CN113536923B - Structure local model-free nonlinear positioning identification technology based on monitoring data driving - Google Patents
Structure local model-free nonlinear positioning identification technology based on monitoring data driving Download PDFInfo
- Publication number
- CN113536923B CN113536923B CN202110657150.XA CN202110657150A CN113536923B CN 113536923 B CN113536923 B CN 113536923B CN 202110657150 A CN202110657150 A CN 202110657150A CN 113536923 B CN113536923 B CN 113536923B
- Authority
- CN
- China
- Prior art keywords
- unit
- nonlinear
- wavelet
- units
- response data
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000012544 monitoring process Methods 0.000 title description 6
- 238000005516 engineering process Methods 0.000 title description 2
- 238000000034 method Methods 0.000 claims abstract description 76
- 230000004044 response Effects 0.000 claims abstract description 59
- 238000009826 distribution Methods 0.000 claims abstract description 47
- 230000005284 excitation Effects 0.000 claims abstract description 39
- 238000013016 damping Methods 0.000 claims description 14
- 230000006870 function Effects 0.000 claims description 6
- 238000005259 measurement Methods 0.000 claims description 5
- 238000013519 translation Methods 0.000 claims description 4
- 238000003860 storage Methods 0.000 claims description 2
- 239000010410 layer Substances 0.000 description 25
- 230000001133 acceleration Effects 0.000 description 9
- 238000010586 diagram Methods 0.000 description 8
- 239000013598 vector Substances 0.000 description 7
- 230000000694 effects Effects 0.000 description 5
- 238000001914 filtration Methods 0.000 description 5
- 230000036541 health Effects 0.000 description 5
- 230000002093 peripheral effect Effects 0.000 description 5
- 238000005070 sampling Methods 0.000 description 5
- 230000009471 action Effects 0.000 description 4
- 238000006073 displacement reaction Methods 0.000 description 4
- 239000000463 material Substances 0.000 description 4
- 239000011159 matrix material Substances 0.000 description 4
- 238000004088 simulation Methods 0.000 description 4
- 238000012795 verification Methods 0.000 description 4
- 238000013461 design Methods 0.000 description 3
- 238000001514 detection method Methods 0.000 description 3
- 230000008569 process Effects 0.000 description 3
- 238000005316 response function Methods 0.000 description 3
- 238000000605 extraction Methods 0.000 description 2
- 239000011229 interlayer Substances 0.000 description 2
- 230000004807 localization Effects 0.000 description 2
- 238000013178 mathematical model Methods 0.000 description 2
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 238000012546 transfer Methods 0.000 description 2
- 230000001131 transforming effect Effects 0.000 description 2
- 101100136092 Drosophila melanogaster peng gene Proteins 0.000 description 1
- 229910000831 Steel Inorganic materials 0.000 description 1
- 238000013459 approach Methods 0.000 description 1
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000006399 behavior Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000007596 consolidation process Methods 0.000 description 1
- 230000006735 deficit Effects 0.000 description 1
- 238000000802 evaporation-induced self-assembly Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 230000000737 periodic effect Effects 0.000 description 1
- 230000002787 reinforcement Effects 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000029058 respiratory gaseous exchange Effects 0.000 description 1
- 230000002441 reversible effect Effects 0.000 description 1
- 230000035945 sensitivity Effects 0.000 description 1
- 238000010008 shearing Methods 0.000 description 1
- 239000010959 steel Substances 0.000 description 1
- 238000012360 testing method Methods 0.000 description 1
- 230000009466 transformation Effects 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/11—Complex mathematical operations for solving equations, e.g. nonlinear equations, general mathematical optimization problems
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/14—Fourier, Walsh or analogous domain transformations, e.g. Laplace, Hilbert, Karhunen-Loeve, transforms
- G06F17/148—Wavelet transforms
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
- G06F2218/02—Preprocessing
- G06F2218/04—Denoising
- G06F2218/06—Denoising by applying a scale-space analysis, e.g. using wavelet analysis
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Theoretical Computer Science (AREA)
- Computational Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Pure & Applied Mathematics (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- General Engineering & Computer Science (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Computer Vision & Pattern Recognition (AREA)
- Artificial Intelligence (AREA)
- Operations Research (AREA)
- Signal Processing (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The disclosure provides a nonlinear unit positioning method of an engineering structure, comprising the following steps: acquiring strain response data of each unit of the target engineering structure to which external excitation is applied; acquiring wavelet energy probability distribution of each unit based on strain response data of each unit; acquiring the relative wavelet entropy of each unit and other units based on the wavelet energy probability distribution of each unit; and acquiring nonlinear units of the target engineering structure based on the relative wavelet entropy of each unit and other units. The present disclosure also provides a nonlinear force identification method.
Description
Technical Field
The disclosure belongs to the technical field of safety monitoring of civil engineering structures, and particularly relates to a nonlinear unit positioning and nonlinear force identification method of an engineering structure.
Background
Civil engineering structures often develop significant non-linear behavior under fatigue loading or strong excitation (e.g., earthquakes), such as breathing cracks in concrete, yielding of steel reinforcement, etc. While structures often require health assessment after experiencing fatigue loading or strong excitation to ensure their safety and reliability.
The theory in the linear structures such as the transfer ratio function, the frequency response function and the like is not applicable any more because the structure enters a nonlinear state, and the nonlinear unit has various types and a complex model. The identification of nonlinear units in a multiple degree of freedom system based on vibration signals is therefore a very important issue in civil engineering. To date, little or no limitation has been placed on how to effectively and accurately identify nonlinear units of an in-service structure.
Existing nonlinear positioning methods can be classified into model-based methods and methods that do not require a model. Model-based methods often require mathematical models of known or established nonlinear restoring forces. Although these model parameters have clear physical significance, it is a very difficult task to build a mathematical model of the nonlinear restoring force, so in recent years research on model-free nonlinear positioning has gained more and more attention.
Peng 1 proposes a method for detecting a nonlinear position in a periodic structure based on the characteristics of a nonlinear output frequency response function. Lang 2 is used to detect and locate linear and nonlinear impairments in multi-degree of freedom structures by introducing a transfer ratio function of the nonlinear output frequency response function. The above approach assumes that only one nonlinear element is present in the system and that the external load is required to be known. Li 3,4 proposes a data-driven nonlinear unit positioning method based on time-frequency characteristic fractal dimension, firstly, utilizing wavelet transformation to obtain time-frequency characteristic of signal, then utilizing fractal dimension to etch out the difference of time-frequency characteristic so as to implement nonlinear positioning. Wang [5,6] projects the nonlinear force vector caused by the nonlinear element onto the measurable degree of freedom in a reduced order, referred to as a reduced order pseudo force. The nonlinear element is located by comparing the magnitude and phase properties of the reduced order pseudo force in each degree of freedom. But this method requires a structural action of the swept excitation. Wavelet entropy can represent the degree of order/disorder of signals and has been widely studied and applied in structural detection in recent years [7-9]. And Ren and Sun 10 propose damage identifying features such as wavelet entropy, relative wavelet entropy and the like, and vibration signals measured by comparing an undamaged structure and a damaged structure are detected and positioned. Diao et al [11] take wavelet entropy in both the intact structure and the damaged state as damage index, and input it into the neural network to locate the damaged position of the structure. Li et al [12] propose a method based on wavelet packet singular entropy to identify damage by analyzing the dynamic response of a curvilinear continuous beam bridge under seismic excitation. However, the above methods all require a signal of structural integrity. But for most existing structures, particularly older structures, health data is generally lacking. Lee et al [13] propose a baseline-free damage localization algorithm based on continuous relative wavelet entropy and apply it to bolt loosening localization of truss structures. According to the method, acceleration response data are decomposed through continuous wavelet changes, wavelet coefficients are normalized, continuous relative wavelet entropy of different positions is further calculated and compared, and therefore damage positioning is achieved. Therefore, how to perform nonlinear cell positioning of in-service structures based on structure response monitoring data is a key issue to be solved in the case of unknown nonlinear models and lack of health data.
In addition, the identification of the restoring force of the nonlinear unit can further quantify the type and degree of nonlinearity. The existing non-linear restoring force identification method without a model has certain limitations, such as difficulty in determining the expansion order [14-15] in series expansion, requirement of response information [16-17] of all degrees of freedom, requirement of known external excitation or non-linear force action position [18-20], and the like. How to identify nonlinear cell characteristics in a structure based on monitoring data drive of the structure response is also a problem to be solved in the case of unknown nonlinear models.
Reference is made to:
[1]Peng,Z.K.,Lang,Z.Q.,Chu,F.L.,et al.Locating nonlinear components in periodic structures using nonlinear effects[J].Structural Health Monitoring,2010,9(5):401-411.
[2]Lang,Z.,Park,Gyeshin.,Farrar,Charles.,Todd,Michael.,Mao,Zhu.,Zhao,L.&Worden,K.Transmissibility of non-linear output frequency response functions with application in detection and location of damage in MDOF structural systems.International Journal of Non-Linear Mechanics,2011,46:841-853.
[3] Tao Dongwang structural seismic damage identification method based on data driven and physical model research [ D ]. Harbin university of industry, 2013.
[4]Li,H.,Tao,D.,Huang,Y.,et al.A data-driven approach for seismic damage detection of shear-type building structures using the fractal dimension of time–frequency features[J].Structural Control and Health Monitoring,2013,20.
[5]Wang,X.,Khodaparast,H.H.,Shaw,A.D.,et al.Localisation of local nonlinearities in structural dynamics using spatially incomplete measured data[J].Mechanical Systems and Signal Processing,2018,99:364-383.
[6] Wang Xing kinetic calculations and experimental identification of local nonlinear structures [ D ].2016.
[7] Sun Zengshou, fan Keju beam-slab combined bridge damage identification study based on lifting wavelet entropy index [ J ] vibration and impact 2012,31 (11): 114-117.
[8]Yun,G.J.,Lee,S.G.,Carletta,J.,et al.Decentralized damage identification using wavelet signal analysis embedded on wireless smart sensors[J].Engineering Structures,2011,33(7):2162-2172.
[9] Chen Liang structural damage identification based on wavelet energy entropy [ D ].
[10]Ren,W.X.,Sun,Z.S.Structural damage identification by using wavelet entropy[J].Engineering Structures,2008,30(10):2840-2849.
[11]Diao,Y.,Zhang,X.,Sun,Z.,et al.Wavelet entropy based structural damage identification under seismic excitation[J].Smart Materials and Structures,2018,27(10).
[12]Li,D.,Cao,M.,Deng,T.,Zhang,S.Wavelet Packet Singular Entropy-Based Method for Damage Identification in Curved Continuous Girder Bridges under Seismic Excitations.Sensors(Basel).2019;19(19):4272.
[13]Lee,S.G.,Yun,G.J.,Shang,S.Reference-free damage detection for truss bridge structures by continuous relative wavelet entropy method[J].Structural Health Monitoring,2014,13(3):307-320.
[14]Xu,B.,He,J.,&Masri,S.F.Data-based model-free hysteretic restoring force and mass identification for dynamic systems.Computer-Aided Civil and Infrastructure Engineering,2015,30(1),2–18.
[15] Xu, structural restoring force under unknown earthquake excitation, and quality non-parameterized identification [ J ]. Engineering mechanics, 2019,36 (09): 180-187.
[16]Zhou,C.,Chase,J.G.,Rodgers,G.W.,Tomlinson,H.,&Xu,C.Physical parameter identification of structural systems with hysteretic pinching.Computer-Aided Civil and Infrastructure Engineering,2015,30(4),247–262.
[17]Zhou,C.,Chase,J.G.,Rodgers,G.W.,Xu,C.Comparing model-based adaptive LMS filters and a model free hysteresis loop analysis method for structural health monitoring.Mechanical Systems and Signal Processing.2017,84,384-398.
[18]Li,H.,Mao,C.X.,&Ou,J.P.(2013).Identification of hysteretic dynamic systems by using hybrid extended Kalman filter and wavelet multiresolution analysis with limited observation.Journal of Engineering Mechanics-ASCE.139(5),547-558.
[19]Yang,X.J.,Su,H.,Liu,L.J.,&Lei,Y.Identification of the nonlinear characteristics of rubber bearings in model-free base-isolated buildings using partial measurements of seismic responses.Journal of Low Frequency Noise Vibration and Active Control,2019,39(3),690-703.
[20]Su,H.,Yang,X.J.,Liu,L.J.,&Lei,Y.Identifying nonlinear characteristics of model-free MR dampers in structures with partial response data.Measurement,2018,130,362-371.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention provides an innovative technology for positioning and identifying nonlinear units in engineering structures based on structural response monitoring data, achieves the purpose of monitoring and evaluating performance changes of the structures in the service life and service cycle, and has important technical innovation significance and practical application value.
The present disclosure provides a method for positioning a structural nonlinear unit and identifying a nonlinear restoring force, aiming at the problems existing in the prior art. And the model-free nonlinear unit positioning based on the strain response data driving is realized by taking the increase of the disturbance degree of the system caused by the nonlinear unit and the high sensitivity of the strain response to the nonlinear unit into consideration and adopting the relative wavelet entropy as an index. After the positioning is finished, the restoring force of the nonlinear unit at the positioned position is regarded as 'additional virtual force' acting on the linear structure, the nonlinear restoring force is subjected to model-free recognition by adopting Kalman filtering (GKF-UI) (CN 201811533410.7) under generalized unknown excitation, the nonlinear unit positioning can be realized without needing baseline data, and a nonlinear unit model is not required to be assumed or established in the positioning and recognition processes, so that the method has the characteristics of technical innovation and meeting the actual application requirements.
According to one aspect of the present disclosure, there is provided a nonlinear unit positioning method of an engineering structure, including:
acquiring strain response data of each unit of the target engineering structure to which external excitation is applied;
acquiring wavelet energy probability distribution of each unit based on strain response data of each unit;
Acquiring the relative wavelet entropy of each unit and other units based on the wavelet energy probability distribution of each unit; and
And acquiring the nonlinear unit of the target engineering structure based on the relative wavelet entropy of each unit and other units.
According to a nonlinear unit positioning method of an engineering structure of at least one embodiment of the present disclosure, a wavelet energy probability distribution of each unit is obtained based on strain response data of each unit, including:
for strain response data x (t), the wavelet expansion is expressed as:
Wherein, psi (t) is a wavelet basis function, j and k are discrete expansion parameters and translation parameters respectively, j, k epsilon Z, Z is a set of positive integers, and alpha j,k is a wavelet coefficient;
the wavelet energy probability distribution is expressed as:
Wherein the value of p jk is the ratio of the energy of a certain specific coefficient alpha j,k to the total energy, and the value of p jk is the wavelet energy probability distribution, so that the sum of the values of all p jk is 1.
According to a nonlinear unit positioning method of an engineering structure of at least one embodiment of the present disclosure, a relative wavelet entropy of each unit to other units is obtained based on a wavelet energy probability distribution of each unit, including:
the relative wavelet entropy of each cell to the other cells is obtained by:
Where p and q represent wavelet energy probability distributions of strain response data for different cells and α and β represent wavelet coefficients for different cells, respectively.
According to a non-linear cell positioning method of an engineering structure of at least one embodiment of the present disclosure,
Based on the relative wavelet entropy of each unit and other units, obtaining a nonlinear unit of the target engineering structure, including:
Acquiring nonlinear units of the target engineering structure through baseline-free identification indexes, wherein the baseline-free identification indexes are obtained based on the relative wavelet entropy of each unit and other units through the following formula:
Where n represents a total number of measurement locations corresponding to a number of sensors used to collect strain response data for each cell of the target engineered structure.
The nonlinear unit positioning method of an engineering structure according to at least one embodiment of the present disclosure further includes:
seismic external excitation is applied to the target engineering structure.
According to a nonlinear unit positioning method of an engineering structure of at least one embodiment of the present disclosure, strain response data of each unit of the target engineering structure is acquired using a sensor, respectively.
According to a non-linear cell positioning method of an engineering structure of at least one embodiment of the present disclosure, the external excitation is preferably an El-Centro seismic wave as the external excitation.
According to another aspect of the present disclosure, there is provided a nonlinear unit positioning apparatus of an engineering structure, comprising:
A strain response data acquisition module that acquires strain response data of each unit of the target engineering structure to which external excitation is applied;
The device comprises a wavelet energy probability distribution generation module, a first module and a second module, wherein the wavelet energy probability distribution generation module acquires the wavelet energy probability distribution of each unit based on strain response data of each unit;
the relative wavelet entropy generation module is used for acquiring the relative wavelet entropy of each unit and other units based on wavelet energy probability distribution of each unit; and
And the nonlinear unit acquisition module acquires nonlinear units of the target engineering structure based on the relative wavelet entropy of each unit and other units.
According to still another aspect of the present disclosure, there is provided a nonlinear force recognition method based on the nonlinear unit positioning method of any one of the above, including:
Constructing a motion equation of each unit of the target engineering structure based on the mass, damping and unit structure restoring force of each unit and external excitation; and
Solving the motion equation based on the known mass, damping and stiffness matrixes of each unit to obtain the restoring force of the unit structure, wherein the restoring force of the unit structure is the nonlinear force.
According to a nonlinear force identification method of at least one embodiment of the present disclosure, solving the equation of motion based on the known mass, damping, and stiffness matrices of the respective cells to obtain the cell structure restoring force includes:
the equation of motion is solved using kalman filtering under generalized unknown excitation (kf-UI) to obtain the cell structure restoring force.
According to a nonlinear force identification method of at least one embodiment of the present disclosure, the equation of motion is constructed as:
Wherein the method comprises the steps of And x is the n-dimensional column vector of the acceleration, velocity and displacement of the unit structure, f is the external excitation vector, eta is the matrix of the external excitation action position, M, C represents the mass and damping of the unit structure, respectively,N-dimensional column vectors of restoring force of the unit structure, wherein z is a system parameter;
wherein the target engineering structure has an n-layer structure.
A nonlinear force identification method according to at least one embodiment of the present disclosure further includes:
Extracting additional virtual force from the motion equation, and solving the motion equation by using Kalman filtering (GKF-UI) under generalized unknown excitation to obtain the additional virtual force, wherein the additional virtual force is expressed as f u Where K is the stiffness matrix of the cell structure.
According to the nonlinear force identification method of at least one embodiment of the present disclosure, the unit structure restoring force is acquired based on the obtained additional virtual force
According to the nonlinear force identification method of at least one embodiment of the present disclosure, the equation of motion is an equation of motion in a relative motion coordinate system.
According to a nonlinear force identification method of at least one embodiment of the present disclosure, additional virtual force extraction is performed on the equation of motion, including:
Transforming the equation of motion into And is further deformed into
According to still another aspect of the present disclosure, there is provided a nonlinear force recognition apparatus of a nonlinear unit positioning apparatus based on the above-described engineering structure, comprising:
The motion equation building module builds a motion equation of each unit of the target engineering structure based on the mass, the damping and the unit structure restoring force of each unit and external excitation; and
And the nonlinear solving module solves the motion equation based on the known mass, damping and rigidity matrixes of each unit to obtain the restoring force of the unit structure, wherein the restoring force of the unit structure is the nonlinear force.
According to still another aspect of the present disclosure, there is provided an electronic apparatus including:
A memory storing execution instructions; and
A processor executing the memory-stored execution instructions, causing the processor to perform the method of any one of the above.
According to yet another aspect of the present disclosure, there is provided a readable storage medium having stored therein execution instructions which when executed by a processor are adapted to carry out the method of any one of the above.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the principles of the disclosure.
Fig. 1 is a flow chart of a method of nonlinear cell positioning of an engineered structure according to one embodiment of the present disclosure.
Fig. 2 is a flow chart of a nonlinear force identification method according to one embodiment of the present disclosure.
Fig. 3 is a block schematic diagram of a nonlinear element positioning apparatus in the form of an electronic device according to one embodiment of the present disclosure.
Fig. 4 is a block schematic diagram of a nonlinear force recognition apparatus in the form of an electronic device in accordance with one embodiment of the present disclosure.
Fig. 5 is a block schematic diagram of a nonlinear element positioning and nonlinear force recognition apparatus implemented based on the same electronic device according to one embodiment of the present disclosure.
Fig. 6 to 9 are graphs of single nonlinear unit positioning results of 2-unit nonlinearity, 4-unit nonlinearity, 6-unit nonlinearity, and 8-unit nonlinearity, respectively.
Fig. 10 and 11 are a nonlinear restoring force time course comparison chart and a nonlinear restoring force hysteresis loop comparison chart for nonlinear force identification using a layer 2 nonlinear unit as an example, respectively.
Fig. 12 to 15 are two nonlinear unit positioning result diagrams of 3, 6, 4, 7, 5, 6, 2, 8 unit nonlinearities, respectively.
Fig. 16 and 17 show a nonlinear restoring force time course comparison chart (bilinear) and a nonlinear restoring force hysteresis loop comparison chart (bilinear), respectively, of nonlinear force identification by taking a layer 3 nonlinear unit as an example.
Fig. 18 and 19 show a nonlinear restoring force time course comparison chart (three-linearity) and a nonlinear restoring force hysteresis loop comparison chart (three-linearity) for nonlinear force identification by taking a layer 6 nonlinear unit as an example, respectively.
Fig. 20 to 23 are graphs of single nonlinear unit (rod unit) positioning results of 1 unit nonlinearity, 4 unit nonlinearity, 8 unit nonlinearity, and 9 unit nonlinearity, respectively.
Fig. 24 and 25 show a nonlinear restoring force time course comparison chart and a nonlinear restoring force hysteresis loop comparison chart, respectively, for nonlinear force identification by taking the nonlinear occurrence of the 6 th lever as an example.
Detailed Description
The present disclosure is described in further detail below with reference to the drawings and the embodiments. It is to be understood that the specific embodiments described herein are merely illustrative of the relevant content and not limiting of the present disclosure. It should be further noted that, for convenience of description, only a portion relevant to the present disclosure is shown in the drawings.
In addition, embodiments of the present disclosure and features of the embodiments may be combined with each other without conflict. The technical aspects of the present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Unless otherwise indicated, the exemplary implementations/embodiments shown are to be understood as providing exemplary features of various details of some ways in which the technical concepts of the present disclosure may be practiced. Thus, unless otherwise indicated, features of the various implementations/embodiments may be additionally combined, separated, interchanged, and/or rearranged without departing from the technical concepts of the present disclosure.
The use of cross-hatching and/or shading in the drawings is typically used to clarify the boundaries between adjacent components. As such, the presence or absence of cross-hatching or shading does not convey or represent any preference or requirement for a particular material, material property, dimension, proportion, commonality between illustrated components, and/or any other characteristic, attribute, property, etc. of a component, unless indicated. In addition, in the drawings, the size and relative sizes of elements may be exaggerated for clarity and/or descriptive purposes. While the exemplary embodiments may be variously implemented, the specific process sequences may be performed in a different order than that described. For example, two consecutively described processes may be performed substantially simultaneously or in reverse order from that described. Moreover, like reference numerals designate like parts.
When an element is referred to as being "on" or "over", "connected to" or "coupled to" another element, it can be directly on, connected or coupled to the other element or intervening elements may be present. However, when an element is referred to as being "directly on," "directly connected to," or "directly coupled to" another element, there are no intervening elements present. For this reason, the term "connected" may refer to physical connections, electrical connections, and the like, with or without intermediate components.
For descriptive purposes, the present disclosure may use spatially relative terms such as "under … …," under … …, "" under … …, "" lower, "" above … …, "" upper, "" above … …, "" upper "and" side (e.g., in "sidewall") to describe one component's relationship to another (other) component as illustrated in the figures. In addition to the orientations depicted in the drawings, the spatially relative terms are intended to encompass different orientations of the device in use, operation, and/or manufacture. For example, if the device in the figures is turned over, elements described as "under" or "beneath" other elements or features would then be oriented "over" the other elements or features. Thus, the exemplary term "below … …" may encompass both an orientation of "above" and "below". Furthermore, the device may be otherwise positioned (e.g., rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. Furthermore, when the terms "comprises" and/or "comprising," and variations thereof, are used in the present specification, the presence of stated features, integers, steps, operations, elements, components, and/or groups thereof is described, but the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof is not precluded. It is also noted that, as used herein, the terms "substantially," "about," and other similar terms are used as approximation terms and not as degree terms, and as such, are used to explain the inherent deviations of measured, calculated, and/or provided values that would be recognized by one of ordinary skill in the art.
Fig. 1 is a diagram illustrating a method for positioning a nonlinear unit of an engineering structure according to an embodiment of the present disclosure, and as shown in fig. 1, a method 100 for positioning a nonlinear unit of an engineering structure according to the present embodiment includes:
102. acquiring strain response data of each unit of the target engineering structure to which external excitation is applied;
104. Acquiring wavelet energy probability distribution of each unit based on strain response data of each unit;
106. Acquiring the relative wavelet entropy of each unit and other units based on the wavelet energy probability distribution of each unit; and
108. Based on the relative wavelet entropy of each unit and other units, nonlinear units of the target engineering structure are obtained.
The target engineering structure is divided into a plurality of unit structures, and strain response data of each unit structure are acquired respectively.
For the nonlinear cell positioning method 100 of the engineering structure of the above embodiment, preferably, obtaining the wavelet energy probability distribution of each cell based on the strain response data of each cell includes:
for strain response data x (t), the wavelet expansion is expressed as:
Wherein, psi (t) is a wavelet basis function, j and k are discrete expansion parameters and translation parameters respectively, j, k epsilon Z, Z is a set of positive integers, and alpha j,k is a wavelet coefficient;
the wavelet energy probability distribution is expressed as:
Wherein the value of p jk is the ratio of the energy of a certain specific coefficient alpha j,k to the total energy, and the value of p jk is the wavelet energy probability distribution, so that the sum of the values of all p jk is 1.
For the nonlinear cell positioning method 100 of the engineering structure of the above embodiment, preferably, obtaining the relative wavelet entropy of each cell and other cells based on the wavelet energy probability distribution of each cell includes:
the relative wavelet entropy of each cell to the other cells is obtained by:
Where p and q represent wavelet energy probability distributions of strain response data for different cells and α and β represent wavelet coefficients for different cells, respectively.
Wherein the relative wavelet entropy is equal to zero when p jk＝qjk, this property can be used for structure detection. When a structure is in good condition, the wavelet energy probability distribution p jk,qjk at different locations is almost the same, and the relative wavelet entropy is close to zero. The probability distribution of wavelet energy of the response signal is typically changed to some extent when the structure is nonlinear, and the p jk value of the structure is changed, increasing the relative wavelet entropy of the structure.
Wherein, wavelet entropy can be expressed as:
the degree of disorder of the vibration signal of the structure measured is increased due to the system variation caused by the nonlinearity of the unit structure, the degree of disorder of the vibration signal of the structure is increased, the probability distribution p jk of wavelet energy described above is changed, and the entropy is increased. In this way, wavelet entropy can accurately measure wavelet energy probability distribution changes. To characterize the change in wavelet entropy, the relative wavelet entropy described above was introduced.
For the method 100 for locating a nonlinear unit of an engineering structure in the foregoing embodiments, preferably, obtaining a nonlinear unit of a target engineering structure based on the relative wavelet entropy of each unit and other units includes:
Acquiring nonlinear units of the target engineering structure through baseline-free identification indexes, wherein the baseline-free identification indexes are obtained based on the relative wavelet entropy of each unit and other units through the following formula:
Where n represents the total number of measurement locations corresponding to the number of sensors used to collect strain response data for each cell of the target engineered structure.
By the baseline-free identification index of the present embodiment, the vibration signal of the measurement point is compared with the vibration signals of other reference points, thereby realizing nonlinear detection without using lossless state data. Assuming that the alpha position is non-linear, all terms of SRWE(pα|q1),SRWE(pα|q2),......SRWE(pα|qn) show a higher value (except S RWE(pα|qα) equal to 0.
For the nonlinear unit positioning method 100 of the engineering structure of each of the above embodiments, preferably, the method further includes:
seismic external excitation is applied to the target engineering structure.
For the nonlinear cell positioning method 100 of the engineering structure of each of the above embodiments, strain response data of each cell of the target engineering structure is preferably acquired using a sensor, respectively.
Wherein the sensor is a strain sensor.
For the engineering structure nonlinear element positioning method 100 of the various embodiments described above, the external excitation is preferably an El-Centro seismic wave as the external excitation.
According to one embodiment of the present disclosure, a nonlinear unit positioning apparatus 1000 of the present disclosure includes:
the strain response data acquisition module 1002, the strain response data acquisition module 1002 acquiring strain response data of each unit of the target engineering structure to which external excitation is applied;
A wavelet energy probability distribution generation module 1004, the wavelet energy probability distribution 1004 obtaining a wavelet energy probability distribution for each cell based on strain response data for each cell;
The relative wavelet entropy generation module 1006, the relative wavelet entropy 1006 obtains the relative wavelet entropy of each unit and other units based on the wavelet energy probability distribution of each unit; and
The nonlinear unit acquisition module 1008, the nonlinear unit acquisition module 1008 acquires nonlinear units of the target engineering structure based on the relative wavelet entropy of each unit and other units.
Fig. 3 is a block schematic diagram of a nonlinear element positioning apparatus in the form of an electronic device according to one embodiment of the present disclosure.
As shown in fig. 3, a nonlinear element positioning apparatus 1000 in the form of an electronic device may include corresponding modules that perform each or several of the steps in the flowcharts described above. Accordingly, each step or several steps of the above-described flowcharts may be performed by a respective module, and the nonlinear unit positioning apparatus 1000 may include one or more of these modules. A module may be one or more hardware modules specifically configured to perform the respective steps, or be implemented by a processor configured to perform the respective steps, or be stored within a computer-readable medium for implementation by a processor, or be implemented by some combination.
As shown in fig. 3, the nonlinear cell positioning apparatus 1000 may be implemented using a bus architecture. The bus architecture may include any number of interconnecting buses and bridges depending on the specific application of the hardware and the overall design constraints. Bus 1100 connects together various circuits including one or more processors 1200, memory 1300, and/or hardware modules. Bus 1100 may also connect various other circuits 1400, such as peripherals, voltage regulators, power management circuits, external antennas, and the like.
Bus 1100 may be an industry standard architecture (ISA, industry Standard Architecture) bus, a peripheral component interconnect (PCI, PERIPHERAL COMPONENT) bus, or an extended industry standard architecture (EISA, extended Industry Standard Component) bus, among others. The buses may be divided into address buses, data buses, control buses, etc. For ease of illustration, only one connection line is shown in the figure, but not only one bus or one type of bus.
Fig. 2 is a flow chart of a nonlinear force identification method of one embodiment of the present disclosure.
As shown in fig. 2, a method 200 for performing nonlinear force recognition on a nonlinear unit of a target engineering structure obtained by the nonlinear positioning method 100 according to any one of the above embodiments includes:
202. Constructing a motion equation of each unit of the target engineering structure based on mass, damping and unit structure restoring force of each unit (nonlinear unit), and external excitation; and
204. Solving a motion equation based on the known mass, damping and stiffness matrixes of each unit to obtain a unit structure restoring force, wherein the unit structure restoring force is nonlinear force.
For the nonlinear force recognition method 200 of the above embodiment, preferably, solving the equation of motion based on the known mass, damping, and stiffness matrices of each cell to obtain the cell structure restoring force includes:
The equation of motion is solved using kalman filtering under generalized unknown excitation (kf-UI) to obtain the cell structure restoring force.
For the nonlinear force identification method 200 of the above embodiments, preferably, the equation of motion is constructed as:
Wherein the method comprises the steps of And x is the n-dimensional column vector of the acceleration, velocity and displacement of the unit structure, f is the external excitation vector, eta is the matrix of the external excitation action position, M, C represents the mass and damping of the unit structure, respectively,N-dimensional column vectors of restoring force of the unit structure, wherein z is a system parameter;
Wherein the target engineering structure has an n-layer structure.
For the nonlinear force identification method 200 of each of the above embodiments, it is preferable that the method further includes:
Extracting additional virtual force from the motion equation, and solving the motion equation by using Kalman filtering (GKF-UI) under generalized unknown excitation to obtain the additional virtual force, wherein the additional virtual force is expressed as f u, and Where K is the stiffness matrix of the cell structure. /(I)
Preferably, the cell structure restoring force is obtained based on the obtained additional virtual force
For the nonlinear force identification method 200 of the above-described respective embodiments, the equation of motion is preferably an equation of motion in a relative motion coordinate system.
For the nonlinear force identification method 200 of the above embodiments, preferably, the additional virtual force extraction on the equation of motion includes:
Transforming the equation of motion into And is further deformed into
According to one embodiment of the present disclosure, a nonlinear force recognition apparatus 2000 of the present disclosure includes:
The motion equation establishing module 2002, wherein the motion equation establishing module 2002 establishes a motion equation of each unit of the target engineering structure based on the mass, the damping and the unit structure restoring force of each unit and external excitation; and
The nonlinear solving module 2004 solves the equation of motion based on the known mass, damping and stiffness matrices of each unit, and obtains a unit structure restoring force, which is the nonlinear force.
Fig. 4 is a block schematic diagram of a nonlinear force recognition apparatus in the form of an electronic device in accordance with one embodiment of the present disclosure.
As shown in fig. 4, a nonlinear force recognition apparatus 2000 in the form of an electronic device may include corresponding modules that perform each or several of the steps in the flowcharts described above. Accordingly, each step or steps of the flowcharts described above may be performed by respective modules, and the nonlinear force identification apparatus 2000 may include one or more of these modules. A module may be one or more hardware modules specifically configured to perform the respective steps, or be implemented by a processor configured to perform the respective steps, or be stored within a computer-readable medium for implementation by a processor, or be implemented by some combination.
As shown in fig. 4, the nonlinear force recognition device 2000 may also be implemented using the bus architecture described above. The bus architecture may include any number of interconnecting buses and bridges depending on the specific application of the hardware and the overall design constraints. The bus 2100 connects together various circuits including one or more processors 2200, memory 2300, and/or hardware modules. The bus 2100 may also connect various other circuits 2400 such as peripherals, voltage regulators, power management circuits, external antennas, and the like.
According to a preferred embodiment of the present disclosure, the nonlinear unit positioning apparatus 1000 and the nonlinear force recognition apparatus 2000 of the present disclosure may be implemented based on the same electronic device or may be implemented based on different electronic devices.
Fig. 5 illustrates a nonlinear cell positioning and nonlinear force recognition apparatus 3000 implemented based on the same electronic device according to one embodiment of the present disclosure.
As shown in fig. 5, the nonlinear element positioning and nonlinear force recognition apparatus 3000 includes the strain response data acquisition module 1002, the wavelet energy probability distribution generation module 1004, the relative wavelet entropy generation module 1006, the nonlinear element acquisition module 1008 of the nonlinear element positioning apparatus 1000 described above, and the equation of motion establishment module 2002 and the nonlinear force solution module 2004 of the nonlinear force recognition apparatus 2000 described above.
As shown in fig. 5, the nonlinear cell positioning and nonlinear force recognition apparatus 3000 may also be implemented using the bus architecture described above. The bus architecture may include any number of interconnecting buses and bridges depending on the specific application of the hardware and the overall design constraints. Bus 3100 connects together various circuits including one or more processors 3200, memory 3300, and/or hardware modules. Bus 3100 may also connect various other circuits 3400 such as peripherals, voltage regulators, power management circuits, external antennas, and the like.
The nonlinear unit positioning method solves the problem of local nonlinearity of an engineering structure, can accurately measure the disturbance degree of a system based on the relative wavelet entropy driven by strain response data (the adopted relative wavelet entropy is used for comparing the disturbance degree among units and is not compared with the state of a healthy structure, and can realize the positioning of nonlinear units without baseline data), and the accurate nonlinear positioning result is realized under the condition of unknown nonlinear unit model.
The nonlinear unit positioning method also solves the problem of positioning of nonlinear units under the condition of lack of structural health data, and the relative wavelet entropy is compared among units, so that the data of the health structure is not needed to serve as a base line, positioning of the nonlinear units without the base line data is realized (the difference among the units can be accurately measured by adopting the relative wavelet entropy index driven based on the strain response data, and the nonlinear units are positioned without a nonlinear model through the monitored response data of the units).
The nonlinear force identification method solves the problem of nonlinear force identification under the condition that a structural local nonlinear unit model is unknown, can solve the problems that a complex nonlinear unit is difficult to model and an approximation method has errors, and achieves the aim of nonlinear characteristic identification based on the monitored structural response (driven by structural response monitoring data, the preferably adopted GKF-UI method can accurately identify nonlinear force characteristics without assuming a nonlinear model or approximating the nonlinear force by series expansion and the like).
The technical effects of the nonlinear unit positioning method and the nonlinear force identification method of the present disclosure are verified by specific simulation experiments.
1) Numerical simulation of shearing frames for technical effects
The verification is performed using a 10-layer shear frame under seismic excitation as an example. The El-Centro seismic wave is adopted as external excitation, the sampling time length is 31.2s, and the sampling frequency is 200Hz. The observed information for nonlinear cell positioning is the strain of each layer of column cells. The observation information for nonlinear restoring force identification is the strain of each layer of column units plus the acceleration of a certain two/three layer floor. And solving a nonlinear motion equation by adopting a fourth-order Runge-Kutta method, and adding Gaussian white noise with standard deviation of 5% into the obtained numerical simulation response data.
(1) Single nonlinear element location and identification
A Bouc-Wen hysteresis nonlinear model is adopted to simulate the force-interlayer displacement relationship, so that the nonlinear condition of a single unit is simulated. The top strain response of all the storey column units is used as observation information. The resulting strain response is first wavelet transformed to obtain wavelet coefficients and wavelet energy probability distribution are calculated. The relative wavelet entropy is then calculated along with a positioning index at each sensor location. Finally, the indexes are compared to locate the nonlinear position.
Fig. 6 to 9 are graphs of single nonlinear unit positioning results of 2-unit nonlinearity, 4-unit nonlinearity, 6-unit nonlinearity, and 8-unit nonlinearity, respectively. In fig. 6 to 9, the vertical axis is the relative wavelet entropy.
Taking the layer 2 nonlinear unit as an example for nonlinear force identification, the acceleration of the layer 3 and the layer 4 is added as an observed quantity in addition to the strain information of all the storey columns. Based on the nonlinear unit positioning result, the nonlinear force at the nonlinear unit is used as an 'additional virtual force' on the linear structure, and the 'additional virtual force' is identified by adopting GKF-UI.
Fig. 10 and 11 show a nonlinear restoring force time course comparison chart and a nonlinear restoring force hysteresis loop comparison chart for nonlinear force identification using a layer 2 nonlinear unit as an example, respectively.
(2) Multiple nonlinear unit positioning and identification
It is assumed that there are two nonlinear units in the structure. And respectively adopting a bilinear and trilinear hysteresis nonlinear model to simulate the relationship between force and interlayer displacement. And calculating the relative wavelet entropy between each floor unit by taking the top end strain response of all the floor column units as observation information. The strain response is first wavelet transformed to obtain wavelet coefficients and wavelet energy probability distribution are calculated. The relative wavelet entropy is then calculated along with a positioning index at each sensor location. Finally, the indexes are compared to locate the nonlinear position.
Fig. 12 to 15 are two nonlinear unit positioning result diagrams of 3, 6, 4, 7, 5,6, 2, 8 unit nonlinearities, respectively. In fig. 12 to 15, the vertical axis is the relative wavelet entropy.
Layer 3 and layer 6 nonlinear units are used as routine nonlinear force identification. In addition to the strain information of all storeys, the accelerations of layer 1, layer 4 and layer 7 are also added as observables. Based on the nonlinear unit positioning result, the nonlinear force at the nonlinear unit is used as an 'additional virtual force' on the linear structure, and the 'additional virtual force' is identified by adopting the GKF-UI.
Fig. 16 and 17 show a nonlinear restoring force time course comparison chart (bilinear) and a nonlinear restoring force hysteresis loop comparison chart (bilinear), respectively, of nonlinear force identification by taking a layer 3 nonlinear unit as an example.
Fig. 18 and 19 show a nonlinear restoring force time course comparison chart (three-linearity) and a nonlinear restoring force hysteresis loop comparison chart (three-linearity) for nonlinear force identification by taking a layer 6 nonlinear unit as an example, respectively.
2) Truss numerical model verification of technical effects
The verification is performed by taking a single-span truss under seismic excitation as an example. The truss consists of 11 poles, each node containing both lateral and vertical degrees of freedom, for a total of 11 degrees of freedom. The external excitation is an El-Centro seismic wave, the sampling time length is 31.2s, and the sampling frequency is 1000Hz. And solving a nonlinear motion equation by adopting a fourth-order Runge-Kutta method. The observed information for nonlinear cell positioning is the strain of each cell. The observation information for nonlinear restoring force identification is the strain of each cell plus a small amount of acceleration in degrees of freedom. And adding Gaussian white noise with a mean square error of 5% into the obtained numerical simulation response data.
The unit nonlinearity is modeled using a bilinear model and is assumed to occur between two degrees of freedom in the axial direction of the rod unit. The relative wavelet entropy between the individual rod unit strains is calculated as described above to effect the positioning of the nonlinear units using the strain responses of all rod units as observations.
Fig. 20 to 23 are graphs of single nonlinear unit (rod unit) positioning results of 1 unit nonlinearity, 4 unit nonlinearity, 8 unit nonlinearity, and 9 unit nonlinearity, respectively. In fig. 20 to 23, the vertical axis is the relative wavelet entropy.
Nonlinear force recognition is performed by taking the nonlinear occurrence of the 4 th bar as an example. In addition to the strain information of all rod units, the lateral acceleration of the 2,3,4 node is also added as an observed quantity. Based on the nonlinear unit positioning result, the nonlinear force at the nonlinear rod unit is used as an 'additional virtual force' on the linear structure, and the 'additional virtual force' is identified by adopting GKF-UI.
Fig. 24 and 25 show a nonlinear restoring force time course comparison chart and a nonlinear restoring force hysteresis loop comparison chart, respectively, for nonlinear force identification by taking the nonlinear occurrence of the 6 th lever as an example.
3) Verification of shear frame test model with technical effect
Five-layer shear frame structure experiments with MR dampers were employed to demonstrate the effectiveness of the proposed method. The frame node connection adopts double rows of bolts, and the connection between the support and the floor can be approximately considered as consolidation. The exciter is used for exciting horizontal white noise on the layer 3 of the structure, the duration of the excitation is 6s, and the sampling frequency is 1000Hz. The observed information for nonlinear cell positioning is the top strain of each layer of column cells. The observation information for nonlinear restoring force identification is the strain of each layer of column units plus the acceleration of two layers of floors.
In the description of the present specification, reference to the terms "one embodiment/manner," "some embodiments/manner," "example," "a particular example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment/manner or example is included in at least one embodiment/manner or example of the present disclosure. In this specification, the schematic representations of the above terms are not necessarily for the same embodiment/manner or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments/modes or examples. Furthermore, the various embodiments/modes or examples described in this specification and the features of the various embodiments/modes or examples can be combined and combined by persons skilled in the art without contradiction.
Furthermore, the terms "first," "second," and the like, are used for descriptive purposes only and are not to be construed as indicating or implying a relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defining "a first" or "a second" may explicitly or implicitly include at least one such feature. In the description of the present disclosure, the meaning of "a plurality" is at least two, such as two, three, etc., unless explicitly specified otherwise.
It will be appreciated by those skilled in the art that the above-described embodiments are merely for clarity of illustration of the disclosure, and are not intended to limit the scope of the disclosure. Other variations or modifications will be apparent to persons skilled in the art from the foregoing disclosure, and such variations or modifications are intended to be within the scope of the present disclosure.
Claims (8)
1. A method for locating a nonlinear unit of an engineering structure, comprising:
acquiring strain response data of each unit of the target engineering structure to which external excitation is applied;
acquiring wavelet energy probability distribution of each unit based on strain response data of each unit;
Acquiring the relative wavelet entropy of each unit and other units based on the wavelet energy probability distribution of each unit; and
Acquiring nonlinear units of the target engineering structure based on the relative wavelet entropy of each unit and other units;
Wherein obtaining wavelet energy probability distributions for each cell based on strain response data for each cell comprises:
for strain response data x (t), the wavelet expansion is expressed as:
Wherein, psi (t) is a wavelet basis function, j and k are discrete expansion parameters and translation parameters respectively, j, k epsilon Z, Z is a set of positive integers, and alpha j,k is a wavelet coefficient;
the wavelet energy probability distribution is expressed as:
Wherein the value of p jk is the ratio of the energy of a certain specific coefficient alpha j,k to the total energy, the value of p jk is the wavelet energy probability distribution, and the sum of the values of all p jk is 1;
wherein obtaining the relative wavelet entropy of each cell to other cells based on the wavelet energy probability distribution of the respective cell comprises:
the relative wavelet entropy of each cell to the other cells is obtained by:
Wherein p and q represent wavelet energy probability distributions of strain response data of different units, and α and β represent wavelet coefficients of different units, respectively;
based on the relative wavelet entropy of each unit and other units, obtaining a nonlinear unit of the target engineering structure, including:
Acquiring nonlinear units of the target engineering structure through baseline-free identification indexes, wherein the baseline-free identification indexes are obtained based on the relative wavelet entropy of each unit and other units through the following formula:
Where n represents a total number of measurement locations corresponding to a number of sensors used to collect strain response data for each cell of the target engineered structure.
2. The method for locating a nonlinear unit of an engineered structure of claim 1, further comprising:
seismic external excitation is applied to the target engineering structure.
3. The method of claim 1 or 2, wherein strain response data of each cell of the target engineering structure is acquired using a sensor, respectively.
4. A method of positioning nonlinear units of an engineered structure according to any one of claims 1 to 2, wherein the external excitation is El-Centro seismic waves.
5. A nonlinear unit positioning device of an engineering structure, comprising:
A strain response data acquisition module that acquires strain response data of each unit of the target engineering structure to which external excitation is applied;
The device comprises a wavelet energy probability distribution generation module, a first module and a second module, wherein the wavelet energy probability distribution generation module acquires the wavelet energy probability distribution of each unit based on strain response data of each unit;
the relative wavelet entropy generation module is used for acquiring the relative wavelet entropy of each unit and other units based on wavelet energy probability distribution of each unit; and
The nonlinear unit acquisition module acquires nonlinear units of the target engineering structure based on the relative wavelet entropy of each unit and other units;
Wherein obtaining wavelet energy probability distributions for each cell based on strain response data for each cell comprises:
for strain response data x (t), the wavelet expansion is expressed as:
Wherein, psi (t) is a wavelet basis function, j and k are discrete expansion parameters and translation parameters respectively, j, k epsilon Z, Z is a set of positive integers, and alpha j,k is a wavelet coefficient;
the wavelet energy probability distribution is expressed as:
Wherein the value of p jk is the ratio of the energy of a certain specific coefficient alpha j,k to the total energy, the value of p jk is the wavelet energy probability distribution, and the sum of the values of all p jk is 1;
wherein obtaining the relative wavelet entropy of each cell to other cells based on the wavelet energy probability distribution of the respective cell comprises:
the relative wavelet entropy of each cell to the other cells is obtained by:
Wherein p and q represent wavelet energy probability distributions of strain response data of different units, and α and β represent wavelet coefficients of different units, respectively;
based on the relative wavelet entropy of each unit and other units, obtaining a nonlinear unit of the target engineering structure, including:
Acquiring nonlinear units of the target engineering structure through baseline-free identification indexes, wherein the baseline-free identification indexes are obtained based on the relative wavelet entropy of each unit and other units through the following formula:
Where n represents a total number of measurement locations corresponding to a number of sensors used to collect strain response data for each cell of the target engineered structure.
6. A nonlinear force recognition method based on the nonlinear unit positioning method according to any one of claims 1 to 4, characterized by comprising:
Constructing a motion equation of each unit of the target engineering structure based on the mass, damping and unit structure restoring force of each unit and external excitation; and
Solving the motion equation based on the known mass, damping and stiffness matrixes of each unit to obtain the restoring force of the unit structure, wherein the restoring force of the unit structure is the nonlinear force.
7. An electronic device, comprising:
A memory storing execution instructions; and
A processor executing the memory-stored execution instructions, causing the processor to perform the method of any one of claims 1 to 4, 6.
8. A readable storage medium having stored therein execution instructions which when executed by a processor are adapted to carry out the method of any one of claims 1 to 4, 6.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110657150.XA CN113536923B (en) | 2021-06-11 | 2021-06-11 | Structure local model-free nonlinear positioning identification technology based on monitoring data driving |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202110657150.XA CN113536923B (en) | 2021-06-11 | 2021-06-11 | Structure local model-free nonlinear positioning identification technology based on monitoring data driving |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN113536923A CN113536923A (en) | 2021-10-22 |
| CN113536923B true CN113536923B (en) | 2024-04-19 |
Family
ID=78095920
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202110657150.XA Active CN113536923B (en) | 2021-06-11 | 2021-06-11 | Structure local model-free nonlinear positioning identification technology based on monitoring data driving |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN113536923B (en) |
Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB873904A (en) * | 1958-02-20 | 1961-08-02 | Fairey Air Surveys Ltd | Improvements relating to apparatus for the dynamic testing of resilient units |
| US4724923A (en) * | 1986-06-24 | 1988-02-16 | Fokker B.V. | Vibration absorber with controllable resonance frequency |
| CN1997999A (en) * | 2004-03-29 | 2007-07-11 | 彼德·T·杰尔曼 | Systems and methods for determining material elasticity |
| CN101587007A (en) * | 2009-06-19 | 2009-11-25 | 同济大学 | Output-only wavelet analytical method for recognizing flexible bridge structure kinetic parameter |
| CN102687041A (en) * | 2009-08-07 | 2012-09-19 | 埃克森美孚上游研究公司 | Methods to estimate downhole drilling vibration indices from surface measurement |
| CN109614720A (en) * | 2018-12-14 | 2019-04-12 | 厦门大学 | Real-time identification method for model-free nonlinear characteristics of in-service isolation/damping devices |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9702349B2 (en) * | 2013-03-15 | 2017-07-11 | ClearMotion, Inc. | Active vehicle suspension system |
| FR3049989B1 (en) * | 2016-04-08 | 2022-08-05 | Ifp Energies Now | METHOD FOR DETERMINING THE EXCITATION FORCE EXERCISED BY THE INCIDENT WAVE ON A MOBILE MEANS OF A WAVE MOTOR SYSTEM BY MEANS OF A RADIATION FORCE MODEL |
-
2021
- 2021-06-11 CN CN202110657150.XA patent/CN113536923B/en active Active
Patent Citations (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| GB873904A (en) * | 1958-02-20 | 1961-08-02 | Fairey Air Surveys Ltd | Improvements relating to apparatus for the dynamic testing of resilient units |
| US4724923A (en) * | 1986-06-24 | 1988-02-16 | Fokker B.V. | Vibration absorber with controllable resonance frequency |
| CN1997999A (en) * | 2004-03-29 | 2007-07-11 | 彼德·T·杰尔曼 | Systems and methods for determining material elasticity |
| CN101587007A (en) * | 2009-06-19 | 2009-11-25 | 同济大学 | Output-only wavelet analytical method for recognizing flexible bridge structure kinetic parameter |
| CN102687041A (en) * | 2009-08-07 | 2012-09-19 | 埃克森美孚上游研究公司 | Methods to estimate downhole drilling vibration indices from surface measurement |
| CN109614720A (en) * | 2018-12-14 | 2019-04-12 | 厦门大学 | Real-time identification method for model-free nonlinear characteristics of in-service isolation/damping devices |
Non-Patent Citations (7)
| Title |
|---|
| 基于部分加速度测量的结构Bouc-Wen非线性恢复力及质量识别;程骄阳;许斌;贺佳;;噪声与振动控制;20180418(第02期);全文 * |
| 基础隔震结构橡胶支座时变非线性特性识别;杜永峰;赵丽洁;李万润;唐少玉;;振动.测试与诊断;20160215(第01期);全文 * |
| 杜永峰 ; 赵丽洁 ; 李万润 ; 唐少玉 ; .基础隔震结构橡胶支座时变非线性特性识别.振动.测试与诊断.2016,(第01期),全文. * |
| 程骄阳 ; 许斌 ; 贺佳 ; .基于部分加速度测量的结构Bouc-Wen非线性恢复力及质量识别.噪声与振动控制.2018,(第02期),全文. * |
| 结构减隔震控制系统性能监测、评估与提升;朱宏平等;《工程力学》;20200604;全文 * |
| 邓百川 ; 郭玉荣 ; 许斌 ; .部分加速度测量下结构恢复力与质量非参数化识别方法.振动与冲击.2020,(第08期),全文. * |
| 部分加速度测量下结构恢复力与质量非参数化识别方法;邓百川;郭玉荣;许斌;;振动与冲击;20200428(第08期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN113536923A (en) | 2021-10-22 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Lee et al. | Neural networks-based damage detection for bridges considering errors in baseline finite element models | |
| Wickramasinghe et al. | Vibration characteristics and damage detection in a suspension bridge | |
| Chang et al. | Structural health monitoring | |
| Johnson et al. | Phase I IASC-ASCE structural health monitoring benchmark problem using simulated data | |
| CN103116759B (en) | A kind of damnification recognition method being applicable to spatial mesh structure | |
| CN104517036A (en) | Simply-supported piece damage identification method based on strain statistical moment | |
| Cheung et al. | The application of statistical pattern recognition methods for damage detection to fielddata | |
| CN104406757B (en) | It is applicable to the integrated apparatus that small bridge fast and safely diagnoses | |
| Chen et al. | Damage detection of long-span bridges using stress influence lines incorporated control charts | |
| Pan et al. | Capacity-curve-based damage evaluation approach for reinforced concrete buildings using seismic response data | |
| CN102759573A (en) | Frequency change-based structure damage positioning and damage degree evaluating method | |
| CN110008520B (en) | Structural damage identification method based on displacement response covariance parameters and Bayesian fusion | |
| Abasi et al. | Damage detection of 3D structures using nearest neighbor search method | |
| Monavari et al. | Structural deterioration detection using enhanced autoregressive residuals | |
| Guan et al. | Web‐based structural health monitoring of an FRP composite bridge | |
| CN113536923B (en) | Structure local model-free nonlinear positioning identification technology based on monitoring data driving | |
| Lakshmi et al. | Output-only damage localization technique using time series model | |
| Du et al. | Online model updating method with multiple inputs considering realistic boundary conditions in hybrid tests | |
| Mehboob et al. | Numerical study for evaluation of a vibration based damage index for effective damage detection | |
| Xiang et al. | Pattern matching-based structural damage identification using mode shape difference ratio with limited sensors | |
| Wang | Damage assessment in asymmetric buildings using vibration techniques | |
| CN117574110A (en) | Global bridge damage rapid identification method, device and medium | |
| Nagarajaiah et al. | Current directions of structural health monitoring and control in USA | |
| Li et al. | A non-contact method for estimating the pre-tension of a rectangular membrane structure | |
| CN115169151A (en) | A seismic reliability analysis method for double-groove aqueduct structures under strong earthquakes |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |