A product structure safety reliability determination method and device and a storage medium
Patent Information
- Application Number
- CN202211520365.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-11-30
- Publication Date
- 2026-08-28
- Estimated Expiration
- 2042-11-30
AI Technical Summary
[0002]对于DA1170C驱动桥、XE550KD散热器等工程机械产品的零部件与整机的可靠性评估,工程中复杂的环境通常无法用通用的概率模型进行描述,从而使得概率方法不适用于此类情形的不确定性评估,因此非概率的方法被许多专家提出
[0062]本发明提供的产品结构安全性可靠度确定方法,无模型对称假设,适用于对称和非对称的数据点情形,边缘模型引入了测量值,通过引入的测量值进行扩展,实时更新,充分包络了参数信息,避免了较强的模型约束。
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Figure CN115906494B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to a method, apparatus, and storage medium for determining the reliability of product structural safety, belonging to the technical field of product structural safety uncertainty analysis. Background Technology
[0002] For reliability assessments of components and complete machines in engineering machinery products such as the DA1170C drive axle and XE550KD radiator, the complex environments encountered in engineering projects often cannot be described using general probabilistic models. This makes probabilistic methods unsuitable for uncertainty assessments in such situations, leading many experts to propose non-probabilistic methods. Commonly used non-probabilistic models include symmetrical intervals, ellipses, and parallelograms. However, these models are highly constrained, and due to the assumption of symmetry, deviations in individual data often result in excessively large envelope ranges, making them unsuitable for complex engineering data. Summary of the Invention
[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method, device and storage medium for determining the structural safety and reliability of a product, which is applicable to both symmetrical and asymmetrical data point situations, can fully encompass parameter information and avoid strong model constraints.
[0004] To achieve the above objectives, the present invention is implemented using the following technical solution:
[0005] In a first aspect, the present invention provides a method for determining the structural safety and reliability of a product, the method comprising:
[0006] Two independent bounded uncertainty parameters related to the safety of the product structure are selected, and the range of values for the two selected independent bounded uncertainty parameters is determined based on historical information of the product structure and expert experience.
[0007] Establish a coordinate system using the two selected independent bounded uncertain parameters, and construct a rectangular value interval based on the value range of the two independent bounded uncertain parameters;
[0008] A boundary model containing unknown constants is established based on the largest Cassini ovoid that can be enclosed within the range of values of the rectangle.
[0009] Based on the definition of the Cassini oval line, the characteristics of the unknown constants in the boundary model and the four endpoints of the rectangular value interval are determined;
[0010] Based on the characteristics of the unknown constant, for the limiting cases where the four endpoints of the rectangular value interval are located on the Cassini oval line, the values of the unknown constant under different limiting cases are determined, and the values of the unknown constant are substituted into the boundary model to determine the basic Cassini oval line equation under different limiting cases;
[0011] The basic Cassini ovoid equation is extended based on the measured values of two independent bounded uncertainty parameters to obtain the extended boundary model;
[0012] Based on the extended boundary model and limit state function, the reliability value of the product structure safety is determined.
[0013] In conjunction with the first aspect, further, the range of values for the two independent bounded uncertain parameters is: The mean of the rectangular value interval is The interval radius is ,but
[0014] ;
[0015] in, ;X i This represents the range of values for the i-th uncertain parameter; This represents the lower limit of the value of the i-th uncertain parameter; The upper limit of the value of the i-th uncertain parameter.
[0016] In conjunction with the first aspect, the expression for the boundary model containing unknown constants is as follows:
[0017] ;
[0018] in, , These are unknown constants, all of which are positive real numbers; x1 represents the value of the first uncertain parameter; x2 represents the value of the second uncertain parameter; This represents the interval mean of the first uncertain parameter; The interval mean of the second uncertain parameter is represented; the focus of the maximum Cassini oval is: , .
[0019] In conjunction with the first aspect, further, the unknown constant satisfies At this point, the four endpoints of the determined rectangular value interval are respectively , When all four endpoints lie on the Cassini oval line, there is .
[0020] In conjunction with the first aspect, further, the values of the unknown constants and the basic Cassini ovoid equation are determined by classification under different limiting conditions, including:
[0021] (a) when endpoints At the Cassini ovoid line
[0022] ;
[0023] ;
[0024] in, This represents the Euclidean distance between the two endpoints;
[0025] Accordingly, the basic Cassini ovoid equation is:
[0026] ;
[0027] (b) When endpoint At the Cassini ovoid line
[0028] ;
[0029] ;
[0030] Accordingly, the basic Cassini ovoid equation is:
[0031] .
[0032] In conjunction with the first aspect, further, the step of extending the basic Cassini oval line equation based on the measured values of two independent bounded uncertainty parameters to obtain the extended boundary model includes:
[0033] From the measured value to distance and The ratio serves as a measure of its reliability. , ;
[0034] Correspondingly, the extended boundary model The expression is as follows:
[0035] ;
[0036] in, n1 is the number of measurements of the first uncertain parameter; n2 is the number of measurements of the second uncertain parameter; .
[0037] In conjunction with the first aspect, further, determining the reliability value of the product structural safety based on the extended boundary model and limit state function includes:
[0038] a) At this time, the parameter value range Reliability ;
[0039] b) At this time, the parameter value range Reliability ;
[0040] c) If the limit state function equation curve is tangent to the parameter value boundary, then the probability of taking countable points is 0, i.e. If the limit state function equation curve intersects with the parameter value boundary, then the parameter value region and the failure region overlap. In this case, the Monte Carlo sampling method or geometric algorithm is used to calculate the reliability.
[0041] The methods for reliability calculation using Monte Carlo sampling include:
[0042] i) in Uniformly sampled , ;
[0043] ii) From Uniformly sampled , ;
[0044] iii) Select one of them that makes The point is recorded as One, simultaneously making , The point is denoted as indivual;
[0045] iv) Reliability ;
[0046] Where N1 is The number of samples; N2 is The number of samples; This represents the minimum value of the first uncertain parameter; The maximum value of the first uncertain parameter; This represents the minimum value of the second uncertain parameter; The maximum value of the second uncertain parameter; Describes the limit state function. Let be a coordinate point on the limit state function, satisfying ,and , ;
[0047] Methods for reliability calculation using geometric algorithms include:
[0048] Calculate the area S of the coincidence between the limit state function equation curve and the parameter range curve.a ;
[0049] ) Calculate the range of parameter values and the area S enclosed by the curve. b ;
[0050] ) Calculate the reliability R=S a / S b .
[0051] Secondly, the present invention provides a device for determining the structural safety and reliability of a product, the device comprising:
[0052] The first determination module is used to select two independent bounded uncertainty parameters related to the safety of the product structure, and to determine the range of values for the two selected independent bounded uncertainty parameters based on historical information of the product structure and expert experience.
[0053] The construction module is used to establish a coordinate system based on two selected independent bounded uncertain parameters and to construct a rectangular value interval based on the value range of the two independent bounded uncertain parameters.
[0054] Model building module: used to build a boundary model containing unknown constants based on the maximum Cassini ovoid that can be enclosed within the rectangular value range;
[0055] The second determining module is used to determine the characteristics of the unknown constants in the boundary model and the four endpoints of the rectangular value interval according to the definition of the Cassini oval line.
[0056] The third determining module is used to classify and determine the value of the unknown constant under different limiting conditions based on the characteristics of the unknown constant and for the limiting cases where the four endpoints of the rectangular value interval are located on the Cassini oval line, and substitute the value of the unknown constant into the boundary model to determine the basic Cassini oval line equation under different limiting conditions.
[0057] Extension module: used to extend the basic Cassini ovoid equation based on the measured values of two independent bounded uncertainty parameters, and obtain the extended boundary model;
[0058] The fourth determination module is used to determine the reliability value of the product's structural safety based on the extended boundary model and limit state function.
[0059] Thirdly, the present invention provides an electronic terminal, including a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the method described in any one of the first aspects are performed.
[0060] Fourthly, the present invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any of the first aspects.
[0061] Compared with the prior art, the beneficial effects achieved by the present invention are as follows:
[0062] The product structure safety and reliability determination method provided by this invention has no model symmetry assumption and is applicable to both symmetric and asymmetric data point scenarios. The edge model introduces measured values, which are then used for expansion and real-time updates, fully encompassing parameter information and avoiding strong model constraints. Attached Figure Description
[0063] Figure 1 This is a flowchart of a method for determining the structural safety and reliability of a product, provided in an embodiment of the present invention.
[0064] Figure 2 This is an asymmetric model of response data points provided in the embodiments of the present invention. Detailed Implementation
[0065] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.
[0066] Example 1:
[0067] Figure 1 This is a flowchart illustrating a method for determining the structural safety and reliability of a product according to Embodiment 1 of the present invention. This flowchart merely shows the logical sequence of the method described in this embodiment; however, in other possible embodiments of the present invention, different methods may be used, provided there are no conflicts. Figure 1 Complete the steps shown or described in the order indicated.
[0068] The product structure safety reliability determination method provided in this embodiment can be applied to terminals and can be executed by a product structure safety reliability determination device. This device can be implemented in software and / or hardware and can be integrated into the terminal, such as any smartphone, tablet, or computer device with communication capabilities. See also... Figure 1 The method implemented in this way specifically includes the following steps:
[0069] Step 1: Select two independent bounded uncertainty parameters related to the product structure safety, and determine the value range of the two selected independent bounded uncertainty parameters based on historical information of the product structure and expert experience;
[0070] There are many parameters that affect the structural safety of a product. In this embodiment of the invention, two independent bounded uncertain parameters are selected for evaluation each time. The range of values for the two independent bounded uncertain parameters can be denoted as... , ;X i This represents the range of values for the i-th uncertain parameter; This represents the lower limit of the value of the i-th uncertain parameter; The upper limit of the value of the i-th uncertain parameter.
[0071] Step 2: Establish a coordinate system based on the two selected independent bounded uncertain parameters, and construct a rectangular value interval according to the value range of the two independent bounded uncertain parameters;
[0072] Let it be Let the two parameters take the values of the x and y coordinates of the coordinate axes, then the range of their values is... This forms a rectangular interval of values, assuming the mean of this interval is... The radius of the interval is The corresponding calculation formulas are as follows:
[0073] .
[0074] Step 3: Establish a boundary model containing unknown constants based on the largest Cassini oval line that can be enclosed within the rectangular value range;
[0075] Let the focus of the Cassini ovoid be: , The maximum Cassini ovoid constant value is set to , , All are positive real numbers, meaning they contain unknown constants. , The boundary model is:
[0076] ;
[0077] Where x1 represents the value of the first uncertain parameter; x2 represents the value of the second uncertain parameter; This represents the interval mean of the first uncertain parameter; This represents the interval mean of the second uncertain parameter.
[0078] Step 4: Based on the definition of the Cassini oval line, determine the characteristics of the unknown constants in the boundary model and the four endpoints of the rectangular value interval;
[0079] To ensure that the Cassini oval curve is enveloped within the rectangular range of values, the Cassini oval curve should be as smooth as possible. At this point, the rectangle's value range has four endpoints, namely... , To ensure that the Cassini ovoid curve falls within the rectangular range of values, it should be such that... or On the Cassini oval, considering that all four endpoints lie simultaneously on the Cassini oval, we have:
[0080] .
[0081] Step 5: Based on the characteristics of the unknown constant, for the limiting cases where the four endpoints of the rectangular value interval are located on the Cassini oval line, classify and determine the values of the unknown constant under different limiting cases, and substitute the values of the unknown constant into the boundary model to determine the basic Cassini oval line equation under different limiting cases;
[0082] a) endpoints At the Cassini ovate line, based on the characteristics of the Cassini ovate line, we can know that:
[0083] ;
[0084] in, This represents the Euclidean distance between the two endpoints;
[0085] ;
[0086] Therefore, the basic Cassini ovoid equation is established as follows:
[0087] ;
[0088] b) endpoints At the Cassini ovate line, based on the characteristics of the Cassini ovate line, we can know that:
[0089] ;
[0090] but
[0091] ;
[0092] Therefore, the basic Cassini ovoid equation is established as follows:
[0093] .
[0094] Step Six: Extend the basic Cassini ovoid equation based on the measured values of two independent bounded uncertainty parameters to obtain the extended boundary model;
[0095] Since the Cassini oval curve, within its rectangular range, cannot completely cover the range of uncertain parameters, it is necessary to extend the generalized Cassini oval curve based on the measured data points, thus expanding the model. Specifically, this includes:
[0096] From the measured value to distance and The ratio serves as a measure of its reliability. , ;
[0097] Correspondingly, the extended boundary model The expression is as follows:
[0098] ;
[0099] in, n1 is the number of measurements of the first uncertain parameter; n2 is the number of measurements of the second uncertain parameter; .
[0100] It should be noted that the parameter value boundaries and upper and lower bounds change according to each data point introduced. Figure 2 As shown.
[0101] Step 7: Determine the reliability value of the uncertain parameters based on the extended boundary model and limit state function.
[0102] Assume the limit state function The range of values for the product's uncertain parameter failure is: There is a little bit on M. satisfy ,and The calculations are as follows, depending on the specific circumstances:
[0103] a) At this time, the parameter value range Reliability ;
[0104] b) At this time, the parameter value range Reliability ;
[0105] c) If the limit state function equation curve is tangent to the parameter value boundary, then the probability of taking countable points is 0, i.e. If the limit state function equation curve intersects with the parameter value boundary, then the parameter value region and the failure region overlap. In this case, the reliability can be calculated using Monte Carlo sampling or a geometric algorithm.
[0106] As an embodiment of the present invention, the method for reliability calculation using Monte Carlo sampling includes:
[0107] i) in Uniformly sampled , ;
[0108] ii) From Uniformly sampled , ;
[0109] iii) Select one of them that makes The point is recorded as One, simultaneously making , The point is denoted as indivual;
[0110] iv) Reliability ;
[0111] Where N1 is The number of samples; N2 is The number of samples; This represents the minimum value of the first uncertain parameter; The maximum value of the first uncertain parameter; This represents the minimum value of the second uncertain parameter; The maximum value of the second uncertain parameter; .
[0112] As another embodiment of the present invention, the method for reliability calculation using a geometric algorithm includes:
[0113] Calculate the area S of the coincidence between the limit state function equation curve and the parameter range curve. a ;
[0114] ) Calculate the range of parameter values and the area S enclosed by the curve. b ;
[0115] ) Calculate the reliability R=S a / S b .
[0116] In summary, the product structure safety and reliability determination method provided by this invention has no model symmetry assumptions and is applicable to both symmetric and asymmetric data point scenarios. The edge model introduces measured values, which are then used for expansion and real-time updates, fully encompassing parameter information and avoiding strong model constraints.
[0117] Example 2:
[0118] This invention provides a device for determining the structural safety and reliability of a product. This device can implement the method described in Embodiment 1. The device includes:
[0119] The first determination module is used to select two independent bounded uncertainty parameters related to the safety of the product structure, and to determine the range of values for the two selected independent bounded uncertainty parameters based on historical information of the product structure and expert experience.
[0120] The construction module is used to establish a coordinate system based on two selected independent bounded uncertain parameters and to construct a rectangular value interval based on the value range of the two independent bounded uncertain parameters.
[0121] Model building module: used to build a boundary model containing unknown constants based on the maximum Cassini ovoid that can be enclosed within the rectangular value range;
[0122] The second determining module is used to determine the characteristics of the unknown constants in the boundary model and the four endpoints of the rectangular value interval according to the definition of the Cassini oval line.
[0123] The third determining module is used to classify and determine the value of the unknown constant under different limiting conditions based on the characteristics of the unknown constant and for the limiting cases where the four endpoints of the rectangular value interval are located on the Cassini oval line, and substitute the value of the unknown constant into the boundary model to determine the basic Cassini oval line equation under different limiting conditions;
[0124] Extension module: used to extend the basic Cassini ovoid equation based on the measured values of two independent bounded uncertainty parameters, and obtain the extended boundary model;
[0125] The fourth determination module is used to determine the reliability value of the product's structural safety based on the extended boundary model and limit state function.
[0126] The apparatus provided in the embodiments of the present invention can execute the methods provided in any embodiment of the present invention, and has the corresponding functional modules and beneficial effects for executing the methods.
[0127] Example 3:
[0128] This invention provides an electronic terminal, including a processor and a memory connected to the processor. The memory stores a computer program, and when the computer program is executed by the processor, it performs the steps of the method described in any one of the embodiments.
[0129] Example 4:
[0130] This invention provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method described in any one of the embodiments.
[0131] 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.
[0132] 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 processor, 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, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0133] 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.
[0134] 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.
[0135] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.
Claims
1. A method for determining the structural safety and reliability of a product, characterized in that, The method includes: Two independent bounded uncertainty parameters related to the safety of the product structure are selected, and the range of values for the two selected independent bounded uncertainty parameters is determined based on historical information of the product structure and expert experience. Establish a coordinate system using the two selected independent bounded uncertain parameters, and construct a rectangular value interval based on the value range of the two independent bounded uncertain parameters; A boundary model containing unknown constants is established based on the largest Cassini ovoid that can be enclosed within the range of values of the rectangle. Based on the definition of the Cassini oval line, the characteristics of the unknown constants in the boundary model and the four endpoints of the rectangular value interval are determined; Based on the characteristics of the unknown constant, for the limiting cases where the four endpoints of the rectangular value interval are located on the Cassini oval line, the values of the unknown constant under different limiting cases are determined, and the values of the unknown constant are substituted into the boundary model to determine the basic Cassini oval line equation under different limiting cases; The basic Cassini ovoid equation is extended based on the measured values of two independent bounded uncertainty parameters to obtain the extended boundary model; Based on the extended boundary model and limit state function, the reliability value of the product structure safety is determined.
2. The method for determining the structural safety and reliability of a product according to claim 1, characterized in that, The range of values for the two independent bounded uncertain parameters is: The mean of the rectangular value interval is The radius of the interval is ,but ; in, ;X i This represents the range of values for the i-th uncertain parameter; This represents the lower limit of the value of the i-th uncertain parameter; The upper limit of the value of the i-th uncertain parameter.
3. The method for determining the structural safety and reliability of a product according to claim 2, characterized in that, The expression for the boundary model containing unknown constants is as follows: ; in, , These are unknown constants, all of which are positive real numbers; x1 represents the value of the first uncertain parameter; x2 represents the value of the second uncertain parameter; This represents the interval mean of the first uncertain parameter; The interval mean of the second uncertain parameter is represented; the focus of the maximum Cassini oval is: , .
4. The method for determining the structural safety and reliability of a product according to claim 3, characterized in that, The unknown constant satisfies The four endpoints of the determined rectangular value interval are respectively , When all four endpoints lie on the Cassini oval line, then .
5. The method for determining the structural safety and reliability of a product according to claim 4, characterized in that, The classification determines the values of the unknown constants and the basic Cassini oval line equation under different limiting conditions, including: (a) when endpoint At the Cassini ovoid line ; ; in, This represents the Euclidean distance between the two endpoints; Accordingly, the basic Cassini ovoid equation is: ; (b) When endpoint At the Cassini ovoid line ; ; Accordingly, the basic Cassini ovoid equation is: 。 6. The method for determining the structural safety and reliability of a product according to claim 5, characterized in that, The step of extending the basic Cassini oval line equation based on the measured values of two independent bounded uncertainty parameters to obtain the extended boundary model includes: From the measured value to distance and The ratio serves as a measure of its reliability. , ; Correspondingly, the extended boundary model The expression is as follows: ; in, n1 is the number of measurements of the first uncertain parameter; n2 is the number of measurements of the second uncertain parameter; .
7. The method for determining the structural safety and reliability of a product according to claim 6, characterized in that, The process of determining the reliability value of product structural safety based on the extended boundary model and limit state function includes: a) At this time, the parameter value range Reliability ; b) At this time, the parameter value range Reliability ; c) If the limit state function equation curve is tangent to the parameter value boundary, then the probability of taking countable points is 0, i.e. If the limit state function equation curve intersects with the parameter value boundary, then the parameter value region and the failure region overlap. In this case, the Monte Carlo sampling method or geometric algorithm is used to calculate the reliability. The methods for reliability calculation using Monte Carlo sampling include: i) in Uniformly sampled , ; ii) From Uniformly sampled , ; iii) Select one of them that makes The point is denoted as One, simultaneously making , The point is denoted as indivual; iv) Reliability ; Where N1 is The number of samples; N2 is The number of samples; This represents the minimum value of the first uncertain parameter; The maximum value of the first uncertain parameter; This represents the minimum value of the second uncertain parameter; The maximum value of the second uncertain parameter; Describes the limit state function. Let be a coordinate point on the limit state function, satisfying ,and , ; Methods for reliability calculation using geometric algorithms include: Calculate the area S of the coincidence between the limit state function equation curve and the parameter range curve. a ; ) Calculate the range of parameter values and the area S enclosed by the curve. b ; III) Calculate the reliability R=S a / S b .
8. A device for determining the structural safety and reliability of a product, characterized in that, The device includes: The first determination module is used to select two independent bounded uncertainty parameters related to the safety of the product structure, and to determine the range of values for the two selected independent bounded uncertainty parameters based on historical information of the product structure and expert experience. The construction module is used to establish a coordinate system based on two selected independent bounded uncertain parameters and to construct a rectangular value interval based on the value range of the two independent bounded uncertain parameters. Model building module: used to build a boundary model containing unknown constants based on the maximum Cassini ovoid that can be enclosed within the rectangular value range; The second determining module is used to determine the characteristics of the unknown constants in the boundary model and the four endpoints of the rectangular value interval according to the definition of the Cassini oval line. The third determining module is used to classify and determine the value of the unknown constant under different limiting conditions based on the characteristics of the unknown constant and for the limiting cases where the four endpoints of the rectangular value interval are located on the Cassini oval line, and substitute the value of the unknown constant into the boundary model to determine the basic Cassini oval line equation under different limiting conditions; Extension module: used to extend the basic Cassini ovoid equation based on the measured values of two independent bounded uncertainty parameters, and obtain the extended boundary model; The fourth determination module is used to determine the reliability value of the product's structural safety based on the extended boundary model and limit state function.
9. An electronic terminal, characterized in that, The method includes a processor and a memory connected to the processor, wherein a computer program is stored in the memory, and when the computer program is executed by the processor, the steps of the method as described in any one of claims 1 to 7 are performed.
10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the steps of the method according to any one of claims 1 to 7.
Citation Information
Patent Citations
Mechanical structure uncertainty parameter quantification and correlation analysis method
CN113139247A
System and method for estimating a treatment region for a medical treatment device
US20100250209A1