Non-intrusive chaotic polynomial cartridge receiver assembly structure uncertainty analysis method

Abstract

The invention discloses a non-intrusive chaotic polynomial uncertainty analysis method for a cartridge receiver assembly structure, and belongs to the field of uncertainty analysis of cartridge receiver assembly structures. The method comprises the following steps: step SS1: carrying out dynamic modeling on a cartridge receiver component; step SS2: carrying out dynamic modeling on the cartridge receiver assembly structure; step SS3, obtaining a probability distribution model of the matching size and the tightening torque according to the experimental sample; step SS4, selecting a chaotic polynomial order P, and generating a chaotic polynomial expansion item; sS5, calculating the coefficient of each chaotic polynomial expansion item by adopting a Bayesian compressed sensing method; sS6, determining the change range of each order of modal frequency of the cartridge receiver assembly structure based on the established non-intrusive chaotic polynomial model; step SS7, if the judgment result is not convergent, P = P + 1, executing the step SS4, and if the judgment result is convergent, outputting the result and ending. The method is used for uncertainty analysis of each order of modal frequency of the cartridge receiver assembly structure, and the calculation efficiency is improved while the analysis precision is ensured.

Description

Technical Field

[0001] The invention relates to a non-invasive chaotic polynomial casing assembly structure uncertainty analysis method, belonging to the technical field of various-order modal variation range analysis of casing assembly structures caused by matching size and tightening torque uncertainty. Background Art

[0002] The casing structure of an aircraft turbine engine is usually assembled from multiple casings. It is the main load-bearing component in the engine and a key component that bears load and contains the engine. The casing is usually a thin-walled cylindrical structure. There are many uncertainties in the processing and manufacturing process, which leads to certain uncertainties in the dynamic characteristics of the casing structure, and ultimately affects the dynamic characteristics of the rotor-support-casing system of the aircraft turbine engine. Therefore, in the design stage of aircraft turbine engines, it is very necessary to establish a dynamic uncertainty analysis model for the casing assembly structure based on a small amount of test data and analyze the dynamic characteristics of the casing structure.

[0003] In recent decades, polynomial chaos expansion has become a major technology for quantifying the uncertainty of system response. PCE methods are divided into intrusive polynomial chaos and non-intrusive polynomial chaos (NIPC). Intrusive polynomial chaos expansion replaces all dependent variables and random inputs in the system control equation with their polynomial chaos expansions, and uses a certain number of integral points or sampling points to construct a polynomial chaos expansion model of the random response quantity of interest. On this basis, uncertainty analysis is performed to quickly obtain the statistical characteristics of the response output. Based on the NIPC method, the present invention constructs a dynamic analysis method that takes into account the uncertainty of the casing assembly structure. Summary of the invention

[0004] The purpose of the present invention is to overcome the technical defects of the prior art, solve the above-mentioned technical problems, and propose a non-invasive chaotic polynomial casing assembly structure uncertainty analysis method for analyzing the various modal variation ranges of the casing assembly structure caused by the uncertainty of the matching size and the tightening torque, thereby improving the calculation efficiency while ensuring the analysis accuracy.

[0005] The present invention specifically adopts the following technical solution: a non-invasive chaotic polynomial casing assembly structure uncertainty analysis method, comprising the following steps:

[0006] Step SS1: dynamic modeling of the casing components;

[0007] Step SS2: dynamic modeling of the casing assembly structure;

[0008] Step SS3: Obtain the probability distribution model of the matching size and tightening torque according to the experimental samples;

[0009] Step SS4: Select the chaotic polynomial order P and generate chaotic polynomial expansion terms;

[0010] Step SS5: using the Bayesian compressed sensing method to calculate the coefficients of each chaotic polynomial expansion term;

[0011] Step SS6: determining the variation range of each modal frequency of the casing assembly structure based on the established non-intrusive chaotic polynomial model;

[0012] Step SS7: If the result is not converged, P=P+1, and the process goes to step SS4 for execution. If the result is converged, the process outputs the result and ends.

[0013] As a preferred embodiment, the chaotic polynomial expansion term in step SS4 is Ψ=[ψ0 ψ1 …ψ P ], P is the number of terms in the polynomial expansion.

[0014] As a preferred embodiment, the coefficient of each chaotic polynomial expansion term in step SS5 is c, where:

[0015] As a preferred embodiment, step SS5 specifically includes:

[0016] Step SS51: Select basis function ψ i ;

[0017] Step SS52: Update γ in the following equation (2): i ;

[0018]

[0019] Step SS53: Update μ and Σ using the following formula (3);

[0020]

[0021] Step SS54: Update s using the following formula (4) i and q i ;

[0022]

[0023] Step SS55: Update λ using the following formula (5);

[0024]

[0025] Step SS56: Establish a chaotic polynomial model of casing assembly structure uncertainty:

[0026] Y=Ψc\*MERGEFORMAT(6)

[0027] Among them, Y is the modal frequency of each order of the casing assembly structure.

[0028] As a preferred embodiment, step SS6 specifically includes: calculating the variation range of each order modal frequency of the box assembly structure based on formula (6).

[0029] As a preferred embodiment, step SS7 specifically includes: repeating steps SS4 to SS6 until the variation range of each order modal frequency converges.

[0030] The beneficial effects achieved by the present invention are as follows: In the uncertainty analysis method for the casing assembly structure based on non-invasive chaotic polynomials proposed in the present invention, the variation range of each order modal frequency of the casing assembly structure is taken as the analysis target, a casing component dynamics model and a casing assembly structure dynamics model are established, the probability distribution model of the fitting size and the tightening torque is obtained according to the experimental samples, and an uncertainty analysis proxy model of the target quantity is constructed based on the non-invasive chaotic polynomials, so as to realize accurate and rapid analysis of the variation range of each order modal frequency of the casing assembly structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 It is a flow chart of the casing assembly structure uncertainty analysis method of the non-invasive chaotic polynomial of the present invention.

[0032] Figure 2 This is a test model diagram of the fan compressor connected to the casing.

[0033] Figure 3 It is the frequency response function diagram of the fan compressor connection casing modal test.

[0034] Figure 4 It is the 2000Hz modal frequency and vibration shape diagram before the fan compressor connection casing test.

[0035] Figure 5 It is a schematic diagram of the finite element model of the fan compressor connection casing.

[0036] Figure 6 It is the normal distribution curve of the matching size.

[0037] Figure 7 It is a schematic diagram of the geometric model of the fan compressor connection casing.

[0038] Figure 8 is the normal distribution curve of connection stiffness.

[0039] Fig. 9 It is the normal distribution curve of elastic modulus.

[0040] Fig.10 It is a histogram of the first four modal frequencies of the connection casing in 1000 sample spaces.

[0041] Fig.11 It is the distribution diagram of the second-order test frequency in the sample frequency interval.

[0042] Fig.12 It is the distribution diagram of the fourth-order test frequency in the sample frequency interval. DETAILED DESCRIPTION

[0043] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0044] In the uncertainty analysis method of the casing assembly structure based on non-invasive chaotic polynomials proposed in the present invention, the variation range of each order modal frequency of the casing assembly structure is taken as the analysis target, and a dynamic model of the casing components and a dynamic model of the casing assembly structure are established. The probability distribution model of the fitting size and the tightening torque is obtained according to the experimental samples, and an uncertainty analysis proxy model of the target quantity is constructed based on the non-invasive chaotic polynomials to achieve accurate and rapid analysis of the variation range of each order modal frequency of the casing assembly structure.

[0045] Taking the fan and compressor casing assembly structure of a certain engine as an example, the uncertainty analysis method of casing assembly structure based on chaotic polynomials proposed by the present invention is explained below.

[0046] The finite element model and geometric model of the fan compressor connection case are as follows: Figure 5 and Figure 7 As shown, the fan casing and the compressor casing are connected by bolts. There are 20 bolts at the connection, and the bolt specification is M4.

[0047] (1) Perform modal test on the fan compressor connection casing. The test is as follows: Figure 2 As shown in the figure, the test point layout is consistent with the single component test. In order to identify the possible heavy modal characteristics, three acceleration sensors are arranged. The frequency response function obtained from the fan compressor connection case test is as follows: Figure 3 As shown in the figure, the test frequency range is 0-2000Hz. The modal frequency and vibration mode of the first 2000Hz modal test are as follows: Figure 4 As shown in the figure, a thin layer is used to replace bolts, and the finite element model of the fan compressor connection case is shown in the figure. Figure 5 As shown, through the theoretical calculation formula of the elastic modulus of the thin layer unit, the connection stiffness is 4.91e9N / m and the thin layer elastic modulus is 6.53e9Pa. The finite element model of the fan compressor connection casing is established, and the modal frequency and vibration shape of the first 2000Hz are calculated.

[0048] (2) In the modeling of casing assembly connection, thin-layer units are often used instead of bolt connections to simplify the model and reduce the difficulty of calculation. When there are differences in the matching dimensions of the fan and compressor casings, the connection surfaces of the fan casing and the compressor casing will be different, which will lead to uncertainty in the casing connection stiffness, and then the equivalent thin-layer unit connection stiffness is also uncertain. The gap sizes of the compressors with five different matching dimensions are: 0.014mm, 0.0064mm, -0.0096mm, -0.0189mm and -0.0034mm. Modal tests were carried out on the five compressor and fan connection casings to obtain their first 2000Hz modal frequencies, and the distribution of modal frequencies under different matching dimension uncertainties was analyzed. The casing connection stiffness and thin-layer unit elastic modulus were identified through the modal frequencies, and whether the frequency satisfies the normal distribution under different matching dimensions. The different matching dimensions are shown in Table 1.

[0049] Table 1 Distribution parameters of different matching sizes

[0050]

[0051] The modal frequencies within 2000 Hz of the compressor fan connection case test for the first five different matching sizes are shown in Table 2.

[0052] Table 2 2000 Hz modal frequencies of 5 compressor fan-connected casings with different matching sizes before testing

[0053]

[0054] (3) Assuming that the size of the fit is normally distributed, the test tested 5 kinds of fit sizes that meet the normal distribution, with a mean of -0.0023mm and a variance of 0.0001378mm. The fit sizes were sampled 1000 times, and the normal distribution curve of the fit size is as follows: Figure 6 As shown, the matching size distribution range is [-0.04 0.03] mm.

[0055] The geometric model of the fan compressor connection casing containing solid thin layer units is established. The thin layer thickness is 1 mm. The geometric model is as follows: Figure 7 As shown in the figure, based on the connection stiffness and thin-layer unit elastic modulus theory, the initial casing connection stiffness is solved to be 4.91×10 9 N / m, elastic modulus is 6.53×10 9 Pa, the modal frequency of the first 2000 Hz of the connecting casing is calculated based on the elastic modulus of the thin layer, as shown in Table 3.

[0056] Table 3 Modal frequencies of the first 2000 Hz of the finite element model of the fan compressor connection casing

[0057] Order 1 2 3 4 Frequency (Hz) 815.55 816.3 1564.1 1564.1

[0058] The first and second orders of the fan compressor connection casing are heavy modes, and the third and fourth orders are heavy modes. The second-order modal frequency obtained by experimental test is used to identify the casing connection stiffness and thin layer elastic modulus. The identified casing connection stiffness and thin layer unit elastic modulus are shown in Table 4.

[0059] Table 4 Connection stiffness and thin layer elastic modulus of different matching sizes of casings

[0060] No. 1 No. 2 No.3 No. 4 No. 5 Mean variance <![CDATA[Elastic modulus × 10 9 Pa]]> 5.34 7.38 3.64 4.35 6.69 5.48 2.439 <![CDATA[Connection stiffness × 10 9 N / m]]> 4.02 5.04 2.73 3.27 4.78 3.97 0.958

[0061] The fan compressor casing connection stiffness and thin layer unit elastic modulus are normally distributed. The normal distribution curves of connection stiffness and thin layer elastic modulus are as follows: Figure 8 and Fig. 9 As shown, the connection stiffness distribution range is [1.175 6.966]×10 9 N / m, the distribution range of the thin layer elastic modulus is [0.793 10.22]×10 9 Pa.

[0062] (4) Select the order of the chaotic polynomial and generate the chaotic polynomial expansion term Ψ=[ψ0 ψ1 … ψ P ], P is the number of polynomial expansion terms:

[0063] (5) Using the Bayesian compressed sensing method to calculate the coefficients c of each chaotic polynomial expansion term;

[0064]

[0065] This step includes the following steps:

[0066] a) Choose the basis function ψ i (The initial corresponding constant regressor is selected);

[0067] b) Update γ in the following formula i ;

[0068]

[0069] c) Update μ and Σ using the following formula;

[0070]

[0071] d) Update s using the following formula i and q i ;

[0072]

[0073] e) Update λ using the following formula:

[0074]

[0075] Establishing a chaotic polynomial model for uncertainty in casing assembly structure

[0076] Y=Ψc (6)

[0077] Y is the modal frequency of the casing assembly structure.

[0078] (6) Based on the constructed chaotic polynomial, the uncertainty analysis of the modal frequency within 2000 Hz before the fan compressor is connected to the casing in the 1000 thin layer elastic modulus sample interval is performed.

[0079] (7) Repeat steps (4)-(6) until the analysis results converge. The first four modal frequency distributions of the casing assembly structure are obtained as follows: Fig.10 As shown. The first-order modal frequency distribution interval is [808.9816.15] Hz, the second-order modal frequency distribution interval is [809.67816.91] Hz, the third-order modal frequency distribution interval is [1551.091565.6] Hz, and the fourth-order modal frequency distribution interval is [1551.091565.6] Hz. Fig.10 It can be seen that in the 1000 sample space, the first four modal frequencies of the fan compressor connecting the casing are all distributed in a left-skewed manner.

[0080] In the uncertainty analysis method of the casing assembly structure based on non-invasive chaotic polynomials proposed by the present invention, the variation of the matching size and tightening torque is considered to analyze the variation range of the modal frequency of the casing assembly structure, and only five sets of tests are needed. Compared with the 100 tests required by the traditional Monte Carlo method, the analysis time is shortened by 95%, and the analysis efficiency is greatly improved. The comparison of the measurement results of the two is as follows: Fig.11 and 12 As shown, the accuracy of the method of the present invention is basically consistent with the result of the traditional Monte Carlo method, which shows the superiority of the method of the present invention.

[0081] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0082] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be stored in a computer-readable memory that can guide a computer or other programmable data processing device to work in a specific way, so that the instructions stored in the computer-readable memory produce a product including an instruction device, which implements the functions specified in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide for implementing the process in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0083] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the relevant field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A non-invasive chaotic polynomial casing assembly structure uncertainty analysis method, characterized in that: The steps include: Step SS1: dynamic modeling of the casing components; Step SS2: dynamic modeling of the casing assembly structure; Step SS3: Obtain the probability distribution model of the matching size and tightening torque according to the experimental samples; Step SS4: Select the chaotic polynomial order P and generate chaotic polynomial expansion terms; Step SS5: using the Bayesian compressed sensing method to calculate the coefficients of each chaotic polynomial expansion term; Step SS6: determining the variation range of each modal frequency of the casing assembly structure based on the established non-intrusive chaotic polynomial model; Step SS7: If the result is not converged, P=P+1, and the process goes to step SS4 for execution. If the result is converged, the process outputs the result and ends.

2. The non-invasive chaotic polynomial casing assembly structure uncertainty analysis method according to claim 1 is characterized in that: The chaotic polynomial expansion term in step SS4 is Ψ=[ψ0 ψ1…ψ P ], P is the number of terms in the polynomial expansion.

3. The non-invasive chaotic polynomial casing assembly structure uncertainty analysis method according to claim 1 is characterized in that: The coefficient of each chaotic polynomial expansion term in step SS5 is c, where 4. The non-invasive chaotic polynomial casing assembly structure uncertainty analysis method according to claim 3 is characterized in that: The step SS5 specifically includes: Step SS51: Select basis function ψ i ; Step SS52: Update γ in the following equation (2): i ; Step SS53: Update μ and Σ using the following formula (3); Step SS54: Update s using the following formula (4) i and q i ; Step SS55: Update λ using the following formula (5); Step SS56: Establish a chaotic polynomial model of casing assembly structure uncertainty: Y=Ψc (6) Among them, Y is the modal frequency of each order of the casing assembly structure.

5. The non-invasive chaotic polynomial casing assembly structure uncertainty analysis method according to claim 4 is characterized in that: The step SS6 specifically includes: calculating the variation range of each order modal frequency of the box assembly structure based on formula (6).

6. The non-invasive chaotic polynomial casing assembly structure uncertainty analysis method according to claim 5 is characterized in that: The step SS7 specifically includes: repeating steps SS4 to SS6 until the variation range of each order modal frequency converges.

Images