CN116186838A - Structural random response analysis method, device and storage medium based on harmonic wavelet - Google Patents
Structural random response analysis method, device and storage medium based on harmonic wavelet Download PDFInfo
- Publication number
- CN116186838A CN116186838A CN202211688590.2A CN202211688590A CN116186838A CN 116186838 A CN116186838 A CN 116186838A CN 202211688590 A CN202211688590 A CN 202211688590A CN 116186838 A CN116186838 A CN 116186838A
- Authority
- CN
- China
- Prior art keywords
- wavelet
- structural
- excitation
- response
- harmonic
- 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.)
- Pending
Links
- 230000004044 response Effects 0.000 title claims abstract description 105
- 238000004458 analytical method Methods 0.000 title claims abstract description 62
- 230000005284 excitation Effects 0.000 claims abstract description 78
- 239000011159 matrix material Substances 0.000 claims abstract description 53
- 230000003595 spectral effect Effects 0.000 claims abstract description 49
- 239000013598 vector Substances 0.000 claims abstract description 45
- 238000006073 displacement reaction Methods 0.000 claims abstract description 39
- 230000006870 function Effects 0.000 claims abstract description 32
- 238000000034 method Methods 0.000 claims abstract description 25
- 238000001228 spectrum Methods 0.000 claims abstract description 12
- 238000013519 translation Methods 0.000 claims abstract description 5
- 230000000737 periodic effect Effects 0.000 claims description 13
- 230000001133 acceleration Effects 0.000 claims description 10
- 238000004590 computer program Methods 0.000 claims description 6
- 238000013016 damping Methods 0.000 claims description 5
- 230000002195 synergetic effect Effects 0.000 claims description 4
- 230000001052 transient effect Effects 0.000 description 13
- 238000010586 diagram Methods 0.000 description 5
- 230000000694 effects Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 238000004891 communication Methods 0.000 description 2
- 238000010276 construction Methods 0.000 description 2
- 238000005516 engineering process Methods 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 238000006467 substitution reaction Methods 0.000 description 2
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004364 calculation method Methods 0.000 description 1
- 230000000052 comparative effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000010295 mobile communication Methods 0.000 description 1
- 230000003287 optical effect Effects 0.000 description 1
- 230000008569 process Effects 0.000 description 1
- 238000012545 processing Methods 0.000 description 1
- 238000004088 simulation Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 230000007723 transport mechanism Effects 0.000 description 1
- 230000005428 wave function Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/10—Geometric CAD
- G06F30/13—Architectural design, e.g. computer-aided architectural design [CAAD] related to design of buildings, bridges, landscapes, production plants or roads
-
- 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
- G06F17/15—Correlation function computation including computation of convolution operations
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
- Y02T90/00—Enabling technologies or technologies with a potential or indirect contribution to GHG emissions mitigation
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Optimization (AREA)
- Mathematical Analysis (AREA)
- Geometry (AREA)
- Computational Mathematics (AREA)
- Pure & Applied Mathematics (AREA)
- General Engineering & Computer Science (AREA)
- Data Mining & Analysis (AREA)
- Computer Hardware Design (AREA)
- Mathematical Physics (AREA)
- Algebra (AREA)
- Architecture (AREA)
- Computing Systems (AREA)
- Civil Engineering (AREA)
- Structural Engineering (AREA)
- Evolutionary Computation (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- Supply And Distribution Of Alternating Current (AREA)
- Testing Of Devices, Machine Parts, Or Other Structures Thereof (AREA)
Abstract
The application provides a structural random response analysis method, equipment and storage medium based on harmonic wavelets, wherein the method comprises the following steps: setting wavelet scale parameters, wavelet time translation parameters and excitation duration according to the harmonic wavelet random response analysis requirements, and constructing connection coefficients of wavelet functions and wavelet coefficient vectors of displacement and excitation in wavelet scales; obtaining an assembly connection coefficient matrix; constructing a wavelet connection coefficient matrix of the whole axle system according to the wavelet coefficient vector and the assembly connection coefficient matrix, and carrying out deterministic analysis by using the wavelet connection coefficient matrix; establishing a power spectrum density matrix of random load, and establishing an unchanged power spectrum density linear equation of the axle system through a wavelet connection coefficient matrix; the power spectral density of each response of the axle system is solved using a power spectral density linear equation. The method and the device effectively reduce the error of the result of the structural random response analysis, and improve the accuracy and reliability of the structural random response analysis.
Description
Technical Field
The invention relates to the technical field of vibration analysis of civil structures, in particular to a structural random response analysis method, equipment and a storage medium based on harmonic wavelets.
Background
The actual civil structure is subjected to a variety of non-stationary random excitations, such as seismic excitations, wind excitations, moving vehicle excitations, wave excitations, etc. These non-stationary excitations may cause a structural transient response component and a steady state response component. Classical structural dynamics states that the transient response component has the same frequency as the natural frequency of the structure; and when the excitation time is not long, the transient response component amplitude may be much greater than the steady state response component amplitude. Notably, the duration of the numerous excitations present in the civil structure is short (such as seismic excitation, vehicle excitation, and wave excitation), and does not exceed the structure self-oscillation period, obviously the transient response component has a significant effect on the random response of the structure. Therefore, the transient response component should be considered in the random response analysis.
In recent decades, a great deal of work has been done on the analysis of the non-stationary random response of civil structures under the effect of non-stationary random excitation. However, the existing research only considers the frequency characteristic of the steady-state response component, ignores the component frequency characteristic of the transient response, and leads to a large error in the result of the structural random response analysis.
Disclosure of Invention
The invention aims to overcome the technical defects, and provides a structural random response analysis method, device and storage medium based on harmonic wavelets, which solve the technical problem that the structural random response analysis result in the prior art has larger error.
In order to achieve the technical purpose, in a first aspect, the technical scheme of the invention provides a structural random response analysis method based on harmonic wavelets, which comprises the following steps:
setting wavelet scale parameters, wavelet time translation parameters and excitation duration according to the harmonic wavelet random response analysis requirements, and constructing connection coefficients of wavelet functions and wavelet coefficient vectors of displacement and excitation in wavelet scales;
obtaining an assembled connection coefficient matrix according to the wavelet scale parameter, the wavelet time shift parameter, the excitation duration and the connection coefficient of the wavelet function;
constructing a wavelet connection coefficient matrix of the whole axle system according to the wavelet coefficient vector and the assembly connection coefficient matrix, and carrying out deterministic analysis by using the wavelet connection coefficient matrix;
establishing a power spectrum density matrix of random load, and establishing an unchanged power spectrum density linear equation of the axle system through the wavelet connection coefficient matrix;
the power spectral density of each response of the axle system is solved using a power spectral density linear equation.
Compared with the prior art, the invention has the beneficial effects that:
according to the structural random response analysis method based on the harmonic wavelet, the periodic generalized cooperative wavelet considering the rigid displacement component is utilized to establish the motion formula of the multi-degree-of-freedom structural system, the linear algebraic formulas of the response and the excitation wavelet coefficients are respectively established, then the connection formula of the wavelet coefficients under each scale is established, the transient component is contained in the response, the time-varying power spectral density function of the structural response is obtained in a semi-analytic mode, the error of the structural random response analysis result is effectively reduced, and the accuracy and the reliability of the structural random response analysis are improved.
According to some embodiments of the invention, the wavelet coefficient vector of displacement and excitation in the wavelet scale comprises: a displacement response vector and a random excitation vector.
According to some embodiments of the invention, the construction formula of the displacement response vector and the random excitation vector is as follows:
wherein m, c and k are mass, damping and stiffness matrices of the multiple degree of freedom system; q is a displacement response vector, f is a random excitation vector, T 0 Indicating the excitation duration.
According to some embodiments of the invention, constructing connection coefficients of a wavelet function comprises the steps of: using orthogonality, the connection coefficients of the wavelet functions are defined as periodic generalized synergy magnitudesThe inner product between the wave function and its derivative function can be expressed as: frequency domain resolution
Temporal resolution->
wherein ,
the connection coefficient of the wavelet function is that the wavelet scale parameter is n s Wavelet time shift parameter n t 。
According to some embodiments of the invention, a wavelet connectivity coefficient matrix for the entire axle system is constructed from the wavelet coefficient vector and the assembled connectivity coefficient matrix, expressed as:
wherein A represents a connection coefficient matrix of the whole dynamic system, W q Representing the displacement response vector, W f Representing a random excitation vector.
According to some embodiments of the invention, the power spectral density equation of the dynamic signal is expressed as:
wherein 
and />
Respectively represent the same timeInstantaneous t k ＝(k+0.5)T 0 /n t And the same frequency omega i ＝(m i +n i ) An automatic power spectral density of Dω/2; />
and />
Respectively representing the cross power spectral densities of two different time instants and two different frequencies; />
and />
Is m x m.
According to some embodiments of the invention, the relationship between the power spectral density of the random excitation and the displacement is:
wherein Sqq and Sff Power spectral density matrix representing displacement and excitation, respectively, with dimensions N W *N W 。
According to some embodiments of the invention, the power spectral density of the velocity and acceleration may be determined by the following formula:
in a second aspect, a technical solution of the present invention provides an electronic device, including: a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the structural stochastic response analysis method according to any one of the first aspects when the computer program is executed.
In a third aspect, the present invention provides a computer-readable storage medium storing computer-executable instructions for causing a computer to perform the structural stochastic response analysis method according to any one of the first aspects.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
The foregoing and/or additional aspects and advantages of the present invention will become apparent and may be better understood from the following description of embodiments taken in conjunction with the accompanying drawings, in which the summary drawings are to be fully consistent with one of the drawings of the specification:
FIG. 1 is a flow chart of a method for analyzing structural stochastic response based on harmonic wavelets according to an embodiment of the invention;
FIG. 2 is a schematic diagram of a three-layer shear type structure of a method for analyzing a structural stochastic response based on harmonic wavelets according to another embodiment of the present invention;
FIG. 3 is a graph showing the power spectral density contrast of the three shear building layers with different displacement and acceleration responses predicted and accurate time-varying according to another embodiment of the invention;
FIG. 4 is a graph showing the comparison of the time and frequency scales of the estimated displacement and acceleration power spectral densities of the structural stochastic response analysis method based on harmonic wavelets according to another embodiment of the present invention 。
Detailed Description
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
It should be noted that although functional block diagrams are depicted as block diagrams, and logical sequences are shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the block diagrams in the system. The terms first, second and the like in the description and in the claims and in the above-described figures, are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order.
The invention provides a structural random response analysis method based on harmonic wavelets, which utilizes periodic generalized cooperative wavelets considering rigid displacement components to establish a motion formula of a multi-degree-of-freedom structural system, respectively establishes linear algebraic formulas of response and excitation wavelet coefficients, then establishes a connection formula of the wavelet coefficients under each scale, and includes transient components in the response to obtain a time-varying power spectral density function of the structural response in a semi-analytic form, thereby effectively reducing errors of results of structural random response analysis and improving accuracy and reliability of structural random response analysis.
Embodiments of the present invention will be further described below with reference to the accompanying drawings.
Referring to fig. 1, fig. 1 is a flowchart of a structural stochastic response analysis method based on harmonic wavelets according to an embodiment of the invention; structural stochastic response analysis methods based on harmonic wavelets include, but are not limited to, the following steps:
step S110, setting wavelet scale parameters, wavelet time shift parameters and excitation duration according to the harmonic wavelet random response analysis requirement, and constructing connection coefficients of wavelet functions and wavelet coefficient vectors of displacement and excitation in wavelet scales;
step S120, obtaining an assembled connection coefficient matrix according to the wavelet scale parameter, the wavelet time shift parameter and the excitation duration and the connection coefficient of the wavelet function;
step S130, constructing a wavelet connection coefficient matrix of the whole axle system according to the wavelet coefficient vector and the assembly connection coefficient matrix, and carrying out deterministic analysis by using the wavelet connection coefficient matrix;
step S140, a power spectrum density matrix of random load is established, and a constant power spectrum density linear equation of the axle system is established through a wavelet connection coefficient matrix;
step S150, solving the power spectral density of each response of the axle system using a power spectral density linear equation.
In one embodiment, the structural stochastic response analysis method based on harmonic wavelets comprises the following steps: setting wavelet scale parameters, wavelet time translation parameters and excitation duration according to the harmonic wavelet random response analysis requirements, and constructing connection coefficients of wavelet functions and wavelet coefficient vectors of displacement and excitation in wavelet scales; obtaining an assembled connection coefficient matrix according to the wavelet scale parameter, the wavelet time shift parameter, the excitation duration and the connection coefficient of the wavelet function; constructing a wavelet connection coefficient matrix of the whole axle system according to the wavelet coefficient vector and the assembly connection coefficient matrix, and carrying out deterministic analysis by using the wavelet connection coefficient matrix; establishing a power spectrum density matrix of random load, and establishing an unchanged power spectrum density linear equation of the axle system through a wavelet connection coefficient matrix; the power spectral density of each response of the axle system is solved using a power spectral density linear equation.
According to the structural random response analysis method based on the harmonic wavelet, the periodic generalized cooperative wavelet considering the rigid body displacement component is utilized to establish a motion formula of the multi-degree-of-freedom structural system, linear algebraic formulas of response and excitation wavelet coefficients are respectively established, then a connection formula of the wavelet coefficients under each scale is established, transient components are contained in the response, a time-varying power spectral density function of the structural response is obtained in a semi-analytic mode, errors of a structural random response analysis result are effectively reduced, and accuracy and reliability of the structural random response analysis are improved.
Referring to fig. 2 to 4, fig. 2 is a schematic diagram of a three-layer shear type structure of a structural stochastic response analysis method based on harmonic wavelets according to another embodiment of the invention. FIG. 3 is a graph showing the power spectral density contrast of the three shear building layers with different displacement and acceleration responses predicted and accurate in time-varying manner based on the harmonic wavelet-based structural stochastic response analysis method according to another embodiment of the present invention.
Fig. 4 is a graph comparing displacement and acceleration power spectral densities estimated by different methods of a harmonic wavelet based structural stochastic response analysis method according to another embodiment of the invention on a time scale and a frequency scale.
And analyzing the three-layer shear structure by using a structural random response analysis method based on harmonic wavelets, and evaluating the accuracy of the method by considering the three-layer shear building structure. The mass, damping and rigidity of the shear building are respectively m l ＝m 2 ＝m 3 ＝5.63×10 5 kg，c 1 ＝c 2 ＝c 3 ＝1.3×10 2 N·s/m，k 1 ＝3.06×10 7 N/m，k 2 ＝2.97×10 7 N/m，k 3 ＝1.51×10 7 N/m. The natural frequencies were 3.08rad/s, 7.33rad/s and 12.25rad/s, respectively.
A deterministic analysis is first performed. We consider three harmonic excitations acting on a three-layer shear building. The form of third harmonic excitation is f (t) =f m sin(ω，0≤t≤t 0 Wherein the amplitude, frequency and duration are f m ＝1.63×10 4 N, ω=3.58 rad/s and t o =10.00 s. Thus, the frequency of the harmonic excitation is very close to the fundamental frequency (ω) of the building n =3.08 rad/s), the excitation duration is not significantly longer than the fundamental frequency period (2.03 s). In the method, wavelet parameters are set to n respectively s＝32 and nt ＝64。
In order to verify the effectiveness of the proposed stochastic seismic response analysis method, a non-stationary stochastic analysis was performed on a three-layer shear building under seismic excitation. For this purpose, non-stationary seismic excitations matching the Kanai Tajimi seismic model are considered in the numerical simulation. Time-varying power spectral density S of seismic excitation g (ω, t) is given by
Wherein the parameters are ω g ＝6.0rad/s，ζ＝0.24，S 0 ＝/690m 2 /s 3 rad, k=9.79, α=0.15 and β=0.25. Notably, when t=40.0 s, the amplitude of the defined time-varying power spectral density decays to almost zero, and thus in the numerical calculationThe excitation duration is set to t 0 =40.0 s seconds. The MCM was used to provide a comparative baseline in which 30000 excitation samples were generated in total in the numerical calculation. FIG. 3 shows the time-varying power spectral density of the displacement and acceleration response, S y, and Sa Calculated by the methods herein, MCM and Kong, respectively. We can find that the results of the method herein agree well with those of MCM, whereas the non-stationary random analysis method has a large error in the predicted results due to the ignoring transient response components in the Kong method. The three methods are shown in pairs of details on the frequency scale and the time scale such as in fig. 4. In particular in the Kong method, the time-varying power spectral density of the displacement and acceleration response estimated by the method peaks around the initial time, which is not true because MCM results show that the structural vibration energy may gradually increase. Therefore, the traditional stochastic seismic analysis method does not consider the transient response of the structure, and a large error exists in estimating the time-varying power spectral density. However, harmonic wavelet based methods can accurately predict the time-varying power spectral density of the structural response when considering non-stationary seismic excitations.
By the set wavelet scale parameter n s Wavelet time shift parameter n t Duration of excitation T 0 Thereby determining the frequency domain resolution
Temporal resolution->
The motion of the time-invariant multiple degree of freedom system is given here:
wherein m, c and k are mass, damping and stiffness matrices of the multiple degree of freedom system. q and f are displacement response vectors and random excitation vectors, respectively; t (T) 0 Indicating the excitation duration. The dimensions of q and f are m×1.
The excitation duration is generally not significantly longer than the structural vibration period, especially for high-rise or large-span structures. According to research, the edge effects of generalized synergetic wavelets may cause non-negligible errors at the beginning and end of the signal (including transient response and short-term excitation). This may significantly reduce the accuracy of the transient response solution.
To solve this problem, the present invention employs periodicity of the excitation. By applying a standard periodic procedure of the function, periodic excitation can be obtained:
fp(t)＝p(t-n a t0)(2)
wherein the superscript "p" denotes a period; n is n a Representing t divided by t 0 Is a quotient of (2).
The periodic excitation fp (t) is periodic with a fundamental period of t 0 . Notably, the periodicity process is only to improve the wavelet expansion accuracy of excitation and response, and does not affect the dynamic analysis results of the structural system.
Using orthogonality, the connection coefficients of a wavelet function are defined as the inner product between a periodic generalized synergetic wavelet function and its derivative function, which can be expressed as
wherein ,
is a wavelet connection coefficient.
The linear algebraic expression of the wavelet coefficients of the response solution may be established as:
wherein A represents a connection coefficient matrix of the whole dynamic system, W f Wavelet coefficient vectors representing all scale excitations. A has a size of (N w +2M)×(B w +2M)，w f Is that]N w ×1]. The connection coefficient matrix a is a square with full rankAn array, which may be expressed as
wherein ,
is N w ×N w A diagonal block matrix; a is that t Is N w X m rectangular matrix.
Then the wavelet coefficients of the response are calculated from the wavelet coefficients of the periodic excitation, i.e
By using the calculated wavelet coefficients, the deterministic response can be directly determined by inverse fast wavelet transform. Thus, a deterministic response analysis is established based on the periodic generalized cooperative wavelet.
The power spectral density of a dynamic signal can be described in terms of the desired square modulus of the wavelet coefficients as follows:
wherein 
and />
Respectively represent the simultaneous instant t k ＝(k+0.5)T 0 /n t And the same frequency omega i ＝(m i +n i ) An automatic power spectral density of Dω/2; />
and />
Respectively representing the cross power spectral densities of two different time instants and two different frequencies; />
and />
Is m x m.
The relation between the power spectral density and the displacement of the random excitation is obtained by the method
wherein Sqq and Sff Power spectral density matrix representing displacement and excitation, respectively, with dimensions N w ×N w 。
The power spectral density of velocity and acceleration can be determined by the following formula:
in one embodiment, the structural stochastic response analysis method based on harmonic wavelets comprises the following steps: setting wavelet scale parameters, wavelet time translation parameters and excitation duration according to the harmonic wavelet random response analysis requirements, and constructing connection coefficients of wavelet functions and wavelet coefficient vectors of displacement and excitation in wavelet scales; obtaining an assembled connection coefficient matrix according to the wavelet scale parameter, the wavelet time shift parameter, the excitation duration and the connection coefficient of the wavelet function; constructing a wavelet connection coefficient matrix of the whole axle system according to the wavelet coefficient vector and the assembly connection coefficient matrix, and carrying out deterministic analysis by using the wavelet connection coefficient matrix; establishing a power spectrum density matrix of random load, and establishing an unchanged power spectrum density linear equation of the axle system through a wavelet connection coefficient matrix; the power spectral density of each response of the axle system is solved using a power spectral density linear equation. The wavelet coefficient vector of displacement and excitation in wavelet scale includes: a displacement response vector and a random excitation vector.
Further, the construction formula of the displacement response vector and the random excitation vector is as follows:
wherein m, c and k are mass, damping and stiffness matrices of the multiple degree of freedom system; q is a displacement response vector, f is a random excitation vector, T 0 Indicating the excitation duration.
Further, constructing connection coefficients of the wavelet function includes the steps of:
using orthogonality, the connection coefficients of a wavelet function are defined as the inner product between a periodic generalized synergetic wavelet function and its derivative function, which can be expressed as: frequency domain resolution
Temporal resolution->
wherein ,
the connection coefficient of the wavelet function is that the wavelet scale parameter is n s Wavelet time shift parameter n t 。
Further, a wavelet connection coefficient matrix of the whole axle system is constructed according to the wavelet coefficient vector and the assembly connection coefficient matrix, and is expressed as:
wherein A represents the entire dynamic stateConnection coefficient matrix of system, W q Representing the displacement response vector, W f Representing a random excitation vector.
Further, the power spectral density equation of the dynamic signal is expressed as:
wherein 
and />
Respectively represent the simultaneous instant t k ＝(k+0.5)T 0 /n t And the same frequency omega i ＝(m i +n i ) An automatic power spectral density of Dω/2; />
and />
Respectively representing the cross power spectral densities of two different time instants and two different frequencies; />
and />
Is m x m.
Further, the relation between the power spectral density of the random excitation and the displacement is:
wherein Sqq and Sff Power spectral density matrix representing displacement and excitation, respectively, with dimensions N W *N W 。
Further, the power spectral density of the velocity and acceleration can be determined by the following formula:
the invention also provides an electronic device, comprising: the system comprises a memory, a processor and a computer program stored in the memory and capable of running on the processor, wherein the processor realizes the structural random response analysis method based on harmonic waves when executing the computer program.
The processor and the memory may be connected by a bus or other means.
The memory, as a non-transitory computer readable storage medium, may be used to store non-transitory software programs as well as non-transitory computer executable programs. In addition, the memory may include high-speed random access memory, and may also include non-transitory memory, such as at least one magnetic disk storage device, flash memory device, or other non-transitory solid state storage device. In some embodiments, the memory optionally includes memory remotely located relative to the processor, the remote memory being connectable to the processor through a network. Examples of such networks include, but are not limited to, the internet, intranets, local area networks, mobile communication networks, and combinations thereof.
The above described apparatus embodiments are merely illustrative, wherein the units illustrated as separate components may or may not be physically separate, i.e. may be located in one place, or may be distributed over a plurality of network elements. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
Furthermore, an embodiment of the present invention provides a computer-readable storage medium storing computer-executable instructions that are executed by a processor or controller, for example, by one of the processors in the above-described terminal embodiment, and cause the above-described processor to perform the structural stochastic response analysis method based on harmonic waves in the above-described embodiment.
Those of ordinary skill in the art will appreciate that all or some of the steps, systems, and methods disclosed above may be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components may be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on computer readable media, which may include computer storage media (or non-transitory media) and communication media (or transitory media). The term computer storage media includes both volatile and nonvolatile, removable and non-removable media implemented in any method or technology for storage of information such as computer readable instructions, data structures, program modules or other data, as known to those skilled in the art. Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital Versatile Disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by a computer. Furthermore, as is well known to those of ordinary skill in the art, communication media typically embodies computer readable instructions, data structures, program modules or other data in a modulated data signal such as a carrier wave or other transport mechanism and includes any information delivery media.
While the preferred embodiment of the present invention has been described in detail, the present invention is not limited to the above embodiment, and various equivalent modifications and substitutions can be made by those skilled in the art without departing from the spirit of the present invention, and these equivalent modifications and substitutions are intended to be included in the scope of the present invention as defined in the appended claims.
The above-described embodiments of the present invention do not limit the scope of the present invention. Any other corresponding changes and modifications made in accordance with the technical idea of the present invention shall be included in the scope of the claims of the present invention.
Claims (10)
1. The structural random response analysis method based on harmonic wavelet is characterized by comprising the following steps of:
setting wavelet scale parameters, wavelet time translation parameters and excitation duration according to the harmonic wavelet random response analysis requirements, and constructing connection coefficients of wavelet functions and wavelet coefficient vectors of displacement and excitation in wavelet scales;
obtaining an assembled connection coefficient matrix according to the wavelet scale parameter, the wavelet time shift parameter, the excitation duration and the connection coefficient of the wavelet function;
constructing a wavelet connection coefficient matrix of the whole axle system according to the wavelet coefficient vector and the assembly connection coefficient matrix, and carrying out deterministic analysis by using the wavelet connection coefficient matrix;
establishing a power spectrum density matrix of random load, and establishing an unchanged power spectrum density linear equation of the axle system through the wavelet connection coefficient matrix;
the power spectral density of each response of the axle system is solved using a power spectral density linear equation.
2. The method of harmonic wavelet based structural stochastic response analysis according to claim 1, wherein the wavelet coefficient vectors of displacements and excitations in the wavelet scale comprise: a displacement response vector and a random excitation vector.
3. The structural stochastic response analysis method of claim 2, wherein the displacement response vector and the stochastic excitation vector are constructed as follows:
wherein m, c and k are mass, damping and stiffness matrices of the multiple degree of freedom system; q is a displacement response vector, f is randomExcitation vector, T 0 Indicating the excitation duration.
4. A method of analyzing a structural stochastic response based on harmonic wavelets as recited in claim 3, wherein constructing the connection coefficients of the wavelet functions comprises the steps of:
using orthogonality, the connection coefficients of a wavelet function are defined as the inner product between a periodic generalized synergetic wavelet function and its derivative function, which can be expressed as: frequency domain resolution
Temporal resolution->
wherein ,
the connection coefficient of the wavelet function is that the wavelet scale parameter is n s Wavelet time shift parameter n t 。
5. The method of harmonic wavelet based structural random response analysis of claim 4 wherein constructing a wavelet connectivity coefficient matrix for an entire axle system based on said wavelet coefficient vector and said assembled connectivity coefficient matrix is expressed as:
wherein A represents a connection coefficient matrix of the whole dynamic system, W q Representing the displacement response vector, W f Representing a random excitation vector.
6. The method of harmonic-based structural stochastic response analysis of claim 5, wherein the power spectral density equation of a dynamic signal is expressed as:
wherein 
and />
Respectively represent the simultaneous instant t k ＝(k+0.5)T 0 /n t And the same frequency omega i ＝(m i +n i ) An automatic power spectral density of Dω/2; />
and />
Respectively representing the cross power spectral densities of two different time instants and two different frequencies;
and />
Is m x m.
7. The method of analyzing the structural stochastic response of a harmonic-based structure according to claim 6, wherein the relationship between the power spectral density and the displacement of the stochastic excitation is:
wherein Sqq and Sff Power spectral density matrix representing displacement and excitation, respectively, with dimensions N W *N W 。
8. The method of harmonic wavelet based structural stochastic response analysis according to claim 6, wherein the power spectral densities of velocity and acceleration are determined by the following equation:
9. an electronic device, comprising: a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing the structural stochastic response analysis method according to any one of claims 1 to 8 when the computer program is executed.
10. A computer-readable storage medium storing computer-executable instructions for causing a computer to perform the structural stochastic response analysis method according to any one of claims 1 to 8.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211688590.2A CN116186838A (en) | 2022-12-27 | 2022-12-27 | Structural random response analysis method, device and storage medium based on harmonic wavelet |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211688590.2A CN116186838A (en) | 2022-12-27 | 2022-12-27 | Structural random response analysis method, device and storage medium based on harmonic wavelet |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN116186838A true CN116186838A (en) | 2023-05-30 |
Family
ID=86437558
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211688590.2A Pending CN116186838A (en) | 2022-12-27 | 2022-12-27 | Structural random response analysis method, device and storage medium based on harmonic wavelet |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN116186838A (en) |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106682277A (en) * | 2016-12-06 | 2017-05-17 | 西南交通大学 | Fast simulation method for non-stationary random process |
| WO2019076015A1 (en) * | 2017-10-16 | 2019-04-25 | 东南大学 | Dual modal equation based dynamic response analysis method under random noise environment |
| WO2020168589A1 (en) * | 2019-02-19 | 2020-08-27 | 大连理工大学 | Method for automatically detecting free vibration response of high-speed rail bridge to identify mode |
| CN114692473A (en) * | 2022-06-01 | 2022-07-01 | 成都理工大学 | Method for solving response of uncertain axle coupling vibration system |
-
2022
- 2022-12-27 CN CN202211688590.2A patent/CN116186838A/en active Pending
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN106682277A (en) * | 2016-12-06 | 2017-05-17 | 西南交通大学 | Fast simulation method for non-stationary random process |
| WO2019076015A1 (en) * | 2017-10-16 | 2019-04-25 | 东南大学 | Dual modal equation based dynamic response analysis method under random noise environment |
| WO2020168589A1 (en) * | 2019-02-19 | 2020-08-27 | 大连理工大学 | Method for automatically detecting free vibration response of high-speed rail bridge to identify mode |
| CN114692473A (en) * | 2022-06-01 | 2022-07-01 | 成都理工大学 | Method for solving response of uncertain axle coupling vibration system |
Non-Patent Citations (3)
| Title |
|---|
| 孔凡;李杰;: "基于小波-Galerkin方法的结构随机动力响应功率谱的确定", 计算力学学报, no. 02 * |
| 肖祥等: "A stochastic analysis method of transient responses using harmonic wavelets, Part 1: Time-invariant structural systems", 《MECHANICAL SYSTEMS AND SIGNAL PROCESSING》, pages 3 * |
| 陈水生;赵辉;李锦华;夏钰桓;: "车桥耦合振动的非平稳桥面激励的模拟", 沈阳建筑大学学报(自然科学版), no. 05 * |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Qu et al. | Mode identification by eigensystem realization algorithm through virtual frequency response function | |
| Al-Hussein et al. | Novel unscented Kalman filter for health assessment of structural systems with unknown input | |
| Nayeri et al. | Study of time-domain techniques for modal parameter identification of a long suspension bridge with dense sensor arrays | |
| Sundar et al. | Time variant reliability model updating in instrumented dynamical systems based on Girsanov’s transformation | |
| Waezi et al. | Stochastic non-stationary model for ground motion simulation based on higher-order crossing of linear time variant systems | |
| Mahato et al. | Adaptive HHT (AHHT) based modal parameter estimation from limited measurements of an RC‐framed building under multi‐component earthquake excitations | |
| Shi et al. | Substructural time-varying parameter identification using wavelet multiresolution approximation | |
| Rizzi et al. | Comparison of nonlinear random response using equivalent linearization and numerical simulation | |
| CN116186838A (en) | Structural random response analysis method, device and storage medium based on harmonic wavelet | |
| Xin et al. | Enhanced vibration decomposition method based on multisynchrosqueezing transform and analytical mode decomposition | |
| Bao et al. | Signal denoising method for modal analysis of an offshore platform | |
| CN112578458B (en) | Pre-stack elastic impedance random inversion method and device, storage medium and processor | |
| Quqa et al. | Instantaneous identification of densely instrumented structures using line topology sensor networks | |
| Kord et al. | Parametric system identification of large‐scale structure using decoupled synchronized signals | |
| Lei et al. | Simultaneous assessment of damage and unknown input for large structural systems by UKF-UI | |
| Guo et al. | The generalized EPC method for the non-stationary probabilistic response of nonlinear dynamical system | |
| Dosiek et al. | Model order sensitivity in ARMA-based electromechanical mode estimation algorithms under ambient power system conditions | |
| CN113341463A (en) | Pre-stack seismic data non-stationary blind deconvolution method and related components | |
| Sundaram et al. | Optimal state estimators for linear systems with unknown inputs | |
| Kim et al. | Cumulative power spectral density‐based damping estimation | |
| Yang et al. | Identification of gradually varying physical parameters based on discrete cosine transform using partial measurements | |
| Geerardyn et al. | Improving the H∞ norm estimate of an active vibration isolation system using local rational models | |
| Kaneko | Effect of strong ground motion duration on the expected peak values of floor response spectra in elastic buildings | |
| García-Illescas et al. | A matrix projection method for on line stable estimation of 1D and 3D shear building models | |
| RU2366914C1 (en) | Method for testing of spacecraft structural elements, in particular honeycomb panels, by mechanical actions |
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 |