High time resolution flow field test method based on sparse moment measurement value and intelligent power system

Abstract

The invention discloses a high-time-resolution flow field testing method and system based on sparse moment measured values and an intelligent power system, and belongs to the field of flow field testing and data reconstruction in bridge wind engineering. According to the method, overall low-frequency and local high-frequency sparse flow field data are obtained through a four-pulse fixed-frequency variable-frequency laser system and a four-exposure high-speed imaging PIV sampling system; a 32-dimensional nonlinear modal coefficient is extracted through a multi-scale convolution flow field sparse feature extraction model, then an unsampled time step coefficient is predicted through an LSTM intelligent power system model, and finally the unsampled time step coefficient is input into a multi-scale convolution auto-encoder to reconstruct a high-time-resolution flow field. The method does not need to depend on a pressure sequence, reduces the hardware and data processing cost through sparse sampling, accurately captures the flow field dynamics characteristics through intelligent modeling, solves the problems of expensive high-frequency hardware, loss of low-frequency reconstruction data and difficulty in model training in a traditional PIV test, and is suitable for flow field dynamics research and engineering optimization.

Description

Technical Field

[0001] This invention relates to the field of flow field testing and data reconstruction in bridge wind engineering, specifically to a high temporal resolution flow field testing method based on sparse time-based measurements and intelligent dynamic systems. Background Technology

[0002] In fluid mechanics research and engineering applications, the temporal resolution of the flow field directly affects the accuracy of the analysis of fluid dynamic characteristics. Traditional flow field data acquisition relies on techniques such as particle image velocimetry (PIV). To obtain a high temporal resolution flow field, high-frequency, high-energy lasers and high-speed sampling cameras are required. Not only are the equipment expensive, but the massive amounts of data generated also increase the burden of storage and processing.

[0003] In existing PIV testing methods, some schemes rely on the mapping relationship between pressure sequences and flow fields to obtain nonlinear modal coefficients. However, these methods have hardware and software limitations: the flow field and pressure samples must correspond one-to-one, and sampling high-frequency pressure sequences is difficult in some cases. In the field of flow field reconstruction, the conversion from low-frequency data to high-frequency data faces two major challenges. First, low-frequency data naturally lacks high-frequency components, leading to data loss and missing details. The model must generate the missing information, which is mathematically challenging. Second, due to the small dataset size resulting from low-frequency sampling, the model struggles to learn the underlying dynamic laws of the high-frequency flow field, making model training difficult, prone to overfitting, and resulting in poor generalization performance. Researchers have proposed some methods to address these problems. For example, by combining spatial averaging and dynamic observers, high-resolution reconstruction and synchronization of the flow field can be achieved under noisy conditions, providing new theoretical support and practical solutions for flow field reconstruction. Based on sparse representation theory, sparse signals can be reconstructed using a small number of samples, but current techniques have not effectively combined this with multi-scale flow field feature extraction and time series modeling, making it difficult to simultaneously guarantee testing accuracy and generalization ability.

[0004] Therefore, there is an urgent need for a testing method that does not rely on pressure sequences, is low-cost, and can accurately model the temporal characteristics of nonlinear flow fields. Summary of the Invention

[0005] To address the aforementioned shortcomings, this invention provides a method for achieving high temporal resolution flow field testing using only flow field sampling data. This aims to solve the problems of high hardware cost for high-frequency sampling, loss of high-frequency data during low-frequency reconstruction, difficulty in model training, and reliance on pressure sequences in existing PIV testing techniques. This invention achieves efficient and high-precision spatiotemporal reconstruction of the flow field by integrating sparse measurement techniques with intelligent dynamic system modeling.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems, comprising the following steps:

[0007] Step 1: In the wind tunnel test, a four-pulse fixed-frequency and variable-frequency laser system and a four-exposure high-speed imaging PIV sampling system are used. In each sampling cycle, the laser system emits four consecutive laser pulses. The time interval of these four laser pulses is divided into a fixed part and an adjustable part, thereby realizing a mixed mode of overall low-frequency sampling and local high-frequency sampling. Four exposures refer to the high-speed camera and the laser system being completely synchronized. Each time a laser pulse is received, the particle is exposed once. The PIV high-speed camera with four-way beam combining and dual optical guide arms is used for measurement. Finally, the position of the particle at four time points is recorded on one image, and the overall low-frequency and local high-frequency flow field dataset is obtained.

[0008] Step 2: Construct a multi-scale convolutional flow field sparse feature extraction model. Input the flow field results measured by PIV into the multi-scale convolutional flow field sparse feature extraction model for feature extraction.

[0009] Step 3: Based on LSTM, identify the intelligent dynamic system model, solve the problem of time dependence modeling of nonlinear modal coefficients, and predict the coefficients of unsampled time steps;

[0010] Step 4: Input the unsampled time-step nonlinear mode coefficients predicted by the intelligent dynamic system model into the trained multi-scale convolutional autoencoder model to reconstruct high-time-resolution flow field data around the cylinder.

[0011] Furthermore, in step one, the sampled flow field dataset is two-dimensional data of flow around an incompressible cylinder with a Reynolds number of 3900, corresponding to a Strouhal number of approximately 0.207. A fixed-frequency laser ensures an overall sampling frequency of 10⁻¹⁰, which matches the low-frequency sampling requirements and reduces hardware costs. A variable-frequency laser increases the frequency in local time periods to achieve local high-frequency sampling. Four-exposure high-speed imaging simultaneously captures particle motion trajectories, and one frame of local high-frequency flow field image is randomly sampled from two consecutive overall low-frequency flow field images.

[0012] Furthermore, in step two, the multi-scale convolutional flow field sparse feature extraction model includes four parallel sub-encoders, each employing... , , , Convolutional kernels capture local details, mesoscale features, macroscopic flow field structure, and large vortex motion, respectively. Each sub-encoder is processed by convolution + ReLU + max pooling + MLP to output 8-dimensional nonlinear mode coefficients. The outputs of the four branches are concatenated along the channel dimension to obtain 32-dimensional nonlinear mode coefficients that fuse multi-scale features. In the decoder, upsampling and convolution operations are used to map the 32-dimensional coefficients back to a 61×101-dimensional flow field, achieving the inverse mapping from features to the flow field. All activation functions use the ReLU function, as shown in the following expression:

[0013] ,

[0014] The operation process of a convolutional layer is expressed as follows:

[0015] ,

[0016] In the formula, For the first Layer output; It is the sigmoid activation function; The number of convolution kernels; The kernel size; As weight; For bias;

[0017] The latent vector is obtained through encoder operations. Then the output is obtained through decoder operations. The expression for the loss function of a convolutional autoencoder is as follows:

[0018] ,

[0019] In the formula, The original velocity field; The velocity field reconstructed by the decoder; m is the number of velocity fields;

[0020] The multi-scale convolutional autoencoder employs a training strategy that trains concurrent and transverse data separately to avoid the impact of the magnitude difference between the two. It uses an initial training followed by full-data training method to monitor relative reconstruction error, thereby improving accuracy by fully utilizing the data while avoiding overfitting.

[0021] Furthermore, in step three, the LSTM network for recognizing the intelligent dynamic system model consists of an input layer, a hidden layer, and an output layer. The hidden layer uses LSTM units that include input gates, forget gates, output gates, and cell states. This structure is specifically designed to address the gradient vanishing or exploding problems encountered by traditional RNNs when processing long sequence data, thereby effectively capturing long-term temporal features. The input to the LSTM-based intelligent dynamic system model is the 32-dimensional nonlinear mode coefficients output by the multi-scale convolutional autoencoder model, and the output is the predicted high-dimensional nonlinear mode coefficients for the next time step. The loss function of the LSTM model is:

[0022] ,

[0023] In the formula, This represents the training error of the Long Short-Term Memory (LSTM) network. The size of the training set; These are the nonlinear mode coefficients of the encoder in a multi-scale convolutional autoencoder. This represents the output of the Long Short-Term Memory network at the corresponding time point;

[0024] The training objective is to minimize the mean square error between the LSTM output and the true coefficients. If a time step is not sampled, the output of the LSTM at the previous time step is used as the current input to iteratively generate a complete high-frequency coefficient sequence.

[0025] Furthermore, in step three, the complete computation flow of LSTM in a single time step is as follows:

[0026] Step 1: Input concatenation, hiding the previous state. With the current input Concatenate to obtain a vector ;

[0027] The second step is the forgetting gate calculation, which determines how much historical cell state is forgotten. The formula is as follows:

[0028] ,

[0029] Step 3: Input gate calculation. The gate selection determines how much new information is retained. The formula is as follows:

[0030] ,

[0031] Candidate cell states are used to generate new information, as shown in the following formula:

[0032] ,

[0033] Step 4: Cell state update, integrating historical and new information, using the following formula:

[0034] ,

[0035] Step 5: Output gate calculation. The output gate weights determine how much information is output. The formula is as follows:

[0036] ,

[0037] The hidden state at the current moment is generated using the following formula:

[0038] ,

[0039] In the formula, The sigmoid activation function is represented by sigmoid; the hyperbolic tangent activation function is represented by tanh. , , , These are the weight matrices for the corresponding gates; , , , These are the bias terms for the corresponding gates; This represents the current cell state. This refers to the previous cell state; This is the current hidden state; This is the previous hidden state; The input vector at the current time step; This indicates element-wise multiplication.

[0040] Furthermore, in step four, the unsampled time-step nonlinear mode coefficients predicted by the intelligent dynamic system model are input into the trained multi-scale convolutional autoencoder model to reconstruct high-temporal-resolution flow field data around the cylinder. The differences between the original flow field and the data are then defined. To characterize the average relative error of the entire flow field in the time domain, we define... To characterize the relative error distribution of the entire flow field in the spatial domain:

[0041] ,

[0042] ,

[0043] In the formula, This represents the relative error of position x within the time domain. At position x The true value of velocity at any given moment; At position x The reconstructed value of velocity at each moment; n is the total number of times;

[0044] ,

[0045] In the formula, for The reconstructed value of the velocity at position x at time x; N is the total number of positions.

[0046] This invention also provides a high temporal resolution flow field testing system based on sparse time-series measurements and intelligent dynamic systems, including an image acquisition module, a sparse feature extraction module, a modal coefficient prediction module, and a flow field reconstruction and error evaluation module. This system enables the implementation of the flow field testing method described above, based on sparse time-series measurements and intelligent dynamic systems. Specifically, the image acquisition module acquires overall low-frequency and locally high-frequency flow field data through a PIV sampling system; the sparse feature extraction module constructs a multi-scale convolutional flow field sparse feature extraction model, inputs the flow field results measured by PIV into the model, and outputs 32-dimensional nonlinear modal coefficients that fuse multi-scale features; the modal coefficient prediction module uses LSTM to recognize the intelligent dynamic system model, inputs the 32-dimensional nonlinear modal coefficients, and predicts the nonlinear modal coefficients for unsampled time steps; and the flow field reconstruction and error evaluation module inputs the predicted nonlinear modal coefficients into a trained multi-scale convolutional autoencoder model to reconstruct high temporal resolution flow field data around a cylinder, and characterizes the reconstruction accuracy through relative errors in the time and spatial domains.

[0047] The present invention also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems as described above.

[0048] The present invention also provides a computer program product, which, when executed by a processor, implements the high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems as described above.

[0049] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which is executed by a processor to implement the high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems as described above.

[0050] The advantages of this invention are:

[0051] (1) This invention addresses the problems of high hardware cost for high-frequency sampling, loss of high-frequency data in low-frequency reconstruction, difficulty in model training, and dependence on pressure sequences in existing PIV testing technologies. It provides a method for achieving high temporal resolution testing using only flow field sampling data. A closed-loop process of "sparse sampling—multi-scale feature extraction—intelligent time series prediction—flow field reconstruction" is constructed to achieve high temporal resolution flow field testing. Specifically, sparse time-series measurements can effectively acquire overall low-frequency and local high-frequency information of the flow field data. Multi-scale features are extracted using a multi-scale convolutional flow field sparse feature extraction model, and then combined with an LSTM-based intelligent dynamic system model to model the time series relationships, ultimately achieving accurate reconstruction of the high-frequency flow field.

[0052] (2) This invention does not rely on pressure sequences and can achieve reconstruction only through flow field sampling data, breaking through the hardware and software limitations of traditional methods and making it applicable to a wider range of scenarios;

[0053] (3) Employing sparse sampling with overall low frequency and local high frequency significantly reduces equipment investment and data processing costs;

[0054] (4) The combination of sparse moment measurements and intelligent dynamic system methods has excellent generalization performance for unsampled data and good dynamic consistency. It can accurately capture core dynamic features such as the shedding of the main vortex and can be used for flow field dynamics research and engineering optimization. Attached Figure Description

[0055] Figure 1 This is a schematic diagram of the principle of a high-speed camera with dual light guide arms and a four-way beam combining design as described in Implementation 1.

[0056] Figure 2 This is a schematic diagram of the multi-scale convolutional autoencoder in the high temporal resolution flow field testing method based on sparse temporal measurements and intelligent dynamic systems described in Implementation Method 1.

[0057] Figure 3 This is a schematic diagram of the LSTM architecture for identifying the intelligent dynamic system model in the high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems described in Implementation Method 1.

[0058] Figure 4 This is a schematic diagram of the flow field reconstruction results in the high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems described in Implementation Method 1. Detailed Implementation

[0059] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0060] Example 1

[0061] This implementation addresses the problems of high hardware cost for high-frequency sampling, loss of high-frequency data during low-frequency reconstruction, difficulty in model training, and dependence on pressure sequences in existing PIV testing technologies. It provides a method to achieve high temporal resolution testing using only flow field sampling data, balancing accuracy, cost, and generalization ability. High temporal resolution flow field testing is achieved by constructing a closed-loop process of "sparse sampling—multi-scale feature extraction—intelligent temporal prediction—flow field reconstruction." The steps include:

[0062] Step 1: In the wind tunnel test, a four-pulse fixed-frequency / variable-frequency laser system and a four-exposure high-speed imaging PIV sampling system are used. Within each sampling cycle, the laser system emits four consecutive laser pulses. The time interval between these four laser pulses is divided into a fixed part and an adjustable part, thus achieving a mixed mode of overall low-frequency sampling and local high-frequency sampling. Four exposures refer to the high-speed camera and laser system being completely synchronized; for each laser pulse received, the particle is exposed once. Figure 1 As shown, a high-speed PIV camera with four-way beam combining and dual optical guide arms was used to measure the flow field. The positions of particles at four time points were recorded on a single image, acquiring an overall low-frequency and locally high-frequency flow field dataset. The PIV system successfully acquired high-frequency flow field data of 400Hz and ultra-high-frequency random discrete flow field data of 2000Hz. The sampled flow field dataset is two-dimensional data of flow around an incompressible cylinder with a Reynolds number of 3900. The spatial range is 5D downstream and 3D transverse, with an interval of 0.05D between adjacent velocity points. The discrete velocity field at each time point is represented as follows: The matrix consists of 61 × 101 spatial points in both the downstream and cross-current directions. The technical principle of the PIV high-speed camera is as follows: Figure 1 As shown, the time intervals between the first, second, third, and fourth pulses of light and exposure are equal, i.e., dt1 = dt3, while dt2 is adjustable. Dt is the duty cycle, which is the reciprocal of the frequency. By adjusting dt2, 400Hz high-frequency flow field data and 2000Hz ultra-high-frequency random discrete flow field data can be obtained.

[0063] Step Two, as follows Figure 2 As shown, a multi-scale convolutional flow field sparse feature extraction model is constructed. The flow field results measured by PIV are input into the multi-scale convolutional flow field sparse feature extraction model for feature extraction. The multi-scale convolutional flow field sparse feature extraction model includes four parallel sub-encoders, each employing... , , , Convolutional kernels capture local details, mesoscale features, macroscopic flow field structure, and large vortex motion, respectively. Each sub-encoder is processed by convolution + ReLU + max pooling + MLP to output 8-dimensional nonlinear mode coefficients. The outputs of the four branches are concatenated along the channel dimension to obtain 32-dimensional nonlinear mode coefficients that fuse multi-scale features. In the decoder, upsampling and convolution operations are used to map the 32-dimensional coefficients back to a 61×101-dimensional flow field, achieving the inverse mapping from features to the flow field. All activation functions use the ReLU function, as shown in the following expression:

[0064] ,

[0065] The operation process of a convolutional layer is expressed as follows:

[0066] ,

[0067] In the formula, For the first Layer output; It is the sigmoid activation function; The number of convolution kernels; The kernel size; As weight; For bias;

[0068] The latent vector is obtained through encoder operations. Then the output is obtained through decoder operations. The expression for the loss function of a convolutional autoencoder is as follows:

[0069] ,

[0070] In the formula, The original velocity field; is the velocity field reconstructed by the decoder; m is the number of velocity fields.

[0071] Step 3, as follows Figure 3 As shown, an LSTM-based intelligent dynamic system model is used to address the time-dependent modeling problem of nonlinear mode coefficients and predict coefficients at unsampled time steps. The LSTM network for recognizing the intelligent dynamic system model consists of an input layer, hidden layers, and an output layer. The hidden layer uses LSTM units containing input gates, forget gates, output gates, and cell states to solve the gradient explosion or vanishing problem of traditional RNNs, ensuring long-term temporal feature capture capability. The input to the LSTM-based intelligent dynamic system model is the 32-dimensional nonlinear mode coefficients output by a multi-scale convolutional autoencoder model, and the output is the predicted high-dimensional nonlinear mode coefficients for the next time step. The loss function of the LSTM model is:

[0072] ,

[0073] In the formula, This represents the training error of the Long Short-Term Memory (LSTM) network. The size of the training set; These are the nonlinear mode coefficients of the encoder in a multi-scale convolutional autoencoder; This represents the output of the Long Short-Term Memory network at the corresponding time point;

[0074] The training objective is to minimize the mean squared error between the LSTM output and the true coefficients. If no samples are taken at a certain time step, the output of the LSTM at the previous time step is used as the current input to iteratively generate a complete sequence of high-frequency coefficients. The model is trained using the loss function of the LSTM model, ultimately yielding the modal coefficients and decoder of the flow field data.

[0075] The complete computation process for a single time step of LSTM is as follows:

[0076] Step 1: Input concatenation, hiding the previous state. With the current input Concatenate to obtain a vector ;

[0077] The second step is the forgetting gate calculation, which determines how much historical cell state is forgotten. The formula is as follows:

[0078] ,

[0079] Step 3: Input gate calculation. The gate selection determines how much new information is retained. The formula is as follows:

[0080] ,

[0081] Candidate cell states are used to generate new information, as shown in the following formula:

[0082] ,

[0083] Step 4: Cell state update, integrating historical and new information, using the following formula:

[0084] ,

[0085] Step 5: Output gate calculation. The output gate weights determine how much information is output. The formula is as follows:

[0086] ,

[0087] The hidden state at the current moment is generated using the following formula:

[0088] ,

[0089] In the formula, The sigmoid activation function is represented by sigmoid; the hyperbolic tangent activation function is represented by tanh. , , , These are the weight matrices for the corresponding gates; , , , These are the bias terms for the corresponding gates; This represents the current cell state. This refers to the previous cell state; This is the current hidden state; This is the previous hidden state; The input vector at the current time step; This indicates element-wise multiplication.

[0090] Step 4: Input the unsampled time-step nonlinear mode coefficients predicted by the intelligent dynamic system model into the trained multi-scale convolutional autoencoder model to reconstruct high-temporal-resolution flow field data around the cylinder. Compare the differences with the original flow field and define... To characterize the average relative error of the entire flow field in the time domain, we define... To characterize the relative error distribution of the entire flow field in the spatial domain:

[0091]

[0092]

[0093] In the formula, This represents the relative error of position x within the time domain. This represents the true value of the velocity at position x at time t. is the reconstructed velocity value at position x at time t; n is the total number of times.

[0094]

[0095] In the formula, for The reconstructed value of the velocity at position x at time x; N is the total number of positions.

[0096] This step integrates the ultra-high temporal resolution modal coefficients reconstructed from the intelligent dynamic system model based on LSTM into the decoder of a multi-scale convolutional autoencoder. Combined with the characteristics of convolutional LSTM, this effectively reconstructs the flow field with ultra-high temporal resolution. For example... Figure 4 As shown, the high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems can reconstruct complete ultra-high temporal resolution flow field data.

[0097] The above methods reconstruct complete flow field data with ultra-high temporal resolution, and solve the problems of high hardware cost for high-frequency sampling, loss of high-frequency data in low-frequency reconstruction and difficulty in model training, and dependence on stress sequences in existing PIV testing technologies.

Claims

1. A high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems, characterized in that, Includes the following steps: Step 1: In the wind tunnel test, a four-pulse fixed-frequency and variable-frequency laser system and a four-exposure high-speed imaging PIV sampling system are used. In each sampling cycle, the laser system emits four consecutive laser pulses. The time interval of these four laser pulses is divided into a fixed part and an adjustable part, thereby realizing a mixed mode of overall low-frequency sampling and local high-frequency sampling. Four exposures refer to the high-speed camera and the laser system being completely synchronized. Each time a laser pulse is received, the particle is exposed once. The PIV high-speed camera with four-way beam combining and dual optical guide arms is used for measurement. Finally, the position of the particle at four time points is recorded on one image, and the overall low-frequency and local high-frequency flow field dataset is obtained. Step 2: Construct a multi-scale convolutional flow field sparse feature extraction model. Input the flow field results measured by PIV into the multi-scale convolutional flow field sparse feature extraction model for feature extraction. Step 3: Based on LSTM, identify the intelligent dynamic system model, solve the problem of time dependence modeling of nonlinear modal coefficients, and predict the coefficients of unsampled time steps; Step 4: Input the unsampled time-step nonlinear mode coefficients predicted by the intelligent dynamic system model into the trained multi-scale convolutional autoencoder model to reconstruct high-time-resolution flow field data around the cylinder.

2. The high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems according to claim 1, characterized in that, In step one, the sampled flow field dataset is two-dimensional data of flow around an incompressible cylinder with a Reynolds number of 3900, corresponding to a Strouhal number of approximately 0.

207.

3. The high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems according to claim 1, characterized in that, In step two, the multi-scale convolutional flow field sparse feature extraction model includes four parallel sub-encoders, each employing... , , , Convolutional kernels capture local details, mesoscale features, macroscopic flow field structure, and large vortex motion, respectively. Each sub-encoder is processed by convolution + ReLU + max pooling + MLP to output 8-dimensional nonlinear mode coefficients. The outputs of the four branches are concatenated along the channel dimension to obtain 32-dimensional nonlinear mode coefficients that fuse multi-scale features. In the decoder, upsampling and convolution operations are used to map the 32-dimensional coefficients back to a 61×101-dimensional flow field, achieving the inverse mapping from features to the flow field. All activation functions use the ReLU function, as shown in the following expression: , The operation process of a convolutional layer is expressed as follows: , In the formula, For the first Layer output; It is the sigmoid activation function; The number of convolution kernels; The kernel size; As weight; For bias; The latent vector is obtained through encoder operations. Then the output is obtained through decoder operations. The expression for the loss function of a convolutional autoencoder is as follows: ， In the formula, The original velocity field; is the velocity field reconstructed by the decoder; m is the number of velocity fields.

4. The high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems according to claim 3, characterized in that, In step three, the LSTM network for recognizing the intelligent dynamic system model based on LSTM consists of an input layer, a hidden layer, and an output layer. The hidden layer uses LSTM units that include input gates, forget gates, output gates, and cell states. The input to the LSTM-based intelligent dynamic system model is the 32-dimensional nonlinear mode coefficients output by the multi-scale convolutional autoencoder model, and the output is the predicted high-dimensional nonlinear mode coefficients for the next time step. The loss function of the LSTM model is: ， In the formula, This represents the training error of the Long Short-Term Memory (LSTM) network. The size of the training set; These are the nonlinear mode coefficients of the encoder in a multi-scale convolutional autoencoder; This represents the output of the Long Short-Term Memory network at the corresponding time point; The training objective is to minimize the mean square error between the LSTM output and the true coefficients. If a time step is not sampled, the output of the LSTM at the previous time step is used as the current input to iteratively generate a complete high-frequency coefficient sequence.

5. The high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems according to claim 4, characterized in that, In step three, the complete computation flow of LSTM in a single time step is as follows: Step 1: Input concatenation, hiding the previous state. With the current input Concatenate to obtain a vector ; The second step is the forgetting gate calculation, which determines how much historical cell state is forgotten. The formula is as follows: ， Step 3: Input gate calculation. The gate selection determines how much new information is retained. The formula is as follows: ， Candidate cell states are used to generate new information, as shown in the following formula: ， Step 4: Cell state update, integrating historical and new information, using the following formula: ， Step 5: Output gate calculation. The output gate weights determine how much information is output. The formula is as follows: ， The hidden state at the current moment is generated using the following formula: ， In the formula, The sigmoid activation function is represented by sigmoid; the hyperbolic tangent activation function is represented by tanh. , , , These are the weight matrices for the corresponding gates; , , , These are the bias terms for the corresponding gates; This represents the current cell state. This refers to the previous cell state; This is the current hidden state; This is the previous hidden state; The input vector at the current time step; This indicates element-wise multiplication.

6. The high temporal resolution flow field testing method based on sparse time-series measurements and intelligent dynamic systems according to claim 5, characterized in that, In step four, the unsampled time-step nonlinear mode coefficients predicted by the intelligent dynamic system model are input into the trained multi-scale convolutional autoencoder model to reconstruct high-temporal-resolution flow field data around the cylinder. The differences between the original flow field and the data are then defined. To characterize the average relative error of the entire flow field in the time domain, we define... To characterize the relative error distribution of the entire flow field in the spatial domain: ， ， In the formula, Let x be the relative error of the position in the time domain. At position x The true value of velocity at any given moment. At position x The reconstructed value of velocity at each moment; n is the total number of times; ， In the formula, for The reconstructed value of the velocity at position x at time x; N is the total number of positions.

7. A high temporal resolution flow field testing system based on sparse time-series measurements and an intelligent dynamic system, characterized in that, The system includes an image acquisition module, a sparse feature extraction module, a modal coefficient prediction module, and a flow field reconstruction and error evaluation module. It is capable of implementing the flow field testing method based on sparse time-domain measurements and an intelligent dynamic system as described in any one of claims 1-6. Specifically, the image acquisition module acquires overall low-frequency and locally high-frequency flow field data through a PIV sampling system; the sparse feature extraction module constructs a multi-scale convolutional flow field sparse feature extraction model, inputs the flow field results measured by PIV into the model, and outputs 32-dimensional nonlinear modal coefficients that fuse multi-scale features; the modal coefficient prediction module uses LSTM to recognize the intelligent dynamic system model, inputs the 32-dimensional nonlinear modal coefficients, and predicts the nonlinear modal coefficients at unsampled time steps; and the flow field reconstruction and error evaluation module inputs the predicted nonlinear modal coefficients into a trained multi-scale convolutional autoencoder model to reconstruct high-temporal-resolution flow field data around a cylinder, and characterizes the reconstruction accuracy through relative errors in the time and spatial domains.

8. An electronic device, characterized in that, include: The system includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement a high temporal resolution flow field testing system based on sparse time-series measurements and intelligent dynamic systems as described in claim 7.

9. A computer program product, characterized in that, When the computer program / instructions are executed by the processor, they implement the high temporal resolution flow field testing system based on sparse time-series measurements and intelligent dynamic systems as described in claim 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, The program is executed by the processor to implement a high temporal resolution flow field testing system based on sparse time-series measurements and intelligent dynamic systems as described in claim 7.

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