Mechanical response field reconstruction method based on multi-source data multilayer fusion

Abstract

The invention provides a mechanical response field reconstruction method based on multi-source data multilayer fusion, and relates to the technical field of modern industry and engineering, and the method comprises the steps: S1, obtaining multi-source data of a mechanical response field; wherein the multi-source data comprises local high-precision strain field data, global finite element field data and high-precision strain gauge measurement data; performing coordinate transformation on the multi-source data to obtain a unified data coordinate; based on the unified data coordinates, performing first-level data fusion on the local high-precision strain field data and the global finite element field data to obtain a first-level fusion field; and performing secondary data fusion on the first-level fusion field and high-precision strain gauge measurement data, performing analysis by using a position prediction model to obtain a second-level fusion field, and completing reconstruction of the mechanical response field. The problems of how to accurately fuse multi-type data and how to improve the accuracy and reliability of large-scale structure test monitoring are solved.

Description

Technical Field

[0001] This specification relates to the fields of modern industry and engineering technology, and in particular to a method for reconstructing mechanical response fields based on multi-source data multi-layer fusion. Background Technology

[0002] In modern industry and engineering, accurate assessment of structural safety and performance is crucial. Especially in aerospace, weapons and ammunition manufacturing, and heavy industry, large structures often encounter large deformations and complex mechanical response field distributions during service. These issues are closely related to the structure's stability and load-bearing capacity. Traditional testing and monitoring methods, such as finite element analysis, sensors, and DIC measurements, while providing some information on the structure's mechanical response, each have their limitations.

[0003] Finite element method (FEM) relies on simplified assumptions about actual working conditions and may not be able to fully capture the complex mechanical response field under actual loading conditions. Sensor measurements, on the other hand, are limited by the number and location of measurement points, making it difficult to comprehensively cover the entire structure, especially in areas of large deformation. Digital image correlation (DIC) technology, as a non-contact measurement method, can overcome these limitations to some extent, providing full-field displacement and strain data. However, DIC technology still faces challenges in terms of measurement accuracy, field of view, and environmental adaptability. Furthermore, the acquisition and processing of DIC data requires sophisticated hardware and algorithms, and its performance is affected by data loss or occlusion. Therefore, how to effectively integrate finite element method, DIC, and strain gauge data to achieve high-precision reconstruction of the mechanical response field of large thin-walled structures has become a pressing technical challenge.

[0004] The development of response field reconstruction methods offers a new approach to solving this problem. Response field reconstruction refers to a virtual digital copy of a physical entity that can reflect its state and performance in real time. By constructing a response field reconstruction model, multi-source data can be integrated to achieve real-time monitoring and prediction of structural health. Although response field reconstruction technology shows great potential, accurately fusing multiple types of data, especially in the case of microstructures and complex mechanical response fields, remains a technical challenge in practical applications. Summary of the Invention

[0005] In view of the above-mentioned shortcomings in the prior art, the present invention provides a mechanical response field reconstruction method based on multi-source data multi-layer fusion, which solves the problem of how to accurately fuse multiple types of data and improve the accuracy and reliability of large structure testing and monitoring.

[0006] To achieve the aforementioned objectives, the technical solution adopted by this invention is: a method for reconstructing a mechanical response field based on multi-source data multi-layer fusion, comprising:

[0007] S1: Acquire multi-source data of the mechanical response field; where multi-source data includes local high-precision strain field data, global finite element field data, and high-precision strain gauge measurement data;

[0008] S2: Perform coordinate transformation on multi-source data to obtain unified data coordinates;

[0009] S3: Based on unified data coordinates, first-level data fusion is performed on local high-precision strain field data and global finite element field data to obtain the first-level fused field;

[0010] S4: The first-level fused field is fused with high-precision strain gauge measurement data in a second-level data fusion process. The resulting data is then analyzed using a position prediction model to obtain the second-level fused field, thus reconstructing the mechanical response field. The position prediction model is obtained through training.

[0011] Further, S1 includes:

[0012] Using measuring equipment, the initial geometric defects of test pieces of different sizes were collected. The measured geometric defects were then introduced into the finite element analysis model to obtain a finite element analysis model of the thin-walled cylindrical shell structure that takes into account the geometric defects.

[0013] By analyzing the finite element analysis model of a thin-walled cylindrical shell structure considering geometric defects, finite element results including the structural strain field and displacement field are obtained.

[0014] By calculating the finite element results, the engineering strain and element coordinates are obtained;

[0015] Based on engineering strain and element coordinates, data is acquired using strain gauges to obtain multi-source data.

[0016] Further, S2 includes:

[0017] Under the global coordinate system O-XYZ, the local coordinate systems of the local high-precision strain field data, the global finite element field data, and the high-precision strain gauge measurement data are O1-X1Y1Z1, O2-X2Y2Z2, and O3-X3Y3Z3, respectively. By establishing coordinate transformation relationships, coordinate transformation is performed to obtain unified data coordinates.

[0018] Further, S3 includes:

[0019] A proxy model based on finite element nodal coordinates and strain values ​​is constructed using radial basis functions;

[0020] Using a surrogate model, the strain values ​​at the coordinates of local high-precision strain field measurement points in the global finite element field data are predicted, and the strain value prediction results are obtained.

[0021] Based on the strain value prediction results and local high-precision strain field data, the additive scaling factor at the measuring point is obtained through calculation.

[0022] Based on the additive scaling factor, first-level data fusion is performed using radial basis functions and finite element field functions to obtain the first-level fused field.

[0023] Furthermore, the expression for the first-level fusion field is:

[0024] ;

[0025] ;

[0026] in, This represents the first-level fusion field. Represents unified data coordinates. Indicates the additive scaling factor. This represents the proxy model. This indicates the coordinates of the finite element field at the DIC measurement point. This represents the actual measured DIC strain value.

[0027] Further, S4 includes:

[0028] Based on the first-level fusion field, the strain value at the coordinates of the strain gauge measurement point is predicted to obtain the fusion field prediction value;

[0029] Using the fused field predictions and high-precision strain gauge measurement data, additive bridge function reference factors and multiplicative bridge function reference factors are constructed respectively;

[0030] Based on the reference factors of the additive bridge function and the multiplicative bridge function, a hybrid bridge function is obtained through radial basis functions and linear combination;

[0031] By using a location prediction model to analyze the hybrid bridge function, the second-level fusion field is obtained, thus completing the reconstruction of the mechanical response field.

[0032] Furthermore, the expression for the hybrid bridge function is:

[0033] ;

[0034] ;

[0035] ;

[0036] in, Represents the hybrid bridge function. Represents unified data coordinates. Indicates the fusion weight coefficient. This represents the additive reference factor based on the strain gauge measurement point. This represents the first-level fusion field. This represents the multiplication reference factor based on the strain gauge measurement point. This indicates the coordinates at the strain gauge measurement point. This represents the actual strain gauge measurement value.

[0037] The beneficial effects of this invention are as follows: This invention provides a mechanical response field reconstruction method based on multi-source data multi-layer fusion, aiming to improve the testing and monitoring accuracy of fine structures under complex working conditions, and is particularly suitable for the reconstruction problem of complex mechanical response field distributions such as weakening grooves. The method establishes a multi-level data fusion model by synergistically fusing finite element analysis, digital image correlation technology, and strain gauge measurement data, thereby reconstructing the mechanical response field of the structure with high precision, and ultimately realizing a complete and mature software system. (1) It overcomes the difficulty of detecting microstructures and achieves accurate and complete reconstruction of the response field of microstructures, especially at the weakening groove; (2) It achieves temporal and spatial unification of multiple types of data, thereby enabling real-time monitoring of the structure; (3) It adopts a neural network to dynamically optimize the fusion ratio of the addition and multiplication bridge functions, and can adaptively adjust the fusion strategy according to structural characteristics and load conditions; (4) It adopts a multi-level fusion method to utilize the advantages of multiple types of data, thereby ensuring accurate prediction of the response field results; (5) It achieves collaborative fusion of multi-source heterogeneous data from finite element, DIC to strain gauge, forming a complete software system that can cover the entire process from data acquisition, preprocessing to full-field reconstruction and verification; (6) Through a multi-level fusion structure and cross-validation mechanism, the system has strong fault tolerance for partial sensor failure or image quality degradation. It ensures the accuracy of the strain reconstruction field even when there is defocusing in some areas of DIC or local debonding of the strain gauge. Attached Figure Description

[0038] This specification will be further described by way of exemplary embodiments, which will be described in detail with reference to the accompanying drawings. These embodiments are not limiting; in these embodiments, the same reference numerals denote the same structures, wherein:

[0039] Figure 1 This is an exemplary flowchart illustrating a mechanical response field reconstruction method based on multi-source data multi-layer fusion, according to some embodiments of this specification. Detailed Implementation

[0040] The specific embodiments of the present invention are described below to enable those skilled in the art to understand the present invention. However, it should be understood that the present invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the present invention as defined and determined by the appended claims. All inventions utilizing the concept of the present invention are protected.

[0041] Example

[0042] Figure 1 This is an exemplary flowchart illustrating a mechanical response field reconstruction method based on multi-source data multi-layer fusion, according to some embodiments of this specification. Figure 1 As shown, the process includes the following steps. In some embodiments, the process may be executed by a processor.

[0043] S1: Acquire multi-source data of the mechanical response field; the multi-source data includes local high-precision strain field data, global finite element field data, and high-precision strain gauge measurement data.

[0044] In some embodiments, the processor can employ high-precision measurement equipment such as a 360-degree ring-shaped DIC array camera and a SCAN laser scanner to achieve rapid acquisition of initial geometric defects in test pieces of different sizes. The shape and amplitude of the measured geometric defects are approximated by Fourier series. By using mesh node adjustment, the measured geometric defects are introduced into a perfect finite element analysis model, establishing a finite element analysis model of a thin-walled cylindrical shell structure considering geometric defects, and conducting numerous related verification experiments.

[0045] In some embodiments, the processor can obtain structural strain field, displacement field, and other result files through finite element modeling and analysis. Subsequently, based on the finite element result files, all element numbers and strains under different loads are extracted. The element strain calculated by the finite element method is the true strain, obtained based on the length integration after deformation; because it is expressed in exponential form, it is also called exponential strain. In actual experiments, the strain measured by strain gauges does not consider the deformation process and is obtained based on the length change before and after deformation; this is called engineering strain. Under small structural deformation, logarithmic strain and engineering strain are almost equal. When the structural deformation is large, the difference between logarithmic strain and engineering strain is significant. Converting the finite element logarithmic strain to engineering strain facilitates comparison between experimental measurements and finite element strain. Furthermore, a geometric model file containing element-node correspondences and node coordinates is obtained. To simplify the calculation process, the average value of all node coordinates of an element is taken as the equivalent coordinates of that element. Assuming the element has... Each node is used to calculate the element number and element coordinates of all elements. Finally, the coordinates and strains of all finite element elements are obtained by matching the element numbers. Digital image data is acquired: high-contrast speckle patterns are prepared on the structural surface, and image sequences during the loading process are captured using a high-speed camera. Displacement and deformation data of the structural surface are obtained through image processing software analysis. Strain gauge data is measured: strain gauges are placed at key locations on the structure, and strain data are recorded in real time through a data acquisition system.

[0046] In some embodiments, the processor can employ measuring devices to collect initial geometric defects of test specimens of different sizes, introduce the measured geometric defects into the finite element analysis model, and obtain a finite element analysis model of the thin-walled cylindrical shell structure considering the geometric defects; by analyzing the finite element analysis model of the thin-walled cylindrical shell structure considering the geometric defects, finite element results containing the structural strain field and displacement field are obtained, namely, local high-precision strain field data and global finite element field data; by calculating the finite element results, engineering strain and element coordinates are obtained; based on the engineering strain and element coordinates, data is collected using strain gauges as high-precision strain gauge measurement data to obtain multi-source data.

[0047] In some embodiments, the expression for engineering strain is:

[0048] ;

[0049] in, Indicates engineering strain. It represents logarithmic strain.

[0050] In some embodiments, the expressions for all element coordinates and element strains in a finite element method are:

[0051] ;

[0052] in, , , This represents the coordinates of the i-th node. Indicates the number of unit nodes.

[0053] S2: Perform coordinate transformation on multi-source data to obtain unified data coordinates.

[0054] In some embodiments, the processor can operate within the global coordinate system O-XYZ, with the local coordinate systems for the finite element, strain gauge, and DIC data being O1-X1Y1Z1, O2-X2Y2Z2, and O3-X3Y3Z3, respectively. To enable comparative analysis and data fusion of multiple data types, the coordinates of the finite element, strain gauge, and DIC data must be unified within the same coordinate system O-XYZ. The finite element model coordinate system O1-X1Y1Z1 is fixed within the global coordinate system O-XYZ, and coordinate transformation relationships are established between the strain gauge coordinate system O2-X2Y2Z2, the DIC coordinate system O3-X3Y3Z3, and the finite element coordinate system O1-X1Y1Z1. Structurally, n marker points not on a straight line are selected, and their coordinates in the finite element, strain gauge, and DIC local coordinate systems are obtained. A coordinate transformation relationship (R1, t1) is established between the DIC coordinate system O3-X3Y3Z3 and the finite element coordinate system O1-X1Y1Z1, as well as a coordinate transformation relationship (R2, t2) between the finite element coordinate system and the strain gauge coordinate system. After establishing these two coordinate transformation relationships, both strain gauge and DIC data are unified into the finite element coordinate system, providing a unified set of multi-type data coordinates for multi-level digital twin field reconstruction.

[0055] In some embodiments, the processor can perform coordinate transformations in the global coordinate system O-XYZ, and the local coordinate systems of the local high-precision strain field data, the global finite element field data, and the high-precision strain gauge measurement data are O1-X1Y1Z1, O2-X2Y2Z2, and O3-X3Y3Z3, respectively. By establishing coordinate transformation relationships, a unified data coordinate system can be obtained.

[0056] S3: Based on unified data coordinates, perform first-level data fusion on local high-precision strain field data and global finite element field data to obtain the first-level fused field.

[0057] In some embodiments, the processor can construct a proxy model based on the coordinates of finite element nodes and strain values ​​using radial basis functions; using the proxy model, the strain values ​​at the coordinates of the measuring points in the local high-precision strain field are predicted based on the global finite element field data, and the strain value prediction results are obtained; based on the strain value prediction results and the local high-precision strain field data, the additive scaling factor at the measuring point is obtained by calculation; based on the additive scaling factor, the radial basis functions and finite element field functions are used to perform first-level data fusion to obtain the first-level fused field.

[0058] In some embodiments, the processor may employ radial basis functions to construct a model based on finite element node coordinates. With strain value proxy model This is used to describe the global finite element strain field; based on the surrogate model Predict the coordinates of the finite element field at the DIC measurement point. strain value at ; Based on finite element prediction of strain values ​​at DIC measurement points Compared with actual DIC strain measurement values Calculate the additive scaling factor at each DIC measurement point. Based on the additive scaling factor at each DIC measurement point and its coordinates Construct a global addition bridge function using radial basis functions. Based on the additive bridge function and the finite element field function, a first-level fusion field is constructed. .

[0059] In some embodiments, the expression for the first-level fusion field is:

[0060] ;

[0061] ;

[0062] in, This represents the first-level fusion field. Represents unified data coordinates. Indicates the additive scaling factor. This represents the proxy model. This indicates the coordinates of the finite element field at the DIC measurement point. This represents the actual measured DIC strain value.

[0063] S4: The first-level fusion field is fused with the high-precision strain gauge measurement data in a second-level data fusion process. The location prediction model is then used for analysis to obtain the second-level fusion field, thus completing the reconstruction of the mechanical response field. The location prediction model is obtained through training.

[0064] In some embodiments, the processor may be based on a first-level fusion field Predict the coordinates of the strain gauge measurement points strain value at Predicted values ​​of the fused field at strain gauge measurement points Compared with actual strain gauge measurements Reference factors for the additive bridge function and the multiplicative bridge function are constructed respectively; the additive reference factor is based on the strain gauge measurement point. With coordinates Construct a global addition bridge function using radial basis functions. Based on the multiplication reference factor at the strain gauge measurement point With coordinates Construct a global multiplication bridge function using radial basis functions. The hybrid bridge function is a linear combination of the addition bridge function and the multiplication bridge function.

[0065] In some embodiments, the processor may include, in S4:

[0066] Based on the first-level fusion field, the strain value at the coordinates of the strain gauge measurement point is predicted to obtain the fusion field prediction value;

[0067] Using the fused field predictions and high-precision strain gauge measurement data, additive bridge function reference factors and multiplicative bridge function reference factors are constructed respectively;

[0068] Based on the reference factors of the additive bridge function and the multiplicative bridge function, a hybrid bridge function is obtained through radial basis functions and linear combination;

[0069] By using a location prediction model to analyze the hybrid bridge function, the second-level fusion field is obtained, thus completing the reconstruction of the mechanical response field.

[0070] In some embodiments, the expression for the hybrid bridge function is:

[0071] ;

[0072] ;

[0073] ;

[0074] in, Represents the hybrid bridge function. Represents unified data coordinates. Indicates the fusion weight coefficient. This represents the additive reference factor based on the strain gauge measurement point. This represents the first-level fusion field. This represents the multiplication reference factor based on the strain gauge measurement point. This indicates the coordinates at the strain gauge measurement point. This represents the actual strain gauge measurement value.

[0075] In some embodiments, the input features of the location prediction model include location coordinates. First-level fusion field gradient Local strain fluctuation variance And payload type encoding; output features include the fusion weight coefficients at the corresponding positions. The location prediction model uses a three-layer feedforward neural network with ReLU activation function in the hidden layer and Sigmoid activation function in the output layer to ensure that the output range is [0,1].

[0076] In some embodiments, the training objective of the location prediction model is to minimize the reconstruction error at the strain gauge measurement points, and supervised training is performed using the mean square error loss function.

[0077] In some embodiments, the processor can calculate the final multi-level digital twin field strain values ​​based on the hybrid bridge function. .

[0078] In some embodiments, the processor may use average error (AvgErr) and maximum error (MaxErr) as evaluation metrics to evaluate the accuracy of strain field reconstruction. The closer the average error and maximum error are to 0, the higher the accuracy of strain field reconstruction.

[0079] In some embodiments, the expressions for the average error and the maximum error are:

[0080] ;

[0081] ;

[0082] in, Indicates the number of sensor inspection points. and These represent the actual strain values ​​at the test points. and predicted strain values .

[0083] Based on whether or not sensors are involved in strain field reconstruction, the true strain value and predicted strain values The acquisition methods fall into two categories. The first category addresses error assessment for sensorless strain field reconstruction methods, such as finite element fields based on finite element analysis, using the strain field on the target area of ​​the test specimen. strain value of each sensor (i=1, 2, 3, …, -1, (The value is the true value; calculate the finite element strain value of the finite element field at the sensor location.) (i=1, 2, 3, …, -1, The first category uses the predicted value. The second category, for strain field reconstruction methods involving sensors, such as sensor interpolation field reconstruction methods, employs leave-one-out verification to evaluate the strain field error. strain value of each sensor (i=1, 2, 3, …, -1, ) represents the actual value, and is used sequentially. One sensor is used to build the strain field model, and one sensor is reserved for error evaluation. This process is repeated nc times for a total of strain field model construction and error evaluation, yielding the results... Predicted strain values ​​at each sensor location (i=1, 2, 3, …, -1, ).

[0084] In some embodiments, the present invention achieves high-precision reconstruction of the mechanical response field of large thin-walled structures, significantly improving the accuracy and reliability of testing and monitoring, and finally obtaining quantitative results, which has important engineering application value.

[0085] In some embodiments of this specification, a method for reconstructing the mechanical response field based on multi-source data multi-layer fusion is provided, aiming to improve the testing and monitoring accuracy of fine structures under complex working conditions, and is particularly suitable for reconstructing complex mechanical response field distributions such as attenuation grooves. The method establishes a multi-level data fusion model by synergistically fusing finite element analysis, digital image correlation technology, and strain gauge measurement data, thereby reconstructing the mechanical response field of the structure with high precision, and ultimately realizing a fully functional and mature software system. (1) It overcomes the difficulty of detecting microstructures and achieves accurate and complete reconstruction of the response field of microstructures, especially at the weakening groove; (2) It achieves temporal and spatial unification of multiple types of data, thereby enabling real-time monitoring of the structure; (3) It adopts a neural network to dynamically optimize the fusion ratio of the addition and multiplication bridge functions, and can adaptively adjust the fusion strategy according to structural characteristics and load conditions; (4) It adopts a multi-level fusion method to utilize the advantages of multiple types of data, thereby ensuring accurate prediction of the response field results; (5) It achieves collaborative fusion of multi-source heterogeneous data from finite element, DIC to strain gauge, forming a complete software system that can cover the entire process from data acquisition, preprocessing to full-field reconstruction and verification; (6) Through a multi-level fusion structure and cross-validation mechanism, the system has strong fault tolerance for partial sensor failure or image quality degradation. It ensures the accuracy of the strain reconstruction field even when there is defocusing in some areas of DIC or local debonding of the strain gauge.

Claims

1. A method for reconstructing a mechanical response field based on multi-source data and multi-layer fusion, characterized in that, include: S1: Acquire multi-source data of the mechanical response field; where multi-source data includes local high-precision strain field data, global finite element field data, and high-precision strain gauge measurement data; S2: Perform coordinate transformation on multi-source data to obtain unified data coordinates; S3: Based on unified data coordinates, first-level data fusion is performed on local high-precision strain field data and global finite element field data to obtain the first-level fused field; S4: The first-level fusion field is fused with the high-precision strain gauge measurement data in a second-level data fusion process. The location prediction model is then used for analysis to obtain the second-level fusion field, thus completing the reconstruction of the mechanical response field. The location prediction model is obtained through training.

2. The mechanical response field reconstruction method based on multi-source data multi-layer fusion according to claim 1, characterized in that, S1 includes: Using measuring equipment, the initial geometric defects of test pieces of different sizes were collected. The measured geometric defects were then introduced into the finite element analysis model to obtain a finite element analysis model of the thin-walled cylindrical shell structure that takes into account the geometric defects. By analyzing the finite element analysis model of a thin-walled cylindrical shell structure considering geometric defects, finite element results including the structural strain field and displacement field are obtained. By calculating the finite element results, the engineering strain and element coordinates are obtained; Based on engineering strain and element coordinates, data is acquired using strain gauges to obtain multi-source data.

3. The mechanical response field reconstruction method based on multi-source data multi-layer fusion according to claim 1, characterized in that, S2 includes: Under the global coordinate system O-XYZ, the local coordinate systems of the local high-precision strain field data, the global finite element field data, and the high-precision strain gauge measurement data are O1-X1Y1Z1, O2-X2Y2Z2, and O3-X3Y3Z3, respectively. By establishing coordinate transformation relationships, coordinate transformation is performed to obtain unified data coordinates.

4. The mechanical response field reconstruction method based on multi-source data multi-layer fusion according to claim 1, characterized in that, S3 includes: A proxy model based on finite element nodal coordinates and strain values ​​is constructed using radial basis functions; Using a surrogate model, the strain values ​​at the coordinates of local high-precision strain field measurement points in the global finite element field data are predicted, and the strain value prediction results are obtained. Based on the strain value prediction results and local high-precision strain field data, the additive scaling factor at the measuring point is obtained through calculation. Based on the additive scaling factor, first-level data fusion is performed using radial basis functions and finite element field functions to obtain the first-level fused field.

5. The mechanical response field reconstruction method based on multi-source data multi-layer fusion according to claim 4, characterized in that, The expression for the first-level fusion field is: ； ； in, This represents the first-level fusion field. Represents unified data coordinates. Indicates the additive scaling factor. This represents the proxy model. This indicates the coordinates of the finite element field at the DIC measurement point. This represents the actual measured DIC strain value.

6. The mechanical response field reconstruction method based on multi-source data multi-layer fusion according to claim 1, characterized in that, S4 includes: Based on the first-level fusion field, the strain value at the coordinates of the strain gauge measurement point is predicted to obtain the fusion field prediction value; Using the fused field predictions and high-precision strain gauge measurement data, additive bridge function reference factors and multiplicative bridge function reference factors are constructed respectively; Based on the reference factors of the additive bridge function and the multiplicative bridge function, a hybrid bridge function is obtained through radial basis functions and linear combination; By using a location prediction model to analyze the hybrid bridge function, the second-level fusion field is obtained, thus completing the reconstruction of the mechanical response field.

7. The mechanical response field reconstruction method based on multi-source data multi-layer fusion according to claim 6, characterized in that, The expression for the hybrid bridge function is: ； ； ； in, Represents the hybrid bridge function. Represents unified data coordinates. Indicates the fusion weight coefficient. This represents the additive reference factor based on the strain gauge measurement point. This represents the first-level fusion field. This represents the multiplication reference factor based on the strain gauge measurement point. This indicates the coordinates at the strain gauge measurement point. This represents the actual strain gauge measurement value.

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