Digital twinning uncertain parameter analysis method, device, equipment, medium and product

Abstract

The invention relates to the technical field of aerospace, and particularly provides a digital twinning uncertain parameter analysis method, device and equipment, a medium and a product, and the method comprises the steps: obtaining a log-likelihood function of a digital twinning model, and calculating conditional expectation; solving a plurality of uncertain parameters based on conditional expectation; obtaining output variances corresponding to the uncertain parameters, and obtaining expressions of a first sensitivity parameter and a second sensitivity parameter of each uncertain parameter based on a mapping relation between the uncertain parameters and the corresponding output variances; and inputting the plurality of acquired sample matrixes into the digital twin model, and calculating a first sensitivity parameter and a second sensitivity parameter of each uncertain parameter based on an output result corresponding to each sample matrix. By calculating the first sensitivity parameter and the second sensitivity parameter of the uncertain parameters, the parameter space can be effectively dimensionally reduced, the uncertainty is reduced, the complexity of the model is reduced, and compared with other analysis methods, the calculation amount is small, and the accuracy is higher.

Description

Technical Field

[0001] The present disclosure relates to the field of aerospace technology, and in particular to a digital twin uncertain parameter analysis method, device, equipment, medium and product. Background Art

[0002] In the aerospace field, due to the complex structure, high cost and high testing cost of physical equipment (such as electromechanical actuators), digital twin models are generally needed to simulate the behavior and characteristics of physical equipment during the operation cycle to achieve comprehensive coverage of the behavior and characteristics of physical equipment. However, digital twin models usually include many uncertain parameters, which are highly nonlinear, high-dimensional, and have long operation times. In addition, they also have dynamic changes as the operation phase progresses, resulting in high computational complexity and uncertainty in digital twin models.

[0003] In this regard, according to the principle of sparse main effects, important uncertain parameters can be divided from numerous uncertain parameters by sensitivity, and the remaining unimportant uncertain parameters can be ignored, thereby achieving the purpose of reducing the dimension of the parameter space. At present, the global derivative sensitivity index is usually used to analyze the sensitivity of uncertain parameters, but because the global derivative sensitivity index involves the estimation of partial derivatives, it has the disadvantages of large amount of calculation, difficulty in obtaining partial derivatives, and difficulty in controlling calculation accuracy. This analysis method is still not conducive to reducing the computational complexity and uncertainty of the digital twin model. Summary of the invention

[0004] The present disclosure is proposed in view of the above-mentioned problems and provides a digital twin uncertain parameter analysis method, device, equipment, medium and product.

[0005] According to one aspect of the present disclosure, a digital twin uncertain parameter analysis method is provided, comprising:

[0006] Obtaining a log-likelihood function of the constructed digital twin model, and calculating the conditional expectation of the log-likelihood function;

[0007] Based on the conditional expectation, solving multiple uncertain parameters of the digital twin model;

[0008] Obtain the output variance of the digital twin model corresponding to each of the uncertain parameters, and based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtain the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters according to the preset Sobol indicator construction process, wherein the first sensitivity parameter is used to characterize the contribution of each of the uncertain parameters to the total variance effect, and the second sensitivity parameter is used to characterize the contribution of each of the uncertain parameters combined with the remaining uncertain parameters to the total variance effect;

[0009] The multiple sample matrices obtained are input into the digital twin model, and the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter are calculated based on the output results of the digital twin model corresponding to each sample matrix and the expressions of the first sensitivity parameter and the second sensitivity parameter.

[0010] In addition, the digital twin uncertain parameter analysis method according to one aspect of the present disclosure further includes: obtaining a log-likelihood function of the constructed digital twin model, and calculating the conditional expectation of the log-likelihood function, including:

[0011] Based on the constructed digital twin model, the distribution form of noise parameters is confirmed;

[0012] According to the distribution form, collecting all data of the digital twin model and obtaining a log-likelihood function of the all data, wherein the all data includes a parameter set, an observation data set, and a latent variable set;

[0013] Based on the acquired implicit parameter expectation and the estimation formula of the noise unknown distribution parameter, the conditional expectation of the log-likelihood function is calculated.

[0014] In addition, the digital twin uncertain parameter analysis method according to one aspect of the present disclosure further includes: based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, according to the preset Sobol indicator construction process, obtaining the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters, including:

[0015] Based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtaining a mapping relationship set;

[0016] According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is decomposed to obtain an expression of a total variance effect, and an expression of a variance main effect and a joint variance effect of each of the uncertain parameters is obtained, wherein the expression of the joint variance effect is determined based on the output variance of each of the uncertain parameters and the output variance of the remaining uncertain parameters;

[0017] Based on the expression of the total variance effect and the expression of the main effect of the variance of each of the uncertain parameters, the expression of the first sensitivity parameter of each of the uncertain parameters is obtained; and based on the expression of the total variance effect and the expression of the joint variance effect of each of the uncertain parameters, the expression of the second sensitivity parameter of each of the uncertain parameters is obtained.

[0018] In addition, the digital twin uncertain parameter analysis method according to one aspect of the present disclosure also includes: according to a preset Sobol indicator construction process, decomposing the output variance in the mapping relationship set, obtaining an expression of the total variance effect, and obtaining an expression of the variance main effect and the joint variance effect of each of the uncertain parameters, including:

[0019] According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is divided into a plurality of dimensional parameters, and the nth dimensional parameter is the output variance corresponding to any n uncertain parameters;

[0020] Based on all the dimensional parameters, obtaining a decomposition formula of the mapping relationship set;

[0021] Based on the decomposition formula, an expression of the total variance effect is obtained, and an expression of the variance main effect and the joint variance effect of each of the uncertain parameters is obtained.

[0022] In addition, the digital twin uncertain parameter analysis method according to one aspect of the present disclosure further includes: inputting the acquired multiple sample matrices into the digital twin model, including:

[0023] According to the interval range and distribution probability of the sample parameters input into the digital twin model, an interval sample matrix and a probability sample matrix are obtained;

[0024] Replace the i-th column data of the interval sample matrix with the i-th column data of the probability sample matrix to obtain a cross sample matrix;

[0025] The interval sample matrix, the probability sample matrix and the cross sample matrix are input into the digital twin model as sample matrices.

[0026] In addition, the digital twin uncertain parameter analysis method according to one aspect of the present disclosure further includes: calculating the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters based on the output result of the digital twin model corresponding to each of the sample matrices, the expressions of the first sensitivity parameter and the second sensitivity parameter, including:

[0027] Based on the output results of the digital twin model corresponding to each of the sample matrices, the total variance effect and the variance main effect of each of the uncertain parameters are calculated, and the joint variance effect of each of the uncertain parameters is calculated;

[0028] Based on the expression of the first sensitivity parameter, the total variance effect and the main effect of the variance of each of the uncertain parameters, the first sensitivity parameter of each of the uncertain parameters is calculated; and based on the expression of the second sensitivity parameter, the total variance effect and the joint variance effect of each of the uncertain parameters, the second sensitivity parameter of each of the uncertain parameters is calculated.

[0029] According to another aspect of the present disclosure, a digital twin uncertain parameter analysis device is provided, comprising:

[0030] A first calculation module is used to obtain a log-likelihood function of the constructed digital twin model and calculate the conditional expectation of the log-likelihood function;

[0031] A solution module, used for solving multiple uncertain parameters of the digital twin model based on the conditional expectation;

[0032] An acquisition module is used to obtain the output variance of the digital twin model corresponding to each of the uncertain parameters, and based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtain the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters according to the preset Sobol indicator construction process; the first sensitivity parameter is used to characterize the contribution of each of the uncertain parameters to the total variance effect, and the second sensitivity parameter is used to characterize the contribution of each of the uncertain parameters combined with the remaining uncertain parameters to the total variance effect;

[0033] The second calculation module is used to input the acquired multiple sample matrices into the digital twin model, and calculate the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter based on the output results of the digital twin model corresponding to each sample matrix and the expressions of the first sensitivity parameter and the second sensitivity parameter.

[0034] According to another aspect of the present disclosure, a computer device is provided, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method of the above aspect.

[0035] According to another aspect of the present disclosure, a computer-readable storage medium is provided, on which a computer program is stored. When the computer program is executed by a processor, the method of the above aspect is implemented.

[0036] According to another aspect of the present disclosure, a computer program product is provided, including a computer program, and when the computer program is executed by a processor, the method of the above aspect is implemented.

[0037] As will be described in detail below, according to a digital twin uncertain parameter analysis method, device, equipment, medium and product of an embodiment of the present disclosure, through the mapping relationship between each uncertain parameter and the corresponding output variance, according to the preset Sobol indicator construction process, the expression of the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter is obtained, and then the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter are calculated. It is possible to divide many uncertain parameters according to the first sensitivity parameter and the second sensitivity parameter, and retain some uncertain parameters with high sensitivity (i.e., importance). It is possible to effectively reduce the dimension of the parameter space and reduce the uncertainty of the digital twin model, thereby reducing the complexity of the digital twin model. Compared with other sensitivity analysis methods, it also has the advantages of small computational complexity and high accuracy.

[0038] It is to be understood that both the foregoing general description and the following detailed description are exemplary, and are intended to provide further explanation of the technology as claimed. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The above and other purposes, features and advantages of the present disclosure will become more apparent by describing the embodiments of the present disclosure in more detail in conjunction with the accompanying drawings. The accompanying drawings are used to provide a further understanding of the embodiments of the present disclosure and constitute a part of the specification. Together with the embodiments of the present disclosure, they are used to explain the present disclosure and do not constitute a limitation of the present disclosure. In the accompanying drawings, the same reference numerals generally represent the same components or steps.

[0040] Figure 1 is a flowchart illustrating the application of the digital twin uncertain parameter analysis method according to an embodiment of the present disclosure.

[0041] Figure 2 It is another flowchart illustrating the application of the digital twin uncertain parameter analysis method according to the embodiment of the present disclosure.

[0042] Figure 3 It is a diagram illustrating a calculation process of a sensitivity index according to an embodiment of the present disclosure.

[0043] Figure 4 It is a structural schematic diagram illustrating a digital twin uncertain parameter analysis device according to an embodiment of the present disclosure.

[0044] Figure 5 It is a schematic diagram illustrating the structure of a computer device according to an embodiment of the present disclosure.

[0045] Figure 6 is a schematic diagram illustrating a computer program product according to an embodiment of the present disclosure. DETAILED DESCRIPTION

[0046] In order to make the purpose, technical solution and advantages of the present disclosure more obvious, the exemplary embodiments according to the present disclosure will be described in detail with reference to the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present disclosure, rather than all the embodiments of the present disclosure, and it should be understood that the present disclosure is not limited to the exemplary embodiments described here.

[0047] In the aerospace field, due to the complex structure, high cost and high testing cost of physical equipment (such as electromechanical actuators), digital twin models are generally needed to simulate the behavior and characteristics of physical equipment during the operation cycle to achieve comprehensive coverage of the behavior and characteristics of physical equipment. Digital twin models usually include many uncertain parameters, which are highly nonlinear, high-dimensional and have long operation times. In addition, as the operation stage progresses, the uncertain parameters also have the characteristics of dynamic changes. For complex models such as digital twin models, these uncertain parameters lead to high computational complexity and uncertainty of digital twin models.

[0048] The sparse proxy model of the uncertainty propagation method shows that according to the sparse main effect principle, the uncertain parameters in the digital twin model can be divided into two types, namely, a small number of important uncertain parameters and the remaining unimportant uncertain parameters. Therefore, how to divide the important uncertain parameter set from the numerous uncertain parameters based on sensitivity and then ignore the remaining uncertain parameters with low importance is an important research direction of current digital twin applications.

[0049] In response to the above problems, the global derivative sensitivity index is usually used to calculate the sensitivity of uncertain parameters, but this method has the following disadvantages: (1) The amount of calculation is large. The global derivative sensitivity index involves estimating the partial derivatives of the original model to be analyzed, and the Monte Carlo method is generally used for approximate calculation. Since the Monte Carlo method itself has the problems of slow convergence speed and low efficiency, the global derivative sensitivity index based on Monte Carlo calculation requires a large number of runs of the original model to be analyzed to achieve sufficient calculation accuracy. (2) Partial derivatives are difficult to obtain, and approximate calculations of finite differences are required in a local range. This means that the step size in the difference method will affect the calculation accuracy of the partial derivatives, which to some extent deepens the uncertainty.

[0050] Therefore, it is urgent to develop a new and efficient sensitivity calculation method for uncertain parameters, which can effectively reduce the dimension of the parameter space, reduce the uncertainty of the digital twin model, and thus reduce the complexity of the digital twin model, so as to better assist the aviation hydraulic pump in comprehensively and thoroughly mapping all behavioral characteristics during operation, and provide reliable and sufficient theoretical support for the efficient implementation of subsequent digital twin model refinement, analysis and prediction, and optimization management.

[0051] In the above, with reference to the accompanying drawings, a digital twin uncertain parameter analysis method, apparatus, equipment, medium and product according to an embodiment of the present disclosure are described. Through the mapping relationship between each uncertain parameter and the corresponding output variance, according to the preset Sobol indicator construction process, the expression of the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter is obtained, and then the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter are calculated. It is possible to divide many uncertain parameters according to the first sensitivity parameter and the second sensitivity parameter, and retain some uncertain parameters with high sensitivity. It is possible to effectively reduce the dimension of the parameter space and reduce the uncertainty of the digital twin model, thereby reducing the complexity of the digital twin model. Compared with other sensitivity analysis methods, it also has the advantages of small computational complexity and high accuracy, and can be applied to complex physical equipment with complex structure, high energy density and strict volume requirements, such as modeling and uncertainty analysis of mechatronic equipment.

[0052] To facilitate understanding of this embodiment, a digital twin uncertain parameter analysis method disclosed in the embodiment of the present disclosure is first introduced in detail. The execution subject of the digital twin uncertain parameter analysis method provided in the embodiment of the present disclosure is generally a computer device with certain computing capabilities, and the computer device includes, for example: a terminal device or a server or other processing device, and the terminal device can be a user equipment (User Equipment, UE), a mobile device, a user terminal, a terminal, a cellular phone, a cordless phone, a personal digital assistant (Personal DiTital Assistant, PDA), a handheld device, a computing device, a vehicle-mounted device, a wearable device, etc. In some possible implementations, the digital twin uncertain parameter analysis method can be implemented by a processor calling a computer-readable instruction stored in a memory.

[0053] like Figure 1 As shown, it is a flowchart of the digital twin uncertain parameter analysis method provided by the embodiment of the present disclosure, and the method includes S101-S104:

[0054] S101: Obtain the log-likelihood function of the constructed digital twin model, and calculate the conditional expectation of the log-likelihood function.

[0055] Specifically, S101 includes the following steps 1-3:

[0056] Step 1: Based on the constructed digital twin model, confirm the distribution form of noise parameters.

[0057] Among them, the noise parameters include observation noise and state transition noise. The distribution form is as follows: observation noise r k It obeys Laplace distribution, the scale variable is unknown; the state transition noise e k It follows a Gaussian distribution with zero mean and unknown variance.

[0058] Step 2: Collect all the data of the digital twin model according to the distribution form and obtain the log-likelihood function of the whole data.

[0059] The full data includes parameter set, observation data set and latent variable set, which can be expressed as:

[0060] θ={θ f ,θ g ,σ e ,σ r}

[0061] C obs ={y 1:N ,u 1:N} PT

[0062] C mis ={x 1:N ,z 1:N} PT

[0063] Among them, Θ represents the parameter set, C obs represents the observed data set, C mis represents a set of latent variables.

[0064] The log-likelihood function of the entire data can be expressed as:

[0065] logp(C obs ,C mis |Θ) PT =logp(y 1:N ,u 1:N ,x 1:N ,z 1:N |Θ) PT

[0066] =logp(y 1:N |u 1:N x 1:N ,z 1:N ,Θ) PT

[0067] +logp(z 1:N |u 1:N ,x 1:N ,Θ) PT

[0068] +logp(x 1:N |u 1:N ,Θ) PT

[0069] +logp(u 1:N |Θ) PT

[0070] Among them, logp(C obs ,C mis |Θ) PT represents the log-likelihood function.

[0071] Step 3: Based on the obtained implicit parameter expectation and the estimation formula of the unknown distribution parameter of the noise, calculate the conditional expectation of the log-likelihood function.

[0072] Specifically, the complex formula of conditional expectation can be directly obtained based on the log-likelihood function:

[0073]

[0074] Among them, Q(Θ|Θ s ) represents the conditional expectation, <z k > indicates implicit parameter expectation.

[0075] According to the estimation formula of unknown noise distribution parameters:

[0076]

[0077] Among them, σ e and σ r Both represent unknown distribution parameters of noise.

[0078] Substituting the estimation formula of the unknown distribution parameters of the noise into the complex conditional expectation formula, the final conditional expectation (Q function) is obtained as follows:

[0079]

[0080] S102: Based on conditional expectation, solve multiple uncertain parameters of the digital twin model.

[0081] For example:

[0082]

[0083] Among them, θ f and θ g All represent uncertain parameters.

[0084] Specifically,

[0085]

[0086] S103: Obtain the output variance of the digital twin model corresponding to each uncertain parameter, and based on the mapping relationship between each uncertain parameter and the corresponding output variance, obtain the expressions of the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter according to the preset Sobol indicator construction process.

[0087] The first sensitivity parameter is used to characterize the contribution of each uncertain parameter to the total variance effect, and the second sensitivity parameter is used to characterize the contribution of each uncertain parameter combined with the remaining uncertain parameters to the total variance effect.

[0088] The preset Sobol indicator construction process can decompose all output variances, indicating that no output variance effect will be missed in the complete sensitivity analysis. S103 specifically includes the following steps 1-3:

[0089] Step 1: Based on the mapping relationship between each uncertain parameter and the corresponding output variance, a mapping relationship set is obtained.

[0090] Step 2: According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is decomposed to obtain the expression of the total variance effect, as well as the expression of the variance main effect and the joint variance effect of each uncertain parameter.

[0091] The expression of the joint variance effect is determined based on the output variance of each uncertain parameter and the output variance of the remaining uncertain parameters. Specifically, step 2 includes the following steps 21-23:

[0092] Step 21: According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is divided into multiple dimensional parameters, and the nth dimensional parameter is the output variance corresponding to any n uncertain parameters.

[0093] Step 22: Based on all dimensional parameters, obtain a decomposition formula of the mapping relationship set.

[0094] The decomposition formula is:

[0095]

[0096] Among them, f0=E[f(X)] is a constant term. Considering the situation that each polynomial is orthogonal to each other, therefore, x i represents the i-th uncertain parameter, f i (x i ) represents the first dimension parameter, that is, the output variance obtained by inputting any uncertain parameter, f ij (x i ,x j ) represents the second dimension parameter, that is, the output variance obtained by inputting any two uncertain parameters, f 1,2,…d (x1,x2,…x d ) represents the d-th dimension parameter, that is, the output variance obtained by inputting all (d) uncertain parameters.

[0097] Step 23: Based on the decomposition formula, obtain the expression of the total variance effect, and obtain the expressions of the variance main effect and the joint variance effect of each uncertain parameter.

[0098] Specifically, the expression of the total variance effect is:

[0099]

[0100] Where V[Y] represents the total variance effect, X is the parameter space, and X includes the input vector of all uncertain parameters.

[0101] The expressions of variance main effect and joint variance effect are:

[0102] V i =∫f i 2 (x i )ρ(x i )dx i

[0103]

[0104] Among them, V i represents the variance main effect, represents the joint variance effect.

[0105] Step 3: Based on the expression of the total variance effect and the expression of the main effect of the variance of each uncertain parameter, obtain the expression of the first sensitivity parameter of each uncertain parameter, and based on the expression of the total variance effect and the expression of the joint variance effect of each uncertain parameter, obtain the expression of the second sensitivity parameter of each uncertain parameter.

[0106] For example, the expression of the first sensitivity parameter is:

[0107]

[0108] Among them, S i Represents the first sensitivity parameter, V i represents the main effect of the variance of each uncertain parameter, and V[Y] represents the total variance effect.

[0109] The expression of the second sensitivity parameter is:

[0110]

[0111] in, Represents the second sensitivity parameter, V i represents the variance main effect of each uncertain parameter, V[Y] represents the total variance effect, X ～i =[x1,x2,…x i-1 ,x i+1,…x d ], which is the input vector of the remaining uncertain parameters other than the uncertain parameter i in X (parameter space).

[0112] S104: Input the obtained multiple sample matrices into the digital twin model, and calculate the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter based on the output results of the digital twin model corresponding to each sample matrix and the expressions of the first sensitivity parameter and the second sensitivity parameter.

[0113] S104 specifically includes the following steps 1-5:

[0114] Step 1: According to the interval range and distribution probability of the sample parameters input into the digital twin model, obtain the interval sample matrix and probability sample matrix.

[0115] Specifically, the interval sample matrix L A for:

[0116]

[0117] Probability sample matrix L B for:

[0118]

[0119] Step 2: Replace the data in the i-th column of the interval sample matrix with the data in the i-th column of the probability sample matrix to obtain the cross sample matrix.

[0120] Get the cross sample matrix L Ci for:

[0121]

[0122] Step 3: Input the interval sample matrix, probability sample matrix, and cross sample matrix into the digital twin model as sample matrices.

[0123] Step 4: Based on the output results of the digital twin model corresponding to each sample matrix, calculate the total variance effect and the variance main effect of each uncertain parameter, and calculate the joint variance effect of each uncertain parameter.

[0124] The output result of the digital twin model corresponding to the interval sample matrix is:

[0125] The output of the digital twin model corresponding to the probability sample matrix is:

[0126] The output of the digital twin model corresponding to the cross sample matrix is:

[0127] Step 5: Based on the expression of the first sensitivity parameter, the total variance effect and the main effect of the variance of each uncertain parameter, calculate the first sensitivity parameter of each uncertain parameter; and based on the expression of the second sensitivity parameter, the total variance effect and the joint variance effect of each uncertain parameter, calculate the second sensitivity parameter of each uncertain parameter.

[0128] Among them, the first sensitivity parameter S i for:

[0129]

[0130] Second sensitivity parameter for:

[0131]

[0132] like Figure 2 As shown, it is another flow chart of the digital twin uncertain parameter analysis method provided by the embodiment of the present disclosure, and the method includes S201-S205:

[0133] S201: Build a digital twin model and confirm the distribution form of noise parameters.

[0134] The distribution form information of some artificially designed unmeasurable parameters (such as noise parameters) in the digital twin parameter space is corrected through identification and parameter estimation. It is expected that the uncertain parameters can be estimated through the observed response of the physical equipment and the corrected parameter space and response distribution can be applied to the global sensitivity analysis.

[0135] The form of the digital twin model is defined as a discrete state space form of disturbance decoupling, specifically:

[0136]

[0137] Where k is the sampling time point, k = {1, 2, ..., N}, u k ∈R nu ,u k represents the input vector of the digital twin model, represents the state parameters of the digital twin model, Represents the observed output of the digital twin model; r k and e k are noise parameters, r k represents the observation noise, e k represents the state transition noise; f(·) represents the state transfer function, g(·) represents the observation function, θ f and θ g is an uncertain parameter.

[0138] The recognition goal of this step is: given the physical space input u PT = {u 1:N} PT and the observed output Y PT ={y 1:N} PT , taking into account the observation noise, the uncertain parameter θ is robustly estimated f and θ g .

[0139] Among them, the state transition noise e k It obeys a Gaussian distribution with zero mean and unknown variance, that is:

[0140] e k ~N(e k |0,σ e )

[0141] Observation noise r k It obeys the Laplace distribution, and the scale variable is unknown, that is:

[0142] r k ~Laplace(r k |0,σ r )

[0143] σ e represents the unknown distribution parameter of the state transition noise, σ r represents the unknown distribution parameter of the observation noise.

[0144] Observation output It follows a normal distribution and can be decomposed into a cascade form:

[0145]

[0146] In this embodiment, preferably, the observation output It can be further decomposed into the weighted properties of countless Gaussian distributions:

[0147]

[0148] S202: Solving uncertain parameters based on the expectation-maximization identification algorithm (EM algorithm).

[0149] Based on the EM algorithm framework, the sampling control method is used in the expectation step (E step) to estimate the posterior probability distribution of the hidden state, calculate the conditional expectation of the log-likelihood function of the full data (ie, the Q function), and then optimize the solution of the uncertain parameters in the maximum step (M step).

[0150] The full data includes parameter set, observation data set and latent variable set, which can be expressed as:

[0151] θ={θ f ,θ g ,σ e ,σ r}

[0152] C obs ={y 1:N ,u 1:N} PT

[0153] C mis ={x 1:N ,z 1:N} PT

[0154] Among them, Θ represents the parameter set, c obs represents the observed data set, c mis Represents a set of latent variables. Based on the collected data in the physical space, the log-likelihood function can be expressed as:

[0155] logp(C obs ,C mis |Θ) PT =logp(y 1:N ,u 1:N ,x 1:N ,z 1:N |Θ) PT

[0156] =logp(y 1:N |u 1:N x 1:N ,z 1:N ,Θ) PT

[0157] +logp(z 1:N |u 1:N ,x 1:N ,Θ) PT

[0158] +logp(x 1:N |u 1:N ,Θ) PT

[0159] +logp(u 1:N |Θ) PT

[0160] Therefore, the conditional expectation (i.e., Q function) can be expressed as:

[0161]

[0162] After sorting out the Q function, we get:

[0163]

[0164] 1) Expected step (E step)

[0165] The final simplified formula of the Q function can be obtained:

[0166]

[0167] Among them, k > represents the implicit parameter expectation, the estimation formula for the unknown distribution parameters of state transition noise and observation noise is:

[0168]

[0169] 2) Maximum step (M step)

[0170] Substituting the estimation formula of the unknown distribution parameters of state transition noise and observation noise into the final simplified formula of the Q function, we get:

[0171]

[0172] Therefore, at the maximum step, the uncertain parameters can be estimated by the following formula:

[0173]

[0174] Among them, θ f and θ g All represent uncertain parameters.

[0175] Specifically,

[0176]

[0177] S203: Confirm the uncertain parameter space and corresponding output space of the digital twin model.

[0178] The output response under the influence of uncertain parameters is expressed as:

[0179]

[0180] Where y represents the output space, x represents the uncertainty vector in d dimensions, x = (x1, x2, … x d ), x includes state parameters Input vector u k , uncertain parameters θ f and θ g , for the uncertainty in each dimension Considering relative independence, f(x) is the output of the digital twin model corresponding to x.

[0181] x: It represents the process of selecting finite parameter samples from an infinite parameter space, X is the uncertain parameter space, and f: represents the response function or observation model of a specific system in the physical space, Y is the mapping relationship between x and f(x), and y is the set of all Y, that is, y is the uncertainty response of the digital twin model under the influence of uncertain parameters. The process of screening limited responses from the infinite uncertainty response space is expressed as: y: This process is also called the selection of uncertain parameter quantities of interest.

[0182] S204: According to the Sobol indicator construction process, expressions of the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter are obtained.

[0183] The Sobol indicator construction process can decompose all output variances, which means that no output variance effect will be missed in the complete sensitivity analysis. Assume that a digital twin model Y = f(X) with a clear output in a certain state is given, E[f 2 (X)]<∞. Where Y=f(X) is the output of the digital twin model, X=[x1,x2,…x d ], X is the uncertain parameter space, which can be decomposed into the sum of a series of polynomials according to the Sobol indicator construction process:

[0184]

[0185] Among them, f i (x i ) represents the first dimension parameter, that is, the output variance obtained by inputting any uncertain parameter, f ij (x i ,x j ) represents the second dimension parameter, that is, the output variance obtained by inputting any two uncertain parameters, f 1,2,…d (x1,x2,…x d ) represents the d-th dimension parameter, that is, the output variance obtained by inputting all (d) uncertain parameters.

[0186] Since the Sobol indicator construction process can decompose all output variances and consider the interrelationships of all uncertain parameters, this ensures that no variance effect of any output variance is missed in the complete sensitivity analysis. Therefore, on the right side of the equation, there are 2 d The polynomial terms are added together. Among them, f0=E[f(X)], which is a constant term. Considering that there are two orthogonal polynomials, therefore, represents the i-th uncertain parameter. According to the orthogonality characteristics of the right side of the equation, the total variance effect can be obtained as:

[0187]

[0188] Furthermore, the expression of the total variance effect is:

[0189]

[0190] Where V[Y] represents the total variance effect, X is the parameter space, and X includes the input vector of all uncertain parameters.

[0191] The expressions of variance main effect and joint variance effect are:

[0192] V i =∫f i 2 (x i )ρ(x i )dx i

[0193]

[0194] Among them, V i represents the variance main effect, Represents the joint variance effect of m dimensional parameters.

[0195] In the Sobol indicator construction process, the ratio of the joint variance effect is used as an indicator of sensitivity:

[0196]

[0197] Further we can get:

[0198]

[0199] Among them, represents the variance main effect corresponding to each uncertain parameter, represents the first sensitivity parameter, which is used to measure any uncertain parameter x i The independent contribution to the total variance effect V[Y]; represents the second sensitivity parameter, which is used to measure the i The total contribution of all output variances to the total variance effect V[Y], including x i The independent contribution part includes x i The contribution of the interaction with other uncertain parameters. Based on this, the expression of the first sensitivity parameter is:

[0200]

[0201] The expression of the second sensitivity parameter is:

[0202]

[0203] Among them, X ～i=[x1,x2,…x i-1 ,x i+1 ,…x d ], which is the input vector of the remaining uncertain parameters other than the uncertain parameter i in X (parameter space).

[0204] S205: Based on the Sobol indicator construction process, calculate the sensitivity index, namely the first sensitivity parameter and the second sensitivity parameter.

[0205] like Figure 3 As shown in the figure, the calculation process of the sensitivity index is as follows. Since the sensitivity index involves the calculation of two low-order moments, expectation and variance, it is usually estimated by numerical calculation. For a calculation method of Sobol sensitivity factor, the specific calculation process is as follows

[0206] (1) According to the interval range and distribution probability of the sample parameters of the input digital twin model, two sample matrices are randomly generated: the interval sample matrix L A and the probability sample matrix L B This embodiment is presented in the form of a parameter sample matrix designed by LHD, and the specific form of the matrix is, for example:

[0207]

[0208] Among them, a row of the sample matrix represents a sample, and a column represents an input parameter variable dimension. Replace the i-th column of the interval sample matrix with the i-th column of the probability sample matrix to obtain the cross sample matrix L Ci :

[0209]

[0210] (2) The interval sample matrix L A , probability sample matrix L B and the cross-sample matrix L Ci The samples in are used as inputs of the digital twin model, and the simulation model is run to obtain the following results:

[0211] The output result of the digital twin model corresponding to the interval sample matrix is:

[0212] The output of the digital twin model corresponding to the probability sample matrix is:

[0213] The output of the digital twin model corresponding to the cross sample matrix is:

[0214] (3) According to the output results of the digital twin model, combined with the expressions of the first sensitivity parameter and the second sensitivity parameter, it is calculated that:

[0215]

[0216] Among them, v j is the output result of the digital twin model for the j-th row of parameter input, N is the total number of parameter samples, and a total of N(d+2) operations are required to calculate the first sensitivity parameter and the second sensitivity parameter. From the above calculation process, it can be seen that the calculation amount of the Sobol sensitivity index increases linearly with the increase of the input variable dimension d.

[0217] Preferably, in the embodiment of the present disclosure, the following optimizations may be performed for (1) and (2) of S205:

[0218] In order to further improve the utilization rate of the parameter sampling set, this embodiment provides a spatial partitioning (SP) calculation form of the global sensitivity index that only depends on a set of samples. The sample space is divided into equal probability and the variance-based global sensitivity index can be completed through the following steps.

[0219] 1) According to the probability distribution information of the parameter space, obtain the parameter set {X (1) ,X (2) ,X (3) ,…,X (M)}, and output the corresponding response set {Y (1) ,Y (2) ,Y (3) ,…,Y (M)}, where the variance of Y can be obtained by the variance of the sample set Make an estimate.

[0220] 2) X i The sample space of is divided into s continuous, uniform and non-overlapping subintervals A k =[a k-1 ,a k ),1≤k≤s.

[0221] 3) The response set {Y (1) ,Y (2) ,Y (3) ,…,Y (M)} is divided into B k , as follows:

[0222]

[0223] The calculation process of variance is:

[0224]

[0225] 4) X constructed based on the sample space iThe variance of can be estimated as:

[0226]

[0227] And, the main sensitivity of the Sobol indicator is defined as:

[0228]

[0229] According to another aspect of the embodiments of the present disclosure, a digital twin uncertain parameter analysis device is provided, such as Figure 4 As shown, the device comprises:

[0230] The first calculation module 101 is used to obtain the log-likelihood function of the constructed digital twin model and calculate the conditional expectation of the log-likelihood function;

[0231] A solution module 102, used for solving a plurality of uncertain parameters of the digital twin model based on the conditional expectation;

[0232] An acquisition module 103 is used to obtain the output variance of the digital twin model corresponding to each of the uncertain parameters, and based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtain the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters according to the preset Sobol indicator construction process;

[0233] The second calculation module 104 is used to input the acquired multiple sample matrices into the digital twin model, and calculate the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters based on the output results of the digital twin model corresponding to each of the sample matrices and the expressions of the first sensitivity parameter and the second sensitivity parameter.

[0234] In one or more embodiments, the first computing module 101 is used to:

[0235] Based on the constructed digital twin model, the distribution form of noise parameters is confirmed;

[0236] According to the distribution form, collecting all data of the digital twin model and obtaining a log-likelihood function of the all data, wherein the all data includes a parameter set, an observation data set, and a latent variable set;

[0237] Based on the acquired implicit parameter expectation and the estimation formula of the noise unknown distribution parameter, the conditional expectation of the log-likelihood function is calculated.

[0238] In one or more embodiments, the acquisition module 103 is used to:

[0239] Based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtaining a mapping relationship set;

[0240] According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is decomposed to obtain an expression of a total variance effect, and an expression of a variance main effect and a joint variance effect of each of the uncertain parameters is obtained, wherein the expression of the joint variance effect is determined based on the output variance of each of the uncertain parameters and the output variance of the remaining uncertain parameters;

[0241] Based on the expression of the total variance effect and the expression of the main effect of the variance of each of the uncertain parameters, the expression of the first sensitivity parameter of each of the uncertain parameters is obtained; and based on the expression of the total variance effect and the expression of the joint variance effect of each of the uncertain parameters, the expression of the second sensitivity parameter of each of the uncertain parameters is obtained.

[0242] In one or more embodiments, the acquisition module 103 is further configured to:

[0243] According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is divided into a plurality of dimensional parameters, and the nth dimensional parameter is the output variance corresponding to any n uncertain parameters;

[0244] Based on all the dimensional parameters, obtaining a decomposition formula of the mapping relationship set;

[0245] Based on the decomposition formula, an expression of the total variance effect is obtained, and an expression of the variance main effect and the joint variance effect of each of the uncertain parameters is obtained.

[0246] In one or more embodiments, the second calculation module 104 is configured to:

[0247] According to the interval range and distribution probability of the sample parameters input into the digital twin model, an interval sample matrix and a probability sample matrix are obtained;

[0248] Replace the i-th column data of the interval sample matrix with the i-th column data of the probability sample matrix to obtain a cross sample matrix;

[0249] The interval sample matrix, the probability sample matrix and the cross sample matrix are input into the digital twin model as sample matrices.

[0250] In one or more embodiments, the second calculation module 104 is configured to:

[0251] Based on the output results of the digital twin model corresponding to each of the sample matrices, the total variance effect and the variance main effect of each of the uncertain parameters are calculated, and the joint variance effect of each of the uncertain parameters is calculated;

[0252] Based on the expression of the first sensitivity parameter, the total variance effect and the main effect of the variance of each of the uncertain parameters, the first sensitivity parameter of each of the uncertain parameters is calculated; and based on the expression of the second sensitivity parameter, the total variance effect and the joint variance effect of each of the uncertain parameters, the second sensitivity parameter of each of the uncertain parameters is calculated.

[0253] The digital twin uncertain parameter analysis device provided in the embodiment of the present disclosure and the digital twin uncertain parameter analysis method provided in the embodiment of the present disclosure are based on the same inventive concept and have the same beneficial effects as the methods adopted, operated or implemented therein.

[0254] The present disclosure also provides a computer device to execute the above-mentioned digital twin uncertain parameter analysis method. Figure 5 It shows a schematic diagram of a computer device provided by some embodiments of the present disclosure. Figure 5 As shown, the computer device 8 includes: a processor 800, a memory 801, a bus 802 and a communication interface 803, and the processor 800, the communication interface 803 and the memory 801 are connected via the bus 802; the memory 801 stores a computer program that can be run on the processor 800, and when the processor 800 runs the computer program, the digital twin uncertain parameter analysis method provided in any of the aforementioned embodiments of the present disclosure is executed.

[0255] The memory 801 may include a high-speed random access memory (RAM), and may also include a non-volatile memory, such as at least one disk storage. The communication connection between the device network element and at least one other network element is realized through at least one communication interface 803 (which may be wired or wireless), and the Internet, wide area network, local area network, metropolitan area network, etc. may be used.

[0256] The bus 802 may be an ISA bus, a PCI bus, or an EISA bus, etc. The bus may be divided into an address bus, a data bus, a control bus, etc. Among them, the memory 801 is used to store programs, and the processor 800 executes the program after receiving the execution instruction. The digital twin uncertain parameter analysis method disclosed in any implementation of the aforementioned embodiment of the present disclosure may be applied to the processor 800, or implemented by the processor 800.

[0257] The processor 800 may be an integrated circuit chip with signal processing capabilities. In the implementation process, each step of the above method can be completed by the hardware integrated logic circuit or software instructions in the processor 800. The above processor 800 can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application-specific integrated circuit (ASIC), a ready-made programmable gate array (FPTA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components. The disclosed methods, steps and logic block diagrams in the embodiments of the present disclosure can be implemented or executed. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor. The steps of the method disclosed in conjunction with the embodiments of the present disclosure can be directly embodied as a hardware decoding processor to be executed, or a combination of hardware and software modules in the decoding processor can be executed. The software module can be located in a mature storage medium in the field such as a random access memory, a flash memory, a read-only memory, a programmable read-only memory or an electrically erasable programmable memory, a register, etc. The storage medium is located in the memory 801, and the processor 800 reads the information in the memory 801 and completes the steps of the above method in combination with its hardware.

[0258] The computer device provided in the embodiment of the present disclosure and the digital twin uncertain parameter analysis method provided in the embodiment of the present disclosure are based on the same inventive concept and have the same beneficial effects as the methods adopted, run or implemented therein.

[0259] An embodiment of the present disclosure also provides a computer-readable storage medium corresponding to the digital twin uncertain parameter analysis method provided in the aforementioned embodiment. The computer-readable storage medium is a CD on which a computer program (i.e., a computer program product) is stored. When the computer program is run by a processor, it will execute the digital twin uncertain parameter analysis method provided in any of the aforementioned embodiments.

[0260] It should be noted that examples of the computer-readable storage medium may also include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other optical or magnetic storage media, which are not listed here one by one.

[0261] The computer-readable storage medium provided by the above-mentioned embodiments of the present disclosure and the digital twin uncertain parameter analysis method provided by the embodiments of the present disclosure are based on the same inventive concept and have the same beneficial effects as the methods adopted, run or implemented by the application programs stored therein.

[0262] The present disclosure also provides a computer program product. Figure 6 The computer program product 600 carries a program code, namely a computer program 601. The instructions included in the computer program 601 can be used to execute the steps of the digital twin uncertain parameter analysis method described in the above method embodiment. For details, please refer to the above method embodiment, which will not be repeated here.

[0263] The computer program product may be implemented in hardware, software or a combination thereof. In one optional embodiment, the computer program product is implemented as a computer storage medium. In another optional embodiment, the computer program product is implemented as a software product, such as a software development kit (SDK).

[0264] The basic principles of the present disclosure are described above in conjunction with specific embodiments. However, it should be noted that the advantages, strengths, effects, etc. mentioned in the present disclosure are only examples and not limitations, and it cannot be considered that these advantages, strengths, effects, etc. are required by each embodiment of the present disclosure. In addition, the specific details disclosed above are only for the purpose of illustration and ease of understanding, and are not limitations. The above details do not limit the present disclosure to the necessity of adopting the above specific details to be implemented.

[0265] The block diagrams of the devices, apparatuses, equipment, and systems involved in this disclosure are only illustrative examples and are not intended to require or imply that they must be connected, arranged, and configured in the manner shown in the block diagrams. As will be appreciated by those skilled in the art, these devices, apparatuses, equipment, and systems can be connected, arranged, and configured in any manner. Words such as "including," "comprising," "having," and the like are open words, referring to "including but not limited to," and can be used interchangeably therewith. The words "or" and "and" used herein refer to the words "and / or," and can be used interchangeably therewith, unless the context clearly indicates otherwise. The word "such as" used herein refers to the phrase "such as but not limited to," and can be used interchangeably therewith.

[0266] Additionally, as used herein, "or" used in a list of items beginning with "at least one" indicates a separate list, so that, for example, a list of "at least one of A, B, or C" means A or B or C, or AB or AC or BC, or ABC (i.e., A and B and C). Furthermore, the word "exemplary" does not mean that the example described is preferred or better than other examples.

[0267] It should also be noted that in the system and method of the present disclosure, each component or each step can be decomposed and / or recombined. Such decomposition and / or recombination should be regarded as equivalent solutions of the present disclosure.

[0268] Various changes, substitutions, and modifications of the techniques described herein may be made without departing from the teachings defined by the appended claims. Furthermore, the scope of the claims of the present disclosure is not limited to the specific aspects of the processes, machines, manufactures, compositions of events, means, methods, and actions described above. Currently existing or later to be developed processes, machines, manufactures, compositions of events, means, methods, or actions that perform substantially the same functions or achieve substantially the same results as the corresponding aspects described herein may be utilized. Thus, the appended claims include such processes, machines, manufactures, compositions of events, means, methods, or actions within their scope.

[0269] The above description of the disclosed aspects is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these aspects will be readily apparent to those skilled in the art, and the general principles defined herein may be applied to other aspects without departing from the scope of the present disclosure. Therefore, the present disclosure is not intended to be limited to the aspects shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

[0270] The above description has been given for the purpose of illustration and description. In addition, this description is not intended to limit the embodiments of the present disclosure to the forms disclosed herein. Although multiple example aspects and embodiments have been discussed above, those skilled in the art will recognize certain variations, modifications, changes, additions and sub-combinations thereof.

Claims

1. A digital twin uncertain parameter analysis method, characterized in that: include: Obtaining a log-likelihood function of the constructed digital twin model, and calculating the conditional expectation of the log-likelihood function; Based on the conditional expectation, solving multiple uncertain parameters of the digital twin model; Obtain the output variance of the digital twin model corresponding to each of the uncertain parameters, and based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtain the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters according to the preset Sobol indicator construction process, wherein the first sensitivity parameter is used to characterize the contribution of each of the uncertain parameters to the total variance effect, and the second sensitivity parameter is used to characterize the contribution of each of the uncertain parameters combined with the remaining uncertain parameters to the total variance effect; The multiple sample matrices obtained are input into the digital twin model, and the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter are calculated based on the output results of the digital twin model corresponding to each sample matrix and the expressions of the first sensitivity parameter and the second sensitivity parameter.

2. The digital twin uncertainty parameter analysis method according to claim 1, characterized in that: Obtaining the log-likelihood function of the constructed digital twin model, and calculating the conditional expectation of the log-likelihood function, including: Based on the constructed digital twin model, the distribution form of noise parameters is confirmed; According to the distribution form, collecting all data of the digital twin model and obtaining a log-likelihood function of the all data, wherein the all data includes a parameter set, an observation data set, and a latent variable set; Based on the acquired implicit parameter expectation and the estimation formula of the noise unknown distribution parameter, the conditional expectation of the log-likelihood function is calculated.

3. The digital twin uncertainty parameter analysis method according to claim 1, characterized in that: Based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, according to the preset Sobol indicator construction process, the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters are obtained, including: Based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtaining a mapping relationship set; According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is decomposed to obtain an expression of a total variance effect, and an expression of a variance main effect and a joint variance effect of each of the uncertain parameters is obtained, wherein the expression of the joint variance effect is determined based on the output variance of each of the uncertain parameters and the output variance of the remaining uncertain parameters; Based on the expression of the total variance effect and the expression of the main effect of the variance of each of the uncertain parameters, the expression of the first sensitivity parameter of each of the uncertain parameters is obtained; and based on the expression of the total variance effect and the expression of the joint variance effect of each of the uncertain parameters, the expression of the second sensitivity parameter of each of the uncertain parameters is obtained.

4. The digital twin uncertainty parameter analysis method according to claim 3, characterized in that: According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is decomposed to obtain the expression of the total variance effect, and the expression of the variance main effect and the joint variance effect of each of the uncertain parameters is obtained, including: According to the preset Sobol indicator construction process, the output variance in the mapping relationship set is divided into a plurality of dimensional parameters, and the nth dimensional parameter is the output variance corresponding to any n uncertain parameters; Based on all the dimensional parameters, obtaining a decomposition formula of the mapping relationship set; Based on the decomposition formula, an expression of the total variance effect is obtained, and an expression of the variance main effect and the joint variance effect of each of the uncertain parameters is obtained.

5. The digital twin uncertainty parameter analysis method according to claim 1, characterized in that: Inputting the obtained multiple sample matrices into the digital twin model includes: According to the interval range and distribution probability of the sample parameters input into the digital twin model, an interval sample matrix and a probability sample matrix are obtained; Replace the i-th column data of the interval sample matrix with the i-th column data of the probability sample matrix to obtain a cross sample matrix; The interval sample matrix, the probability sample matrix and the cross sample matrix are input into the digital twin model as sample matrices.

6. The digital twin uncertainty parameter analysis method according to claim 1, characterized in that: Calculating the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters based on the output results of the digital twin model corresponding to each of the sample matrices, and expressions of the first sensitivity parameter and the second sensitivity parameter, including: Based on the output results of the digital twin model corresponding to each of the sample matrices, the total variance effect and the variance main effect of each of the uncertain parameters are calculated, and the joint variance effect of each of the uncertain parameters is calculated; Based on the expression of the first sensitivity parameter, the total variance effect and the main effect of the variance of each of the uncertain parameters, the first sensitivity parameter of each of the uncertain parameters is calculated; and based on the expression of the second sensitivity parameter, the total variance effect and the joint variance effect of each of the uncertain parameters, the second sensitivity parameter of each of the uncertain parameters is calculated.

7. A digital twin uncertain parameter analysis device, characterized in that: include: A first calculation module is used to obtain a log-likelihood function of the constructed digital twin model and calculate the conditional expectation of the log-likelihood function; A solution module, used for solving multiple uncertain parameters of the digital twin model based on the conditional expectation; An acquisition module is used to obtain the output variance of the digital twin model corresponding to each of the uncertain parameters, and based on the mapping relationship between each of the uncertain parameters and the corresponding output variance, obtain the expressions of the first sensitivity parameter and the second sensitivity parameter of each of the uncertain parameters according to the preset Sobol indicator construction process; the first sensitivity parameter is used to characterize the contribution of each of the uncertain parameters to the total variance effect, and the second sensitivity parameter is used to characterize the contribution of each of the uncertain parameters combined with the remaining uncertain parameters to the total variance effect; The second calculation module is used to input the acquired multiple sample matrices into the digital twin model, and calculate the first sensitivity parameter and the second sensitivity parameter of each uncertain parameter based on the output results of the digital twin model corresponding to each sample matrix and the expressions of the first sensitivity parameter and the second sensitivity parameter.

8. A computer embedded device, comprising a memory, a processor and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the method according to any one of claims 1 to 6.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

10. A computer program product, comprising a computer program, characterized in that When the computer program is executed by a processor, the method according to any one of claims 1 to 6 is implemented.

Images