WO2013113111A1 - Système et procédé de prédiction de signaux autosemblables - Google Patents

Système et procédé de prédiction de signaux autosemblables Download PDF

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WO2013113111A1
WO2013113111A1 PCT/CA2013/050062 CA2013050062W WO2013113111A1 WO 2013113111 A1 WO2013113111 A1 WO 2013113111A1 CA 2013050062 W CA2013050062 W CA 2013050062W WO 2013113111 A1 WO2013113111 A1 WO 2013113111A1
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signal
self
similar signal
statistical
scale
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English (en)
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Chi-Guhn LEE
Jue Wang
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The Governing Council Of The University Of Toronto
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    • 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
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/02—Detecting, measuring or recording pulse, heart rate, blood pressure or blood flow; Combined pulse/heart-rate/blood pressure determination; Evaluating a cardiovascular condition not otherwise provided for, e.g. using combinations of techniques provided for in this group with electrocardiography or electroauscultation; Heart catheters for measuring blood pressure
    • A61B5/021—Measuring pressure in heart or blood vessels
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235—Details of waveform analysis
    • A61B5/7253—Details of waveform analysis characterised by using transforms
    • A61B5/726—Details of waveform analysis characterised by using transforms using Wavelet transforms
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7235—Details of waveform analysis
    • A61B5/7264—Classification of physiological signals or data, e.g. using neural networks, statistical classifiers, expert systems or fuzzy systems
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61B—DIAGNOSIS; SURGERY; IDENTIFICATION
    • A61B5/00—Measuring for diagnostic purposes; Identification of persons
    • A61B5/72—Signal processing specially adapted for physiological signals or for diagnostic purposes
    • A61B5/7271—Specific aspects of physiological measurement analysis
    • A61B5/7275—Determining trends in physiological measurement data; Predicting development of a medical condition based on physiological measurements, e.g. determining a risk factor
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00—Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/08—Feature extraction

Definitions

  • TECHNICAL FIELD [0002] The following relates generally to signal prediction and more specifically to prediction of self-similar signals.
  • Various models have been proposed for analyzing physiological signal data and extracting information from them, including time series models.
  • Several conventional time series models have been applied to physiological signals, such as autoregressive and moving average model (ARMA) and Hidden Markov model (HMM).
  • HMM Hidden Markov model
  • Another model is fractional Brownian motion (fBM).
  • MAP mean arterial pressure
  • Fig. 1 An examination of a mean arterial pressure (MAP) signal, an example of which is shown in Fig. 1, reveals its fractal property: parts of the signal resemble the whole. More specifically, the statistical properties of the signal remains the same when measured at different time scales, also known as statistical self-similarity.
  • a fractal pattern can be understood as a recurring pattern in a chaotic environment.
  • a number of physiological signals including heart rate variability, arterial blood pressure, respiratory rate, gait, as well as spatial patterns of physiological structures such as blood vessels, dendrites in neurons and airways in the lung, have been found to exhibit the statistical self-similarity property.
  • a (MAP) signal is a representative self-similar signal.
  • Fig. 2 shows a comparison of simulated signals using an autoregressive (AR) model (Fig. 2(a)), a HMM model (Fig. 2(b)) of a MAP signal and a real observed MAP signal (Fig. 2(c)) which illustrates disadvantages of the models.
  • AR autoregressive
  • Fig. 2(a) a HMM model
  • Fig. 2(b) real observed MAP signal
  • the AR model displays a uniform variation with no fundamental shifts.
  • the HMM model may represent a non-homogeneous signal with piece-wise stationarity.
  • a real MAP signal which is characterized by irregular fluctuations with random bursts, is like neither of the modeled signals.
  • SSS processes are generally considered difficult to model.
  • Classical models such as ARMA model typically only model processes with exponentially decreasing autocorrelation function, while the autocorrelation function of a SSS process decreases hyperbolically.
  • a method for predicting a substantially self-similar signal comprising: (a) obtaining an observed substantially self-similar signal; (b) discretizing the observed substantially self-similar signal into a plurality of intervals; (c) performing a mathematical transformation to generate a statistical value for each of the plurality of intervals at a plurality of time scales; (d) generating, by one or more processors, at least one additional statistical value from an across-scale relationship of at least a subset of the statistical values; and (e) predicting the substantially self-similar signal from the at least one additional statistical value.
  • a system for predicting a substantially self-similar signal comprising a signal prediction engine operable to: (a) obtain an observed substantially self-similar signal; (b) discretize the observed substantially self-similar signal into a plurality of intervals; (c) perform a mathematical transformation to generate a statistical value for each of the plurality of intervals at a plurality of time scales; (d) generate at least one additional statistical value from an across-scale relationship of at least a subset of the statistical values; and (e) predict the substantially self-similar signal from the at least one additional statistical value.
  • FIG. 1 is a representative MAP signal
  • FIG. 2 is a comparison of simulated signals using an autoregressive (AR) model (a), a HMM model (b) and a real observed MAP signal (c);
  • FIG. 3 is a block diagram illustrating a system for predicting self-similar signals;
  • FIG. 4 is a flow chart illustrating a method for predicting self-similar signals;
  • FIG. 5 is a hierarchical illustration of the relationships between the discrete signal X consent and wavelet coefficients; [0019] FIG.
  • FIG. 6 is a plot of the autocorrelation of an original MAP signal and its corresponding Haar wavelet coefficients;
  • FIG. 7 is an illustration of partial correlation of wavelet coefficients for MAP signal;
  • FIG. 8 is an illustration of an across-scale prediction scheme;
  • FIG. 9 is an illustration of a down-sampling algorithm with moving implementation;
  • FIG. 10 is a comparison of an across-scale predicted mean and within-scale predicted mean;
  • FIG. 11 is a receiver operating characteristic (ROC) curve for arterial blood pressure prediction;
  • FIG. 12 is an illustration of a desired prediction time and corresponding time intervals of the input signal; and
  • FIG. 13 is a ROC curve for heart rate variability prediction.
  • any module, engine, unit, application, component, server, computer, terminal or device exemplified herein that executes instructions may include or otherwise have access to computer readable media such as storage media, computer storage media, or data storage devices (removable and/or non-removable) such as, for example, magnetic disks, optical disks, or tape.
  • Computer storage media may include volatile and non-volatile, removable and non-removable media implemented in any method or technology for storage of information, such as computer readable instructions, data structures, program modules, or other data.
  • Examples of computer storage media include RAM, ROM, EEPROM, flash memory or other memory technology, CD-ROM, digital versatile disks (DVD) or other optical storage, magnetic cassettes, magnetic tape, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to store the desired information and which can be accessed by an application, module, or both. Any such computer storage media may be part of the device or accessible or connectable thereto. Any application, module or engine herein described may be implemented using computer readable/executable instructions that may be stored or otherwise held by such computer readable media. [0029] A system and method for predicting a self-similar signal are provided. The prediction is made based on historical data of the self-similar signal (hereinafter also referred to as simply a "signal").
  • a system (300) for predicting self-similar signals comprises a signal prediction engine (302), a signal input (304) and a signal output (306).
  • the signal input (302) is operable to obtain an input signal (308) from a signal source (310).
  • the signal input (304) provides the input signal (308) to the signal prediction engine (302), which generates an output signal (312).
  • the signal prediction engine provides the output signal (312) to the signal output (306), which may provide the output signal (312) to any signal storage (314) or signal di spl ay (316) medi a .
  • the signal prediction engine (302) may comprise a processor (318) and a memory (320).
  • the memory (320) may have stored thereon computer instruction which, when executed by the processor (318), provide the functionality described herein.
  • the memory (320) may, for example, comprise any one or more of a magnetic disk, RAM, ROM, Flash, EPROM, EEPROM, or other storage media.
  • the processor (318), when providing the functionality described herein, may temporarily or permanently store the input signal (308) and/or output signal (312) on the memory (320), which may be used for further analysis.
  • the input signal need not be "strictly" self-similar. That is, the signal X filament need not strictly satisfy the scale invariance property wherein the statistical properties of an SSS process remain unchanged when the scale is enlarged or reduced.
  • the signal prediction engine may apply mathematical transformation to the input signal to model the output signal.
  • Exemplary transformations comprise wavelet analysis, Fourier transform, statistical moments and autocorrelation.
  • Statistical moments may comprise mean, variance, skewness and kurtosis.
  • the signal prediction engine (302) obtains an observed self-similar signal X grasp from the signal input.
  • the signal prediction engine applies an across-scale prediction model (404) to generate the predicted signal using the obtained signal X grasp.
  • the signal prediction engine discretizes the signal (406) or a subset thereof into a set of n intervals. The number and time duration of intervals selected for discretization may determine the time period for which the output signal can be predicted.
  • the signal prediction engine generates a statistical value, which for a wavelet transformation may be a wavelet coefficient (408), for each of the n intervals, for example by applying a discrete wavelet transform (DWT) to each of the n intervals.
  • the DWT may be applied recursively (410) based on the desired prediction time period for the signal to generate (or predict) wavelet coefficients across multiple time scales.
  • at least one wavelet coefficient may be predicted (410).
  • the at least one predicted wavelet coefficient may be transformed to a predicted signal (412) which may be output (414) as the output signal.
  • the wavelet coefficients may be expressed as d j+ J:story and may be generated from the original obtained signal X grasp as follows.
  • the signal prediction engine applies a wavelet transform to the input signal.
  • the wavelet transform may, for example, comprise a Haar wavelet transform.
  • the Haar wavelet transform is based on a piecewise constant function (also referred to as the mother wavelet) expressed as: [0039] By dilating and translating the mother wavelet function, an orthonormal dyadic wavelet basis of L 2 (R) may be generated: where j, ) G TL. Any finite energy signal X t may be decomposed over this Haar wavelet basis:
  • the discrete wavelet transform computes the wavelet coefficients of a discrete signal X n recursively:
  • the above equation is herein referred to as the "wavelet equation”.
  • the wavelet equation reveals a powerful relationship obtainable from X grasp.
  • the wavelet equation illustrates that the wavelet coefficient is actually the scaled difference between the average X grasp in interval AB (i.e., tne avera g e -3 ⁇ 4 m interval (i.e., x ⁇ ).
  • the signal prediction engine may predict the wavelet coefficient d j+ j : resonate to indirectly predict average X tract in the window BC.
  • the signal prediction engine may predict the wavelet coefficient at one level (scale) higher in order to transform it into the average X grasp in the next 2 1 period through the wavelet.
  • the prediction of original variables along the time axis may be transformed into the prediction of wavelet coefficients across different scales.
  • a higher scale may be referred to as a coarser scale relative to a lower scale which may be referred to as a finer scale.
  • the signal prediction engine may select the appropriate coarsest scale used for the prediction based on the particular application and the particular requirements for prediction duration.
  • the signal prediction engine may further select the discrete time period for each interval based on the particular application and the particular requirements for prediction duration.
  • a desired prediction time (shown as prediction window EF) for certain diagnoses may be 10 minutes.
  • the signal prediction engine may discretize the input signal into a plurality of 10 minute intervals (shown as windows AB, BC and CD). It will be appreciated that the signal prediction engine may be configured suitably for different applications that require signal prediction in fractions of a second to many years.
  • the signal prediction engine further applies a covariance function to predict the wavelet coefficient of a different scale.
  • ⁇ / ⁇ ( ⁇ ) d the covariance of an arbitrary pair of wavelet coefficients may be expressed by: jj ⁇ ) ⁇ ] ⁇ ( ⁇ ) ⁇ / ⁇ , (u + v)dudv ⁇ f( )2 (]+ ⁇ (2 ] ⁇ ) (2 f ⁇ ) where ⁇ ( ⁇ ) is the complex conjugate of ⁇ ( ⁇ ).
  • J j '
  • Fig. 6 shows the within-scale autocorrelation function of the original MAP signal versus its Haar wavelet coefficients. It is clear that the autocorrelation structures of wavelet coefficients are similar across different scales. Furthermore, the discrete wavelet transform (DWT) significantly reduces the magnitude of within-scale autocorrelation. Such a "decorrelation" property allows the wavelet coefficients to be modeled by classical time series model. [0050] However, the across-scale decorrelation for wavelet coefficients is less powerful since
  • the correlation between D15 and D10 may be significantly conditional on D13 and other wavelet coefficients.
  • wavelet coefficients at several scales apart e.g. D15 and D4
  • the signal prediction engine may apply a modified vector autoregressive (VAR) model to model both within-scale and cross- scale correlations of wavelet coefficients.
  • VAR vector autoregressive
  • Traditional VAR models are flexible time series models that may capture complex dynamic interrelations among multiple time series. They may also infer the structural relation such as causality among those multiple time series.
  • the signal prediction engine may either "pad" the coarse scales with more wavelet coefficients (which may be referred to as a redundant wavelet transform) or down-sample the fine scales in order to match the number of wavelet coefficients per scale. Both methods may synchronize the wavelet coefficients before feeding them into the VAR model.
  • the signal prediction engine may apply a redundant wavelet transform to the selected set of wavelet coefficients.
  • the dyadic wavelet transform specified by the wavelet equation is a decimated algorithm, with the wavelet coefficient d j: jos being updated every 2 1 periods, resulting in unequal number of coefficients in different scales.
  • the signal prediction engine may apply a non-decimated or redundant Haar wavelet transform to generate the same number of coefficients by updating d j: participate for all scales at every period, as follows:
  • the indexing in redundant wavelet transform is different from the original index.
  • the signal prediction engine further implements down sampling.
  • the use of redundant wavelet transform traditionally imposes serial correlation to the wavelet coefficients. 1 The serial correlation results from the fact that two adjacent coarser scale (parent) wavelet
  • the signal prediction engine may
  • the signal prediction engine may predict the
  • the signal prediction engine may achieve parsimony while maintaining completeness using the
  • the signal prediction engine may select the autoregressive order p by choosing the integer that minimizes the Akaike information criteria (AIC):
  • AIC(p) ln ⁇ (p) ⁇ + ⁇ p(j + 2) 2
  • the signal prediction engine may estimate the VAR model, for example by implementing the Yule-Walker method or maximum likelihood method. Since the down-sampling approach is updated every 2 1 periods of time, the signal prediction engine may apply a moving implementation, as shown in Fig. 9, to fully exploit the coefficients at all scales. In the moving implementation, when a new observation X n (or do ,n ) becomes available, a new wavelet coefficients vector D tripod may be computed and a new prediction of D n+2 i may be generated.
  • a multi-step ahead prediction may also be generated by treating the predicted value as historical data for processing by the signal prediction engine.
  • the across-scale correlation of wavelet coefficients may be generated using alternate processes, including, for example, hidden Markov tree, linear regression and Markov-switching Multifractal model.
  • Hidden Markov tree HMT
  • HMT Hidden Markov tree
  • Linear regression model may also enable the quantification of dependences among wavelet coefficients across different scales. The wavelet coefficients in the target scale can be selected as the response variable in the linear regression, with wavelet coefficients from finer scales as the design variables.
  • One advantage of linear regression is its simplicity of
  • Markov-switching Multifractal model models the volatility of a signal by multiplying together a finite number of random first-order Markov components.
  • MSM enables a multifrequency stochastic volatility model with a closed-form likelihood.
  • the MSM model captures long-memory features, intermediate frequency volatility dynamics, and thick tails in distributions all with the single regime-switching approach.
  • the signal prediction engine may apply parameter estimation. Parameters may be estimated from historical data using statistical estimation methods. Two exemplary implementations of parameter estimation include maximum likelihood estimation and Bayesian estimation.
  • an optimal value of a parameter in a given model may be generated by maximizing the likelihood, whereas in Bayesian estimation, a posterior distribution may be generated using Bayes' theorem from a given prior on the parameters and the historical data.
  • the signal prediction engine may provide estimation by implementing simulation techniques, such as Markov chain Monte Carlo, for example, which applies simulation to sample the posterior distribution and provide approximate estimations.
  • the signal prediction engine may be applied to estimate an observed coarse scale signal at a finer scale. In this embodiment, the accuracy of estimation may be improved using the information from different (coarser or finer) time scales.
  • the signal prediction engine may be used to predict an arterial blood pressure signal.
  • the arterial blood pressure signal may be obtained by the signal input from a device present in an intensive care unit (ICU).
  • ICU intensive care unit
  • Table 1 illustrates the result from one patient as an example.
  • Table 2 shows the out-of-sample prediction MSE from across-scale VAR(l) model and within-scale AR(1) model.
  • Table 2 shows that, for this example, the across-scale prediction is better in terms of mean squared error (with 14% reduction in MSE) than the within-scale prediction.
  • MSE is not the only criterion, and not necessarily the best criterion, to assess prediction performance.
  • Pearson correlation for example, is an alternative criterion measuring the consistency of relative trends between two time series.
  • the across-scale model achieves a higher Pearson correlation than the within-scale model. The high correlation indicates that when the cross-scale model predicts an increase, the corresponding value of actual signal also increases. It is the relative change or trend that is common for predicted and actual signals, although the values may be far from equal.
  • FIG. 10 A comparison of predicted signals and the actual signal is shown in Fig. 10. Although both predictions generate smaller ranges compared with the actual signal, the across-scale prediction has a more consistent trend with the actual signal, especially in the major decreases and increases. Such property is highly valuable in clinical practice, where the relative change is sometimes more important than the exact values. This is because every patient has her/his own baseline values, but typically when a critical illness develops the common phenomenon is a change deviating from the baseline value. [0083] In the intensive care units, a sudden decrease of MAP is usually more dangerous than a sudden increase. This is because the decrease of MAP may indicate insufficient circulation which requires immediate treatment. Therefore we should be more interested in predicting the drop than the rise.
  • a good prediction should give a relatively large positive wavelet coefficient before the major decrease episode, although the exact value of the predicted wavelet coefficient does not have to be close to 20.
  • the ROC curve may be used to quantify the prediction performance.
  • the ROC curve summarizes the true positive rate (TPR) and false positive rate (FPR) for different critical thresholds on the predicted signal. It is suitable for the present example to measure whether a predicted large wavelet coefficient also corresponds to a large actual one, although the exact values may not be matched.
  • the averaged ROC curve for across-scale prediction based on the 120 patients is shown in Fig. 11.
  • the area under the curve (AUC) for different prediction windows are compared between across-scale model and within-scale model in Table 3. Table 3
  • the prediction performance is significantly better in across-scale model for short prediction window.
  • the signal prediction engine may be implemented as a component of suitable devices applied in various fields.
  • the signal prediction engine may be provided as a component of a monitoring device.
  • a blood pressure monitoring device may comprise typical blood pressure monitoring components suitable for a typical blood pressuring monitoring device.
  • the blood pressure monitoring device may further comprise a signal prediction engine operable to obtain an input signal that is also provided to the typical blood pressure monitoring components.
  • the signal prediction engine may be linked to a display of the blood pressure monitoring device or another signal output to provide the predicted signal.
  • the blood pressure monitoring device may further be configured to display an alert if the predicted signal meets preconfigured criteria, such as that corresponding to a predicted warning condition or fatal condition.
  • the signal prediction engine could be implemented in a standalone device, or in a device comprising the signal prediction engine, the signal input and the signal output.
  • a plurality of signal prediction engines may be provided wherein each one of the signal prediction engines is configured to provide a predicted signal of a different desired time period. Predicted signals of a shorter time period may provide a more accurate predicted signal while predicted signals of a longer time period may provide more advanced warning of a condition.
  • the signal prediction engines may be configured to operate in parallel, with the signal input providing the input signal to each signal prediction engine.
  • the monitoring device could be any other device for monitoring or diagnosing any condition on the basis of a physiological signal including heart rate variability, arterial blood pressure, respiratory rate, insulin uptake data for diabetics, gait, as well as spatial patterns of physiological structures such as blood vessels, dendrites in neurons and airways in the lung; or could be any other device for monitoring or diagnosing any other condition of a non-physiological signal including natural and social phenomena, including natural geometric objects, turbulence, natural temperature variations, noise in electrical components, traffic in Ethernet network, financial time series (e.g., market fluctuations), sound, digital images and molecular motion.
  • Several illustrative examples of such signals are now described.
  • Fractal geometry has become a common tool to describe objects or phenomena in which a scale invariance of some sort exists.
  • the variety of scientific applications is large as such structures exist from physics to astrophysics, from biology to chemistry but also in market fluctuations analysis.
  • Mainstream capital market theory for example, is based on efficient market assumptions, even though the markets themselves exhibit characteristics that are symptomatic of nonlinear dynamic systems. Financial markets are fractal in this way, as the general observer would be unable to view an unlabeled price chart and determine whether it is an hourly, monthly, or even 5 minute chart of trading activity. Fractal market analysis is used to discover and characterize the order hidden within seemingly random financial markets, and determines the probability of future events.
  • the signal prediction engine is operable to generate a projection of market activity given historical market activity.
  • One benefit of knowing these fractal patterns and projections is they identify specific critical balance points where the potential energy may resolve in one direction or another.
  • the signal prediction engine is operable to generate a predicted heartbeat time-series. Careful analysis of heartbeat time-series could give cardiologists diagnostic tools in the battle against heart disease. Similar analyses of brain waves and stride length in walking could give researchers insights into such conditions as epilepsy and Parkinsons disease.
  • HRV heart rate variability
  • the signal prediction engine is operable to generate a DNA model given a DNA barcode. It has been determined that very short stretches of DNA, such as a DNA barcode which usually represents less than one one-millionth of the genome, can enable identification of most animal species.
  • DNA barcoding is effective since patterns seen in very short DNA sequences usually reflect patterns seen in longer sequences. In this way, DNA barcodes demonstrate self-similarity. In other words, for unsequenced genomes, the DNA barcodes can provide a quick preview of the whole genome. [0097] Overall, the patterning of barcode differences supports the emerging view that selective sweeps prune mitochondrial diversity within species and mitochondrial and nuclear co- evolution are tightly linked. [0098] Fractal dimension has also been used to quantify the structures of a wide range of objects in biology and medicine and the signal prediction engine may be applied to signals relating to these objects. Fractal analysis has found widespread application in the field of neuroscience and is being used in many other areas. [0099] Network traffic patterns can also be predicted by the signal prediction engine.
  • Ethernet local area network (LAN) traffic has been found to exhibit statistical self-similarity.
  • Commonly used traffic models are not able to capture this fractal behavior, although that behavior has serious implications for the design, control, and analysis of high-speed, cell-based networks.
  • a critical characteristic of this self-similar traffic is that there is no natural length of a "burst": at every time scale ranging from a few milliseconds to minutes and hours, similar- looking traffic bursts are evident; we find that aggregating streams of such traffic typically intensifies the self-similarity ("burstiness") instead of smoothing it.
  • the signal prediction engine may further be operable to predict traffic patterns in other traffic applications, including, for example, traffic in transportation systems or in any other system having traffic flows in a network of traffic channels. [00100] Additionally, the signal prediction engine is operable to generate a signal
  • fractal statistics where examples range from the frequency-size statistics of earthquakes to the time series of the Earth's magnetic field.
  • the scaling property of fractal signal applies to descriptions of many geological features. Based on well-log measurements, Earth's physical properties have been found to exhibit fractal behaviour. For phenomena like earthquakes that show a fractal distribution of frequency of occurrence this relationship can be used to infer the recurrence interval of a given size earthquake in an area. It may also give insight into the dynamics of earthquakes. Estimation of earthquake recurrence interval may be beneficial to seismic hazard assessment, in engineering, and hazard mitigation. Fractals can further generate estimations of surface area or roughness.
  • the signal prediction engine may be applied to the many archaeological patterns that are fractal.
  • the signal prediction engine may further be applied to vibrations in domains with boundaries or interfaces of irregular geometry. It is known that objects of irregular shape or geometry are bad resonators. Thus, optimal object geometries can be developed using the output of the signal prediction engine.
  • noise reducing surfaces or chambers may be developed by shares that absorb incident acoustic energy in the audio spectrum.
  • An exemplary application is the reduction or normalization of traffic noise.
  • the absorption and acoustic properties of such structures are linked to the spectral properties of the Laplacian operator in complex domains, and wave localization.

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Abstract

La présente invention concerne un système et un procédé de prédiction d'un signal autosemblable. La prédiction est réalisée par l'obtention d'un signal observé et la génération de coefficients d'ondelette de l'échelle de temps d'origine correspondant chacun à des intervalles multiples du signal observé. Au moins un coefficient d'ondelette à travers l'échelle est prédit sur la base des coefficients d'ondelette de l'échelle de temps d'origine sur la base de la corrélation à travers l'échelle. Le signal peut être prédit sur la base du coefficient d'ondelette prédit.
PCT/CA2013/050062 2012-01-30 2013-01-29 Système et procédé de prédiction de signaux autosemblables WO2013113111A1 (fr)

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CN110974242A (zh) * 2019-12-26 2020-04-10 浙江福祉医疗器械有限公司 一种用于可穿戴式设备的步态异常程度评价方法及该设备
CN112436975A (zh) * 2020-10-09 2021-03-02 北京邮电大学 一种天地一体化信息网络流量预测方法及装置
CN113368403A (zh) * 2021-06-24 2021-09-10 深圳市恒康泰医疗科技有限公司 一种可以提高心肺功能的智能理疗系统
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CN113632105A (zh) * 2019-01-31 2021-11-09 摩根士丹利服务集团有限公司 基于人工智能的混沌系统异常响应
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CN110974242A (zh) * 2019-12-26 2020-04-10 浙江福祉医疗器械有限公司 一种用于可穿戴式设备的步态异常程度评价方法及该设备
CN110974242B (zh) * 2019-12-26 2023-02-10 浙江福祉科创有限公司 一种用于可穿戴式设备的步态异常程度评价方法及该设备
CN112436975A (zh) * 2020-10-09 2021-03-02 北京邮电大学 一种天地一体化信息网络流量预测方法及装置
CN113368403A (zh) * 2021-06-24 2021-09-10 深圳市恒康泰医疗科技有限公司 一种可以提高心肺功能的智能理疗系统
CN113368403B (zh) * 2021-06-24 2022-01-04 深圳市恒康泰医疗科技有限公司 一种可以提高心肺功能的智能理疗系统
CN116629843A (zh) * 2023-07-25 2023-08-22 山东比沃斯机电工程有限公司 智能化柴油发电机组的远程预警与维护决策支持系统
CN116629843B (zh) * 2023-07-25 2023-10-20 山东比沃斯机电工程有限公司 智能化柴油发电机组的远程预警与维护决策支持系统

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