Linear elastic equation parameter estimation method for adaptive regularization parameter selection
Through the linear elastic equation parameter estimation method of adaptive regularization parameter selection, the problem that the Morozov deviation criterion is not applicable in nonlinear inverse problems is solved, and stable output and efficient convergence are achieved under different noise levels and parameter distributions are achieved.
Patent Information
- Application Number
- CN202411385286.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-30
- Publication Date
- 2025-02-28
AI Technical Summary
The classic Morozov deviation criterion is not applicable in nonlinear inverse problems, resulting in difficulty in selecting regularized parameters.
The linear elastic equation parameter estimation method with adaptive regularization parameter selection is used to solve the problem by setting initialization parameters, iteratively updating regularization parameters, determining search intervals, and determining the optimal regularization parameters based on preset search methods.
It basically eliminates human subjectivity, can obtain stable output under different noise levels and parameter distributions, reduces the sensitivity to initial guesses, pays only a small part of the calculation cost to quickly achieve solution accuracy, and has efficient convergence characteristics.
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Figure CN119537744A_ABST
Abstract
Description
Technical Field
[0001] The present application relates to the technical field of data processing, and in particular to a method for estimating parameters of a linear elastic equation by adaptive regularization parameter selection. Background Art
[0002] The problem of parameter identification of online elastic equations is a nonlinear inverse problem. Its objective function includes two parts: the sum of squares of the deviations between the calculated elastic displacement and the measured value, and the regularization term. Usually, in variable coefficient problems, the regularization term uses the integral of the square of the derivative of the parameter, and in constant coefficient problems, it uses the integral of the square of the parameter. These two parts constitute the objective function of the inverse problem by weighting the regularization term with a regularization parameter and combining it with the deviation between the elastic displacement and the measured value.
[0003] The main methods used for selecting regularization parameters are trial and error, L-curve method and generalized cross validation method. The trial and error method refers to selecting a series of possible regularization parameters, solving the inverse problem respectively, and finally selecting a suitable result among all the regularization parameters, but this method requires a large amount of data storage and multiple calculations. The L-curve method selects the regularization parameter by plotting the double logarithmic graph of the norm of the solution and the corresponding residual norm, and finding the inflection point of the curve to balance the stability of the solution and the fitting accuracy, but this method is highly subjective in the selection of the inflection point of the curve. The generalized cross validation method minimizes the cross validation error estimate and selects the regularization parameter that can effectively balance the fitting error and the risk of overfitting, thereby optimizing the solution of the inverse problem, but this method has high computational complexity and high requirements on data quality.
[0004] The classic Morozov's Discrepancy Principle has been very mature in the application of linear inverse problems. It shows that when a specific regularization parameter is used to solve the inverse problem, when the deviation between the calculated value and the measured value in the solution is close to the noise level in the measured value, the regularization parameter selected at this time is optimal. However, in nonlinear inverse problems, this criterion is not necessarily satisfied. Summary of the invention
[0005] The present application provides a linear elastic equation parameter estimation method for adaptive regularization parameter selection to solve the problem in the prior art that the classic Morozov deviation criterion is not applicable to nonlinear inverse problems.
[0006] Correspondingly, the present application also provides an electronic device and a computer-readable storage medium to ensure the implementation and application of the above method.
[0007] In order to solve the above technical problems, the present application discloses a linear elastic equation parameter estimation method for adaptive regularization parameter selection, the method comprising:
[0008] Set the initialization parameters, including the initial regularization parameter, the regularization parameter decrease rate q, and the stop parameter c1 that controls the iteration;
[0009] When the initial regularization parameter satisfies the first preset condition, the regularization parameter is iteratively updated at a decreasing rate of q to obtain the target regularization parameter; the first preset condition is that the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is greater than 1+c1 times the noise level;
[0010] Determine the search interval based on the target regularization parameter and the regularization parameter of the previous iteration;
[0011] When the target regularization parameter does not meet the second preset condition, the optimal regularization parameter is determined from the search interval based on a preset search method; the second preset condition is that the deviation between the elastic displacement under the target regularization parameter and the noisy measurement value is greater than or equal to 1 times the noise level and less than or equal to 1+c1 times the noise level;
[0012] The parameters of the linear elastic equations are calculated based on the optimal regularization parameters.
[0013] The present application also discloses an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, one or more methods described in the present application are implemented.
[0014] The present application also discloses a computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, one or more methods described in the present application are implemented.
[0015] In the present application, an initial regularization parameter, a regularization parameter decrease rate q, and a stop parameter c1 for controlling iteration are set. When the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is greater than 1+c1 times the noise level, the regularization parameter is iteratively updated at a decrease rate of q to obtain the target regularization parameter; a search interval is determined based on the target regularization parameter and the regularization parameter of the previous iteration step; when the deviation between the elastic displacement under the target regularization parameter and the noisy measurement value does not satisfy a noise level greater than or equal to 1 times, and is less than or equal to 1+c1 times the noise level, the optimal regularization parameter is determined from the search interval based on a preset search method; finally, the parameters of the linear elastic equation are calculated based on the optimal regularization parameter. The method basically eliminates human subjectivity in the process of selecting the regularization parameter, can obtain a relatively stable output under different noise levels and different parameter distributions, and has a low sensitivity to the initial guess of the parameter, and only pays a small part of the calculation cost to quickly achieve the corresponding solution accuracy, and has efficient convergence characteristics in nonlinear variable coefficient elastic problems.
[0016] Additional aspects and advantages of the present application will be given in the following description, which will become apparent from the following description, or will be understood through the practice of the present application. BRIEF DESCRIPTION OF THE DRAWINGS
[0017] The above and / or additional aspects and advantages of the present application will become apparent and easily understood from the following description of the embodiments in conjunction with the accompanying drawings, in which:
[0018] Figure 1 A flow chart of a linear elastic equation parameter estimation method for adaptive regularization parameter selection provided in an embodiment of the present application;
[0019] Figure 2 A result diagram of the solution and relative error of the algorithm provided in the embodiment of the present application for the linear variable coefficient problem;
[0020] Figure 3 A result diagram of the solution and relative error of the algorithm provided in the embodiment of the present application for the nonlinear variable coefficient problem;
[0021] Figure 4 A result diagram of the relative error of the algorithm provided in the embodiment of the present application under different initial parameter guesses;
[0022] Figure 5 This is a graph showing the stability of the number of nonlinear iterations of the algorithm provided in the embodiment of the present application under different initial parameter guesses;
[0023] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION
[0024] The embodiments of the present application are described in detail below, and examples of the embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals throughout represent the same or similar elements or elements having the same or similar functions. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present application, and cannot be interpreted as limiting the present application.
[0025] It will be understood by those skilled in the art that, unless expressly stated, the singular forms "one", "said", and "the" used herein may also include plural forms. It should be further understood that the term "comprising" used in the specification of the present application refers to the presence of features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or combinations thereof. It should be understood that when we refer to an element as being "connected" or "coupled" to another element, it may be directly connected or coupled to the other element, or there may be an intermediate element. In addition, the "connection" or "coupling" used herein may include wireless connection or wireless coupling. The term "and / or" used herein includes all or any unit and all combinations of one or more associated listed items.
[0026] Those skilled in the art will appreciate that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as those generally understood by those skilled in the art in the field to which the present invention belongs. It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with the meanings in the context of the prior art, and will not be interpreted with idealized or overly formal meanings unless specifically defined as here.
[0027] The solution provided in the embodiment of the present application can be executed by any electronic device, such as a terminal device or a server, wherein the server can be an independent physical server, a server cluster or a distributed system composed of multiple physical servers, or a cloud server providing cloud computing services. The terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, etc., but is not limited to this. The terminal and the server can be directly or indirectly connected via wired or wireless communication, and the present application is not limited here. For the technical problems existing in the prior art, the present application provides a method for estimating the parameters of linear elastic equations with adaptive regularization parameter selection, which is intended to solve at least one of the technical problems of the prior art.
[0028] The technical solution of the present application and how the technical solution of the present application solves the above-mentioned technical problems are described in detail below with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments. The embodiments of the present application will be described below in conjunction with the accompanying drawings.
[0029] The embodiment of the present application corrects the classical Morozov deviation criterion for its inadaptability in elastic equations. Through a large number of numerical examples, it is found that in nonlinear inverse problems, the optimal regularization parameter is approximately a value slightly larger than one noise level, and this value may be different in different examples. Based on this, the embodiment of the present application provides a possible implementation method, such as Figure 1 As shown, a flowchart of a method for estimating parameters of a linear elastic equation with adaptive regularization parameter selection is provided. The method can be executed by any electronic device, and optionally, can be executed on a server or terminal device.
[0030] like Figure 1 As shown in , the method may include the following steps:
[0031] Step 101, setting initialization parameters, the initialization parameters include an initial regularization parameter, a regularization parameter decrease rate q, and a stop parameter c1 for controlling iterations.
[0032] Step 102, when the initial regularization parameter satisfies the first preset condition, iteratively update the regularization parameter at a decreasing rate of q to obtain the target regularization parameter; the first preset condition is that the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is greater than 1+c1 times the noise level.
[0033] Optionally, in the embodiment of the present application, the initial regularization parameter is expressed as α0, z δ represents the measured value with noise of size δ, Denotes the regularization parameter as α j When the measured value has a noise of size δ, the solved parameters are It means that when the regularization parameter is α j When the measured value has noise of size δ, the elastic displacement obtained can be expressed as follows:
[0034]
[0035] In the embodiment of the present application, the initial regularization parameter α0 is iteratively updated to obtain a target regularization parameter that does not satisfy the first preset condition. Specifically, in the first iteration process, the initial regularization parameter α0 and the stop parameter c1 for controlling the iteration are used as inputs to determine whether the expression of the above-mentioned first preset condition is established. If not, the initial regularization parameter α0 is used as the target regularization parameter; if established, the initial regularization parameter α0 is decreased at a set ratio to obtain an updated regularization parameter, and the next iteration process is performed based on the updated regularization parameter until the expression of the above-mentioned first preset condition is not satisfied.
[0036] Step 103: determine the search interval based on the target regularization parameter and the regularization parameter of the previous iteration step.
[0037] Step 104, when the target regularization parameter does not meet the second preset condition, determine the optimal regularization parameter from the search interval based on a preset search method; the second preset condition is that the deviation between the elastic displacement under the target regularization parameter and the noisy measurement value is greater than or equal to 1 times the noise level and less than or equal to 1+c1 times the noise level.
[0038] Optionally, the second preset condition can be expressed as:
[0039]
[0040] In the embodiment of the present application, the target regularization parameter is iteratively updated to obtain the optimal regularization parameter. In the first iteration, it is determined whether the expression of the first preset condition is established based on the target regularization parameter. If established, the target regularization parameter is used as the optimal regularization parameter; if not established, the regularization parameter in the next iteration is determined from the search interval using a preset search method until the expression of the second preset condition is satisfied.
[0041] Step 105: Calculate and obtain the parameters of the linear elastic equation based on the optimal regularization parameter.
[0042] In the embodiment of the present application, an initial regularization parameter, a regularization parameter decrease rate q, and a stop parameter c1 for controlling iteration are set. When the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is greater than 1+c1 times the noise level, the regularization parameter is iteratively updated at a decrease rate of q to obtain the target regularization parameter; a search interval is determined based on the target regularization parameter and the regularization parameter of the previous iteration step; when the deviation between the elastic displacement under the target regularization parameter and the noisy measurement value does not satisfy a noise level greater than or equal to 1 times, and is less than or equal to 1+c1 times the noise level, the optimal regularization parameter is determined from the search interval based on a preset search method; finally, the parameters of the linear elastic equation are calculated based on the optimal regularization parameter. The method basically eliminates human subjectivity in the process of selecting the regularization parameter, can obtain a relatively stable output under different noise levels and different parameter distributions, and has a low sensitivity to the initial guess of the parameter, and only pays a small part of the calculation cost to quickly achieve the corresponding solution accuracy, and has efficient convergence characteristics in nonlinear variable coefficient elastic problems.
[0043] In an optional embodiment, when the initial regularization parameter satisfies the first preset condition, iteratively updating the regularization parameter at a decreasing rate of q to obtain the target regularization parameter includes:
[0044] When the initial regularization parameter satisfies the first preset condition, the regularization parameter is iteratively updated at a decreasing rate of q until the updated regularization parameter does not satisfy the first preset condition, and the updated regularization parameter is used as the target regularization parameter.
[0045] In an optional embodiment, the value range of the regularization parameter decrease rate q is 0 <q<1。
[0046] In the embodiment of the present application, the iterative decrease of the initial regularization parameter can be implemented by the following pseudo code until the target regularization parameter is obtained:
[0047]
[0048] In an optional embodiment, determining the search interval based on the target regularization parameter and the regularization parameter of the previous iteration step includes:
[0049] The target regularization parameter is used as the lower bound and the regularization parameter of the previous iteration step is used as the upper bound to obtain the search interval.
[0050] In the present application, α min,j and α max,j Indicates the lower and upper bounds of the search interval. Specifically, the pseudo code is set as:
[0051] α max,j =αj-1 ,α min,j =α j ;
[0052] Among them, α j-1 represents the regularization parameter of the previous iteration, α j represents the target regularization parameter.
[0053] In an optional embodiment, when the target regularization parameter does not satisfy the second preset condition, determining the optimal regularization parameter from the search interval based on a preset search method includes:
[0054] When the target regularization parameter does not satisfy the second preset condition, an update operation is performed until the updated regularization parameter satisfies the second preset condition, thereby obtaining an optimal regularization parameter;
[0055] The updating operation is: determining the regularization parameter of the next iteration step from the search interval by using a preset search method, and updating the search interval based on the solution result of the regularization parameter of the next iteration step.
[0056] In an optional embodiment, the preset search method may be a binary search method, and the regularization parameter of the next iteration step is determined from the search interval using the preset search method, including:
[0057] The midpoint of the search interval is used as the regularization parameter for the next iteration.
[0058] In an optional embodiment, updating the search interval based on the solution result of the regularization parameter of the next iteration step includes:
[0059] If the regularization parameter of the next iteration step satisfies the first preset condition, the regularization parameter of the next iteration step is updated to the upper bound of the search interval;
[0060] If the regularization parameter of the next iteration step satisfies the third preset condition, the regularization parameter of the next iteration step is updated to the lower bound of the search interval; the third preset condition is that the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is less than 1 times the noise level.
[0061] The third preset condition can be expressed as:
[0062]
[0063] In the embodiment of the present application, the iterative update of the target regularization parameter can be implemented by the following pseudo code until the optimal regularization parameter is obtained:
[0064]
[0065] Finally, based on the optimal regularization parameter output
[0066] The method in the embodiment of the present application only requires a small amount of computational cost to quickly achieve the corresponding solution accuracy.
[0067] In the embodiment of the present application, relatively satisfactory results can be obtained by using two different numerical examples of linear variable coefficients and nonlinear variable coefficients. The details are as follows:
[0068] The Poisson's ratio is set to 0.48, and the parameter distribution of Young's modulus is restored by the measured value. The calculation area is a square area of (0,1)×(0,1), where the boundary conditions and material forces are set as follows:
[0069]
[0070] Adding 1% relative random noise to all measurements, the results obtained are as follows Figure 2-5 As shown. Among them, Figure 2 (a)-(c) show the actual solution, solution result and relative error of the algorithm for the linear variable coefficient problem respectively; Figure 3 (a)-(c) show the actual solution, solution result and relative error of the algorithm in the nonlinear coefficient problem respectively; Figure 4 and Figure 5 It shows that the algorithm in the embodiment of the present application can obtain relatively stable convergence results on different initial value guesses; Figure 4 The horizontal axis is the initial value guess, and the vertical axis is the average relative error. Figure 5 The horizontal axis is the initial value guess, and the vertical axis is the number of nonlinear iterations required for convergence.
[0071] according to Figure 2-5 It can be seen that the average relative error of the linear variable coefficient problem is 4.3271%, and a total of 41 nonlinear iterative steps are used. The average relative error of the nonlinear variable coefficient problem is 2.0015%, and a total of 29 nonlinear iterative steps are used.
[0072] The method in the embodiment of the present application can be applied to other types of biomechanical problems, or the algorithm can be adjusted for different inverse problem models to improve versatility.
[0073] Based on the same principle as the method shown in the embodiment of the present application, the embodiment of the present application also provides an electronic device, which may include but is not limited to: a processor and a memory; a memory for storing a computer program; a processor for executing the linear elastic equation parameter estimation method for adaptive regularization parameter selection shown in any optional embodiment of the present application by calling a computer program. Compared with the prior art, the linear elastic equation parameter estimation method for adaptive regularization parameter selection provided by the present application basically eliminates human subjectivity in the process of selecting regularization parameters, can obtain a relatively stable output under different noise levels and different parameter distributions, and has a low sensitivity to the initial guess of the parameters, and only pays a small part of the calculation cost to quickly achieve the corresponding solution accuracy, and has efficient convergence characteristics in nonlinear variable coefficient elastic problems.
[0074] In an optional embodiment, an electronic device is also provided, such as Figure 6 As shown, Figure 6 The electronic device 600 shown may be a server, including: a processor 601 and a memory 603. The processor 601 and the memory 603 are connected, such as through a bus 602. Optionally, the electronic device 600 may further include a transceiver 604. It should be noted that in actual applications, the transceiver 604 is not limited to one, and the structure of the electronic device 600 does not constitute a limitation on the embodiments of the present application.
[0075] Processor 601 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It may implement or execute various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this application. Processor 601 may also be a combination that implements computing functions, such as a combination of one or more microprocessors, a combination of a DSP and a microprocessor, and the like.
[0076] The bus 602 may include a path to transmit information between the above components. The bus 602 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus. The bus 602 may be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 6 Only one thick line is used in the diagram, but this does not mean that there is only one bus or only one type of bus.
[0077] The memory 603 can be a ROM (Read Only Memory) or other types of static storage devices that can store static information and instructions, a RAM (Random Access Memory) or other types of dynamic storage devices that can store information and instructions, or an EEPROM (Electrically Erasable Programmable Read Only Memory), a CD-ROM (Compact Disc Read Only Memory) or other optical disk storage, optical disk storage (including compressed optical disk, laser disk, optical disk, digital versatile disk, Blu-ray disk, etc.), a magnetic disk storage medium or other magnetic storage device, or any other medium that can be used to carry or store the desired program code in the form of instructions or data structures and can be accessed by a computer, but is not limited to these.
[0078] The memory 603 is used to store the application code for executing the solution of the present application, and the execution is controlled by the processor 601. The processor 601 is used to execute the application code stored in the memory 603 to implement the contents shown in the above method embodiment.
[0079] Among them, electronic devices include but are not limited to: mobile terminals such as mobile phones, laptops, digital broadcast receivers, PDAs (personal digital assistants), PADs (tablet computers), PMPs (portable multimedia players), vehicle-mounted terminals (such as vehicle-mounted navigation terminals), and fixed terminals such as digital TVs and desktop computers. Figure 6 The electronic device shown is merely an example and should not bring any limitation to the functions and scope of use of the embodiments of the present application.
[0080] The server provided in this application may be an independent physical server, or a server cluster or distributed system composed of multiple physical servers, or a cloud server that provides basic cloud computing services such as cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms. The terminal may be a smart phone, tablet computer, laptop computer, desktop computer, smart speaker, smart watch, etc., but is not limited to this. The terminal and the server may be directly or indirectly connected via wired or wireless communication, which is not limited in this application.
[0081] An embodiment of the present application provides a computer-readable storage medium, on which a computer program is stored. When the computer-readable storage medium is run on a computer, the computer can execute the corresponding content in the aforementioned method embodiment.
[0082] It should be understood that, although the steps in the flowchart of the accompanying drawings are displayed in sequence as indicated by the arrows, these steps are not necessarily executed in sequence in the order indicated by the arrows. Unless otherwise specified herein, there is no strict order restriction on the execution of these steps, and they can be executed in other orders. Moreover, at least a part of the steps in the flowchart of the accompanying drawings may include multiple sub-steps or multiple stages, and these sub-steps or stages are not necessarily executed at the same time, but can be executed at different times, and their execution order is not necessarily sequential, but can be executed in turn or alternately with other steps or at least a part of the sub-steps or stages of other steps.
[0083] It should be noted that the computer-readable storage medium mentioned above in the present application can also be a computer-readable signal medium or a combination of a computer-readable storage medium and a computer-readable storage medium. The computer-readable storage medium can be, for example, but not limited to, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, device or device, or any combination of the above. More specific examples of computer-readable storage media may include, but are not limited to: an electrical connection with one or more wires, a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disk read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the above. In the present application, a computer-readable storage medium can be any tangible medium containing or storing a program that can be used by or in combination with an instruction execution system, device or device. In the present application, a computer-readable signal medium may include a data signal propagated in a baseband or as part of a carrier wave, which carries a computer-readable program code. This propagated data signal can take a variety of forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination of the above. The computer readable signal medium may also be any computer readable medium other than a computer readable storage medium, which may send, propagate or transmit a program for use by or in conjunction with an instruction execution system, apparatus or device. The program code contained on the computer readable medium may be transmitted using any suitable medium, including but not limited to: wires, optical cables, RF (radio frequency), etc., or any suitable combination of the above.
[0084] The computer-readable medium may be included in the electronic device, or may exist independently without being installed in the electronic device.
[0085] The computer-readable medium carries one or more programs. When the one or more programs are executed by the electronic device, the electronic device executes the method shown in the above embodiment.
[0086] According to one aspect of the present application, a computer program product or a computer program is provided, the computer program product or the computer program comprising computer instructions, the computer instructions being stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium, and the processor executes the computer instructions, so that the computer device executes the linear elastic equation parameter estimation method for adaptive regularization parameter selection provided in the above-mentioned various optional implementations.
[0087] Computer program code for performing the operations of the present application may be written in one or more programming languages or a combination thereof, including object-oriented programming languages such as Java, Smalltalk, C++, and conventional procedural programming languages such as "C" or similar programming languages. The program code may be executed entirely on the user's computer, partially on the user's computer, as a separate software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., via the Internet using an Internet service provider).
[0088] The flow chart and block diagram in the accompanying drawings illustrate the possible architecture, function and operation of the system, method and computer program product according to various embodiments of the present application. In this regard, each square box in the flow chart or block diagram can represent a module, a program segment or a part of a code, and the module, the program segment or a part of the code contains one or more executable instructions for realizing the specified logical function. It should also be noted that in some alternative implementations, the functions marked in the square box can also occur in a sequence different from that marked in the accompanying drawings. For example, two square boxes represented in succession can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each square box in the block diagram and / or flow chart, and the combination of the square boxes in the block diagram and / or flow chart can be implemented with a dedicated hardware-based system that performs a specified function or operation, or can be implemented with a combination of dedicated hardware and computer instructions.
[0089] The above description is only a preferred embodiment of the present application and an explanation of the technical principles used. Those skilled in the art should understand that the scope of disclosure involved in the present application is not limited to the technical solution formed by a specific combination of the above technical features, but should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above disclosed concept. For example, the above features are replaced with the technical features with similar functions disclosed in this application (but not limited to) by each other to form a technical solution.
Claims
1. A method for estimating parameters of linear elastic equations with adaptive regularization parameter selection, characterized in that: The method comprises: Setting initialization parameters, wherein the initialization parameters include an initial regularization parameter, a regularization parameter decrease rate q, and a stop parameter c1 for controlling iterations; When the initial regularization parameter satisfies a first preset condition, the regularization parameter is iteratively updated at a decreasing rate of q to obtain a target regularization parameter; the first preset condition is that the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is greater than 1+c1 times the noise level; Determine the search interval based on the target regularization parameter and the regularization parameter of the previous iteration; In the case where the target regularization parameter does not satisfy a second preset condition, determining the optimal regularization parameter from the search interval based on a preset search method; the second preset condition is that the deviation between the elastic displacement under the target regularization parameter and the noisy measurement value is greater than or equal to 1 times the noise level and less than or equal to 1+c1 times the noise level; The parameters of the linear elastic equation are calculated based on the optimal regularization parameter.
2. The linear elastic equation parameter estimation method for adaptive regularization parameter selection according to claim 1, characterized in that: When the initial regularization parameter satisfies the first preset condition, iteratively updating the regularization parameter at a decreasing rate of q to obtain a target regularization parameter includes: When the initial regularization parameter satisfies the first preset condition, the regularization parameter is iteratively updated at a decreasing rate of q until the updated regularization parameter does not satisfy the first preset condition, and the updated regularization parameter is used as the target regularization parameter.
3. The linear elastic equation parameter estimation method for adaptive regularization parameter selection according to claim 1, characterized in that: The step of determining the search interval based on the target regularization parameter and the regularization parameter of the previous iteration step includes: The target regularization parameter is used as a lower bound, and the regularization parameter of the previous iteration step is used as an upper bound to obtain the search interval.
4. The method for estimating parameters of linear elastic equations by adaptive regularization parameter selection according to claim 1, characterized in that: The step of determining the optimal regularization parameter from the search interval based on a preset search method when the target regularization parameter does not satisfy the second preset condition includes: When the target regularization parameter does not satisfy the second preset condition, an update operation is performed until the updated regularization parameter satisfies the second preset condition, thereby obtaining the optimal regularization parameter; The updating operation is: determining the regularization parameter of the next iteration step from the search interval by using a preset search method, and updating the search interval based on the solution result of the regularization parameter of the next iteration step.
5. The method for estimating parameters of linear elastic equations by adaptive regularization parameter selection according to claim 4, characterized in that: The method of determining the regularization parameter of the next iteration step from the search interval by using a preset search method includes: The midpoint of the search interval is used as the regularization parameter for the next iteration step.
6. The method for estimating parameters of linear elastic equations by adaptive regularization parameter selection according to claim 4, characterized in that: The updating of the search interval based on the solution result of the regularization parameter of the next iteration step includes: If the regularization parameter of the next iteration step satisfies the first preset condition, the regularization parameter of the next iteration step is updated to the upper bound of the search interval; If the regularization parameter of the next iteration step satisfies the third preset condition, the regularization parameter of the next iteration step is updated to the lower bound of the search interval; the third preset condition is that the deviation between the elastic displacement under the regularization parameter of the current iteration step and the noisy measurement value is less than 1 times the noise level.
7. The method for estimating parameters of linear elastic equations by adaptive regularization parameter selection according to claim 2, characterized in that: The value range of the regularization parameter decrease rate q is 0 <q<1。 8. An electronic device, characterized in that: The invention comprises a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method according to any one of claims 1 to 7 is implemented.
9. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.