes, where a matching is a set of edges, and any two edges in the set have no common vertices. The maximum matching set refers to the matching with the largest number of matching edges among all the matchings in the network; the matching reversal theorem is used to continuously replace one of the nodes with an in-degree greater than 0 to obtain a new minimum driving node set; the nodes are updated, and the incoming and outgoing edges corresponding to the two nodes participating in the matching reversal are deleted from the network respectively; the above process is repeated until the in-degree of all nodes in the minimum driving node set is 0; all minimum driving node sets are summarized; the assembly indicators corresponding to the nodes contained in each minimum driving node set constitute a node control scheme that can be adopted to achieve global assembly quality control.

[0118] Then, the structural controllability theory is used to calculate and compare the average control centrality of all nodes in all minimum driving node sets, thereby providing a theoretical reference for determining the optimal assembly quality optimization strategy.

[0119] Step 6: Establish a cost model for assembly error, solve each node control scheme based on the genetic algorithm, obtain the assembly quality optimization strategy corresponding to each node control scheme and optimize it, so as to minimize the assembly cost.

[0120] The assembly cost-error function is constructed as the cost model of assembly error as follows:

[0121] C(T)=ae -bT (15)

[0122] Where T is the level of assembly index, C(T) is the assembly cost, a is the benchmark cost, and b is a constant related to process complexity.

[0123] In step 6, multiple minimum driving point sets are obtained. Each minimum driving point set contains a set of nodes corresponding to the assembly index, that is, a node control scheme.

[0124] According to the assembly regulations of aircraft engine manufacturers, the assembly indicators are divided into five assembly levels, for example, 0-0.2 is level 1, 0.2-0.4 is level 2, and so on. For the assembly indicators included in each node control scheme, an initial assembly level is first assigned to each assembly indicator. The initial assembly level can be, for example, the specific value of the original assembly indicator provided by the manufacturer. The initial assembly level of each assembly indicator in each node control scheme is used as the input of the genetic algorithm, and the parameters of the genetic algorithm are set, including population size, maximum number of iterations, crossover probability, and mutation probability. The assembly cost of the node control scheme is calculated as the fitness according to formula (15), and the global optimal solution is updated according to the fitness. After the number of iterations is reached, the final global optimal solution is output, that is, the level of a set of optimal assembly indicators is used as the assembly quality optimization strategy obtained by optimizing the node control scheme, that is, the level of the assembly indicators that need to be adjusted under the minimum driving node set scheme.

[0125] By using the same method, the assembly quality optimization strategies corresponding to different node control schemes are obtained. The levels of assembly indicators contained in the assembly quality optimization strategies are introduced into the cost model of assembly error (15). The assembly costs of all assembly quality optimization strategies are compared, and the assembly quality optimization strategy with the minimum assembly cost is selected as the optimal strategy.

[0126] When there are multiple minimum assembly costs, it is necessary to consider the node average control centrality of each minimum driving node set obtained in step 6. At this time, the assembly quality optimization strategy with the minimum assembly cost and the maximum node average control centrality is selected as the optimal strategy.

[0127] Example:

[0128] This example uses a specific aircraft engine manufacturer as the research object, collecting assembly and test data for 90 turbofan aircraft engines of a certain model. The data collected for each engine includes 90 assembly data points and 6 test run indicators. The assembly quality inspection points mainly include several key units and the links involved in the assembly process of the complete engine. These key units include the fan, compressor, high-pressure turbine, and low-pressure turbine. The inspection items mainly include assembly characteristics such as imbalance, assembly dimensions, torque, and other 90 assembly data items, as shown in Table 1:

[0129] Table 1 Description of assembly quality inspection indicators

[0130]

[0131]

[0132]

[0133] The six test run index parameters are test run indicators related to vibration. The assembly quality of an aircraft engine directly affects its performance during the test run. Errors generated during the assembly process are often reflected through vibration characteristics. Vibration amplitudes exceeding a certain threshold will affect the matching accuracy of engine components and overall performance. In mild cases, this will reduce operating efficiency and lead to performance degradation. In severe cases, it may cause component damage, thereby threatening the safe operation of the aircraft. Therefore, test run indicators related to vibration are used to reflect the assembly quality of aircraft engines. The specific indicators are shown in Table 2:

[0134] Table 2 Test index description

[0135]

[0136] In this embodiment, the error propagation network of the local sub-assembly process constructed for one aircraft engine is as follows: Figure 2 shown.

[0137] In order to evaluate the error transmission of the assembly process of the aircraft engine constructed by the present invention, this embodiment performs an error transmission simulation on a single aircraft engine to obtain a scatter plot between the predicted values ​​of the vibration indicators of each aircraft engine and the vibration values ​​measured during the actual test run, as shown in FIG. Figure 3 As shown in the figure, verification shows that the predicted values ​​exhibit a strong linear positive correlation with the vibration values ​​measured during the actual test run, demonstrating the effectiveness of the assembly quality prediction method. The model can effectively simulate the transmission of assembly data errors. Furthermore, based on the actual test run requirements, the thresholds for the predicted vibration indices for test run indicator nodes 1 through 6 at steady-state are 0.7, 0.6, 0.5, 0.5, 0.6, and 0.6, respectively.

[0138] To optimize aircraft engine assembly quality, this example applies the maximum matching theory of complex networks to find all minimum driver node sets. The average control centrality of nodes in different minimum driver node sets is compared to identify nodes that are important for system control. Table 3 shows the control centrality of different node types in this example. The experimental results show that the minimum driver node set 9 performs well in all three centrality metrics.

[0139] Table 3 Comparison of centrality of different minimum driver node sets

[0140]

[0141] In order to solve the complex nonlinear and multi-constraint problems in the aircraft engine assembly quality optimization model, the assembly data is divided into 5 assembly levels according to the manufacturer's original assembly regulations. The smaller the assembly level, the smaller the error range, and the corresponding assembly accuracy requirement is higher. The relationship between the error band range and the error level is as follows: Figure 4, the genetic algorithm is used to solve the assembly parameters to ensure that the cost is minimized while meeting the assembly quality requirements. The specific optimal assembly level adjustment of a certain aircraft engine is shown in Table 4:

[0142] Table 4 Optimal adjustment strategy for the assembly of a certain aircraft engine

[0143]

[0144]

[0145] In order to verify the effectiveness of the assembly quality optimization method constructed by the present invention, the assembly quality of the optimization algorithm is compared with that of the original assembly data. Figure 5 As shown, Figure 5 The blue scatter points in the middle represent the minimum costs corresponding to different thresholds under the optimal adjustment strategy, and the red scatter points represent the assembly costs and predicted values ​​of the dynamic steady state of the 90 engines based on the original data. The proposed optimal control strategy can effectively improve test performance and reduce costs.

[0146] The examples show that the error transfer model for the assembly process of an aircraft engine constructed by the present invention has a predicted value of the test performance that is proportional to the actual value, and has a good effect in predicting the assembly quality. This means that the method of the present invention can numerically and quantitatively analyze the error transfer behavior in the assembly process of an aircraft engine; the aircraft engine optimization model proposed by the present invention can effectively improve the test performance and reduce costs, providing a scientific basis and practical guidance for the improvement of the aircraft engine assembly process.

[0147] The above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the various embodiments of the present application, and should all be included in the scope of protection of the present application.

Claims

1. The method for optimizing the assembly quality of an aero-engine based on a complex network is characterized by: include: Obtain assembly data and test data for aircraft engines, screen assembly and test indicators, and use the screened assembly and test indicators as monitoring indicators; Using monitoring indicators as nodes, the observation network of aircraft engines is constructed using complex network theory combined with the maximum information coefficient; For the observation network of aircraft engines, the network deconvolution method is used to eliminate the indirect correlation between monitoring indicators, thereby constructing a direct correlation network of aircraft engines; Information geometry causal reasoning is used to identify the direction of the edges between monitoring indicators in a directly associated network. An assembly process error transmission network for aircraft engines is established, and local sub-assembly process error transmission networks related to test run indicators are extracted. An assembly process error transmission model for aircraft engines is constructed. Based on the error transmission networks of each local sub-assembly process, the assembly process error transmission model is used to determine the steady-state value of the test run indicator for predicting the assembly quality of aircraft engines.

2. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: The method further comprises: For the error propagation network of the assembly process of aircraft engines, combined with the maximum matching theory of complex networks, the minimum driving point set is determined, and each minimum driving point set is used to form a node control scheme; A cost model of assembly error is established, and each node control scheme is solved based on the genetic algorithm. The assembly quality optimization strategy corresponding to each node control scheme is obtained and optimized, thereby minimizing the assembly cost.

3. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: Using monitoring indicators as nodes, the observation network of aircraft engines is constructed using complex network theory combined with the maximum information coefficient, including: The correlation between monitoring indicators is abstracted into edges between nodes to construct an observation network for aircraft engines. The correlation between monitoring indicators is represented by the maximum information coefficient. The adjacency matrix of the observation network is constructed using the correlation between monitoring indicators, and a construction threshold is set to limit the value of the correlation.

4. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: For the observation network of aircraft engines, the network deconvolution method is used to eliminate the indirect correlation between monitoring indicators, thereby constructing a direct correlation network of aircraft engines, including: The adjacency matrix of the observation network is defined as G obs , the part of the observation network formed by the transmission coupling effect is an indirect correlation network, and its adjacency matrix is ​​defined as G indir ; After the observation network removes the indirect association network, the remaining part is the direct association network, and its adjacency matrix is ​​defined as G dir , then the relationship between the three is: G obs =G dir +G indir The adjacency matrix G of the indirect connection network indir Using the adjacency matrix G dir Characterize and use the infinite geometric series summation formula to calculate the adjacency matrix G of the observation network obs : G obs =G dir (IG dir ) -1 To G obs With G dir Eigenvalue decomposition can be performed to obtain the eigenvalue matrix and eigenvector matrix: Where U is the decomposed eigenvector matrix, U -1 is the inverse matrix of U, Σ obs and Σ dir is the adjacency matrix G obs With G dir The corresponding eigenvalue matrix; Combine the eigenvalue decomposition results and the adjacency matrix G obs The expression of eigenvalue matrix ∑ obs and Σ dir The relationship between the eigenvalues ​​in , based on the adjacency matrix G of the observation network obs Get the adjacency matrix G of the directly connected network dir , achieving the elimination of indirect associations.

5. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: Information geometry causal reasoning is used to identify the direction of the edges between monitoring indicators in a direct association network, and an error propagation network for the assembly process of an aircraft engine is established, including: By determining the causal relationship between the monitoring indicators in the direct correlation network, the direct correlation network is converted into a directed network, that is, the assembly process error transmission network is obtained; Directly associated with monitoring indicators x in the network i and x j Causal relationship It is expressed as follows: when When the edge direction is inferred as the monitoring indicator x i Pointing monitoring indicator x j ;when When is the monitoring indicator x j Pointing monitoring indicator x i Where and Represents the monitoring index x i and monitoring indicators x j The exponential family of "smooth" reference distributions, and Represents monitoring indicator x i and monitoring indicators x j The probability density of , D(·) represents the relative entropy distance or Kullback Leibler divergence; The adjacency matrix A of the assembly process error propagation network is expressed as follows: Among them A ij Represents the element in row i and column j in the adjacency matrix A.

6. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: Extract the local sub-assembly process error propagation network related to the test run indicators, including: In the assembly process error propagation network, the test run indicator node in the most downstream node of the assembly process error propagation network is found as the target node; starting from each target node, the breadth-first search algorithm is used to trace back along the direction of the edges of each node to determine all reachable assembly indicator nodes; finally, the target node and all its reachable assembly indicator nodes, as well as all the edges between them, are extracted from the assembly process error propagation network to form a local sub-assembly process error propagation network corresponding to each target node and the corresponding adjacency matrix.

7. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: Construct an error propagation model for the assembly process of an aircraft engine. Based on the error propagation network of each local sub-assembly process, the assembly process error propagation model is used to determine the steady-state value of the test index to predict the assembly quality of the aircraft engine, including: The error propagation model of the aircraft engine assembly process is as follows: Where t is the time parameter, x i 、x j They represent the i-th and j-th monitoring indicators in the error transmission network of the local sub-assembly process, I i is the initial state of the i-th monitoring indicator, B i represents the rate of change of the monitoring indicator itself, β represents the transmission rate between adjacent monitoring indicators, and A ij ′ represents the adjacency matrix of the error propagation network of the local sub-assembly process; By giving a given time t, the specific values ​​of each monitoring indicator are brought into the local sub-assembly process error transfer network to obtain the corresponding adjacency matrix A ij ′, the steady-state values ​​of various test indicators are calculated through the error propagation model of the aircraft engine assembly process; the lower the steady-state value, the better the assembly quality of the aircraft engine.

8. The method for optimizing aircraft engine assembly quality based on complex networks according to claim 1, characterized in that: For the error propagation network of the assembly process of aircraft engines, combined with the maximum matching theory of complex networks, the minimum driving point set is determined. Each minimum driving point set is used to form a node control scheme, including: Among all the nodes in the assembly process error propagation network, the test run indicator is designated as the target node, and the remaining test run indicators are the source nodes. The Hungarian algorithm is first used to obtain an initial maximum matching set and minimum driving node set of the assembly process error propagation network from all source nodes. The matching reversal theorem is then used to continuously replace one of the nodes with an in-degree greater than 0 to obtain a new minimum driving node set. The nodes are updated, and the incoming and outgoing edges corresponding to the two nodes involved in the matching reversal are deleted from the network respectively. The above process is repeated until the in-degree of all nodes in the minimum driving node set is 0. All minimum driving node sets are summarized. The assembly indicators corresponding to the nodes contained in each minimum driving node set constitute a node control scheme that can be adopted to achieve global assembly quality control.

9. The method for optimizing the assembly quality of an aero-engine based on a complex network according to claim 1, characterized in that: Establish an assembly error cost model, solve each node control scheme based on a genetic algorithm, obtain the assembly quality optimization strategy corresponding to each node control scheme, and optimize it to minimize the assembly cost, including: The cost model of assembly error is constructed using the level of assembly index; The assembly indicators are divided into multiple assembly levels. For each assembly indicator included in the node control scheme, an initial assembly level is first assigned to each assembly indicator. The initial assembly level of each assembly indicator is used as the input of the genetic algorithm, and the parameters of the genetic algorithm are set. The assembly cost of the node control scheme is calculated as the fitness based on the cost model, and the global optimal solution is updated based on the fitness. After the number of iterations is reached, the final global optimal solution is output, which is a set of optimal assembly indicator levels as the assembly quality optimization strategy obtained by optimizing the node control scheme. Determine the assembly quality optimization strategies corresponding to different node control schemes, bring the levels of assembly indicators contained in the assembly quality optimization strategies into the cost model formula, compare the assembly costs of all assembly quality optimization strategies, and select the assembly quality optimization strategy with the lowest assembly cost as the optimal strategy.

10. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the complex network-based aircraft engine assembly quality optimization method according to any one of claims 1 to 9 is implemented.

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