CN110489800B - Structural dynamic load sparse identification method based on matrix regularization - Google Patents
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Abstract
The invention discloses a structural dynamic load sparse identification method based on matrix regularization, which comprises the following steps of: establishing a structure finite element model according to the actually measured modal information of the structure; intercepting structural acceleration response information under the action of dynamic load through a time window, and establishing a response matrix; establishing a load identification matrix equation according to the structural finite element model, the response matrix, the load influence factors and the initial condition influence factors; adopting matrix regularization to construct a load identification optimization problem; solving an optimization equation by adopting a rapid iteration threshold compression algorithm to obtain a sparse identification result of the dynamic load of the structure; the method realizes the integrity sparse solution of the long-time dynamic load identification problem, is suitable for the integrity sparse solution of the large-scale dynamic load identification problem, and can be widely applied to the technical field of structure monitoring.
Description
Technical Field
The invention relates to the technical field of structure monitoring, in particular to a structure dynamic load sparse identification method based on matrix regularization.
Background
The accurate understanding of the dynamic load of the structure is beneficial to monitoring, controlling, identifying, optimizing and the like of the structure. Therefore, how to obtain the dynamic load of the structure is particularly necessary, and the method has basic research value in various engineering researches such as aerospace, vehicle engineering, ship engineering, civil engineering, mechanical automation and the like. Direct measurement and indirect identification methods are two common methods for acquiring dynamic loads of structures. The direct method is to directly measure the dynamic load of a structure by using a load sensor, but under the influence of factors such as environment and equipment, in many practical projects, a proper force sensor mounting position is difficult to find, so that the direct method is difficult to realize application. Unlike direct measurement of structural loads, structural vibrational responses, such as acceleration response, displacement response, and strain response, are relatively easy to directly measure. Based on this, compared with a direct method, the method for inverting the dynamic load of the structure by indirectly utilizing the measured structure response has unique advantages.
In the past, structural dynamic load identification is highly valued by researchers, and a plurality of structural dynamic load identification methods are developed at present. From the solution thinking of the load identification method, the existing methods can be generally summarized into three types: direct solution, regularization, probability statistics. Mathematically, direct solver and regularization methods generally belong to deterministic analysis methods, while probabilistic statistical methods belong to non-deterministic analysis methods. The important feature of the latter is the introduction of uncertainty in the parameters of measurement noise or system noise, etc., thereby enabling such methods to provide a more comprehensive understanding of load identification. However, the corresponding probabilistic statistical method also requires more measurement data and more time-consuming calculation. In contrast, deterministic analysis does not consider the randomness of variables, and for direct solution, the load identification problem of linear systems can be generally solved by a linear equation system, so that an inverse matrix or a generalized inverse matrix can be conveniently used for solving. However, due to the ill-posed nature of the load identification inverse problem, direct solution is often particularly sensitive to noise, which is not practical.
At present, the regularization-based structural dynamic load identification technology is widely accepted, and occupies an important position in structural dynamic load inversion research. However, it is not difficult to find that the existing method mostly belongs to vector regularization by analyzing the existing regularization-based live load identification technology, that is, both the structural response and the unknown load are stored in a vector form in the identification process. The information storage mode of the vector is simple and clear, and the physical significance is clear. However, when considering the problem of identifying a load with a long time span, a problem easily arises in that the corresponding system matrix dimension is too large, especially for a dynamic load identification equation established in the time domain. It is noted that the identification and solution are time-consuming due to the fact that the system matrix is too large, and the rapid inversion or real-time monitoring of the dynamic load is obviously not facilitated. In the prior art, aiming at the load identification problem with long time span or high real-time requirement, a moving time window can be selected to sequentially intercept short-time responses for dynamic load identification, but the technology needs to divide one problem into a plurality of problems to solve, and the integrity consideration is relatively deficient.
Disclosure of Invention
In view of this, the embodiment of the present invention provides a structural dynamic load sparse identification method based on matrix regularization, so as to implement integral sparse identification on structural dynamic loads.
The embodiment of the invention provides a structural dynamic load sparse identification method based on matrix regularization, which comprises the following steps of:
establishing a structure finite element model according to the actually measured modal information of the structure;
intercepting structural acceleration response information under the action of dynamic load through a time window, and establishing a response matrix;
establishing a load identification matrix equation according to the structural finite element model, the response matrix, the load influence factors and the initial condition influence factors;
adopting matrix regularization to construct a load identification optimization problem;
and solving an optimization equation by adopting a rapid iteration threshold compression algorithm to obtain a sparse identification result of the dynamic load of the structure.
Further, the step of establishing a finite element model of the structure according to the actually measured modal information of the structure comprises the following steps:
obtaining structural modal information through structural test modal analysis, wherein the structural modal information comprises the frequency, the vibration mode and the damping ratio of a structure;
and establishing a structure finite element analysis model according to the structure modal information and by combining the design parameters and the material information of the structure.
Further, the step of intercepting the structural acceleration response information under the action of the dynamic load through the time window and establishing a response matrix comprises the following steps:
determining the time length to be identified and the initial time according to the dynamic load identification problem;
determining the window length of a time window according to the time length to be identified;
based on the determined window length, intercepting the actually measured acceleration response information of the structure through a time window to generate a response matrix;
the response matrix is represented as:
wherein B represents a response matrix; b i Indicates the ith samplingAcceleration response information corresponding to the sampling points; w represents the total number of time windows, and k is the number of sampling points contained in each time window; k is a radical of 0 The number of sampling points for the overlapping portion.
Further, the step of establishing the load identification matrix equation according to the structural finite element model, the response matrix, the load influence factors and the initial condition influence factors comprises the following steps:
determining a discrete trigonometric function;
discrete sampling is carried out on the discrete trigonometric function, and a vector is constructed by the obtained discrete data;
after carrying out normalization processing on the vector, acquiring a load basic component through a discrete trigonometric function;
taking the modal regular coordinate into consideration, and developing the initial condition of the structure by using a modal space;
calculating the structural acceleration response under the action of the unit load component and the unit initial condition component by a vibration mode superposition method to form a load identification system matrix;
and adjusting the load identification system matrix according to the acceleration response information caused by the load component, and further establishing a load identification matrix equation.
Further, in the step of constructing the load identification optimization problem by adopting the matrix regularization, an expression of the load identification optimization problem is as follows:
wherein, P identified Representing the matrix identification result; symbol
Representing a minimization optimization problem; symbol | | | purple F 2 Expressing the square of the F norm of a matrix; a represents a system matrix; p represents a structure excitation matrix, including structure load and initial conditions; b represents a response matrix; λ represents a regularization parameter; p (i, j) denotes the ith row and the jth column of the matrix P.
Further, the step of solving the optimization equation by using the fast iteration threshold compression algorithm to obtain the sparse identification result of the structural dynamic load comprises the following steps:
calculating the maximum eigenvalue of a load identification system matrix;
performing iterative computation on the identification optimization problem according to a preset regularization parameter and an initial iteration value;
judging whether the iteration times reach the maximum iteration times, if so, outputting a calculation result of identifying the optimization problem; otherwise, updating the iteration value and continuously carrying out iterative calculation on the identification optimization problem until the iteration times reach the maximum iteration times;
extracting a load participation coefficient matrix from a calculation result of the identification optimization problem;
and calculating according to the load participation coefficient matrix to obtain a time course identification result of the dynamic load of the structure.
Further, the step of solving the optimization equation by using the fast iteration threshold compression algorithm to obtain the sparse identification result of the structural dynamic load further comprises the following steps:
and for the load identification results included by different time windows at the same time, determining that the final identification result at the time is the average value of the identification results of the different time windows.
The technical scheme in the embodiment of the invention has the following advantages: according to the embodiment of the invention, a load identification matrix equation is constructed, a load identification optimization problem is constructed by adopting matrix regularization, and finally an optimization equation is solved by adopting a fast iteration threshold compression algorithm to obtain a sparse identification result of the structural dynamic load; the method realizes the integrity sparse solution of the long-time dynamic load identification problem, and is suitable for the integrity sparse solution of the large-scale dynamic load identification problem.
Drawings
FIG. 1 is a flowchart illustrating the overall steps of an embodiment of the present invention;
FIG. 2 is a schematic view of a cantilever beam model used in an embodiment of the present invention;
FIG. 3 illustrates a simulated measured structural acceleration response of an embodiment of the present invention;
FIG. 4 is a schematic diagram of a structure dynamic load identification result in the embodiment of the present invention;
fig. 5 is a partial schematic diagram of a structure dynamic load identification result in an embodiment of the present invention.
Detailed Description
The invention is further explained and illustrated in the following description with reference to the figures and the specific embodiments thereof. The step numbers in the embodiments of the present invention are set for convenience of illustration only, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.
Referring to fig. 1, an embodiment of the present invention provides a method for sparse identification of a structural dynamic load based on matrix regularization, including the following steps:
establishing a structure finite element model according to the actually measured modal information of the structure;
intercepting structural acceleration response information under the action of dynamic load through a time window, and establishing a response matrix;
establishing a load identification matrix equation according to the structural finite element model, the response matrix, the load influence factors and the initial condition influence factors;
adopting matrix regularization to construct a load identification optimization problem;
and solving an optimization equation by adopting a fast iterative threshold compression algorithm to obtain a sparse identification result of the structural dynamic load.
Further as a preferred embodiment, the step of establishing a finite element model of the structure according to the information of the measured modal of the structure includes the following steps:
obtaining structural modal information through structural test modal analysis, wherein the structural modal information comprises the frequency, the vibration mode and the damping ratio of a structure;
and establishing a structure finite element analysis model according to the structure modal information and by combining the design parameters and the material information of the structure.
Specifically, the acceleration sensor is adopted in the embodiment to pick up the acceleration response of the structure, and the arrangement position of the specific sensor can be properly adjusted to acquire more vibration information of the structure as far as possible;
in addition, in the embodiment, a structural finite element analysis model is established by combining key information such as structural design parameters, material information, actually measured dynamic behavior and the like, and is used for approximately describing a real vibration structure.
Further as a preferred embodiment, the step of intercepting the structural acceleration response information under the action of the dynamic load through a time window and establishing a response matrix includes the following steps:
determining the time length to be identified and the initial time according to the dynamic load identification problem;
determining the window length of a time window according to the time length to be identified;
based on the determined window length, intercepting the actually measured acceleration response information of the structure through a time window to generate a response matrix;
the response matrix is represented as:
wherein B represents a response matrix; b is a mixture of i Representing acceleration response information corresponding to the ith sampling point; w represents the total number of time windows, and k is the number of sampling points contained in each time window; k is a radical of formula 0 The number of points is sampled for the overlapping portion.
Specifically, in the embodiment, a time window is adopted to intercept the structural response, and the structural response is stored one by one in columns to form a response matrix;
considering the dynamic load identification problem, the time length to be identified is recorded as T in the embodiment total Let initial time be t 1 =0s; selecting a time window with the window length of T to intercept the actually-measured acceleration response, wherein T is less than or equal to T total (ii) a Making the length of the overlapping part of two adjacent time windows be half window length, namely T/2; the time interval corresponding to each time window is as follows: (t) 1 ,t 1 +T]、(t 2 ,t 2 +T]、……、(t j ,t j +T]、……、(t w ,t w +T](ii) a Wherein t is j Represents the starting time of the jth time window and satisfies t j+1 -t j Table of = T/2,wShowing the total number of time windows; the number of sampling points contained in each time window is counted as k, and the number of sampling points in the overlapped part is counted as k 0 Then, after the responses of the time windows are stored in columns, the obtained response matrix is expressed as:
wherein B represents a response matrix, B i Representing the acceleration response corresponding to the ith sampling point;
further as a preferred embodiment, the step of establishing a load identification matrix equation according to the structural finite element model, the response matrix, the load influencing factors and the initial condition influencing factors includes the following steps:
determining a discrete trigonometric function;
discrete sampling is carried out on the discrete trigonometric function, and a vector is constructed by the obtained discrete data;
after carrying out normalization processing on the vector, acquiring a load basic component through a discrete trigonometric function;
taking the modal regular coordinate into consideration, and developing the initial condition of the structure by using a modal space;
calculating structural acceleration response under the action of unit load component and unit initial condition component by using a vibration mode superposition method to form a load identification system matrix;
and adjusting the load identification system matrix according to the acceleration response information caused by the load component, and further establishing a load identification matrix equation.
Specifically, the present embodiment considers the influence of the unknown load and the unknown initial condition, and establishes a load identification matrix equation;
first, in the jth time window (t) j ,t j +T]For example, a discrete trigonometric function is defined as:
wherein d is i j Represent toI-th function component of j-th time window, n t Representing the number of discrete trigonometric functions;
further, each trigonometric function is first discretely sampled at time intervals Δ t f Then using the discrete data to construct a vector d i j And 2 norm normalization is carried out, namely, | | d is satisfied i j || 2 =1; and then, using a discrete trigonometric function to expand unknown load to obtain:
wherein f is j A discrete load vector, alpha, representing the jth time window i j Representing the ith load component d i j The participation coefficient of (a);
taking each load component d in turn i j As input load, calculating corresponding acceleration response by adopting a modal superposition method, and recording the response as h i j Based on the linear superposition principle, the method comprises the following steps:
in the formula (4), b f j Representing the acceleration response of the jth time window caused by the load, H f j Represents a transfer matrix, a, for the payload in the jth time window j Representing a load participation coefficient vector;
further, a free vibration system caused by an initial condition is considered, wherein the initial condition refers to a structural vibration state corresponding to the starting moment of the current time window;
the embodiment utilizes a structural front m-order modal system to approximate a vibration system; selecting a regular modal coordinate, namely, the mode shape matrix satisfies the following conditions: phi T M Φ = I, where Φ = [ ] 1 ,φ 2 ,…,φ m ]Represents the mode matrix, phi i Representing the ith order mode, and M represents a structural mass matrix; using an approximate modal system, initial strips of the structureThe pieces may be organized as y j (0) Namely:
in the formula, y Ni (0) And
respectively representing the ith-order initial modal displacement and the initial modal velocity of the structure; the acceleration response due to the initial conditions is expressed as:
in the formula, b y j Representing the acceleration response of the jth time window due to the initial conditions, H y j Representing the transfer matrix for the initial condition in the jth time window, h yi j The acceleration response caused by the unit component of the ith initial condition is represented, and the acceleration response can be solved according to a single-degree-of-freedom vibration theory; acceleration response b caused by load and initial conditions according to the formula (4) and the formula (6) in the jth time window j Can be expressed as:
in this embodiment, considering the position of the load acting as constant, the system matrix [ H ] for each time window f j ,H y j ]Are all equal to the system matrix for the other time windows, so considering w time windows, the acceleration response matrix of the structure can be expressed as:
wherein [ H ] f ,H y ]＝[H f j ,H y j ]Represents the system matrix, F =[ɑ 1 ,ɑ 2 ,…,ɑ w ]Represents a load participation coefficient matrix, Y = [ Y ] 1 (0),y 2 (0),…,y w (0)]Representing an initial condition matrix; meanwhile, the load and the initial condition are considered, and the corresponding system matrix elements have larger difference in numerical value, so that the system matrix is further properly adjusted on the basis of a formula (8); first, a representative value RV for the load transfer matrix is calculated as:
in the formula, H f (i) represents a matrix H f The ith column; then, a new system matrix a is constructed, taking:
A＝[H f ,H ytemp ]
according to equation (10), the matrix relationship between the structural acceleration response and the structural input, including the load and the initial conditions, can be expressed as:
wherein P = [ F ] T ,Y adjusted T ] T Representing the structural excitation matrix, including structural loading and initial conditions, Y adjusted Representing the adjusted initial condition matrix;
further as a preferred embodiment, in the step of constructing the load identification optimization problem by using matrix regularization, an expression of the load identification optimization problem is as follows:
wherein, P identified Representing the matrix identification result; symbol
Representing a minimization optimization problem; symbol | | | purple F 2 Expressing the square of the norm of a matrix F; a represents a system matrix; p represents a structure excitation matrix, including structure load and initial conditions; b represents a response matrix; λ represents a regularization parameter; p (i, j) denotes the ith row and jth column of the matrix P.
Specifically, the embodiment adopts matrix regularization to construct a load identification optimization problem; based on equation (11), the optimization problem is constructed in combination with the regularization of the matrix as follows:
in the formula, λ represents a regularization parameter for adjusting contribution degrees of the preceding term and the subsequent term in the formula (12), and in specific application, the parameter may be selected according to engineering experience or a regularization posterior criterion method, such as a Bayesian information criterion, that is, bayesian information criterion, abbreviated as BIC; p (i, j) represents the ith row and jth column of matrix P; note that the optimization variable P in equation (12) is a matrix, not a vector, which is one of the main distinguishing features of the present invention from the existing vector regularization identification technology.
Further as a preferred embodiment, the step of solving the optimization equation by using the fast iterative threshold compression algorithm to obtain the sparse identification result of the structural dynamic load includes the following steps:
calculating the maximum eigenvalue of a load identification system matrix;
performing iterative computation on the identification optimization problem according to a preset regularization parameter and an initial iteration value;
judging whether the iteration times reach the maximum iteration times, if so, outputting a calculation result of identifying the optimization problem; otherwise, updating the iteration value and continuously carrying out iterative calculation on the identification optimization problem until the iteration times reach the maximum iteration times;
extracting a load participation coefficient matrix from a calculation result of the identification optimization problem;
and calculating according to the load participation coefficient matrix to obtain a time course identification result of the dynamic load of the structure.
Further as a preferred embodiment, the step of solving the optimization equation by using the fast iterative threshold compression algorithm to obtain the sparse identification result of the structural dynamic load further includes the following steps:
and for the load identification results included by different time windows at the same time, determining that the final identification result at the time is the average value of the identification results of the different time windows.
Specifically, the present embodiment uses an improved fast iterative threshold compression algorithm to solve the optimization equation, i.e. equation (12);
the classical fast iterative threshold compression algorithm is mainly developed and solved aiming at vector regularization, the invention expands the vector regularization to matrix regularization, and the main implementation flow of improving the fast iterative threshold compression algorithm is as follows:
beginning:
step (a): computing the matrix A T The maximum characteristic value of A is recorded as gamma max Let L =2 γ max Giving a regularization parameter lambda;
step (b): let iteration start value P 0 =0, taking the temporary variable P temp ＝P 0 Let the iterative process variable tt 1 ＝kk＝1；
Step (c): sequentially calculating a formula:
step (d): judging whether the maximum iteration times is reached; if yes, executing step (e); if not, let kk = kk +1, then jump to step (c) to continue execution;
a step (e): output result P kk ；
Finishing;
finally, the present embodiment derives the optimization result P identified Extracting a load participation coefficient matrix F, and calculating a load time interval identification result by combining a formula (3); when the load time interval recognition results are considered comprehensively, if the same time is included in different time windows, the final recognition result at the time is the average value of the recognition results of the time windows.
The implementation steps of the structural dynamic load sparse identification method based on matrix regularization are described in detail by taking the dynamic load identification problem of the cantilever beam structure as an example in combination with the attached drawings of the specification:
as shown in FIG. 2, the length of the cantilever beam of the present embodiment is l =697mm, and the bending rigidity EI =734.861880N m -2 Linear density ρ A =3.774747kg m -1 . The structure is divided into 10 beam units, and each beam unit comprises 2 nodes and 4 degrees of freedom. A dynamic load [2 ] is applied at 0.6l of the cantilever end]Reference numeral 1 in fig. 2 denotes an acceleration sensor; reference numeral 2 represents a structural dynamic load;
the load time-course signal of this embodiment is:
f(t)＝10[1-cos(10πt)]sin(30πt)N--(17)
in this embodiment, the first 4 orders of modal information of the structure is utilized, a vibration mode superposition method is selected to simulate the structural vibration response, and the damping ratio of the first 4 orders of modal is: 0.0080,0.0014,0.0016 and 0.0015. The time discrete interval for the positive analysis is taken as Δ t f = 1/(2 × 4096) s, and the spot sampling frequency is 4096Hz. As shown in fig. 2, the acceleration sensor 1 is arranged at 0.8l from the cantilever end, and the simulation formula is as follows, considering the influence of 5% measurement noise:
in the formula, b n And b respectively represents responses with noise and without noise, n represents the number of elements in b, lev represents the noise level, and rand represents a random vector and meets the standard normal distribution. The simulation measures the sampling time length 8s, and the corresponding acceleration response is shown in FIG. 3.
Referring to fig. 1, based on the above simulated actual measurement response, the structural dynamic load identification of this embodiment specifically includes the following steps:
s1, picking up structural acceleration response by an acceleration sensor; the acceleration sensor was placed 0.8l from the cantilever end and the measured acceleration response is shown in figure 3.
And S2, establishing a structural finite element model as shown in the attached figure 2.
S3, intercepting structural responses by adopting a time window, and storing the responses one by one in a row to form a response matrix; intercepting responses by adopting 15 time windows; each time window is 1s long and contains 4096 acceleration sampling points; two adjacent time windows are overlapped for 0.5s and contain 2048 acceleration sampling points; the time interval corresponding to each time window is as follows: (0 s,1s ], (0.5s, 1.5s ], (1s, 2s ], (1.5s, 2.5s ], (2s, 3s ], (2.5s, 3.5s ], (3s, 4s ], (3.5s, 4.5s ], (4 s,5s ], (4.5s, 5.5s ], (5s, 6s ], (5.5s, 6.5s ], (6 s,7s ], (6.5s, 7.5s ], (7 s,8s ]; the response matrix B generated based on a given time window sequence has 6 rows and 15 columns in total.
S4, according to the structural finite element model, considering the influence of unknown load and unknown initial conditions to establish a load identification matrix equation; when the discrete trigonometric function is selected to expand the unknown load, the number of the selected load components is n t =600; considering the first 4 th order mode of the structure, the corresponding initial condition components are 8; the system matrix a thus created has 4096 rows 608 columns and a corresponding structural excitation response P has 608 rows 15 columns.
S5, adopting matrix regularization to construct a load identification optimization problem, wherein the matrix regularization model is composed of two items, one item is a response fitting error and is defined as an F norm of a difference value of an estimated response matrix and an actually measured response matrix; the other term is a sparse penalty function term defined as the sum of the absolute values of the elements of the matrix P.
S6, solving an optimization equation by adopting an improved rapid iteration threshold compression algorithm, wherein during iterative solution, the shutdown conditions are as follows: the maximum iteration number is 2500; the regularization parameters are selected as: λ =0.0002 × β max Wherein beta is max Representation matrix A T The maximum value of the absolute value of the element in B; obtaining matrix P by iterative method identified Then, the matrix P is extracted identified The elements corresponding to the first 600 rows and 15 columns are combined with a formula (3) to back calculate the load time course information of each time window; finally, for the discrete points included by different time windows at the same time, the final recognition result at the time is taken as the average value of the recognition results of the multiple time windows.
Fig. 4 compares the structure-simulated dynamic load with the recognition dynamic load, and fig. 5 shows the recognition result of fig. 4 in a partial time period. As can be seen from the attached drawings 4 and 5, the structural dynamic load sparse identification method based on the matrix regularization can effectively invert the structural dynamic load and has high identification precision. In addition, when the system matrix in the embodiment of the present invention is established, only the time length of one window, that is, 1s, needs to be considered. It is noted that this value is only 1/8 of the total time span, therefore, the present invention can process the large-scale dynamic load identification problem with long time span with a system matrix with smaller dimension. Because the system matrix is closely related to the load identification time consumption, the method is favorable for fast solving of the identification process.
The invention integrates the advantages of a moving time window and information sparse representation, and popularizes a vector regularization load identification method to a matrix regularization form by considering the influence of unknown initial conditions, thereby disclosing a structural dynamic load sparse identification method based on matrix regularization and realizing the integral sparse identification of the structural dynamic load.
In addition, the influence of unknown initial conditions is not considered in the prior art, the used regularization method is vector regularization, namely, the load to be identified and the response are both organized according to a vector form, so that the method is not suitable for identifying the dynamic load of the unknown initial conditions, and meanwhile, when the problem of long-time dynamic load identification is solved, the rectangular dimension of an identification equation system is too large, and the time consumption for solving is obvious; on the contrary, the method considers the influence of unknown initial conditions, segments time sections by using time windows, stores the responses corresponding to different time windows in a column sequence to form a matrix representation form of the responses, and constructs a matrix regularization identification equation for identification on the basis. The dynamic load identification method is suitable for dynamic load identification under unknown initial conditions, can integrally process the problem of long-time dynamic load identification by using a system matrix with smaller dimension, and can reduce the time consumption of calculation.
The prior art focuses on moving load identification, namely the acting position and the amplitude of a load change along with time; the invention aims at the problem of dynamic load identification of a fixed action position, and does not consider the change of a load position along with time. The invention ensures that different time windows have consistent system matrixes, and is the theoretical and technical basis for establishing a matrix regularization method.
The embodiment of the invention also provides a device for recognizing the sparse structure dynamic load based on the matrix regularization, which comprises the following steps:
at least one processor;
at least one memory for storing at least one program;
when executed by the at least one processor, cause the at least one processor to implement the method for sparse identification of structural payloads based on matrix regularization.
The contents in the above method embodiments are all applicable to the present apparatus embodiment, the functions specifically implemented by the present apparatus embodiment are the same as those in the above method embodiments, and the advantageous effects achieved by the present apparatus embodiment are also the same as those achieved by the above method embodiments.
In addition, a storage medium is further provided, where processor-executable instructions are stored, and when executed by a processor, the processor-executable instructions are configured to perform the method for sparse identification of structural dynamic loads based on matrix regularization.
In alternative embodiments, the functions/acts noted in the block diagrams may occur out of the order noted in the operational illustrations. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality/acts involved. Furthermore, the embodiments presented and described in the flow charts of the present invention are provided by way of example in order to provide a more thorough understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is changed and in which sub-operations described as part of larger operations are performed independently.
Furthermore, although the present invention is described in the context of functional modules, it should be understood that, unless otherwise indicated to the contrary, one or more of the described functions and/or features may be integrated in a single physical device and/or software module, or one or more functions and/or features may be implemented in separate physical devices or software modules. It will also be appreciated that a detailed discussion of the actual implementation of each module is not necessary for an understanding of the present invention. Rather, the actual implementation of the various functional modules in the apparatus disclosed herein will be understood within the ordinary skill of an engineer, given the nature, function, and internal relationship of the modules. Accordingly, those of ordinary skill in the art will be able to practice the invention as set forth in the claims without undue experimentation. It is also to be understood that the specific concepts disclosed are merely illustrative of and not intended to limit the scope of the invention, which is defined by the appended claims and their full scope of equivalents.
The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a computer readable storage medium. Based on such understanding, the technical solution of the present invention or a part thereof which substantially contributes to the prior art may be embodied in the form of a software product, which is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.
The logic and/or steps represented in the flowcharts or otherwise described herein, e.g., an ordered listing of executable instructions that can be considered to implement logical functions, can be embodied in any computer-readable medium for use by or in connection with an instruction execution system, apparatus, or device, such as a computer-based system, processor-containing system, or other system that can fetch the instructions from the instruction execution system, apparatus, or device and execute the instructions. For the purposes of this description, a "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device.
It should be understood that portions of the present invention may be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, various steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, any one or combination of the following techniques, which are known in the art, may be used: discrete logic circuits with logic gates for implementing logic functions on data information, application specific integrated circuits with appropriate combinational logic gates, programmable Gate Arrays (PGAs), field Programmable Gate Arrays (FPGAs), etc.
In the description herein, references to the description of the term "one embodiment," "some embodiments," "an example," "a specific example," or "some examples," etc., mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (5)
1. A structural dynamic load sparse identification method based on matrix regularization is characterized in that: the method comprises the following steps:
establishing a structure finite element model according to the actually measured modal information of the structure;
intercepting structural acceleration response information under the action of dynamic load through a time window, and establishing a response matrix;
establishing a load identification matrix equation according to the structural finite element model, the response matrix, the load influence factors and the initial condition influence factors;
adopting matrix regularization to construct a load identification optimization problem;
solving an optimization equation by adopting a fast iterative threshold compression algorithm to obtain a sparse identification result of the structural dynamic load;
the step of establishing the structure finite element model according to the structure actual measurement modal information comprises the following steps:
obtaining structural modal information through structural test modal analysis, wherein the structural modal information comprises the frequency, the vibration mode and the damping ratio of a structure;
according to the structural modal information, combining the design parameters and the material information of the structure, and establishing a structural finite element analysis model;
the step of intercepting the structural acceleration response information under the action of the dynamic load through a time window and establishing a response matrix comprises the following steps:
determining the time length to be identified and the initial time according to the dynamic load identification problem;
determining the window length of a time window according to the time length to be identified;
based on the determined window length, intercepting the actually measured acceleration response information of the structure through a time window to generate a response matrix;
the response matrix is represented as:
wherein B represents a response matrix; b i Representing acceleration response information corresponding to the ith sampling point; w represents the total number of time windows, and k is the number of sampling points contained in each time window; k is a radical of formula 0 The number of points is sampled for the overlapping portion.
2. The method for sparsely identifying the structural dynamic load based on the matrix regularization according to claim 1, characterized in that: the step of establishing the load identification matrix equation according to the structural finite element model, the response matrix, the load influence factors and the initial condition influence factors comprises the following steps:
determining a discrete trigonometric function;
performing discrete sampling on the discrete trigonometric function to obtain discrete data and construct a vector;
after the vector is normalized, obtaining a discrete load component through a discrete trigonometric function;
considering the modal regular coordinate, and developing the initial condition of the structure by using a modal space;
calculating the structural acceleration response under the action of the unit load component and the unit initial condition component by a vibration mode superposition method to form a load identification system matrix;
and adjusting the load identification system matrix according to the acceleration response information caused by the load component, and further establishing a load identification matrix equation.
3. The method for sparse recognition of structural dynamic loads based on matrix regularization according to claim 1, characterized in that: in the step of constructing the load identification optimization problem by adopting the matrix regularization, the expression of the load identification optimization problem is as follows:
wherein, P identified Representing a matrix identification result; symbol
Representing a minimization optimization problem;
(symbol)
expressing the square of the F norm of a matrix; a represents a system matrix; p represents a structure excitation matrix, including structure load and initial conditions; b represents a response matrix; λ represents a regularization parameter; p (i, j) denotes the ith row and jth column of the matrix P.
4. The method for sparse recognition of structural dynamic loads based on matrix regularization according to claim 1, characterized in that: the step of solving the optimization equation by adopting the fast iteration threshold compression algorithm to obtain the sparse identification result of the structural dynamic load comprises the following steps:
calculating the maximum characteristic value of a load identification system matrix;
performing iterative computation on the identification optimization problem according to a preset regularization parameter and an initial iteration value;
judging whether the iteration times reach the maximum iteration times, if so, outputting a calculation result for identifying the optimization problem; otherwise, updating the iteration value and continuing to perform iterative calculation on the identification optimization problem until the iteration number reaches the maximum iteration number;
extracting a load participation coefficient matrix from a calculation result of the identification optimization problem;
and calculating according to the load participation coefficient matrix to obtain a time course identification result of the dynamic load of the structure.
5. The method according to claim 4, characterized in that: the method comprises the following steps of solving an optimization equation by adopting a fast iteration threshold compression algorithm to obtain a sparse identification result of the dynamic load of the structure, and further comprises the following steps:
and for the load identification results included by different time windows at the same time, determining that the final identification result at the time is the average value of the identification results of the different time windows.
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