Complex system uncertainty digital model simulation verification method based on data characteristic measurement analysis

Abstract

A complex system uncertainty digital model simulation verification method based on data feature measurement comprises the following steps: under the condition of considering uncertainty, extracting feature vectors of simulation output and real installation test output parameter data from multiple angles to construct a feature matrix; and the statistical similarity between the corresponding digital model and the real installation data feature vector is measured through the probability distribution difference, so that the consistency degree between the digital model and the real installation test data is obtained. According to the method, the problem of multivariable digital model verification complexity can be effectively solved, and the confidence coefficient of complex system digital model verification is improved.

Description

Technical Field

[0001] The present invention relates to the field of complex system digital model calibration and verification under uncertain conditions, and in particular to a complex system digital model verification method based on data feature metric analysis, which can be widely used for consistency verification needs of single-sample / multi-sample actual installation test data and simulation data (static / dynamic). Background Art

[0002] In the process of complex system optimization and design, in order to ensure product design accuracy, building a high-fidelity digital model is the key to ensuring product design accuracy. Digital model verification and validation refers to the quantitative evaluation of the uncertainty of numerical simulation results based on test data, thereby determining whether the constructed digital model is credible.

[0003] Due to the limitations of test cost and cycle, there are fewer combinations of conditions for physical tests. However, deterministic test conditions are part of the factors that determine the state of physical test data, and usually do not consider the uncertainty caused by the model, parameters or test.

[0004] The traditional digital model verification and validation method measures the consistency between simulation output and test output data under the same input conditions. However, complex system digital models have uncertainties such as environmental deviation, complex system performance parameter deviation, parameter coupling effect deviation, and material manufacturing deviation, which are also important factors in determining the state of physical tests. At this time, if only the traditional simulation result verification method is used, the confidence of the digital model verification results will be low and the variable information will be incomplete.

[0005] As digital models evolve towards high complexity, strong nonlinearity, and different types of output parameters, while considering uncertainty, the research on digital model verification methods that combine multidimensional variable data and probability distribution differences has been widely used for complex systems with multiple output variables. Summary of the invention

[0006] The traditional digital model verification and validation method is essentially to use distance measurement methods to evaluate the consistency based on the measured simulation data and actual test data. However, in fact, the simulation verification and validation of digital models of complex systems with uncertainty will inevitably encounter problems such as complex system uncertainty parameter characterization, test sample design, and digital model multivariate parameter verification. At the same time, there are also situations where there are few or even single samples of physical test data. Therefore, how to accurately verify the accuracy of digital models of complex systems under the condition of limited product actual installation data has become a practical problem, which is very important for improving the simulation reliability and robustness design of complex systems.

[0007] In this regard, the present invention provides a simulation and verification method for non-deterministic digital models of complex systems based on the combination of data feature measurement and probability distribution difference. Combined with the actual test profile, under the condition of considering uncertainty, the characteristic vectors of the simulation output and the actual test output parameter data are extracted from multiple angles to construct a characteristic matrix. The statistical similarity between the characteristic vectors of the corresponding digital model and the actual data is measured by the probability distribution difference, so as to obtain the degree of consistency between the digital model and the actual test data.

[0008] The present invention provides a complex system non-deterministic digital model simulation verification method, which specifically includes the following steps:

[0009] S1: For the task profile of the actual test of the complex system, characterize the uncertainty parameters, carry out the test design, determine the sample size of the digital test, carry out the digital test, and obtain the digital test data;

[0010] S2: Based on the physical system and the corresponding digital model, under the same initial conditions, the actual installation data X is obtained. r ={x r1 ,x r2 ,…,x rm} and simulation data Y s ={y s1 ,y s2 ,…,y sm}, m is the number of simulation output variables, where X r , Y s The static data in is represented as random variables, and the dynamic data is represented as a set of multiple time series;

[0011] S3: For actual installation test data X r And simulation test data Y s Perform preprocessing to meet the data consistency analysis and calculation requirements;

[0012] S4: Determine the data feature measurement model set: Determine the static / dynamic simulation output characteristics of the digital model based on the actual situation of the complex simulation system output variable parameters, and form the data feature model set M of the verified complex system digital model ′ ={M1,M2,…,M n};

[0013] S5: Carry out corresponding feature difference consistency analysis and calculation based on the output data features of the constructed complex system digital model, including static data feature consistency check and dynamic data feature consistency analysis.

[0014] Furthermore, in step S2, the data structure of the static data and the dynamic data is:

[0015] Let ysi ,y sj Respectively represent a static and dynamic output parameter,

[0016]

[0017] Among them, i,J∈[1,m], i≠j; N is the length of the time series, and n is the test sample size, that is, the number of sampling times of the uncertainty input parameter.

[0018] Furthermore, in step S3, the preprocessing method specifically includes:

[0019] The static data type random data adopts the singular value elimination method,

[0020] The time series data adopts one or more of average sliding filtering, outlier removal and interpolation.

[0021] Furthermore, the step S4 specifically includes:

[0022] (1) Digital model static data: select the data itself as the variable feature, y si ,y ri They are the static output variables of the equipment model digital test and the physical test, and their data characteristics are described as follows:

[0023]

[0024] (2) Digital model dynamic data:

[0025] Assume M k is a dynamic parameter difference feature measurement model set, then for the digital model dynamic output y sij (t), y rik (t),i=1,2,…,m; j=1,2,…,n s ; k = 1, 2, ..., n r , select n s 、n r The output mean curve obtained from the system operation is used as a benchmark, and compared with the output curve obtained from each test to obtain the corresponding characteristics:

[0026] Combined with the characteristics of the test data, the dynamic output data characteristics are determined from two levels: distance and shape:

[0027] In the i-th sample y output of the j-th digital trial sij (t) The difference in distance from the mean value used as a benchmark and shape differences The characteristic measurement method is:

[0028]

[0029] Among them,

[0030] Then the difference metric matrix of the dynamic output variable with respect to the k-th feature is Where

[0031]

[0032] Furthermore, in step S5, the static data feature consistency test adopts the rank sum test. When the sample sizes of the two samples are less than 10;

[0033] Specifically, it includes the following steps:

[0034] Mix the two sample data and rank them from small to large. The smallest data is ranked 1, and the largest data is ranked n1 + n2;

[0035] Add up the ranks of the data in the sample with the smaller capacity, that is, the rank sum, denoted by R;

[0036] Compare the R value with the critical value in the rank sum test table at the given α significance level. If R1 < R < R2, then; the difference between the two samples is not significant. If R1 ≠ R or R ≥ R2, then the difference between the two samples is significant;

[0037] When the sample sizes of the two samples are greater than 10, it is considered that the distribution of the rank sum R is close to the normal distribution, and the Z test is adopted.

[0038]

[0039] Among them, Z is the rank sum of the smaller sample. Compare the |Z| value with the critical value at the given significance level in the normal distribution. If |Z| < R, then the difference between the two samples is not significant; otherwise, the difference between the two samples is significant.

[0040] Furthermore, in step S5, the dynamic data feature consistency analysis includes the following steps:

[0041] Use the probability distribution of multi-dimensional random variables to define the joint CDF distribution of x1, x2, …, x k :

[0042] F(x1, x2, …, x k ) = P{(X1 ≤ x1) ∪ (X2 ≤ x2) ∪ … ∪ (X k ≤ x k )};

[0043] Calculate the difference D(F r , F s )

[0044] D(F r , Fs )=∫∫…∫|F s (x1,x2,…,x k )-F r (x1,x2,…,x k )|dx1dx2…dx k

[0045] =∫F s (x)dx-∫F r (x)dx

[0046] Calculate dynamic data credibility based on the difference of joint CDF

[0047]

[0048] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) a complex system non-deterministic simulation model verification method based on the output data characteristics of the digital model is proposed, which fully considers the static and dynamic data types and data characteristics of the complex system digital model, and obtains the consistency of different types of data by constructing data characteristics, so as to comprehensively obtain the credibility of the complex system digital model by weighting and other methods, which can solve the complexity problem of multivariable digital model verification;

[0049] (2) The influence of uncertainty in the digital model of complex systems is comprehensively considered. By characterizing uncertainty parameters such as internal performance parameters and external environmental variables of complex systems, their influence is fully propagated to the performance indicators of complex systems, and the test profile of complex systems is covered as much as possible, thereby improving the confidence of verification of digital models of complex systems;

[0050] (3) Based on the characteristics of digital experiments, the large sample output data of the digital model is fully combined with the actual test samples, and the probability distribution difference method (joint CDF) is used to measure the consistency of the joint probability distribution of the digital model and the actual test data, and the statistical characteristics of the data are refined and further converted into the consistency of the complex system verification variables. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The above and other objects, features and advantages of the present disclosure will become more apparent through a more detailed description of exemplary embodiments of the present disclosure in conjunction with the accompanying drawings, wherein like reference numerals generally represent like components throughout the exemplary embodiments of the present disclosure.

[0052] Figure 1 is a flow chart of the present disclosure;

[0053] Figure 2 A six-degree-of-freedom simulation model of an aircraft in an exemplary embodiment;

[0054] Figure 3It is a schematic diagram of a flight simulation of a certain aircraft in a test section in the embodiment;

[0055] Figure 4 It is a characterization of uncertainty of some parameters of a certain aircraft in a digital test in the embodiment;

[0056] Figure 5 The static data and dynamic variable simulation data of a certain aircraft in a digital test in the embodiment;

[0057] Figure 6 This is a schematic diagram of dynamic output data filtering processing in an embodiment;

[0058] Figure 7 It is a data processing comparison curve in the embodiment;

[0059] Figure 8 It is a comparison curve of probability distribution function of simulation / actual data of complex system variables in the embodiment;

[0060] Fig. 9 It is a CDF comparison curve of complex system variable simulation / actual data in the embodiment. DETAILED DESCRIPTION

[0061] The preferred embodiments of the present disclosure will be described in more detail below with reference to the accompanying drawings. Although the preferred embodiments of the present disclosure are shown in the accompanying drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided to make the present disclosure more thorough and complete, and to fully convey the scope of the present disclosure to those skilled in the art.

[0062] The present invention provides a method for simulating and verifying a complex system non-deterministic digital model based on data features. The flowchart is shown in the attached figure. Figure 1 As shown, the specific steps are:

[0063] Step 1: For a complex system installation test task profile, fully consider the complex internal and external uncertainty parameters and characterize the uncertainty parameters.

[0064] Table 1 Description of uncertainty parameters

[0065]

[0066]

[0067] Conduct test design, determine the sample size of digital test, conduct digital test, obtain digital test data, digital model, simulation scenario, and some uncertain parameter sampling, such as Figure 2-Figure 4 As shown;

[0068] Step 2: For a complex system, where S r and Ss Represent the physical system and the corresponding digital model respectively. Under the same initial conditions, the actual installation data X r ={x r1 ,x r2 ,…,x rm} and simulation data Y s ={y s1 ,y s2 ,…,y sm}, m is the number of simulation output variables, output data X r , Y s The static data in the simulation are represented as random variables, and the dynamic data are represented as a set of multiple time series. Some static / dynamic simulation data are as follows: Figure 5 shown.

[0069] Step 3: Install test data X r And simulation test data Y s Preprocessing is performed, using methods such as singular value removal for static data type random data, and using methods such as average sliding filtering, outlier removal, and interpolation for time series data to meet the requirements of data consistency analysis and calculation;

[0070] (1) The sliding average filtering algorithm can use a five-point cubic smoothing algorithm to eliminate random fluctuations in time series or test data. Each data point is replaced by the weighted average of the five nearby data points to obtain a smoothing effect:

[0071]

[0072] where y s (i) is the i-th data point in the original data sequence, y s (i-2), y s (i-1), y s (i+1), y s (i+2) are the values ​​of the two points before and after the current point.

[0073] (2) Using Lagrange interpolation method,

[0074]

[0075] The sliding average filter algorithm is used to perform data interpolation. Figure 6-7 shown.

[0076] Step 4: Determine the data feature measurement model set. According to the actual situation of the complex simulation system output variable parameters, determine the static / dynamic simulation output characteristics of the digital model, and form the data feature model set M of the verified complex system digital model. ′ ={M1,M2,…,M n};

[0077] (1) Static data of the digital model: Select the data itself as the variable feature, y si 、y ri are the static output variables of the digital test and physical test of the equipment model respectively, and their data characteristics can be described as

[0078]

[0079] (2) Dynamic data of the digital model: M k is the difference feature measurement model. For the dynamic output y sij (t), y rik (t), i = 1, 2, …, m, j = 1, 2, …, n d , k = 1, 2, …, n r , select the output mean value curves obtained from n d 、n r sub - system runs as the benchmark, compare and analyze with the output curves obtained from each test, and obtain the corresponding features; combine the test data characteristics to determine the dynamic output data characteristics from two levels of distance and shape; in the i - th sample of the j - th digital test output, the distance and shape differences of y sij (t) The feature measurement method is:

[0080]

[0081] Among them, then the difference measurement matrix of the dynamic output variable with respect to the k - th feature is

[0082]

[0083] Step Five: For the output data characteristics of the complex system digital model constructed, carry out the corresponding feature difference consistency analysis and calculation:

[0084] (1) Static data feature consistency test: Use the rank - sum test. When the sample sizes of the two samples are less than 10,

[0085] ① Mix the two sample data and rank them from small to large (the smallest data is ranked 1, and the largest data is ranked n1 + n2);

[0086] ② Add up the ranks of the data in the sample with the smaller capacity, that is, the rank sum, denoted by R;

[0087] ③ Compare the R value with the critical value under the given α significance level in the rank - sum test table. If R1 < R < R2, then the difference between the two samples is not significant; if R1 ≠ R or R ≥ R2, then the two samples are significantly different;

[0088] When the sample sizes of both samples are greater than 10, it is considered that the distribution of the rank sum R is close to the normal distribution, and the Z - test is adopted.

[0089]

[0090] Among them, Z is the rank sum of the smaller sample. Compare the value of |Z| with the critical value under the given significance level in the normal distribution. If |Z| < T, the difference between the two samples is not significant; otherwise, the difference between the two samples is significant.

[0091] (2) Consistency analysis of dynamic data characteristics

[0092] ① Define the joint CDF distribution of x1, x2, …, x k using the probability distribution of multi - dimensional random variables:

[0093] F(x1, x2, …, x k ) = P{(X1 ≤ x1) ∪ (X2 ≤ x2) ∪ … ∪ (X k ≤ x k )}

[0094] ② Calculate the difference D(F r , F s )

[0095] D(F r , F s ) = ∫∫…∫|F s (x1, x2, …, x k ) - F r (x1, x2, …, x k )|dx1dx2…dx k

[0096] = ∫F s (x)dx - ∫F r (x)dx

[0097] ③ Calculate the credibility of dynamic data based on the difference of the joint CDF

[0098]

[0099] Among them, the curve of the difference of the probability distribution function is calculated as shown in Figure 8 , and the curve of the difference of the joint CDF is as shown in Fig. 9 .

[0100] Application Examples

[0101] Taking the performance analysis model of a certain aircraft as an example, as shown in Figure 2 , the verification method of the non - deterministic simulation digital model of complex systems based on data - characteristic measurement is specifically described.

[0102] Step 1: For a complex system installation test task profile, fully consider the complex internal and external uncertainty parameters and characterize the uncertainty parameters.

[0103] Table 1 Description of uncertainty parameters

[0104]

[0105] Carry out Latin hypercube test design, determine the digital test sample size of 1000, carry out digital tests, obtain digital test data, digital models, simulation scenarios, and some uncertain parameter sampling such as Figure 2-Figure 4 As shown;

[0106] Step 2: For a complex system, where S r and S s Represent the physical system and the corresponding digital model respectively. Under the same initial conditions, the actual installation data X r ={x r1 ,x r2 ,…,x rm} and simulation data Y s ={y s1 ,y s2 ,…,y sm}, m is the number of simulation output variables, output data X r , Y s The static data in the simulation are represented as random variables, and the dynamic data are represented as a set of multiple time series. Some static / dynamic simulation data are as follows: Figure 5 shown.

[0107] Step 3: Install test data X r And simulation test data Y s Preprocessing is performed. For static data type random data, singular value removal and other methods are used. For time series data, average sliding filtering, outlier removal, interpolation and other methods are used to meet the requirements of data consistency analysis and calculation. The sliding average filtering algorithm is used to perform data interpolation. Figure 6-7 shown.

[0108] Step 4: Determine the data feature measurement model set. According to the actual situation of the complex simulation system output variable parameters, determine the static / dynamic simulation output characteristics of the digital model, and form the data feature model set M of the verified complex system digital model. ′ ={M1,M2,…,M n};

[0109] (1) Digital model static data: select the data itself as the variable feature, y si ,y riThey are the static output variables of the equipment model digital test and the physical test, and their data characteristics can be described as

[0110]

[0111] (2) Digital model dynamic data: M k is a differential feature measurement model, then for the digital model dynamic output y sik (t), y rik (t),i=1,2,…,m,j=1,2,…,n s ,k=1,2,…,n r , select n s 、n r The output mean curve obtained from the system operation is used as a benchmark, and compared with the output curve obtained from each test to obtain the corresponding characteristics; combined with the test data characteristics, the dynamic output data characteristics are determined from the two levels of distance and shape;

[0112] Table 2. Data on the difference of characteristics of some variables

[0113] Serial number Shape characteristics Distance feature 1. 0.0219 0.0220 2. 0.0220 0.0218 3. 0.0221 0.0220 4. 0.0217 0.0221 5. 0.0220 0.0219 6. 0.0220 0.0220 7. 0.0218 0.0221 8. 0.0219 0.0218 9. …… ……

[0114] Step 5: Carry out the corresponding characteristic difference consistency analysis and calculation based on the output data characteristics of the constructed complex system digital model:

[0115] (1) Static data feature consistency test: The rank sum test was used. When the capacity of the two samples was greater than 10, the distribution of the rank sum R was close to the normal distribution. The Z test was used and Z = -0.658 was calculated. At this time, |Z| < 1.96, and the difference between the two groups was not significant.

[0116] (2) Dynamic data feature consistency analysis

[0117] ①Use multidimensional random variable probability distribution to define x1,x2,…,x k The joint CDF distribution of

[0118] F(x1,x2,…,x k )=P{(X1≤x1)∪(X2≤x2)∪…∪(X k ≤x k )}

[0119] ② Calculate the difference D(F) of the joint CDF r ,F s )

[0120] D(F r ,F s )=∫F s (x)dx-∫F r (x)dx

[0121] ③ Calculate the credibility of dynamic data based on the difference of joint CDF

[0122]

[0123] Calculate the probability distribution function difference curve as Figure 8 As shown, the difference curve of the joint CDF is Fig. 9 shown.

[0124] Table 3 Comprehensive credibility of complex system digital models

[0125]

[0126] The above technical scheme is only an exemplary embodiment of the present invention. For those skilled in the art, it is easy to make various types of improvements or modifications based on the application methods and principles disclosed in the present invention, and it is not limited to the method described in the above specific embodiment of the present invention. Therefore, the method described above is only preferred and does not have a restrictive meaning.

Claims

1. A simulation verification method for an uncertain digital model of a complex system based on data feature metric analysis, comprising the following steps: S1: For the mission profile of the complex system's actual installation test, perform uncertainty parameter characterization, conduct experimental design, determine the digital test sample size, conduct digital tests, and obtain digital test data; S2: Based on the physical system and the corresponding digital model, under the same initial conditions, the actual installation data X is obtained. r ={x r1 ,x r2 ,…,x rm } and simulation data Y s ={y s1 ,y s2 ,…,y sm }, m is the number of simulation output variables, where X r , Y s The static data in is represented as random variables, and the dynamic data is represented as a set of multiple time series; S3: For actual installation test data X r And simulation test data Y s Perform preprocessing to meet the data consistency analysis and calculation requirements; S4: Determine the data feature measurement model set: Determine the static / dynamic simulation output characteristics of the digital model based on the actual situation of the complex simulation system output variable parameters, and form the data feature model set M of the verified complex system digital model ′ ={M1,M2,…,M n }; S5: For the output data features of the constructed complex system digital model, carry out corresponding characteristic difference consistency analysis calculations, including static data feature consistency tests and dynamic data feature consistency analysis.

2. The method according to claim 1, characterized in that In the said step S2, the data structure forms of the static data and dynamic data are: Let y si ,y sj Respectively represent a static and dynamic output parameter, Wherein, i, j ∈ [1, m], i ≠ j; N is the length of the time series, and n is the test sample size, that is, the sampling times of the uncertain input parameters.

3. The method according to claim 1 or 2, characterized in that: In the said step S3, the specific method of the preprocessing includes: For static data type random data, the singular value elimination method is adopted, For time series data, one or more of average sliding filtering, outlier elimination, and interpolation are adopted.

4. The method according to claim 2, characterized in that: The said step S4 specifically includes: (1) Digital model static data: select the data itself as the variable feature, y si ,y ri They are the static output variables of the equipment model digital test and the physical test, and their data characteristics are described as follows: (2) Digital model dynamic data: Assume M k is a dynamic parameter difference feature measurement model set, then for the digital model dynamic output y sij (t), y rik (t),i=1,2,…,m; j=1,2,…,n s ; k = 1, 2, ..., n r , select n s 、n r The output mean curve obtained from the system operation is used as a benchmark, and compared with the output curve obtained from each test to obtain the corresponding characteristics: Combined with the characteristics of the test data, determine the dynamic output data features from two levels of distance and shape: In the i-th sample y output of the j-th digital trial sij (t) The difference in distance from the mean value used as a benchmark and shape differences The characteristic measurement method is: in, Then the difference measurement matrix of the dynamic output variable about the kth feature is formed as in 5. The method according to claim 1, characterized in that In the said step S5, when the static data feature consistency test adopts the rank sum test and the sample sizes of the two samples are less than 10; Specifically, it includes the following steps: Mix the two sample data and arrange them in ascending order of magnitude. The smallest data rank is numbered 1, and the largest data rank is numbered n1 + n2; Add up the ranks of each data in the sample with the smaller capacity, that is, the rank sum, represented by R; Compare the R value with the critical value under the given α significance level in the rank sum test table. If R1 < R < R2, then; the difference between the two samples is not significant. If R1 ≠ R or R ≥ R2, then the difference between the two samples is significant; When the sample sizes of the two samples are greater than 10, it is considered that the distribution of the rank sum R is close to the normal distribution, and the Z test is adopted, Wherein, Z is the rank sum of the smaller sample. Compare the |Z| value with the critical value under the given significance level in the normal distribution. If |Z| < R, then the difference between the two samples is not significant; otherwise, the difference between the two samples is significant.

6. The method according to claim 1, characterized in that In the said step S5, the dynamic data feature consistency analysis includes the following steps: Define x1,x2,…,x using the probability distribution of multidimensional random variables k The joint CDF distribution of is: F(x1,x2,…,x k )=P{(X1≤x1)∪(X2≤x2)∪…∪(X k ≤x k )}? Calculate the difference of the joint CDF D(F r ,F s ) D(F r ,F s )=∫∫…∫|F s (x1,x2,…,x k )-F r (x1,x2,…,x k )|dx1dx2…dx k =∫F s (x)dx-∫F r (x)dx Calculate the dynamic data credibility based on the difference of the joint CDF

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