CN111651728B - Method for identifying non-stationarity and non-stationarity of actually measured wind speed - Google Patents
Method for identifying non-stationarity and non-stationarity of actually measured wind speed Download PDFInfo
- Publication number
- CN111651728B CN111651728B CN202010482171.8A CN202010482171A CN111651728B CN 111651728 B CN111651728 B CN 111651728B CN 202010482171 A CN202010482171 A CN 202010482171A CN 111651728 B CN111651728 B CN 111651728B
- Authority
- CN
- China
- Prior art keywords
- wind speed
- time
- stationary
- stationarity
- actually measured
- 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
- 238000000034 method Methods 0.000 title claims abstract description 83
- 238000001228 spectrum Methods 0.000 claims abstract description 109
- 230000008569 process Effects 0.000 claims abstract description 20
- 230000005654 stationary process Effects 0.000 claims abstract description 14
- 230000008707 rearrangement Effects 0.000 claims abstract description 11
- 238000005516 engineering process Methods 0.000 claims abstract description 10
- 238000012850 discrimination method Methods 0.000 claims abstract description 5
- 230000006870 function Effects 0.000 claims description 26
- 238000004364 calculation method Methods 0.000 claims description 25
- 230000004044 response Effects 0.000 claims description 15
- 238000012360 testing method Methods 0.000 claims description 8
- 238000012795 verification Methods 0.000 claims description 8
- 230000008859 change Effects 0.000 claims description 4
- 238000009499 grossing Methods 0.000 claims description 4
- 238000012545 processing Methods 0.000 claims description 4
- 230000003595 spectral effect Effects 0.000 claims description 4
- 230000002159 abnormal effect Effects 0.000 claims description 3
- 238000003908 quality control method Methods 0.000 claims description 3
- 238000010183 spectrum analysis Methods 0.000 claims 1
- 241000208422 Rhododendron Species 0.000 description 15
- 238000004458 analytical method Methods 0.000 description 12
- 238000005259 measurement Methods 0.000 description 6
- 230000009977 dual effect Effects 0.000 description 5
- 230000001360 synchronised effect Effects 0.000 description 5
- 238000005315 distribution function Methods 0.000 description 4
- 230000000694 effects Effects 0.000 description 4
- 238000000605 extraction Methods 0.000 description 4
- 238000011160 research Methods 0.000 description 4
- 238000004088 simulation Methods 0.000 description 4
- 238000006467 substitution reaction Methods 0.000 description 4
- 239000000725 suspension Substances 0.000 description 4
- 238000010998 test method Methods 0.000 description 4
- 238000012935 Averaging Methods 0.000 description 3
- 150000001875 compounds Chemical class 0.000 description 3
- 238000000354 decomposition reaction Methods 0.000 description 3
- 230000007547 defect Effects 0.000 description 3
- 238000013461 design Methods 0.000 description 3
- 238000005457 optimization Methods 0.000 description 3
- 230000009466 transformation Effects 0.000 description 3
- 230000003044 adaptive effect Effects 0.000 description 2
- 230000002776 aggregation Effects 0.000 description 2
- 238000004220 aggregation Methods 0.000 description 2
- 230000001174 ascending effect Effects 0.000 description 2
- 230000008901 benefit Effects 0.000 description 2
- 238000011161 development Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 238000006073 displacement reaction Methods 0.000 description 2
- 238000001125 extrusion Methods 0.000 description 2
- 238000013139 quantization Methods 0.000 description 2
- 238000005070 sampling Methods 0.000 description 2
- 238000000528 statistical test Methods 0.000 description 2
- 230000007704 transition Effects 0.000 description 2
- 208000031953 Hereditary hemorrhagic telangiectasia Diseases 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000004422 calculation algorithm Methods 0.000 description 1
- 230000007812 deficiency Effects 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 239000006185 dispersion Substances 0.000 description 1
- 230000005284 excitation Effects 0.000 description 1
- 239000000284 extract Substances 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 239000000463 material Substances 0.000 description 1
- 238000000691 measurement method Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 230000010355 oscillation Effects 0.000 description 1
- 238000012805 post-processing Methods 0.000 description 1
- 238000011002 quantification Methods 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
Images
Classifications
-
- 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
- G06F17/18—Complex mathematical operations for evaluating statistical data, e.g. average values, frequency distributions, probability functions, regression analysis
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Data Mining & Analysis (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Physics (AREA)
- Computational Mathematics (AREA)
- Mathematical Analysis (AREA)
- Life Sciences & Earth Sciences (AREA)
- Operations Research (AREA)
- Probability & Statistics with Applications (AREA)
- Bioinformatics & Cheminformatics (AREA)
- Algebra (AREA)
- Evolutionary Biology (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Bioinformatics & Computational Biology (AREA)
- Measurement Of Mechanical Vibrations Or Ultrasonic Waves (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses a method for identifying the non-stationarity and the non-stationarity of an actually measured wind speed, which comprises the following steps of S1: based on the time domain and time-frequency domain angles, adopting a round method combined with a VMD-SET secondary discrimination method to check whether the actually measured wind speed sample has non-stationarity, if the actually measured wind speed sample has the non-stationarity, turning to the step S2, otherwise, exiting the process; step S2: obtaining a time-varying power spectrum and an average marginal spectrum of the wind speed by adopting a multi-taper window method with optimized window width and a time-frequency rearrangement technology, and judging that an actually measured wind speed sample with non-stationarity is an intensity non-stationary process or a complete non-stationary process according to the number of extreme points of the average marginal spectrum and whether the moments corresponding to the maximum values of different frequency components are consistent; and step S3: and measuring the non-stationary intensity degree of the actually measured wind speed sample by adopting a non-stationary quantitative index, and respectively providing thresholds for judging stationary, weak stationary and strong stationary wind speeds.
Description
Technical Field
The invention relates to the technical field of structural wind engineering, in particular to a method for identifying the non-stationarity and the non-stationarity of an actually measured wind speed.
Background
The loads such as wind, wave, earthquake and the like in nature have randomness, and with the development of modern structures towards large span and high rise directions and the use of light high-strength materials, the non-stationarity of the random signals becomes a key factor of the fine design of a complex structure and is a difficulty of current research. According to the correlation definition of a random signal, if the mean and variance (first and second moments of the random process) are independent of time, it is called generalized stationary, also simply stationary, and conversely, it is called non-stationary. This classical definition of stationarity divides the random signal into two absolute halves, namely stationary and non-stationary. In practical engineering application, for convenience, the non-stationary signal is often roughly processed as a stationary, semi-stationary, piecewise stationary signal, and this simplified processing will cause a calculation deviation of a subsequent structural vibration response result, resulting in a structural design biased to insecurity.
The non-stationarity of the random signal is a relatively complex characteristic, sometimes the random signal is non-stationary for a long time, but each part is stationary; in addition, if a transition signal is added to a stationary random signal, the random signal may be considered to be almost stationary if it is long enough, but not stationary when viewed from near the transition. The non-stationarity of the identification signal depends largely on the observation duration. Essentially, the presence or absence of non-stationary effects on the signal is closely related to the observation time scale.
Generally, the non-stationarity of the random signal is mainly represented in both intensity and frequency, and we refer to the variation of the intensity with time as intensity non-stationarity, and refer to the dual variation of the intensity and frequency as complete non-stationarity. Therefore, we need not only to identify whether there is non-stationarity in the random signal? Which class of non-stationary types can be classified? It is also necessary to provide a quantitative index of the Degree of instability (abbreviated as DNS) of the random signal so as to reflect the quantitative Degree of how far the unstable signal deviates from the stability.
In the field of structural wind engineering, is the wind speed non-stationary? Which type of non-stationary form? The selection of a structural wind-induced vibration theory method and the accuracy and reliability of a calculation result are determined, the qualitative measurement of non-stationarity can reduce the calculation complexity, and particularly for a wind speed sample with weak non-stationarity indexes, the structural wind-induced response analysis frame is very complex under the action of non-stationary wind speed, and the algorithm consumes a long time. In order to improve the calculation efficiency, the wind speed with weak non-stationary degree can be processed according to the stationary theory.
In summary, the current research on the non-stationary aspect of wind speed is still in the development stage, how to find a suitable identification and measurement method is a major technical challenge to be faced by using a suitable measurement index, and breakthrough of the technologies has important application value in the field of structural wind engineering.
Disclosure of Invention
The invention aims to: aiming at the problems in the prior art, a method for identifying the non-stationarity and the non-stationarity of the actually measured wind speed is provided.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for identifying measured wind speed non-stationarity and non-stationarity comprises the following steps:
step S1: based on the time domain and time-frequency domain angles, adopting a round method combined with a VMD-SET secondary discrimination method to check whether the actually measured wind speed sample has non-stationarity, if the actually measured wind speed sample has the non-stationarity, turning to the step S2, otherwise, exiting the process; the step is the first level and is used for identifying whether the measured wind speed has non-stationarity.
Step S2: obtaining a time-varying power spectrum and an average marginal spectrum of the wind speed by adopting a multi-taper window method of window width optimization and a time-frequency rearrangement technology, and judging that the actually measured wind speed sample with non-stationarity is an intensity non-stationary process or a complete non-stationary process according to the number of extreme points of the average marginal spectrum and whether the moments corresponding to the maximum values of different frequency components are consistent; this step is the second level for discriminating whether the measured wind speed is non-stationary in intensity or completely non-stationary.
And step S3: measuring the non-stationary intensity degree of the actually measured wind speed sample by using a non-stationary quantitative index, wherein the non-stationary quantitative index has a calculation formula as follows:
in the formula, DNS is a non-smoothness quantitative index theta 1 Characteristic distance of measured wind speed sample
Fluctuation in time scale, [ theta ] 0 (j) Characteristic distance ^ of substitute data sample for jth group>
The fluctuation in the time scale, J is the number of substitute data samples. The step is the third level and is used for calculating the non-stationarity quantitative index of the actually measured wind speed.
According to statistics of measured samples of thunderstorm winds, typhoons (hurricanes), tornadoes and the like in mountainous areas and relevant experience of seismic fluctuation nonstationary research, nonstationary wind speeds often show strong fluctuation and intermittence, and the wind speeds have a sudden change mode and a drifting mode on an observation time scale and can be regarded as expression forms of nonstationary intensity. On the other hand, the "intermittency" of vortices of different scales on the observation time scale can be seen as a manifestation of non-stationary frequency. Generally, in the field of civil engineering, random excitations such as extreme wind speeds, seismic oscillations, etc., while having amplitude non-stationarities, are often accompanied by frequency non-stationarities.
The method for identifying the non-stationarity of the signal in the prior art mainly comprises the following steps: time-frequency domain methods (such as wavelet transform, hilbert transform based on pattern decomposition, data substitution method, etc.); time domain class methods (Reverse order test method), round test method (Run test method), feature root test method (Eigenvalue test), recursion graph method (Recurrence plot), etc.).
The time domain class method has the following defects: only non-stationary signals with a tendency to mean are valid and are not suitable for detecting non-stationarity of complex signals, especially signals with frequency non-stationarity.
The time-frequency domain method has the following defects: including short-time Fourier transforms, wavelet transforms (generalized harmonious wavelets), HHTs, S transforms, multi-window spectral estimation methods, priestly methods, etc. The time frequency spectrum is three-dimensional distribution of time-frequency-energy, and time-varying characteristics of instantaneous frequency and instantaneous amplitude are clearly shown. However, the conventional Time Frequency Analysis (Time Frequency Analysis) technique has various disadvantages, such as uncertainty criteria (Time domain and Frequency domain resolutions cannot be optimized at the same Time), cross terms, modal aliasing, boundary effects, parameter values, and the like. These deficiencies seriously interfere with the fine portrayal of signal characteristics, and cause the time-varying rule to be not obvious enough and difficult to effectively identify. Therefore, a time-frequency analysis post-processing technology (such as synchronous extrusion/synchronous extraction transformation) introduces a synchronous extrusion/extraction operator, the operator only extracts a coefficient which is most closely related to the time-varying characteristic of the signal in the time-frequency analysis result, and therefore energy diffusion is suppressed.
A first level:
in view of the defects of the time domain type and the time-frequency domain type analysis method, the invention adopts a secondary discrimination method combining a time domain (round method) with a time-frequency domain (VMD-SET, variation modal decomposition and synchronous extraction transformation) to test whether the actually measured wind speed sample has non-stationarity.
Specifically, the method comprises the following steps:
step S11: performing quality control on the actually measured wind speed sample, and eliminating abnormal values existing in the actually measured wind speed sample;
step S12: based on a time domain angle, performing non-stationarity test on the actually measured wind speed sample by adopting a round method, if the test result is non-stationarity, turning to the step S13 to perform verification again, and if not, exiting the process;
step S13: and performing VMD (variational modal decomposition) -SET (synchronous extraction transformation) processing on the actually measured wind speed sample based on the time-frequency domain angle to obtain a three-dimensional time-frequency spectrogram, verifying according to the change characteristics of the instantaneous amplitude and the instantaneous frequency of the time-frequency spectrogram, if the verification result is non-stable, turning to the step S2, and otherwise, exiting the process. And if the verification result is stable and contradicts the result of the step S12, taking the result obtained in the step as a standard, and exiting the process.
And a second level:
assuming that the wind speed has non-stationarity in both intensity and frequency, the sample x (t) with non-stationarity in wind speed is represented as a superposition of a series of zero-mean independent uniformly modulated gaussian processes:
in the formula: p is the number of sub-processes; x k (t) is the kth uniformly modulated sub-process; y is k (t) is a zero mean stationary gaussian process; g k (t) is the intensity modulation function and t is time. In order to be able to take into account the "rise" and "fall" characteristics of the wind speed amplitude over the observation period, a modified form of the gamma exponential function is used:
in the formula: eta k And λ k Is a positive constant; zeta k The moment when the wind speed of the kth sub-process reaches a measuring point; h (t) is a unit step function.
Single sided power spectrum of kth subprocess
Expressed as:
wherein f is the Hertz frequency, A k 、B k 、α k 、β k 、γ k Is a undetermined constant.
In summary, the unified model considering the dual non-stationary of the pulsating wind speed intensity and frequency is represented as:
on the one hand, the feature that the magnitude of the Gama modulation function increases first and then starts to decrease at a certain moment with the increase of the observation time, which may characterize the non-stationarity of the wind speed in terms of intensity; on the other hand, the frequency instability can be characterized by inconsistent extreme value moments of the subprocesses, namely k subprocesses do not reach the extreme value at the same moment, and a plurality of local extreme value points exist on the spectrogram. Thus, the above formula is a unified model that considers both intensity and frequency non-stationarities.
Specifically, the step S2 of determining whether the actually measured wind speed is the intensity non-stationary process or the complete non-stationary process includes the following steps:
step S21: dividing the actually measured wind speed sample into a time-varying average wind speed component and a fluctuating wind speed component, and assuming that the fluctuating wind speed has double non-stationarity in the aspects of intensity and frequency;
step S22: obtaining a time-varying power spectrum of the pulsating wind speed by adopting a multi-taper window method of window width optimization and a time-frequency rearrangement technology;
step S23: based on an improved quasi-Newton iteration method and the numerical calculation result of the time-varying power spectrum obtained in the step S22, fitting all undetermined parameters in the time-varying power spectrum analytical expression;
step S24: integrating the time t, and calculating the average marginal spectrum of the time-varying power spectrum;
step S25: and judging the number of extreme points of the average marginal spectrum, if the number of the extreme points is less than or equal to 1, judging the intensity non-stationary process, if the number of the extreme points is more than 1, further judging whether the moments corresponding to the maximum values of the different frequency components are consistent, and if the moments are not consistent, judging the intensity non-stationary process.
Once the pulsating wind speed is judged to be only the intensity nonstationary process, the unified model can be simplified, namely a local variance sequence of the pulsating wind speed sample is obtained by utilizing the time-varying power spectrum, and the local variance sequence is an intensity envelope function.
Wherein f is the Hertz frequency,. DELTA.f j J is a variable and N is the number of frequency discrete points for frequency resolution.
The intensity non-stationary wind velocity spectrum model is represented as:
in the formula (I), the compound is shown in the specification,
is a normalized wind spectrum.
As a preferable embodiment of the present invention, the step S22 includes the steps of:
step S221: due to the fact that the orthogonal Hermite function has high aggregation in a time frequency plane, the Hermite function is selected as a window function, and the value range of the window width is determined;
step S222: k Hermite window functions are utilized to obtain independent time-frequency rearrangement spectrum estimation, and a time-varying power spectrum is obtained
Wherein x (t) is the pulsating wind speed h k (τ -t) is the Hermite function, τ is the integral variable, t is time, f is the Hertz frequency;
step S223: optimizing a window width value by adopting a Renyi entropy value corresponding to time-frequency energy distribution, namely, the minimum value of the Renyi entropy value corresponds to an optimal window width;
step S224: to further reduce the "sampling fluctuation" on a time scale, a time-averaging window function [ omega ] is used T (n)，n＝1，2，...，N]Smoothing is carried out to obtain the smoothed time-varying power spectrum, wherein omega is T (N) is a window function for a smooth spectrogram, N is a time dispersion point, and T is a duration.
As a preferable embodiment of the present invention, the step S23 includes the steps of:
step S231: dividing sub-blocks according to the local extreme value distribution characteristics of the time-varying power spectrum;
step S232: fitting the sub-blocks based on a modified quasi-Newton iteration method (adaptive least squares);
step S233: and after the fitting of all the sub-blocks is completed in sequence, using the fitting parameters of all the sub-blocks as iteration initial values of the fitting parameters of the time-varying power spectrum, and obtaining all undetermined parameters in the time-varying power spectrum analytical expression S (t, f) based on an improved Newton iteration method to obtain S (t, f).
And a third level:
essentially, with the use of time-varying power spectrum "local" features and "global" features, the non-stationarity is defined by the distance between the time-varying power spectrum S (t, f) and the generally generalized stationary power spectrum S (f):
in the formula: < > represents time averaging.
The generalized stationary power spectrum closest to normal is the time scale mean spectrum, denoted as:
<S(t，f)>＝S(f)。
as can be seen, for non-stationary wind speeds, DNS > 0, while for stationary wind speeds DNS is constantly equal to 0. However, the above formula is disadvantageous in that the global and local measurement means only uses simple euclidean distance, and the non-stationarity index lacks lateral contrast, and cannot effectively measure the non-stationarity degree.
Data substitution is a statistical method, the principle of which is: firstly, fourier transform is carried out on the actually measured non-stationary wind speed sequence, secondly, the amplitude of the Fourier transform is kept unchanged, and the phase position is adjusted
Is at [ - π, π]And randomizing uniformly distributed variables, and finally obtaining substitute data by utilizing inverse Fourier transform. The purpose of data substitution is to eliminate all non-stationary information contained in the original measured wind speed,and the data substitution sample has an amplitude spectrum completely consistent with the original measured wind speed, and is generalized and stable.
It is conceivable that: (1) A random stationary sample generated by replacing the data can be used for obtaining a threshold value for judging whether the wind speed has non-stationarity; (2) The threshold value can also be obtained according to a good steady pulsating wind sample generated by Simu spectrum simulation in the Highway bridge wind resistance design Specification (JTG/T3360-01-2018) in China.
Specifically, in the step S3, calculating the non-stationarity quantitative index includes the following steps:
step S31: calculating the characteristic distance between the local and the global of the actually measured wind speed sample
In the formula, S (t) n F) is time t n The measured time-varying power spectrum of the wind speed,<S(t n ，f)> n measured wind speed mean power spectrum, D (S (t), for n moments n ，f)，<S(t n ，f)> n ) Is S (t) n F) and<S(t n ，f)> n the distance between the two points is N, N is a variable, and N is a time discrete point;
similarly, J sets of substitute data samples { s } j (t), J = 1.. J., J } "local" to "global" feature distance
In the formula (I), the compound is shown in the specification,
at a time t n Alternative to (2)The time-varying power spectrum of the data, device for selecting or keeping>
For n time instants replacing the mean power spectrum of the data->
Is->
And &>
The distance between the two points, N is a variable, and N is a time discrete point;
step S32: calculating the characteristic distance of the actually measured wind speed sample
Fluctuations theta on the time scale 1 And J sets of characteristic distances ∑ of the replacement data samples>
Fluctuation theta in time scale 0 (j)：
In the formula, var (. Cndot.) represents the calculation of the sequence variance.
Due to theta 0 (j) And obtaining random variables by J groups of random substitute data samples. Therefore, a probability density distribution function of the random variable is easy to obtain (the tested Gamma distribution has a good fitting effect), so that an upper quantile point with the confidence coefficient of alpha can be calculated, namely the upper quantile point is a threshold value for judging whether the wind speed has non-stationarity. Further on theta 1 Performing statistical test when the theta is higher than the standard value 1 When it is greater than the threshold value, it isThe initial wind speed is considered as non-stationary when theta 1 When the wind speed is less than or equal to the threshold value, the original wind speed is considered to be stable.
Step S33: according to the theta 1 And Θ 0 (j) And calculating the distance DNS between the time-varying power spectrum and the generalized stationary power spectrum, and taking the DNS as a non-stationary quantitative index.
It should be noted that the above-mentioned measurement of the distance between the global spectrum and the local spectrum is the key to accurately calculate the non-stationary quantization index, and the effective method for measuring the characteristic distance includes: kullback-Leibler divergence D KL Distance D from Hellinger H Adapted to frequency modulated signals; distance D of logarithmic spectrum LSD Suitable for amplitude modulated signals. Due to D H Has stronger robustness and better performance than D KL Therefore, it proposes D H +D LSD The combination makes a distance measure of the intensity and frequency non-stationary wind speed.
In the formula, G and H are a local spectrum and a global spectrum respectively;
respectively corresponding normalized spectra; d H Is the Hellinger distance; d LSD Is the log spectral distance; λ is the adjustment coefficient, and can take the value of 1.
The invention further proposes a step S34: determining the upper and lower bounds [ theta ] of the non-stationarity quantitative index threshold low ，Θ upper ]The method can classify the non-stationary wind speed samples according to the intensity degree thereof:
wherein, due to theta 0 And obtaining random variables by J groups of random substitute data samples. Therefore, the probability density distribution function of random variables is easily obtained, and the Gamma distribution is adopted to fit theta 0 (j) The confidence is set to 95%, i.e. α =0.05, and the upper α quantile of the confidence interval is the lower threshold bound Θ low 。
Determining a threshold using a difference between structural wind-induced dynamic responses under two calculated conditionsUpper value bound Θ upper And calculating a first working condition by analyzing the wind speed according to a non-stationary theory, and calculating a second working condition by simplifying the wind speed into a stationary theory.
When the maximum response difference value of the two calculation working conditions is 5% -10%, the theta corresponding to the group of non-steady wind speeds is determined 1 The value is the upper threshold limit theta upper 。
When theta is higher than theta 1 ＜Θ low Meanwhile, the wind speed is a steady sample; when theta is satisfied low ≤Θ 1 ≤Θ upper Meanwhile, the wind speed is a weak and steady wind speed; when theta is satisfied 1 ＞Θ upper In time, the wind speed is a strong non-steady wind speed.
Thus, a non-stationary indicator threshold interval [ Θ ] is utilized low ，Θ upper ]The weak non-steady wind speed can be simplified into the steady wind speed to carry out structural wind-induced response analysis, and the calculation efficiency is greatly improved by hundreds of times.
The invention provides a threshold value for judging stable, weak stable and strong stable wind speed based on wind-induced response analysis of a 628m large-span suspension bridge structure low ＝0.026(DNS＝1.59)，Θ upper ＝0.115(DNS＝2.45)。
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
(1) The method for judging the unsteady and unsteady type of the actually measured wind speed has the advantages of simplicity, accuracy and quickness;
(2) A multi-taper window method for optimizing window width and a time-frequency rearrangement technology are provided, and a time-varying power spectrum estimation value with high resolution can be obtained;
(3) A measurement means of the distance between the global spectrum and the local spectrum is provided, and the technical bottleneck that the effective calculation cannot be carried out in the existing method is solved;
(4) By adopting the non-stationarity judging index, the stationary and non-stationary samples in the actually measured wind speed can be effectively distinguished, the identification precision of the wind characteristic parameter can be improved, and the modeling method of the pulsating wind spectrum can be simplified;
(5) The non-stationary indicator can reflect a measure of how far the non-stationary signal deviates from the stationary threshold. The actually measured wind speed with the judgment index smaller than the critical value is simplified and processed into a stable sample, so that the calculation complexity can be reduced, and the calculation efficiency of wind-induced response is remarkably improved by hundreds of times.
Drawings
FIG. 1 is a flow chart of a method for identifying non-stationarity and non-stationarity of an actually measured wind speed according to the present invention.
Fig. 2 is a numerical simulation am/fm signal according to embodiment 1 of the present invention.
Fig. 3 shows the VMD-SET analysis result of the simulation signal according to embodiment 1 of the present invention.
Fig. 4 is a time-varying power spectrum of a simulated signal according to embodiment 1 of the invention.
FIG. 5 is the average margin spectrum of the simulated signal described in example 1 of the present invention.
FIG. 6 is a sample of the alternative data described in example 1 of the present invention.
Fig. 7 is a stationary time spectrum (J = 50) of the substitute data sample according to embodiment 1 of the present invention.
FIG. 8 shows the graphic symbols Θ used in example 1 of the present invention 0 (j) The probability density distribution and the Gamma distribution are fitted to a schematic diagram.
FIG. 9 is the measured thunderstorm wind speed of example 2 of the present invention.
FIG. 10 is a sample of typhoon "rhododendron" according to example 2 of the present invention.
FIG. 11 shows the strongest 1h wind speed in the typhoon "Rhododendron" sample according to example 2 of the present invention
FIG. 12 is a time varying spectrum of measured thunderstorm wind speed as described in example 2 of the present invention.
FIG. 13 is the average margin spectrum of the measured thunderstorm wind speed according to example 2 of the present invention.
FIG. 14 is a time varying spectrum of a measured typhoon "azalea" sample according to example 2 of the present invention.
FIG. 15 is the average margin spectrum of the measured typhoon "rhododendron" samples according to example 2 of the present invention.
FIG. 16 shows the data values Θ of example 2 of the present invention 0 (j) The probability density distribution and the Gamma distribution are fitted to a schematic diagram.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings.
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
A method for identifying measured wind speed non-stationarity and non-stationarity comprises the following steps:
the first layer is as follows: and identifying whether the measured wind speed has non-stationarity.
Step S1: and (3) based on time domain and time-frequency domain angles, adopting a round method combined with a VMD-SET secondary discrimination method to check whether the actually measured wind speed sample has non-stationarity, if the actually measured wind speed sample has the non-stationarity, turning to the step S2, and if not, exiting the process.
Specifically, the step S1 includes the following steps:
step S11: performing quality control on the actually measured wind speed sample, and eliminating abnormal values existing in the actually measured wind speed sample;
step S12: based on a time domain angle, performing non-stationarity test on the actually measured wind speed sample by adopting a round method, if the test result is non-stationarity, turning to the step S13 to perform verification again, and if not, exiting the process;
step S13: and performing VMD-SET processing on the actually measured wind speed sample based on a time-frequency domain angle to obtain a three-dimensional time-frequency spectrogram, verifying according to the change characteristics of the instantaneous amplitude and the instantaneous frequency of the time-frequency spectrogram, if the verification result is non-stable, turning to the step S2, and if not, exiting the process. And if the verification result is stable and contradicts the result of the step S12, taking the result obtained in the step as a standard, and exiting the process.
And a second level: and judging whether the actually measured wind speed is unstable in intensity or completely unstable.
Step S2: and obtaining a time-varying power spectrum and an average marginal spectrum of the wind speed by adopting a multi-taper window method of window width optimization and a time-frequency rearrangement technology, and judging that the actually measured wind speed sample with non-stationarity is a non-stationary intensity process or a non-stationary complete process according to the number of extreme points of the average marginal spectrum and whether the moments corresponding to the maximum values of different frequency components are consistent.
Specifically, the step S2 includes the following steps:
step S21: the measured wind speed samples are divided into time varying average wind speed and fluctuating wind speed components, and the fluctuating wind speed is assumed to have dual non-stationarities in intensity and frequency.
Step S22: and obtaining the time-varying power spectrum of the fluctuating wind speed by adopting a multi-cone window method with optimized window width and a time-frequency rearrangement technology.
The step S22 includes the steps of:
step S221: due to the fact that the orthogonal Hermite function has high aggregation in a time frequency plane, the Hermite function is selected as a window function, and the value range of the window width is determined;
step S222: k Hermite window functions are utilized to obtain independent time-frequency rearrangement spectrum estimation, and a time-varying power spectrum is obtained
Wherein x (t) is the pulsating wind speed, h k (τ -t) is the Hermite function, τ is the integral variable, t is time, f is the Hertz frequency;
step S223: optimizing a window width value by adopting a Renyi entropy value corresponding to time-frequency energy distribution, namely, the minimum value of the Renyi entropy value corresponds to an optimal window width;
step S224: to further reduce the "sampling fluctuation" on a time scale, a time-averaging window function [ omega ] is used T (n)，n＝1，2，...，N]Smoothing is carried out to obtain the smoothed time-varying power spectrum, wherein omega is T (N) is a window function for a smooth spectrogram, N is a time discrete point, and T is wind speed duration.
Step S23: and fitting all undetermined parameters in the time-varying power spectrum analytical expression based on an improved quasi-Newton iteration method and the numerical calculation result of the time-varying power spectrum obtained in the step S22.
The step S23 includes the steps of:
step S231: dividing sub-blocks according to the extreme value distribution characteristics of the time-varying power spectrum;
step S232: fitting the sub-blocks based on a modified quasi-Newton iteration method (adaptive least squares);
step S233: and after the fitting of all the sub-blocks is completed in sequence, using the fitting parameters of all the sub-blocks as iteration initial values of the fitting parameters of the time-varying power spectrum, and obtaining all undetermined parameters in the time-varying power spectrum analytical expression S (t, f) based on an improved Newton iteration method to obtain S (t, f).
Step S24: and integrating the time t, and calculating the average marginal spectrum of the time-varying power spectrum.
Step S25: and judging the number of extreme points of the average marginal spectrum, if the number of the extreme points is less than or equal to 1, judging the intensity non-stationary process, if the number of the extreme points is more than 1, further judging whether the moments corresponding to the maximum values of the different frequency components are consistent, and if the moments are not consistent, judging the intensity non-stationary process.
And a third level: and calculating the unsteady quantitative index of the actually measured wind speed.
And step S3: measuring the non-stationary intensity degree of the actually measured wind speed sample by using a non-stationary quantitative index, wherein the non-stationary quantitative index has a calculation formula as follows:
in the formula, DNS is a non-smoothness quantitative index, theta 1 Characteristic distance of measured wind speed sample
Fluctuation in time scale, [ theta ] 0 (j) Characteristic distance ^ of substitute data sample for jth group>
The fluctuation in the time scale, J is the number of substitute data samples.
Specifically, the step S3 includes the following steps:
step S31: calculating the characteristic distance between the local and the global of the actually measured wind speed sample
In the formula, S (t) n F) is time t n The measured wind speed time-varying power spectrum of (a),<S(t n ，f)> m is the measured wind speed mean power spectrum, D (t) at n times n ，f)，(S(t n ，f)> n ) Is S (t) n F) and<S(t n ，f)> m the distance between the two points is N, N is a variable, and N is a time discrete point;
similarly, J sets of substitute data samples { s } j (t), J = 1.. J., J } "local" to "global" feature distance
In the formula (I), the compound is shown in the specification,
at a time t n Is greater than or equal to the replacement data time-varying power spectrum>
Replacement of the power spectrum of the mean value of the data for n moments>
Is->
And &>
The distance between the two points is N, N is a variable, and N is a time discrete point;
step S32: calculating the characteristic distance of the measured wind speed sample
Fluctuations theta on the time scale 1 And J sets of characteristic distances ∑ of the replacement data samples>
Fluctuation theta in time scale 0 (j)：
In the formula, var (. Cndot.) represents the calculation of the sequence variance.
Since theta 0 (j) And obtaining the random variable by J groups of random substitute data samples. Therefore, a probability density distribution function of a random variable (tested that the Gamma distribution fitting effect is good) is easy to obtain, so that an upper quantile point with the confidence coefficient of alpha can be calculated, namely the upper quantile point is a threshold value for judging whether the wind speed has non-stationarity. Further to theta 1 Performing statistical test when theta 1 Above the threshold, the original wind speed is considered non-stationary, when Θ is 1 And when the wind speed is less than or equal to the threshold value, the original wind speed is considered to be stable.
Step S33: according to the theta 1 And Θ 0 (j) Calculating the distance DNS between the time-varying power spectrum and the generalized stationary power spectrum, and taking the DNS as notAnd (4) a stability quantitative index.
It should be noted that the above-mentioned measurement of the distance between the global spectrum and the local spectrum is the key to accurately calculate the non-stationary quantization index, and the effective method for measuring the characteristic distance includes: kullback-Leibler divergence D KL Distance D from Hellinger H Adapted to frequency modulated signals; distance D of logarithmic spectrum LSD Suitable for amplitude modulated signals. Due to D H Has stronger robustness and performance superior to D KL Therefore, it proposes D H +D LSD The combination makes a distance measure of the intensity and frequency non-stationary wind speed.
In the formula, G and H are a local spectrum and a global spectrum respectively;
respectively corresponding normalized spectra; d H Is the Hellinger distance; d LSD Is the log spectral distance; λ is the adjustment coefficient, and can take the value of 1.
Step S34: determining the upper and lower bounds [ theta ] of the non-stationarity quantitative index threshold low ，Θ upper ]Therefore, the non-stationary wind speed samples can be classified according to the intensity degree:
wherein, due to theta 0 (j) And obtaining the random variable by J groups of random substitute data samples. Therefore, the probability density distribution function of random variables is easily obtained, and the Gamma distribution is adopted to fit theta 0 The confidence is set to 95%, i.e. α =0.05, and the upper α quantile of the confidence interval is the lower threshold bound Θ low 。
Determining an upper threshold theta by using the difference value of structural wind-induced dynamic response under two calculation working conditions upper And calculating a first working condition by analyzing the wind speed according to a non-stationary theory, and calculating a second working condition by simplifying the wind speed into a stationary theory.
When the maximum response difference value of the two calculation working conditions is 5% -10%, the theta corresponding to the group of non-steady wind speeds is determined 1 The value is the upper threshold limit theta upper 。
When theta is higher than theta 1 ＜Θ low Meanwhile, the wind speed is a steady sample; when theta is higher than theta low ≤Θ 1 ≤Θ upper When the wind speed is weak and stable; when theta is satisfied 1 ＞Θ upper In time, the wind speed is a strong non-steady wind speed.
Based on the wind-induced response analysis of a 628m large-span suspension bridge structure, a threshold theta for judging stable, weak stable and strong stable wind speeds is provided low ＝0.026(DNS＝1.59)，Θ upper ＝0.115(DNS＝2.45)。
Example 1
The example is to illustrate a numerical simulation AM-FM signal, which is in the range of 0 s-10 s and has the frequency of [10Hz,40Hz]The amplitude of the signal changes with the time coordinate by a gaussian function, and the signal is a typical amplitude and frequency dual non-stationary signal, as shown in fig. 2. FIG. 3 shows the VMD-SET analysis result, which is determined to be a non-stationary signal according to the variation characteristics of the instantaneous amplitude and the instantaneous frequency. Fig. 4 shows the estimation result of the time-varying power spectrum of the signal, and fig. 5 shows the average margin spectrum corresponding to the time-varying power spectrum, and it can be seen from the figure that the number of extreme points is 2, which indicates that the signal is an amplitude and frequency dual non-stationary signal. Fig. 6-7 show a set of alternative data samples and a stationary time spectrum (J = 50). FIG. 8 shows 50 sets of substitute data Θ 0 (j) With a confidence of 95% of the threshold Θ 0 ＝0.005。Θ 1 =0.68, and the measure of the degree of non-stationarity DNS =16.67, indicating that the signal has strong non-stationarity.
Example 2
The measured storm wind speed in mountainous areas and typhoon "rhododendron" samples are taken as examples for explanation, as shown in fig. 9-11. It can be observed from the figure that the variation trends of the two groups of wind speeds are basically consistent and sequentially consist of an ascending section and a descending section, and the maximum instantaneous wind speeds are 21.76m/s and 29.18m/s respectively. However, a thunderstorm wind speed only needs 10min to go through a remarkable ascending and descending process, and a typhoon wind speed needs 50h. Selecting a 1h wind speed sample with the strongest non-stationarity from typhoon samples, and equally dividing the 1h wind speed sample into 6 samples (each sample is 10min in duration and respectively numbered as typhoon 'rhododendron' sample 1-typhoon 'rhododendron' sample 6) for research.
A first level: the results of the round method and the VMD-SET analysis show that the actually measured thunderstorm wind speed and typhoon 'rhododendron' samples 1,2, 3, 5 and 6 have non-stationarity, while the typhoon 'rhododendron' sample 4 has stable wind speed; and a second level: fig. 12 to 15 show the time-varying spectrum and the average marginal spectrum of the actually measured thunderstorm wind speed and the typhoon "azalea" sample (taking typhoon "azalea" sample 1 as an example), and it can be seen from the graphs that the number of the extreme points is 1, which indicates that the thunderstorm wind speed and the typhoon "azalea" are only non-stationary in amplitude and very weak in frequency. And a third level: FIG. 16 shows 50 sets of substitute data Θ 0 (j) The fitting result of (2) is obtained by calculating a lower threshold theta with a guarantee rate of 95% low Is 0.026.
Table 1 shows the quantification of the degree of non-stationarity, where the value outside the parenthesis is DNS and the value inside the parenthesis is theta upper . Table 2 shows the comparison of the maximum wind-induced response (lateral displacement) values of main beams of a 628m suspension bridge in a certain main span, and by comparing the wind-induced structural response calculation results of the working condition 1 and the working condition 2, the differences of typhoon rhododendron samples 1, 3, 5 and 6 are all within the range of 5%, and the typhoon rhododendron samples are represented as weak and unstable, theta upper The value is taken to be 0.115, and the typhoon 'rhododendron' sample 2 shows strong non-stationarity due to the great difference of the structural response results.
TABLE 1 quantitative comparison of non-stationary indicators
TABLE 2 comparison of maximum lateral displacement of main girder of suspension bridge in 628m span of certain main span (m)
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (8)
1. A method for identifying measured wind speed non-stationarity and non-stationarity is characterized by comprising the following steps: step S1: based on the time domain and time-frequency domain angles, adopting a round method combined with a VMD-SET secondary discrimination method to check whether the actually measured wind speed sample has non-stationarity, if the actually measured wind speed sample has the non-stationarity, turning to the step S2, otherwise, exiting the process; step S2: obtaining a time-varying power spectrum and an average marginal spectrum of the wind speed by adopting a multi-taper window method with optimized window width and a time-frequency rearrangement technology, and judging whether the actually measured wind speed sample with non-stationarity is an intensity non-stationary process or a complete non-stationary process according to the number of extreme points of the average marginal spectrum and whether the moments corresponding to the maximum values of different frequency components are consistent; and step S3: measuring the non-stationary intensity degree of the actually measured wind speed sample by using a non-stationary quantitative index, wherein the non-stationary quantitative index has a calculation formula as follows:
in the formula, DNS is a non-smoothness quantitative index, and theta 1 is the characteristic distance ^ of the actually measured wind speed sample>
On a time scale, Θ 0 (j) is the characteristic distance { [ beta ] } of the jth group of substitute data samples>
Fluctuations on a time scale, J being the number of substitute data samples,xin order to be able to pulsate the wind speed,s j is a firstjA number of the substitute data samples are selected,nare variables representing different moments of the sample.
2. The method for identifying non-stationarity and non-stationarity of measured wind speed according to claim 1, wherein the step S1 comprises the steps of: step S11: performing quality control on the actually measured wind speed sample, and eliminating abnormal values existing in the actually measured wind speed sample; step S12: based on a time domain angle, performing non-stationarity test on the actually measured wind speed sample by adopting a round method, if the test result is non-stationarity, turning to the step S13 for verifying again, and if not, exiting the process; step S13: performing VMD-SET processing on the actually measured wind speed sample based on a time-frequency domain angle to obtain a three-dimensional time-frequency spectrogram, verifying according to the change characteristics of the instantaneous amplitude and the instantaneous frequency of the time-frequency spectrogram, if the verification result is non-stable, turning to the step S2, and if not, exiting the process; and if the verification result is stable and contradicts the result of the step S12, taking the result obtained in the step as a standard, and exiting the process.
3. The method of claim 2, wherein the step S2 comprises the steps of: step S21: dividing the actually measured wind speed sample into a time-varying average wind speed component and a fluctuating wind speed component, and assuming that the fluctuating wind speed has double non-stationarity in the aspects of intensity and frequency; step S22: obtaining a time-varying power spectrum of the fluctuating wind speed by adopting a multi-cone window method with optimized window width and a time-frequency rearrangement technology; step S23: based on an improved quasi-Newton iteration method and the numerical calculation result of the time-varying power spectrum obtained in the step S22, fitting all undetermined parameters in the time-varying power spectrum analytical expression; step S24: integrating the time t, and calculating the average marginal spectrum of the time-varying power spectrum; step S25: and judging the number of extreme points of the average marginal spectrum, if the number of the extreme points is less than or equal to 1, judging the intensity non-stationary process, if the number of the extreme points is more than 1, further judging whether the moments corresponding to the maximum values of the different frequency components are consistent, and if the moments are not consistent, judging the intensity non-stationary process completely.
4. The method of claim 3, wherein the step S22 comprises the steps of: step S221: selecting Hermite function as window function and determining window widthA range of values; step S222: k Hermite window functions are utilized to obtain independent time-frequency rearrangement spectrum estimation, and a time-varying power spectrum is obtained
Wherein x (t) is the fluctuating wind speed, hk (tau-t) is a Hermite function, tau is an integral variable, t is time, and f is Hertz frequency; step S223: optimizing a window width value by adopting a Renyi entropy value corresponding to time-frequency energy distribution, namely, the minimum value of the Renyi entropy value corresponds to an optimal window width; step S224: using a time-averaged window function [ ω T (N), N =1,2]And smoothing to obtain the smoothed time-varying power spectrum, wherein in the formula, ω T (N) is a window function for smoothing the spectrogram, N is a time discrete point, and T is duration.
5. The method for identifying non-stationarity and non-stationarity of measured wind speed according to claim 3, wherein the step S23 comprises the steps of: step S231: dividing sub-blocks according to the local extreme value distribution characteristics of the time-varying power spectrum; step S232: fitting the sub-blocks based on an improved quasi-Newton iteration method; step S233: and after the fitting of all the sub-blocks is completed in sequence, using the fitting parameters of all the sub-blocks as iteration initial values of the fitting parameters of the time-varying power spectrum, and obtaining all undetermined parameters in the time-varying power spectrum analysis expression based on an improved Newton iteration method.
6. The method of claim 3, wherein the step S3 comprises the steps of: step S31: calculating the characteristic distance of the actually measured wind speed sample
In the formula, S(tn, f) is the measured wind speed time-varying power spectrum at time tn,<S(tn，f)>n is the power spectrum of the mean value of the measured wind speed at n moments, D (S (tn, f),<S(tn，f)>n) is S (tn, f) and<S(tn，f)>n, N being a time discrete point; the characteristic distance of the J set of substitute data samples { sj (t), J = 1.., J } - ] { (J) } is greater than or equal to>
In combination with>
Time-varying power spectrum for the replacement data of the time instant tn @>
Replacement of the power spectrum of the mean value of the data for n moments>
Is->
And
the distance between the two points, N is a variable, and N is a time discrete point; the following combination formula is established
In the formula, G and H are a local spectrum and a global spectrum respectively;
Respectively corresponding normalized spectra; DH is Hellinger distance; DLSD is the log spectral distance; lambda is an adjustment coefficient; step S32: calculating a characteristic distance ≥ of the measured wind speed sample>
Fluctuation in time scale Θ 1 and J groupsCharacteristic distance of said replacement data sample>
Fluctuation Θ 0 (j) on the time scale:
In the formula, var (·) represents the calculation of the sequence variance, and step S33: and calculating the distance DNS between the time-varying power spectrum and the generalized stationary power spectrum according to the theta 1 and the theta 0 (j), and taking the DNS as a non-stationary quantitative index.
7. The method of claim 6, wherein the step S3 further comprises the step S34 of: determining upper and lower bounds [ theta low, theta upper ] of the non-smoothness quantitative index threshold value: fitting theta 0 (j) by adopting Gamma distribution, setting the confidence coefficient to be 95 percent, namely alpha =0.05, determining an upper alpha split point of a confidence interval to be a lower threshold theta 1ow, and determining an upper threshold theta upper by utilizing a difference value of structural wind-induced dynamic response under two calculation working conditions, wherein the first calculation working condition is to analyze the wind speed according to a non-stationary theory, the second calculation working condition is to simplify the wind speed to be a stationary theory, and when the maximum response difference value of the two calculation working conditions is 5% -10%, the theta 1 value corresponding to the non-stationary wind speed is the upper threshold theta upper.
8. The method of claim 7, wherein when Θ 1 < Θ low, the wind speed is a stationary sample; when the theta low is not less than the theta 1 and not more than the theta upper, the wind speed is weak and stable; when Θ 1 > Θ uper, the wind speed is a strong non-stationary wind speed.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010482171.8A CN111651728B (en) | 2020-05-29 | 2020-05-29 | Method for identifying non-stationarity and non-stationarity of actually measured wind speed |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202010482171.8A CN111651728B (en) | 2020-05-29 | 2020-05-29 | Method for identifying non-stationarity and non-stationarity of actually measured wind speed |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN111651728A CN111651728A (en) | 2020-09-11 |
| CN111651728B true CN111651728B (en) | 2023-03-28 |
Family
ID=72352751
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202010482171.8A Active CN111651728B (en) | 2020-05-29 | 2020-05-29 | Method for identifying non-stationarity and non-stationarity of actually measured wind speed |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN111651728B (en) |
Families Citing this family (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN113670605A (en) * | 2021-07-02 | 2021-11-19 | 中国地质大学（武汉） | VGSET time-frequency analysis method, device, equipment and storage medium for bearing fault signals |
| CN113625371B (en) * | 2021-08-06 | 2023-08-15 | 国网安徽省电力有限公司 | Graded detection method for high-frequency strong wind of non-stationary weather system |
| CN114838924A (en) * | 2022-04-14 | 2022-08-02 | 东南大学 | Structural damping ratio identification method based on wind-induced vibration non-stationary response |
| CN117668597B (en) * | 2023-11-13 | 2024-06-11 | 华南理工大学 | Structural modal parameter identification method and system considering excitation non-stationarity |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW201314567A (en) * | 2011-09-23 | 2013-04-01 | Univ Nat Central | Method for quantifying and modeling degree of nonlinearity, combined nonlinearity, and nonstationarity |
| CN109242204A (en) * | 2018-09-30 | 2019-01-18 | 淮阴工学院 | Ultra-short term wind speed forecasting method based on optimal VMD and Synchronous fluorimetry |
| CN109934206A (en) * | 2019-04-08 | 2019-06-25 | 中国矿业大学(北京) | A kind of rotary machinery fault diagnosis method under non-stationary operating condition |
Family Cites Families (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US9460478B2 (en) * | 2012-12-17 | 2016-10-04 | Arizona Board Of Regents On Behalf Of Arizona State University | System and method for wind generation forecasting |
| EP2781937B1 (en) * | 2013-03-22 | 2022-09-28 | CGG Services SAS | Vector-dip filtering of seismic data in the time-frequency domain |
-
2020
- 2020-05-29 CN CN202010482171.8A patent/CN111651728B/en active Active
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| TW201314567A (en) * | 2011-09-23 | 2013-04-01 | Univ Nat Central | Method for quantifying and modeling degree of nonlinearity, combined nonlinearity, and nonstationarity |
| CN109242204A (en) * | 2018-09-30 | 2019-01-18 | 淮阴工学院 | Ultra-short term wind speed forecasting method based on optimal VMD and Synchronous fluorimetry |
| CN109934206A (en) * | 2019-04-08 | 2019-06-25 | 中国矿业大学(北京) | A kind of rotary machinery fault diagnosis method under non-stationary operating condition |
Non-Patent Citations (5)
| Title |
|---|
| Malvaldi, J Dowell, S Weiss, D Infield.Wind prediction enhancement by exploiting data non-stationarity.《 2nd IET International Conference on Intelligent Signal Processing 2015 (ISP)》.2016,1-5. * |
| 夏冬生.北京城区大气稳定性及近地强风特性实测研究.《中国优秀硕士学位论文全文数据库 工程科技Ⅱ辑》.2015,C038-139. * |
| 宋淳宸,苏延文,黄国庆,刘瑞莉,杨成.基于多元EMD-AM/FM分解的多点非平稳雷暴风速模拟.《工程力学》.2019,第36卷(第7期),109-115+125. * |
| 苏延文,黄国庆,曾永平.强弱非平稳风速对大跨桥梁抖振响应影响研究.《铁道工程学报》.2019,第36卷(第12期),41-47. * |
| 陈喆,王荣,周文颖,殷殷,殷福亮.非平稳信号度量方法综述.《数据采集与处理》.2017,第32卷(第4期),667-683. * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN111651728A (en) | 2020-09-11 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN111651728B (en) | Method for identifying non-stationarity and non-stationarity of actually measured wind speed | |
| WO2022111423A1 (en) | Method for real-time identification, monitoring, and early warning of vortex-induced vibration event of long-span suspension bridge | |
| WO2019161589A1 (en) | Real-time tracking method for structural modal parameter | |
| US20230229725A1 (en) | Online fast processing method for real-time data based on edge computing | |
| CN112149296B (en) | Method for judging stability type of hydrologic time sequence | |
| CN114117953B (en) | Hydrologic model structure diagnosis method, runoff forecasting method and device | |
| CN111310109B (en) | Off-state wind speed modeling method based on VMD-ARMA-GARCH model | |
| CN114583767B (en) | Data-driven wind power plant frequency modulation response characteristic modeling method and system | |
| CN106407955B (en) | A kind of low-frequency oscillation of electric power system mode on-line identification method | |
| CN116933982B (en) | Method and system for evaluating influence of rainfall on river water quality | |
| Tang et al. | Predicting housing price based on ensemble learning algorithm | |
| CN117131360A (en) | Broadband oscillation monitoring method and system based on waveform data | |
| CN113987416B (en) | Oil gas resource amount calculation method and system based on confidence level | |
| CN114584432B (en) | Signal detection method based on improved smooth periodogram algorithm | |
| Song et al. | Nonstationary dynamic stochastic error analysis of fiber optic gyroscope based on optimized Allan variance | |
| Duan et al. | A novel adaptive fault diagnosis method for wind power gearbox | |
| Deng et al. | A fractional hilbert transform order optimization algorithm based DE for bearing health monitoring | |
| Fu et al. | Automated identification and long-term tracking of modal parameters for a super high-rise building | |
| CN106602551A (en) | Load model parameter identifiability determination method based on likelihood profile method | |
| Xu et al. | Wavelet-transform-based damping identification of a super-tall building under strong wind loads | |
| CN111524036A (en) | Transient power quality disturbance classification method | |
| CN114324974B (en) | Single-star radiation source passive monitoring target motion attribute distinguishing method | |
| CN117668597B (en) | Structural modal parameter identification method and system considering excitation non-stationarity | |
| CN111914721B (en) | Machining state identification method based on linear regression and Gaussian threshold | |
| Jonscher et al. | Bayesian operational modal analysis of closely spaced modes for monitoring wind turbines |
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 |