Mechanical structure reliability analysis method based on active learning
By combining evidence theory and active learning methods of convolutional neural networks, the problem of lack of information on uncertain parameters in the reliability analysis of engineering machinery structures is solved, efficient focal element recognition and classification is achieved, computing efficiency and model accuracy are improved, and the security of the structure is ensured.
Patent Information
- Application Number
- CN202510655993.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-05-21
- Publication Date
- 2025-08-26
AI Technical Summary
When dealing with complex mechanical structures, the existing reliability analysis methods of engineering machinery are faced with the problem of insufficient applicability of the probability model, large calculation amount and inefficient efficiency, and excessive sample focal elements, resulting in high training cost of convolutional neural networks.
Using an active learning method, combining evidence theory and convolutional neural network, through Latin hypercube experimental design and genetic algorithm, focal element samples are gradually selected and marked, convolutional neural network model is constructed and updated, and focal element recognition and classification of focal element pools is optimized.
It effectively reduces the uncertainty deviation of the construction machinery structure, improves the calculation efficiency and model accuracy, and ensures the safety and reliability analysis of the structure.
Smart Images
Figure CN120541995A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a mechanical structure reliability analysis method based on active learning, and in particular to a reliability analysis method based on evidence theory and active learning focal element selection, which is applicable to problems with uncertainty in structural reliability and performance evaluation. Background Art
[0002] With the increasing complexity of engineering structures and mechanical system designs, there are usually a large number of uncertainties, so it is of great significance to apply reliability optimization design to the design of complex mechanical structures.
[0003] The reliability analysis methods for existing engineering machinery structures still have the following deficiencies:
[0004] 1. Existing engineering machinery design methods typically use well-established probabilistic models to describe and characterize uncertainty. However, probabilistic models require a large amount of uncertainty information to construct an accurate distribution of random variables. In practical applications, the lack of sufficient relevant information or the prohibitive cost of obtaining samples often prevents accurate distributions of certain parameters, limiting the applicability of traditional probabilistic models to complex mechanical structure design.
[0005] 2. Regarding the reliability optimization design method of engineering machinery structures, the existing structural reliability analysis method based on evidence theory faces the problems of excessive computational complexity and low efficiency. Especially when the number of focal elements in the joint identification framework increases significantly, the computational complexity of extreme value analysis increases exponentially.
[0006] 3. Regarding the reliability optimization design method of engineering machinery structures, in the existing structural reliability analysis method based on evidence theory, the traditional sampling method has too many sample focal elements, which leads to high training cost of convolutional neural network model and reduces computational efficiency. Summary of the Invention
[0007] In order to overcome the above problems, the present invention proposes a mechanical structure reliability analysis method based on active learning to solve the above problems.
[0008] The technical solution adopted by the present invention to solve the technical problem is: a mechanical structure reliability analysis method based on active learning, characterized by comprising the following steps:
[0009] Step 1: Analyze the uncertainty factors in the design process of complex mechanical structures, and determine the identification framework and basic credibility distribution of evidence variables based on the information of sample points. Then, establish the limit state function g(X) for the reliability assessment of complex mechanical structures, as shown below:
[0010] g(X)=g0 Formula (1)
[0011] In formula (1), X represents the independent evidence variables X1, X2, ..., X n The n-dimensional evidence vector is composed of g(X), g(X) is the response function of the structure, which is used to determine whether the structure is safe. g0 represents the allowable response value of the structural response function. A safe region can be defined based on g(X) and g0:
[0012] G={X|g(X)≤g0} Formula (2)
[0013] Step 2: Construct a joint identification framework for evidence theory reliability analysis problem Θ X With joint focal element A X , using the joint recognition framework Θ X Upper l n The joint focus elements are constructed into a joint focus element pool U:
[0014]
[0015] In formula (3), Θ X For the joint identification framework, A i and are the focal element of the i-th dimension variable and the power set A corresponding to the identification framework X represents the joint focal element, a i,j ,j=1,2,…,k i Representation recognition framework Θ i The focal element of the upper adjacent subinterval; the joint focal element A X It is composed in the form of Cartesian product, and its corresponding joint basic credibility distribution m(A X ), as shown below:
[0016]
[0017] In formula (4), m(A X ) is the joint focal element A X The basic credibility distribution, m i (A i ) is the focal element A i Basic credibility distribution;
[0018] Step 3: Based on the Latin Hypercube Design (LHD), a small number of s initial sample focal elements are extracted from the focal element pool, and the genetic algorithm (GA) is used to solve the focal element classification. The focal element classification formula is as follows:
[0019]
[0020] In formula (5), the focal element is completely in the safety domain, and this type of focal element is called type I focal element, with a label of 0. In formula (6), the focal element is partially in the safety domain and partially in the failure domain, and this type of focal element is called type II focal element, with a label of 1. In formula (7), the focal element is completely in the failure domain, and this type of focal element is called type III focal element, with a label of 2.
[0021] Step 4: Construct the initial state training set L0 with the initial sample focal element, as shown in formula (8), and use the initial training set L0 to train the initial convolutional neural network model M0;
[0022]
[0023] In formula (8), L0 represents the training set, Lab represents the label set corresponding to the training set, te represents the target set, I = {x1, x2, ..., x j} are the j type I focal elements calculated by genetic algorithm, II = {y1,y2,…,y k} is the number of type II focal elements k obtained by genetic algorithm, III={z1,z2,…,z h} are the h type III focal elements calculated by genetic algorithm, and there are q focal elements to be identified {t1, t2, …, t q};
[0024] Step 5: Based on the trained convolutional neural network model, predict all focal elements in the focal element pool U and select the most valuable focal element based on the most uncertain indicator. The formula is as follows:
[0025]
[0026] In formula (9), p i0 ,p i1 ,p i2 They represent the predicted probability that sample i belongs to category 0, 1, and 2, respectively, and p i0 +p i1 +p i2 =1;
[0027] Step 6: Use the genetic algorithm to label the optimal focal element, then add it to the updated training set. At this time, the number of focal elements in the training set is s = s + 1.
[0028] Step 7: Train the convolutional neural network model using the updated training set to obtain an updated convolutional neural network model;
[0029] Step 8: As the iteration proceeds, the number of focal units in the training set increases, and the performance of the convolutional neural network model also improves. When the iteration reaches a certain level, recorded as the qth iteration, the active learning method no longer selects new unlabeled focal units from the focal unit pool U. At this time, the training set no longer adds new sample focal units. At the same time, the performance of the convolutional neural network model converges on the entire focal unit pool. The training set L at the qth iteration is q Trained convolutional neural network model M q The output model after active learning focal element selection;
[0030] Step 9: Identify and classify the joint focal elements in the joint recognition framework focal element pool U to obtain the classification label, as shown in the following formula:
[0031] M q (t) = T Formula (10)
[0032] In formula (10), t is the input focal element and T is the corresponding category label;
[0033] Step 10: Based on the result of the joint focal element category label T in the focal element pool U, calculate the reliability interval [Bel(G), Pl(G)] according to formula (11), as shown below:
[0034]
[0035] In formula (11), Bel(G) is the sum of the probability distribution functions of the first-class focal elements, and Pl(G) is the sum of the probability distribution functions of the first-class focal elements and the second-class focal elements.
[0036] Preferably, in step 5, a large number of unlabeled samples are used to form an unlabeled sample pool through an active learning method based on the unlabeled sample pool, and the most "valuable" samples are selected from the unlabeled sample pool by using a designed sample screening strategy to be labeled first.
[0037] Preferably, step 8 uses active learning to select a convolutional neural network model for sample training, and deepens the number of network layers and increases the number of parameters of each network layer according to the increase in the number of focus element categories contained in the sample focus elements.
[0038] The beneficial effects of the present invention are:
[0039] 1. In response to the first point raised in the background technology, the present invention adopts evidence theory to describe some uncertain parameters in the design of engineering machinery structures, thereby effectively reducing the deviation between the actual working performance and the expected working performance of the engineering machinery structures, and effectively ensuring the safety of the engineering machinery structures.
[0040] 2. In response to the second point raised in the background technology, the present invention combines a powerful convolutional neural network with active learning to avoid the large-scale focal element extreme value analysis calculations faced by traditional evidence theory reliability calculations, thereby effectively solving the problems of excessive calculation volume and low efficiency of traditional evidence theory.
[0041] 3. In response to the third point raised in the background technology, the present invention adopts the most uncertain indicator in the uncertainty strategy as an active learning method, continuously selects the most valuable focal elements to update the convolutional neural network model, and effectively improves the accuracy of the model.
[0042] Note: The above designs are not listed in any particular order, and each one makes the present invention distinctive and significantly advanced compared to the prior art. BRIEF DESCRIPTION OF THE DRAWINGS
[0043] The present invention will be further described below with reference to the accompanying drawings and embodiments:
[0044] Figure 1 This is a flow chart of the mechanical structure reliability analysis method based on active learning of the present invention.
[0045] Figure 2 This is a schematic diagram of a simulation model of an arm-type bucket wheel excavator structure in a specific embodiment.
[0046] In the figures, the reference numerals are as follows:
[0047] 1. Front pull rod 2. Arm 3. Door post structure 4. Counterweight pull rod 5. Counterweight frame DETAILED DESCRIPTION
[0048] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings;
[0049] like Figure 1 As shown in FIG, a mechanical structure reliability analysis method based on active learning includes the following steps:
[0050] Step 1: Analyze the uncertainty factors in the design process of complex mechanical structures, and determine the identification framework and basic credibility distribution of evidence variables based on the information of sample points. Then, establish the limit state function g(X) for the reliability assessment of complex mechanical structures, as shown below:
[0051] g(X)=g0 Formula (1)
[0052] In formula (1), X represents the independent evidence variables X1, X2, ..., X n The n-dimensional evidence vector is composed of g(X), g(X) is the response function of the structure, which is used to determine whether the structure is safe. g0 represents the allowable response value of the structural response function. A safe region can be defined based on g(X) and g0:
[0053] G={X|g(X)≤g0} Formula (2)
[0054] Step 2: Construct a joint identification framework for evidence theory reliability analysis problem Θ X With joint focal element A X , using the joint recognition framework Θ X Upper l n The joint focus elements are constructed into a joint focus element pool U:
[0055]
[0056] In formula (3), Θ X For the joint identification framework, A i and are the focal element of the i-th dimension variable and the power set A corresponding to the identification framework X represents the joint focal element, a i,j ,j=1,2,…,k i Representation recognition framework Θ i The focal element of the upper adjacent subinterval; the joint focal element A X It is composed in the form of Cartesian product, and its corresponding joint basic credibility distribution m(A X ), as shown below:
[0057]
[0058] In formula (4), m(A X ) is the joint focal element A X The basic credibility distribution, m i (A i ) is the focal element A i Basic credibility distribution;
[0059] Step 3: Based on the Latin Hypercube Design (LHD), a small number of s initial sample focal elements are extracted from the focal element pool, and the genetic algorithm (GA) is used to solve the focal element classification. The focal element classification formula is as follows:
[0060]
[0061] In formula (5), the focal element is completely in the safety domain, and this type of focal element is called type I focal element, with a label of 0. In formula (6), the focal element is partially in the safety domain and partially in the failure domain, and this type of focal element is called type II focal element, with a label of 1. In formula (7), the focal element is completely in the failure domain, and this type of focal element is called type III focal element, with a label of 2.
[0062] Step 4: Construct the initial state training set L0 with the initial sample focal element, as shown in formula (8), and use the initial training set L0 to train the initial convolutional neural network model M0;
[0063]
[0064] In the above formula, L0 represents the training set, Lab represents the label set corresponding to the training set, te represents the target set, I = {x1, x2, ..., x j} are the j type I focal elements calculated by genetic algorithm, II = {y1,y2,…,y k} is the number of type II focal elements k obtained by genetic algorithm, III={z1,z2,…,z h} are the h type III focal elements calculated by genetic algorithm, and there are q focal elements to be identified {t1, t2, …, t q};
[0065] Step 5: Based on the trained convolutional neural network model, predict all focal elements in the focal element pool U and select the most valuable focal element based on the most uncertain indicator. The formula is as follows:
[0066]
[0067] In formula (9), p i0 ,p i1 ,p i2 They represent the predicted probability that sample i belongs to category 0, 1, and 2, respectively, and p i0 +p i1 +p i2 =1;
[0068] Step 6: Use the genetic algorithm to label the optimal focal element, then add it to the updated training set. At this time, the number of focal elements in the training set is s = s + 1.
[0069] Step 7: Train the convolutional neural network model using the updated training set to obtain an updated convolutional neural network model;
[0070] Step 8: As the iteration proceeds, the number of focal units in the training set increases, and the performance of the convolutional neural network model also improves. When the iteration reaches a certain level, recorded as the qth iteration, the active learning method no longer selects new unlabeled focal units from the focal unit pool U. At this time, the training set no longer adds new sample focal units. At the same time, the performance of the convolutional neural network model converges on the entire focal unit pool. The training set L at the qth iteration is q Trained convolutional neural network model M q The output model after active learning focal element selection;
[0071] Step 9: Identify and classify the joint focal elements in the joint recognition framework focal element pool U to obtain the classification label, as shown in the following formula:
[0072] M q (t) = T Formula (10)
[0073] In formula (10), t is the input focal element and T is the corresponding category label;
[0074] Step 10: Based on the result of the joint focal element category label T in the focal element pool U, calculate the reliability interval [Bel(G), Pl(G)] according to formula (11), as shown below:
[0075]
[0076] In formula (11), Bel(G) is the sum of the probability distribution functions of the first-class focal elements, and Pl(G) is the sum of the probability distribution functions of the first-class focal elements and the second-class focal elements.
[0077] To further explain the present invention in detail, the following describes the solution of the present invention in conjunction with a specific embodiment. This embodiment uses the reliability analysis of the arm-type bucket wheel excavator structure as an example, and is implemented based on the technical solution of the present invention. A detailed implementation method and specific operation process are provided, but the scope of protection of the present invention is not limited to the following embodiment.
[0078] like Figure 2 As shown in the figure, it is a simulation model of the arm bucket wheel machine structure of a specific embodiment. Figure 1 The process shown is used to analyze the reliability of the arm bucket wheel excavator. The specific steps are as follows:
[0079] Step 1: The maximum Von Mises stress inside the bucket wheel superstructure is used as the system response to evaluate the reliability of the bucket wheel superstructure during operation. The steel plate thickness T of the gate structure, the circular cross-section radius R1 of the front tie rod, the circular cross-section radius R2 of the counterweight tie rod, the digging resistance F1 of the bucket wheel, and the bulk material load F2 on the boom are regarded as independent evidence variables. The corresponding BPA structure is shown in Table 1:
[0080] Table 1 BPA table of evidence variables T, R1, R2, F1, and F2 of the upper structure of the boom-type bucket wheel crane
[0081]
[0082] At this time, the limit state function of the superstructure can be defined as shown in formula (12):
[0083] Z(T,R1,R2,F1,F2)=σ0-σ max (T, R1, R2, F1, F2) Formula (12)
[0084] In formula (12), σ0 represents the allowable response value of the maximum Von Mises stress inside the superstructure, σ max Indicates the use of radial basis functions to construct an approximate model of the maximum Von Mises stress inside the superstructure;
[0085] Step 2: Construct the joint identification framework Θ for the reliability analysis of the above-mentioned bucket wheel excavator device X With joint focal element A X , using the joint recognition framework Θ X Top 5 5 = 3125 joint focal elements are constructed into a joint focal element pool U:
[0086]
[0087] In formula (13), Θ X For the joint identification framework, A i and are the focal element of the i-th dimension variable and the power set A corresponding to the identification framework X represents the joint focal element, a i,j ,j=1,2,…,k i Representation recognition framework Θ i The focal element of the upper adjacent subinterval; the joint focal element A X It is composed in the form of Cartesian product, and its corresponding joint basic credibility distribution m(A X ), as shown below:
[0088]
[0089] In formula (14), m(A X ) is the joint focal element A X The basic credibility distribution, m i (A i ) is the focal element A i Basic credibility distribution;
[0090] Step 3: Based on the Latin Hypercube Design (LHD), a small number of s initial sample focal elements are extracted from the focal element pool, and the genetic algorithm (GA) is used to solve the focal element classification, as shown in Table 2. The focal element classification formula is as follows:
[0091]
[0092] In formula (15), the focal element is completely in the safety domain, and this type of focal element is called type I focal element, with a label of 0. In formula (16), the focal element is partially in the safety domain and partially in the failure domain, and this type of focal element is called type II focal element, with a label of 1. In formula (17), the focal element is completely in the failure domain, and this type of focal element is called type III focal element, with a label of 2.
[0093] Table 2 Number of focal elements in the initial state samples of each threshold
[0094]
[0095] Step 4: Construct the initial state training set L0 with the initial sample focal element, as shown in formula (18); and use the initial training set L0 to train the initial convolutional neural network model M0;
[0096]
[0097] In formula (18), L0 represents the training set, Lab represents the label set corresponding to the training set, te represents the target set, I = {x1, x2, ..., x j} are the j type I focal elements calculated by genetic algorithm, II = {y1,y2,…,y k} is the number of type II focal elements k obtained by genetic algorithm, III={z1,z2,…,z h} are the h type III focal elements calculated by genetic algorithm, and there are q focal elements to be identified {t1, t2, …, t q};
[0098] Step 5: Based on the trained convolutional neural network model, predict all focal elements in the focal element pool U and select the most valuable focal element based on the most uncertain indicator. The formula is as follows:
[0099]
[0100] In formula (19), p i0 ,p i1 ,p i2 They represent the predicted probability that sample i belongs to category 0, 1, and 2, respectively, and p i0 +p i1 +p i2 =1;
[0101] Step 6: Use the genetic algorithm to label the optimal focal element, then add it to the updated training set. At this time, the number of focal elements in the training set is s = s + 1.
[0102] Step 7: Train the convolutional neural network model using the updated training set to obtain an updated convolutional neural network model;
[0103] Step 8: As the iteration proceeds, the number of focal units in the training set increases, and the performance of the convolutional neural network model also improves. When the iteration reaches a certain level, recorded as the qth iteration, the active learning method no longer selects new unlabeled focal units from the focal unit pool U. At this time, the training set no longer adds new sample focal units. At the same time, the performance of the convolutional neural network model converges on the entire focal unit pool. The number of sample focal units added by the active learning iteration of each threshold is shown in Table 3. The training set L in the qth iteration is q Trained convolutional neural network model M q The output model after active learning focal element selection;
[0104] Table 3 Number of focal elements added in active learning iterations for each threshold
[0105]
[0106] Step 9: Identify and classify the joint focal elements in the joint recognition framework focal element pool U to obtain the classification label, as shown in the following formula:
[0107] M q (t) = T Formula (20)
[0108] In formula (20), t is the input focal element and T is the corresponding category label;
[0109] Step 10: Based on the result of the joint focal element category label T in the focal element pool U, calculate the reliability interval [Bel(G), Pl(G)] according to formula (21), as shown below:
[0110]
[0111] In formula (21), Bel(G) is the sum of the probability distribution functions of the first-class focal elements, and Pl(G) is the sum of the probability distribution functions of the first-class focal elements and the second-class focal elements. The 3125 focal elements in the focal element pool are identified and classified using the convolutional neural network model with active learning iterative output. The reliability interval is solved based on the classification results of the model. The results are shown in Table 4:
[0112] Table 4 Reliability interval results
[0113]
[0114] The above detailed description is a specific description of a feasible embodiment of the present invention. The embodiment is not intended to limit the patent scope of the present invention. Any equivalent implementation or modification that does not depart from the present invention should be included in the patent scope of this case.
Claims
1. A mechanical structure reliability analysis method based on active learning, characterized in that: The steps include: Step 1: Analyze the uncertainty factors in the design process of complex mechanical structures, and determine the identification framework and basic credibility distribution of evidence variables based on the information of sample points. Then, establish the limit state function g(X) for the reliability assessment of complex mechanical structures, as shown below: g(X)=g0 Formula (1) In formula (1), X represents the independent evidence variables X1, X2, ..., X n The n-dimensional evidence vector is composed of g(X), g(X) is the response function of the structure, which is used to determine whether the structure is safe. g0 represents the allowable response value of the structural response function. A safe region can be defined based on g(X) and g0 as follows: G={X|g(X)≤g0} Formula (2) Step 2: Construct a joint identification framework for evidence theory reliability analysis problem Θ X With joint focal element A X , using the joint recognition framework Θ X Upper l n The joint focus elements are constructed into a joint focus element pool U: In formula (3), Θ X For the joint identification framework, A i and are the focal element of the i-th dimension variable and the power set A corresponding to the identification framework X represents the joint focal element, a i,j ,j=1,2,…,k i Representation recognition framework Θ i The focal element of the upper adjacent subinterval; the joint focal element A X It is composed in the form of Cartesian product, and its corresponding joint basic credibility distribution m(A X ), as shown below: In formula (4), m(A X ) is the joint focal element A X The basic credibility distribution, m i (A i ) is the focal element A i Basic credibility distribution; Step 3: Based on the Latin Hypercube Design (LHD), a small number of s initial sample focal elements are extracted from the focal element pool, and the genetic algorithm (GA) is used to solve the focal element classification. The focal element classification formula is as follows: In formula (5), the focal element is completely in the safety domain, and this type of focal element is called type I focal element, with a label of 0. In formula (6), the focal element is partially in the safety domain and partially in the failure domain, and this type of focal element is called type II focal element, with a label of 1. In formula (7), in the third case, the focal element is completely in the failure domain, and this type of focal element is called type III focal element, with a label of 2. Step 4: Construct the initial state training set L0 with the initial sample focal element, as shown in formula (8), and use the initial training set L0 to train the initial convolutional neural network model M0: In formula (8), L0 represents the training set, Lab represents the label set corresponding to the training set, te represents the target set, I = {x1, x2, ..., x j } are the j type I focal elements calculated by genetic algorithm, II = {y1,y2,…,y k } is the number of type II focal elements k obtained by genetic algorithm, III={z1,z2,…,z h } are the h type III focal elements calculated by genetic algorithm, and there are q focal elements to be identified {t1, t2, …, t q }; Step 5: Based on the trained convolutional neural network model, predict all focal elements in the focal element pool U and select the most valuable focal element based on the most uncertain indicator. The formula is as follows: In formula (9), p i0 ,p i1 ,p i2 They represent the predicted probability that sample i belongs to category 0, 1, and 2, respectively, and p i0 +p i1 +p i2 =1; Step 6: Use the genetic algorithm to label the optimal focal element, then add it to the updated training set. At this time, the number of focal elements in the training set is s = s + 1. Step 7: Train the convolutional neural network model using the updated training set to obtain an updated convolutional neural network model; Step 8: As the iteration proceeds, the number of focal units in the training set increases, and the performance of the convolutional neural network model also improves. When the iteration reaches a certain level, recorded as the qth iteration, the active learning method no longer selects new unlabeled focal units from the focal unit pool U. At this time, the training set no longer adds new sample focal units. At the same time, the performance of the convolutional neural network model converges on the entire focal unit pool. The training set L at the qth iteration is q Trained convolutional neural network model M q The output model after active learning focal element selection; Step 9: Identify and classify the joint focal elements in the joint recognition framework focal element pool U to obtain the classification label, as shown in the following formula: M q (t) = T Formula (10) In formula (10), t is the input focal element and T is the corresponding category label; Step 10: Based on the result of the joint focal element category label T in the focal element pool U, calculate the reliability interval [Bel(G), Pl(G)] according to formula (11), as shown below: In formula (11), Bel(G) is the sum of the probability distribution functions of the first-class focal elements, and Pl(G) is the sum of the probability distribution functions of the first-class focal elements and the second-class focal elements.
2. The mechanical structure reliability analysis method based on active learning according to claim 1, characterized in that: In step 5, a large number of unlabeled samples are used to form an unlabeled sample pool through an active learning method based on the unlabeled sample pool, and the most "valuable" samples are selected from the unlabeled sample pool by using a designed sample screening strategy to give priority to labeling.
3. The mechanical structure reliability analysis method based on active learning according to claim 1, characterized in that: The step 8 uses active learning to select and add sample training convolutional neural network models, and deepens the number of network layers and increases the number of parameters of each layer of the network according to the increase in the number of focus element categories contained in the sample focus elements.