LCM dynamic flow field reconstruction method and system based on sensor quantity optimization

Abstract

This invention belongs to the technical field of liquid molding of composite materials and discloses a dynamic flow field reconstruction method and system for LCM based on sensor number optimization. The method includes: constructing a three-dimensional structural model of the composite material part to be molded; performing finite element mesh generation on the three-dimensional structural model and initializing the physical parameters; setting different injection pressures and performing composite material injection molding simulation to obtain the total flow field data matrix and corresponding orthonormal basis for each mesh at different times; firstly, setting the number of sensors and the mesh number corresponding to each sensor location using a sensor number optimization algorithm; obtaining the measurement matrix representing the sensor location using the mesh number corresponding to the sensor location; and reconstructing the flow field using the orthonormal basis of the total flow field data matrix and the measurement matrix. This invention solves the problems of high computational complexity or low accuracy caused by too many or too few sensors.

Description

Technical Field

[0001] This invention belongs to the technical field of liquid molding of composite materials, and more specifically, relates to a method and system for dynamic flow field reconstruction of LCM based on sensor number optimization. Background Technology

[0002] The low-cost manufacturing advantage of liquid molding (LCM) for composite materials has led to its increasing application. However, due to the limitations of LCM technology, defects may exist within the resulting fiber composite materials, which can degrade the overall performance of the parts and pose safety hazards. Real-time acquisition of the flow field during LCM can optimize resin injection strategies, reduce internal defects, and improve the quality of finished fiber composite products. However, most LCM methods rely on non-transparent molds, making it impossible to directly acquire flow data using optical technologies such as cameras. Furthermore, the internal structure of large 3D components is too complex, making echolocation methods like ultrasound ineffective for structural analysis, and it's impractical to deploy numerous sensors within the mold. Simultaneously, the LCM process is complex and variable; a single simulation under varying injection conditions and material properties is insufficient to understand the time-varying flow field. Therefore, there is a need for reconstruction algorithms that combine sensor data and simulation datasets to obtain complete dynamic flow field information within the mold, guiding process adjustments and optimizations.

[0003] Traditional flow field reconstruction techniques for composite material liquid forming mainly rely on sensor arrays or only reconstruct the flow front, failing to capture the entire flow field. Sensor array solutions primarily use fiber optics, thermocouples, and pressure sensor arrays, often requiring a large number of sensors to be deployed inside the mold. While the system is relatively simple, it significantly impacts the overall mold structure and can only monitor the flow field in the deployed area. Building on this, C. Fratta et al. from ETH Zurich proposed a channel-based monitoring method that can reconstruct the flow front with a small number of sensors. However, this system is based on a two-dimensional pressure field analytical function, resulting in weak generalization ability and unquantified reconstruction accuracy. In recent years, with the development of machine learning, such as ANN, CNN, and PINN, their powerful function fitting capabilities allow them to extract useful information from large amounts of data, making them suitable for handling complex, nonlinear, high-dimensional, and large-scale fluid dynamics problems. However, they require large amounts of training data, necessitate significant computational resources, and are highly sensitive to network structure and parameter adjustments, making model training and optimization complex.

[0004] Monitoring systems based on sensor arrays suffer from high complexity due to the large number of sensors, significantly impacting the overall mold structure and limiting monitoring to the flow field within the designated area. Machine learning-based methods require substantial training data and computational resources, making model training and optimization complex. Flow channel-based monitoring methods, while simpler with fewer sensors, rely solely on empirical formulas, resulting in insufficient accuracy and a lack of generalization ability. Therefore, a suitable method is urgently needed to address the issues of high system complexity associated with sensor arrays or machine learning solutions, or low accuracy due to flow channel-based approaches. Summary of the Invention

[0005] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides an LCM dynamic flow field reconstruction method and system based on sensor number optimization, solving the problems of high system complexity or low accuracy caused by too many or too few sensors.

[0006] To achieve the above objectives, according to one aspect of the present invention, a dynamic flow field reconstruction method for LCM based on sensor number optimization is provided, the method comprising the following steps:

[0007] Finite element mesh generation is performed on the three-dimensional structural model of the composite material part to be molded, and the physical parameters are initialized.

[0008] An optimization model aimed at maximizing the efficiency function during the injection process is solved to obtain the optimal number of sensors. Different injection pressures and measurement positions of each sensor are set to simulate the injection molding of composite materials. During the simulation, the total flow field data matrix, the sensor position measurement matrix, and the flow field data obtained by the actual sensor measurements are measured.

[0009] The flow field is reconstructed using the total flow field data matrix, the sensor position measurement matrix, and the flow field data obtained from the actual sensor measurements.

[0010] More preferably, the flow field reconstruction adopts an intrinsic orthogonal decomposition method based on missing data, wherein the flow field data is the liquid pressure value, liquid velocity, or sensor capacitance value of the flow field.

[0011] More preferably, the formula for the flow field reconstruction is as follows:

[0012] f reconstruct_all =Φ r [(CΦ r ) T CΦ r ] -1 (CΦ r ) T Cf real

[0013] Where, Φ rIt is the orthonormal basis of the total flow field data matrix, C is the measurement matrix of the sensor position, and f real It is the flow field data actually measured by the sensor. This flow field data is the flow field data at different locations measured by the sensor. It is a column vector formed by arranging the flow field data at different locations in ascending order of grid number.

[0014] More preferably, the orthonormal basis of the total flow field data matrix is ​​obtained in the following manner:

[0015] The flow field characteristic mode matrix is ​​obtained by performing singular value decomposition on the total flow field data matrix;

[0016] The matrix formed by the first r columns of the flow field characteristic mode matrix that satisfy the preset conditions is used as the flow field standard orthogonal basis.

[0017] More preferably, the flow field characteristic modes are obtained using principal component analysis.

[0018] More preferably, the preset condition is:

[0019]

[0020] Where, σ i It is the i-th singular value obtained by performing singular value decomposition on the total flow field data matrix, where r is the singular value number and n is the total number of singular values.

[0021] More preferably, the measurement matrix is ​​calculated in the following manner:

[0022] C = [e β1 T e β2 T , ...e βi T ...., e βq T ]

[0023] Where C is the measurement matrix, e βi The βth of the identity matrix i List.

[0024] More preferably, the number of sensors is calculated according to the following optimization model:

[0025]

[0026] η(L)=αμ(L)+(1-α)ξ(L)

[0027]

[0028]

[0029] Where N is the total number of sensors in the system, L is the actual number of sensors used for sensing, η(L) is the system performance function, α represents the weighting of complexity and reconstruction accuracy in the system (α = 0 means the system does not consider complexity), μ(L) is the system's effective sensor resource function, and Φ r It is the orthonormal basis used for reconstruction, C is the measurement matrix representing the sensor position, and f real H0 represents the flow field data obtained from sensor measurements, and H0 represents the required flow field reconstruction accuracy.

[0030] More preferably, the initialization setting of physical parameters includes assigning values ​​to the permeability, nozzle pressure, and resin viscosity of each region in the three-dimensional model.

[0031] According to another aspect of the present invention, an LCM dynamic flow field reconstruction system based on sensor number optimization is provided. The system includes a model building module, a simulation module, a sensor measurement module, and a flow field reconstruction module, wherein:

[0032] The model building module is used to perform finite element mesh generation and initialization of physical parameters for the three-dimensional structural model of the composite material part to be molded.

[0033] The simulation module is used to perform injection molding simulation and obtain the total flow field data matrix corresponding to each grid at different times.

[0034] The sensor measurement module is used to acquire the measurement matrix of the sensor position and the flow field data;

[0035] The flow field reconstruction module is used to reconstruct the flow field using the total flow field data matrix, the sensor position measurement matrix, and the flow field data obtained by sensor measurements.

[0036] In summary, the technical solutions conceived by this invention have the following beneficial effects compared with the prior art:

[0037] 1. This invention uses an optimization model to optimize the number of sensors. Compared with a large number of sensors for sampling, it reduces the complexity of mold modification and the impact on the overall performance of the mold. In the case study, only a small number of sensors are needed to reconstruct the complete field with high accuracy, greatly reducing the number of sensors. For components of the same size, the traditional sensor array method generally requires 20-80 sensors. This invention achieves a balance between complexity and reconstruction accuracy, solving the problem of high system complexity or low accuracy caused by too many or too few sensors.

[0038] 2. This invention utilizes the total flow field data matrix and measurement matrix to reconstruct the flow field through flow field data measurement. Based on the fact that the entire flow field in liquid molding can be represented as a linear superposition of characteristic modes (orthogonal bases), and that these characteristic modes encompass the entire flow field information, the reconstructed values ​​at sensor points are made closer to the measured values ​​through the linear combination of orthogonal bases. The reconstruction coefficients are calculated, enabling accurate reconstruction of unmeasured flow field regions, thus improving the accuracy and completeness of flow field reconstruction during the liquid molding process of composite materials.

[0039] 3. The flow field reconstruction method of this invention is the GAPPY POD algorithm, which comprehensively considers system complexity and flow field reconstruction accuracy. It reconstructs the flow field with missing data, and simultaneously reconstructs the complete dynamic flow field in real time by matching the time step of the simulation data with the actual process time, providing strong support for subsequent optimization of the molding process. This invention is the first to realize the dynamic real-time reconstruction of the entire flow field in a non-transparent mold based on a small amount of sensor data, and gives the optimal number of sensors when the system efficiency is maximized. It can obtain the full flow field information when the injection pressure varies within a certain range without the need for repeated simulation in the actual process.

[0040] 4. Under actual working conditions and injection pressure fluctuations, this invention can reconstruct any field within a given pressure range, broadening the application scenarios and stability of the algorithm, without the need for repeated simulations in actual processes;

[0041] 5. This invention helps improve the quality stability and consistency of composite material products, promotes the development and application of controlled liquid molding technology for composite materials, and the reconstructed field can serve as the control target of the control system and provide real-time feedback on the flow within the mold, which helps to achieve closed-loop and intelligent control of the molding process. The results show that the algorithm has advantages such as high prediction accuracy, strong stability, and low dependence on the amount of database data. Attached Figure Description

[0042] Figure 1 This is a flowchart of a sensor-number-optimized LCM dynamic flow field reconstruction method constructed according to a preferred embodiment of the present invention;

[0043] Figure 2 This is a schematic diagram of a three-dimensional model of a composite material component constructed according to a preferred embodiment of the present invention;

[0044] Figure 3 This is a schematic diagram of the total flow field data matrix constructed according to a preferred embodiment of the present invention;

[0045] Figure 4 This is a schematic diagram of a flow field reconstructed based on the intrinsic orthogonal decomposition of missing data, constructed according to a preferred embodiment of the present invention.

[0046] In all the accompanying drawings, the same reference numerals are used to denote the same elements or structures, wherein:

[0047] 1-Glue opening, 2-Flow guide net, 3-Ventilation opening, 4-Fiber cloth, 5-Flow channel. Detailed Implementation

[0048] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0049] like Figure 1 As shown, a dynamic flow field reconstruction method for liquid chromatography (LCM) based on sensor number optimization is presented. According to the actual process, considering both system complexity and flow field reconstruction accuracy, the optimal number of sensors is selected. The GAPPY POD algorithm is used to reconstruct the flow field with missing data, enabling real-time visualization of the complete LCM flow field. This promotes the controllability and intelligence of composite material liquid molding. The method includes the following steps:

[0050] S1 as Figure 2 As shown, a 3D structural model is obtained by 3D modeling of the composite material component to be molded, and then meshing is performed. It is best to use meshes of exactly the same size and shape (volume) to partition the mesh into sections such as the glue inlet 1, the guide mesh 2, the vent 3, the fiber cloth 4, and the flow channel.

[0051] The parameters such as fiber cloth permeability, glue pressure, and resin viscosity in each region of the three-dimensional structural model are assigned values, and the pressure field during the molding process is calculated in parallel.

[0052] S2 takes k different injection pressures and performs a simulation for each case, for a total of k simulations. The data output time step is set, for example, outputting data every 10 seconds (simulation timescale, not real time). After the calculation is complete, the pressure / flow rate / liquid content and corresponding grid number are obtained for each grid.

[0053] The exported data are used to form the total flow field data matrix F∈R. n*kThe specific arrangement method is as follows: If the total simulation time is 4000s, the output time step is 50s in the first 2000s and 100s in the last 2000s, then there are 2000 / 50 + 2000 / 100 = 60 sets of flow field data f50, f1000, f150, ..., f3800, f3900, f4000 in a single simulation. Each set of data includes the pressure / data of all grids (for example, if the number of grids is 10000, then these 60 sets of data are arranged in a column according to the time order of 0-4000s, n = 60 * 10000 = 600000). Then, the k sets of data (f_p1-f_pk) under different injection pressures are arranged horizontally to form matrix F. An example is as follows: Let the flow field data at injection pressure p1 at simulation time 50s be f50_p1∈R. n The overall matrix is ​​arranged as follows: Figure 3 As shown.

[0054]

[0055] Use POD to find an optimal set of orthonormal bases Φ such that the flow field data x∈R n The projections onto this basis decrease rapidly, and the first r-order modes Φ containing higher energies are extracted. r ∈R n*r (Generally, we take the r terms for which the sum of the corresponding eigenvalues ​​of the modes is greater than 99% of the sum of the total eigenvalues), as shown in the following equation. The first r columns Φ of the orthonormal basis are used. r ∈R n*r Expand (reconstruction coefficients s) GAPPY ∈R r To obtain an approximate description of high-order data.

[0056] x = Φ r s GAPPY

[0057] Due to FF T The eigenvectors of the matrix are the left singular vectors of the singular value decomposition (SVD) of matrix F. The total orthonormal basis Φ can be calculated by performing SVD decomposition on the total flow field data matrix F. r ∈R n×r It is the first r columns of the total orthonormal basis Φ. In general, the dimension n of the F matrix is ​​much greater than k.

[0058] The simplified calculation is performed on matrix F using reduced singular value decomposition (SVD). The result of the reduced singular value decomposition is denoted as F = Φ * S * V, where Φ ∈ R. n*k , S∈R k* k, V∈R k*kIn this matrix, each column of Φ and V is orthogonal, and the S matrix has non-zero elements only on its diagonal, representing the singular values ​​corresponding to each mode. The singular values ​​are the square roots of their corresponding eigenvalues. The columns of Φ represent the characteristic modes of the flow field. Generally, it is considered that the sum of the eigenvalues ​​must exceed 99% of the total sum of n eigenvalues ​​to accurately reconstruct the flow field. That is, the sum of the squares of the r singular values ​​must be greater than 99% of the total sum of squares. The constraint condition that r needs to satisfy is shown in the following equation.

[0059] Let the first r columns of Φ be denoted as Φ. r ∈R n*r .

[0060]

[0061] S3 arranges a certain number of sensors (commercial / capacitive) within the mold. The sensors are preferably pre-integrated liquid pressure / flow rate / liquid content sensors within the mold. For large, three-dimensional composite parts, capacitive sensors can be used. Sensing data is collected and its position β is recorded, where β is the grid number in the three-dimensional mesh corresponding to the sensor position in the mold, used to calculate CΦ. r Where C is the measurement matrix, and assuming there are q sensors, C∈R p*n .

[0062] The calculation method for C is as follows, for the identity matrix I∈R n*n It can be denoted as [e1, e2, ..., e] n ], where e i Let be the i-th column of the identity matrix, and n be the total number of grid cells. For q sensor positions β1, β2, ..., βq, β... i This refers to the grid number in the 3D mesh corresponding to the sensor position in the mold. For example, if n = 3000 and β1 = 1000, the sensor corresponds to grid number 1000. β1 The 1000th column of a 3000x3000 identity matrix. C = [e β1 T e β2 T ....e βq T ].

[0063] S4 GAPPY POD is used to fill in missing data in a flow field when the number of sensors is small and the sensor data is sparse. The main objective of the GAPPY POD method is to minimize the error between the measured and reconstructed values ​​at the sensors. The error function E is expressed as the sum of squares of the differences between the reconstructed and measured values ​​at q points, as shown in the following equation, f real This represents the flow field data at the sensor's actual measurement points. reconstruct Reconstruct the flow field data for this point. reconstruct =CΦr s GAPPY Φ r ∈R n*r s GAPPY ∈R r These are the reconstruction coefficients.

[0064]

[0065] Since the error function E is a convex function, the error function is applied to each reconstruction coefficient (s) GAPPYi That is, take the partial derivative of the i-th reconstruction coefficient; the point where the error is minimized is when all partial derivatives are 0.

[0066]

[0067] Therefore, p equations can be used to establish a system of linear equations as shown above, and the solution s can be obtained. GAPPY , which is the reconstruction coefficient where the error is minimized. reconstruct_all The reconstructed full flow field is shown in the following equation:

[0068] s GAPPY =[(CΦ r ) T CΦ r ] -1 (CΦ r ) T Cf real

[0069] Φ r s GAPPY =f reconstruct_all

[0070] f reconstruct_all =Φ r [(CΦ r ) T CΦ r ] -1 (CΦ r ) T Cf real

[0071] Generally, the data measured at the sensor point is retained, and the flow field data at other missing sensor locations can be calculated using the following formula to fill in the missing data at any value within the injection pressure range of the simulation set.

[0072] Arranging sensors within the mold is complex, and the number of sensors affects reconstruction accuracy. To verify reconstruction accuracy, several additional sensors are typically placed, and sensors are also pre-installed in the mold. Therefore, the total number of sensors N is generally greater than the actual number of sensors used for sensing, L. The algorithm for determining the optimal number of sensors based on maximizing system efficiency is given below:

[0073] First, define the system performance function:

[0074] η(L)=αμ(L)+(1-α)ξ(L)

[0075] μ(L) represents the system complexity, ξ(L) represents the reconstruction accuracy, and α represents the weighting of complexity and reconstruction accuracy. The optimization objective is to maximize the η(L) function under the constraint that the flow field reconstruction accuracy is greater than a preset threshold H0 (e.g., 95%), as shown in the following equation.

[0076]

[0077] η(L)=αμ(L)+(1-α)ξ(L)

[0078]

[0079]

[0080] When the noise impact is small in actual working conditions, ξ(L) increases monotonically with the increase of the number of sensors.

[0081] Therefore, the discussion is as follows:

[0082] Case 1: α = 0, equivalent to neglecting system complexity. Since ξ(L) monotonically increases when the operating noise is very small, the number of sensors can be determined based on the condition ξ(L) ≥ H0. This case is ideal and rarely seen in actual processes. Φ r C is a function of L.

[0083] Case 2: α≠0, the optimal number of sensors is modified to... In system design, both system performance and complexity must be considered, and an effective trade-off must be made between the two.

[0084] like Figure 4 As shown, the non-zero elements in the measurement matrix C correspond to the actual positions of the sensors within the three-dimensional structure. Using the reconstruction coefficients s... GAPPY A linear combination of the basis vectors Φ is performed to make the flow field pressure value at the sensor point as close as possible to the measured pressure value f. real Ultimately, the three-dimensional flow field is visualized.

[0085] The relative mean square error between the reconstructed process and the actual flow field is calculated as follows, where m is the total number of grids and i is the grid number.

[0086]

[0087] In embodiments of the present invention, five different injection pressure flow fields P=1 0 were used. 5 Pa, 1.1 × 105 Pa, 1.2 × 10 5 Pa, 1.3 × 10 5 Pa, 1.5 × 10 5 Pa, and select P = 1.33 × 10 5 Pa is used as the target field for reconstruction. The molded part is a thin-walled square composite material with two square holes. MATLAB calculation shows that the reconstruction error of a single sensor point in the flow field is 1.87%, proving that the reconstruction effect is good. The error does not change much when the number of sensors changes, and is always less than 3%. The data is imported into the visualization program and the dynamic reconstruction effect is observed. The trend is consistent with the original flow field. The optimal number of sensors can be obtained by finding the maximum value of the system performance function η(L)=αμ(L)+(1-α)ξ(L) in the interval [1,N], where α is selected according to the requirements.

[0088] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for reconstructing dynamic flow field in a liquid flow meter (LCM) based on sensor number optimization, characterized in that, The method includes the following steps: Finite element mesh generation is performed on the three-dimensional structural model of the composite material part to be molded, and the physical parameters are initialized. An optimization model aimed at maximizing the efficiency function during the injection process is solved to obtain the optimal number of sensors. Different injection pressures and measurement positions of each sensor are set to simulate the injection molding of composite materials. During the simulation, the total flow field data matrix, the sensor position measurement matrix, and the flow field data obtained by the actual sensor measurements are measured. The flow field is reconstructed using the total flow field data matrix, the sensor position measurement matrix, and the flow field data obtained from the actual sensor measurements. The flow field reconstruction adopts the intrinsic orthogonal decomposition method based on missing data, wherein the flow field data is the liquid pressure value, liquid velocity, or sensor capacitance value of the flow field; The formula for the reconstructed flow field is as follows: in, It is the standard orthogonal basis of the total flow field data matrix. It is a measurement matrix of sensor positions. It is the flow field data actually measured by the sensor. This flow field data is the flow field data at different locations measured by the sensor. It is a column vector formed by arranging the flow field data at different locations in ascending order of grid number. The number of sensors was calculated using the following optimization model: ； ； ； in, This is the total number of sensors in the system. This refers to the actual number of sensors used for sensing. It is the system performance function. This represents the weighting of complexity and reconstruction accuracy in the system. That is, the system does not consider complexity. It is the system's effective sensor resource function. It is an orthonormal basis used for reconstruction. It is a measurement matrix representing the sensor position. It is the flow field data obtained by sensor measurement. To achieve the required accuracy in reconstructing the flow field, It refers to the accuracy of reconstruction.

2. The LCM dynamic flow field reconstruction method based on sensor number optimization as described in claim 1, characterized in that, The orthonormal basis of the total flow field data matrix is ​​obtained in the following manner: The flow field characteristic mode matrix is ​​obtained by performing singular value decomposition on the total flow field data matrix; The matrix formed by the first r columns of the flow field characteristic mode matrix that satisfy the preset conditions is used as the flow field standard orthogonal basis.

3. The LCM dynamic flow field reconstruction method based on sensor number optimization as described in claim 2, characterized in that, The characteristic modes of the flow field were obtained using principal component analysis.

4. A method for reconstructing dynamic flow field in LCM based on sensor number optimization as described in claim 2 or 3, characterized in that, The preset conditions are: ≥99% in, It is the i-th singular value obtained by performing singular value decomposition on the total flow field data matrix, where r is the singular value number and n is the total number of singular values.

5. A method for reconstructing dynamic flow field in LCM based on sensor quantity optimization as described in claim 1 or 2, characterized in that, The measurement matrix is ​​calculated in the following manner: C = [ e β1 T ， e β2 T ，… e βi T ….， e βq T ] in, e βi The βth of the identity matrix i List.

6. The LCM dynamic flow field reconstruction method based on sensor number optimization as described in claim 1, characterized in that, The initialization setting of physical parameters includes assigning values ​​to the permeability, nozzle pressure, and resin viscosity of each region in the three-dimensional model.

7. A system for dynamic flow field reconstruction using the LCM dynamic flow field reconstruction method based on sensor number optimization as described in any one of claims 1-6, characterized in that, The system includes a model building module, a simulation module, a sensor measurement module, and a flow field reconstruction module, among which: The model building module is used to perform finite element mesh generation and initialize physical parameters for the three-dimensional structural model of the composite material part to be molded. The simulation module is used to perform injection molding simulation and obtain the total flow field data matrix corresponding to each grid at different times. The sensor measurement module is used to acquire the measurement matrix of the sensor position and the flow field data; The flow field reconstruction module is used to reconstruct the flow field using the total flow field data matrix, the sensor position measurement matrix, and the flow field data obtained by sensor measurement.

Images