RU190531U1 - The device indicating the change in risk of strong earthquakes on the results of multichannel observation with interruptions - Google Patents

Abstract

The device of indication of change in risk according to the results of multichannel observation with interruptions (URI) is a device designed to analyze time series (BP) in order to detect the anomalous behavior of the observed object (s). URI can be used when building complexes for rapid assessment of changes and predicting the risks of strong earthquakes, for example, from observations of volumetric radon concentrations from sensors located in a seismically dangerous area. The calculators of the main components 1; storage and sampling unit 2; syndrome calculator 3; a unit for computing a collective behavior signal 4; assessment and decision block 5, which can be performed as a risk indicator for utility model No. 159604. The design of the ACM is resistant to changes in the number of observed time series (for example, due to sensor failure); This stability is ensured by combining the storage and sampling unit 2 and the syndrome 3 calculator that were used to analyze the part of the BP observation history that corresponds to the processing channels currently functioning (in a particular case, to the functioning sensors). radon concentration from sensors of the observation system of the geodynamic test site of the Kamchatka Branch of the Geophysical Survey of the Russian Academy of Sciences gave satisfactory results at Nke risk of strong (with a magnitude above 5.6) earthquakes and showed the stability of the work to failure of 20-30% of sensors. 4 hp f-ly, 16 ill.

Description

Technical field

The device indicating the change in the risk of strong earthquakes according to the results of multichannel observation with interruptions (URI) is a device designed to detect reference points when analyzing time series (BP) of radon concentration [11], with the aim of short-term prediction of strong earthquakes.

The device can be used in areas of practical activity, where there is the task of monitoring a certain set of BP in order to identify the anomalous behavior of the object (s).

Weir can be applied:

- when identifying precursors of natural hazards and anomalous behavior of technical objects in order to prevent man-made disasters;

- to diagnose the status of operators in critical areas of manual control,

It can also improve the quality and functionality:

- various security systems;

- systems of medical equipment used to monitor the condition of patients, etc.

The level of technology. Analogs and their disadvantages

For the analysis of BP, among others, analyzers are used, which, when representing BP, use the eigenvectors (SV) of the covariance matrices (QM) and the main components (PS) [6, 7]. A utility model [1] is such an analyzer, called “Eigenvector Analyzer and Signal Component” or “Eigenoscope” (from the “eigenvector” - “eigenvector”). The design of the eigenoscope is shown in FIG. 1. In this construction, from the initial BP, subjected to scaling and analog-to-digital conversion in block 18, in block 19 a matrix of mixed moments is formed (in the simplest case KM), then in block 20 its EI and eigenvalues (SOC) are calculated; thus obtained CBs are used to represent the initial BP in block 21; In the same block, the signs of BP, CB and C3 are analyzed using various statistical methods.

Calculating the CM in the current time requires the accumulation of data on BP. After the data have been accumulated, they need to be turned into a CM estimate. Getting CB and Sz from KM also requires some time to calculate. Thus, there is some delay from the start of the BP analysis to the receipt of the NE and SZ. If BP is non-stationary, the CM changes over time, and its evaluation periodically needs to be updated.

After the eigenoscope has entered the established mode of operation (i.e., the current KM evaluation is formed), at the output of block 20 at each moment of time there is a set of SVs that correspond to the current KM assessment. These CBs are used to represent BP; for this, in the eigenoscope, at each current time, a matrix-column of the coefficients of the BP decomposition in the orthonormal basis of the SV, that is, the column-matrix, is calculated:

ψ _{M × M} (T) is a square matrix of size M × M, the columns of which are SV for KM at time T,

X (T) is the BP segment (matrix-column) on the interval of analysis of the length M, immediately preceding the current moment T,

α (T) is the matrix-column of the Ledger at the moment of time T,

M - the length of the analysis interval, (coincides with the dimension of KM and the number of CB),

T is the current time

(...) '- transpose.

и

, каждый столбец которых представляет собой столбец ГК некоторых сегментов BP.From the Ledger, obtained using the relation (1), can be formed matrix

and

, each column of which is a GC column of some BP segments.

Matrices A _{M × n} (T) and B _{M × m} (T) can be used at each time point T to detect changes using discriminant analysis methods (YES).

и

и формирует матрицы наблюдений А_М×n(Т) и B_T×m(T) с использованием значений ГК для этих последовательностей времен. Значение ДК совпадает со значением критерия дискриминации, определенного на основании матриц A_M×n(Т) и B_T×m(Т) для каждого текущего момента времени Г.For the first time, the problem of identifying differences between two sets of multidimensional observations was proposed and solved by Fisher [5] and later received [6] the name of the YES problem. To identify differences with the use of YES, the so-called discriminant function (DF) is constructed [5]. The quality of the solution of the YES problem is evaluated by the discrimination criterion. In the case when the dependence of the discrimination criterion value [6] on time is used to detect changes in BP, the discriminant function (DF) is generalized to the so-called. discriminant functional or discriminant collector (DC) - [3, 4]. DK uses in its work two functionally associated with the current time T sequence of times

and

and generates observation matrices A _{M × n} (T) and B _{T × m} (T) using the values of the Ledger for these sequences of times. The value of the DC coincides with the value of the discrimination criterion, determined on the basis of the matrices A _{M × n} (T) and B _{T × m} (T) for each current time point G.

In DC there are: type, structure and capacity. Type DK is determined by the criterion that is used in the construction of the DF. The structure is determined by the mutual arrangement of points in time in the sequences t _A and t _B. Capacities are determined by the values of m and n.

This approach is implemented in the utility model [2], which was called the Signaling Device for Significant Differences, the design of which is shown in FIG. 2

The disadvantage of this construction is the delays associated with the need to form for each moment of the current discrete time T two observation matrices А _{М × n} (T) and B _{T × n} (T) from GC corresponding to previous positions of BP segments, and the quality of detecting changes can depend on m and n. The increase in these values, on the one hand, increases the reliability of the detection of changes, and on the other, it may be unacceptable to reduce the forecast horizon.

This disadvantage is eliminated in the “Signaling device for changes in principal components” (SIGC) [9], in which it is proposed to use the product of the Ledger (or the value of the geometric mean (SG) - [7] monotonically associated with this product) as a statistic to make a decision without delay. ).

FIG. 3 shows the design of SIGK. The time series from the SIGK input is fed to the input of the scaling unit and ADC - 18, from the output of which goes to the covariance matrix calculating unit - 32. In block 32 for a certain time interval preceding the current moment, usually several tens of times larger than KM M , using any known algorithm [7], we construct the estimate KM K _{M × M} (T). From the output of block 32, this estimate is fed to the input of the block for calculating eigenvectors 33. In block 33, the problem of calculating CB for K _{M × M} (T) is solved. The matrix CB is transmitted from the output of block 33 to the first input of the calculator of scalar products and multiplication 34. The digitized BP enters the second input of block 34 from the output of scaling unit 1 and ADC. In block 34, for each current point in time, a matrix is formed in a column of a BP segment of duration M, consisting of M samples preceding the current point in time. Next is the calculation of the civil code by the formula (1). Thus, at each moment of time T, a matrix-column of the Ledger α (T) is obtained, which includes M values. Then these GCs are multiplied, and the resulting value is fed to the output of the device. The value of the product is compared with a user-defined decision threshold. Exceeding the threshold is considered as a reference point (a precursor of the predicted event).

Prototype

As a prototype, the device of the indicator of changes of the main components is chosen - FIG. 3. We emphasize that the disadvantage of the prototype is the partial loss of properties when individual sensors fail to be connected to its input.

Indeed, when using in real conditions analogs and prototypes for processing geophysical data, a problem arises related to the nonideality of the used multidimensional time series (MVR); Since MVR is obtained from sensors that have ultimate reliability, gaps appear in one-dimensional time series (BP) (together with the components of the MVR), which leads to partial loss of performance.

Disclosure of utility model

Purpose and benefits: ensuring minimal loss of performance and automatic restructuring of the structure - in the conditions of interruptions in observations coming from part of the sensors.

The result is achieved due to the fact that in the proposed design, each processing channel generates a significant number of main components, which allows to maintain the performance characteristics of the structure even in the event of a failure of several sensors.

In the prototype, a change in the number of working sensors requires a restart of the device, while in the proposed utility model, due to the design features, uninterrupted operation is provided while maintaining the potentially possible performance characteristics.

FIG. 4, 5, 6, 7 shows the design of the devices offered in the utility model. These devices differ from each other only in the design of their output part, included after block 4. Therefore, we begin the description with the general part of these structures.

Each input of the ACI (the number of inputs of the ACM is equal to U) is connected to its block 1 of the main component calculator, the design of which has the form shown in FIG. five.

Block 1 consists of a block for calculating the matrix of mixed moments 7, a block for calculating and selecting eigenvectors 8, a calculator for scalar products 6 and works as a specialized eigenoscope with a design similar to [1].

All U outputs of the calculator of the main components 1 are connected to the 1st - Um inputs of the storage and sampling sets of the values of the main components 2, in which the sets of GC values from all U outputs of blocks 1 are accumulated for successive points of discrete time. At each of the discrete points in time at the output 1 of block 2, a set of bursts appears, which is fed to the input of the syndrome calculation unit 3. This set of bills corresponds to the last analyzed time point.

To explain how the Syndrome 3 Computing Unit works, the following should be clarified. BG in blocks 1 may not be always calculated. The reason for the impossibility of calculating the Ledger is the failure of the sensors connected to the inputs of the URI, which leads to interruptions in the BP arriving at the inputs of the URI. We consider this situation in more detail below; now it is enough to note that in the case when any of the U blocks of 1 cannot calculate the GC, instead of the numerical value of the GC, it writes into memory of block 2 some special code that captures (identifies) the situation “there is no GC value”. We will abbreviate to call this identifier no GK. Let us enumerate in order all GCs arriving at the inputs of block 2. A syndrome is a vector that has a dimension that coincides with the number of GCs entering the input of block 2. Syndrome coordinate is 1 if the corresponding GC syndrome coordinate number is numeric; the coordinate of the syndrome takes the value 0 if the corresponding coordinates of the GC syndrome number have the identifier “no GK”. Thus, in block 3, the syndrome is calculated for each current point in time, and its value is fed to the 2nd input of the block for computing the signal of collective behavior of the main components 4.

From the output 2 of the block 2 to the 1st input of the block 4 the sets of bills are received for all successive moments of time, including the last one. Each of the sets of GC is a vector, the dimension of which corresponds to the dimension of the syndromes. In the unit for computing the signal of collective behavior of the main components 4, the GC vector is compared with the values of the syndromes. If in the Ledger vector at the positions corresponding to the single positions of the syndrome, there are numerical values, then for such sets of Ledger, the EUC is calculated, which is then fed to the input of the upper unit for the likelihood ratio of the occurrence of an earthquake at the current time and making a decision on the prediction of the occurrence of an earthquake 5 .

The top estimator for the likelihood ratio of the occurrence of an earthquake at the current time and the decision to predict the occurrence of an earthquake 5, shown in FIG. 6, consists of a block for selecting the last value of the collective behavior signal of the main components 9, a block for calculating quantile 10 and a block for visual analysis and comparison 11. In block 10, based on a sample of the values of the UPC input to the block from the output of block 4, the quantile scale is calculated transmitted to the second input of block 11, in which the evaluation and comparison of the last value of the EUCS received from the output of block 9 to the first input of block 11 takes place, with the value of quantile and the detection of anomalies of the UPC.

In the design of the ACU presented in FIG. 7 (item 2 of the MTF), as the upper unit of assessment for the likelihood ratio of earthquake occurrence at the current time and making a decision on the prediction of an earthquake 5, an indicator of the risk of a strong earthquake is used, having the design of a risk indicator according to item 1 In this case, a digitized series of anomalous events (OPAC) - earthquakes - is fed to the first input of block 5 of the strong earthquake risk indicator, and its second input is connected to the output of block 4. At the output of block 5, the upper estimate for the likelihood function - a posteriori (obtained in the result of observations) of the probability of an earthquake to its a priori (before observation) probability and the likelihood ratio for the time of occurrence of earthquakes, obtained by convolution from the top for the right function Similarity to the adaptive filter configured on the OPAC values - [15]. The design of a risk indicator for a strong earthquake, made in the form of a risk indicator according to claim 1 of the MTF [15], is shown in FIG. eight.

Let us dwell on the work of blocks 1-4 of the construction of FIG. 4 and FIG. 7 and their relationships in detail. Let us begin with block 1 of the main component calculator, the design of which is shown in FIG. 5. In block 7, the current KM estimate is calculated.

^(Z) K _{M, M} (T) - KM estimate for Z-th BP,

^(Z) X _{M, (T-M + 1)} - trajectory matrix of size M × (T-M + 1) for Z-th BP,

(...) '- matrix transposition,

(Z) k _{i, j} is the covariance coefficient for the i-th and j-th samples of the Z-th BP on the analysis interval,

m is the analysis interval, T is the current time of the discrete time T> M.

The coefficients of covariance and the trajectory matrix are determined by the relations:

Where

^(Z) S _i - i-th count of Z-th BP

d is the element number of the ensemble, taking all integer values from 1 to T-M + 1. In the general case, the index d takes a value from some set of integers in the range from 1 to T-M + 1 (for example, with a fixed non-unit step).

In the block of calculation and selection of eigenvectors 8 for each point in time, according to the estimate of CM (2), using standard means, we calculate the CB and SZ, which satisfy the relation [7]

where ^(Z) ψ _i (T) and ^(Z) λ _i (T) - i-th CB (matrix-column) and i-th СЗ (number), corresponding to KM Z-th BP, determined at the moment of discrete time T .

Since only CBs are used in the work of CID and SZ are not used, it is sufficient to use only the numerator when calculating the CM using the formulas (2) or (3).

When selecting CBs, used later in calculating the Ledger, a visual analysis of the spectrum of eigenvalues can be used. This analysis uses the normalized spectrum of eigenvalues, which is not affected by the denominator (2) and (3). The question of analyzing the NW spectrum is discussed in detail in the description [1].

и

.We will denote the numerator, which is a matrix proportional to the covariance, and its elements, respectively

and

.

, а результирующая оценка определяется как их суммаAs follows from the above ratios, the assessment of the CM and the CBs determined for it vary (are updated) for each point in time. If there are interruptions in the operation of sensors connected to the URM inputs, then for each j-th BP segment a partial value is estimated without interruptions

and the resulting estimate is defined as their sum

Where

D is the number of continuous (without interruptions) BP segments, the duration of which is not less than M, preceding the current time of the discrete time T,

^(Z) T _j - the moment of termination of the j-th continuous segment of the Z-th BP.

The eigenvectors ^(Z) ψ _i (T) are determined to estimate the matrix (6). It is from these CBs that L CBs are selected, which are fed to input 2 of the calculator of scalar products 6. In the general case, each processing channel can use its own number of CBs.

Each of the sets of selected CBs calculated for the matrix (6) of a specific BP consists of L CBs, which are further used for analysis — each of its own BP. GK BP at a discrete point in time T are determined in block 6 by a relation similar to (1)

Where

- матрица-столбец размера L, в которой каждый j-ый элемент представляет собой скалярное произведение ^(Z)Х(Т) и j-го столбца ^(Z)Ψ_L(T),

- a column matrix of size L, in which each j-th element is the scalar product of ^(Z) X (T) and the j-th column ^(Z) Ψ _L (T),

- матрица-столбец, состоящая из последних М отсчетов Z-ого BP, предшествующих текущему моменту времени Т,

- matrix-column, consisting of the last M samples of Z-th BP, preceding the current time T,

- матрица размера М×L, в которую в качестве столбцов записан Z-ый комплект отобранных СВ.

- matrix of size M × L, in which the Z-th set of selected CBs are recorded as columns.

Naturally, relation (7) is used only when ^(Z) X (T) has no interruptions.

To the number of the most effective ways of forming the UPC in block 4 should be attributed to the geometric mean (SG) for the GC modules [14]. The values of SG for moments of discrete time, starting with the M-th moment after the start of BP or the end of the break BP, is calculated by the formula

Where

H (T) - SG, defined for the moment of discrete time T> M,

- число работающих входов УИР, используемых для вычисления СКП в текущий момент времени,

- the number of active inputs of the ACM used to calculate the EUC at the current time,

L is the number selected in block 8 CB.

When using other methods of forming the UPC, H (t) is calculated by one of the formulas of table 2. The methods of forming the UPC in block 4 of the URI are described in table 2.

The technical result from the use of the design proposed in the prototype, is to significantly reduce the delay due to the replacement of statistical processing (for example YES) on the calculation of the product of the coefficients of decomposition of the BP segment by specially selected CB. The calculation of such a work is possible with almost no delay, as was shown in the description [9].

The most effective significant differences (anomalies) of the collective behavior of the main components are revealed if the quantile scale is used as a threshold for fixing them in time. Recall that quantile

H _q (T) of order q is determined by the relation [7]

Where

H _q (T) is a time-varying quantile,

q is the quantile order,

F _T (...) is the time-varying estimate of the distribution function of the SJS H (T).

Comparison of the last value of the UPC, selected in block 9, with the current value of the quantile value, determined by the formula (9) in block 10 of the structure shown in FIG. 6, is made in the block of visual analysis and comparison 11, the first input of which receives the current value of quantile, and the second - the last value of the UPC.

матрицу строку, имеющую размер М, элементы которой равны единице (если датчик с соответствующим номером работает) и нулю (если датчик с соответствующим номером не работает). Матрица-строка g(T) и есть ранее упоминаемый синдром.As already noted, with devices that implement utility models [2] and [9] in real devices, the problem of interruptions in the operation of sensors arises. This leads to the fact that at each instant of time, the UPC (in the particular case, the geometric mean) is calculated for different numbers of BPs. Naturally, at each moment in time, a quantile should be used as a threshold, determined throughout the whole history, when the sensors operating at time T also worked. Denote

matrix row with the size of M, whose elements are equal to one (if the sensor with the corresponding number works) and zero (if the sensor with the corresponding number does not work). Matrix-row g (T) is the previously mentioned syndrome.

The syndrome is formed in block 3. Note that the sample at the input of block 4 is obtained by selecting those values from those stored in block 2 for which there is a single key value

Where

A - the set of numbers of the unit coordinates of the syndrome, coming through the (U + 1) -th input of block 2,

z _k (t) - at a discrete point in time t takes a single value if the k-th component of the Ledger has a numeric code, and takes a zero value if the k-th component of the Ledger corresponds to the code "no Ledger".

Let the sample at the input of block 10 to the current discrete point in time T be written by the matrix line

Where

H _o (i) - the values of the UPC, calculated from the selected in accordance with (10) of the civil code,

W - the number of selected sets of GC.

по возрастанию и обозначим упорядоченную матрицу-строку

. Тогда оценка квантили, H_q(T) определенная по выборке (11) будет равна

Order

ascending and denote the ordered matrix row

. Then the quantile estimate, H _q (T) determined by the sample (11) will be equal to

Where

floor (...) is the whole part.

The quantile value calculated using (12) is used in block 11.

Let us give a more detailed description of the work of the TLI blocks (Fig. 5 - Fig. 8), revealing the cause-and-effect relationships of the technical result, consisting in the automatic restructuring of the structure - in the conditions of interruptions in observations coming from part of the sensors.

FIG. 7 shows the design of the device indicating the change in the risk of strong earthquakes according to the results of multichannel observation with interruptions (to item 2 of the formula of the utility model).

Block 1 converts the original BP into several BP principal components. The number of CCs depends on the number of CBs selected in block 10, which is part of block 1. In the event that a break appears in the original BP, then the identifier “no ledger” appears at the output of the block, which is transmitted to the corresponding input of block 2 instead of a numeric value.

The input of block 2 of block 1 receives the numerical values of the Ledger or identifiers "no Ledger". All channels of income GK numbered. All incoming at the input of block 2 values are stored in the memory of the block in the form of sets of values GK. Each value of the ledger corresponds to a unique number of the civil code and the number of a discrete point in time.

The set of Ledger values corresponding to the last analyzed (current) moment of discrete time is fed to the input of block 3, in which the syndrome is defined (the vector, the single and zero components of which, in the order of the Ledger numbering, correspond to the numerical values of the Ledger and the no-GK identifiers, respectively). The syndrome is further used to determine the quantile scale, which corresponds to a set of channels of receipt of numerical GK values at the current time.

Sets of bills for all successive points in time, including the last, are transmitted from block 2 for further processing.

In the block for calculating syndrome 3, the syndrome is calculated using the formula

- цикл, V - общее число ГК, F_i - координата синдрома. Результат передается на выход блока.Where

- cycle, V - total number of HAs, F _i - coordinate of the syndrome. The result is transmitted to the output of the block.

In the unit for calculating the collective behavior signal of the main components 4, for each selected matrix of the GC column corresponding to relation (7), the value of the EUC is calculated from the coordinates that correspond to the unit coordinates of the syndrome. So at the output of block 4 a sample of values of the UPC is formed.

In the upper estimator for the likelihood ratio of earthquake occurrence at the current time and deciding on the forecast of occurrence of an earthquake 5, the indicator of the risk of a strong earthquake converts the EUCS coming from the output of block 4 into an amount proportional to the upper estimate for the likelihood ratio of the occurrence of an earthquake at the current time. Predicts the occurrence of earthquakes by smoothing the top estimate for likelihood ratios using adaptive filtering.

FIG. 5 shows the design of the device indicating the change in the risk of strong earthquakes according to the results of multichannel observation with interruptions (under item 3 of the formula of the utility model).

In the calculator block of scalar products 6, the relation (7) is realized for those selected in block 8 CB. If the matrix column ^(Z) X (T) has interruptions (at any position), then at the output of block 6, the identifier “no ledger” is issued.

In block 7, the sum of the components is calculated by the formula (6), representing matrices proportional to the covariance determined for each of the segments of the original BP that have a duration greater than the analysis interval.

Block 8 calculates and selects the eigenvectors for the covariance matrix entering the input of the block - for each current point in time.

FIG. 6 shows the design of the device indicating the change in risk of strong earthquakes as a result of multichannel observation with interruptions (in accordance with paragraph 5 of the MTF).

In block 9, the last value of the ACC CC is selected for further comparison with the quantile value.

In block 10, based on a sample of values of signals of the collective behavior of the main components, a quantile scale of a given level is constructed.

In block 11, the sequence of the current values of the collective behavior signal in the interior of the quantile scale calculated for each current point in time is visualized.

FIG. 8 shows the construction of a risk indicator for a strong earthquake, made in the form of a risk indicator according to claim 1 of the MTF [15].

In block 12 for each discrete point in time T:

1. Based on a sample of the EUCS preceding this current point in time, an estimate of the sample distribution function (VFR) —F _T (x) is constructed.

.2. For the current value of the UPC - X _T , arriving at the second input of the IL, the probability of the current value being exceeded is determined by the VFR using

.

- оценка сверху для отношения правдоподобия возникновения землетрясения, которая подается на вход блока фильтров 14.In block 13, the value is formed

- the top estimate for the likelihood ratio of the occurrence of an earthquake, which is fed to the input of the filter bank 14.

, каждый из которых является сверткой входного сигнала Y_t, с ИХ адаптивного фильтра.In block 14, a group of signals is formed

, each of which is a convolution of the input signal Y _t , with an IH adaptive filter.

In block 15 is determined by the similarity of OPAC - earthquakes and signals from the output of the filter unit 14.

Block 16 outputs at its output a signal from the filter whose number entered the second input of block 16.

In block 17, the values of the upper likelihood estimate of the occurrence of an earthquake and decision making are visualized.

Evidence of technical results. Causal relationships

The main technical results from the use of the claimed structures are:

the stability of the work of the structure of the ACP during interruptions in the operation of the sensors, leading to interruptions in the time series.

FIG. 9-12 are illustrations of the operation of the construction of FIG. 4 and FIG. 7 in conditions where all sensors are working. These illustrations are almost identical to those given in [9]. FIG. 9 shows baseline BP obtained from radon concentration sensors; FIG. 10 - GK values; in FIG. 11 - geometric geometric mean, in FIG. 12 - geometric geometric mean (semi-log scale).

For the period from November 1, 2013 to May 2014, earthquakes in Kamchatka with a magnitude Ml greater than 5.6 were selected (summarized in Table 3).

We illustrate the achievement of the claimed technical results arising from the use of the structures shown in FIG. 4 and 7, and causal relationships leading to the achievement of these technical results.

It is more convenient to begin the illustration with the construction shown in FIG. 7. As a starting point, take the situation presented in FIG. 13.

. Такая визуализация позволяет на одном графике отслеживать поведение синдромов всех датчиков одновременно.FIG. 13a illustrates the unfolding in time of the calculation of the SG and its quantile of the order of 0.75 and 0.95. As can be seen from the upper graph, as the observation continues, the quantile values change, which is a consequence of the change in the estimation of the DF for the SG over time. From the lower graph of FIG. 13a shows that the syndromes of all sensors are rare, which indicates that there are no interruptions in their work. Note that in the lower graph, syndromes are visualized as follows. To the number of the sensor is added the magnitude of the syndrome multiplied by

. Such visualization allows to monitor the behavior of the syndromes of all sensors simultaneously on one graph.

FIG. 13b shows the signal at the output of block 5 shown in FIG. 7. As can be seen from the graph, there are two dominant maxima (reference points), which correspond to 30 and 100 days from the start of the observation (11/01/2013). These reference points correspond with high likelihood anomalies of the UPC.

To convert the upper estimate of the likelihood function of the UPC anomalies into a quantity proportional to the upper estimate of the earthquake likelihood function, a Gaussian filter was used with a characteristic that was optimized on the 2013 data (shown in Fig. 16). As can be seen from the graph of FIG. 13c after the observed increase in the values of the upper estimate of the likelihood function for the occurrence of earthquakes, in fact, two series of three and two earthquakes with a magnitude Ml> 5.6 were observed, respectively.

The situation described above will be considered as basic and we will model the option of sensor failure. FIG. 14 and 15 two variants are presented: FIG. 14 illustrates the interruption situation in the operation of 4 sensors, which began on the 35th day and ended on the 125th day. FIG. 15 shows the situation of complete failure of the 4th sensor. In these two variants, the second sensor did not work during the entire analysis period. The sensor state described above is illustrated by the graphs of the syndromes for the options under consideration (the lower graphs of Figs. 14a and 15a, respectively).

As can be seen from the graphs of FIG. 14b, 15b, 14b, and 15b, likelihood ratios (both for the UPC anomalies and for the moment of the occurrence of an earthquake), make it possible to confidently predict the localization of upcoming earthquakes in time.

This is a consequence of the fact that each processing channel generates a significant number of GCs (in our case, they are GCs, which correspond to CBs with numbers from 2 to 27, that is, there are 26 of them for each sensor); the behavior of the HA in the case of anomalies of the UPC is largely synchronous (see the sharp almost simultaneous increase in all the HAs in Fig. 12); this preserves the operability of the structure even in the conditions of failure of two sensors out of six.

In the prototype, the failure of the sensor led to the fact that the channel was removed from the processing for an indefinite time. Restoring the sensor required restarting the device, which led to its withdrawal from the monitoring mode for the period required for its adaptation (from one month to two months), which, under conditions of time-localized UPC anomalies, leads to an increased probability of missing anomalies.

In the examples discussed above, it is easy to imagine a situation where a break in the fourth sensor would occur on the 25th day, which would mean that we for the first series (out of three earthquakes) would get the results shown in FIG. 15 - until the device is fully adapted after the malfunction of the sensor has been removed. Suppose that the working capacity would be restored within 20 days, and the adaptation period took 60 days, thus the full working capacity of the prototype would be restored to 100 days. Thus, the results of the prototype would be close to the situation presented in FIG. 15. Although the operability of the device (prototype) remains, it is lower than in the case of the claimed design.

Thus, the technical result for the design of FIG. 7 is to maintain efficiency due to the lack of its reduction due to interruptions in work necessary to reconfigure the device after restoring the health of defective sensors. The technical result is caused by the design of the device.

In the case of the construction of FIG. 4 the situation is similar. The only difference is that the quantile is exceeded (not less than about 0.95) as an anomaly of the UPC, after which earthquakes are considered probable for 50-60 days with a probability of 1 / (1-q), where q is the quantile level.

Description of figures - drawings

FIG. 1. Igenoscope - eigenvector analyzer and signal component (Utility Model 116242 RU): 18 - scaling unit and ADC, 19 - calculator of the matrix of mixed moments, 20 - block for calculating eigenvectors and eigenvalues, 21 - calculator for scalar products and analyzer signs.

FIG. 2. Signaling device of significant differences (Utility Model No. 133642 RU): 22 — a unit of measurement, preprocessing, and the formation of a matrix of observations; 23 is a block for calculating the discriminant function; 24 is a block of memory, visualization, control and decision making; 25 - block indexing matrices of compared sets; 26 - unit of measurement, storage and sampling; 27 - block computing scalar products; 28 — block of formation of observation matrices; 29 - block calculator matrix of mixed moments; 20 is a block for calculating eigenvectors and eigenvalues; 31 - eigenvector selector block.

FIG. 3. The signaling device for changes in the main components (Utility Model No. 141416): 18 — a scaling unit and an ADC; 32 - block calculator covariance matrix; 33 — eigenvector calculation unit; 34 - block calculator scalar products and multiplication.

FIG. 4. The device indicating the change in risk of strong earthquakes according to the results of multichannel observation with interruptions (to item 1 of the formula of the utility model): block 1 - calculator of the main components; block 2 is a block for storing and retrieving sets of values for the main components; block 3 is a block for calculating the syndrome; block 4 is a block for calculating the signal of collective behavior of the main components; block 5 is a top estimation block for the likelihood ratio of the occurrence of an earthquake at the current time and making a decision on the forecast of the occurrence of an earthquake.

FIG. 5. The device indicating the change in risk of strong earthquakes according to the results of multichannel observation with interruptions - the construction of unit 1 (according to clause 3 of the formula of the utility model): unit 6 - calculator of scalar products; 7 - block of the calculator of the matrix of mixed moments; 8 is a block for calculating and selecting eigenvectors.

FIG. 6. The device indicating the change in the risk of strong earthquakes according to the results of multichannel observation with interruptions (in accordance with clause 5 of the MTF): block 9 is a block for selecting the last value of the ACS of the AC; 10 — quantile computing unit; 11 - block visual analysis and comparison.

FIG. 7. The device indicating the change in risk of strong earthquakes according to the results of multichannel observation with interruptions (to item 2 of the formula of the utility model): block 1 - calculator of the main components; block 2 is a block for storing and retrieving sets of values for the main components; block 3 is a block for calculating the syndrome; block 4 is a block for calculating the signal of collective behavior of the main components; 5 - the unit of evaluation from above for the likelihood ratio of the occurrence of an earthquake at the current time and the decision on the forecast of the occurrence of an earthquake, made in the form of an indicator of the risk of a strong earthquake on the construction of a risk indicator according to paragraph 1 of the MTF [15].

FIG. 8. The design of the risk indicator of a strong earthquake, made in the form of a risk indicator according to paragraph 1 of the MTF [15]: 12 - unit for estimating the likelihood of exceedance; 13 is a nonlinear conversion unit; 14 - filter unit; 15 is a similarity evaluation unit; 16 - switching unit; 17 - block visualization and decision making.

FIG. 9. Six baseline BP obtained from radon concentration sensors at a geodynamic test site in the area of Petropavlovsk-Kamchatsky in the period from November 1, 2013 to February 12, 2014. The abscissa axis is time from November 1, 2013 in days. The sampling time is 30 minutes.

FIG. 10. The main components (GK) of the initial BP are 2-14 SV of the covariance matrix of size 96 (analysis interval 2 days with a sampling time of 30 minutes).

FIG. 11. The geometric mean of the GC modules, determined according to FIG. 9. The quantile scale is shown (levels 0.95 and 0.99).

FIG. 12. The geometric mean of the GC modules, determined according to FIG. 9 on a semi-log scale.

FIG. 13. An example of calculating the geometric mean and its quantile of the order of 0.75 (dashed line) and 0.95 (dash-dotted line) (the upper graph of Fig. 13a). In the lower graph of FIG. 13a shows sensor syndromes. From the plots of syndromes it follows that all sensors on the analysis interval function. FIG. Figure 13b shows the top estimate for the likelihood ratio versus time when collective behavior anomalies are detected. As can be seen from the graph, significant anomalies are observed at points close to 30 and 100 days from the beginning of the treatment. FIG. 13c shows a smoothed upper likelihood ratio estimate (smoothing was performed using a Gaussian filter with a delay of 50 days and a value of σ = 10 days, the impulse response of which is shown in Fig. 16). The vertical lines in FIG. Figures 13b and 13c show the moments of earthquakes with magnitudes greater than 5.6 (table 3). Used CB with numbers 2-27.

FIG. 14. An example of calculating the geometric mean and its quantile of the order of 0.75 (dashed line) and 0.95 (dash-dotted line) (the upper graph of Fig. 14a). In the lower graph of FIG. 14a shows sensor syndromes. From the plots of syndromes it follows that in the work of the 4th sensor there is a break from 35 to 125 days, and the 2nd sensor did not work during the entire period of analysis; also starting from the 165th day, the first sensor stopped working. FIG. Figure 14b shows the top estimate for the likelihood ratio versus time when a collective behavior anomaly is detected. As can be seen from the graph, significant anomalies are observed at points close to 30 and 100 days from the beginning of the treatment. FIG. 14c shows a smoothed upper likelihood ratio estimate (smoothing was performed using a Gaussian filter with a delay of 50 days and a value of σ = 10 days, the impulse response of which is shown in Fig. 16). The vertical lines in FIG. 14b and 14c show moments of earthquakes with magnitudes greater than 5.6. The comparison of FIG. 14b and FIG. 14b shows that the breaks led to a decrease in the smoothed likelihood estimate from 7 to 6 (the second maximum), as well as to a decrease in the first maximum from 35 to 7.

FIG. 15. An example of calculating the geometric mean and its quantile of the order of 0.75 (dashed line) and 0.95 (dash-dotted line) (the upper graph of Fig. 15a). In the lower graph of FIG. 15a shows sensor syndromes. From the plots of syndromes it follows that the 2nd and 4th sensors did not function on the entire analysis interval, and the 1st one stopped working from 165 days. FIG. 15b shows a top estimate for the likelihood ratio versus time when a collective behavior anomaly is detected. As can be seen from the graph, significant anomalies are observed at points close to 30 and 100 days from the beginning of the treatment. FIG. 15c shows a smoothed upper likelihood ratio estimate (smoothing was performed using a Gaussian filter with a delay of 50 days and a value of σ = 10 days, the impulse response of which is shown in Fig. 16). The vertical lines in FIG. 15b and 15c show the moments of earthquakes with magnitudes greater than 5.6. The comparison of FIG. 14b and FIG. 15c shows that the breaks led to a decrease in the smoothed likelihood estimate from 7 to 6 (the second maximum), as well as to a decrease in the first maximum from 35 to 7.

FIG. 16. Impulse response of a Gaussian filter with which the likelihood ratio evaluation was smoothed. The filter has a delay of 50 days and the parameter σ = 10 days.

The implementation of the invention

The proposed design is used in the construction of complexes of short-term forecasting and rapid assessment of the risk of strong earthquakes.

The design is implemented as a software and hardware complex.

Information sources

1. Grunskaya L.V., Isakevich D.V., Isakevich V.V. Analyzer of eigenvectors and signal components. Useful model RU 116242. Patent holders of BusinessSoftService LLC, Isakevich DV, Isakevich V.V. http://bankpatentov.ru/node/207042

2. Isakevich D.V., Isakevich V.V. Signaling device significant differences. Utility model №133642 RU. The patent holders of BusinessSoftService LLC, Isakevich DV, Isakevich VV, Balakirev A.N. http://bankpatentov.ru/node/414199

3. Isakevich V.V. and others. Identification of non-stationary areas using a non-linear model of the process // Radio Engineering and Electronics. 1995, vol. 40, No. 2, p. 255-260.

4. Grunskaya L.V., Isakevich D.V., Isakevich V.V. and other. Cascades of discriminant functionals in problems of time series analysis in the bases of eigenvectors of covariance matrices. The nonlinear world, No 4, 2012.

5. Fisher R.A. The Use of Multiple Measurements in Taxonomic Problems // Annals of Eugenics. - 1936 T.7. - p. 179-188.

6. Kendall M., Stuart A. Statistical findings and communication. The main editors of the physical and mathematical literature of the publishing house "Science", 1973.

7. Korn G., Korn T. Handbook of mathematics for scientists and engineers: Definitions, theorems, formulas: Trans. from English M .: Science, 1970. 720 p.

8. Isakevich V.V., Firstov P.P., Isakevich D.V., Grunskaya L.V., Makarov E.O. Using the discriminant functionals technique for identifying reference points in the time series of soil radon concentration on the network of points of the Petropavlovsk-Kamchatka geodynamic test site / Problems of integrated geophysical monitoring of the Russian Far East. Proceedings of the Fourth Scientific and Technical Conference. Petropavlovsk-Kamchatsky. September 29 - October 5, 2013 / Otv. ed. V.N. Chebrov. - Obninsk: GS RAS, 2013. P.59-63.

9. Isakevich V.V., Isakevich D.V., Grunskaya L.V., Firstov P.P. Signaling device of main component changes. Useful model №141416. Patentee of the Vladimir State University.

10. Lyubushin A.A. (ml) Aggregated signal of low-frequency geophysical monitoring systems // Physics of the Earth. 1998. №1. Pp. 69-74.

11. Makarov E.O., Firstov PP, Voloshin V.N. Equipment complex for recording the concentration of subsurface gases in order to search for precursor anomalies of strong earthquakes in Southern Kamchatka // Seismic devices. 2012. Volume 48. №1.

12. http://www.emsd.ru/ The official site of the Kamchatka Branch of the Geophysical Service of the Russian Academy of Sciences. Home Page. Section "The last 10 earthquakes of Kamchatka with Ml> 4.5"

13. Ackoff R., Emery F. On purposeful systems. Per. from English Ed. I.A. Ushakov. M .: Owls. Radio, 1974, 272 p.

14. Firstov PL., Isakevich V.V., Makarov E.O., Isakevich D.V., Grunskaya L.V. Testing the method of igenoscopy to search for precursors of strong earthquakes in the field of soil radon ( ²²² Rn) in Kamchatka (August 2012 - August 2013), Seismic instruments, 2014, Т.50, №3, pp. 63-75.

15. Isakevich D.V., Isakevich V.V., Lukyanov V.E. Risk indicator Utility Model RU 159604. Patentee OOO Own Vector, Isakevich DV, Isakevich VV, Balakirev A.N., Chernikov SV.

Claims (5)

1. The device indicating the change in risk of strong earthquakes according to the results of multichannel observation with interruptions, consisting of blocks of the calculator of the main components 1, the storage unit and sampling of the sets of the values of the main components 2, the calculator of the syndrome 3, the unit for calculating the signal of collective behavior of the main components 4, the evaluation unit for the likelihood ratio of the occurrence of an earthquake at the current time and the decision to predict the occurrence of an earthquake 5, characterized in that the inputs of all U blocks of divisors components main device 1 are the inputs, outputs blocks calculators principal component 1 are connected to the 1st - U-th inputs of sets of storage and retrieval unit values of principal component 2; the first output of the storage unit and sampling sets of values of the main component 2 is connected to the input of the calculator of the syndrome 3, which calculates a vector with a dimension that matches the number of the main components entering the input of the block 2, and the coordinate of the syndrome takes the value 1 if the corresponding coordinate number of the syndrome is the main component has a numeric value; the syndrome coordinate takes the value 0 if the main component corresponding to the syndrome coordinate number has an identifier indicating the absence of the main component; the output of the syndrome calculation unit 3 is connected to the second input of the unit for computing the signal of collective behavior of the main components 4; the second output of the storage unit and sampling sets of values of the main components 2 is connected to the first input of the unit for calculating the collective behavior signal of the main components 4, the output of which is connected to the input of the upper estimator for the likelihood ratio of the occurrence of an earthquake at the current time and deciding about the forecast of an earthquake 5; the output of the evaluation unit from the top for the likelihood ratio of the occurrence of an earthquake at the current time and the decision to predict the occurrence of an earthquake 5 is the output of the device; the main component calculator unit 1 transmits a numeric value to the input of the storage and sampling unit of the main component 2 value sets if the main component can be calculated; if the main component cannot be calculated due to a sensor failure, the main component calculator unit 1 transmits an identifier to the storage and sampling unit of the main component 2 values indicating that the main component is missing. 2. The device indicating the change in the risk of strong earthquakes according to the results of multichannel observation with interruptions according to claim 1, characterized in that the indicator of the risk of an earthquake 5 is used as the evaluation unit from above for the likelihood ratio of the occurrence of an earthquake , the second input of which is connected to the output of the unit for computing the signal of collective behavior of the main components 4, to the first input of the evaluation unit from above for the relationship of truth approving the occurrence of an earthquake at the current time and making a decision on the prediction of the occurrence of an earthquake; 5 a digitized series of anomalous events has occurred. 3. The device indicating the change in risk of strong earthquakes according to the results of multichannel observation with interruptions according to claim 1, characterized in that the calculator units of the main components 1 consist of a computing unit for scalar products 6, a computing unit for the matrix of mixed moments 7, a computing unit and selecting eigenvectors 8 at the same time, the input signal of the main component calculator unit 1 is simultaneously connected to the first input of the scalar product calculating unit 6 and to the input of the matrix of the mixed moments 7, the output to torogo connected to the input calculation unit and selecting eigenvectors 8; the output of the computing unit and selection of eigenvectors 8 is connected to the second input of the computing unit for scalar products 6, the output of which is the output of the calculator of the main components 1. 4. The device indicating the change in the risk of strong earthquakes according to the results of multichannel observation with interruptions according to claim 2, characterized in that the calculator units of the main components 1 consist of the computing unit of scalar products 6, the computing unit of the matrix of mixed moments 7, the computing unit and selecting the eigenvectors 8 at the same time, the input signal of the main component calculator unit 1 is simultaneously connected to the first input of the scalar product calculating unit 6 and to the input of the matrix of the mixed moments 7, the output to torogo connected to the input calculation unit and selecting eigenvectors 8; the output of the computing unit and selection of eigenvectors 8 is connected to the second input of the computing unit for scalar products 6, the output of which is the output of the calculator of the main components 1. 5. The device indicating the change of risk of strong earthquakes according to the results of multichannel observation with interruptions according to claim 1, characterized in that the upper unit of assessment for the likelihood ratio of the occurrence of an earthquake at the current time and the decision to forecast the occurrence of an earthquake 5 consists of a unit selecting the last signal value collective behavior of the main components 9, the quantile computing unit 10 and the visual analysis and comparison unit 11, while the input signal of the evaluation unit is from above for the relationship of truth the similarity of the occurrence of an earthquake at the current time and the decision to predict the occurrence of an earthquake 5 are simultaneously connected to the first input of the quantile computing unit 10 and to the input of the selection unit of the last value of the collective component main behavior signal 9, whose output is connected to the first input of the visual analysis and comparison unit 11 , the output of the quantile calculation unit 10 is connected to the second input of the visual analysis and comparison unit 11; the output of the unit of visual analysis and comparison 11 is the output of the upper unit of assessment for the likelihood ratio of the occurrence of an earthquake at the current time and the decision to predict the occurrence of an earthquake 5.

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