A method for determining similarity between a measured stress tensor and a predicted stress tensor and related devices

Abstract

This application discloses a method and related equipment for determining the similarity between measured and predicted stress tensors. The method includes: acquiring the measured stress tensor and predicted stress tensor of a target area, wherein the predicted stress tensor is obtained based on the results of numerical back analysis of the geostress field; calculating a first Euclidean distance based on the measured and predicted stress tensors; calculating a second Euclidean distance between the measured stress tensor and the origin; calculating the Euclidean distance similarity between the measured points based on the first and second Euclidean distances; and determining the similarity level of the numerical back analysis of the geostress field based on the Euclidean distance similarity. This method eliminates the multi-index problem existing in the two current non-tensor methods, resulting in more accurate similarity analysis results.

Description

Technical Field

[0001] This specification relates to the field of numerical inverse analysis of geostress fields. More specifically, this application relates to a method and related equipment for determining the similarity between measured and predicted stress tensors. Background Technology

[0002] In-situ stress, as a crucial parameter in rock engineering, determines the mechanical behavior of rock masses. Therefore, understanding the original stress distribution in the engineering rock mass through in-situ stress measurement technology is essential before excavating large, deep underground structures. However, due to complex geological conditions and high testing costs, in-situ stress measurement data is limited and struggles to reflect the macroscopic distribution of the initial stress field in the engineering area. To address the difficulties of limited and unrepresentative stress measurement data, three-dimensional inverse analysis of the initial stress field based on numerical simulation has gradually developed. As a point-to-field inverse analysis process, a key aspect is evaluating the similarity between the measured stress tensor at the measurement point and the inverse analysis-predicted stress tensor, thereby preliminarily determining the accuracy of the inverse analysis-predicted stress field.

[0003] In existing numerical inverse analysis of geostress fields and even rock mechanics research, the second-order stress tensor is usually decomposed into tensor components or principal stress values ​​and directions for characteristic statistics and similarity evaluation. Among these, principal stress indices are the most widely used due to their physical significance and close connection to practical engineering. However, both of these non-tensor indices suffer from an excessive number of indices. Furthermore, the decomposed elements are independent of each other, meaning their correlation is ignored. This can lead to contradictions among the indices, ultimately preventing accurate and quantitative similarity evaluation results from being obtained. Therefore, how to solve the problems of multiple indices and inconsistencies in existing non-tensor evaluation methods remains a problem worth addressing. Summary of the Invention

[0004] The summary section introduces a series of simplified concepts, which will be further explained in detail in the detailed description section. This summary section is not intended to limit the key and essential technical features of the claimed technical solution, nor is it intended to determine the scope of protection of the claimed technical solution.

[0005] Firstly, this application proposes a method for determining the similarity between measured and predicted stress tensors, the method comprising:

[0006] The measured stress tensor and the predicted stress tensor of the target area are obtained, wherein the predicted stress tensor is obtained based on the results of numerical back analysis of the geostress field.

[0007] The first Euclidean distance is calculated based on the measured stress tensor and the predicted stress tensor.

[0008] The Euclidean distance between the measured stress tensor and the origin is calculated as the second Euclidean distance;

[0009] Calculate the Euclidean distance similarity based on the first and second Euclidean distances mentioned above;

[0010] The similarity level of the numerical back analysis of the geostress field is determined based on the above Euclidean distance similarity.

[0011] Optionally, the Euclidean distance similarity is calculated based on the first and second Euclidean distances mentioned above, including:

[0012] The similarity is determined based on the ratio of the first Euclidean distance to the second Euclidean distance.

[0013] Optionally, determining the similarity based on the ratio of the first Euclidean distance to the second Euclidean distance includes:

[0014] The similarity evaluation index EDS is obtained according to the following formula:

[0015]

[0016] In the formula, d(S,S')=||S-S'|| F Let d(S,O) be the first Euclidean distance, then d(S,O) = ||S|| F This is the second Euclidean distance. Where S is the measured stress tensor at a certain measuring point, expressed as: S includes the stress component σ x ,σ y ,σ z ,τ xy ,τ xz and τ yz , τ xy =τ yx ,τ xz =τ zx ,τ yz =τ zy S' is the predicted stress tensor at the corresponding measuring point, expressed as... S' includes σ' x ,σ' y ,σ' z ,τ' xy ,τ' xz and τ' yz ,τ' xy =τ' yx ,τ' xz =τ' zx ,τ' yz =τ' zy .

[0017] Optionally, the above methods also include:

[0018] The stress tensor is decomposed into the magnitude and orientation of the principal stresses to obtain a second expression for the first Euclidean distance:

[0019]

[0020] Where σ1, σ2, and σ3 represent the maximum, intermediate, and minimum principal stresses, respectively. i ,m i ,n i These are the direction cosines of the angle between the new principal stress axis and the original principal stress axis.

[0021] Optionally, the similarity level for determining the numerical back-analysis of the geostress field based on the aforementioned Euclidean distance similarity includes:

[0022] Establish the correspondence between preset threshold intervals and similarity levels, principal stress values, and orientation errors;

[0023] Based on the aforementioned principal stress value and orientation error, the Euclidean distance similarity threshold for different similarity levels is calculated using the second expression formula described above.

[0024] The similarity level of the above geostress field numerical back-analysis prediction results is determined based on the above Euclidean distance similarity threshold and the preset similarity correspondence.

[0025] Optionally, a correspondence is constructed between a preset threshold range and similarity level, principal stress value, and orientation error, including:

[0026] Construct the correspondence between preset threshold ranges and similarity levels, principal stress values, and orientation errors, including:

[0027] Determine the error thresholds for principal stress values ​​and Euler angles of rotation about the principal stress axes;

[0028] The EDS threshold is calculated based on the above-mentioned quantity error threshold, the above-mentioned Euler angle error threshold, and the above-mentioned second expression formula;

[0029] Based on the above EDS thresholds, construct the correspondence between the threshold interval and the preset similarity level, principal stress value and orientation error.

[0030] Optionally, the aforementioned measurement error thresholds include a first measurement error threshold, a second measurement error threshold, and a third measurement error threshold. The first measurement error is determined by a first weighting coefficient and the maximum principal stress, the second measurement error is determined by a second weighting coefficient and the intermediate principal stress coefficient, and the third measurement error is determined by a third weighting coefficient and the minimum principal stress coefficient. The first weighting coefficient is less than the second weighting coefficient and the third weighting coefficient.

[0031] Secondly, this application also proposes a device for determining the similarity between measured and predicted stress tensors, comprising:

[0032] The acquisition unit is used to acquire the measured stress tensor and the predicted stress tensor of the target area, wherein the predicted stress tensor is obtained based on the results of numerical back analysis of the geostress field.

[0033] The first calculation unit is used to calculate the first Euclidean distance based on the above measured stress tensor and the above predicted stress tensor.

[0034] The second calculation unit is used to calculate the Euclidean distance between the measured stress tensor and the origin as the second Euclidean distance.

[0035] The third calculation unit is used to calculate the Euclidean distance similarity based on the first Euclidean distance and the second Euclidean distance mentioned above.

[0036] The defined unit is used to determine the similarity of the numerical back-analysis of the geostress field based on the aforementioned Euclidean distance similarity.

[0037] Thirdly, an electronic device includes: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program stored in the memory to implement the steps of the measured and predicted stress tensor similarity determination method as described in any of the first aspects above.

[0038] Fourthly, this application also proposes a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the method for determining the similarity between measured and predicted stress tensors of any of the above claims in the first aspect.

[0039] In summary, the method for determining the similarity between measured and predicted stress tensors in this application includes: acquiring the measured stress tensor and predicted stress tensor of the target area, wherein the predicted stress tensor is obtained based on the results of numerical back analysis of the geostress field; calculating a first Euclidean distance based on the measured stress tensor and the predicted stress tensor; calculating a second Euclidean distance between the measured stress tensor and the origin; calculating a similarity of the Euclidean distance based on the first and second Euclidean distances; and determining the similarity level of the numerical back analysis of the geostress field based on the Euclidean distance similarity. The method for determining the similarity between measured and predicted stress tensors proposed in this application eliminates the multi-index problem existing in the two existing non-tensor methods by obtaining the first Euclidean distance between the stress tensor and the predicted stress tensor, and obtaining the second Euclidean distance between the measured stress tensor and the origin, calculating the similarity of the Euclidean distance based on the first and second Euclidean distances, and evaluating the similarity of the numerical back analysis of the geostress field based on the Euclidean distance similarity. This results in a more accurate similarity analysis.

[0040] The method for determining the similarity between measured and predicted stress tensors proposed in this application, along with other advantages, objectives, and features of this application, will be partly apparent from the following description and partly understood by those skilled in the art through research and practice of this application. Attached Figure Description

[0041] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit this specification. Furthermore, the same reference numerals denote the same parts throughout the drawings. In the drawings:

[0042] Figure 1 A schematic flowchart of a method for determining the similarity between measured and predicted stress tensors provided in an embodiment of this application;

[0043] Figure 2 A schematic diagram illustrating the principle of numerical inverse analysis of geostress field provided in this application embodiment;

[0044] Figure 3 A schematic diagram of a stress tensor similarity index provided for an embodiment of this application;

[0045] Figure 4 A schematic diagram illustrating the principle of rotational sequence of principal stress axes and Euler angles provided for embodiments of this application;

[0046] Figure 5 A contour diagram of EDS and initial principal stress provided for an embodiment of this application;

[0047] Figure 6 Another contour diagram of EDS and initial principal stress provided for an embodiment of this application;

[0048] Figure 7 A further contour diagram of EDS and initial principal stress provided for an embodiment of this application;

[0049] Figure 8 An EDS contour map and a schematic diagram of principal stress magnitude error are provided for embodiments of this application;

[0050] Figure 9 Another EDS contour plot and schematic diagram of principal stress magnitude error provided for an embodiment of this application;

[0051] Figure 10 Another EDS contour plot and schematic diagram of principal stress magnitude error provided for embodiments of this application;

[0052] Figure 11 A contour diagram of EDS and Euler angles provided for embodiments of this application;

[0053] Figure 12 Another contour diagram of EDS and Euler angles provided for an embodiment of this application;

[0054] Figure 13 A contour diagram of the EDS and Euler angles provided for an embodiment of this application;

[0055] Figure 14 A schematic diagram illustrating the sensitivity of EDS to the error of principal stress value provided in an embodiment of this application;

[0056] Figure 15 A schematic diagram illustrating the sensitivity of an EDS to Euler angles, provided for an embodiment of this application;

[0057] Figure 16 A schematic diagram of a device for determining the similarity between measured and predicted stress tensors provided in an embodiment of this application;

[0058] Figure 17 This is a schematic diagram of an electronic device structure for determining the similarity between measured and predicted stress tensors, provided as an embodiment of this application. Detailed Implementation

[0059] The method for determining the similarity between measured and predicted stress tensors proposed in this application calculates the first Euclidean distance between the stress tensor and the predicted stress tensor, and the second Euclidean distance between the measured stress tensor and the origin. The similarity of the Euclidean distance is calculated using the first and second Euclidean distances. The similarity of the numerical back-analysis of the geostress field is evaluated based on the Euclidean distance similarity, thus eliminating the multi-index problem of the two existing non-tensor methods and resulting in more accurate similarity analysis results.

[0060] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus. The technical solutions of the embodiments of this application will now be clearly and completely described in conjunction with the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them.

[0061] The basic idea of ​​three-dimensional initial stress field numerical inverse analysis is to obtain the macroscopic stress field of the engineering area through numerical simulation and inverse analysis based on limited measured stress data. It is an inverse analysis process from point to field, such as... Figure 2 As shown, after obtaining the predicted stress field, evaluating the similarity between the measured stress tensor (S) and the predicted stress tensor (S') at the same measuring point is a crucial issue. Only when the two are relatively close can the stress field obtained from the inverse analysis be preliminarily considered correct. The measured stress tensor and the predicted stress tensor at the i-th measuring point are expressed as:

[0062]

[0063] In the formula, σ and τ represent normal stress and shear stress, respectively.

[0064] In existing numerical inverse analysis of geostress fields, the similarity evaluation of stress states at measuring points mainly relies on two non-tensor methods: the scalar approach (based on tensor component indices) and the scalar vector approach (based on principal stress indices). The scalar approach evaluates stress state similarity using stress component indices, comparing and evaluating the six components of the stress tensor separately. For ease of representation, a semi-vector function vech(·) is introduced for the stress tensor S, yielding a vector...

[0065] s = vech(S) = [σ x σ y σ z τ xy τ yz τ xz ] T (2)

[0066] It contains 6 stress components. Therefore, there will also be 6 stress tensor similarity evaluation indices based on the scalar method:

[0067]

[0068] In the formula, sim(·) represents the similarity, and its unit is Pa; s i s represents the i-th measurement point; i This is the measured value; s' i These are predicted values.

[0069] The scalar / vector approach evaluates stresses based on principal stress indices. This method decomposes the second-order stress tensor into eigenvalues ​​(principal stress values) and eigenvectors (principal stress directions), and then compares and evaluates them separately. Similarly, the semi-vectorization function vech(·) is introduced here to obtain the vector:

[0070]

[0071] It contains nine elements, including the principal stress values ​​and directions. In the formula, σ represents the principal stress value; α represents the principal stress azimuth angle; β represents the principal stress tilt angle; and 1, 2, and 3 represent the maximum, intermediate, and minimum values, respectively. Therefore, there will be nine stress tensor similarity evaluation indices based on the scalar / vector method:

[0072]

[0073] In the formula, sim(·) P The similarity of principal stress values ​​is represented by sim(·), and its unit is Pa. p P represents the directional similarity of the principal stresses, and its unit is degrees; i and p i P is the measured value. i 'and p' i These are predicted values.

[0074] Both of these non-tensor methods suffer from significant multi-index problems when evaluating the similarity of stress tensors, making the evaluation process cumbersome. Furthermore, the elements formed after the stress tensor is decomposed (e.g., tensor components, principal stress values, and directions) are independent of each other; in other words, their correlation is ignored, which can lead to contradictions among the indices. For example, in the scalar method, the similarity of normal stress is within a normal range, but the similarity of shear stress is usually low; while in the scalar / vector method, the magnitude and orientation similarity of the maximum principal stress are easier to control, while the magnitude and orientation similarity of the intermediate and minimum principal stresses are highly variable. In such cases, the predicted stress field cannot be accurately determined. Therefore, how to solve this deficiency remains a scientific problem worth exploring. This application provides a schematic flowchart of a method for determining the similarity of measured and predicted stress tensors; please refer to [link / reference]. Figure 1 Specifically, it can include:

[0075] S110. Obtain the measured stress tensor and the predicted stress tensor of the target area, wherein the predicted stress tensor is obtained based on the results of numerical back analysis of the geostress field.

[0076] For example, the target area is the geological area to be evaluated, the measured stress tensor is the stress tensor of the geological area in the target area measured in the field, and the predicted stress tensor is the stress tensor at the corresponding measuring point location obtained from the results of numerical back analysis of the geostress field.

[0077] S120. Calculate the first Euclidean distance based on the measured stress tensor and the predicted stress tensor.

[0078] For example, Euclidean distance is a commonly used definition of distance, representing the straight-line distance between two points in m-dimensional space, or the natural length of a vector (i.e., the distance from that point to the origin). The traditional formula for calculating Euclidean distance is:

[0079]

[0080] In the formula, X and Y are two eigenvectors, x i Let y be the coordinate of the i-th dimension of vector X. i Let represent the i-th dimension coordinate of vector Y, and m be the spatial dimension. For the stress tensor S, it can be considered as a point in 9-dimensional Euclidean space, and its Euclidean distance to the predicted stress tensor S' is:

[0081]

[0082] The first Euclidean distance is the measured stress tensor and the predicted stress tensor, which are calculated according to equation (7).

[0083] S130. Calculate the Euclidean distance between the measured stress tensor and the origin as the second Euclidean distance.

[0084] For example, the second Euclidean distance is calculated by the measured stress tensor and the Euclidean distance from the origin according to equation (7), where the stress value at the origin is 0.

[0085] S140. Calculate the Euclidean distance similarity based on the first and second Euclidean distances mentioned above.

[0086] For example, if similarity is defined by distance, the Euclidean distance between the measured and predicted points will differ due to varying stress levels in different projects. This makes it difficult to determine a universal threshold for defining similarity. Similar to the non-tensor method mentioned above, we eliminate the influence of dimensions and define Euclidean distance similarity as the ratio of the Euclidean distance (d(S,S')) between the measured and predicted stress tensors to the Euclidean distance (d(S,O)) from the measured stress tensor to the origin.

[0087]

[0088] S150. Determine the similarity level of the numerical back analysis of the geostress field based on the above Euclidean distance similarity.

[0089] For example, the similarity level of the EDS geostress field numerical back-analysis prediction results is evaluated based on Euclidean distance similarity. A two-dimensional schematic diagram is used here for illustration. Figure 3As shown, the closer the EDS (Euclidean distance similarity) is to 0, the more similar the stress states of the two methods are. Comparing the two non-tensor methods, it can be seen that the introduction of Euclidean distance treats the stress tensor as a whole for similarity evaluation, eliminating the multi-index problem present in the two existing non-tensor methods.

[0090] In summary, the method for determining the similarity between measured and predicted stress tensors proposed in this application calculates the first Euclidean distance between the stress tensor and the predicted stress tensor, and the second Euclidean distance between the measured stress tensor and the origin. The similarity of the Euclidean distance is calculated using the first and second Euclidean distances, and the similarity of the numerical back-analysis of the geostress field is evaluated based on the Euclidean distance similarity. This eliminates the multi-index problem existing in the two existing non-tensor methods, and the obtained similarity analysis results are more accurate.

[0091] In some examples, Euclidean distance similarity is calculated based on the first and second Euclidean distances mentioned above, including:

[0092] The similarity is determined based on the ratio of the first Euclidean distance to the second Euclidean distance.

[0093] In some examples, the determination of the similarity based on the ratio of the first Euclidean distance to the second Euclidean distance includes:

[0094] The similarity evaluation index EDS is obtained according to the following formula:

[0095]

[0096] In the formula, d(S,S')=||S-S'|| F Let d(S,O) be the first Euclidean distance, then d(S,O) = ||S|| F This is the second Euclidean distance. Where S is the measured stress tensor at a certain measuring point, expressed as: S includes the stress component σ x ,σ y ,σ z ,τ xy ,τ xz and τ yz , τ xy =τ yx ,τ xz =τ zx ,τ yz =τ zy S' is the predicted stress tensor at the corresponding measuring point, expressed as... S' includes σ' x ,σ' y ,σ'z ,τ' xy ,τ' xz and τ' yz ,τ' xy =τ' yx ,τ' xz =τ' zx ,τ' yz =τ' zy .

[0097] In some examples, the above method also includes:

[0098] The stress tensor is decomposed into the magnitude and orientation of the principal stresses to obtain a second expression for the first Euclidean distance:

[0099]

[0100] Where σ1, σ2, and σ3 represent the maximum, intermediate, and minimum principal stresses, respectively. i ,m i ,n i These are the direction cosines of the angle between the new principal stress axis and the original principal stress axis.

[0101] For example, for stress tensor similarity evaluation, the principal stress index can also be used to derive the EDS. The stress tensor is decomposed into the magnitude and orientation of the principal stresses, and the first Euclidean distance is represented by the second expression method. Similarly, the second Euclidean distance can also be represented by the second expression method. First, let's introduce the stress principal axis rotation angle: Assuming that the initial stress principal axes coincide with the world coordinate system, the rotation angles of the stress principal axes around the X(σ1), Y(σ2) and Z(σ3) axes are called Euler angles. Here, we take the second and third rotations around the partially rotated principal stress axes, with the rotation order being σ1, σ2, σ3, and the rotation angles being θ1, θ2, θ3, respectively. Figure 4 As shown, the rotation matrix at this time is:

[0102]

[0103] In the formula, c1 = cosθ1, s1 = sinθ1, etc. i ,m i ,n i These are the direction cosines of the angles between the new principal stress axes and the original principal stress axes. Assume three stress states:

[0104] The initial stress state has the following stress tensor:

[0105]

[0106] In the formula, σ1, σ2, and σ3 represent the maximum, intermediate, and minimum principal stresses, respectively. Introducing the semi-vectorized function vech(·), we obtain the principal stress vector t = vech(T) = [σ1 σ2 σ3].

[0107] Under secondary stress conditions, the principal stress values ​​change, and the stress tensor is...

[0108]

[0109] In the formula The principal stress value change matrix is ​​given by e1, e2, and e3, which represent the maximum, intermediate, and minimum principal stress changes, respectively. The semi-vectorized function vech(·) is introduced to obtain the principal stress value change vector e = vech(E) = [e1 e2 e3].

[0110] In the third stress state, both the magnitude and orientation of the principal stresses change, and the stress tensor is:

[0111]

[0112] The stress tensor similarity EDS between σ and σ” is:

[0113]

[0114] Therefore, EDS is a function containing nine variables, including the initial principal stress values ​​(σ1, σ2, σ3), the principal stress value errors (e1, e2, e3), and the Euler angles of the stress principal axis rotation (θ = [θ1θ2θ3]).

[0115] In some examples, the similarity level for determining the numerical inverse analysis of the geostress field based on the aforementioned Euclidean distance similarity includes:

[0116] Establish the correspondence between preset threshold intervals and similarity levels, principal stress values, and orientation errors;

[0117] Based on the principal stress value and the orientation error, the Euclidean distance similarity thresholds at different similarity levels are calculated according to the second expression formula;

[0118] The similarity level of the numerical back-analysis prediction results of the geostress field is determined based on the Euclidean distance similarity threshold and the preset similarity correspondence.

[0119] For example, the threshold range can be obtained based on empirical analysis, and the similarity rating can be divided into extremely high, high, normal, low, and extremely low. After obtaining the similarity evaluation index, the current threshold range in which the Euclidean distance similarity evaluation falls is determined based on the aforementioned similarity evaluation index. The similarity level of the numerical back-analysis of the geostress field is then determined based on the current threshold range and the aforementioned preset correspondence. For example, if the obtained EDS value is 0.13, and the current EDS value is less than the EDS threshold of 0.1582, then its corresponding similarity level is extremely high; or, for example, if the obtained EDS value is 0.16, and the current EDS value is greater than the EDS threshold of 0.1582 but less than the EDS threshold of 1896, then its corresponding similarity level is high.

[0120]

[0121]

[0122] Table 1 shows the preset correspondence between EDS and similarity levels.

[0123] In some examples,

[0124] Construct the correspondence between preset threshold ranges and similarity levels, principal stress values, and orientation errors, including:

[0125] Construct the correspondence between preset threshold ranges and similarity levels, principal stress values, and orientation errors, including:

[0126] Determine the error thresholds for principal stress values ​​and Euler angles of rotation about the principal stress axes;

[0127] The EDS threshold is calculated based on the above-mentioned quantity error threshold, the above-mentioned Euler angle error threshold, and the above-mentioned second expression formula;

[0128] Based on the above EDS thresholds, construct the correspondence between the threshold interval and the preset similarity level, principal stress value and orientation error.

[0129] For example, as shown in Table 1, σ1, σ2, and σ3 are weighted according to different weight coefficients to obtain the value error threshold, and Euler angle error is set according to the threshold interval. The EDS threshold is calculated according to the second expression formula (13) to determine the threshold interval corresponding to the similarity level. The preset correspondence between the threshold interval and the similarity level, the principal stress value, and the orientation error is constructed according to the EDS threshold interval.

[0130] In some examples, the aforementioned measurement error thresholds include a first measurement error threshold, a second measurement error threshold, and a third measurement error threshold. The first measurement error is determined by a first weighting coefficient and the maximum principal stress, the second measurement error is determined by a second weighting coefficient and the intermediate principal stress coefficient, and the third measurement error is determined by a third weighting coefficient and the minimum principal stress coefficient. The first weighting coefficient is less than the second weighting coefficient and the third weighting coefficient.

[0131] For example, the EDS threshold is related to the principal stress value error threshold and the Euler angle error threshold for rotation around the principal stress axes. The magnitude error threshold includes error terms related to σ1, σ2, and σ3, and the Euler angle error threshold includes error terms related to Euler angles rotated around the three principal stress axes. When determining the EDS threshold, sensitivity analysis of the stress values ​​σ1, σ2, and σ3 and the rotated Euler angles is required. Since hyperdimensional surfaces are difficult to draw, the controlled variable method is used here, and the factors that need to be controlled are defined as secondary factors, while the remaining factors are primary factors. The specific analysis results are as follows:

[0132] A. Sensitivity analysis of EDS and initial principal stress:

[0133] First, control the secondary factors: principal stress value error e = [0 0 0] MPa, Euler angle θ = [20 20 20]. Simultaneously control the primary factors: initial principal stress levels σ1:σ2:σ3 = 2.5:1.5:1. Plot the graph of EDS versus any two initial principal stresses. Figures 5 to 7 As shown in the figure, overall, the principal stress difference is small in the middle of the surface, and both the EDS value and the surface curvature are relatively small; at the boundary positions (e.g., Figure 5 The principal stress difference is greatest at the section where σ3=0, and the EDS value and surface curvature increase sharply. This indicates that EDS is positively correlated with the difference between the initial principal stress values, i.e., EDS∝(σ1-σ3,σ2-σ3,σ1-σ2). Furthermore... Figure 5 and Figure 7 The curvature of the surface at the boundary of the intermediate EDS changes more drastically, which indicates that the influence of the principal stress difference on the EDS is: σ1-σ3≈σ2-σ3>σ1-σ2, further showing that the influence of the initial intermediate principal stress on the EDS cannot be ignored.

[0134] B. Sensitivity analysis of EDS and principal stress error:

[0135] Secondary factors were controlled: initial principal stress values ​​σ = [20 10 5], Euler angles θ = [20 20 20], while primary factors were controlled: one principal stress error was set to 0. A three-dimensional graph of EDS and the other two principal stress errors was plotted. Figures 8 to 10 ).Depend on Figure 14It can be seen that after the principal stress axis is deflected, EDS is an asymmetric concave surface, and the EDS peak appears at one corner of the concave surface; in addition, observing the peak coordinates, it can be found that the peak coordinates of EDS(e1,e3) and EDS(e1,e2) are both e1=5MPa and e3=-5MPa. Figure 8 , Figure 9 The peak coordinates of EDS(e2,e3) are e2=-5MPa, e2=-5MPa. Figure 9 This indicates that, under the premise of the same error value, when the maximum principal stress error e1 is positive and the intermediate and minimum principal stress errors e2 and e3 are negative, EDS is the largest, that is: EDS max (e)=[+e -e -e], then EDS min (e) = [-e +e +e]

[0136] To further verify this, a two-dimensional curve of EDS versus principal stress error was plotted. Figure 11 As shown in the figure, the influence of principal stress error on EDS varies. The degree of influence is always: e1 > e2 > e3, that is, the error in the value of the maximum principal stress has the greatest impact.

[0137] C. EDS and Euler angle sensitivity analysis:

[0138] Controlling secondary factors: initial principal stress value σ = [20 10 5], principal stress value error e = [2 2 2], controlling primary factors: one Euler angle is 0°, plot the three-dimensional graph of EDS and the other two Euler angles ( Figures 11 to 13 As shown in the figure, EDS varies with Euler angles in a wave-like manner, with a period of π and an axis of symmetry of π / 2. also Figure 13 The amplitude of the waveform in the EDS varies: EDS(θ2,θ3)>EDS(θ1,θ2)>EDS(θ1,θ3), which shows that different Euler angles have different effects on the EDS.

[0139] To further verify this, the two-dimensional curve of EDS as a function of Euler angles is shown below. Figure 12 As shown in the figure, the influence of Euler angles on EDS is: θ2 > θ3 > θ1. This is because Euler angle θ2 controls the rotation of the principal stress axes σ1 and σ3, which further illustrates that the influence of the initial principal stress EDS is: σ1 > σ3 > σ2.

[0140] The specific results of the perceptual analysis are shown in the figure below. Figure 14 and Figure 15As shown, the error control of σ1 is relatively easy and accurate, while the magnitude and orientation errors of σ2 and σ3 are much higher than those of σ1. The first weighting coefficient related to the first magnitude error σ1 is smaller than the second weighting coefficient and the third weighting coefficient.

[0141] Please see Figure 16 One embodiment of the device for determining the similarity between measured and predicted stress tensors in this application may include:

[0142] The acquisition unit 21 is used to acquire the measured stress tensor and the predicted stress tensor of the target area, wherein the predicted stress tensor is acquired based on the results of numerical back analysis of the geostress field.

[0143] The first calculation unit 22 is used to calculate the first Euclidean distance based on the measured stress tensor and the predicted stress tensor.

[0144] The second calculation unit 23 is used to calculate the Euclidean distance between the measured stress tensor and the origin as the second Euclidean distance.

[0145] The third calculation unit 24 is used to calculate the Euclidean distance similarity based on the first Euclidean distance and the second Euclidean distance mentioned above.

[0146] Unit 25 is used to determine the similarity of the numerical back analysis of the geostress field based on the above-mentioned Euclidean distance similarity.

[0147] like Figure 17 As shown, this application embodiment also provides an electronic device 300, including a memory 310, a processor 320, and a computer program 311 stored in the memory 310 and executable on the processor. When the processor 320 executes the computer program 311, it implements the steps of any of the above-described methods for determining the similarity between measured and predicted stress tensors.

[0148] Since the electronic device described in this embodiment is the device used to implement the device for determining the similarity of measured and predicted stress tensors in the embodiments of this application, those skilled in the art can understand the specific implementation method and various variations of the electronic device in this embodiment based on the method described in the embodiments of this application. Therefore, how the electronic device implements the method in the embodiments of this application will not be described in detail here. Any device used by those skilled in the art to implement the method in the embodiments of this application falls within the scope of protection of this application.

[0149] In practical implementation, when the computer program 311 is executed by the processor, it can achieve the following: Figure 1 Any of the corresponding implementation methods in the embodiments.

[0150] It should be noted that the descriptions of each embodiment in the above embodiments have different focuses. For parts that are not described in detail in a certain embodiment, please refer to the relevant descriptions in other embodiments.

[0151] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0152] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create a machine for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0153] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0154] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0155] This application also provides a computer program product, which includes computer software instructions. When the computer software instructions are run on a processing device, the processing device executes the process of determining the similarity between measured and predicted stress tensors in the corresponding embodiment.

[0156] A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, computer instructions may be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium may be any available medium that a computer can store or a data storage device such as a server or data center that integrates one or more available media. The available medium may be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid-state disk (SSD)).

[0157] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the specific working processes of the systems, devices, and units described above can be referred to the corresponding processes in the foregoing method embodiments, and will not be repeated here.

[0158] In the several embodiments provided in this application, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces, or indirect coupling or communication connection between apparatuses or units, and may be electrical, mechanical, or other forms.

[0159] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment, depending on actual needs.

[0160] Furthermore, the functional units in the various embodiments of this application can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0161] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0162] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit it. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A method for determining the similarity between measured and predicted stress tensors, characterized in that, include: The measured stress tensor and the predicted stress tensor of the target area are obtained, wherein the predicted stress tensor is obtained based on the results of numerical back analysis of the geostress field. Calculate the first Euclidean distance based on the measured stress tensor and the predicted stress tensor; The Euclidean distance between the measured stress tensor and the origin is calculated as the second Euclidean distance; Calculate the Euclidean distance similarity based on the first Euclidean distance and the second Euclidean distance; The similarity level of the numerical back-analysis of the geostress field is determined based on the Euclidean distance similarity.

2. The method according to claim 1, characterized in that, Calculating Euclidean distance similarity based on the first Euclidean distance and the second Euclidean distance includes: The similarity is determined based on the ratio of the first Euclidean distance to the second Euclidean distance.

3. The method according to claim 2, characterized in that, Determining the similarity based on the ratio of the first Euclidean distance to the second Euclidean distance includes: The similarity EDS is calculated using the following formula: In the formula, = This is the first Euclidean distance. = This is the second Euclidean distance. , ,in, Let the measured stress tensor at a certain measuring point be expressed as: S includes stress components and , ; The predicted stress tensor for the corresponding measuring point is expressed as: , Including and , .

4. The method according to claim 3, characterized in that, Also includes: The stress tensor is decomposed into the magnitude and orientation of the principal stresses to obtain a second expression formula for the similarity: in, These represent the maximum, intermediate, and minimum principal stresses, respectively. These are the direction cosines of the angle between the new principal stress axis and the original principal stress axis.

5. The method according to claim 4, characterized in that, The determination of the similarity level for the numerical inverse analysis of the geostress field based on the Euclidean distance similarity includes: Establish the correspondence between preset threshold intervals and similarity levels, principal stress values, and orientation errors; Based on the principal stress value and the orientation error, the Euclidean distance similarity thresholds at different similarity levels are calculated according to the second expression formula; The similarity level of the numerical back-analysis prediction results of the geostress field is determined based on the Euclidean distance similarity threshold and the preset similarity correspondence.

6. The method according to claim 5, characterized in that, Construct the correspondence between preset threshold ranges and similarity levels, principal stress values, and orientation errors, including: Determine the error thresholds for principal stress values ​​and Euler angles of rotation about the principal stress axes; The EDS threshold is calculated based on the magnitude error threshold, the Euler angle error threshold, and the second expression formula; Based on the EDS threshold, a correspondence is constructed between the threshold range and the preset similarity level, principal stress value, and orientation error.

7. The method according to claim 6, characterized in that, The measurement error thresholds include a first measurement error threshold, a second measurement error threshold, and a third measurement error threshold. The first measurement error is determined by a first weighting coefficient and the maximum principal stress. The second measurement error is determined by a second weighting coefficient and the intermediate principal stress coefficient. The third measurement error is determined by a third weighting coefficient and the minimum principal stress coefficient. The first weighting coefficient is less than the second weighting coefficient and the third weighting coefficient.

8. A device for determining the similarity between measured and predicted stress tensors, characterized in that, include: The acquisition unit is used to acquire the measured stress tensor and the predicted stress tensor of the target area, wherein the predicted stress tensor is acquired based on the results of numerical back analysis of the geostress field. The first calculation unit is used to calculate the first Euclidean distance based on the measured stress tensor and the predicted stress tensor. The second calculation unit is used to calculate the Euclidean distance between the measured stress tensor and the origin as the second Euclidean distance; The third calculation unit is used to calculate the Euclidean distance similarity based on the first Euclidean distance and the second Euclidean distance; The unit is determined, and the similarity level of the numerical back-analysis of the geostress field is determined based on the Euclidean distance similarity.

9. An electronic device, comprising: The memory and processor are characterized in that the processor, when executing a computer program stored in the memory, implements the steps of the method for determining the similarity between measured and predicted stress tensors according to any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by the processor, it implements the steps of the method for determining the similarity between measured and predicted stress tensors according to any one of claims 1-7.

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