EP1134712B1 - Method for the processing of the signal in a danger detector, and detector with means for the implementation of such method - Google Patents

Abstract

The signals from an alarm, comprising at least one sensor (2, 3, 4), for monitoring characteristic hazard values and an analytical electronic unit (1), connected to the at least one sensor (2, 3, 4), are compared with pre-set parameters. Furthermore, the signals are analysed for repeated or regular occurrence and repeated, or regularly occurring alarm signals are classed as error signals. The classification of signals as error signals gives rise to a corresponding adjustment of the parameter. When an error signal arises, before the parameter is adjusted, the validity of the signal analysis for the at least one sensor (2, 3, 4) is checked and the parameter adjustment is carried out, depending upon the result of said validity check. An alarm with the means for carrying out said method comprises at least one sensor (2, 3, 4), for a characteristic hazard value and an electronic analysis unit (1), containing a microprocessor (6), for the evaluation and analysis of the signal from the at least one sensor (2, 3, 4). The microprocessor (6) has a software programme with an adaptive algorithm based on multiple solutions for the analysis of the signals from the at least one sensor (2, 3, 4).

Description

The present invention relates to a method for processing the signals of a hazard detector, which has at least one sensor for monitoring risk parameters and the at least one sensor associated evaluation, wherein the monitoring of the hazard parameters by comparing the signals of at least one sensor with predetermined parameters by means. The hazard detector can be, for example, a smoke detector, a flame detector, a passive infrared detector, a microwave detector, a dual detector (passive infrared + microwave sensor), or a sound detector.

The US 6011464 describes how, in a method for frequency analysis of a signal of a hazard detector, a wavelet transformation is combined with a fuzzy logic evaluation. In the transformation by means of an orthonormal or semi-orthonormal wavelet, the original signal is fed to a multi-level filter cascade of high / low pass filter pairs. At each filter stage, a membership function is generated from results of the high pass filter, wavelet coefficients and values of the original signal. These functions are normalized and are used in this form for further evaluation according to fuzzy logic rules. The method is particularly suitable for the evaluation of the output signal of hazard detectors such as flame detectors, noise detectors and the like. The wavelet transformation and fuzzy logic evaluation is performed by a small number of lines of processor code, whereby the evaluation can be realized with a low-cost processor and accelerated at the same or increased accuracy.

Today's hazard detectors have reached such a sensitivity with respect to the detection of hazard parameters that the main problem is no longer to detect a hazard parameter as early as possible, but to reliably distinguish interference signals from true danger signals and thereby avoid false alarms. The distinction between danger and interference signals is made essentially by the use of several different sensors and correlation of their signals or by the analysis various features of the signals of a single sensor and / or by a corresponding signal processing, which has already been achieved by the use of fuzzy logic already a significant improvement in noise immunity.

The fuzzy logic is well known. With regard to the evaluation of the signals from hazard detectors, it should be emphasized that signal values are assigned to so-called fuzzy sets, or fuzzy sets, according to a membership function, the value of the membership function, or the degree of belonging to a fuzzy set, being between zero and one. Importantly, the membership function is normalizable, i. the sum of all values of the membership function is equal to one, whereby the fuzzy logic evaluation allows a clear interpretation of the signal.

By the present invention, a method of the type mentioned above for processing the signals of a hazard detector will now be given, which is further improved in terms of noise immunity and noise immunity.

The inventive method is characterized in that the signals of the at least one sensor are analyzed as to whether they occur more frequently or regularly, and that increasingly or regularly occurring signals are classified as interference signals.

A first preferred development of the method according to the invention is characterized in that the classification of signals as interference signals triggers a corresponding adaptation of the parameters.

The method according to the invention is based on the new knowledge that, for example, a fire detector never "sees" more than a few real fires between two revisions or two power failures, and that increasingly or regularly occurring signals indicate the presence of sources of interference. The interference caused by the sources of interference are recognized as such and the detector parameters are adjusted accordingly. In this way, the detectors operated by the method according to the invention are capable of learning and can better distinguish between real danger signals and interference signals.

A second preferred embodiment of the method according to the invention is characterized in that the occurrence of interference signals before the adaptation of the parameters, the result of the analysis of the signals of the at least one sensor is checked for its validity, and that the adjustment of the parameters in dependence on the result of this validity check ,

A third preferred development is characterized in that the validity check is carried out by means of methods based on multiple resolution.

A fourth preferred development of the method according to the invention is characterized in that wavelets, preferably "biorthogonal" or "second generation" wavelets or "lifting scheme", are used for the validation.

The wavelet transformation is a transformation or mapping of a signal from the time domain into the frequency domain (see, for example, " The Fast Wavelet Transform "by MacA Cody in Dr. Dobb's Journal, April 1992 ); it is basically similar to Fourier transform and Fast Fourier transform. It differs from these, however, by the basic function of the transformation, after which the signal is developed. A Fourier transform uses a sine and cosine function that is sharply localized in the frequency domain and indefinite in the time domain. In a wavelet transformation, a so-called wavelet or wave packet is used. There are various types of these, such as a Gaussian, spline or hair wavelet, which can be arbitrarily shifted in the time domain by two parameters and stretched or compressed in the frequency domain. More recently, new wavelet methods have been introduced, often referred to as "second generation". Such wavelets are constructed with the so-called "lifting-scheme" (Sweldens).

The result is a series of approximations of the original signal, each of which has a coarser resolution than the previous one. The number of operations required for the transformation is in each case proportional to the length of the original signal, while in the Fourier transformation this number is disproportionate to the signal length. The fast wavelet transform can also be performed inversely by restoring the original signal from the approximated values and coefficients for reconstruction. The algorithm for the decomposition and reconstruction of the signal and a table of the coefficients of decomposition and reconstruction are exemplified for a spline wavelet in " An Introduction to Wavelets "by Charles K. Chui (Academic Press, San Diego, 1992 ). See also on this topic " A Wavelet Tour of Signal Processing "by S. Mallat (Academic Press, 1998 ).

A further preferred development of the method according to the invention is characterized in that the expected values for the approximation or the approximation and detail coefficients of the wavelets are determined and compared at different resolutions. The determination of said coefficients preferably takes place in an estimator or by means of a neural network.

The invention further relates to a hazard detector with means for carrying out said method, with at least one sensor for a hazard parameter and with a microprocessor-containing evaluation for the evaluation and analysis of the signals of the at least one sensor.

The danger detector according to the invention is characterized in that the microprocessor contains a software program with a multi-resolution learning algorithm for the analysis of the signals of the at least one sensor.

A first preferred embodiment of the inventive hazard alarm is characterized in that the learning algorithm on the one hand, an analysis of said sensor signals on their repeated or regular occurrence and on the other hand, a validity check of the result of the analysis, and that the learning algorithm for validating wavelets, preferably "biorthogonal" or "second generation" wavelets.

A second preferred embodiment of the inventive hazard detector is characterized in that the learning algorithm uses neuro-fuzzy methods.

und $${\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left(\mathrm{k}\right)\mathrm{=}\mathrm{\Sigma }{\tilde{\mathrm{\varphi }}}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\cdot {\mathrm{y}}_{\mathrm{i}}\mathrm{/}\mathrm{\Sigma }{\tilde{\mathrm{\varphi }}}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\left(\mathrm{\Sigma \; über\; alle\; i}\mathrm{=}1\mathrm{bis\; k}\right)$$

enthält, in denen ϕ_m,n Wavelet Skalierfunktionen, ĉ_m,n Approximations-Koeffizienten und y_k den k-ten Eingangspunkt des neuronalen Netzes bezeichnet, und ϕ̃_m,n die duale Funktion (dual function, Definition siehe S. Mallat) von ϕ_m,n ist.A third preferred embodiment of the inventive hazard detector is characterized in that the learning algorithm the two equations $${\mathrm{f}}_{\mathrm{m}}\left(\mathrm{x}\right)\mathrm{=}\mathrm{\Sigma }{\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\mathrm{\cdot }{\mathrm{\phi }}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left(\mathrm{x}\right)\left(\mathrm{\Sigma \; over\; all\; n}\right)$$

and $${\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left(\mathrm{k}\right)\mathrm{=}\mathrm{\Sigma }{\tilde{\mathrm{\phi }}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\cdot {\mathrm{y}}_{\mathrm{i}}\mathrm{/}\mathrm{\Sigma }{\tilde{\mathrm{\phi }}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\left(\mathrm{\Sigma \; over\; all\; i}\mathrm{=}1\mathrm{to\; k}\right)$$

in which φ _{m, n} wavelet scaling functions, ĉ _{m, n} approximation coefficients and y _k denote the k-th input point of the neural network, and φ _{m, n} the dual function (definition see S. Mallat) of φ _{m, n} is.

Fig. 1

ein Diagramm zur Funktionserläuterung,

Fig. 2

ein Blockschema eines mit Mitteln zur Durchführung des erfindungsgemässen Verfahrens ausgerüsteten Gefahrenmelders,

Fig. 3a, 3b

zwei Varianten eines Details des Gefahrenmelders von Fig. 2; und

Fig. 4

eine weitere Variante eines Details des Gefahrenmelders von Fig. 3.

In the following the invention will be explained in more detail with reference to embodiments and the drawings; it shows:

Fig. 1

a diagram to explain the function,

Fig. 2

1 is a block diagram of a hazard detector equipped with means for carrying out the method according to the invention;

Fig. 3a, 3b

two variants of a detail of the danger detector of Fig. 2 ; and

Fig. 4

another variant of a detail of the hazard detector of Fig. 3 ,

The inventive method, the signals of a hazard detector are processed so that typical noise signals are detected and characterized. If in the present description is mainly mentioned by Brandmeldem, this does not mean that the inventive method is limited to fire detectors. The method is rather suitable for hazard detectors of all kinds, especially for burglar and motion detectors.

The mentioned interference signals are analyzed with a simple and reliable method. An important feature of this method is that it not only detects and characterizes the interfering signals, but verifies the result of the analysis. For this purpose wavelet theory and multiresolution analysis is used. Depending on the result of the check, the parameters of the detector or the algorithms are adjusted. This means, for example, that the sensitivity is reduced or that certain automatic switching between different parameter sets is locked.

The latter should be explained with an example: In the European patent application 99 122 975.8 a fire detector is described which has a scattered light optical sensor, a temperature sensor and a fire gas sensor. The evaluation electronics of the detector contains a fuzzy controller in which the signals of the individual sensors and a diagnosis of the respective type of fire are linked. For each type of fire, a special application-specific algorithm is provided and can be selected based on the diagnosis. In addition, the detector contains various parameter sets for personal protection and property protection, between which an online switchover normally takes place. If interference signals are now diagnosed in the case of the temperature and / or the fire gas sensor, switching between these parameter sets is interlocked.

When using fuzzy logic, one of the problems to be solved in translating the knowledge stored in a database into linguistically interpretable fuzzy rules. Neurofuzzy methods developed for this purpose were not convincing because they sometimes provide very difficult to interpret fuzzy rules. One way to However, obtaining interpretable fuzzy rules offers so-called multi-resolution techniques. Their idea is to use a dictionary of membership functions which form a multi-resolution and to determine which are the membership functions suitable for the description of a control surface.

In Fig. 1 a diagram of such a multiple resolution is shown. Line a shows the course of a signal whose amplitude moves in the areas of small, medium and large. Correspondingly, in line b, the membership functions c1 are "fairly small", c2 "medium" and c3 "rather large". These membership functions form a multiple resolution, meaning that each membership function can be decomposed into a sum of membership functions of a higher resolution level. This results in the membership functions c5 entered in line c "very small", c6 "small to very small", c7 "very medium", c8 "large to very large" and c9 "very large". Thus, according to line d, for example, the triangular spline function c2 can be decomposed into the sum of the translated triangular functions of the higher level of line c.

ausgedrückt. Hier sind A_i linguistische Ausdrücke, x ist die linguistische Eingangsvariable und y ist die Ausgangsvariable. Der Wert der linguistischen Eingangsvariablen kann scharf oder unscharf (fuzzy) sein. Wenn beispielsweise x_i eine linguistische Variable für die Temperatur ist, dann kann der Wert x̂ eine scharfe Zahl wie "30(°C)" oder eine unscharfen Grösse wie "ungefähr 25 (°C)" sein, wobei "ungefähr 25" selbst ein Fuzzy-Set ist.In the Tagaki-Sugeno model, the fuzzy rules follow the equation $${\mathrm{R}}_{\mathrm{i}}\mathrm{:}{\mathrm{if\; x\; is\; A}}_{\mathrm{i}}{\mathrm{then\; y}}_{\mathrm{i}}\mathrm{=}{\mathrm{f}}_{\mathrm{i}}\left({\mathrm{x}}_{\mathrm{i}}\right)$$

expressed. Here A _i linguistic expressions, x is the linguistic input variable and y is the output variable. The value of the input linguistic variables can be sharp or fuzzy. For example, if x _{i is} a linguistic variable for the temperature, then x may be a sharp number such as "30 (° C)" or a fuzzy size such as "about 25 (° C)", with "about 25" itself Fuzzy set is.

wobei der Grad der Erfüllung β_i durch den Ausdruck β_i = µ_Ai(x̂) gegeben ist, in welchem µ_Ai(x̂) die Zugehörigkeitsfunktion zum linguistischen Term A_i bezeichnet. Bei vielen Anwendungen wird eine lineare Funktion genommen: f(x̂) = a^Ti·x̂+b_i. wenn zur Beschreibung des scharfen Ausgangswerts y eine Konstante b_i genommen wird, dann wird das System zu: $${\mathrm{R}}_{\mathrm{i}}\mathrm{:}{\mathrm{wenn\; x\; ist\; A}}_{\mathrm{i}}{\mathrm{dann\; y}}_{\mathrm{i}}\mathrm{=}{\mathrm{b}}_{\mathrm{i}}$$

For a sharp input value, the output value of the fuzzy system is given by: $$\hat{\mathrm{y}}\mathrm{=}{\mathrm{\Sigma \beta }}_{\mathrm{i}}\mathrm{\cdot }\mathrm{f}\left(\hat{\mathrm{x}}\right)\mathrm{/}{\mathrm{\Sigma \beta }}_{\mathrm{i}}$$

wherein the degree of satisfaction β _{i is given} by the expression β _i = μ _Ai ( x ), in which μ _Ai ( x ) denotes the membership function to the linguistic term A _i . In many applications a linear function is taken: f ( x ) = a ^T i x + b _i . if a constant b _{i is} taken to describe the sharp output value y, then the system becomes: $${\mathrm{R}}_{\mathrm{i}}\mathrm{:}{\mathrm{if\; x\; is\; A}}_{\mathrm{i}}{\mathrm{then\; y}}_{\mathrm{i}}\mathrm{=}{\mathrm{b}}_{\mathrm{i}}$$

If spline functions N ^{k are} taken, for example as a membership function μ _Ai (x) = N ^k [2 ^m ( x -n)], then the system of Equation (3) is equivalent to $${\mathrm{y}}_{\mathrm{t}}\mathrm{=}{\mathrm{.sigma..sub.B}}_{\mathrm{i}}{\mathrm{N}}^{\mathrm{k}}\left[{\mathrm{2}}^{\mathrm{m}}\left(\hat{\mathrm{x}}\mathrm{-}\mathrm{n}\right)\right]$$

In this particular case, the output y is a linear sum of translated and extended spline functions. And that means that under equation (4) the Tagaki-Sugeno model is equivalent to a multi-resolution spline model. And it follows that wavelet techniques can be used here.

Fig. 2 shows a block diagram of a equipped with a Neurofuzzy learning algorithm hazard detector. The detector designated by the reference M is, for example, a fire detector and has three sensors 2 to 4 for fire parameters. For example, an optical sensor 2 for scattered light or transmitted light measurement, a temperature sensor 3 and a fire gas, such as a CO sensor 4, is provided. The output signals of the sensors 2 to 4 are fed to a processing stage 1, which has suitable means for processing the signals, such as amplifiers, and passes from this to a microprocessor or microcontroller, hereinafter referred to as μP 6.

In μP 6, the sensor signals are compared with each other as well as individually with specific parameter sets for the individual fire parameters. Of course, the number of sensors is not limited to three. Thus, only a single sensor can be provided, in which case various properties, for example the signal gradient or the signal fluctuation, are extracted and examined from the signal of the one sensor. A neuro-fuzzy network 7 and a validity check (validation) 8 are integrated into the μP 6 by software. If the signal resulting from the neuro-fuzzy network 7 is evaluated as an alarm signal, a corresponding alarm signal is sent to an alarm output device 9 or an alarm center. If the validation 8 shows that interference signals occur repeatedly or regularly, then the parameter sets stored in μP 6 are corrected accordingly.

The neuro-fuzzy network 7 is a series of neural networks using the symmetric scaling functions φ _{m, n} (x) = φ _{m, n} (x) = φ [(xn) * 2 ^m ] as the activation function. The scaling functions are such that {(φ _{m, n} (x)} form a multiple resolution Each neural network uses activation functions of a given resolution The m th neural network optimizes the coefficients ĉ _{m, n} with f _m (x) , the output of the mth neural network. $${\mathrm{f}}_{\mathrm{m}}\left(\mathrm{x}\right)\mathrm{=}\mathrm{\Sigma }{\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\mathrm{\cdot }{\mathrm{\phi }}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left(\mathrm{x}\right)\left(\mathrm{\Sigma \; over\; all\; n}\right)$$

wobei y_k(x) der k-te Eingangspunkt und ϕ̃_m,n(x) die duale Funktion von ϕ_m,n(x) ist. Die beiden Gleichungen (5) und (6) bilden den Hauptalgorithmus des Neuro-Fuzzy-Netzes.The coefficients ĉ _{m, n} are calculated using the following equation: $${\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left(\mathrm{k}\right)\mathrm{=}\mathrm{\Sigma }{\tilde{\mathrm{\phi }}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\cdot {\mathrm{y}}_{\mathrm{i}}\mathrm{/}\mathrm{\Sigma }{\tilde{\mathrm{\phi }}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\left(\mathrm{\Sigma \; over\; all\; i}\mathrm{=}1\mathrm{to\; k}\right)$$

where y _k (x) is the k th entry point and φ _{m, n} (x) is the dual function of φ _{m, n} (x). The two equations (5) and (6) form the main algorithm of the neuro-fuzzy network.

At each iteration step, the values of the various neural networks are cross checked (validated), including a property of the wavelet decomposition, namely that the approximation coefficients ĉ _{m, n of} a level m from the approximation and wavelet coefficients of the level m-1 can be obtained by using the reconstruction or decomposition algorithm.

In a preferred embodiment, φ _{m, n} (x) is a second-order spline function and φ _{m, n} (x) is an interpolation function. In a second embodiment, φ _{m, n} (x) is a spline function and φ _{m, n} (x) is the dual function of φ _{m, n} (x). In a third embodiment, φ _m , _n (x) = φ _{m, n} (x), where φ _{m, n} (x) is the hair function. In these cases, the implementation of the learning algorithm in a simple microprocessor is possible.

In the FIGS. 3a and 3b Two variants of a neuro-fuzzy network 7 and the associated validation stage 8 are shown. In the example of Fig. 3a the input signal is approximated in different resolution levels as a weighted sum of wavelets ψ _{m, n} and scaling functions φ _{m, n} with a given resolution. The validation stage 8 compares the approximation coefficients ĉ _{m, n} with the approximation and detail coefficients of the wavelets at the level of the next lower resolution level. P and q denote wavelet reconstruction filter coefficients.

In the example of Fig. 3b the input signal is approximated in different resolution levels as a weighted sum of scaling functions φ _{m, n} with a given resolution. The validation stage 8 compares the approximation coefficients ĉ _{m, n} with the approximation coefficients at the level of the next lower resolution stage. With g, wavelet are called low-pass decomposition coefficients.

Instead of in a neuro-fuzzy network 7, the determination of said coefficients in a estimator of the in Fig. 4 shown type done. This estimator is a so-called multi-resolution spline estimator, which is used to estimate the coefficients ĉ _{m, n} in the equation f _m (x) = ĉm _{, n} ·φ _{m, n} (x) on the functions φ _{m, n} (x ) based dual-spline estimators used. Wavelet spline estimators are used to adaptively determine the appropriate resolution to locally describe an underlying hypersurface in an online learning process. A well-known estimator is the Nadaraya-Watson estimator, which estimates the equation of the hypersurface f (x) by the following expression: $$\mathrm{f}\left(\mathrm{x}\right)\mathrm{=}{\displaystyle \underset{\mathrm{k}\mathrm{=}\mathrm{1}}{\overset{{\mathrm{k}}_{\mathrm{Max}}}{\mathrm{\Sigma }}}}\mathrm{K}\mathrm{(}\left(\mathrm{x}\mathrm{-}{\mathrm{x}}_{\mathrm{k}}\right)\mathrm{/}\mathrm{\lambda }\mathrm{)}\mathrm{\cdot }{\mathrm{y}}_{\mathrm{k}}\mathrm{/}{\displaystyle \underset{\mathrm{k}\mathrm{=}\mathrm{1}}{\overset{{\mathrm{k}}_{\mathrm{Max}}}{\mathrm{\Sigma }}}}\mathrm{K}\mathrm{(}\left(\mathrm{x}\mathrm{-}{\mathrm{x}}_{\mathrm{k}}\right)\mathrm{/}\mathrm{\lambda }\mathrm{)}\mathrm{,}$$

Nadaraya-Watson estimators have two interesting properties, they are estimators of the local mean square deviation and it can be shown that in the case of a random design they are so-called Bayesian estimators of (x _k , y _k ), where (x _k , y _k ) are iid copies of a continuous random variable (X, Y).

The spline functions φ (x) and their dual function φ (x) can be used as estimators. We first use the function φ (x) to estimate f (x) with λ = 2 ^-m (m is an integer) at x _n with x _n · 2 ^m ∈ Z:

Using the symmetry of φ (x), equation (6) for the dual spline function is equivalent to using an estimator centered at x _n : $$\hat{\mathrm{f}}\left({\mathrm{x}}_{\mathrm{n}}\right)\mathrm{=}{\displaystyle \underset{\mathrm{k}\mathrm{=}\mathrm{1}}{\overset{{\mathrm{k}}_{\mathrm{Max}}}{\mathrm{\Sigma }}}}\stackrel{\mathrm{~}}{\mathrm{\phi }}\mathrm{(}\left({\mathrm{x}}_{\mathrm{k}}\mathrm{-}{\mathrm{x}}_{\mathrm{n}}\right)\mathrm{\cdot }{\mathrm{2}}^{\mathrm{m}}\mathrm{)}\mathrm{\cdot }{\mathrm{y}}_{\mathrm{k}}\mathrm{/}{\displaystyle \underset{\mathrm{k}\mathrm{=}\mathrm{1}}{\overset{{\mathrm{k}}_{\mathrm{Max}}}{\mathrm{\Sigma }}}}\mathrm{K}\mathrm{(}\left({\mathrm{x}}_{\mathrm{k}}\mathrm{-}{\mathrm{x}}_{\mathrm{n}}\right)\mathrm{\cdot }{\mathrm{2}}^{\mathrm{m}}\mathrm{)}\mathrm{,}$$

The expected value of the counter in equation (7) is proportional to the approximation coefficient c _{m, n} . Equation (6) gives an estimate of ĉ _{m, n} in f _m (x) = Σĉ _{m, n ˙} φ _{m, n} (x): $${\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\mathrm{=}\hat{\mathrm{f}}\mathrm{\left(}{\mathrm{x}}_{\mathrm{n}}\mathrm{\right)}\mathrm{,}$$

In the FIG. 4 the available data (values) are indicated by a small square, their projection onto dual spline functions with a small circle and the estimation on a regular grid with a cross.

wobei die Filterkoeffizienten g dem Tiefpass-Zerlegungs-Koeffizienten für Spline-Funktionen entsprechen. Ausserdem wird gefordert, dass $$\mathrm{|}{\displaystyle \mathrm{\sum }_{\mathrm{k}\mathrm{=}\mathrm{1}}^{{\mathrm{k}}_{\max }}}\tilde{\mathrm{\varphi }}\left(\left({\mathrm{x}}_{\mathrm{k}}\mathrm{-}{\mathrm{x}}_{\mathrm{n}}\right)\mathrm{\cdot }{\mathrm{2}}^{\mathrm{m}}\right)\mathrm{|}\mathrm{>}\mathrm{T}$$

damit Teilungen durch sehr kleine Werte verhindert werden.To validate the coefficient ĉ _{m, n} two conditions are necessary: $$\mathrm{|}{\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\mathrm{-}{\displaystyle \underset{\mathrm{p}}{\mathrm{\Sigma }}}{\mathrm{G}}_{\mathrm{p}\mathrm{-}\mathrm{2}\mathrm{n}}\mathrm{\cdot }{\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{+}\mathrm{1}\mathrm{.}\mathrm{p}}\mathrm{|}\mathrm{<}\mathrm{\Delta }$$

wherein the filter coefficients g correspond to the low-pass decomposition coefficient for spline functions. In addition, it is demanded that $$\mathrm{|}{\displaystyle \underset{\mathrm{k}\mathrm{=}\mathrm{1}}{\overset{{\mathrm{k}}_{\mathrm{Max}}}{\mathrm{\Sigma }}}}\stackrel{\mathrm{~}}{\mathrm{\phi }}\left(\left({\mathrm{x}}_{\mathrm{k}}\mathrm{-}{\mathrm{x}}_{\mathrm{n}}\right)\mathrm{\cdot }{\mathrm{2}}^{\mathrm{m}}\right)\mathrm{|}\mathrm{>}\mathrm{T}$$

so that divisions are prevented by very small values.

The strength of this method is that the calculation of a coefficient ĉ _{m, n} requires the storage of only two values of the numerator and the denominator in equation (7). The method is therefore very well suited for online learning with a simple low memory microprocessor.

The method is easily adaptable to density estimation by replacing equations (7) and (8) with the following equation: $${\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{.}\mathrm{n}}=1/{\mathrm{k}}_{\mathrm{Max}}\cdot {\displaystyle \underset{\mathrm{k}\mathrm{=}\mathrm{1}}{\overset{{\mathrm{k}}_{\mathrm{Max}}}{\mathrm{\Sigma }}}}{\stackrel{\mathrm{~}}{\mathrm{\phi }}}_{\mathrm{m}\mathrm{.}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{k}}\right)\mathrm{\cdot }{\mathrm{y}}_{\mathrm{k}}$$

Claims (10)

1. Method for processing the signals of a danger detector, which features at least one sensor (2, 3, 4) for monitoring characteristic danger values and features evaluation electronics assigned to the at least one sensor (2, 3, 4), in which the signals of the at least one sensor (2, 3, 4) are compared with predetermined parameters, characterized in that the signals of the at least one sensor (2, 3, 4) are analysed to establish whether they are occurring more than once or regularly so that signals occurring more than once or regularly can be classed as interference signals and that the result of the analysis of the signals as to their validity is checked by methods which are based on multi-resolution.
2. Method according to claim 1, characterised in that the classification of signals as interference signals triggers a corresponding adaptation of the parameters,
3. Method according to claim 2, characterised in that, on occurrence of interference signals, before the parameters are adapted, the result of the analysis of the signals of the at least one sensor (2, 3, 4) is validated, and that the parameters are adapted depending on the result of this validation,
4. Method according to claim 3, characterised in that wavelets, preferably "biorthogonal" or "second generation" wavelets or a "lifting scheme" are used for the validation.
5. Method according to claim 4, characterised in that the expected values are determined for the approximation coefficients or the approximation and detailed coefficients of the wavelets and are compared at different resolutions.
6. Method according to claim 5, characterised in that the said coefficients are determined in an estimator or by means of a neuronal network.
7. Danger detector with means for executing the method as claimed in claim 1, with at least one sensor (2, 3, 4) for a characteristic danger value and with evaluation electronics (1) containing a microprocessor (6) for evaluation and analysis of the signals of the at least one sensor (2, 3, 4), characterized in that the microprocessor (6) contains a software program with a learning algorithm based on multi-resolution for the analysis of the signals of the at least one sensor (2, 3, 4).
8. Danger detector according to claim 7, characterised in that, through the learning algorithm, on the one hand an analysis of the said sensor signal as to its repeated or regular occurrence and on the other hand a validation of the result of the analysis is undertaken, and that the learning uses wavelets, preferably "biorthogonal" or "second generation" wavelets for the validation.
9. Danger detector according to claim 8, characterised in that the learning algorithm uses neuro-fuzzy methods.
10. Danger detector according to claim 9, characterised in that the learning algorithm contains the two equations $${\mathrm{f}}_{\mathrm{m}}\left(\mathrm{x}\right)\mathrm{=}\mathrm{\Sigma }{\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{,}\mathrm{n}}\mathrm{\cdot }{\mathrm{\varphi }}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left(\mathrm{x}\right)\left(\mathrm{\Sigma \; over\; all\; n}\right)$$

    

    and $${\hat{\mathrm{c}}}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left(\mathrm{k}\right)\mathrm{=}\mathrm{\Sigma }{\mathrm{\varphi }}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\cdot {\mathrm{y}}_{\mathrm{i}}\mathrm{/}\mathrm{\Sigma }{\mathrm{\varphi }}_{\mathrm{m}\mathrm{,}\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}\right)\left(\mathrm{\Sigma \; over\; all\; i}\mathrm{=}1\mathrm{to\; k}\right)$$

    

    in which ϕ_m,n designates scaling functions, ĉ_m,n approximation coefficients and y_k the kth input point of the neuronal network and ϕ_m,n is the dual function of ϕ_m,n.

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