Hybrid uncertainty analysis method, apparatus, device, and storage medium

Abstract

The application provides a hybrid uncertainty analysis method and device, equipment and storage medium, concretely relates to the technical field of hybrid uncertainty analysis, and the method comprises the following steps: a processor obtains a second-order Taylor series of a univariate function of the k+1th round according to a first parameter vector of a harmonic reducer of the k+1th round and a second parameter vector of a harmonic reducer of the kth round; the second-order Taylor series of the univariate function of the k+1th round is processed to obtain a minimum value of an interval limit state function; the minimum value of the interval limit state function is calculated to obtain the second parameter vector of the harmonic reducer of the k+1th round according to the minimum value of the interval corresponding to the minimum value of the interval limit state function; and the reliability index of the k+1th round is determined as the maximum failure probability. The method improves the efficiency of iteration of the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer.

Description

Technical Field

[0001] This application relates to the field of mixed uncertainty analysis technology, and in particular to a mixed uncertainty analysis method, apparatus, device and storage medium. Background Technology

[0002] In modern engineering design, the safety and reliability of structures are paramount, especially in complex engineering environments. Engineering structures are inevitably affected by various uncertainties during design and construction, including material parameters, manufacturing errors, and external loads. These uncertainties not only affect structural performance but can also lead to serious safety hazards. Therefore, reliability analysis of structures with uncertainties has become an important research area in engineering practice. In existing research, uncertainties are generally classified into stochastic uncertainties and cognitive uncertainties. Reliability analysis methods for structures with stochastic or cognitive uncertainties are being gradually improved and are being widely applied.

[0003] However, in practical engineering, for example, many structures of harmonic reducers simultaneously face mixed uncertainties, namely, the coexistence of stochastic and cognitive uncertainties. Although various methods have been developed for mixed uncertainty analysis, such as failure probability bound estimation based on Kriging models, response surface techniques, and Monte Carlo simulations, existing mixed uncertainty analysis techniques, when applied to complex systems under nonlinear constraints, mostly require the construction of surrogate models, followed by extensive sampling experiments based on these models. This results in low computational efficiency, and the results are not consistent across calculations, necessitating a sufficient number of computations to ensure accuracy.

[0004] Therefore, the low efficiency of using surrogate models to perform mixed uncertainty analysis on the parameters of harmonic reducers under nonlinear constraints is a problem that urgently needs to be solved. Summary of the Invention

[0005] In view of this, the purpose of this application is to provide a hybrid uncertainty analysis method, apparatus, device and storage medium to solve the above problems and improve the efficiency of hybrid uncertainty analysis of harmonic reducer parameters under nonlinear constraints.

[0006] In a first aspect, embodiments of this application provide a method for hybrid uncertainty analysis, the method comprising:

[0007] The processor obtains the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round; wherein, the first parameter vector of the harmonic reducer in the k-th round is an n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the harmonic reducer in the k-th round is an m-dimensional interval uncertainty vector in the standard space of the k-th round.

[0008] The processor calculates the reliability index of the k-th round based on the first parameter vector of the harmonic reducer in the k-th round.

[0009] The processor calculates the first parameter vector of the harmonic reducer in the (k+1)th round based on the reliability index of the kth round.

[0010] The processor calculates the reliability index of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round.

[0011] If the difference between the reliability index of round (k+1) and the reliability index of round (k) is less than or equal to the first convergence threshold, the processor calculates the first error value of round (k+1) based on the first parameter vector of the harmonic reducer in round (k+1) and the first parameter vector of the harmonic reducer in round (k).

[0012] If the first error value of the (k+1)th round is less than or equal to the second convergence threshold, then the processor obtains the second-order Taylor series of the single-variable function of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the second parameter vector of the harmonic reducer in the (k)th round.

[0013] The processor processes the second-order Taylor series of the single-variable function in the (k+1)th round to obtain the minimum value of the limit state function within the interval.

[0014] The processor calculates the second parameter vector of the harmonic reducer in the (k+1)th round based on the minimum value of the interval corresponding to the minimum value of the limit state function within the interval.

[0015] The processor calculates the second error value for the (k+1)th round based on the second parameter vector of the harmonic reducer.

[0016] If the second error value in the (k+1)th round is less than or equal to the third convergence threshold, then the processor determines the reliability index of the (k+1)th round as the maximum failure probability.

[0017] Preferably, the reliability index of the k-th round is calculated according to the following formula:

[0018]

[0019] in, Let k be the reliability index for the kth round. Let be the first parameter vector of the harmonic reducer in the k-th round;

[0020] The first parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula:

[0021]

[0022] in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. For control coefficients, Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round. The involution matrix of unit vectors;

[0023] The reliability index for round k+1 is calculated using the following formula:

[0024]

[0025] in, The reliability index for the (k+1)th round. This is the first parameter vector of the harmonic reducer in the (k+1)th round.

[0026] Preferably, the first error value in the (k+1)th round is calculated according to the following formula:

[0027]

[0028] in, This is the first error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round.

[0029] Preferably, the second error value in the (k+1)th round is calculated according to the following formula:

[0030]

[0031] in, This is the second error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the second parameter vector of the harmonic reducer in the (k+1)th round. Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the (k+1)th round.

[0032] Preferably, the second parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula:

[0033]

[0034] in, This is the vector of the second harmonic reducer in the (k+1)th round. Let be the median vector of the interval of the second parameter vector of the harmonic reducer for all iterations. Let be the minimum value of the interval corresponding to the minimum value of the limit state function within the interval. Let be the radius of the interval of the second parameter vector of the harmonic reducer in the kth round.

[0035] Preferably, the first parameter vector and the second parameter vector of the harmonic reducer are determined as follows:

[0036] The processor acquires the first parameter vector and the second parameter vector of the original harmonic reducer; wherein, the first parameter vector of the original harmonic reducer is an n-dimensional probability uncertainty vector conforming to a cumulative distribution, and the second parameter vector of the original harmonic reducer is an m-dimensional interval uncertainty vector conforming to a cumulative distribution.

[0037] The processor performs a normalization transformation on the first parameter vector and the second parameter vector of the original harmonic reducer to obtain the first parameter vector and the second parameter vector of the harmonic reducer.

[0038] Preferably, the method further includes:

[0039] If the difference between the reliability index of round (k+1) and the reliability index of round (k) is greater than the first convergence threshold, then the processor calculates the first parameter vector of the harmonic reducer in round (k+2).

[0040] If the first error value in the (k+1)th round is greater than the second convergence threshold, then the processor calculates the first parameter vector of the harmonic reducer in the (k+2)th round.

[0041] If the second error value in the (k+1)th round is greater than the third convergence threshold, then the processor calculates the first parameter vector of the harmonic reducer in the (k+2)th round.

[0042] The mixed uncertainty analysis method provided in this application has the following beneficial effects:

[0043] This application provides a hybrid uncertainty analysis method. In this method, the processor obtains the second-order Taylor series of the single-variable function of the (k+1)th round based on the first parameter vector and the second parameter vector of the harmonic reducer of the (k)th round. The second-order Taylor series of the single-variable function of the (k+1)th round is processed to obtain the minimum value of the limit state function within the interval. Based on the interval minimum value corresponding to the minimum value of the limit state function within the interval, the second parameter vector of the harmonic reducer of the (k+1)th round is calculated. Based on the second parameter vector of the harmonic reducer of the (k+1)th round, the second error value of the (k+1)th round is calculated. If the first error value of the (k+1)th round is less than or equal to the third convergence threshold, the reliability index of the (k+1)th round is determined as the maximum failure probability; otherwise, the iteration of the first parameter vector and the second parameter vector of the harmonic reducer continues. This method improves the efficiency of iterating the first parameter vector and the second parameter vector of the harmonic reducer by solving the extremum problem of the second-order Taylor series of the single-variable function.

[0044] Secondly, this application also provides a hybrid uncertainty analysis apparatus, the apparatus comprising:

[0045] The acquisition module is used to acquire the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round; wherein, the first parameter vector of the harmonic reducer in the k-th round is an n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the harmonic reducer in the k-th round is an m-dimensional interval uncertainty vector in the standard space of the k-th round.

[0046] The data processing module is used to calculate the reliability index of the k-th round based on the first parameter vector of the harmonic reducer in the k-th round.

[0047] The data processing module is further configured to: calculate the first parameter vector of the harmonic reducer in the (k+1)th round based on the reliability index of the kth round; calculate the reliability index of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round; if the difference between the reliability index of the (k+1)th round and the reliability index of the kth round is less than or equal to a first convergence threshold, then calculate the first error value of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the first parameter vector of the harmonic reducer in the kth round; if the first error value of the (k+1)th round is less than or equal to a second convergence threshold, then calculate the first error value of the harmonic reducer in the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round. The second parameter vector of the harmonic reducer in the k-th round is used to obtain the second-order Taylor series of the single-variable function in the (k+1)-th round. The second-order Taylor series of the single-variable function in the (k+1)-th round is processed to obtain the minimum value of the limit state function within the interval. Based on the interval minimum value corresponding to the minimum value of the limit state function within the interval, the second parameter vector of the harmonic reducer in the (k+1)-th round is calculated. Based on the second parameter vector of the harmonic reducer in the (k+1)-th round, the second error value of the (k+1)-th round is calculated. If the second error value of the (k+1)-th round is less than or equal to the third convergence threshold, then the reliability index of the (k+1)-th round is determined as the maximum failure probability.

[0048] The hybrid uncertainty analysis apparatus provided in this application has the same technical features as the hybrid uncertainty analysis method provided in the above embodiments, so it can also solve the same technical problems and achieve the same technical effects.

[0049] Thirdly, this application provides a computing device, including a memory and a processor;

[0050] The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of the first aspects.

[0051] Fourthly, this application provides a computer-readable storage medium for storing a computer program for performing the method as described in any one of the first aspects.

[0052] Fifthly, this application provides a computer program product comprising one or more computer instructions, wherein when the computer instructions are executed by a computer, the computer performs the method as described in any one of the first aspects.

[0053] Other features and advantages of this application will be set forth in the following description and will be apparent in part from the description or may be learned by practicing the application. The objectives and other advantages of this application are realized and obtained through the structures particularly pointed out in the description and the accompanying drawings.

[0054] To make the above-mentioned objectives, features and advantages of this application more apparent and understandable, preferred embodiments are described below in detail with reference to the accompanying drawings. Attached Figure Description

[0055] To more clearly illustrate the technical solutions in the specific embodiments of this application or the prior art, the drawings used in the description of the specific embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of this application. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0056] Figure 1 This is a schematic diagram of a hybrid uncertainty analysis method provided in an embodiment of this application;

[0057] Figure 2 A comparison chart of maximum failure probabilities provided for embodiments of this application;

[0058] Figure 3 This is a schematic diagram of a hybrid uncertainty analysis device provided in an embodiment of this application;

[0059] Figure 4 This is a schematic diagram of an electronic device structure provided in an embodiment of this application. Detailed Implementation

[0060] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0061] To facilitate understanding of this embodiment, the embodiments of this application will be described in detail below.

[0062] This application provides a hybrid uncertainty analysis method, such as... Figure 1 As shown, Figure 1 This is a schematic flowchart of a hybrid uncertainty analysis method provided in an embodiment of this application. The method includes the following steps:

[0063] S101, the processor obtains the first parameter vector and the second parameter vector of the harmonic reducer in the kth round.

[0064] Among them, the first parameter vector of the harmonic reducer in the k-th round is the n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the harmonic reducer in the k-th round is the m-dimensional interval uncertainty vector in the standard space of the k-th round.

[0065] Specifically, the first parameter vector and the second parameter vector of the harmonic reducer are shown in Table 1 and Table 2, respectively. Table 1 is the first parameter vector of the harmonic reducer, and Table 2 is the second parameter vector table of the harmonic reducer.

[0066] Table 1:

[0067]

[0068] Table 2:

[0069]

[0070] The variable distribution types of the flexible wheel cylinder length, flexible wheel wall thickness, flexible wheel centerline radius, flexible wheel maximum radial deformation, meshing tooth ratio, normal stress concentration factor, shear stress concentration factor, flexible wheel distortion stress growth factor, dynamic load factor, normal stress factor, and shear stress factor in Table 1 above are normal distributions, belonging to the first parameter vector of the harmonic reducer.

[0071] The variable distribution types of output torque, elastic modulus, bending fatigue limit and shear fatigue limit in Table 2 above are interval distributions, which belong to the second parameter vector of the harmonic reducer.

[0072] S102, the processor calculates the reliability index of the k-th round based on the first parameter vector of the harmonic reducer of the k-th round.

[0073] Specifically, the reliability index for the k-th round is calculated using the following formula:

[0074] (1)

[0075] in, Let k be the reliability index for the kth round. Let be the first parameter vector of the harmonic reducer in the k-th round. for The second norm of .

[0076] S103, the processor calculates the first parameter vector of the harmonic reducer in the (k+1)th round based on the reliability index of the kth round.

[0077] Specifically, the first parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula:

[0078] (2)

[0079] in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. For control coefficients, Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round. for The second norm, It is the involution matrix of unit vectors.

[0080] The aforementioned reliability index is used to characterize the probability of failure of the first parameter vector and the second parameter vector of the harmonic reducer.

[0081] S104, the processor calculates the reliability index of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round.

[0082] Specifically, the reliability index for the (k+1)th round is calculated using the following formula:

[0083] (3)

[0084] in, The reliability index for the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. for The second norm of .

[0085] More specifically, formula (2) is obtained from the following process:

[0086] Based on HL-RF (Hasofer-Lind Reliability-based First Order Method with Reliability Index as a Measure of Safety, verification point method), the following formula is obtained:

[0087] (4)

[0088] in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. Let k be the reliability index for the kth round. Let be the limit state function of the first parameter vector of the harmonic reducer in the k-th round and the second harmonic reducer vector in the k-th round. for The second norm of .

[0089] The HL-RF algorithm described above, which relies solely on traditional iterative algorithms to iterate the first parameter vector of the harmonic reducer, may exhibit unstable convergence behavior. This could lead to situations where the first parameter vector of the harmonic reducer fails to converge or only converges to a local optimum. Specifically, if the difference between the reliability index in the (k+1)th round and the reliability index in the kth round is still greater than the first convergence threshold, the iteration of the first parameter vector of the harmonic reducer may cease. Consequently, the accuracy of the first parameter vector of the harmonic reducer cannot be guaranteed.

[0090] As shown above, by introducing a chaotic control algorithm to control the convergence of the first parameter vector of the harmonic reducer in the (k+1)th round, the following formula is obtained:

[0091] (5)

[0092] in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. Let k be the reliability index for the kth round. For control coefficients, Let be the limit state function of the first parameter vector of the harmonic reducer in the k-th round and the second harmonic reducer vector in the k-th round. It is the involution matrix of unit vectors.

[0093] If the above control coefficients =0, then formula (5) can be simplified to At this point, the first parameter vector of the harmonic reducer in the (k+1)th round fails to converge. Since the chaotic control algorithm's calculation process relies on a preset number of iterations, its computational efficiency is relatively low, and there is a possibility of non-convergence. Therefore, a material composition and computational modeling algorithm is used for iteration, resulting in the following formula:

[0094] (6)

[0095] in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. Let be the limit state function of the first parameter vector of the harmonic reducer in the k-th round and the second harmonic reducer vector in the k-th round. For the kth round The unit direction vector in the direction of the negative derivative. For the (k+1)th round The unit direction vector in the direction of the negative derivative. For the (k-1)th round The unit direction vector in the direction of the negative derivative. This is the oscillation judgment factor for the (k+1)th round.

[0096] Formula (6) updates the first parameter vector of the harmonic reducer based on the gradient of the limit state function of the first parameter vector of the harmonic reducer in the k-th round and the second harmonic reducer vector in the k-th round, and introduces the oscillation judgment factor of the (k+1)-th round to evaluate whether the iteration point oscillates. If > 0, then the angle between the first parameter vector of the harmonic reducer in the (k+1)th round and the second parameter vector of the harmonic reducer in the (k+1)th round is less than 90°, and the iteration point does not oscillate; if If >0, then the angle between the first parameter vector of the harmonic reducer in the (k+1)th round and the second parameter vector of the harmonic reducer in the (k+1)th round is less than 90°, and the iteration point does not oscillate. Substituting the above formula (6) into formula (5), we get formula (2).

[0097] This configuration improves the convergence speed and accuracy of the first parameter vector iteration process of the harmonic reducer, while significantly reducing the complexity of multidimensional calculations. Compared with existing technologies, this configuration allows the iteration process of the first parameter vector of the harmonic reducer to converge accurately, thereby improving the accuracy of the first parameter vector of the harmonic reducer.

[0098] S105, the processor determines whether the difference between the reliability index of round (k+1) and the reliability index of round k is less than or equal to the first convergence threshold. If yes, then proceed to step S106; otherwise, proceed to step S114.

[0099] Specifically, the processor determines whether to stop the iteration process of the first parameter vector of the harmonic reducer by the difference between the reliability index of the (k+1)th round and the reliability index of the kth round. The first convergence threshold is preset to 10e-6.

[0100] S106, the processor calculates the first error value of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the first parameter vector of the harmonic reducer in the kth round.

[0101] Specifically, the first error value in the (k+1)th round is calculated using the following formula:

[0102]

[0103] in, This is the first error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round.

[0104] More specifically, the aforementioned first error value is a pre-set convergence threshold for the first parameter vector of the harmonic reducer in the (k+1)th round to end the iteration, so that the processor can provide a basis for judging whether the first parameter vector of the harmonic reducer should be iterated in the future.

[0105] S107, the processor determines whether the first error value of the (k+1)th round is less than or equal to the second convergence threshold. If yes, then execute step S108; otherwise, execute step S114.

[0106] Specifically, the processor can determine whether to stop iterating on the first parameter vector of the harmonic reducer based on the first error value, and prepare for the subsequent creation of a second-order Taylor series of a single-variable function.

[0107] S108, the processor obtains the second-order Taylor series of the single-variable function in the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the second parameter vector of the harmonic reducer in the kth round.

[0108] Specifically, the second-order Taylor series of the univariate function in the (k+1)th round is calculated according to the following formula:

[0109]

[0110] in, Let be the second-order Taylor series of the univariate function in the (k+1)th round. The interval of the second parameter vector of the harmonic reducer for all round iterations, excluding Other than the median vector, Let j be the j-th variable in the second parameter vector of the harmonic reducer. , Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the radius of the interval of the second parameter vector of the harmonic reducer in the k-th round. Let be the median vector of the interval of the second parameter vector of the harmonic reducer for all iterations. , Let be the limit state function values ​​at the first parameter vector of the (k+1)th harmonic reducer and the second parameter vector of the kth harmonic reducer.

[0111] S109, the processor processes the second-order Taylor series of the single-variable function in the (k+1)th round to obtain the minimum value of the limit state function within the interval.

[0112] Specifically, the minimum value of the limit state function within the interval is calculated using the following formula:

[0113]

[0114] in, Let be the minimum value of the limit state function within the interval. Let m be the second-order Taylor series of the univariate function in the (k+1)th round, and m be the dimension of the second harmonic reducer vector.

[0115] The minimum value of the limit state function within the above interval is based on the multiplicative dimension reduction method. The limit state function of the first parameter vector of the harmonic reducer in the (k+1)th round and the second harmonic reducer vector in the (k+1)th round can be extended to the product form of a second-order Taylor series of a single-variable function at the midpoint of the interval of the second parameter vector of the harmonic reducer.

[0116] S110, the processor calculates the second parameter vector of the harmonic reducer for the (k+1)th round based on the minimum value of the interval corresponding to the minimum value of the limit state function within the interval.

[0117] Specifically, the second harmonic reducer vector for the (k+1)th round is calculated using the following formula:

[0118]

[0119] in, This is the vector of the second harmonic reducer in the (k+1)th round. Let be the median vector of the interval of the second parameter vector of the harmonic reducer for all iterations. Let be the minimum value of the interval corresponding to the minimum value of the limit state function within the interval. Let be the radius of the interval of the second parameter vector of the harmonic reducer in the k-th round.

[0120] More specifically, This refers to the value of the independent variable of the second-order Taylor series of the single-variable function in the (k+1)th round, when the second-order Taylor series of the single-variable function in the (k+1)th round reaches its minimum value within a preset range. The second harmonic reducer vector in the (k+1)th round calculated by the processor provides support for the subsequent calculation of the first error value.

[0121] S111, the processor calculates the second error value of the (k+1)th round based on the second parameter vector of the harmonic reducer in the (k+1)th round.

[0122] Specifically, the second error value in the (k+1)th round is calculated using the following formula:

[0123]

[0124] in, This is the second error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the second parameter vector of the harmonic reducer in the (k+1)th round. Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the (k+1)th round.

[0125] More specifically, the aforementioned second error value is a pre-set convergence threshold for the second parameter vector of the harmonic reducer in the (k+1)th round to end the iteration, so that the processor can provide a basis for judging whether the second parameter vector of the harmonic reducer should be iterated in the future.

[0126] S112, the processor determines whether the second error value of the (k+1)th round is less than or equal to the third convergence threshold. If yes, then proceed to step S113; otherwise, proceed to step S114.

[0127] Specifically, the processor can determine whether to stop iterating on the second parameter vector of the harmonic reducer based on the second error value, that is, to determine whether the second parameter vector of the harmonic reducer has converged.

[0128] S113, the processor determines the reliability index of the (k+1)th round as the maximum failure probability.

[0129] Specifically, once the iteration of the first parameter vector and the second parameter vector of the harmonic reducer stops, the reliability index of the (k+1)th round can be determined as the maximum failure probability. Table 2 shows the maximum failure probability for different control coefficients.

[0130] Table 2:

[0131]

[0132] When the control coefficient is 0.1, 0.2, 0.3, 0.4 or 0.5, the maximum failure probability is 0.13731.

[0133] S114, the processor calculates the first parameter vector of the harmonic reducer in the (k+2)th round.

[0134] Specifically, if the first error value is greater than the second convergence threshold or the second error value is greater than the third convergence threshold, then the first parameter vector and the second parameter vector of the harmonic reducer need to be iterated.

[0135] This application provides a hybrid uncertainty analysis method. In this method, the processor obtains the second-order Taylor series of the single-variable function of the (k+1)th round based on the first parameter vector and the second parameter vector of the harmonic reducer of the (k+1)th round. The second-order Taylor series of the single-variable function of the (k+1)th round is processed to obtain the minimum value of the limit state function within the interval. Based on the interval minimum value corresponding to the minimum value of the limit state function within the interval, the second parameter vector of the harmonic reducer of the (k+1)th round is calculated. Based on the second parameter vector of the harmonic reducer of the (k+1)th round, the second error value of the (k+1)th round is calculated. If the first error value of the (k+1)th round is less than or equal to the third convergence threshold, the reliability index of the (k+1)th round is determined as the maximum failure probability; otherwise, the iteration of the first parameter vector and the second parameter vector of the harmonic reducer continues. This method improves the efficiency of iterating the first parameter vector and the second parameter vector of the harmonic reducer by solving the extremum problem of the second-order Taylor series of the single-variable function. In mixed uncertainty analysis, this method decouples the nested optimization in mixed reliability analysis into a series of iterations consisting of probabilistic reliability analysis and interval analysis, which significantly improves the computational efficiency of the original chaos control method. In interval analysis, the problem is transformed into an extremum problem of multiplying multiple intervals by multiplying through dimensionality reduction, which makes it more feasible.

[0136] Compared to existing techniques that collect a large amount of data within the range of the minimum value corresponding to the minimum value of the limit state function in an interval to iterate the first and second parameter vectors of the harmonic reducer, this method does not require the collection of a large amount of data, the establishment of a polynomial surrogate model, or the use of optimization theory for solution. This method accelerates the iteration efficiency of the first and second parameter vectors of the harmonic reducer, thereby improving the speed of determining the maximum failure probability.

[0137] The following describes how the first and second parameter vectors of the harmonic reducer are determined. The processor obtains the original first and second parameter vectors of the harmonic reducer; the first parameter vector is an n-dimensional probability uncertainty vector conforming to a cumulative distribution, and the second parameter vector is an m-dimensional interval uncertainty vector conforming to a cumulative distribution. The first and second parameter vectors are then standardized to obtain the first and second parameter vectors of the harmonic reducer.

[0138] Specifically, based on the Monte Carlo hybrid reliability analysis method, the first parameter vector and the original second harmonic reducer vector of the original harmonic reducer are transformed to the standard normal distribution space to quantify the influence of interval variables in the hybrid uncertainty, and the first parameter vector and the second harmonic reducer vector of the harmonic reducer are obtained.

[0139] In this method, the first parameter vector and the original second harmonic reducer vector of the original harmonic reducer are converted into the first parameter vector and the second harmonic reducer vector of the harmonic reducer, so as to facilitate the iteration of the first parameter vector and the second harmonic reducer vector of the harmonic reducer.

[0140] The following example illustrates the mixed uncertainty analysis of the first parameter vector and the second parameter vector of a harmonic reducer:

[0141] In the design of harmonic reducers, a safety factor greater than 1.5 is required to ensure reliability and safety.

[0142] like Figure 2 As shown, Figure 2 This is a comparison chart of maximum failure probabilities provided for embodiments of this application. The maximum failure probability calculated by this method is more efficient, more robust, and is the same as the maximum failure probability obtained by existing technologies.

[0143] Based on the above embodiments of the mixed uncertainty analysis method, this application also provides a mixed uncertainty analysis apparatus, such as... Figure 3 As shown, Figure 3 This is a schematic diagram of a hybrid uncertainty analysis device provided in an embodiment of this application. The device includes an acquisition module 31 and a data processing module 32. The functions of each module are as follows:

[0144] The acquisition module 31 is used to acquire the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round; wherein, the first parameter vector of the harmonic reducer in the k-th round is an n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the harmonic reducer in the k-th round is an m-dimensional interval uncertainty vector in the standard space of the k-th round.

[0145] The data processing module 32 is used to calculate the reliability index of the k-th round based on the first parameter vector of the harmonic reducer in the k-th round.

[0146] The data processing module 32 is further configured to calculate the first parameter vector of the harmonic reducer in the (k+1)th round based on the reliability index of the kth round; calculate the reliability index of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round; if the difference between the reliability index of the (k+1)th round and the reliability index of the kth round is less than or equal to a first convergence threshold, then calculate the first error value of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the first parameter vector of the harmonic reducer in the kth round; if the first error value of the (k+1)th round is less than or equal to a second convergence threshold, then calculate the first error value of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round. The second-order Taylor series of the single-variable function in the (k+1)th round is obtained by combining the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round. The second-order Taylor series of the single-variable function in the (k+1)th round is processed to obtain the minimum value of the limit state function within the interval. Based on the minimum value of the interval corresponding to the minimum value of the limit state function within the interval, the second parameter vector of the harmonic reducer in the (k+1)th round is calculated. Based on the second parameter vector of the harmonic reducer in the (k+1)th round, the second error value of the (k+1)th round is calculated. If the second error value of the (k+1)th round is less than or equal to the third convergence threshold, then the reliability index of the (k+1)th round is determined as the maximum failure probability.

[0147] Preferably, the reliability index of the k-th round is calculated according to the following formula:

[0148]

[0149] in, Let k be the reliability index for the kth round. Let be the first parameter vector of the harmonic reducer in the k-th round;

[0150] The first parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula:

[0151]

[0152] in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. For control coefficients, Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round. The involution matrix of unit vectors;

[0153] The reliability index for round k+1 is calculated using the following formula:

[0154]

[0155] in, The reliability index for the (k+1)th round. This is the first parameter vector of the harmonic reducer in the (k+1)th round.

[0156] Preferably, the first error value in the (k+1)th round is calculated according to the following formula:

[0157]

[0158] in, This is the first error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round.

[0159] 4. The hybrid uncertainty analysis method according to claim 1, characterized in that the second error value of the (k+1)th round is calculated according to the following formula:

[0160]

[0161] in, This is the second error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the second parameter vector of the harmonic reducer in the (k+1)th round. Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the (k+1)th round.

[0162] Preferably, the second parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula:

[0163]

[0164] in, This is the vector of the second harmonic reducer in the (k+1)th round. Let be the median vector of the interval of the second parameter vector of the harmonic reducer for all iterations. Let be the minimum value of the interval corresponding to the minimum value of the limit state function within the interval. Let be the radius of the interval of the second parameter vector of the harmonic reducer in the kth round.

[0165] Preferably, the acquisition module 31 is specifically used to acquire the first parameter vector and the second parameter vector of the original harmonic reducer; wherein, the first parameter vector of the original harmonic reducer is an n-dimensional probability uncertainty vector conforming to a cumulative distribution, and the second parameter vector of the original harmonic reducer is an m-dimensional interval uncertainty vector conforming to a cumulative distribution; the first parameter vector and the second parameter vector of the original harmonic reducer are standardized and transformed to obtain the first parameter vector and the second parameter vector of the harmonic reducer.

[0166] Preferably, the data processing module 32 is further configured to: calculate the first parameter vector of the harmonic reducer in the (k+2)th round if the difference between the reliability index of the (k+1)th round and the reliability index of the (k)th round is greater than a first convergence threshold; calculate the first parameter vector of the harmonic reducer in the (k+2)th round if the first error value of the (k+1)th round is greater than a second convergence threshold; and calculate the first parameter vector of the harmonic reducer in the (k+2)th round if the second error value of the (k+1)th round is greater than a third convergence threshold.

[0167] The hybrid uncertainty analysis apparatus provided in this application has the same technical features as the hybrid uncertainty analysis method provided in the above embodiments, so it can also solve the same technical problems and achieve the same technical effects.

[0168] This application also provides a computing device. For example... Figure 4 As shown in the figure, this is a schematic diagram of a computing device provided in an embodiment of this application. The computing device 400 includes a bus 401, a processor 402, a communication interface 403, and a memory 404. The processor 402, the memory 404, and the communication interface 403 communicate with each other via the bus 401.

[0169] Bus 401 can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of representation, Figure 4 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0170] Processor 402 can be any one or more of the following processors: central processing unit (CPU), graphics processing unit (GPU), microprocessor (MP), or digital signal processor (DSP).

[0171] Communication interface 403 is used for communication with external devices. Memory 404 may include volatile memory, such as random access memory (RAM). Memory 404 may also include non-volatile memory, such as read-only memory (ROM), flash memory, hard disk drive (HDD), or solid state drive (SSD).

[0172] The memory 404 stores executable code, and the processor 402 executes the executable code to perform the aforementioned method.

[0173] This application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium capable of being stored by a computing device, or a data storage device such as a data center containing one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state drive). The computer-readable storage medium includes instructions that instruct the computing device to perform the above-described method.

[0174] This application also provides a computer program product comprising one or more computer instructions. When the computer instructions are loaded and executed on a computing device, all or part of the processes or functions described in this application are generated.

[0175] The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions may be transmitted from one website, computer, or data center to another website, computer, or data center via wired (e.g., coaxial cable, fiber optic) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0176] When the computer program product is executed by a computer, the computer performs any of the aforementioned hybrid uncertainty analysis methods. The computer program product can be a software installation package; when any of the aforementioned hybrid uncertainty analysis methods is required, the computer program product can be downloaded and executed on the computer.

[0177] The descriptions of the processes or structures corresponding to the above figures each have their own emphasis. For parts of a process or structure that are not described in detail, please refer to the relevant descriptions of other processes or structures.

[0178] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any changes or substitutions within the technical scope disclosed in this application should be covered within the scope of protection of this application.

Claims

1. A method for analyzing mixed uncertainties, characterized in that, The method includes: The processor obtains the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round; wherein, the first parameter vector of the harmonic reducer in the k-th round is an n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the harmonic reducer in the k-th round is an m-dimensional interval uncertainty vector in the standard space of the k-th round. The processor calculates the reliability index of the k-th round based on the first parameter vector of the harmonic reducer in the k-th round. The processor calculates the first parameter vector of the harmonic reducer in the (k+1)th round based on the reliability index of the kth round. The processor calculates the reliability index of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round. If the difference between the reliability index of round (k+1) and the reliability index of round (k) is less than or equal to the first convergence threshold, the processor calculates the first error value of round (k+1) based on the first parameter vector of the harmonic reducer in round (k+1) and the first parameter vector of the harmonic reducer in round (k). If the first error value of the (k+1)th round is less than or equal to the second convergence threshold, then the processor obtains the second-order Taylor series of the single-variable function of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the second parameter vector of the harmonic reducer in the (k)th round. The processor processes the second-order Taylor series of the single-variable function in the (k+1)th round to obtain the minimum value of the limit state function within the interval. The processor calculates the second parameter vector of the harmonic reducer for the (k+1)th round based on the minimum value of the interval corresponding to the minimum value of the limit state function within the interval. The processor calculates the second error value for the (k+1)th round based on the second parameter vector of the harmonic reducer. If the second error value in the (k+1)th round is less than or equal to the third convergence threshold, then the processor determines the reliability index of the (k+1)th round as the maximum failure probability.

2. The hybrid uncertainty analysis method according to claim 1, characterized in that, The reliability index for round k is calculated using the following formula: in, Let k be the reliability index for the kth round. Let be the first parameter vector of the harmonic reducer in the k-th round; The first parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula: in, Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round. Let be the second parameter vector of the harmonic reducer in the k-th round. For control coefficients, Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round. The involution matrix of unit vectors; The reliability index for round k+1 is calculated using the following formula: in, The reliability index for the (k+1)th round. This is the first parameter vector of the harmonic reducer in the (k+1)th round.

3. The mixed uncertainty analysis method according to claim 1, characterized in that, The first error value in round (k+1) is calculated using the following formula: in, This is the first error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the first parameter vector of the harmonic reducer in the k-th round.

4. The hybrid uncertainty analysis method according to claim 1, characterized in that, The second error value in the (k+1)th round is calculated using the following formula: in, This is the second error value in the (k+1)th round. Let this be the first parameter vector of the harmonic reducer in the (k+1)th round. Let be the second parameter vector of the harmonic reducer in the (k+1)th round. Let be the limit state function of the first parameter vector and the second parameter vector of the harmonic reducer in the (k+1)th round.

5. The mixed uncertainty analysis method according to claim 1, characterized in that, The second parameter vector of the harmonic reducer in the (k+1)th round is calculated according to the following formula: in, This is the vector of the second harmonic reducer in the (k+1)th round. Let be the median vector of the interval of the second parameter vector of the harmonic reducer for all iterations. Let be the minimum value of the interval corresponding to the minimum value of the limit state function within the interval. Let be the radius of the interval of the second parameter vector of the harmonic reducer in the k-th round.

6. The mixed uncertainty analysis method according to claim 1, characterized in that, The first parameter vector and the second parameter vector of the harmonic reducer are determined as follows: The processor acquires the first parameter vector and the second parameter vector of the original harmonic reducer; wherein, the first parameter vector of the original harmonic reducer is an n-dimensional probability uncertainty vector conforming to a cumulative distribution, and the second parameter vector of the original harmonic reducer is an m-dimensional interval uncertainty vector conforming to a cumulative distribution. The processor performs a normalization transformation on the first parameter vector and the second parameter vector of the original harmonic reducer to obtain the first parameter vector and the second parameter vector of the harmonic reducer.

7. The mixed uncertainty analysis method according to claim 1, characterized in that, The method further includes: If the difference between the reliability index of round (k+1) and the reliability index of round (k) is greater than the first convergence threshold, then the processor calculates the first parameter vector of the harmonic reducer in round (k+2). If the first error value in the (k+1)th round is greater than the second convergence threshold, then the processor calculates the first parameter vector of the harmonic reducer in the (k+2)th round. If the second error value in the (k+1)th round is greater than the third convergence threshold, then the processor calculates the first parameter vector of the harmonic reducer in the (k+2)th round.

8. A hybrid uncertainty analysis device, characterized in that, The device includes: The acquisition module is used to acquire the first parameter vector and the second parameter vector of the harmonic reducer in the k-th round; wherein, the first parameter vector of the harmonic reducer in the k-th round is an n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the harmonic reducer in the k-th round is an m-dimensional interval uncertainty vector in the standard space of the k-th round. The data processing module is used to calculate the reliability index of the k-th round based on the first parameter vector of the harmonic reducer in the k-th round. The data processing module is further configured to: calculate the first parameter vector of the harmonic reducer in the (k+1)th round based on the reliability index of the kth round; calculate the reliability index of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round; if the difference between the reliability index of the (k+1)th round and the reliability index of the kth round is less than or equal to a first convergence threshold, then calculate the first error value of the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round and the first parameter vector of the harmonic reducer in the kth round; if the first error value of the (k+1)th round is less than or equal to a second convergence threshold, then calculate the first error value of the harmonic reducer in the (k+1)th round based on the first parameter vector of the harmonic reducer in the (k+1)th round. The second parameter vector of the harmonic reducer in the k-th round is used to obtain the second-order Taylor series of the single-variable function in the (k+1)-th round. The second-order Taylor series of the single-variable function in the (k+1)-th round is processed to obtain the minimum value of the limit state function within the interval. Based on the interval minimum value corresponding to the minimum value of the limit state function within the interval, the second parameter vector of the harmonic reducer in the (k+1)-th round is calculated. Based on the second parameter vector of the harmonic reducer in the (k+1)-th round, the second error value of the (k+1)-th round is calculated. If the second error value of the (k+1)-th round is less than or equal to the third convergence threshold, then the reliability index of the (k+1)-th round is determined as the maximum failure probability.

9. A computing device, characterized in that, Including memory and processor; The memory stores one or more computer programs, the one or more computer programs including instructions; when the instructions are executed by the processor, the computing device performs the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store a computer program for performing the method as described in any one of claims 1 to 7.

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