Data assimilation method for transonic airfoil streaming
Through the data assimilation method for transsonic airfoil flow, the data joint space is updated using the downgrade model and the active learning method, the problems of inefficient and insufficient accuracy of traditional methods are solved, and efficient and accurate data assimilation is achieved, which significantly reduces the calculation cost.
Patent Information
- Application Number
- CN202510230702.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-02-28
- Publication Date
- 2025-06-17
AI Technical Summary
Traditional data assimilation methods are inefficient in data assimilation towards transsonic airfoil flow, and are difficult to adapt to the problems of high computing costs and low efficiency, especially in local complex areas (such as near shock waves) data assimilation accuracy in down-order models is insufficient.
A data assimilation method for transsonic airfoil flow is adopted. By constructing a down-order model, the flow state and flow field observation data are obtained, random perturbations are applied to generate the initial set of flow, the data joint space is constructed, the down-order model is updated using the active learning method, and the Kalman gain is calculated to update the data joint space until the convergence condition is met.
The calculation cost of data assimilation is significantly reduced and the calculation efficiency is improved. Compared with the data assimilation method based on the down-order model, the accuracy is improved by 96.04%, and it quickly converges to the optimal solution under different inflow conditions, showing good robustness.
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Figure CN120163085A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of data assimilation, and particularly to a data assimilation method for transonic airfoil flow around. Background Art
[0002] Computational Fluid Dynamics (CFD) and Experimental Fluid Dynamics (EFD) are important tools for studying fluid mechanics, but both have limitations. The CFD method can provide relatively comprehensive flow field information, but its computational cost is high. Especially when simulating complex non-linear flows, such as transonic flows with shock-wave boundary layer interference, a large amount of time and computing power are often required. Although the experimental data of EFD are relatively accurate and close to the physical true values, due to spatial and technical limitations, the experimental measurement points are sparse, it is difficult to obtain comprehensive data, and experimental operations often have errors, such as moving wall interference, noise error, etc.
[0003] Data Assimilation (DA) technology combines the advantages of CFD and EFD, fuses experimental measurement data with numerical simulation results, thereby reducing uncertainty and improving the accuracy of flow field prediction. However, traditional data assimilation methods usually rely entirely on high-cost CFD solvers for multiple simulations, resulting in low efficiency and being difficult to meet the data assimilation requirements for transonic airfoil flow around.
[0004] In order to improve the efficiency of data assimilation, currently, a data assimilation method based on a reduced-order model (ROM) is often used for data assimilation of transonic airfoil flow around. The reduced-order model extracts the main features of high-dimensional flow field data through dimensionality reduction techniques (such as POD) and establishes a mapping relationship between the input and the flow field features, significantly reducing the computational complexity. However, in local complex regions (such as near the shock wave), the data assimilation accuracy of the reduced-order model may be insufficient and needs further optimization. Summary of the Invention
[0005] In order to solve the above technical problems, the present invention provides a data assimilation method for transonic airfoil flow around, which significantly reduces the computational cost and improves the computational efficiency while ensuring the data assimilation accuracy.
[0006] In order to solve the above problems, the present invention is implemented by adopting the following technical solutions:
[0007] A data assimilation method for transonic airfoil flow around according to the present invention includes the following steps:
[0008] S1: Construct a reduced-order model;
[0009] S2: Obtain the input flow state and the flow field observation data of the transonic airfoil under the input flow state;
[0010] S3: Apply a random perturbation within a given range to the input flow state to generate an initial set of flows;
[0011] S4: Construct a data joint space that includes the flow state and its corresponding flow field simulation data, fill the flow states in the initial set of flows into the data joint space to obtain an initial data joint space;
[0012] S5: Use a reduced - order model to simulate the flow field simulation data of the transonic airfoil under the flow states recorded in the data joint space, and update the data joint space;
[0013] S6: Update the reduced - order model using an active learning method based on the flow field simulation data and the flow field observation data, and update the data joint space;
[0014] S7: Calculate the mean and covariance of the data joint space, and calculate the Kalman gain;
[0015] S8: Combine the flow field observation data and the Kalman gain to update the data joint space;
[0016] S9: Repeat steps S5 to S8 until the convergence condition is met and stop, and the data assimilation is completed.
[0017] In this solution, first, apply a random perturbation within a given range to the input flow state to obtain an initial set of flows containing multiple flow states, fill these flow states into the corresponding positions in the data joint space, use the initially constructed reduced - order model to simulate these flow states, and fill the obtained flow field simulation data into the corresponding positions in the data joint space to complete the update of the data joint space; then, use an active learning method to update the reduced - order model to improve the accuracy of the reduced - order model, and update the data joint space while updating the reduced - order model; finally, calculate the Kalman gain and update the data joint space. After the update is completed, enter the next iteration, that is, repeat the iterative process starting from step S5 until the convergence condition is met and stop, and the data assimilation is completed.
[0018] Preferably, the flow state is represented by a set of flow parameters, and the set of flow parameters includes the angle of attack, Mach number, and Reynolds number.
[0019] Preferably, the data joint space is denoted as The initial data joint space is where N is the number of flow states in the data joint space, u(i) is the set of flow parameters of the i - th flow state, x(i) is the flow field simulation data corresponding to the i - th flow state, u0 (i) is the initial value of the set of flow parameters of the i - th flow state, x0 (i) is the initial value of the flow field simulation data corresponding to the i - th flow state, 1 ≤ i ≤ N.
[0020] Preferably, step S1 includes the following steps:
[0021] S11: Select a flow state, apply a random perturbation within a given range to this flow state to obtain a set of flow states containing F flow states, use the CFD method to simulate the flow field simulation data of the transonic airfoil under these flow states, and obtain a flow field simulation data matrix U with M rows and F columns, where M is the number of grid sampling points;
[0022] S12: Take each column of data in the flow field simulation data matrix U as a snapshot, perform POD decomposition on the flow field simulation data matrix U, select the first r POD modes with a total energy proportion ≥ ε as the POD basis modes, and generate the corresponding POD basis mode coefficients accordingly, where 1 ≤ r ≤ F;
[0023] S13: Use the Kriging interpolation method to establish the mapping relationship between the POD basis mode coefficients and the flow states to obtain a reduced-order model.
[0024] Selecting the first r POD modes with a total energy proportion ≥ ε as the POD basis modes can effectively remove flow field noise.
[0025] Preferably, step S6 includes the following steps:
[0026] S61: Calculate the expected error weight corresponding to each flow state according to the Kriging variance corresponding to each flow state and the mean square error between the flow field simulation data and the flow field observation data;
[0027] S62: Use the CFD method to simulate the flow field simulation data of the transonic airfoil under the flow state with the minimum expected error weight, and update the data joint space;
[0028] S63: Add the flow field simulation data as a new snapshot to the flow field simulation data matrix U to obtain a new flow field simulation data matrix U, project this snapshot onto the POD basis modes, and obtain the corresponding POD basis mode coefficients;
[0029] S64: Use the Kriging interpolation method to update the mapping relationship between the POD basis mode coefficients and the flow states to complete the update of the reduced-order model.
[0030] In step S63, only the new snapshot is added to the original flow field simulation data matrix U, projected onto the originally retained POD basis modes, and the corresponding POD basis mode coefficients are obtained, without the need to perform POD decomposition again, which greatly saves the calculation cost.
[0031] Preferably, the formula for calculating the expected error weight corresponding to the i-th flow state according to the Kriging variance corresponding to the i-th flow state and the mean square error between the flow field simulation data and the flow field observation data in step S61 is as follows:
[0032] EPE v (i) = v * E cp (i) + (1 - v) * S 2 (i),
[0033] Among them, EPE v (i) is the expected error weight corresponding to the i-th flow state, v is the balance factor, and E cp (i) is the mean square error between the flow field simulation data and the flow field observation data corresponding to the i-th flow state, and s 2 (i) is the Kriging variance corresponding to the i-th flow state.
[0034] Preferably, the formula for calculating the mean of the data joint space in step S7 is as follows:
[0035]
[0036] Among them, is the mean of the data joint space.
[0037] Preferably, the formula for calculating the covariance of the data joint space in step S7 is as follows:
[0038]
[0039] Among them, C z is the covariance of the data joint space.
[0040] Preferably, the formula for calculating the Kalman gain in step S7 is as follows:
[0041] K = Cz * H T (H * Cz * H T + I) -1 ,
[0042] Among them, K is the Kalman gain, H is the observation matrix, and I is the identity matrix.
[0043] Preferably, the formula for updating the data joint space by combining the flow field observation data and the Kalman gain in step S8 is as follows:
[0044]
[0045] Among them, y is the flow field observation data.
[0046] The beneficial effects of the present invention are:
[0047] (1) Implement the data assimilation process using a CFD-based data assimilation method, significantly reducing the computational cost of data assimilation and improving computational efficiency. In the data assimilation for transonic airfoil flow, the data assimilation calculation time is reduced to 15.44% of the traditional CFD-based data assimilation method.
[0048] (2) Through the expected error weight, dynamically balance global exploration and local exploitation to significantly improve the accuracy of the reduced-order model in key regions (such as the shock region), improving the data assimilation accuracy. Compared with the data assimilation method based on the reduced-order model (ROM), the accuracy is increased by 96.04%.
[0049] (3) Use POD and Kriging interpolation to implement a fast and efficient reduced-order model, avoiding modification of the CFD source code and being easy to operate.
[0050] (4) Under different inflow conditions, it can quickly converge to the optimal solution, showing good robustness. Description of the Drawings
[0051] Figure 1 is the flowchart of the embodiment;
[0052] Figure 2 is the comparison chart of the assimilation effects of three data assimilation methods;
[0053] Figure 3 is the error comparison chart between the flow field after assimilation by the data assimilation method based on the reduced-order model and the flow field after assimilation by the CFD-based data assimilation method;
[0054] Figure 4 is the error comparison chart between the flow field after assimilation by the method of the embodiment and the flow field after assimilation by the CFD-based data assimilation method. Detailed Embodiment
[0055] The technical solution of the present invention will be further specifically described below through embodiments and in conjunction with the drawings.
[0056] Embodiment: A data assimilation method for transonic airfoil flow in this embodiment, as Figure 1 shown, includes the following steps:
[0057] S1: Construct a reduced-order model.
[0058] Step S1 includes the following steps:
[0059] S11: Select a flow state, apply a random perturbation within a given range to this flow state to obtain a set of flow states containing F flow states, and use the CFD method to simulate the flow field simulation data of the transonic airfoil under these flow states, obtaining a flow field simulation data matrix U with M rows and F columns, where M is the number of grid sampling points and F is the number of flow states in the set of flow states;
[0060]
[0061] Among them, U j，t is the flow field simulation data of the j-th grid point under the t-th flow state, where 1 ≤ j ≤ M and 1 ≤ t ≤ F;
[0062] S12: Take each column of data in the flow field simulation data matrix U as a snapshot, perform POD decomposition on the flow field simulation data matrix U, select the first r POD modes with a total energy proportion ≥ ε as the POD basis modes, and generate the corresponding POD basis mode coefficients accordingly, where 1 ≤ r ≤ F;
[0063] S13: Use the Kriging interpolation method to establish the mapping relationship between the POD basis mode coefficients and the flow states, obtaining a reduced-order model.
[0064] After performing POD decomposition on the flow field simulation data matrix U in step S12, the k-th snapshot can be expressed as:
[0065]
[0066] Among them, U (k) is the k-th snapshot in the flow field simulation data matrix U, φ (t) is the t-th POD mode, and a t (k) is the POD mode coefficient of the k-th snapshot corresponding to the t-th POD mode, where 1 ≤ k ≤ F.
[0067] In this embodiment, the value of ε is 99%. λ p is the energy contained in the p-th POD mode, where 1 ≤ p ≤ r. Each snapshot has a corresponding POD basis mode coefficient, and the POD basis mode coefficient is a vector, such that any flow state can uniquely determine a POD basis mode coefficient. Selecting the first r POD modes with a total energy proportion ≥ ε as the POD basis modes can effectively remove flow field noise.
[0068] S2: Obtain the input flow state and the flow field observation data of the transonic airfoil under the input flow state.
[0069] The flow state is represented by a set of flow parameters, and the set of flow parameters includes the angle of attack, Mach number, and Reynolds number.
[0070] S3: Apply a random perturbation within a given range to the input flow state to generate an initial set of flows containing multiple flow states.
[0071] S4: Construct a data joint space that includes flow states and their corresponding flow field simulation data. Fill the flow states in the initial set of flows into the data joint space to obtain an initial data joint space.
[0072] The data joint space is denoted as The initial data joint space is where N is the number of flow states in the data joint space, u (i) is the flow parameter group of the i-th flow state, x (i) is the flow field simulation data corresponding to the i-th flow state, u0 (i) is the initial value of the flow parameter group of the i-th flow state, x0 (i) is the initial value of the flow field simulation data corresponding to the i-th flow state, z (i) is the i-th data in the data joint space, z0 (i) is the initial value of the i-th data in the data joint space.
[0073] The initial data joint space contains N flow states and their corresponding initial values of flow field simulation data. The initial values of the flow field simulation data in the initial data joint space are zero.
[0074] S5: Use a reduced-order model simulation to obtain the flow field simulation data of the transonic airfoil under the flow states recorded in the data joint space, and update the data joint space.
[0075] Fill the flow field simulation data obtained from the reduced-order model simulation into the corresponding positions in the data joint space to complete the update of the data joint space.
[0076] S6: Update the reduced-order model using an active learning method based on the flow field simulation data and the flow field observation data, and update the data joint space.
[0077] Step S6 includes the following steps:
[0078] S61: Calculate the expected error weight corresponding to each flow state based on the Kriging variance corresponding to each flow state and the mean square error between the flow field simulation data and the flow field observation data;
[0079] The formula for calculating the expected error weight corresponding to the i-th flow state based on the Kriging variance corresponding to the i-th flow state and the mean square error between the flow field simulation data and the flow field observation data is as follows:
[0080] EPE v (i) = v * E cp (i) + (1 - v) * s2 (i),
[0081] wherein, EPE v (i) is the expected error weight corresponding to the i-th flow state, v is the balance factor, and E cp (i) is the mean square error between the flow field simulation data and the flow field observation data corresponding to the i-th flow state, and s 2 (i) is the Kriging variance corresponding to the i-th flow state;
[0082] S62: Select the flow state with the minimum expected error weight, use the CFD method to simulate the flow field simulation data of the transonic airfoil in the flow state with the minimum expected error weight, and fill the simulated flow field simulation data into the corresponding position in the data fusion space to complete the update of the data fusion space;
[0083] S63: Add the flow field simulation data as a new snapshot to the flow field simulation data matrix U to obtain a new flow field simulation data matrix U, project this snapshot onto the POD basis modes to obtain the corresponding POD basis mode coefficients;
[0084] S64: Use the Kriging interpolation method to update the mapping relationship between the POD basis mode coefficients and the flow states to complete the update of the reduced-order model.
[0085] Step S63 only adds the new snapshot to the original flow field simulation data matrix U, projects it onto the originally retained POD basis modes to obtain the corresponding POD basis mode coefficients, and there is no need to perform POD decomposition again, which greatly saves the computational cost.
[0086] S7: Calculate the mean and covariance of the data fusion space, and calculate the Kalman gain.
[0087] The formula for calculating the mean of the data fusion space is as follows:
[0088]
[0089] wherein, is the mean of the data fusion space;
[0090] The formula for calculating the covariance of the data fusion space is as follows:
[0091]
[0092] wherein, C z is the covariance of the data fusion space;
[0093] The formula for calculating the Kalman gain is as follows:
[0094] K = C z * H T (H * Cz *H T +I) -1 ,
[0095] where K is the Kalman gain, H is the observation matrix, and I is the identity matrix.
[0096] S8: Combine the flow field observation data and the Kalman gain update data to jointly update the space.
[0097] The formula for jointly updating the space of the update data is as follows:
[0098]
[0099] where y is the flow field observation data.
[0100] S9: Repeat steps S5 to S8 until the convergence condition is met and stop. The data assimilation is completed.
[0101] In this solution, the flow field data can be the airfoil surface pressure coefficient, lift coefficient, drag coefficient, etc. The construction of the reduced-order model is completed in the offline stage, and the remaining steps are completed in the online stage. The flow state selected for constructing the reduced-order model can be the same as the input flow state.
[0102] In the online stage, first apply a random perturbation within a given range to the input flow state to obtain a flow initial set containing multiple flow states. Fill these flow states into the corresponding positions in the data joint space, use the initially constructed reduced-order model to simulate these flow states, and fill the obtained flow field simulation data into the corresponding positions in the data joint space to complete the update of the data joint space; then, use the active learning method to update the reduced-order model to improve the accuracy of the reduced-order model, dynamically balance the global exploration and local exploitation through the expected error weight, achieve a significant improvement in the accuracy of the reduced-order model in the key region (such as the shock wave region), improve the data assimilation accuracy, use POD and Kriging interpolation to achieve a fast and efficient reduced-order model, avoid modifying the CFD source code, with simple operation, update the data joint space while updating the reduced-order model; finally, calculate the Kalman gain and update the data joint space (correct both the flow state and the flow field simulation data to meet the requirements of transonic flow field analysis). After the update is completed, enter the next iteration, that is, repeat the iteration process starting from step S5 until the convergence condition is met and stop. The data assimilation is completed.
[0103] This method replaces the CFD-based data assimilation method to implement the data assimilation process. While ensuring that the data assimilation accuracy is comparable to that of the CFD-based data assimilation method, it significantly reduces the computational cost and improves the computational efficiency. In the data assimilation for transonic airfoil flow, the data assimilation calculation time is reduced to 15.44% of that of the CFD-based data assimilation method. Compared with the data assimilation method based on the reduced-order model (ROM), the accuracy is increased by 96.04%. Moreover, under different inflow conditions, it can quickly converge to the optimal solution, demonstrating good robustness.
[0104] Taking the NACA 0012 airfoil as an example, the flow is a viscous strong shock transonic flow. The input flow state is an angle of attack of 4.0, a Mach number of 0.70, and a Reynolds number of 4.00×10 6 , the CFD solver is RANS, the shock is a strong shock, and the equilibrium factor v = 0.8;
[0105] The data assimilation is carried out using the CFD-based data assimilation method, the reduced-order model-based data assimilation method, and the method of this embodiment to obtain a comparison chart of the assimilation effects, as Figure 2 shown. In the figure, x / c is the dimensionless position coordinate of the airfoil along the chord line, Cp is the pressure coefficient, Observation is the experimental observation data, Assimilation-CFD is the result of assimilation using the CFD-based data assimilation method, Assimilation-ROM is the result of assimilation using the reduced-order model-based data assimilation method, and Assimilation-AL is the result of assimilation using the method of this embodiment; it can be seen from Figure 2 that the assimilation effect accuracy of the method of this embodiment is comparable to that of the CFD-based data assimilation method. Compared with the reduced-order model-based data assimilation method, the assimilation effect is greatly improved;
[0106] The error comparison chart of the flow field after assimilation by the reduced-order model-based data assimilation method and the flow field after assimilation by the CFD-based data assimilation method is as Figure 3 shown. The error comparison chart of the flow field after assimilation by the method of this embodiment and the flow field after assimilation by the CFD-based data assimilation method is as Figure 4 shown. In the figure, the same color represents different error ranges, and from left to right (from dark to light color) represents larger and larger errors. It can be seen that the errors are mainly distributed at the shock wave. Figure 4 The yellow area ratio in Figure 3 is significantly reduced, indicating that the accuracy is greatly improved, that is, the method of this embodiment has a much higher accuracy compared with the reduced-order model-based data assimilation method.
[0107] Taking 20 flow state samples and 10 iterations of data assimilation as an example, the calculation times of the CFD-based data assimilation method, the reduced-order model-based data assimilation method, and the method of this embodiment are shown in Table 1.
[0108]
[0109] Table 1
[0110] It can be seen from Table 1 that the calculation time of the method of this embodiment is 15.44% of that of the CFD-based data assimilation method.
Claims
1. A data assimilation method for transonic airfoil flow, characterized in that: The following steps are involved: S1: Building a reduced-order model; S2: Obtain input flow state and flow field observation data of the transonic airfoil under the input flow state; S3: applying a random perturbation of a given range to the input flow state to generate an initial flow set; S4: constructing a data joint space including flow states and corresponding flow field simulation data, filling the flow states in the initial flow set into the data joint space, and obtaining an initial data joint space; S5: using the reduced-order model to simulate and obtain the flow field simulation data of the transonic airfoil under the flow state recorded in the data joint space, and updating the data joint space; S6: using active learning methods to update the reduced-order model based on the flow field simulation data and the flow field observation data, and updating the data joint space; S7: Calculate the mean and covariance of the data joint space and calculate the Kalman gain; S8: Combine flow field observation data and Kalman gain to update data joint space; S9: Repeat steps S5 to S8 until the convergence condition is met and the data assimilation is completed.
2. A data assimilation method for transonic airfoil flow according to claim 1, characterized in that: The flow state is represented by a flow parameter group, which includes an angle of attack, a Mach number, and a Reynolds number.
3. The data assimilation method for transonic airfoil flow according to claim 1, characterized in that: The data joint space is denoted as The initial data joint space is Where N is the number of flow states in the data union space, u (i) is the flow parameter set of the ith flow state, x (i) is the flow field simulation data corresponding to the i-th flow state, u0 (i) is the initial value of the flow parameter set of the i-th flow state, x0 (i) is the initial value of the flow field simulation data corresponding to the i-th flow state, 1≤i≤N.
4. The data assimilation method for transonic airfoil flow according to claim 3 is characterized in that: The step S1 comprises the following steps: S11: Select a flow state, apply a random disturbance of a given range to the flow state to obtain a flow state set including F flow states, use CFD method to simulate and obtain the flow field simulation data of the transonic airfoil under these flow states, and obtain a flow field simulation data matrix U with M rows and F columns, where M is the number of grid sampling points; S12: taking each column of the flow field simulation data matrix U as a snapshot, performing POD decomposition on the flow field simulation data matrix U, selecting the first r-order POD modes with a total energy proportion ≥ ε as the POD basic modes, and generating the corresponding POD basic mode coefficients accordingly, 1≤r≤F; S13: The Kriging interpolation method is used to establish the mapping relationship between the POD fundamental modal coefficients and the flow state to obtain the reduced-order model.
5. The data assimilation method for transonic airfoil flow according to claim 4, characterized in that: The step S6 comprises the following steps: S61: Calculate the expected error weight corresponding to each flow state according to the Kriging variance corresponding to each flow state and the mean square error between the flow field simulation data and the flow field observation data; S62: Using CFD method to simulate and obtain the flow field simulation data of the transonic airfoil under the flow state with the minimum expected error weight, and update the data joint space; S63: adding the flow field simulation data as a new snapshot to the flow field simulation data matrix U to obtain a new flow field simulation data matrix U, and projecting the snapshot onto the POD fundamental mode to obtain the corresponding POD fundamental mode coefficient; S64: The mapping relationship between the POD fundamental modal coefficients and the flow state is updated using the Kriging interpolation method to complete the update of the reduced-order model.
6. The data assimilation method for transonic airfoil flow according to claim 5, characterized in that: In step S61, the formula for calculating the expected error weight corresponding to the ith flow state according to the Kriging variance corresponding to the ith flow state, the mean square error between the flow field simulation data and the flow field observation data is as follows: EPE v (i)=v*E cp (i)+(1-v)*s 2 (i), Among them, EPE v (i) is the expected error weight corresponding to the i-th flow state, v is the balance factor, E cp (i) is the mean square error between the flow field simulation data and the flow field observation data corresponding to the i-th flow state, s 2 (i) is the Kriging variance corresponding to the i-th flow state.
7. A data assimilation method for transonic airfoil flow according to claim 6, characterized in that: The formula for calculating the mean of the data joint space in step S7 is as follows: in, is the mean of the joint data space.
8. The data assimilation method for transonic airfoil flow according to claim 7, characterized in that: The formula for calculating the covariance of the data joint space in step S7 is as follows: Among them, C z is the covariance of the joint data space.
9. The data assimilation method for transonic airfoil flow according to claim 8, characterized in that: The formula for calculating the Kalman gain in step S7 is as follows: K=C z *H T (H*C z *H T +I) -1 , Among them, K is the Kalman gain, H is the observation matrix, and I is the unit matrix.
10. The data assimilation method for transonic airfoil flow according to claim 9, characterized in that: The formula for combining the flow field observation data and the Kalman gain to update the data joint space in step S8 is as follows: Among them, y is the flow field observation data.