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

Abstract

The invention provides a hybrid uncertainty analysis method and device, equipment and a storage medium, and particularly relates to the technical field of hybrid uncertainty analysis. The method comprises the steps that a processor obtains the second-order Taylor series of a univariate function of the (k + 1) th round according to a first parameter vector of a harmonic reducer of the (k + 1) th round and a second parameter vector of a harmonic reducer of the kth round; processing the second-order Taylor series of the univariate function of the (k + 1) th round to obtain the minimum value of the limit state function in the interval; according to the interval minimum value corresponding to the minimum value of the limit state function in the interval, calculating to obtain a second parameter vector of the harmonic reducer of the (k + 1) th round; and determining the reliability index of the (k + 1) th round as the maximum failure probability. The method improves the efficiency of iterating the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer.

Description

Technical Field

[0001] The present application relates to the technical field of hybrid uncertainty analysis, and in particular to a hybrid uncertainty analysis method, device, equipment and storage medium. Background Art

[0002] In modern engineering design, the safety and reliability of structures are of vital importance, especially when facing complex engineering environments. Engineering structures are inevitably affected by various uncertainties such as material parameters, manufacturing errors, and external loads during the design and construction process. These uncertainties not only affect the performance of the structure, but may also lead to serious safety hazards. Therefore, reliability analysis of structures with uncertainties has become one of the important research areas in engineering practice. In existing studies, uncertainty is usually divided into random uncertainty and epistemic uncertainty. Structural reliability analysis methods for random uncertainty or epistemic uncertainty are gradually being improved and widely used.

[0003] However, in actual engineering, for example, many structures of harmonic reducers face mixed uncertainty at the same time, that is, random uncertainty and cognitive uncertainty coexist. Although a variety of methods have been developed for mixed uncertainty analysis, such as failure probability limit estimation based on Kriging model, response surface technology and Monte Carlo simulation, when existing mixed uncertainty analysis techniques are applied to complex systems under nonlinear constraints, most of them need to build a proxy model, and then conduct a large number of sampling experiments based on the proxy model, which has low computational efficiency, and the results of each calculation are not the same, requiring a sufficient number of calculations to ensure the accuracy of the results.

[0004] Therefore, the low efficiency of constructing a surrogate model to perform hybrid uncertainty analysis on harmonic reducer parameters under nonlinear constraints is an urgent problem to be solved. Summary of the invention

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

[0006] In a first aspect, an embodiment of the present application provides a hybrid uncertainty analysis method, the method comprising: The processor obtains a first parameter vector of the k-th round harmonic reducer and a second parameter vector of the k-th round harmonic reducer; wherein the first parameter vector of the k-th round harmonic reducer is an n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the k-th round harmonic reducer is an m-dimensional interval uncertainty vector in the standard space of the k-th round; The processor calculates the reliability index of the kth round according to the first parameter vector of the harmonic reducer of the kth round; The processor calculates a first parameter vector of the harmonic reducer of the k+1th round according to the reliability index of the kth round; The processor calculates the reliability index of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round; If the difference between the reliability index of the k+1th round and the reliability index of the kth round is less than or equal to the first convergence threshold, the processor calculates a first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round and the first parameter vector of the harmonic reducer of the kth round; If the first error value of the k+1th round is less than or equal to the second convergence threshold, the processor obtains the second-order Taylor series of the univariate function of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round and the second parameter vector of the harmonic reducer of the kth round; The processor processes the second-order Taylor series of the single variable function of the k+1th round to obtain the minimum value of the limit state function in the interval; The processor calculates a second parameter vector of the k+1th harmonic reducer according to the interval minimum value corresponding to the minimum value of the limit state function in the interval; The processor calculates a second error value of the k+1th wheel according to a second parameter vector of the harmonic reducer of the k+1th wheel; If the second error value of the k+1th round is less than or equal to the third convergence threshold, the processor determines the reliability index of the k+1th round as the maximum failure probability.

[0007] Preferably, the reliability index of the kth round is calculated according to the following formula:

[0008] in, is the reliability index of the kth round, is the first parameter vector of the k-th harmonic reducer; The first parameter vector of the k+1th harmonic reducer is calculated according to the following formula:

[0009] in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the control coefficient, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second parameter vector of the k-th harmonic reducer, is the involution matrix of the unit vector; The reliability index of the k+1th round is calculated according to the following formula:

[0010] in, is the reliability index of the k+1th round, is the first parameter vector of the k+1th harmonic reducer.

[0011] Preferably, the first error value of the k+1th round is calculated according to the following formula:

[0012] in, is the first error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer.

[0013] Preferably, the second error value of the k+1th round is calculated according to the following formula:

[0014] in, is the second error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the second parameter vector of the k+1th harmonic reducer, It is the limit state function of the first parameter vector of the k+1th harmonic reducer and the second parameter vector of the k+1th harmonic reducer.

[0015] Preferably, the second parameter vector of the k+1th harmonic reducer is calculated according to the following formula:

[0016] in, is the second harmonic reducer vector of the k+1th round, is the median vector of the interval of the second parameter vector of the harmonic reducer for all round iterations, is the interval minimum value corresponding to the minimum value of the limit state function in the interval, is the radius of the interval of the second parameter vector of the k-th harmonic reducer.

[0017] Preferably, the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer are determined as follows: The processor obtains a first parameter vector of an original harmonic reducer and a second parameter vector of an 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 standardized conversion on the first parameter vector of the original harmonic reducer and the second parameter vector of the original harmonic reducer to obtain the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer.

[0018] Preferably, the method further comprises: If the difference between the reliability index of the k+1th round and the reliability index of the kth round is greater than the first convergence threshold, the processor calculates and obtains a first parameter vector of the harmonic reducer of the k+2th round; If the first error value of the k+1th round is greater than the second convergence threshold, the processor calculates and obtains the first parameter vector of the harmonic reducer of the k+2th round; If the second error value of the k+1th round is greater than the third convergence threshold, the processor calculates and obtains the first parameter vector of the harmonic reducer of the k+2th round.

[0019] The hybrid uncertainty analysis method provided in this application brings the following beneficial effects: The present application provides a hybrid uncertainty analysis method, in which a processor obtains a second-order Taylor series of a single variable 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, processes the second-order Taylor series of the single variable function of the k+1th round, obtains a minimum value of a limit state function in an interval, calculates a second parameter vector of a harmonic reducer of the k+1th round according to an interval minimum value corresponding to the minimum value of the limit state function in the interval, calculates a second error value of the k+1th round according to the second parameter vector of the harmonic reducer of the k+1th round, and if the first error value of the k+1th round is less than or equal to a third convergence threshold, the reliability index of the k+1th round is determined as the maximum failure probability, otherwise, the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer are continued to be iterated. The method improves the efficiency of iterating the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer by solving the extreme value problem of the second-order Taylor series of a single variable function.

[0020] In a second aspect, the present application further provides a hybrid uncertainty analysis device, the device comprising: An acquisition module, used to acquire a first parameter vector of the k-th harmonic reducer and a second parameter vector of the k-th harmonic reducer; wherein the first parameter vector of the k-th harmonic reducer is an n-dimensional probability uncertainty vector in the standard normal space of the k-th wheel, and the second parameter vector of the k-th harmonic reducer is an m-dimensional interval uncertainty vector in the standard space of the k-th wheel; A data processing module, used for calculating the reliability index of the k-th round according to the first parameter vector of the harmonic reducer of the k-th round; The data processing module is further used to calculate the first parameter vector of the harmonic reducer of the k+1th round according to the reliability index of the kth round; calculate the reliability index of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round; if the difference between the reliability index of the k+1th round and the reliability index of the kth round is less than or equal to the first convergence threshold, calculate the first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round and the first parameter vector of the harmonic reducer of the kth round; if the first error value of the k+1th round is less than or equal to the second convergence threshold, calculate the first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round. The parameter vector and the second parameter vector of the k-th round harmonic reducer obtain the second-order Taylor series of the single variable function 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 in the interval; the second parameter vector of the k+1-th round harmonic reducer is calculated according to the interval minimum value corresponding to the minimum value of the limit state function in the interval; the second error value of the k+1-th round is calculated according to the second parameter vector of the k+1-th round harmonic reducer; if the second 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.

[0021] The hybrid uncertainty analysis device provided in the embodiment of the present application has the same technical features as the hybrid uncertainty analysis method provided in the above-mentioned embodiment, so it can also solve the same technical problems and achieve the same technical effects.

[0022] In a third aspect, the present application provides a computing device, including a memory and a processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method as described in any one of the first aspects.

[0023] In a fourth aspect, the present application provides a computer-readable storage medium, wherein the computer-readable storage medium is used to store a computer program, and the computer program is used to execute the method as described in any one of the first aspects.

[0024] In a fifth aspect, the present application provides a computer program product, wherein the computer program product comprises one or more computer instructions, and when the computer instructions are executed by a computer, the computer executes the method as described in any one of the first aspects.

[0025] Other features and advantages of the present application will be described in the following description, and partly become apparent from the description, or understood by practicing the present application. The purpose and other advantages of the present application are realized and obtained by the structures particularly pointed out in the description and the drawings.

[0026] In order to make the above-mentioned objects, features and advantages of the present application more obvious and easy to understand, preferred embodiments are specifically cited below and described in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] In order to more clearly illustrate the specific implementation methods of the present application or the technical solutions in the prior art, the drawings required for use in the specific implementation methods or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are some implementation methods of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0028] Figure 1 A flow chart of a hybrid uncertainty analysis method provided in an embodiment of the present application; Figure 2 A comparison chart of the maximum failure probability provided in the embodiments of the present application; Figure 3 A schematic diagram of the structure of a hybrid uncertainty analysis device provided in an embodiment of the present application; Figure 4 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0029] In order to make the purpose, technical solution and advantages of the embodiments of the present application clearer, the technical solution of the present application will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the described embodiments are part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present application.

[0030] To facilitate understanding of this embodiment, the embodiments of the present application are described in detail below.

[0031] The present application embodiment provides a hybrid uncertainty analysis method, such as Figure 1 As shown, Figure 1A flow chart of a hybrid uncertainty analysis method provided in an embodiment of the present application. The method comprises the following steps: S101, the processor obtains a first parameter vector of the k-th harmonic reducer and a second parameter vector of the k-th harmonic reducer.

[0032] Among them, the first parameter vector of the k-th round harmonic reducer is the n-dimensional probability uncertainty vector in the standard normal space of the k-th round, and the second parameter vector of the k-th round harmonic reducer is the m-dimensional interval uncertainty vector in the standard space of the k-th round.

[0033] Specifically, the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer are shown in Table 1 and Table 2, where Table 1 is the first parameter vector of the harmonic reducer and Table 2 is the second parameter vector table of the harmonic reducer.

[0034] Table 1:

[0035] Table 2:

[0036] The variable distribution type of the flexspline cylinder length, flexspline wall thickness, flexspline centerline radius, flexspline maximum radial deformation, meshing tooth number ratio, normal stress stress concentration factor, shear stress stress concentration factor, flexspline distortion stress growth factor, flexspline distortion stress growth factor, dynamic load coefficient, normal stress coefficient and shear stress coefficient in Table 1 is normal distribution, which belongs to the first parameter vector of the harmonic reducer.

[0037] The variable distribution type of the output torque, elastic modulus, bending fatigue limit and shear fatigue limit in the above Table 2 is interval distribution, which belongs to the second parameter vector of the harmonic reducer.

[0038] S102, the processor calculates the reliability index of the kth round according to the first parameter vector of the harmonic reducer of the kth round.

[0039] Specifically, the reliability index of the kth round is calculated according to the following formula: (1) in, is the reliability index of the kth round, is the first parameter vector of the k-th harmonic reducer, for The second-order norm of .

[0040] S103, the processor calculates the first parameter vector of the harmonic reducer of the k+1th round according to the reliability index of the kth round.

[0041] Specifically, the first parameter vector of the k+1th harmonic reducer is calculated according to the following formula: (2) in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the control coefficient, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second parameter vector of the k-th harmonic reducer, for The second-order norm of is the involution matrix of the unit vector.

[0042] The above reliability index is used to characterize the probability of failure of the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer.

[0043] S104: The processor calculates the reliability index of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round.

[0044] Specifically, the reliability index of the k+1th round is calculated according to the following formula: (3) in, is the reliability index of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, for The second-order norm of .

[0045] More specifically, formula (2) is obtained according to the following process: 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: (4) in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the reliability index of the kth round, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second harmonic reducer vector of the k-th wheel, for The second-order norm of .

[0046] The above HL-RF only relies on the traditional iterative algorithm to iterate the first parameter vector of the harmonic reducer, which may show unstable convergence behavior, resulting in the first parameter vector of the harmonic reducer not converging or only converging to the local optimum, that is, when the difference between the reliability index of the subsequent k+1th round and the reliability index of the kth round is still greater than the first convergence threshold, the iteration of the first parameter vector of the harmonic reducer is stopped. As a result, the accuracy of the first parameter vector of the harmonic reducer cannot be guaranteed.

[0047] From the above, it can be seen that the chaos control algorithm is introduced to control the convergence of the first parameter vector of the k+1th harmonic reducer, and the following formula is obtained: (5) in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the reliability index of the kth round, is the control coefficient, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second harmonic reducer vector of the k-th wheel, is the involution matrix of the unit vector.

[0048] If the above control coefficient =0, then formula (5) can be simplified to , at this time, the first parameter vector of the k+1th round of the harmonic reducer cannot converge. Since the calculation process of the chaos control algorithm depends on the preset number of iterations, the calculation efficiency is relatively low and there is a possibility of non-convergence. Therefore, it is necessary to use the material composition and computational modeling algorithm for iteration to obtain the following formula: (6) in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second harmonic reducer vector of the k-th wheel, For the kth round The unit direction vector in the direction of the negative derivative of For the k+1th round The unit direction vector in the direction of the negative derivative of For the k-1th round The unit direction vector in the direction of the negative derivative of It is the shock judgment factor of the k+1th round.

[0049] The above formula (6) updates the first parameter vector of the harmonic reducer according to the gradient of the limit state function of the first parameter vector of the k-th harmonic reducer and the second harmonic reducer vector of the k-th round, and introduces the oscillation judgment factor of the k+1th round to evaluate whether the iteration point oscillates. >0, it means that the angle between the first parameter vector of the k+1th harmonic reducer and the second parameter vector of the k+1th harmonic reducer is less than 90°, and the iteration point does not oscillate; if >0, it means that the angle between the first parameter vector of the k+1th harmonic reducer and the second parameter vector of the k+1th harmonic reducer is less than 90°, and the iteration point does not oscillate. Substituting the above formula (6) into formula (5), we get formula (2).

[0050] Such an arrangement improves the convergence speed and accuracy of the iterative process of the first parameter vector of the harmonic reducer, and significantly reduces the complexity of multi-dimensional calculations. Compared with the prior art, such an arrangement allows the iterative 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.

[0051] S105, the processor determines whether the difference between the reliability index of the k+1th round and the reliability index of the kth round is less than or equal to the first convergence threshold, if so, executes step S106, if not, executes step S114.

[0052] 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+1th round and the reliability index of the kth round. The first convergence threshold is preset and is 10e-6.

[0053] S106: The processor calculates a first error value of the k+1th wheel based on the first parameter vector of the harmonic reducer of the k+1th wheel and the first parameter vector of the harmonic reducer of the kth wheel.

[0054] Specifically, the first error value of the k+1th round is calculated according to the following formula:

[0055] in, is the first error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer.

[0056] More specifically, the first error value is a preset convergence threshold for ending iteration of the first parameter vector of the harmonic reducer of the k+1th round, so as to provide a basis for the processor to determine whether to iterate the first parameter vector of the harmonic reducer subsequently.

[0057] S107, the processor determines whether the first error value of the k+1th round is less than or equal to the second convergence threshold, if so, executes step S108, if not, executes step S114.

[0058] Specifically, the processor can determine whether to stop iterating the first parameter vector of the harmonic reducer according to the first error value, and prepare for the subsequent creation of a second-order Taylor series of a single variable function.

[0059] S108, the processor obtains the second-order Taylor series of the univariate function of the k+1th wheel according to the first parameter vector of the harmonic reducer of the k+1th wheel and the second parameter vector of the harmonic reducer of the kth wheel.

[0060] Specifically, the second-order Taylor series of the univariate function of the k+1th round is calculated according to the following formula:

[0061] in, is the second-order Taylor series of the univariate function of the k+1th round, The interval of the second parameter vector of the harmonic reducer for all round iterations is The median vector other than is the jth variable in the second parameter vector of the harmonic reducer, , is the first parameter vector of the k+1th harmonic reducer, is the radius of the interval of the second parameter vector of the k-th harmonic reducer, is the median vector of the interval of the second parameter vector of the harmonic reducer for all round iterations, , It is the function value of the limit state function at the first parameter vector of the k+1th harmonic reducer and the second parameter vector of the kth harmonic reducer.

[0062] S109, the processor processes the second-order Taylor series of the single variable function of the k+1th round to obtain the minimum value of the limit state function in the interval.

[0063] Specifically, the minimum value of the limit state function within the interval is calculated according to the following formula:

[0064] in, is the minimum value of the limit state function in the interval, is the second-order Taylor series of the univariate function of the k+1th round, and m is the dimension of the second harmonic reducer vector.

[0065] The minimum value of the limit state function in the above interval is based on the multiplication dimensionality reduction method. The limit state function of the first parameter vector of the harmonic reducer in the k+1th round and the second harmonic reducer vector in the k+1th round can be expanded to the product form of the second-order Taylor series of the univariate function at the midpoint of the interval of the second parameter vector of the harmonic reducer.

[0066] S110, the processor calculates the second parameter vector of the k+1th harmonic reducer according to the interval minimum value corresponding to the minimum value of the limit state function in the interval.

[0067] Specifically, the second harmonic reducer vector of the k+1th wheel is calculated according to the following formula:

[0068] in, is the second harmonic reducer vector of the k+1th round, is the median vector of the interval of the second parameter vector of the harmonic reducer for all round iterations, is the interval minimum value corresponding to the minimum value of the limit state function in the interval, is the radius of the interval of the second parameter vector of the k-th harmonic reducer.

[0069] More specifically, The value of the independent variable of the second-order Taylor series of the single variable function of the k+1th round when the second-order Taylor series of the single variable function of the k+1th round takes the minimum value within the preset range. The second harmonic reducer vector of the k+1th round calculated by the processor provides support for the subsequent calculation of the first error value.

[0070] S111, the processor calculates the second error value of the k+1th wheel according to the second parameter vector of the harmonic reducer of the k+1th wheel.

[0071] Specifically, the second error value of the k+1th round is calculated according to the following formula:

[0072] in, is the second error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the second parameter vector of the k+1th harmonic reducer, It is the limit state function of the first parameter vector of the k+1th harmonic reducer and the second parameter vector of the k+1th harmonic reducer.

[0073] More specifically, the second error value is a preset convergence threshold for ending iteration of the second parameter vector of the harmonic reducer of the k+1th round, so as to provide a basis for the processor to determine whether to iterate the second parameter vector of the harmonic reducer subsequently.

[0074] S112, the processor determines whether the second error value of the k+1th round is less than or equal to the third convergence threshold, if so, executes step S113, if not, executes step S114.

[0075] Specifically, the processor can determine whether to stop iterating the second parameter vector of the harmonic reducer according to the second error value, that is, determine whether the second parameter vector of the harmonic reducer converges.

[0076] S113, the processor determines the reliability index of the k+1th round as the maximum failure probability.

[0077] Specifically, when the iteration of the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer stops, the reliability index of the k+1th round can be determined as the maximum failure probability. As shown in Table 2, Table 2 is a maximum failure probability table of different control coefficients.

[0078] Table 2:

[0079] When the control coefficient is 0.1, 0.2, 0.3, 0.4 or 0.5, the maximum failure probability is 0.13731.

[0080] S114, the processor calculates and obtains the first parameter vector of the k+2th harmonic reducer.

[0081] 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, the first parameter vector representing the harmonic reducer and the second parameter vector representing the harmonic reducer need to continue to iterate.

[0082] The embodiment of the present application provides a hybrid uncertainty analysis method, in which a processor obtains a second-order Taylor series of a single variable 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, processes the second-order Taylor series of the single variable function of the k+1th round, obtains a minimum value of a limit state function in an interval, calculates a second parameter vector of a harmonic reducer of the k+1th round according to an interval minimum value corresponding to the minimum value of the limit state function in the interval, calculates a second error value of the k+1th round according to the second parameter vector of the harmonic reducer of the k+1th round, and if the first error value of the k+1th round is less than or equal to a third convergence threshold, the reliability index of the k+1th round is determined as the maximum failure probability, otherwise, the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer are continued to be iterated. The method improves the efficiency of iterating the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer by solving the extreme value problem of the second-order Taylor series of a single variable function. In hybrid uncertainty analysis, this method decouples the nested optimization in hybrid 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, through multiplication dimensionality reduction, the problem is converted into an extreme value problem of multiplying multiple intervals, which is more feasible.

[0083] Compared with the prior art, in which a large amount of data is collected within the range of the minimum value of the interval corresponding to the minimum value of the limit state function within the interval to iterate the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer, this method does not need to collect a large amount of data, does not need to establish a polynomial proxy model, and uses optimization theory for solving. This method speeds up the iteration efficiency of the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer, thereby improving the speed of determining the maximum failure probability.

[0084] The following is an introduction to the determination method of the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer. The processor obtains the first parameter vector of the original harmonic reducer 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 that conforms to the cumulative distribution, and the second parameter vector of the original harmonic reducer is an m-dimensional interval uncertainty vector that conforms to the cumulative distribution; the first parameter vector of the original harmonic reducer and the second parameter vector of the original harmonic reducer are standardized and transformed to obtain the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer.

[0085] Specifically, on the basis of the analysis method based on Monte Carlo hybrid reliability, the first parameter vector of the original harmonic reducer and the original second harmonic reducer vector are converted to the standard normal distribution space, the influence of interval variables in the hybrid uncertainty is quantified, and the first parameter vector and the second harmonic reducer vector of the harmonic reducer are obtained.

[0086] In this method, the original first parameter vector of the harmonic reducer and the original second harmonic reducer vector are converted into the first parameter vector and the second harmonic reducer vector of the harmonic reducer, so as to iterate the first parameter vector and the second harmonic reducer vector of the harmonic reducer.

[0087] The following example introduces the mixed uncertainty analysis of the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer: In the design of harmonic reducers, a safety factor greater than 1.5 is required to ensure reliability and safety. like Figure 2 As shown, Figure 2 A comparison chart of the maximum failure probabilities provided in the embodiments of the present application. The maximum failure probability calculated by this method is more efficient and robust, and is the same as the maximum failure probability obtained by the prior art.

[0088] Based on the above hybrid uncertainty analysis method embodiment, the present application embodiment also provides a hybrid uncertainty analysis device, such as Figure 3 As shown, Figure 3 A schematic diagram of the structure of a hybrid uncertainty analysis device provided in an embodiment of the present application. The device includes: an acquisition module 31 and a data processing module 32. The functions of each module are as follows: An acquisition module 31 is used to acquire a first parameter vector of the k-th harmonic reducer and a second parameter vector of the k-th harmonic reducer; wherein the first parameter vector of the k-th harmonic reducer is an n-dimensional probability uncertainty vector in the standard normal space of the k-th wheel, and the second parameter vector of the k-th harmonic reducer is an m-dimensional interval uncertainty vector in the standard space of the k-th wheel; A data processing module 32, configured to calculate the reliability index of the k-th wheel according to the first parameter vector of the harmonic reducer of the k-th wheel; The data processing module 32 is further used to calculate the first parameter vector of the harmonic reducer of the k+1th round according to the reliability index of the kth round; calculate the reliability index of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round; if the difference between the reliability index of the k+1th round and the reliability index of the kth round is less than or equal to the first convergence threshold, calculate the first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round and the first parameter vector of the harmonic reducer of the kth round; if the first error value of the k+1th round is less than or equal to the second convergence threshold, calculate the first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round. A parameter vector and a second parameter vector of the k-th round harmonic reducer obtain a second-order Taylor series of a single variable function of the k+1-th round; the second-order Taylor series of the k+1-th round single variable function is processed to obtain the minimum value of the limit state function in the interval; the second parameter vector of the k+1-th round harmonic reducer is calculated according to the interval minimum value corresponding to the minimum value of the limit state function in the interval; the second error value of the k+1-th round is calculated according to the second parameter vector of the k+1-th round harmonic reducer; if the second 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.

[0089] Preferably, the reliability index of the kth round is calculated according to the following formula:

[0090] in, is the reliability index of the kth round, is the first parameter vector of the k-th harmonic reducer; The first parameter vector of the k+1th harmonic reducer is calculated according to the following formula:

[0091] in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the control coefficient, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second parameter vector of the k-th harmonic reducer, is the involution matrix of the unit vector; The reliability index of the k+1th round is calculated according to the following formula:

[0092] in, is the reliability index of the k+1th round, is the first parameter vector of the k+1th harmonic reducer.

[0093] Preferably, the first error value of the k+1th round is calculated according to the following formula:

[0094] in, is the first error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer.

[0095] 4. The hybrid uncertainty analysis method according to claim 1, wherein the second error value of the k+1th round is calculated according to the following formula:

[0096] in, is the second error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the second parameter vector of the k+1th harmonic reducer, It is the limit state function of the first parameter vector of the k+1th harmonic reducer and the second parameter vector of the k+1th harmonic reducer.

[0097] Preferably, the second parameter vector of the k+1th harmonic reducer is calculated according to the following formula:

[0098] in, is the second harmonic reducer vector of the k+1th round, is the median vector of the interval of the second parameter vector of the harmonic reducer for all round iterations, is the interval minimum value corresponding to the minimum value of the limit state function in the interval, is the radius of the interval of the second parameter vector of the k-th harmonic reducer.

[0099] Preferably, the acquisition module 31 is specifically used to acquire the first parameter vector of the original harmonic reducer 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 that conforms to the cumulative distribution, and the second parameter vector of the original harmonic reducer is an m-dimensional interval uncertainty vector that conforms to the cumulative distribution; the first parameter vector of the original harmonic reducer and the second parameter vector of the original harmonic reducer are standardized and converted to obtain the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer. .

[0100] Preferably, the data processing module 32 is also used to calculate the first parameter vector of the harmonic reducer of the k+2th round if the difference between the reliability index of the k+1th round and the reliability index of the kth round is greater than the first convergence threshold; calculate the first parameter vector of the harmonic reducer of the k+2th round if the first error value of the k+1th round is greater than the second convergence threshold; and calculate the first parameter vector of the harmonic reducer of the k+2th round if the second error value of the k+1th round is greater than the third convergence threshold.

[0101] The hybrid uncertainty analysis device provided in the embodiment of the present application has the same technical features as the hybrid uncertainty analysis method provided in the above-mentioned embodiment, so it can also solve the same technical problems and achieve the same technical effects.

[0102] The present application also provides a computing device. Figure 4 As shown, this figure is a schematic diagram of a computing device provided in an embodiment of the present application, and 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 through the bus 401.

[0103] The bus 401 may be a peripheral component interconnect (PCI) bus or an extended industry standard architecture (EISA) bus. The bus may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 4 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.

[0104] The processor 402 may be any one or more of a central processing unit (CPU), a graphics processing unit (GPU), a microprocessor (MP), or a digital signal processor (DSP).

[0105] The communication interface 403 is used for communicating with the outside. The memory 404 may include a volatile memory, such as a random access memory (RAM). The memory 404 may also include a non-volatile memory, such as a read-only memory (ROM), a flash memory, a hard disk drive (HDD) or a solid state drive (SSD).

[0106] The memory 404 stores executable codes, and the processor 402 executes the executable codes to perform the aforementioned method.

[0107] The embodiment of the present application also provides a computer-readable storage medium. The computer-readable storage medium can be any available medium that can be 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 (such as a floppy disk, a hard disk, a tape), an optical medium (such as a DVD), or a semiconductor medium (such as a solid-state hard disk). The computer-readable storage medium includes instructions that instruct the computing device to execute the above method.

[0108] The embodiment of the present application further provides a computer program product, which includes one or more computer instructions. When the computer instructions are loaded and executed on a computing device, the process or function described in the embodiment of the present application is generated in whole or in part.

[0109] The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium. 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, optical fiber) or wireless (e.g., infrared, wireless, microwave, etc.) means.

[0110] When the computer program product is executed by a computer, the computer executes any of the aforementioned hybrid uncertainty analysis methods. The computer program product may be a software installation package, and when any of the aforementioned hybrid uncertainty analysis methods is needed, the computer program product may be downloaded and executed on a computer.

[0111] The descriptions of the processes or structures corresponding to the above-mentioned figures have different emphases. For parts that are not described in detail in a certain process or structure, please refer to the relevant descriptions of other processes or structures.

[0112] The above description is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions within the technical scope disclosed in the present application should be included in the protection scope of the present application.

Claims

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

2. The hybrid uncertainty analysis method according to claim 1, characterized in that: The reliability index of the kth round is calculated according to the following formula: in, is the reliability index of the kth round, is the first parameter vector of the k-th harmonic reducer; The first parameter vector of the k+1th harmonic reducer is calculated according to the following formula: in, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer, is the second parameter vector of the k-th harmonic reducer, is the control coefficient, is the limit state function of the first parameter vector of the k-th harmonic reducer and the second parameter vector of the k-th harmonic reducer, is the involution matrix of the unit vector; The reliability index of the k+1th round is calculated according to the following formula: in, is the reliability index of the k+1th round, is the first parameter vector of the k+1th harmonic reducer.

3. The hybrid uncertainty analysis method according to claim 1, characterized in that: The first error value of the k+1th round is calculated according to the following formula: in, is the first error value of the k+1th round, is the first parameter vector of the k+1th harmonic reducer, is the first parameter vector of the k-th harmonic reducer.

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

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

6. The hybrid uncertainty analysis method according to claim 1, characterized in that: The first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer are determined as follows: The processor obtains a first parameter vector of an original harmonic reducer and a second parameter vector of an 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 standardized conversion on the first parameter vector of the original harmonic reducer and the second parameter vector of the original harmonic reducer to obtain the first parameter vector of the harmonic reducer and the second parameter vector of the harmonic reducer.

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

8. A hybrid uncertainty analysis device, characterized in that: The device comprises: An acquisition module, used to acquire a first parameter vector of the k-th harmonic reducer and a second parameter vector of the k-th harmonic reducer; wherein the first parameter vector of the k-th harmonic reducer is an n-dimensional probability uncertainty vector in the standard normal space of the k-th wheel, and the second parameter vector of the k-th harmonic reducer is an m-dimensional interval uncertainty vector in the standard space of the k-th wheel; A data processing module, used for calculating the reliability index of the k-th round according to the first parameter vector of the harmonic reducer of the k-th round; The data processing module is further used to calculate the first parameter vector of the harmonic reducer of the k+1th round according to the reliability index of the kth round; calculate the reliability index of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round; if the difference between the reliability index of the k+1th round and the reliability index of the kth round is less than or equal to the first convergence threshold, calculate the first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round and the first parameter vector of the harmonic reducer of the kth round; if the first error value of the k+1th round is less than or equal to the second convergence threshold, calculate the first error value of the k+1th round according to the first parameter vector of the harmonic reducer of the k+1th round. The parameter vector and the second parameter vector of the k-th round harmonic reducer obtain the second-order Taylor series of the single variable function 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 in the interval; the second parameter vector of the k+1-th round harmonic reducer is calculated according to the interval minimum value corresponding to the minimum value of the limit state function in the interval; the second error value of the k+1-th round is calculated according to the second parameter vector of the k+1-th round harmonic reducer; if the second 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.

9. A computing device, characterized in that including memory and processor; One or more computer programs are stored in the memory, and the one or more computer programs include instructions; when the instructions are executed by the processor, the computing device executes the method as claimed 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, and the computer program is used to execute the method according to any one of claims 1 to 7.

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