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

Abstract

The invention belongs to the technical field related to composite material liquid molding, and discloses an LCM dynamic flow field reconstruction method and system based on sensor number optimization. The method comprises the following steps: constructing a three-dimensional structure model of a to-be-formed composite material part, performing finite element mesh generation on the three-dimensional structure model, and performing initialization setting on physical parameters; different injection pressures are set, composite material injection molding simulation is carried out, and a total flow field data matrix corresponding to each grid at different moments and a corresponding standard orthogonal basis are obtained; the method comprises the following steps: firstly, setting the number of sensors and a grid number corresponding to the position of each sensor through a sensor number optimization algorithm, and obtaining a measurement matrix representing the positions of the sensors through the grid numbers corresponding to the positions of the sensors; and performing flow field reconstruction by using the standard orthogonal basis of the total flow field data matrix and the measurement matrix. According to the invention, the problem of high calculation complexity or low precision caused by too many or too few sensors is solved.

Description

Technical Field

[0001] The present invention belongs to the technical field related to composite material liquid molding, and more specifically, relates to a LCM dynamic flow field reconstruction method and system based on sensor quantity optimization. Background Art

[0002] The low-cost manufacturing advantage of the composite liquid molding process (LCM) has led to its increasing application. Due to the limitations of liquid molding technology, defects may exist inside the final fiber composite material, which will lead to a decrease in the overall performance of the product and leave safety hazards. By obtaining the flow field conditions in the composite liquid molding process in real time, the resin injection strategy can be optimized, the generation of internal defects can be reduced, and the quality of fiber composite products can be improved. However, most LCM methods are based on non-transparent molds, and optical technologies such as cameras cannot be used to directly obtain flow conditions. In addition, the interior of large three-dimensional components is too complex, and echo positioning methods such as ultrasound cannot effectively analyze their structures. It is impossible to deploy a large number of sensors in the mold. At the same time, the LCM process is complex and changeable. Under changing injection conditions / material properties, a single simulation is difficult to use to understand the flow field that changes over time. It is urgent to use a reconstruction algorithm to combine sensor data and simulation data sets to obtain complete dynamic flow field information in the mold to guide process adjustment and optimization.

[0003] Traditional composite liquid forming flow field reconstruction technology is mainly based on sensor arrays, or only restores the flow front. It is impossible to obtain the entire flow field. The sensor array solution is mainly optical fiber, thermocouple, pressure sensor array, etc., which often requires a large number of sensors to be laid inside the mold. The system is relatively simple, but it has a great impact on the overall structure of the mold and can only monitor the flow field in the layout area. On this basis, C. Fratta et al. of the Swiss Federal Institute of Technology proposed a flow channel-based monitoring method, which can restore the flow front with a small number of sensors, but the system is based on the analytical function of the pressure field under two-dimensional conditions, with weak generalization ability, and the restoration accuracy is not quantitatively described. In recent years, with the development of machine learning, such as ANN, CNN, PINN, etc., because of its powerful function fitting ability, it can mine useful information from a large amount of data and is suitable for processing fluid mechanics problems with complex nonlinearity, high dimensionality, and large data volume, but it requires a large amount of training data, has a large demand for computing resources, is sensitive to network structure and parameter adjustment, and the model training and tuning process may be more complicated.

[0004] The monitoring method system based on sensor array has a large number of sensors, which brings system complexity, has a great impact on the overall structure of the mold, and can only monitor the flow field in the layout area; the method based on machine learning requires a large amount of training data and computing resources, and the model training and tuning process is complicated. The monitoring method based on flow channel has a small number of sensors and a simple system, but it is only based on empirical formulas, with insufficient accuracy and cannot be generalized. Therefore, there is an urgent need for a method to solve the problem of high system complexity of sensor arrays or machine learning solutions, or low accuracy caused by flow channel solutions. Summary of the invention

[0005] In view of the above defects or improvement needs of the prior art, the present invention provides an LCM dynamic flow field reconstruction method and system based on sensor quantity optimization to solve the problem of high system complexity or low precision caused by too many or too few sensors.

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

[0007] Perform finite element meshing on the three-dimensional structural model of the composite part to be formed and initialize the physical parameters;

[0008] Solve the optimization model with the goal of maximizing the efficiency function during the injection process, obtain the optimal number of sensors, set different injection pressures and the measurement positions of each sensor, and perform composite material injection molding simulation. During the simulation process, measure and obtain the total flow field data matrix, the measurement matrix of the sensor position, and the flow field data obtained by the actual measurement of the sensor;

[0009] The flow field is reconstructed using the total flow field data matrix, the measurement matrix of the sensor position and the flow field data actually measured by the sensor.

[0010] Further preferably, the flow field reconstruction adopts an intrinsic orthogonal decomposition method based on missing data, and the flow field data is a liquid pressure value, a liquid flow rate or a capacitance value of a sensor in the flow field.

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

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

[0013] Among them, Φ ris the standard orthogonal 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. The flow field data is the flow field data at different positions actually measured by the sensor. It is a column vector formed by arranging the flow field data at different positions from small to large according to the grid number.

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

[0015] Perform singular value decomposition on the total flow field data matrix to obtain the flow field characteristic mode matrix;

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

[0017] Further preferably, the flow field characteristic mode is obtained by using a principal component analysis method.

[0018] Further preferably, the preset condition is:

[0019]

[0020] Among them, σ i is the ith singular value obtained by performing singular value decomposition on the total flow field data matrix, r is the number of the singular value, and n is the total number of singular values.

[0021] Further 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 is the βth unit matrix i List.

[0024] Further preferably, the number of the 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 number of sensors actually used for perception, η(L) is the system performance function, α represents the weight distribution of the system to complexity and reconstruction accuracy, α = 0 means that the system does not consider complexity, μ(L) is the system effective sensor resource function, Φ r is the standard orthogonal basis for reconstruction, C is the measurement matrix representing the sensor position, and f real is the flow field data obtained by the sensor, H 0 The required flow field reconstruction accuracy.

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

[0031] According to another aspect of the present invention, there is provided an LCM dynamic flow field reconstruction system based on sensor quantity optimization, the system comprising 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 meshing and initialization setting of physical parameters on the three-dimensional structure model of the composite material part to be formed;

[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 obtain the measurement matrix and flow field data of the sensor position;

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

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

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

[0038] 2. The present invention reconstructs the flow field by using the total flow field data matrix and the measurement matrix, and the flow field data is measured. Based on the fact that the entire flow field of liquid molding can be represented as a linear superposition of characteristic modes (standard orthogonal basis), and the characteristic modes cover the entire flow field information, the reconstruction value at the sensor point is made close to the measured value through the linear combination of the standard orthogonal basis, and the reconstruction coefficient is calculated, so that the flow field area that has not been measured can also be accurately reconstructed, thereby improving the accuracy and integrity of the flow field reconstruction in the process of composite material liquid molding.

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

[0040] 4. The present invention can reconstruct any field within a given pressure range under actual working conditions of injection pressure fluctuations, broadening the application scenarios and stability of the algorithm without the need for repeated simulation in the actual process;

[0041] 5. The present invention helps to improve the quality stability and consistency of composite products, promote the development and application of composite liquid molding controlled forming technology, and the reconstructed field can be used as the control target of the control system and provide real-time feedback on the flow conditions in the mold, which helps to achieve closed-loop and intelligent control of the molding. The results show that the algorithm has the advantages of high prediction accuracy, strong stability and low dependence on the amount of database data. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 is a flow chart of a LCM dynamic flow field reconstruction method based on sensor quantity optimization constructed according to a preferred embodiment of the present invention;

[0043] Figure 2 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 is a schematic diagram of a total flow field data matrix constructed according to a preferred embodiment of the present invention;

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

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

[0047] 1- glue port, 2- flow guide net, 3- vent, 4- fiber cloth, 5- flow channel. DETAILED DESCRIPTION

[0048] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present 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 in the figure, a LCM dynamic flow field reconstruction method based on sensor number optimization is presented. According to the actual process, the system complexity and flow field reconstruction accuracy are comprehensively considered, the optimal number of sensors is selected, and the GAPPY POD algorithm is used to reconstruct the flow field with missing data, and the complete LCM flow field is visualized in real time. This method promotes the controllability and intelligence of composite liquid molding. The method includes the following steps:

[0050] S1 Figure 2 As shown, a three-dimensional model is performed on the composite material component to be formed to obtain a three-dimensional structural model, and then a mesh is divided. It is best to use meshes with exactly the same size and shape (volume) to divide the mesh into meshes for the glue port 1, the guide net 2, the vent 3, the fiber cloth 4, the flow channel, etc.

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

[0052] S2 takes k different injection pressures and simulates each case once, for a total of k groups of simulations. Set the data output time step, for example, output data every 10s (simulation time scale, not real time). After the calculation is completed, the pressure / flow rate / liquid content of each grid and the corresponding grid number are obtained.

[0053] The exported data are combined into the total flow field data matrix F∈R n*k. Specific arrangement method: If the total simulation time is 4000s, the output time step in the first 2000s is 50s, and the output time step in the last 2000s is 100s, then there are 2000 / 50+2000 / 100=60 sets of flow field data f50, f1000, f150,...f3800, f3900, f4000 in a single simulation, and each set of data contains the pressure / data of all grids (for example, if the number of grids is 10,000, then these 60 sets of data are arranged in a vertical column in the time sequence of 0-4000s, n=60*10000=600000). Then arrange the k sets of data (f_p1-f_pk) under different injection pressures horizontally to form a matrix F. An example is as follows: Record the flow field data of injection pressure p1 at the 50th second of the simulation time as f50_p1∈R n , then the total matrix is ​​arranged as follows Figure 3 shown.

[0054]

[0055] Use POD to find a set of optimal standard orthogonal bases Φ so that the flow field data x∈R n The projections on this basis decrease rapidly in sequence, intercepting the first r-order modes with higher energy Φ r ∈R n*r (Generally, take the r terms whose sum of the eigenvalues ​​corresponding to the mode is greater than 99% of the sum of the total eigenvalues), as shown in the following formula. r ∈R n*r Expand (reconstruction coefficient s GAPPY ∈R r ) to obtain an approximate description of the high-order data.

[0056] x=Φ r s GAPPY

[0057] Due to FF T The eigenvector of the matrix is ​​the left singular vector of the singular value decomposition of the F matrix. By performing singular value decomposition (SVD) on the total flow field data matrix F, the total standard orthogonal basis Φ, Φ r ∈R n×r are the first r columns of the total orthonormal basis Φ. In general, the dimension n of the F matrix is ​​much larger than k.

[0058] Perform a reduced singular value decomposition (SVD) on the F matrix to simplify the calculation. The result of the reduced singular value decomposition (SVD) is recorded as F = Φ*S*V, Φ∈R n*k , S∈R k* k,V∈R k*kEach column of Φ and V is orthogonal, and the S matrix has non-zero elements only on the diagonal, which are the singular values ​​corresponding to each mode. The singular value is the square root of the corresponding eigenvalue. The column of Φ is the characteristic mode of the flow field. Generally speaking, it is believed that the sum of the eigenvalues ​​must exceed the sum of the total eigenvalues ​​(a total of n eigenvalues) by at least 99% to restore the flow field well. That is, the sum of the squares of the r singular values ​​is greater than 99% of the total sum of squares, and the constraints that r needs to meet are shown in the following formula.

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

[0060]

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

[0062] The calculation method of C is as follows: for the identity matrix I∈R n*n , which can be written as [e 1 , e 2 , ....e n ], where e i is the i-th column of the identity matrix, and n is the total number of grids. For q sensor positions β1, β 2 , ..., βq, β i is the grid number in the 3D grid corresponding to the sensor position in the mold. For example, n = 3000, β 1 = 1000, the sensor corresponds to the position of grid number 1000, e β1 is the 1000th column of the 3000*3000 identity matrix. β1 T , e β2 T ....e βq T ].

[0063] S4 GAPPY POD is used to fill in the missing data in the flow field when the number of sensors is small and the sensor data is sparse. The main goal of the GAPPY POD method is to minimize the error between the measured value and the reconstructed value at the sensor. The error function E is expressed as the sum of the squares of the difference between the reconstructed value and the measured value at q points, as shown in the following formula, f realis the flow field data of the sensor measurement point. reconstruct Reconstruct the flow field data for this point. reconstruct =CΦ r s GAPPY , Φ r ∈R n*r ,s GAPPY ∈R r is the reconstruction coefficient.

[0064]

[0065] Since the error function E is a convex function, the error function is applied to each reconstruction coefficient (s GAPPYi That is, the i-th reconstruction coefficient) finds the partial derivative, and when the partial derivatives are all 0, it is the point of minimum error

[0066]

[0067] Therefore, p equations can establish a linear equation system as above, solving s GAPPY , which is the reconstruction coefficient with the minimum error. reconstruct_all The reconstructed full flow field is shown as follows:

[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 the remaining missing sensor positions 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 in the mold is somewhat complex, and the number of sensors will affect the accuracy of reconstruction. In order to verify the accuracy of reconstruction, several additional sensors are generally arranged, and sensors are also pre-installed in the mold. Therefore, the total number of sensors N is generally greater than the number of sensors actually used for perception L. The algorithm for the optimal number of sensors based on the maximum efficiency of the system is given as follows:

[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 weight distribution of the system to complexity and reconstruction accuracy. The optimization goal is to achieve the optimal flow field reconstruction accuracy when the flow field reconstruction accuracy is greater than the preset threshold H. 0 Under the constraint condition (for example, 95%), maximize the η(L) function as shown below.

[0076]

[0077] η(L)=αμ(L)+(1-α)ξ(L)

[0078]

[0079]

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

[0081] Therefore, the discussion is as follows:

[0082] Case 1: α = 0, which is equivalent to not considering the system complexity. Since the working noise is very small, ξ(L) increases monotonically, and the number of sensors can be calculated based on ξ(L) ≥ H 0 The conditions are determined. This situation is ideal and rarely seen in actual processes. r and C is a function of L.

[0083] Case 2: α≠0, the optimal number of sensors is changed to In system design, both system performance and complexity are taken into consideration, and an effective compromise is made between the two.

[0084] like Figure 4 As shown in the figure, the non-zero elements in the measurement matrix C correspond to the actual position of the sensor in the three-dimensional component. GAPPY Linearly combine the basis vectors Φ to make the flow field pressure value at the sensor point as close as possible to the measured pressure value f real , and finally visualize the three-dimensional flow field.

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

[0086]

[0087] In the embodiment of the present invention, five groups of different injection pressure flow fields P=1 0 5 Pa, 1.1×10 5 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 reconstructed target field. The molded part is a thin-walled square composite part with two square holes. The error of single sensor point reconstruction of the flow field calculated by MATLAB is 1.87%, which proves that the reconstruction effect is good. The error does not change much when the number of sensors changes, and is less than 3%. Import data into the visualization program and observe the dynamic reconstruction effect. The trend is consistent with the original flow field. The optimal number of sensors can be obtained by maximizing the system efficiency function η(L)=αμ(L)+(1-α)ξ(L) in the interval [1, N], where α is taken according to the requirements.

[0088] It will be easily understood by those skilled in the art that the above description is only 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 in the protection scope of the present invention.

Claims

1. A LCM dynamic flow field reconstruction method based on sensor number optimization, characterized in that: The method comprises the following steps: Perform finite element meshing on the three-dimensional structural model of the composite part to be formed and initialize the physical parameters; Solve the optimization model with the goal of maximizing the efficiency function during the injection process, obtain the optimal number of sensors, set different injection pressures and the measurement positions of each sensor, and perform composite material injection molding simulation. During the simulation process, measure and obtain the total flow field data matrix, the measurement matrix of the sensor position, and the flow field data obtained by the actual measurement of the sensor; The flow field is reconstructed using the total flow field data matrix, the measurement matrix of the sensor position and the flow field data actually measured by the sensor.

2. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 1, characterized in that: The flow field reconstruction adopts an intrinsic orthogonal decomposition method based on missing data, and the flow field data is a liquid pressure value, a liquid flow rate or a capacitance value of a sensor in the flow field.

3. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 2, characterized in that: The formula for flow field reconstruction is as follows: f reconstruct_all =Φ r [(CΦ r ) T CΦ r ] -1 (CΦ r ) T Cf. real Among them, Φ r is the standard orthogonal 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. The flow field data is the flow field data at different positions actually measured by the sensor. It is a column vector formed by arranging the flow field data at different positions from small to large according to the grid number.

4. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 1, characterized in that: The standard orthogonal basis of the total flow field data matrix is ​​obtained in the following manner: Perform singular value decomposition on the total flow field data matrix to obtain the flow field characteristic mode matrix; The matrix formed by the first r columns of the flow field characteristic mode matrix that meet the preset conditions is used as the standard orthogonal basis of the flow field.

5. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 4, characterized in that: The flow field characteristic mode is obtained by using a principal component analysis method.

6. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 4 or 5, characterized in that: The preset conditions are: Among them, σ i is the ith singular value obtained by performing singular value decomposition on the total flow field data matrix, r is the number of the singular value, and n is the total number of singular values.

7. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 1 or 2, characterized in that: The measurement matrix is ​​calculated in the following way: C=[e β1 T ,And β2 T ,...And βi T ....,And βq T ] Where C is the measurement matrix, e βi is the βth unit matrix i List.

8. The LCM dynamic flow field reconstruction method based on sensor quantity optimization according to claim 1 or 2, characterized in that: The number of sensors is calculated according to the following optimization model: η(L)=αμ(L)+(1-α)ξ(L) Where N is the total number of sensors in the system, L is the number of sensors actually used for perception, η(L) is the system performance function, α represents the weight distribution of the system to complexity and reconstruction accuracy, α = 0 means that the system does not consider complexity, μ(L) is the system effective sensor resource function, Φ r is the standard orthogonal basis for reconstruction, C is the measurement matrix representing the sensor position, and f real is the flow field data obtained by sensor measurement, and H0 is the required flow field reconstruction accuracy.

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

10. A LCM dynamic flow field reconstruction system based on sensor quantity optimization, characterized in that: The system includes a model building module, a simulation module, a sensor measurement module and a flow field reconstruction module, wherein: The model building module is used to perform finite element meshing and initialization setting of physical parameters on the three-dimensional structure model of the composite material part to be formed; 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 obtain the measurement matrix and flow field data of the sensor position; The flow field reconstruction module is used to reconstruct the flow field using the total flow field data matrix, the measurement matrix of the sensor position and the flow field data obtained by the sensor measurement.

Images