Engine sensitivity analysis method based on random perturbation collocation method

Abstract

The invention provides an engine sensitivity analysis method based on a random perturbation collocation method, and belongs to the field of engine analysis. The method comprises the following steps: firstly, determining a random variable influencing engine model response and a mean value and a standard deviation corresponding to the random variable, and establishing an input-output relationship between random variable input and engine model response output; secondly, calculating the contribution of each random variable to the response variance of the engine model based on a random perturbation collocation method; and finally, calculating the sensitivity index of each random variable to the response of the engine model. The problem of engine sensitivity analysis is solved through the random perturbation collocation method, and the blank of research in the aspect of engine sensitivity analysis is filled up; a sample point set is constructed based on the idea of a random perturbation point collocation method, the precision is higher, and the calculation amount required by sensitivity analysis is reduced; the method does not depend on a specific engine model construction method, is suitable for engines of different models and types, and can achieve the purpose of efficient engine sensitivity analysis.

Description

Technical Field

[0001] The invention belongs to the field of engine analysis and relates to an engine sensitivity analysis method based on a random perturbation point matching method. Background Art

[0002] Sensitivity analysis of the engine is an important means to study and measure the impact of different random variables on the engine, and can provide an important reference for the subsequent design optimization of the engine. The engine has a complex structure, many parts, and complicated processes. Different processing methods will cause a large number of uncertain variables in the size and assembly of the parts, which ultimately leads to different performance of the finished engine. Therefore, in order to ensure that the mass production of the engine can achieve a high yield rate, it is an indispensable part of engine production and manufacturing to conduct sensitivity analysis on the various uncertain variables that affect the engine and screen out the factors that have the most significant impact on the engine.

[0003] To perform sensitivity analysis of the engine, two key steps need to be completed. The first is to build an accurate input-output model between random variables and engine response, and the second is to sample random variables to build the sample set required for subsequent global sensitivity analysis. Due to the complex structure of the engine and the many uncertain variables involved, sensitivity analysis of the engine is a computationally intensive task. In order to improve computational efficiency and reduce the amount of computation required for sensitivity analysis of the engine, a large number of studies have been conducted. For example, the Chinese invention patent "A global sensitivity analysis method for aircraft engine discs based on Copula" (application number: CN202410126072.4) developed a global sensitivity analysis method for aircraft engine discs based on space segmentation and combined with Kriging proxy model. By using proxy model technology, the amount of computation required for single sample calculation is simplified. The Chinese invention patent "Prediction method for unsteady characteristics of isolated shock wave train based on artificial neural network" (application number: N202410658945.6) applies artificial neural network technology to the global sensitivity analysis of dual-mode scramjet engines and constructs a simplified network model between random variable input and output. The above patents all start from simplifying the key step one, that is, simplifying the input-output model between random variables and engine response, and reducing the calculation amount of a single sample to reduce the calculation amount of the overall sensitivity analysis. However, regarding the key step two, since these methods are still at the level of random sampling, a large number of samples are still required to ensure the calculation accuracy when performing global sensitivity analysis.

[0004] In view of the shortcomings of the prior art, the present invention proposes an engine sensitivity analysis method based on the random perturbation collocation method, which improves the sampling method of sample points, reduces the number of sample points required for calculation under the condition of ensuring calculation accuracy, and further reduces the amount of calculation required for engine sensitivity analysis. The random perturbation collocation method is a numerical method proposed by scholars Wu in solving the problem of quantifying the uncertainty of random variables [Wu F, Gao Q, Xu XM, et al. A modified computational scheme for the stochastic perturbation finiteelement method [J]. Latin American Journal of Solids and Structures, 2015, 12: 2480-2505.], [Wu F, Zhong W X. A modified stochastic perturbation method for stochastic hyperbolic heat conduction problems [J]. Computer Methods in Applied Mechanics and Engineering, 2016, 305: 739-758], and has been used in civil engineering, aerospace, nuclear engineering and other fields. The present invention is based on the idea of ​​random perturbation point collocation method, constructs the sample point set required in the process of engine sensitivity analysis, and solves the difficulty of existing methods that require a large number of sample points to ensure calculation accuracy. Since the present invention starts from improving the sampling method, it is applicable to different existing engine input-output models and can be used in combination with different existing methods. It has strong versatility and can further reduce the overall calculation amount required for engine sensitivity analysis. Summary of the invention

[0005] The present invention mainly solves the problem of large amount of calculation and low calculation efficiency of traditional engine sensitivity analysis methods, and proposes an engine sensitivity analysis method based on random perturbation point matching method. Based on the random perturbation point matching method, the present invention can use fewer sample points to complete the engine sensitivity analysis with multiple random variables, saving cost and time.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is:

[0007] An engine sensitivity analysis method based on random perturbation collocation method, the engine sensitivity analysis method first determines the random variables affecting the engine model response and the mean and standard deviation corresponding to the random variables, and establishes the input-output relationship between the random variable input and the engine model response output. Secondly, based on the random perturbation collocation method, the contribution of each random variable to the engine model response variance is calculated. Finally, the sensitivity index of each random variable to the engine model response is calculated. The method includes the following steps:

[0008] The first step is to determine the random variables that affect the engine model response and the corresponding mean and standard deviation of the random variables, and establish the input-output relationship between the random variables and the engine model response. Specifically:

[0009] Step 1.1, it is known that there are a total of random variables that affect the response of the engine model , put this The random variables are represented as a vector , the corresponding mean vector is , the corresponding standard deviation vector is .in, Representation vector No. Component, corresponding to random variables; Indicates The mean of a random variable; Indicates The standard deviation of a random variable; .

[0010] Step 1.2, transform the random variable vector Convert to a vector of zero-mean random variables ,in , The standard deviation of . Zero mean random variable With the original random variable There is a one-to-one correspondence.

[0011] Step 1.3, construct the numerical model of the engine. The input of the numerical model is the zero-mean random variable vector obtained in step 1.2 , the output of the numerical model is the engine model response .

[0012] After steps 1.1 to 1.3, we get the random variable vector The corresponding zero-mean random variable vector Response to engine model The output-output relationship between them.

[0013] Furthermore, in step 1.3, a numerical model of the engine is constructed using a finite element method or a proxy model method.

[0014] The second step is to calculate the contribution of each random variable to the variance of the engine model response based on the random perturbation collocation method. Specifically:

[0015] Step 2.1, construct two different zero-mean random variable vector sample input sets based on the random perturbation collocation method, and use the input-output relationship obtained in the first step to calculate the corresponding two different engine model response output sets. The calculation method of two different zero-mean random variable vector sample input sets and the corresponding two engine model response output sets is as follows:

[0016] Zero mean random variable vector sample input set 1:

[0017] ,

[0018] in, , represents the zero-mean random variable vector sample input No. Quantity; , represents a zero-mean random variable The expectation of the fourth power and the zero-mean random variable The ratio of the fourth power of the standard deviation of It means to calculate the mathematical expectation; represents a zero-mean random variable vector No. components, is a zero-mean random variable; represents a zero-mean random variable The standard deviation of . When the zero-mean random variable No. Quantity When the distribution of is uniform, ; When the zero-mean random variable No. Quantity When the distribution of is Gaussian, Substitute the zero-mean random variable vector sample input set 1 into the engine model input-output relationship obtained in the first step to obtain the engine model response output set 1 corresponding to one: ;

[0019] Random variable vector sample input set 2:

[0020] , , .

[0021] in, and The calculation method is the same as that of the random variable sample input set 1 The calculation method is the same as that of . Substitute the random variable vector sample input set 2 into the engine model input-output relationship obtained in the first step, and calculate the engine model response output set 2 corresponding to one: .

[0022] Step 2.2, based on the engine model response output set 1 calculated in step 2.1, calculate the zero-mean random variable The absolute contribution to the variance of the engine model response is given by the following formula:

[0023] ,

[0024] in, represents a zero-mean random variable absolute contribution to the variance of the engine model response; , is the intermediate variable used in the calculation; It means that when the random variable vector input The engine model response output when ; It means that when the random variable vector input The engine model response output when ; , is the intermediate variable used in the calculation; It means that when the random variable vector input The engine model response output when ;

[0025] Step 2.3, based on the engine model response output set 2 calculated in step 2.1, calculate the zero-mean random variable and The absolute contribution of the coupling to the variance of the engine model response is given by the following formula:

[0026] ,

[0027] in, represents a zero-mean random variable and Direct contribution of coupling to the variance of engine model response; represents a zero-mean random variable The expectation of the fourth power and the zero-mean random variable The ratio of the fourth power of the standard deviation of The same, just the subscript is different; ; ; , , They are all intermediate variables used in the calculation. The calculation method is as follows:

[0028] .

[0029] in, ; Substitute the random variable vector sample input set 2 into the engine model input-output relationship obtained in the first step, and calculate the zero-mean random variable and The absolute contribution of the coupling to the variance of the engine model response.

[0030] Step 2.4, calculate the variance of the engine model response , .

[0031] After the above steps 2.1 to 2.4, we calculated the variance of the engine model response , zero mean random variable Absolute contribution to the variance of the engine model response , zero mean random variable and Absolute contribution of coupling to the variance of engine model response .

[0032] The third step is to calculate each random variable based on the calculation results of the second step Corresponding sensitivity index and random variable and The sensitivity index corresponding to the coupling relationship is as follows:

[0033] Step 3.1, based on the calculation results of steps 2.2 and 2.4, calculate , reflects a zero-mean random variable Variance The relative contribution of With the original random variable One to one correspondence, Too The corresponding sensitivity index.

[0034] Step 3.2, based on the calculation results of steps 2.3 and 2.4, calculate ,in , Reflects the random variable and The coupling effect of The relative contribution of With the original random variable One to one correspondence, Too and The sensitivity index corresponding to the coupling effect.

[0035] Based on the above steps 3.1 to 3.2, we calculated the original random variable The variance of engine response is affected by the single action Sensitivity index of impact ; The original random variable is also calculated and Coupling effect on engine response variance Sensitivity index of impact .

[0036] Compared with the prior art, the present invention has the following beneficial effects:

[0037] (1) The present invention solves the problem of engine sensitivity analysis by using the random perturbation point collocation method, thus filling the gap in the research of engine sensitivity analysis.

[0038] (2) The present invention constructs a sample point set based on the idea of ​​random perturbation point matching method. Compared with the traditional sensitivity analysis sampling method, it requires fewer sample points and has higher accuracy, thus reducing the amount of calculation required for sensitivity analysis.

[0039] (3) The present invention does not rely on a specific engine model construction method and is applicable to engines of different models and types, thereby achieving the purpose of efficient engine sensitivity analysis. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flow chart of the engine sensitivity analysis method based on the random perturbation collocation method. DETAILED DESCRIPTION

[0041] The present invention is described in detail below in conjunction with the accompanying drawings and specific embodiments. This embodiment is implemented based on the technical solution of the present invention, and provides a detailed implementation method and specific operation process, but the protection scope of the present invention is not limited to the following embodiments.

[0042] refer to Figure 1 The flowchart of the engine sensitivity analysis method based on the random perturbation collocation method is used to perform sensitivity analysis on the pressure of key points in a certain model of four-stroke engine compartment. This implementation case includes the following steps:

[0043] The first step is to establish the input-output relationship between the random variable and the pressure at the key point in the engine compartment. Specifically:

[0044] Step 1.1: It is known that there are a total of random variables that affect the pressure at key points in the engine model cabin: They are ambient pressure, cylinder initial temperature, cylinder initial pressure, engine speed, and air-fuel mixture ratio. These five random variables all satisfy uniform distribution. These five random variables are represented as a vector , the corresponding mean vector is , the corresponding standard deviation vector is .in, Representation vector No. Component, corresponding to random variables; Indicates The mean of a random variable; Indicates The standard deviation of a random variable; .

[0045] Step 1.2, transform the random variable vector Convert to a vector of zero-mean random variables ,in , The standard deviation of . Zero mean random variable With the original random variable There is a one-to-one correspondence.

[0046] Step 1.3, construct the numerical model of the engine using the finite element method. The input of the numerical model is the zero-mean random variable vector obtained in step 1.2 The output of the numerical model is the pressure at the key points in the engine compartment. .

[0047] After the above three steps, we get the random variable vector The corresponding zero-mean random variable vector The pressure at key points in the engine compartment The output-output relationship between them.

[0048] The second step is to calculate the contribution of each random variable to the pressure variance of key points in the engine compartment based on the random perturbation collocation method. Specifically:

[0049] Step 2.1, construct two different zero-mean random variable vector sample input sets based on the random perturbation collocation method, and use the input-output relationship obtained in the first step to calculate the corresponding two different pressure output sets of key points in the engine compartment. The calculation method of two different zero-mean random variable vector sample input sets and the corresponding two pressure output sets of key points in the engine compartment is as follows:

[0050] Zero mean random variable vector sample input set 1:

[0051] ,

[0052] in , represents the zero-mean random variable vector sample input No. Quantity; , represents a zero-mean random variable The expectation of the fourth power and the zero-mean random variable The ratio of the fourth power of the standard deviation of It means to calculate the mathematical expectation; represents a zero-mean random variable vector No. components, is a zero-mean random variable; represents a zero-mean random variable The standard deviation of Since the zero-mean random variable The distribution of is uniform. Substitute the zero-mean random variable vector sample input set 1 into the engine model input-output relationship obtained in the first step, and obtain the pressure output set 1 of the key points in the engine compartment corresponding to each other: ;

[0053] Random variable vector sample input set 2:

[0054] , , .

[0055] in and The calculation method is the same as that of the random variable sample input set 1 The calculation method is the same as that of . Substitute the random variable vector sample input set 2 into the engine model input-output relationship obtained in the first step, and calculate the pressure output set 2 of the key points in the engine compartment that correspond to one by one: .

[0056] Step 2.2, based on the pressure output set 1 of the key points in the engine compartment calculated in step 2.1, calculate the zero-mean random variable The absolute contribution to the pressure variance at key points in the nacelle is given by the following formula:

[0057] ,

[0058] in, represents a zero-mean random variable The absolute contribution to the pressure variance at key points in the nacelle; , is the intermediate variable used in the calculation; It means that when the random variable vector input The pressure output at key points in the engine compartment when It means that when the random variable vector input The pressure output at key points in the engine compartment when , is the intermediate variable used in the calculation; It means that when the random variable vector input The pressure output at key points in the engine compartment when

[0059] Step 2.3, based on the pressure output set 2 of the key points in the engine compartment calculated in step 2.1, calculate the zero-mean random variable and The absolute contribution of the coupling to the pressure variance at key points in the nacelle is given by the following formula:

[0060] ,

[0061] in, represents a zero-mean random variable and Direct contribution of coupling to the pressure variance at critical points in the nacelle; represents a zero-mean random variable The expectation of the fourth power and the zero-mean random variable The ratio of the fourth power of the standard deviation of The same, just the subscript is different; ; ; , , They are all intermediate variables used in the calculation. The calculation method is as follows:

[0062] .

[0063] in ; Substitute the random variable vector sample input set 2 into the engine model input-output relationship obtained in the first step, and calculate the zero-mean random variable and The absolute contribution of the coupling to the pressure variance at critical points in the nacelle.

[0064] Step 2.4, calculate the variance of the pressure at key points in the engine compartment , .

[0065] After the above 4 steps, we calculated the variance of the pressure at the key points in the engine compartment: , zero mean random variable Absolute contribution to the variance of the pressure at key points in the nacelle , zero mean random variable and Absolute contribution of coupling to the pressure at key points in the nacelle .

[0066] The third step is to calculate each random variable based on the calculation results of the second step Corresponding sensitivity index and random variable and The sensitivity index corresponding to the coupling relationship is as follows:

[0067] Step 3.1, based on the calculation results of steps 2.2 and 2.4, calculate , reflects a zero-mean random variable Variance The relative contribution of With the original random variable One to one correspondence, Too The corresponding sensitivity index.

[0068] Step 3.2, based on the calculation results of steps 2.3 and 2.4, calculate , Reflects the random variable and The coupling effect of The relative contribution of With the original random variable One to one correspondence, Too and The sensitivity index corresponding to the coupling effect.

[0069] Based on the above two steps, we calculated the original random variable Variance of pressure acting alone on key points in the engine compartment Sensitivity index of impact (Subscripts 1 to 5 correspond to ambient pressure, cylinder initial temperature, cylinder initial pressure, engine speed, and air-fuel mixture ratio, respectively); the original random variable is also calculated and Coupling effect on engine response variance Sensitivity index of impact The final sensitivity index calculation results are shown in the following table:

[0070]

[0071] According to the data analysis in the table, the pressure at key points in the engine compartment is most affected by the initial cylinder temperature and the air-fuel mixture ratio, and the ambient pressure, initial cylinder pressure, and engine speed have almost no effect on the pressure at key points in the engine compartment.

[0072] The above-described embodiments merely express the implementation methods of the present invention, but they should not be understood as limiting the scope of the present invention. It should be pointed out that for those skilled in the art, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention.

Claims

1. An engine sensitivity analysis method based on random perturbation collocation method, characterized in that: The engine sensitivity analysis method comprises the following steps: The first step is to determine the random variables that affect the engine model response and the mean and standard deviation corresponding to the random variables, and establish an input-output relationship between the random variables and the engine model response; including the following steps: Step 1.1, assume that there are a total of random variables that affect the engine model response , put this The random variables are represented as a vector , the corresponding mean vector is , the corresponding standard deviation vector is ;in, Representation vector No. Component, corresponding to random variables; Indicates The mean of a random variable; Indicates The standard deviation of a random variable; ; Step 1.2, transform the random variable vector Convert to a vector of zero-mean random variables ,in , The standard deviation of ; Zero mean random variable With the original random variable There is a one-to-one correspondence; Step 1.3, construct a numerical model of the engine; the input of the numerical model is the zero-mean random variable vector obtained in step 1.2 , the output of the numerical model is the engine model response ; After steps 1.1 to 1.3, we get the random variable vector The corresponding zero-mean random variable vector Response to engine model The output-output relationship between The second step is to calculate the contribution of each random variable to the variance of the engine model response based on the random perturbation collocation method; The third step is to calculate the sensitivity index of each random variable to the engine model response based on the calculation results of the second step.

2. The engine sensitivity analysis method based on random perturbation collocation method according to claim 1 is characterized in that: In the step 1.3, the numerical model of the engine is constructed by using the finite element method or the proxy model method.

3. The engine sensitivity analysis method based on random perturbation collocation method according to claim 1 is characterized in that: The second step comprises the following steps: Step 2.1, constructing two different zero-mean random variable vector sample input sets based on the random perturbation collocation method, and using the input-output relationship obtained in the first step to calculate the corresponding two different engine model response output sets, including zero-mean random variable vector sample input set 1 and random variable vector sample input set 2; Step 2.2, based on the engine model response output set 1 calculated in step 2.1, calculate the zero-mean random variable absolute contribution to the variance of the engine model response; Step 2.3, based on the engine model response output set 2 calculated in step 2.1, calculate the zero-mean random variable and The absolute contribution of the coupling to the variance of the engine model response; Step 2.4, calculate the variance of the engine model response .

4. The engine sensitivity analysis method based on random perturbation collocation method according to claim 3 is characterized in that: In step 2.1, the calculation method of two different zero-mean random variable vector sample input sets and the corresponding two engine model response output sets is as follows: Zero mean random variable vector sample input set 1: ， in, , represents the zero-mean random variable vector sample input No. Quantity; , represents a zero-mean random variable The expectation of the fourth power and the zero-mean random variable The ratio of the fourth power of the standard deviation of It means to calculate the mathematical expectation; represents a zero-mean random variable vector No. components, is a zero-mean random variable; represents a zero-mean random variable The standard deviation of ; Substitute the zero-mean random variable vector sample input set 1 into the engine model input-output relationship obtained in the first step to obtain the engine model response output set 1 corresponding to one: ; Random variable vector sample input set 2: ， ， ； in, and The calculation method is the same as that of the random variable sample input set 1 The calculation method is the same as that of ; the random variable vector sample input set 2 is brought into the engine model input-output relationship obtained in the first step, and the engine model response output set 2 corresponding to 1 is calculated: .

5. The engine sensitivity analysis method based on random perturbation collocation method according to claim 4 is characterized in that: Calculate the zero-mean random variable vector sample input set 1, when the zero-mean random variable No. Quantity When the distribution of is uniform, ; When the zero-mean random variable No. Quantity When the distribution of is Gaussian, .

6. The engine sensitivity analysis method based on random perturbation collocation method according to claim 4 is characterized in that: The steps 2.2 to 2.4 are specifically as follows: Step 2.2, calculate the zero-mean random variable The formula for the absolute contribution to the variance of the engine model response is: ， in, represents a zero-mean random variable absolute contribution to the variance of the engine model response; , is the intermediate variable used in the calculation; It means that when the random variable vector input The engine model response output when ; It means that when the random variable vector input The engine model response output when ; , is the intermediate variable used in the calculation; It means that when the random variable vector input The engine model response output when ; Step 2.3, calculate the zero-mean random variable and The formula for the absolute contribution of the coupling to the variance of the engine model response is: ， in, represents a zero-mean random variable and Direct contribution of coupling to the variance of engine model response; represents a zero-mean random variable The expectation of the fourth power and the zero-mean random variable The ratio of the fourth power of the standard deviation of The same, just the subscript is different; ; ; , , are all intermediate variables; the random variable vector sample input set 2 is brought into the engine model input-output relationship obtained in the first step to calculate the zero-mean random variable and The absolute contribution of the coupling to the variance of the engine model response; Step 2.4, the formula for calculating the variance of the engine model response is: .

7. The engine sensitivity analysis method based on random perturbation collocation method according to claim 6 is characterized in that: The intermediate variable , , The calculation method is as follows: ； in, ; .

8. The engine sensitivity analysis method based on random perturbation collocation method according to claim 3 is characterized in that: The third step comprises the following steps: Step 3.1, based on the calculation results of steps 2.2 and 2.4, calculate , reflects a zero-mean random variable Variance The relative contribution of With the original random variable One to one correspondence, Too Corresponding sensitivity index; Step 3.2, based on the calculation results of steps 2.3 and 2.4, calculate ,in , Reflecting random variables and The coupling effect of The relative contribution of With the original random variable One to one correspondence, Too and The sensitivity index corresponding to the coupling effect.

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