EP0834845A1 - Method for frequency analysis of a signal - Google Patents

Abstract

The method involves a rapid wavelet transformation and fuzzy logic. The original signal is passed through a cascade of high/low pass filter pairs during wavelet transformation. The rapid wavelet transformation is combined with a fuzzy logic evaluation, whereby a corresp. function is generated from the resultant of the high pass filter for each filter stage. The corresp. function is used for the further analysis of the frequency signal using fuzzy logic rules.

Description

The invention relates to a method for frequency analysis of a signal using wavelets and Fuzzy logic, in particular an output signal from a safety detector such as one Flame detectors, noise detectors, fire detectors, passive infrared detectors or the like to avoid false alarms.

The output signals from safety detectors are often typical for them Frequency spectra marked. By analyzing these frequency spectra, the origin can be determined of the signals can be determined, and especially real alarm signals from interference signals differentiate and avoid false alarms. Especially with flame detectors the typical low frequency flickering of a flame is analyzed to determine the radiation from real flames from a source of interference such as reflected sunlight or to distinguish flickering light source.

The wavelet transform is as described, for example, in "The Fast Wavelet Transform" (Mac A. Cody, Dr. Dobb's Journal, April 1992), a transformation or illustration of a signal from the time domain to the frequency domain and is therefore basically the Fourier transform and Fast Fourier transform similar. It differs from these but through the basic function of the transformation, after which the signal is developed. At a Fourier transform uses a sine and cosine function, which in Frequency range are localized sharply and are undetermined in the time range. With a wavelet transformation a so-called wavelet or wave packet is used. There are of these different types such as a Gaussian, Spline or Haar wavelet, each through two parameters arbitrarily shifted in the time domain and stretched in the frequency domain or can be compressed. A wavelet transformation can therefore be used in both Signals localized in time as well as in the frequency domain are transformed. A fast Wavelet transformation is carried out by the pyramid algorithm according to Mallat, which is based on repeated application of a low-pass and high-pass filter, by which the low-frequency from the high-frequency signal components are separated. Doing so in each case the output signal of the low-pass filter in turn a pair of low / high-pass filters fed. A series of approximations of the original signal results, of which each has a coarser resolution than the previous one. The number of operations for the Transformation is required is proportional to the length of the original signal, while in the Fourier transform this number is disproportionate to the signal length. The fast wavelet transformation can also be performed inversely by using the original signal from the approximated values and coefficients for the reconstruction is restored. The algorithm for the decomposition and reconstruction of the signal as well as a table of the coefficients of the decomposition and reconstruction are based on the example for a spline wavelet in "An Introduction to Wavelets" by Charles K. Chui (Academic Press, San Diego, 1992).

Fuzzy logic is well known. With regard to this invention, it should be emphasized that Signal values known as fuzzy sets, or unsharp amounts, according to a Membership function, where the value of the membership function, or the degree of belonging to a fuzzy set is between zero and one. It is important that the membership function can be normalized, i.e. the sum of all Values of the membership function equal to one, where by the fuzzy logic evaluation one clear interpretation of the signal allowed.

Known applied analyzes for the output signals of security detectors are for For example the Fourier analysis, the Fast Fourier analysis, the zero crossing method or Turning point method. The latter is used in GB 2 277 989 for flame detectors described. Here the time spans between radiation maxima (turning points) measured and checked for their regularities and irregularities. In doing so Irregular radiation maxima as a flame and regular as a disturbance interpreted.

In EP 0 718 814 the frequency of the detected radiation is analyzed and between Distinguish regular and irregular signals in certain frequency ranges. The various signals in the given frequency ranges are evaluated several fuzzy logic rules. This procedure makes a more precise distinction between real flame signals and other interference signals and thus false alarm security enables. The frequency spectrum is generated here, for example, by fast ones Fourier transform, which in terms of the time required for the transformation, the necessary processor and the processor costs is expensive. For determining a Detected signals are sometimes required up to three seconds. A shorter one Evaluation time and response time until the alarm is given in certain applications he wishes. Procedures such as the zero crossing or turning point method accelerate the Decision making process, but are less accurate.

The object of the invention is to provide a method for frequency analysis of a signal create that is combined with a fuzzy logic evaluation and compared to State of the art analysis method with a smaller number of calculation steps is carried out so that in a shorter time a result of the same or higher accuracy is achieved. Furthermore, the method is intended to be a simpler processor and thereby be more cost-effective.

The object is achieved according to the invention by a method for frequency analysis of a Signal solved that a fast wavelet transformation of the signal with a fuzzy logic evaluation united, with the original signal in the wavelet transform a multi-stage filter cascade of high / low pass filter pairs is carried out and by each Level of the filter cascade from the initial values of the high pass filter one Membership function is generated directly in this form for further analysis of the Frequency signal is used according to fuzzy logic rules. In use to one Safety detectors allow the results of the fuzzy evaluation to decide whether an alarm is issued or an interference signal is present. The number of required Computational steps for the wavelet analysis is significant in comparison to Fourier analyzes reduced. This is the necessary computing time to identify the signal, and it this reduces the cost of the processor.

According to the invention, the original digitized signal is first replaced by a fast one Wavelet transformation analyzed. For this, the signal is processed according to the Mallat algorithm through several stages of a cascade of high and low pass filter pairs. From the Results of the high-pass filter then become a membership function at each filter level µ generated, which contains the sum of the calculated values from the high pass filter and by the sum of the squares of the original signal values is divided. The sum of the Membership functions µ that are generated here for each filter level are the same or almost equal to one. These normalized membership functions are then in this Form used for a continuation of frequency analysis with fuzzy logic.

Frequency analysis of this type gives the following advantages. The high-pass filters of the wavelet transform first provide information about the high-frequency signals. This is Particularly advantageous in the flame report, since it contains information about the higher ones Frequencies speeds up the identification of the type of signal and increases its accuracy can be. For example, if a high-frequency signal of over 15 Hz is detected, this interpreted as an interference signal. The subsequent message, fault signal or alarm signal, takes place earlier and is more certain to be correct. Wavelets are often very in their form simple, such as a hair wavelet, and allow analysis with few Arithmetic steps, which additionally shortens the computing time and decision time. Are less Lines of code required, an inexpensive processor can also be used. The Shortening the decision time is not, however, a loss of accuracy Signal identification connected.

In a first embodiment of the invention, a is used for the wavelet transformation orthonormal or semi-orthonormal wavelet or a wavelet packet basis used. The membership functions are derived from the results of the high pass filter and the wavelet coefficient for the reconstruction of the original signal. More specifically, the membership function contains a weighted by the wavelet coefficients Sum of the squared values of the high pass filter and in the denominator the sum of the squared Value of the original signal. The sum of these membership functions is approximate here equal to one, especially if the original signal contains enough values. The membership functions are then used for a fuzzy logic evaluation of the Frequency information used.

In a second embodiment, the wavelet transformation is carried out using an orthonormal or semi-orthonormal wavelet or a wavelet packet basis, where at a membership function is created for each filter level, which is the sum of the squared Output values of the high pass filter and in the denominator the sum of the squared values of the original signal contains. These membership functions are in turn normalized and are used in this form directly for a fuzzy logic evaluation of the frequency information used.

The invention is explained in more detail with reference to FIGS. 1 and 2. Figure 1 shows a block diagram the method with the fast wavelet analysis through several filter stages and Further analysis using fuzzy logic. Figure 2 shows membership functions using the example of a Frequency analysis using a fast hair wavelet transformation.

In the first embodiment of the invention, a fast wavelet transformation is first carried out using any wavelet as is known in the prior art. An orthonormal or semi-orthonormal wavelet or a wavelet packet base is preferably used. In the following, the signal values are denoted by x _{i, k} and y _{i, k} , where x means the original signal values and the values from the low-pass filters (LP) and y the values from the high-pass filters (HP). The index i denotes the level of the filter cascade in increasing numbers, the original signal being at level zero. The index k denotes an individual value of a signal. An original signal x _{0, k} at zero level is assumed, which is transformed by several filterings. The output signal of the first high-pass filter gives the values y _{1, k} and the output signal of the low-pass filter gives the values x _{1, k} , which also forms the input signal for the second filter stage. The output signal of the second high-pass filter gives the values y _{2, y} , that of the low-pass filter x _{2, k} is in turn fed to a third pair of filters _, etc. It should be noted here that the number of values resulting from the filter stages is different for each stage . More precisely, at each level the number of values decreases by a factor of two. At stage i + 1, for example, the output values of a high-pass filter are checked y i + 1 , k = l a l- 2nd k x i, l and the output values of a low-pass filter x i + 1 , k = l b l- 2nd k x i, l expressed. The coefficients a and b for the transformation are generally known and can be calculated using the Chui book mentioned above. For example, for a Haar wavelet, a ₀ = a ₁ = 1/2, b ₀ = 1/2 and b ₁ = -1 / 2. Index 1 takes integer values for which the coefficients are not equal to zero. The original signal is reconstructed in stages by creating the values of each filter stage from the values of the previous stage, namely x i, k = i ( p k- 2nd l x i + 1 , l + q k- 2nd l y i + 1 , l ) . The coefficients p and q for the wavelet reconstruction can again be found in the above-mentioned book.

According to the invention, the membership functions μ _i are now generated from the output values of the high-pass filter of the respective filter stage and the associated coefficients q for the wavelet reconstruction.

It is µ i = l q k -2 l y i, l l ' x 0 , l ' for i = 1, 2, ....., N and µ N + 1 = l p k -2 l x N, l l ' x 0 , l ' for i = N + 1, where N is the number of filter stages. The latter function µ _{N + 1} is thus formed by the output values of the last low-pass filter.

These membership functions are normalized by i µ i = 1

An often good approximation of these membership functions is given by the following equation: µ i = l y il l ' x 0 , l ' for i = 1,2, ....., N, and µ N + 1 = l x N, l l ' x 0 , l ' for i = N + 1.

With this approach, the function is almost normalized by

In a special embodiment of the method, the digitized raw values x ₀ , _{k are} subjected to a quick hair analysis. Membership functions µ _{i are} formed from the values y _{i, k of} each filter stage i, namely: µ i = l y i, l l ' x 0 , l ' for i = 1,2, ....., N, and µ N + 1 = l x N, l l ' x 0 , l ' for i = N + 1.

In this case, these membership functions are normalized by i µ i = 1 is.

In FIG. 2, membership functions μ are shown as a function of the frequency ω, which have been generated from the results of a fast Haar wavelet transformation. Of the various curves, µ _{N + 1} illustrate the degree of affiliation of very low frequencies, µ _N that of low frequencies, and µ ₁ and µ ₂ the degree of affiliation of high and medium frequencies ω. It is clearly evident here that the sum of the curve values is one for each selected frequency ω.

In all executions of the method, these membership functions for the Evaluation according to fuzzy logic rules is used, after which a decision is made as to whether an alarm signal is triggered or the signal is assessed as a fault.

This method is suitable for differentiation when used on flame detectors between interference signals, such as periodic signals above 15 Hz, and real ones Flame signals, such as narrow-band signals of low frequency or broadband signals in the low frequency range. By quickly identifying high-frequency signals are the interference signals of this frequency and their Resonance frequencies eliminated from the signal, which speeds up the frequency analysis of the signal. By accelerating the frequency analysis through the wavelet transformation, the time required to decide on the type of signal and the type of signal to be delivered Message, for example, can be reduced from three seconds to one second.

The procedure for evaluating signals is also passive for noise detectors Infrared detector, for the spectral analysis of the signals of individual pixels in image processing as well as for various sensors such as gas and vibration sensors.

Claims (6)

Method for frequency analysis of a signal using a fast wavelet transformation and fuzzy logic, in which the fast wavelet transform original signal through a multi-stage filter cascade of high / low pass filter pairs is performed, characterized in that the fast wavelet transformation with a Fuzzy logic evaluation is combined by using the wavelet transform at each filter stage a membership function from the results of the high pass filter is generated, which is used for further analysis of the frequency signal according to fuzzy logic rules becomes. Method according to claim 1, characterized in that for the fast Wavelet transform used Wavelet an orthonormal or semi-orthonormal Wavelet or a wavelet packet base and the membership functions generated in each case the sum of the squared values of the weighted by the wavelet coefficients High pass filter (HP) and the sum of the squared values of the original signal included and in normalized form for the further analysis of the frequency signal according to fuzzy logic rules be used. Method according to claim 1, characterized in that for the wavelet transformation Wavelet used an orthonormal or semi-orthonormal wavelet or is a wavelet packet basis and the membership functions generated are each the sum the squared output values of the high pass filter and the sum of the squared values of the Original signal included and in normalized form for the evaluation of the Frequency signal according to fuzzy logic rules are used. Method according to claims 1, 2 or 3, characterized in that the Output signals that are a safety detector. Method according to claim 4, characterized in that the output signals that are a flame detector. Method according to claim 5, characterized in that the frequency analysis and evaluation of the output signals of the flame detector takes 100 ms to 10 s.

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