JP2017227452A - Device and method for calculating propagation loss - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a device and a method for calculating a propagation loss, which are capable of reducing a calculation amount by representing a parameter for determining the propagation loss fluctuating in time by the time fluctuation of a plurality of variables based on a standard normal distribution.SOLUTION: The calculation method for calculating a propagation loss for predicting sonar performance by using a parameter that fluctuates in time and determines the propagation loss performs main component analysis representing the time fluctuation amount of the parameter by a plurality of main components not fluctuating in time and a plurality of independent coefficients x fluctuating in time for the parameter fluctuating time, calculates a polynomial coefficient a for representing the coefficients x by the polynomial of a plurality of variables ξ based on a standard normal distribution, calculates the coefficient x of a main component on the basis of the polynomial coefficient a and the variables ξ, calculates a parameter on the basis of the coefficient of the main component and the main component, calculates a sample propagation loss by using a propagation model on the basis of the parameter, calculates the coefficient h of polynomial chaos development, and calculates the propagation loss as a function of the variables ξ.SELECTED DRAWING: Figure 2

Description

  The present invention relates to a propagation loss calculation apparatus and calculation method when propagation loss fluctuates with time.

  The sonar detects the presence of the target by receiving a sound wave radiated from the target or a sound wave transmitted from the sonar and transmitted by the target and propagated through the ocean. In order to predict the performance of such a sonar, it is indispensable to calculate propagation loss by simulating sound wave propagation.

  Since the sound wave propagation in the ocean is affected by the sound velocity distribution c (r, z), the sound wave propagates while being refracted. Here, in the sound velocity distribution c (r, z), “r” indicates a distance from the sonar. “Z” indicates a depth from the sea surface. Therefore, when the sound speed distribution fluctuates with time, it is necessary to predict the fluctuation of the sonar performance by calculating the fluctuation of the propagation loss according to the fluctuation.

  As a method for predicting the sonar performance along with the variation, for example, there is a method using a Monte Carlo method. This is a method of generating many samples of the sound velocity distribution c (r, z, t) that fluctuate with respect to time t and predicting the sonar performance for each sample. However, this method has a problem that the calculation amount increases because it is necessary to calculate the propagation loss by the sound wave propagation model in the prediction for each sample.

  Therefore, in recent years, a method has been proposed that reduces the amount of calculation for calculating the propagation loss when the Monte Carlo method is used by approximating the propagation loss by polynomial approximation. For example, Non-Patent Document 1 describes a method of reducing the amount of calculation using a method called “polynomial chaos expansion method”.

Here, the polynomial chaos expansion method will be schematically described.
First of all, there is variable ξ _1, ξ _2, ···, function h for _{ξ N (ξ 1, ξ 2} , ···, ξ N) think of. When N variables ξ ₁ , ξ ₂ ,..., Ξ _N independently follow a standard normal distribution, the function h (ξ ₁ , ξ ₂ ,..., Ξ _N ) is Hermitian shown in Equation (1). It can be approximated by a linear combination of polynomials H _m (ξ ₁ , ξ ₂ ,..., Ξ _N ). In Equation (1), “m” indicates the degree of the polynomial, and “h _m ” indicates the coefficient of linear combination.

Further, Hermite polynomials _{H m,} in general, the variable xi] _1, xi] _2, · · ·, for two functions f and g for xi] _N, when you define the inner product as shown in equation (2), Equation (3) The orthonormality shown in FIG. Further, the function w (ξ ₁ , ξ ₂ ,..., Ξ _N ) in the equation (2) is a weight function and can be expressed by the equation (4).

Here, the above-described polynomial chaos expansion is applied to the sonar performance fluctuation prediction due to the temporal variation of the sound velocity distribution, and the variables ξ ₁ , ξ ₂ ,..., Where the temporal variation of the sound velocity distribution follows a plurality of independent standard normal distributions. and it could be represented by xi] _N.
In this case, the propagation losses, these variables _{ξ 1, ξ 2, ···,} ξ N function _{TL (ξ 1, ξ 2,} ···, ξ N) can be expressed as. And this function TL (ξ ₁ , ξ ₂ ,..., Ξ _N ) can be expressed as Equation (5) using the approximate equation of Equation (1) described above. As a result, it is possible to reduce the amount of calculation for predicting the fluctuation of the sonar performance by the Monte Carlo method.

By the way, as a main factor of the time variation of the sound velocity distribution, for example, “internal wave” can be cited. Internal waves are the same as waves generated on the sea surface due to external forces such as winds and tides on the sea surface acting on the seawater that is stratified so that the density gradually increases from the sea surface toward the sea floor. In addition, it is a wave that occurs on a uniform surface below the sea level.
When the displacement in the depth direction of the equal density surface due to the internal wave at time t is ζ (r, z, t) and the sound velocity distribution when no internal wave is generated is c ₀ (r, z), it fluctuates depending on the internal wave. The sound speed distribution c (r, z, t) to be expressed can be expressed by Expression (6) (see Non-Patent Document 2, for example).

Here, the sound speed distribution obtained by the above-described equation (6) is discretized in a space consisting of depth and distance, and the sound speed at each point is expressed as c _ij = c (r _i , z _j , t) (i = 1,2 , ···, I, j = 1,2 , ···, when a J), propagation loss TL that varies according to the speed of sound distribution change, a function of _{c ij TL (c 11, c} 12, · .., C _1J , c ₂₁ , c ₂₂ ,..., C _2J ,..., C _I1 , c _{I2 ,.} Therefore, the fluctuation of the sonar performance can be predicted by calculating the propagation loss according to the fluctuation of the variable c _ij .

Steven Finette, "A stochastic representation of environmental uncertainty and its coupling to acoustic wave propagation in ocean waveguide," J. Acoust. Soc. Am. 120 (5), 2006 John Colosi and Michael Brown, "Efficient numerical simulation of stochastic internal-wave-induced sound-speed perturbation field," J. Acoust. Soc. Am. 103 (4), 1998

However, the variable c _ij described above is not an amount that varies independently according to the standard normal distribution. This is a phenomenon in which the displacement ζ (r _i , z _j , t) due to the internal wave is a wave phenomenon, and the change in sound velocity Δc (r _i , z _j , t) = dc / dz · ζ (r _i ) due to this displacement. , Z _j , t) is not independent for each point (r _i , z _j ).

  Therefore, the propagation loss TL that is a function of the variable cij cannot be approximated as shown in the equation (7) obtained by using the equation (1). Therefore, in this case, it becomes necessary to perform prediction by the Monte Carlo method.

  Therefore, first, let us consider expressing the temporal variation of the sound speed distribution by the variation of a plurality of independent variables. For example, Non-Patent Document 1 described above proposes to apply a method called principal component analysis as a method of representing temporal fluctuations in sound velocity distribution by fluctuations of a plurality of independent variables.

By applying this principal component analysis, the change in sound velocity Δc (r _i , z _j , t) is caused by a plurality of principal components Δc ₁ (r _i , z _j ), Δc ₂ (r _i , z _j ) that do not vary with time. ,..., Δc _L (r _i , z _j ). The change in sound speed Δc (r _i , z _j , t) can be expressed by a linear combination of principal components as shown in equation (8). At this time, L independent coefficients x ₁ (t), x ₂ (t),..., X _L (t) change with time.

Here, if these coefficients x ₁ (t), x ₂ (t),..., X _L (t) can be determined, the sound velocity distribution c (r _i , z _j , t) can be expressed by the formula ( Since it is uniquely determined as shown in 9), the propagation loss TL can also be uniquely determined.

Therefore, when the propagation loss TL is considered to be a function of the coefficient x _l (l = 1, 2,..., L), if the coefficient x _l follows the standard normal distribution, the propagation loss TL is It can be expressed as shown in equation (10) obtained by applying the form of equation (1).

However, for the coefficients x _l of the main component is also not always follow a standard normal distribution. Therefore, even if the propagation loss TL in a case of considering that the function of the coefficient x _l of principal component analysis, it is impossible to express the propagation loss TL in the form of equation (1) as shown in equation (10) There was a problem.

Therefore, in order to express such a propagation loss TL in the form of the equation (1), parameters that determine the propagation loss such as the temporally varying sound velocity distribution c (r _i , z _j , t) are changed to a standard normal distribution. Accordingly, there is a demand for a propagation loss calculation apparatus and calculation method that can be expressed by time variations of a plurality of independent variables and can reduce the amount of calculation.

  A propagation loss calculation apparatus according to the present invention is a calculation apparatus that calculates a propagation loss for predicting the performance of a sonar that detects a target by using a time-varying parameter that determines the propagation loss. The principal component analysis expressing the temporal variation amount of the parameter with a plurality of principal components that do not vary with time and a plurality of independent coefficients x that vary with time is performed on the variation amount of the parameter. A principal component analysis unit, a polynomial coefficient calculation unit for calculating a polynomial coefficient a for representing the coefficient x obtained by the principal component analysis unit by a polynomial of a plurality of variables ξ according to a standard normal distribution, and the polynomial coefficient calculation unit A polynomial approximation unit that calculates a principal component coefficient x based on the polynomial coefficient a obtained by the above and a plurality of variables ξ according to the standard normal distribution given as a sample, and the polynomial approximation Based on the coefficient of the principal component obtained by the unit and the principal component obtained by the principal component analysis unit, the reconstruction unit for calculating the parameter, and the parameter obtained by the reconstruction unit, A sample propagation loss calculation unit that calculates a sample propagation loss using a propagation model, and a polynomial chaos expansion coefficient calculation unit that calculates a coefficient h of a polynomial chaos expansion based on the sample propagation loss obtained by the sample propagation loss calculation unit And a propagation loss calculating unit that calculates the propagation loss as a function of the plurality of variables ξ that temporally vary according to the standard normal distribution.

As described above, according to the present invention, the sound speed distribution c (r _i , z _j , t) that varies with time can be expressed by the time variations of a plurality of independent variables according to the standard normal distribution. Therefore, the calculation amount of the propagation loss TL can be reduced.

It is the schematic for demonstrating the relationship between the variable x distributed arbitrarily and the variable (xi) according to standard normal distribution. It is a block diagram which shows an example of a structure of the calculation apparatus of the propagation loss which concerns on this Embodiment 1. FIG. It is a block diagram which shows an example of a structure of the polynomial coefficient calculation part of FIG.

Embodiment 1 FIG.
Embodiment 1 of the present invention will be described below.
First, before explaining the first embodiment, the principle for expressing the arbitrarily distributed variable x with the variable ξ according to the standard normal distribution will be described.
In this case, the arbitrarily distributed variable x can be expressed by a polynomial of the variable ξ according to the standard normal distribution, as shown in Expression (11). In this equation (11), “a _k ” indicates a coefficient for each degree of the variable ξ in the polynomial (hereinafter referred to as “polynomial coefficient” as appropriate).

At this time, if information indicating the change of the variable x with respect to the change of the variable ξ can be _obtained , the value of the polynomial coefficient a _k can be determined using a method such as a least square method. Therefore, in this example, the following method is adopted as a method for obtaining information indicating the change of the variable x with respect to the change of the variable ξ.

FIG. 1 is a schematic diagram for explaining the relationship between an arbitrarily distributed variable x and a variable ξ according to a standard normal distribution.
As a general method for generating a random number according to an arbitrary cumulative distribution function F (x), for example, a method called “inverse transformation method” can be cited. As shown in FIG. 1A, the variable x is “F (x) = y” for the value y in the range of the closed interval [0, 1]. As shown in FIG. 1A, the function F (x) is a monotonically increasing function that takes a value in the range of the closed interval [0, 1], and therefore the variable x for “F (x) = y” is , It always exists uniquely as the inverse function F ⁻¹ (y) of the function F (x).

Further, as shown in FIG. 1B, a variable ξ that follows the standard normal distribution from the cumulative distribution function F _normal (ξ) of the standard normal distribution with respect to the same value y is converted into “ξ = F _normal ^{− 1} (y) ".
Thereby, the relationship shown in Formula (12) using the value y as a parameter is established between the variable x that is arbitrarily distributed and the variable ξ that follows the standard normal distribution.

Next, a set of R variables (x _r , ξ _r ) is obtained by applying the relationship of Equation (12) to R parameter variables y _r (r = 1, 2,. ) Is considered.
In this case, since the set of these R variables (x _r , ξ _r ) must satisfy the equation (11), the polynomial coefficient a _k (k = 0, 1,..., K ) Can be obtained as simultaneous equations shown in equation (13).

A polynomial coefficient a _k can be obtained by solving the simultaneous equations shown in Expression (13) using a generalized inverse matrix. That is, the polynomial coefficient a _k can be obtained as shown in the equation (14). Note that the symbol “ ^T ” in “X ^T ” in Equation (14) is a symbol indicating that it is a transposed matrix of the matrix X, and the matrix X is expressed as Equation (15).

By calculating the polynomial coefficient a _k in this way, the arbitrarily distributed variable x can be expressed by a variable ξ according to the standard normal distribution.

[Calculation method of propagation loss]
Next, a method for calculating the propagation loss based on such a principle will be described.
In the first embodiment, a first table indicating a cumulative distribution function of an arbitrarily distributed variable x and a second table indicating a cumulative distribution function of a variable ξ according to a standard normal distribution are created. Then, a third table showing the relationship between the variable x and the variable ξ is created based on the created first and second tables, and the polynomial coefficient of the polynomial shown in Expression (11) is created based on the third table. a _k is calculated.

(How to create the first table)
The first table is a table showing a cumulative distribution function F (x) of an arbitrarily distributed variable x. When creating this first table, first, the minimum value X _min and the maximum value of the sample value x ^(p) (p = 1, 2,..., P) of the arbitrarily distributed variable x. The value X _max is determined. Here, “P” indicates the total number of sample values of the variable x, and the sample value “x ^(p) ” indicates the p-th variable x.
Further, a divided value “X _min = X ₀ <X ₁ <... <X _q−1 <X _q <... <S” that divides the sample value between the minimum value X _min and the maximum value X _max by Q. X _Q = X _max (q = 1, 2,..., Q) ”is created.

Next, the number of sample values x ^(p) included in the interval [X _q−1 , X _q ) formed by the two values X _q−1 and X _q is counted. However, when “q = Q”, the number of sample values x ^(p) included in the section [X _q−1 , X _q ] is counted.
A symbol “[” and a symbol “]” indicating a section indicate that an end point is included as a point of the section. The symbols “(” and “)” indicate that the end points are not included as the points of the section. That is, the section [X _q−1 , X _q ) described above indicates a section that includes the value X _q−1 as an end point and does not include the value X _q as an end point.
Then, a value obtained by dividing the number of sample values in the interval by the total number P of sample values is calculated as a probability density p _q for the midpoint “α _q = (X _q−1 + X _q ) / 2” of the interval. .

Finally, based on Expression (16), the cumulative distribution function F (α _q ) is calculated for each of all q (q = 1, 2,..., Q). As a result, (α _q , F (α _q )) (q = 1, 2,..., Q) can be obtained as the first table.

(How to create the second table)
The second table is a table showing the cumulative distribution function F _normal (ξ) of the variable ξ according to the standard normal distribution. When creating this second table, the cumulative distribution function F _nominal (β _s ) for S values β _s (s = 1, 2,..., S) is calculated based on the equation (17). To do. Thereby, (β _s , F _normal (β _s )) (s = 1, 2,..., S) can be obtained as the second table. Note that the function erf (x) in Expression (17) indicates an error function defined by Expression (18).

(How to create the third table)
The third table is a table showing a relationship between an arbitrarily distributed variable x and a variable ξ according to a standard normal distribution. When creating the third table, first, R values y ₁ , y ₂ ,..., Y _R that can take values in the range [0, 1] are created. Here, “R” is set to a value such that “R ≧ K + 1” with respect to the highest degree K of the polynomial shown in Equation (11).

Next, for each of all r (r = 1, 2,..., R), a general table search is performed on the created first table, and “F (α _q′−1 ) ≦ y _r Search for q _{′ satisfying} ≦ F (α _{q ′} ) ”. Then, based on equation (19), to determine the value _{x r} corresponding to the value _{y r.} In the equation (19), (α _q , F (α _q )) (q = 1, 2,..., Q) is a first table showing the cumulative distribution function F (x) of the variable x. .

Similarly, a general table search is performed on the created second table for each of all r (r = 1, 2,..., R), and “F (β _s′−1 )” is obtained. S _{′ satisfying} ≦ y _r ≦ F (β _{s ′} ) ”is searched. Then, based on equation (20), determines the value xi] _r corresponding to the value _{y r.} Note that (β _s , F _normal (β _s )) (s = 1, 2,..., S) in Expression (20) is a second table indicating the cumulative distribution function F _normal (ξ) of the variable ξ. It is.

Finally, (x _r , ξ _r ) (r = 1, 2,..., R) is obtained as a third table showing the relationship between the arbitrarily distributed variable x and the variable ξ according to the standard normal distribution.

(Calculation method of polynomial coefficient)
Next, a method for calculating the polynomial coefficient _ak in the polynomial shown in Expression (11) will be described.
First, with reference to the value ξ _r in the third table (x _r , ξ _r ) (r = 1, 2,..., R) created as described above, the matrix X is calculated based on the equation (21). Create

Then, referring to the value x _r in the third table (x _r , ξ _r ) (r = 1, 2,..., R), the polynomial coefficient a _k (k = 0, k 1, ..., K) is calculated.

(Propagation loss calculation method)
Next, a method for calculating the propagation loss TL will be described.
Based on the calculation method described above, the polynomial coefficients a _{l, k} (K = 0,1,..., K) for the respective principal component analysis coefficients x _l (l = 1, 2,..., L). ) by calculating the coefficient x _l, using the variables xi] _l of a standard normal distribution, it can be expressed by equation (23).

Thereby, the sound velocity distribution c (r _i , z _j , t) can be expressed as shown in Expression (24). That is, the sound speed variation with respect to time can be represented by a variation of a variable ξ _l (t) (l = 1, 2,..., L) according to a plurality of independent standard normal distributions.

Thus, the propagation loss is a function of the sound-velocity distribution _{c (r} i, _{z j)} is a function TL variables xi] _l can be considered _{(ξ 1, ξ 2, ···} , ξ L) as. That is, the propagation loss TL is calculated based on the equation (25) using the above-described equation (1).

Here, the coefficient h _m of the polynomial chaos expansion can be obtained by the following method.
First, random numbers ξ _l ^(u) (l = 1, 2,..., L, u = 1, 2,..., U) according to the standard normal distribution are generated, and the sound speed distribution is based on the equation (24). determining _{^{c (u) (r i,}} z j). Then, based on the sound velocity distribution, propagation loss TL (ξ ₁ ^(u) , ξ ₂ ^(u) ,..., Ξ _L ^(u) ) is calculated by a sound wave propagation model. Thereby, simultaneous equations shown in the equation (26) can be obtained from the relationship of the equation (25).

Then, by solving the simultaneous equations obtained in this way, by using a generalized inverse matrix, it is possible to obtain the coefficients h _m. Thereby, the propagation loss TL with respect to the variable ξ ₁ which is a random number according to the standard normal distribution generated arbitrarily can be calculated using the equation (25).

  As described above, in the first embodiment, the propagation loss can be approximated and calculated using the variable ξ according to the standard normal distribution.

[Configuration of propagation loss calculation device]
Next, the configuration of the propagation loss calculation apparatus according to the first embodiment will be described.
FIG. 2 is a block diagram showing an example of the configuration of the propagation loss calculation apparatus according to the first embodiment.
As shown in FIG. 2, the calculation device 1 includes a principal component analysis unit 2, a polynomial coefficient calculation unit 3, a polynomial approximation unit 4, a sound speed reconstruction unit 5, a sample propagation loss calculation unit 6, a polynomial chaos expansion coefficient calculation unit 7, and The propagation loss calculation unit 8 is configured.

The principal component analysis unit 2 receives a sound velocity distribution c (r _i , z _j , t _p ) as a parameter that determines the propagation loss. Principal component analysis unit 2 performs principal component analysis input sound-velocity distribution _{c (r i, z j,} t p) with respect to this sound-velocity distribution _{c (r i, z j,} t p) and the above-described As shown in Expression (9), it is expressed by a plurality of principal components that do not vary with time and a plurality of independent coefficients x _l ^(p) that vary with time.

The polynomial coefficient calculation unit 3 receives the coefficient x _l ^(p) output from the principal component analysis unit 2, and uses the above-described equations (16) to (22) to represent the polynomial coefficients in the polynomial shown in the equation (23). a _{l, k} is calculated. The detailed configuration of the polynomial coefficient calculation unit 3 will be described later.

Based on the polynomial coefficients a _{l, k} calculated by the polynomial coefficient calculation unit 3, the polynomial approximation unit 4 changes the coefficient x _l ^(u) according to the standard normal distribution as shown in the above equation (23). Is approximated by a polynomial based on a variable ξ _l ^(u) and a plurality of polynomial coefficients a _{l, k} .
The sound speed reconstruction unit 5 is based on the coefficient x _l ^(u) output from the polynomial approximation unit 4 and the principal component Δc _l (r _i , z _j ) output from the principal component analysis unit 2, ), The sound velocity distribution c ^(u) (r _i , z _j ) is calculated.

The sample propagation loss calculation unit 6 uses the sound propagation model based on the sound velocity distribution c ^(u) (r _i , z _j ) output from the sound velocity reconstructing unit 5 to generate the sample propagation loss TL (ξ ₁ ^(u) , ξ ₂ ^(u) ,... ξ _L ^(u) ) are calculated.
The polynomial chaos expansion coefficient calculating unit 7 is based on the sample propagation loss TL (ξ ₁ ^(u) , ξ ₂ ^(u) ,..., Ξ _L ^(u) ) output from the sample propagation loss calculating unit 6. calculating the coefficients _{h m} of the polynomial chaos expansion using (26).
The propagation loss calculation unit 8 calculates the propagation loss TL (ξ ₁ , ξ ₂ ,..., Ξ _L ) using Equation (25) based on an arbitrary random number ξ _{l according} to the standard normal distribution.

(Configuration of polynomial coefficient calculation unit)
FIG. 3 is a block diagram showing an example of the configuration of the polynomial coefficient calculation unit 3 in FIG.
As shown in FIG. 3, the polynomial coefficient calculation unit 3 includes a cumulative distribution function estimation device 10, a cumulative distribution function calculation device 20, a relationship table creation device 30, and a polynomial coefficient calculation device 40.

The cumulative distribution function estimation device 10 receives a sample value x ^{(p) of} a variable x that is arbitrarily distributed. The cumulative distribution function estimation device 10 uses a first table (α _q , F) indicating the cumulative distribution function F (x) of the variable x using the above-described equation (16) based on the input sample value x ^(p). (Α _q )) is generated and output.

The cumulative distribution function calculation device 20 uses the above-described Expression (17) and Expression (18), and uses the second table (β _s , F _normal ) that indicates the cumulative distribution function F _normal (ξ) of the variable ξ according to the standard normal distribution. (Β _s )) is generated and output.

The relationship table creation device 30 includes a first table (α _q , F (α _q )) output from the cumulative distribution function estimation device 10 and a second table (β _s ) output from the cumulative distribution function calculation device 20. , F _normal (β _s )). Based on these input tables, the relationship table creation device 30 uses the above-described equations (19) and (20) to indicate the relationship between the variable x arbitrarily distributed and the variable ξ according to the standard normal distribution. The table (x _r , ξ _r ) is created and output.

The polynomial coefficient calculation device 40 receives the third table (x _r , ξ _r ) output from the relationship table creation device 30. The polynomial coefficient calculation device 40 uses the above-described Expression (21) and Expression (22) based on the input third table (x _r , ξ _r ), and the polynomial coefficient a _k in the polynomial shown in Expression (11). Is calculated and output.

  As described above, the propagation loss calculation apparatus 1 according to the first embodiment uses a propagation loss for predicting the performance of a sonar for detecting a target as a temporally varying sound speed distribution that determines the propagation loss. The sound velocity distribution is calculated by using a principal component analysis that represents a temporal fluctuation amount of the sound velocity distribution by a plurality of principal components that do not vary with time and a plurality of independent coefficients x that vary with time. And a polynomial coefficient calculation unit for calculating a polynomial coefficient a for expressing the coefficient x obtained by the principal component analysis unit 2 by a polynomial of a plurality of variables ξ according to a standard normal distribution. 3 and the polynomial approximation unit 4 for calculating the principal component coefficient x based on the polynomial coefficient a obtained by the polynomial coefficient calculation unit 3 and a plurality of variables ξ according to the standard normal distribution given as a sample. Obtained Based on the principal component coefficients obtained and the principal component obtained by the principal component analysis unit, the sound speed reconstruction unit 5 that calculates the sound speed distribution, and the propagation model based on the sound speed distribution obtained by the sound speed reconstruction unit 5 A sample propagation loss calculation unit 6 that calculates a sample propagation loss using the sample propagation loss, a polynomial chaos expansion coefficient calculation unit 7 that calculates a coefficient h of the polynomial chaos expansion based on the sample propagation loss obtained by the sample propagation loss calculation unit 6; A propagation loss calculating unit 8 that calculates the propagation loss as a function of a plurality of variables ξ that temporally vary according to the standard normal distribution;

  As described above, according to the first embodiment, the propagation loss TL necessary for predicting the sonar performance can be expressed as a function of the variable ξ according to the standard normal distribution. Therefore, when calculating the propagation loss TL, a polynomial chaos expansion method can be used, and the amount of calculation can be reduced.

Embodiment 2. FIG.
Next, a second embodiment of the present invention will be described.
In the first embodiment described above, the underwater sound speed distribution c (r, z) is focused on as a parameter for determining the propagation loss. However, such a parameter can be applied to other than the sound speed distribution. Therefore, in the second embodiment, “depth” is focused as a parameter other than the sound velocity distribution that determines the propagation loss.

For example, the target depth Z for which the presence of the sonar is to be detected is one of the parameters that determine the propagation loss, but the depth is often unknown in advance.
When the uncertainty of the target depth Z is expressed by a normal distribution with an expected value Z ₀ and a variance σ _z ² , the target depth Z can be expressed as in Expression (27) using a variable ξ _z according to the standard normal distribution. it can.

  Therefore, the propagation loss TL can be expressed as in Expression (28) by using the form of Expression (1) described above.

On the other hand, when the uncertainty of the target depth Z cannot be expressed by a normal distribution, the target depth Z can be expressed as in Expression (29) by using the form of Expression (11) described above.
Then, by obtaining the polynomial count a _{z, k} that satisfies this equation (29), the target depth Z can be expressed by a variable ξ _z according to the standard normal distribution, so that the propagation loss TL is expressed by the equation (28). It is possible to express as follows.

The parameters that determine the propagation loss are not limited to the sound velocity distribution or the target depth, and include, for example, the water depth, the sound wave reflection coefficient at the seabed, and the frequency. The same applies to these parameters. It is.
Further, when there are a plurality of uncertain parameters, the influence of the plurality of uncertainties on the propagation loss can be expressed using the form of equation (1). For example, when the sound velocity distribution is expressed by Expression (24) and the target depth is expressed by Expression (29), the propagation loss can be approximated as shown in Expression (30).

  As described above, according to the second embodiment, even when the target depth is a parameter that determines the propagation loss, as in the first embodiment, the variable in which the propagation loss varies with time according to the standard normal distribution. It can be approximated as a function of ξ.

  As mentioned above, although Embodiment 1 and Embodiment 2 were demonstrated, this invention is not limited to Embodiment 1 and Embodiment 2 mentioned above, In the range which does not deviate from the summary of this invention, it is various. Various modifications and applications are possible.

  For example, in the first embodiment, linear interpolation is used to create the third table indicating the relationship between the variable x that is arbitrarily distributed and the variable ξ that follows the standard normal distribution. Any method may be used as long as the sample values set in can be interpolated. Specifically, for example, a method called spline interpolation can be used as such an interpolation method.

  Further, in the above-described example, when calculating the polynomial coefficient, specifically, the solution is calculated by minimizing the sum of squares of the difference using, for example, a generalized inverse matrix, but the present invention is not limited to this. The polynomial coefficient may be calculated using another method. Specifically, for example, the solution may be calculated so as to minimize the sum of the absolute values of the differences.

  DESCRIPTION OF SYMBOLS 1 Calculation apparatus, 2 Principal component analysis part, 3 Polynomial coefficient calculation part, 4 Polynomial approximation part, 5 Sonic reconstruction part, 6 Sample propagation loss calculation part, 7 Polynomial chaos expansion coefficient calculation part, 8 Propagation loss calculation part, 10 Cumulative Distribution function estimation device, 20 cumulative distribution function calculation device, 30 relation table creation device, 40 polynomial coefficient calculation device.

Claims (6)

A calculation device that calculates a propagation loss for predicting the performance of a sonar that detects a target using a time-varying parameter that determines the propagation loss,
A principal component analysis in which a temporal variation amount of the parameter is represented by a plurality of principal components that do not vary with time and a plurality of independent coefficients x that vary with time is performed on the variation amount of the parameter. Component analysis unit;
A polynomial coefficient calculation unit for calculating a polynomial coefficient a for expressing the coefficient x obtained by the principal component analysis unit by a polynomial of a plurality of variables ξ according to a standard normal distribution;
A polynomial approximation unit for calculating a principal component coefficient x based on the polynomial coefficient a obtained by the polynomial coefficient calculation unit and the plurality of variables ξ according to the standard normal distribution given as a sample;
A reconstruction unit for calculating the parameter based on the coefficient of the principal component obtained by the polynomial approximation unit and the principal component obtained by the principal component analysis unit;
Based on the parameters obtained by the reconstruction unit, a sample propagation loss calculation unit that calculates a sample propagation loss using a propagation model;
A polynomial chaos expansion coefficient calculation unit that calculates a coefficient h of polynomial chaos expansion based on the sample propagation loss obtained by the sample propagation loss calculation unit;
A propagation loss calculation apparatus comprising: a propagation loss calculation unit that calculates the propagation loss as a function of the plurality of variables ξ that temporally vary according to the standard normal distribution. The polynomial coefficient calculation unit includes:
The cumulative distribution function F of the coefficient x that is arbitrarily distributed is estimated, and the inverse function F ⁻¹ (y) of the estimated cumulative distribution function F with respect to a plurality of values y that can take a value in the range of 0 to 1 A cumulative distribution function estimation device whose value is the coefficient x;
A cumulative distribution function calculation apparatus using the variable ξ as a value of the inverse function F ⁻¹ _normal (y) of the standard normal distribution cumulative distribution function F _normal for the plurality of values y;
The apparatus according to claim 1, further comprising a polynomial coefficient calculation device that calculates the polynomial coefficient a based on a plurality of sets (x, ξ) based on the coefficient x and the variable ξ corresponding to the same value y. Propagation loss calculation device. The polynomial coefficient calculation unit includes:
A first table (α _q , F (α _q )) indicating a cumulative distribution function of the coefficient x that is arbitrarily distributed is created by the cumulative distribution function estimation device;
A second table (β _s , F _normal (β _s )) indicating a cumulative distribution function of the variable ξ according to a standard normal distribution is created by the cumulative distribution function calculation device,
Based on the first table, a value _{q ′} that satisfies F (α _q′−1 ) ≦ y ≦ F (α _{q ′} ) with respect to the value y, and a value y based on the second table. On the other hand, a value s _{′ that} satisfies F (β _s′−1 ) ≦ y ≦ F (β _{s ′} ) is searched,
Based on the obtained value q ′, the coefficient x is calculated by interpolation,
3. The propagation loss calculation apparatus according to claim 2, wherein the variable ξ is calculated by interpolation based on the obtained value s ′. The parameter is
The propagation loss calculation apparatus according to any one of claims 1 to 3, wherein the sound loss distribution is based on a distance from the sonar and a depth from the sea surface. The parameter is
It is the depth of the said target object, The propagation loss calculation apparatus as described in any one of Claims 1-4 characterized by the above-mentioned. A calculation method for calculating a propagation loss for predicting the performance of a sonar for detecting a target using a time-varying parameter that determines the propagation loss,
Analysis in which a principal component analysis that represents a temporal variation amount of the parameter as a plurality of principal components that do not vary with time and a plurality of independent coefficients x that varies with time is performed on the variation amount of the parameter. Steps,
A polynomial coefficient calculating step for calculating a polynomial coefficient a for expressing the coefficient x obtained by the principal component analysis by a polynomial of a plurality of variables ξ according to a standard normal distribution;
A polynomial approximation step for calculating a principal component coefficient x based on the polynomial coefficient a obtained by the polynomial coefficient calculation step and the plurality of variables ξ according to the standard normal distribution given as a sample;
A reconstruction step of calculating the parameters based on the coefficients of the principal components obtained by the polynomial approximation step and the principal components obtained by the principal component analysis;
A sample propagation loss calculation step for calculating a sample propagation loss using a propagation model based on the parameters obtained by the reconfiguration step;
A polynomial chaos expansion coefficient calculation step for calculating a coefficient h of polynomial chaos expansion based on the sample propagation loss obtained by the sample propagation loss calculation step;
A propagation loss calculating step of calculating the propagation loss as a function of a plurality of the variables ξ that temporally vary according to the standard normal distribution.

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