CN109858356A - A kind of detection method and device of unknown complex system input signal - Google Patents
A kind of detection method and device of unknown complex system input signal Download PDFInfo
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Abstract
The invention discloses a kind of detection method and device of unknown complex system input signal.The detection method of the unknown complex system input signal includes: to obtain the Observable output signal of unknown complex system；Higher-dimension observation space is constructed according to the Observable output signal；Linear evolutional path and equivalent inpnt driving signal of the unknown complex system in low-dimensional approximation phase space are constructed according to the higher-dimension observation space；The input signal of the unknown complex system is detected according to the linear evolutional path and the equivalent inpnt driving signal, to effectively improve the reliability to the detection of unknown complex system input signal.
Description
Technical field
The present invention relates to information technology fields, particularly relate to the detection method and dress of a kind of unknown complex system input signal
It sets.
Background technique
Authentic data processing and information extraction under complicated unknown mechanisms scene, explore basic natural science (as biology,
The discovery of Physical Mechanism) with application to engineering practice (under such as complex scene information transmit) play more and more crucial effect.Herein
It take Bayes statistical method (Bayesian statistical methods) as the Optimum signal detection and letter of representative under background
Cease processing method, it will faces enormous challenge.In many actual scenes, since unknown system to be analyzed is multiple with height
Polygamy (being for example related to complex linear dynamics or nonlinear kinetics) and unobservability, only can be defeated by observable system
It responds out, to detect or infer that unknown system inputs information.Therefore, also just can not directly establish Unknown worm and output response it
Between probability mapping relations, cause the bayes method of mainstream that can not detect, extract Unknown worm information, more leisure opinion is to unknown
Unknown complex system mechanism is analyzed and is reconstructed.
At the same time, it is constantly improve by the machine learning of representative and artificial intelligence approach of deep learning, in recent years in work
Rapid development is achieved in journey practice, for example computer vision and disease such as diagnose at the fields automatically.However, current such model-free
Method still relies primarily on a large amount of training sample (huge training-corpus) and strong supervised learning process (strong
Supervised-learning), become difficult to put to good use in unmarked, small sample signal detection and information processing scene.Separately
Outside, unknown complex system to be analyzed mostly shows dynamic characteristic, i.e., in the case where giving identical input, internal system machine
Reason also occurs dynamic with Observable output at any time and changes, and existing machine learning method imitates the study of such open dynamic environment
Fruit is not good enough, can not tracking system dynamic migration characteristic in time, cause poor performance or even learning process to dissipate, can not obtain good
Good effect.
Summary of the invention
In view of this, it is an object of the invention to propose the detection method and dress of a kind of unknown complex system input signal
It sets, the reliability to the detection of unknown complex system input signal can be effectively improved.
Detection method based on above-mentioned purpose unknown complex system input signal provided by the invention, comprising:
Obtain the Observable output signal of unknown complex system；
Higher-dimension observation space is constructed according to the Observable output signal；
Linear evolution of the unknown complex system in low-dimensional approximation phase space is constructed according to the higher-dimension observation space
Track and equivalent inpnt driving signal；
The defeated of the unknown complex system is detected according to the linear evolutional path and the equivalent inpnt driving signal
Enter signal.
Further, described that higher-dimension observation space is constructed according to the Observable output signal, it specifically includes:
The Observable output signal is sampled, Observable output sequence y (n) ∈ R is obtainedN×1；
The local average energy basic function y of the Observable output signal is constructed according to the Observable output sequence1
(n), local variance changes basic function y2(n), local energy changes basic function y3(n), Local standard deviation concavity and convexity basic function y4
(n) and amplitude characteristic basic function y5(n), to obtain the higher-dimension observation space Ψ={ yi(n), i=1,2,3,4,5 }；
y2(n)=var [y (n+1:n+Q)]-var [y (n-Q:n-1)]；
y5(n)=abs [y (n)]；
Wherein, n is the discrete sampling time, and Q is local evaluation length.
Further, described that the unknown complex system is constructed in low-dimensional approximation phase space according to the higher-dimension observation space
In linear evolutional path and equivalent inpnt driving signal, specifically include:
R main feature mode signal is extracted from the higher-dimension observation space Ψ；
The low-dimensional approximation phase space M of the unknown complex system is constructed according to the r main feature mode signalv(n)；
Based on linear inverse modeling analysis, the unknown complex system is constructed in low-dimensional approximation phase space Mv(n) line in
Property evolutional path and equivalent inpnt driving signal.
Further, described that r main feature mode signal is extracted from the higher-dimension observation space Ψ, it specifically includes:
Obtain each basic function y in the higher-dimension observation space Ψi(n) time embeded matrix H(i), and by all base letters
Several time embeded matrixs merges into recombination time embeded matrix Y=[H(1)；H(2)；H(3)；H(4)；H(5)]；
Unusual decomposition is carried out to the recombination time embeded matrix Y, and to the singular value obtained in decomposable process according to drop
Sequence arrangement；
Right singular matrix row vector v corresponding to r singular value will be arranged in front1:r(t) it is used as r main feature mode
Signal；
Wherein, M is insert depth；
Mv(n)=[v1(n)v2(n)vr(n)]T∈Rr。
Further, described to be based on linear inverse modeling analysis, it is approximate mutually empty in low-dimensional to construct the unknown complex system
Between Mv(n) linear evolutional path and equivalent inpnt driving signal in, specifically include:
Based on linear inverse modeling analysis, by preceding r-1 main feature mode signal v1:r-1(t) according to linear relationship dynamic
Develop, by r-th of main feature mode signal vr(t) it is used as equivalent inpnt driving signal vr(t), the unknown complex system is constructed
System is in low-dimensional approximation phase space Mv(n) the linear evolutional path in；
Wherein, the linear evolutional path are as follows:
Vl=V (2:N-M, 1:r), Vr=V (1:N-M-1,1:r.).
Further, it is described detected according to the linear evolutional path and the equivalent inpnt driving signal it is described unknown
The input signal of complication system, specifically includes:
According to the linear evolutional path and the equivalent inpnt driving signal vr(t) equivalent detection signal d (t) is constructed；
According to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t)
Abnormal sudden change region；
According to the distribution character of equivalent detection signal d (t), detected from the abnormal sudden change region described unknown
The input signal of complication system
Further, described according to the linear evolutional path and the equivalent inpnt driving signal vr(t) it constructs equivalent
It detects signal d (t), specifically includes:
It obtains in the linear evolutional pathR-1 dimension data yr-1(t), according to data yr-1(t) and it is described
Equivalent inpnt driving signal vr(t) the equivalent detection signal d (t) is constructed；
Wherein, d (t)=vr(t)+yr-1(t)。
Further, described according to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt
Driving signal vr(t) abnormal sudden change region, specifically includes:
According to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t)
Detection threshold dth, according to the detection threshold dthDetermine the abnormal sudden change region；
Wherein, t is amplitude variations, and t` is amplitude and specific, σ2 r,1For random distribution variance.
Further, the distribution character according to equivalent detection signal d (t), from the abnormal sudden change region
Detect the input signal of the unknown complex systemIt specifically includes:
According to equivalent detection signal d (t) construction detection measurement D [d (t)]；
According to the distribution character of detection measurement D [d (t)], the optimum detection door of detection measurement D [d (t)] is determined
Limit γD；
In the abnormal sudden change region, by detection measurement D [d (t)] and the optimum detection thresholding γDCompared
Compared with, and detect according to comparison result the input signal of the unknown complex system
γD=argmin { Pr [D [d (t)] > γ, H0]+Pr [D [d (t)] < γ, H1]}；
Correspondingly, the embodiment of the present invention also provides a kind of detection device of unknown complex system input signal, can be realized
The detection method of above-mentioned unknown complex system input signal, described device include:
Observation space module, for obtaining the Observable output signal of unknown complex system, and it is defeated according to the Observable
Signal constructs higher-dimension observation space out；
Low-dimensional system dynamics approximate module exists for constructing the unknown complex system according to the higher-dimension observation space
Linear evolutional path and equivalent inpnt driving signal in low-dimensional approximation phase space；
Signal detection module, it is described for being detected according to the linear evolutional path and the equivalent inpnt driving signal
The input signal of unknown complex system.
From the above it can be seen that the detection method and device of unknown complex system input signal provided by the invention,
The Observable output signal that unknown complex system can be utilized constructs informative higher-dimension observation space, and then utilizes higher-dimension
Observation space reconstructs linear evolutional path of the unknown complex system in low-dimensional approximation phase space, approaches unknown complex system with equivalent
The kinetic characteristics of system finally detect the input of unknown complex system based on linear evolutional path and equivalent inpnt driving signal
Signal realizes the detection of the robust signal without prior model and supervised learning, has been obviously improved the reliability of signal detection,
There are applications well potentiality in fields such as the following complex biological, physics and engineerings.
Detailed description of the invention
Fig. 1 is the flow diagram of the detection method of unknown complex system input signal provided in an embodiment of the present invention；
Fig. 2 is Observable output sequence in the detection method of unknown complex system input signal provided in an embodiment of the present invention
With the waveform diagram of constructed basic function；
Fig. 3 is time embeded matrix in the detection method of unknown complex system input signal provided in an embodiment of the present invention
Singular value schematic diagram；
Fig. 4 is equivalent inpnt driving letter in the detection method of unknown complex system input signal provided in an embodiment of the present invention
Number amplitude statistical distribution schematic diagram；
Detection method and in the prior art base of the Fig. 5 for unknown complex system input signal provided in an embodiment of the present invention
In the performance comparison schematic diagram of the optimum detection method of model, detection method based on supervised learning；
Fig. 6 is the structural schematic diagram of the detection device of unknown complex system input signal provided in an embodiment of the present invention.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.
It is the process signal of the detection method of unknown complex system input signal provided in an embodiment of the present invention referring to Fig. 1
Figure.The detection method of the unknown complex system input signal may comprise steps of:
101, the Observable output signal of unknown complex system is obtained.
In the present embodiment, it since unknown complex system has unobservability, is exported by observable system
Response, to obtain the Observable output signal of unknown complex system.
102, higher-dimension observation space is constructed according to the Observable output signal.
In the present embodiment, the more abundant higher-dimension of information can be further constructed using Observable output signal to observe
Space.It needs, the building of higher-dimension observation space depends on one group of specific basic function, preferably in natural world
5 kinds of basic functions the most general, i.e. local average energy basic function y1(n), local variance changes basic function y2(n), local energy
Change basic function y3(n), Local standard deviation concavity and convexity basic function y4(n) and amplitude characteristic basic function y5(n)。
Specifically, step 102 includes:
The Observable output signal is sampled, Observable output sequence y (n) ∈ R is obtainedN×1；
The local average energy basic function y of the Observable output signal is constructed according to the Observable output sequence1
(n), local variance changes basic function y2(n), local energy changes basic function y3(n), Local standard deviation concavity and convexity basic function y4
(n) and amplitude characteristic basic function y5(n), to obtain the higher-dimension observation space Ψ={ yi(n), i=1,2,3,4,5 }.
Wherein, local average energy basic function y1(n) in major embodiment Observable output sequence signal energy value office
Portion's variation characteristic, is defined as:
Wherein, n is the discrete sampling time, and Q is given local evaluation length.Local average energy can be effectively suppressed considerable
The noise component(s) in output sequence y (n) is surveyed, while can further extract the mutation letter caused by the input of unknown complex system
Breath.
Local variance changes basic function y2(n) in major embodiment Observable output sequence signal standards difference localized variation
Characteristic, is defined as:
y2(n)=var [y (n+1:n+Q)]-var [y (n-Q:n-1)]
Wherein, var (x) defines the standard deviation of finite length (2Q) stochastic variable x.In general, unknown complex system is defeated
The change of Observable output signal standard deviation will be caused by entering signal, that is, meet E { y2(n) | s (n)=1 } > 0 and E { y2(n)|s
(n)=1 } → 0.
Local energy changes basic function y3(n) in major embodiment Observable output sequence adjacent part areas energy quantitative change
Change characteristic, is defined as:
Similarly, meet E { y3(n) | s (n)=1 } > 0 and E { y3(n) | s (n)=1 } → 0, thus can be used to characterize unknown
The change of the caused system output information of complication system input.
Local standard deviation concavity and convexity basic function y4(n) major embodiment Observable output sequence in regional area may be in
The standard deviation concavo-convex characteristic revealed, is defined as:
Amplitude characteristic basic function y5(n) the major embodiment amplitude characteristic of system output sequence, is defined as:
y5(n)=abs [y (n)]
Wherein, abs (x) indicates the operation that takes absolute value to signal x.
It should be noted that although above-mentioned 5 basic functions embody non-zero system input, caused similar output is prominent
Become characteristic, as shown in Fig. 2, but correlation very little, such as maximum y between different basic functions2(n) and y3(n) related coefficient is only
0.048.Therefore, multiple and different basic functions further can provide certain observation diversity in observation space
(diversity effect)。
On the one hand the present embodiment has obtained informative higher-dimension observation space, on the other hand pass through design local processor
System, effectively reduces noise effect, then promotes subsequent processing and analysis performance.
103, to construct the unknown complex system according to the higher-dimension observation space linear in low-dimensional approximation phase space
Evolutional path and equivalent inpnt driving signal.
In the present embodiment, according to constructed higher-dimension observation space Ψ, and the theory based on data-driven, reconstruct are unknown
Linear evolutional path of the complication system in low-dimensional approximation phase space, that is, reconstruct the dynamic behavior of unknown complex system.
In the prior art, system dynamics behavior can be by time delay manifold My(n)(time-delayedmanifold)
In output state evolutional path characterized My(n)=[y (n) y (n-1) ... y (n-L)]T∈RL.However, in order to sufficiently complete
Site preparation embodies phylogeny behavior, usually requires that the dimension L of above-mentioned time delay manifold is very big.Meanwhile above-mentioned time delay stream
In shape, the possible highly significant of noise effect is unfavorable for further analyzing the system dynamics behavior of fining.Therefore, this implementation
Example will establish the phase space M of another differomorphism by data-driven methodv(n), dimension r < < L, simultaneity factor evolution rail
Noise effect in mark obtains to be inhibited to a certain extent, it may be assumed that Mv(n)∈Rr, r < < L.
Specifically, step 103 includes:
R main feature mode signal is extracted from the higher-dimension observation space Ψ；
The low-dimensional approximation phase space M of the unknown complex system is constructed according to the r main feature mode signalv(n)；
Based on linear inverse modeling analysis, the unknown complex system is constructed in low-dimensional approximation phase space Mv(n) line in
Property evolutional path and equivalent inpnt driving signal.
Wherein, described that r main feature mode signal is extracted from the higher-dimension observation space Ψ, it specifically includes:
Obtain each basic function y in the higher-dimension observation space Ψi(n) time embeded matrix H(i), and by all base letters
Several time embeded matrixs merges into recombination time embeded matrix Y；
Unusual decomposition is carried out to the recombination time embeded matrix Y, and to the singular value obtained in decomposable process according to drop
Sequence arrangement；
Right singular matrix row vector v corresponding to r singular value will be arranged in front1:r(t) it is used as r main feature mode
Signal.
It should be noted that first for each individually basic function yi(n), the time embeded matrix H that insert depth is M is obtained(i),By merging multiple basic function information, i.e., by all basic functions when
Between embeded matrix merge, obtain the recombination time embeded matrix Y, Y=[H of unified higher-dimension observation space(1)；H(2)；H(3)；
H(4)；H(5)]。
In turn, singular value decomposition (SVD) is carried out to recombination time embeded matrix Y, extracts different character modules to decompose
Formula signal, i.e. Y=U Σ V*, wherein U and V, which is respectively indicated, carries out the left and right singular matrix that SVD is decomposed for Y.It will decompose
The singular value obtained in the process is arranged according to descending, is denoted as σ1>σ2>…>σk.As shown in figure 3, for common unknown complex system
For system, singular value can choose the singular value of front r further combined with the analysis target of signal detection with decrease of speed quickly
Corresponding right singular matrix row vector v1:r(t) it is used as r main feature mode signal.
In turn, the low-dimensional for reconstructing to obtain recombination time embeded matrix according to r main feature mode signal is approximate:
It can be proved that the approximate error of the low-dimensional are as follows:
In turn, according to r main feature mode signal, the phase space of approximate differential homeomorphism, i.e. unknown complex can be constructed
The low-dimensional approximation phase space M of systemv(n):
Mv(n)=[v1(n)v2(n)…vr(n)]T∈Rr
Further, described to be based on linear inverse modeling analysis, it is approximate mutually empty in low-dimensional to construct the unknown complex system
Between Mv(n) linear evolutional path and equivalent inpnt driving signal in, specifically include:
Based on linear inverse modeling analysis, by preceding r-1 main feature mode signal v1:r-1(t) according to linear relationship dynamic
Develop, by r-th of main feature mode signal vr(t) it is used as equivalent inpnt driving signal vr(t), the unknown complex system is constructed
System is in low-dimensional approximation phase space Mv(n) the linear evolutional path in.
It should be noted that obtaining low-dimensional approximation phase space Mv(n) and on the basis of r main feature mode signal,
Low-dimensional approximation phase space M can further be constructedv(n) the linear evolutional path of dominance in.R main feature mode signal is adopted
With linear analysis or linear inverse modeling analysis, that is, have:
Wherein, r main feature mode signal is divided into two groups, before (r-1) a main feature mode signal according to line
Sexual intercourse dynamic evolution, and r-th of main feature mode signal is then used as equivalent inpnt driving signal.Wherein, linear regression system
Matrix number W ∈ R(r)×(r-1)With g ∈ R(r-1)×1It can be directly obtained by calculating, it may be assumed that
Vl=V (2:N-M, 1:r), Vr=V (1:N-M-1,1:r)
Based on above-mentioned linear inverse modeling analysis, it is linear in low-dimensional approximation phase space that unknown complex system can be obtained
Evolution properties.In turn, in known initial system output state y (0)=v1:r-1(0) restructural to obtain unknown complex in the case where
The linear dynamics characteristic of system, i.e., linear evolutional path:
After passing through linear regression and reconstruct, new equivalent outputAs Main Patterns signal v1:r-1(t) replace
In generation, provides the signal version of a noise suppressed and signal enhancing, thus the equivalent output newly reconstructed can be usedTo divide
The Dynamic Evolution of unknown complex system is analysed, and realizes the input signal detection of unknown complex system with this.It needs to illustrate
Be, by above-mentioned time embeded matrix, main feature schema extraction and linear evolutional path restructuring procedure, can be convenient fromIt obtainsIt in other words is the basic function for realizing Koopman operator K (), i.e. K (y (t))=y (t+1).
Koopman operator is of great significance in nonlinear fluid mechanics analysis, is different from the prior art, and the present embodiment organically combines
The thought of Koopman operator and data-driven, to realize small sample, the unsupervised letter under unknown complex system complex mechanism
Number detection.
Low-dimensional approximation phase space constructed by the present embodiment, difference postpones manifold space with usual time, embedding using the time
Enter matrix and extract main feature mode signal, noise has effectively been restrained by the decomposition of signal space, while utilizing low-dimensional line
Property thought obtain and dominate linear evolutional path, to analyze unknown Complex Nonlinear System provide it is a kind of simple and effective
Approach, have important theory and practice meaning.
104, the unknown complex system is detected according to the linear evolutional path and the equivalent inpnt driving signal
Input signal.
Specifically, step 104 includes:
According to the linear evolutional path and the equivalent inpnt driving signal vr(t) equivalent detection signal d (t) is constructed；
According to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t)
Abnormal sudden change region；
According to the distribution character of equivalent detection signal d (t), detected from the abnormal sudden change region described unknown
The input signal of complication system
It should be noted that when there are the input signal of unknown complex system, constructed equivalent inpnt driving signal
It will be mutated, therefore know the input of unknown complex system by the abnormal sudden change region of detection equivalent inpnt driving signal
Signal region that may be present.And then the input signal in abnormal sudden change region is detected.
Wherein, described according to the linear evolutional path and the equivalent inpnt driving signal vr(t) equivalent detection is constructed
Signal d (t) is specifically included:
It obtains in the linear evolutional pathR-1 dimension data yr-1(t), according to data yr-1(t) and it is described
Equivalent inpnt driving signal vr(t) the equivalent detection signal d (t) is constructed.
It should be noted that equivalent detection signal d (t) mainly to detect constructed equivalent inpnt driving signal automatically
vr(t) abnormal sudden change region.The equivalent detection signal d (t) that the present embodiment uses are as follows:
D (t)=vr(t)+yr-1(t)
Further, described according to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt
Driving signal vr(t) abnormal sudden change region, specifically includes:
According to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t)
Detection threshold dth, according to the detection threshold dthDetermine the abnormal sudden change region.
It should be noted that for common passive dissipative system, the case where real system input is s (t)=0
Under, system output state would be limited in some regional area, height random characteristic is showed, thus carved using Gaussian Profile
Draw the stochastic behaviour of its output state, it may be assumed that
Wherein, σr,0 2Indicating random distribution variance, the variance is related with the noise component(s) in Observable output sequence y (t),
The relating to parameters such as the embedded length M and linear system order r that are used in analysis.Conversely, if real system input s (t) is not 0
In the case of, system output will deviate from regional area, pass through one section of transient state evolutionary process later, be returned to the office when input of no system
Random evolution is done in region in portion.As shown in figure 4, mixed Gaussian process can be used in this case, to equivalent input drive signal
vr(t) state is modeled, that is, is had:
Fig. 4 is to be carried out by the reception signal after unknown complex system to unknown complex system using wideband radar pulse
Low-dimensional is approximate and the result that obtains after linear evolutional path is reconstructed.It should be noted that many unknown multiple at other
In the analysis of miscellaneous system (such as Neural spike train information sequence and abnormal electrocardiographic pattern signal), the equivalent inpnt reconstructed is driven
Dynamic signal vr(t) it also presents identical and stablizes Gaussian mixtures process.For the fanaticism number inspection under unknown complex system mechanism
For survey, embedded length M and linear system order r can be advanced optimized, so that detection process becomes more to be easy, i.e., (r, M)
=argmax (1- γ).
In the present embodiment, pass through the suitable thresholding d of determinationthIt is corresponding aobvious to determine and position equivalent inpnt driving signal
The abnormal sudden change region of work.Utilize equivalent inpnt driving signal vr(t) stablize mixed distribution characteristic specific to, deviate given
In the case where error ε, for the detection threshold d in abnormal sudden change regionthIt can automatically determine.As equivalent inpnt driving signal vr(t)
Amplitude statistical distribution Pr (vr(t)), start to be gradually deviated from theoretical Gaussian Profile in some amplitude and specific t=t ', then the spy
Tentering value t ' is automatic threshold:
The present embodiment is realized using the catastrophe characteristics of the linear evolutional path in approximate low-dimensional phase space to unknown complex system
The reconstruct and extraction for driving signal of uniting.Specifically, the abrupt local characteristic for making full use of linear evolutional path to show, by right
The linear transformation of equivalent inpnt driving signal then constructs the equivalent detection signal of robust, effectively identifies unknown complex system
Abnormal sudden change region in response；The system for the equivalent inpnt driving signal that automatic detection threshold Mechanism establishing is of universal significance
Count characteristic, detection threshold directly can be determined according to Observable output sequence characteristic automatically, shield input signal with it is unknown multiple
The complicated association of miscellaneous system mechanism, simplifies data analysis and signal detection process to greatest extent.
Further, the distribution character according to equivalent detection signal d (t), from the abnormal sudden change region
Detect the input signal of the unknown complex systemIt specifically includes:
According to equivalent detection signal d (t) construction detection measurement D [d (t)]；
According to the distribution character of detection measurement D [d (t)], the optimum detection door of detection measurement D [d (t)] is determined
Limit γD；
In the abnormal sudden change region, by detection measurement D [d (t)] and the optimum detection thresholding γDCompared
Compared with, and detect according to comparison result the input signal of the unknown complex system
It should be noted that Unknown worm is usually { 0,1 } binary signal s (t) ∈ for common communication system,
Unknown complex system representation wireless transmission channel and other non-ideal effects, therefore Observable system output signal is represented by y
(t)=F { h (t), s (t) }+n (t), wherein h (t) indicates unknown complex system parameter, and F indicates complication system receptance function, n (t) table
Show additive Gaussian noise.Under linear system most typically, then there is y (t)=h (t) * s (t)+n (t), wherein * indicates linear convolution
Relationship.In the prior art, it is generally required that emitting additional training sequence estimates unknown system response h (t), shellfish is recycled later
This method of leaf realizes that the detection to unknown message then has by taking maximum a posteriori probability as an example
WhereinTo estimate that obtained band error system responds.But above-mentioned detection method is usually directed to the instruction for expending time energy resource
Practice sequence, while requiring stringent synchronization timing information, in the case where there is timing with channel estimation bias, detection performance will
It can be remarkably decreased.
And the present embodiment proposes a kind of robust without training and detection performance is not influenced by timing with channel estimation bias
Signal detecting method.Specifically, detection measurement is constructed first with equivalent detection signal d (t), it may be assumed that
τs(n|sn=1)=min { t ∈ [(n-1) Tb+1,nTb], s.t.d (t) > dth}
τe(n|sn=1)=max { t ∈ [(n-1) Tb+1,nTb], s.t.d (t) > dth}
Wherein, τs(n|sn=1) and τe(n|sn=1) abnormal area lower bound and the upper bound in n-th of section are respectively corresponded,
It should be noted that assuming that accurate system propagation delay time is unknown in the above process, but mark space TbIt is known.
Although stable transient signal component shows certain correlation in regional area in equivalent detection signal d (t)
Property, but noise component(s) is usually incoherent, therefore equivalent detection measures D [d (t)] for progressive Gaussian distributed.
On this basis, it can determine the optimum detection thresholding of detection measurement, realize the signal detection of lowest difference error rate.?
Under the conditions of unknown complex system input signal etc. is general, optimum detection thresholding is determined by following formula:
γD=argmin { Pr [D [d (t)] > γ, H0]+Pr [D [d (t)] < γ, H1]}
Wherein, it is related to probability distribution and is directly fitted acquisition by data, obtains economics analysis expression formula without deriving.
Finally, by comparing detection measurement D [d (t)] and optimum detection thresholding γD, it is being not necessarily to estimating channel information h (t)
In the case where, the input signal of unknown complex system is detected using constructed linear evolutional path.Specifically, when unknown
When the input signal of complication system is binary system discrete signal { 0,1 }, the input signal can be directly recovered:
For more complicated unknown complex system input signal, possibly its time waveform can not be accurately recovered,
But the specific time region that unknown complex system input signal occurs is extracted by above formula, in many actual complex systems
Abnormality detection and key information area positioning etc. are of great significance in application scenarios and real value.
For increasingly complex unknown nonlinear dynamical system, equally can directly be obtained using the positioning of equivalent detection signal d (t)
Abnormal sudden change region is taken, however detecting measurement D [d (t)] may need to rely on different practical problems, it cannot be simply using part
Accumulative summing mode obtains.For example burst characteristic (burst arrival is showed in equivalent inpnt driving signal
Property) and two equivalent inpnt driving signals are spaced closely together (as much smaller than d (t) transient state die-away time), are needed further
D (t) transient state evolution properties are analyzed, substantially rough local signal template is extracted, are examined finally by deconvolution is carried out to d (t)
Survey unknown burst-input signal.In other words, equivalent detection signal d (t) will provide pre- for subsequent increasingly complex, fine information processing
Input signal that treated.
Without loss of generality, consider the signal detection application scenarios under complicated unknown transmission environment, it is assumed that transmitting radar letter
Number bandwidth be 1GHz, using pulsed operation standard, working frequency range 28GHz.Above-mentioned impulse modulation radiation pattern can be real simultaneously
Existing target positioning distance measuring and information are transmitted, thus in the following ubiquitous Internet of Things and in intelligence manufacture industry internet, have
There is important application potential.Further consider complicated transmission characteristic in enclosure space, reception signal will show extremely intensive more
Diameter transmission effects.The wireless channel theory mould formulated based on IEEE 802.15.4a standard group for practical factory's manufacturing environment
Type it can be found that distinguishable multipath number is close to 100, while showing the transmission characteristic of sub-clustering arrival.Conventional method usually needs
A large amount of pilot frequency sequence and additional energy and time delay expense are wanted, estimates that above-mentioned Complex Channel response is believed with unknown synchronization timing
Breath, the Bayes statistical method of mainstream vulnerable to model bias and noise influence, cause its signal detection performance not good enough.
Fig. 5 is different the performance comparison of signal processing and detection method, and abscissa is signal and noise value, ordinate
To detect the bit error rate.Wherein, energy measuring only needs accurate timing synchronisation information, examines without Complex Channel estimation with coherent signal
Survey method (such as maximum likelihood or maximum a posteriori probability), however this detection performance for realizing simple, most widely used method
It is really extremely limited, while the influence vulnerable to timing offset, for example when timing offset is 3 sampled points, bit error rate performance can
10 times (SNR=0.8dB) can be declined；Relevant detection expends additional energy and the time provides firstly the need of certain length training sequence
Source, estimates channel response using maximum likelihood method, realizes that Optimum signal detection and information differentiate on this basis；However it is practical
In, there are certain deviations for channel estimation, even if considering by Gramer's labor lower bound (Crame-Rao Low Bound, CRLB)
The preferred channels estimated result provided, detection performance are also extremely limited.In contrast, our rule is directly avoided by a large amount of
Additional energy caused by training sequence and time overhead are of great significance for low time delay, low power consumption transmission scene.It is same with this
When, by constructing informative higher-dimension observation space, low-dimensional reconstruction is carried out to unknown complex dynamical system, and design to making an uproar
The detection signal metric of sound robust to realize small sample, unsupervised learning process, and realizes high performance signal detection
Differentiate with information.It is found from simulation result, compared to coherence detection optimal in statistical significance, the present embodiment can also be obtained
The gain of about 0.7dB can be by the bit error rate from the 5 × 10 of best coherence detection by taking SNR=0.8dB as an example-5It is down to 1
×10-5, this, which extracts the high performance information under complicated circumstances not known, has important theory significance and application potential.
In order to further verify the advantage of the present embodiment, analysis compared two kinds of common supervised training learning methods, i.e.,
Return recurrent neural network (RNN) and extreme learning machine (ELM).Wherein, RNN uses two layers of realization structure, input layer and centre
32 and 16 neurons have been respectively configured in layer, and learning rate is set as 0.998；ELM realizes structure using classical single layer, includes
30 neurons.Firstly, supervised learning method in the prior art usually requires a large amount of training sequence, optimal net is obtained
Network weight, and obtain and need a large amount of calibration samples, it needs to expend considerable transmission energy and processing delay, low function can not be suitable for
Consumption, low time delay data processing scene.Change in addition, dynamic may occur for complication system mechanism or unknown transmission channel, this can be straight
Connecing leads to trained network failure and can not work, it is necessary to continually be trained.Furthermore in the situation that training sample is limited
Under, when for example training signal length is 1600 (including 160000 sampled points, i.e., each signal include 100 sampled points), RNN
Similar processing accuracy is obtained with ELM, the bit error rate is about 3 × 10 as SNR=0.8dB-4.In contrast, the present embodiment is straight
The thought using low-dimensional dynamical reconstruction is connect, small sample, unsupervised data processing and signal detection is realized, obtains more
Excellent detection performance avoids the energy and time overhead for obtaining a large amount of calibration samples, is also more suited for not obtaining in practice
Obtain many application scenarios of training sample (such as unknown mechanism is probed into).Simultaneously as the present embodiment essentially provides one
The unsupervised learning frame of kind data-driven can be certainly when new data correspondence system mechanism or the transmission characteristic unknown change of generation
Its low-dimensional evolved behavior is rebuild dynamicly, thus is the authentic data analysis and information extraction under research unknown complex dynamical system,
Provide a kind of completely new robust signal processing frame.
Correspondingly, the embodiment of the present invention also provides a kind of detection device of unknown complex system input signal, can be realized
All processes of the detection method of above-mentioned unknown complex system input signal.
It is the structural representation of the detection device of unknown complex system input signal provided in an embodiment of the present invention referring to Fig. 6
Figure.The detection device of the unknown complex system input signal includes:
Observation space module 1, for obtaining the Observable output signal of unknown complex system, and it is defeated according to the Observable
Signal constructs higher-dimension observation space out；
Low-dimensional system dynamics approximate module 2, for constructing the unknown complex system according to the higher-dimension observation space
Linear evolutional path and equivalent inpnt driving signal in low-dimensional approximation phase space；
Signal detection module 3, for detecting institute according to the linear evolutional path and the equivalent inpnt driving signal
State the input signal of unknown complex system.
Specifically, the low-dimensional system dynamics approximate module 2 includes:
Phase space low-dimensional approximating unit 21, for constructing the low of the unknown complex system according to the higher-dimension observation space
Tie up approximate phase space；
Dynamics reconfiguration unit 22 constructs the unknown complex system in low-dimensional for being based on linear inverse modeling analysis
Approximate phase space Mv(n) the linear evolutional path in.
In conclusion the detection method and device of unknown complex system input signal provided by the invention, are suitble to complexity not
Know system dynamic behaviour reconstruct and the signal detection under mechanism, avoids to the dependence of priori model and by prior model
Severe deviations caused by unreliable, to facilitate the actual mechanism of acquisition unknown complex system；Utilize data-driven thought
It is approximate that low-dimensional carried out to unknown complex system Dynamic Evolution, even if thus in unsupervised trained complex condition, also can from
Dynamic ground reconfiguration system dynamic characteristic and cause and effect driving relationship, avoid traditional supervised learning can not track dynamic evolution rule,
And Optimum signal detection relies on the fundamental limitations of exact mechanism model, to improve the detection of unknown complex system input signal
Reliability, be expected to be widely applied to the fields such as the following complex biological, physics and engineering.
It should be understood by those ordinary skilled in the art that: the discussion of any of the above embodiment is exemplary only, not
It is intended to imply that the scope of the present disclosure (including claim) is limited to these examples；Under thinking of the invention, above embodiments
Or can also be combined between the technical characteristic in different embodiments, step can be realized with random order, and be existed such as
Many other variations of the upper different aspect of the invention, for simplicity, they are not provided in details.
In addition, to simplify explanation and discussing, and in order not to obscure the invention, it can in provided attached drawing
It is connect with showing or can not show with the well known power ground of integrated circuit (IC) chip and other components.Furthermore, it is possible to
Device is shown in block diagram form, to avoid obscuring the invention, and this has also contemplated following facts, i.e., about this
The details of the embodiment of a little block diagram arrangements be height depend on will implementing platform of the invention (that is, these details should
It is completely within the scope of the understanding of those skilled in the art).Elaborating that detail (for example, circuit) is of the invention to describe
In the case where exemplary embodiment, it will be apparent to those skilled in the art that can be in these no details
In the case where or implement the present invention in the case that these details change.Therefore, these descriptions should be considered as explanation
Property rather than it is restrictive.
Although having been incorporated with specific embodiments of the present invention, invention has been described, according to retouching for front
It states, many replacements of these embodiments, modifications and variations will be apparent for those of ordinary skills.Example
Such as, discussed embodiment can be used in other memory architectures (for example, dynamic ram (DRAM)).
The embodiment of the present invention be intended to cover fall into all such replacements within the broad range of appended claims,
Modifications and variations.Therefore, all within the spirits and principles of the present invention, any omission, modification, equivalent replacement, the improvement made
Deng should all be included in the protection scope of the present invention.
Claims (10)
1. a kind of detection method of unknown complex system input signal characterized by comprising
Obtain the Observable output signal of unknown complex system；
Higher-dimension observation space is constructed according to the Observable output signal；
Linear evolutional path of the unknown complex system in low-dimensional approximation phase space is constructed according to the higher-dimension observation space
With equivalent inpnt driving signal；
The input letter of the unknown complex system is detected according to the linear evolutional path and the equivalent inpnt driving signal
Number.
2. the detection method of unknown complex system input signal according to claim 1, which is characterized in that described according to institute
Observable output signal building higher-dimension observation space is stated, is specifically included:
The Observable output signal is sampled, Observable output sequence y (n) ∈ R is obtainedN×1；
The local average energy basic function y of the Observable output signal is constructed according to the Observable output sequence1(n), part
Variance changes basic function y2(n), local energy changes basic function y3(n), Local standard deviation concavity and convexity basic function y4(n) and amplitude
Characteristic basic function y5(n), to obtain the higher-dimension observation space Ψ={ yi(n), i=1,2,3,4,5 }；
y2(n)=var [y (n+1:n+Q)]-var [y (n-Q:n-1)]；
y5(n)=abs [y (n)]；
Wherein, n is the discrete sampling time, and Q is local evaluation length.
3. the detection method of unknown complex system input signal according to claim 2, which is characterized in that described according to institute
It states higher-dimension observation space and constructs linear evolutional path and equivalent inpnt of the unknown complex system in low-dimensional approximation phase space
Driving signal specifically includes:
R main feature mode signal is extracted from the higher-dimension observation space Ψ；
The low-dimensional approximation phase space M of the unknown complex system is constructed according to the r main feature mode signalv(n)；
Based on linear inverse modeling analysis, the unknown complex system is constructed in low-dimensional approximation phase space Mv(n) the linear evolution in
Track and equivalent inpnt driving signal.
4. the detection method of unknown complex system input signal according to claim 3, which is characterized in that described from described
R main feature mode signal is extracted in higher-dimension observation space Ψ, is specifically included:
Obtain each basic function y in the higher-dimension observation space Ψi(n) time embeded matrix H(i), and by all basic functions
Time embeded matrix merges into recombination time embeded matrix Y=[H(1)；H(2)；H(3)；H(4)；H(5)]；
Unusual decomposition is carried out to the recombination time embeded matrix Y, and the singular value obtained in decomposable process is arranged according to descending
Column；
Right singular matrix row vector v corresponding to r singular value will be arranged in front1:r(t) it is used as r main feature mode signal；
Wherein, M is insert depth；
Mv(n)=[v1(n) v2(n)…vr(n)]T∈R r。
5. the detection method of unknown complex system input signal according to claim 4, which is characterized in that described to be based on line
The reversed modeling analysis of property, constructs the unknown complex system in low-dimensional approximation phase space Mv(n) it linear evolutional path in and waits
Input drive signal is imitated, is specifically included:
Based on linear inverse modeling analysis, by preceding r-1 main feature mode signal v1:r-1(t) it is drilled according to linear relationship dynamic
Change, by r-th of main feature mode signal vr(t) it is used as equivalent inpnt driving signal vr(t), the unknown complex system is constructed
In low-dimensional approximation phase space Mv(n) the linear evolutional path in；
Wherein, the linear evolutional path are as follows:
6. the detection method of unknown complex system input signal according to claim 5, which is characterized in that described according to institute
It states linear evolutional path and the equivalent inpnt driving signal detects the input signal of the unknown complex system, it is specific to wrap
It includes:
According to the linear evolutional path and the equivalent inpnt driving signal vr(t) equivalent detection signal d (t) is constructed；
According to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t) different
Normal sudden change region；
According to the distribution character of equivalent detection signal d (t), the unknown complex is detected from the abnormal sudden change region
The input signal of system
7. the detection method of unknown complex system input signal according to claim 6, which is characterized in that described according to institute
State linear evolutional path and the equivalent inpnt driving signal vr(t) equivalent detection signal d (t) is constructed, is specifically included:
It obtains in the linear evolutional pathR-1 dimension data yr-1(t), according to data yr-1(t) and it is described equivalent
Input drive signal vr(t) the equivalent detection signal d (t) is constructed；
Wherein, d (t)=vr(t)+yr-1(t)。
8. the detection method of unknown complex system input signal according to claim 7, which is characterized in that described according to institute
State equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t) abnormal sudden change region,
It specifically includes:
According to the equivalent inpnt driving signal vr(t) distribution character determines the equivalent inpnt driving signal vr(t) inspection
Survey thresholding dth, according to the detection threshold dthDetermine the abnormal sudden change region；
Wherein, t is amplitude variations, and t` is amplitude and specific,For random distribution variance.
9. the detection method of unknown complex system input signal according to claim 7, which is characterized in that described according to institute
The distribution character for stating equivalent detection signal d (t), detects the input of the unknown complex system from the abnormal sudden change region
SignalIt specifically includes:
According to equivalent detection signal d (t) construction detection measurement D [d (t)]；
According to the distribution character of detection measurement D [d (t)], the optimum detection thresholding of detection measurement D [d (t)] is determined
γD；
In the abnormal sudden change region, by detection measurement D [d (t)] and the optimum detection thresholding γDIt is compared, and
The input signal of the unknown complex system is detected according to comparison result
γD=argmin { Pr [D [d (t)] > γ, H0]+Pr [D [d (t)] < γ, H1]}；
10. a kind of detection device of unknown complex system input signal, can be realized as described in any one of claim 1 to 9
The detection method of unknown complex system input signal, which is characterized in that described device includes:
Observation space module for obtaining the Observable output signal of unknown complex system, and exports according to the Observable and believes
Number building higher-dimension observation space；
Low-dimensional system dynamics approximate module, for constructing the unknown complex system in low-dimensional according to the higher-dimension observation space
Linear evolutional path and equivalent inpnt driving signal in approximate phase space；
Signal detection module, it is described unknown for being detected according to the linear evolutional path and the equivalent inpnt driving signal
The input signal of complication system.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110680282A (en) * | 2019-10-09 | 2020-01-14 | 黑龙江洛唯智能科技有限公司 | Method, device and system for detecting temporary abnormal state of brain |
| CN113741176A (en) * | 2021-09-18 | 2021-12-03 | 武汉理工大学 | Ship berthing and departing control method and device based on Koopman analysis and storage medium |
| CN116841307A (en) * | 2023-09-01 | 2023-10-03 | 中国民用航空飞行学院 | Flight trajectory prediction method and device based on Koopman neural network |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7966156B1 (en) * | 2002-10-11 | 2011-06-21 | Flint Hills Scientific Llc | Method, computer program, and system for intrinsic timescale decomposition, filtering, and automated analysis of signals of arbitrary origin or timescale |
| CN102262690A (en) * | 2011-06-07 | 2011-11-30 | 中国石油大学(北京) | Modeling method of early warning model of mixed failures and early warning model of mixed failures |
| CN102866629A (en) * | 2012-09-19 | 2013-01-09 | 北京航空航天大学 | Dyanmic-static mixed nerve network modeling-based anti-interference control method for random system |
| CN104809292A (en) * | 2015-04-28 | 2015-07-29 | 西安理工大学 | On-line recognizing method for nonlinear dynamic model parameter of high-speed train |
| CN106773648A (en) * | 2016-12-19 | 2017-05-31 | 华侨大学 | The Robust Guaranteed Cost design and parameter tuning method of a kind of Active Disturbance Rejection Control |
| CN106855718A (en) * | 2017-01-12 | 2017-06-16 | 防灾科技学院 | MFA control high water tank control system |
| CN107957566A (en) * | 2017-11-17 | 2018-04-24 | 吉林大学 | Magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis |
-
2018
- 2018-12-27 CN CN201811611312.0A patent/CN109858356B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US7966156B1 (en) * | 2002-10-11 | 2011-06-21 | Flint Hills Scientific Llc | Method, computer program, and system for intrinsic timescale decomposition, filtering, and automated analysis of signals of arbitrary origin or timescale |
| CN102262690A (en) * | 2011-06-07 | 2011-11-30 | 中国石油大学(北京) | Modeling method of early warning model of mixed failures and early warning model of mixed failures |
| CN102866629A (en) * | 2012-09-19 | 2013-01-09 | 北京航空航天大学 | Dyanmic-static mixed nerve network modeling-based anti-interference control method for random system |
| CN104809292A (en) * | 2015-04-28 | 2015-07-29 | 西安理工大学 | On-line recognizing method for nonlinear dynamic model parameter of high-speed train |
| CN106773648A (en) * | 2016-12-19 | 2017-05-31 | 华侨大学 | The Robust Guaranteed Cost design and parameter tuning method of a kind of Active Disturbance Rejection Control |
| CN106855718A (en) * | 2017-01-12 | 2017-06-16 | 防灾科技学院 | MFA control high water tank control system |
| CN107957566A (en) * | 2017-11-17 | 2018-04-24 | 吉林大学 | Magnetic resonance depth measurement method for extracting signal based on frequency selection singular spectrum analysis |
Non-Patent Citations (1)
| Title |
|---|
| BINLI等: "Model-Free Information Extraction in Enriched Nonlinear Phase-Space", 《ARXIV》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110680282A (en) * | 2019-10-09 | 2020-01-14 | 黑龙江洛唯智能科技有限公司 | Method, device and system for detecting temporary abnormal state of brain |
| CN113741176A (en) * | 2021-09-18 | 2021-12-03 | 武汉理工大学 | Ship berthing and departing control method and device based on Koopman analysis and storage medium |
| CN113741176B (en) * | 2021-09-18 | 2023-10-03 | 武汉理工大学 | Ship berthing control method and device based on Koopman analysis and storage medium |
| CN116841307A (en) * | 2023-09-01 | 2023-10-03 | 中国民用航空飞行学院 | Flight trajectory prediction method and device based on Koopman neural network |
| CN116841307B (en) * | 2023-09-01 | 2023-12-01 | 中国民用航空飞行学院 | Flight trajectory prediction method and device based on Koopman neural network |
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