Information processing device and program

Abstract

[Problem] To calculate, with higher accuracy than previously, the result of an arithmetic operation of a plurality of parameters having distributions. [Solution] The present invention comprises: an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; a setting unit that sets a first partial region within the range of an output distribution of an output parameter, said first partial region including a first value, and said output parameter being obtained by an arithmetic operation of the first input parameter and the second input parameter; and a generation unit that calculates a distribution value with regard to the first value, on the basis of a distribution value of the first input parameter, a distribution value of the second input parameter, the size of a second partial region, and the size of the first partial region, said distribution value of the first input parameter and said distribution value of the second input parameter each corresponding to the first value and being included in an input parameter range, which is a range defined on the basis of the first input distribution and the second input distribution and is the range formed by the first input parameter and the second input parameter, and said second partial region being included in the input parameter range and corresponding to the first partial region.

Description

[Technical field]

[0001] The present invention relates to an information processing device and a program. [Background technology]

[0002] Conventionally, in a calculation using multiple parameters, if each parameter has a variation (distribution), even if the number of data for each parameter is increased and processed as a distribution, an accurate distribution cannot be obtained, and it is not possible to perform a highly accurate calculation according to the variation of the parameters. This is an essential limit of numerical calculation, and in the calculation of a parameter having a distribution, an accurate calculation can be performed only by performing a distribution calculation based on the distribution of each of the multiple parameters. The distribution calculation is known as a convolution integral. Patent Document 1 discloses a technology for obtaining probability distribution data using a convolution calculation. [Prior art documents] [Patent documents]

[0003] Patent Document 1: Patent Application No. 2014- 12 6500 Summary of the Invention [Problem to be solved by the invention]

[0004] However, convolution and calculus operations are defined for continuous functions and cannot be applied to discrete data such as distributions and histograms extracted from real big data.

[0005] In view of the above problems, an object of the present invention is to obtain the calculation results of a plurality of parameters having distributions with higher accuracy than ever before. [Means for solving the problem]

[0006] The present invention is an information processing device, comprising: an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; a setting unit that sets a first partial region including a first value within a range of an output distribution of an output parameter obtained by an operation between the first input parameter and the second input parameter; a value of the distribution of the first input parameter corresponding to the first value, included in an input parameter range that is a range determined based on the first input distribution and the second input distribution, within a range configured by the first input parameter and the second input parameter; On line A distribution value of the second input parameter and a distribution value of the first partial region included in the input parameter range An area enclosed by a line or an area of ​​the same size as the area in question The apparatus further includes a generating unit that determines a distribution value for the first value based on a size of the second partial region and a size of the first partial region.

[0007] Another aspect of the present invention is an information processing device comprising: an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; and a generation unit that generates a post-change distribution by adding a unit change amount of the second input distribution to the first input distribution, and generates a post-minimal change distribution corresponding to a minimal change amount smaller than the unit change amount based on the first input distribution and the post-change distribution.

[0008] Another aspect of the present invention is a computer including an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter, a setting unit that sets a first partial region including a first value in a range of an output distribution of an output parameter obtained by an operation of the first input parameter and the second input parameter, and a value of the distribution of the first input parameter corresponding to the first value and a value of the distribution of the first input parameter corresponding to the first value, the value being included in an input parameter range that is determined based on the first input distribution and the second input distribution, within a range configured by the first input parameter and the second input parameter. On line A distribution value of the second input parameter and a distribution value of the first partial region included in the input parameter range An area enclosed by a line or an area of ​​the same size as the area in questionThe program is for causing the program to function as a generating unit that determines a distribution value for the first value based on the size of a second partial region and the size of the first partial region.

[0009] Another aspect of the present invention is a program for causing a computer to function as an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter, and a generation unit that generates a post-change distribution by adding a unit change amount of the second input distribution to the first input distribution, and generates a post-minimal change distribution corresponding to a minimal change amount smaller than the unit change amount based on the first input distribution and the post-change distribution. Effect of the Invention

[0010] According to the present invention, it is possible to accurately obtain the calculation results of a plurality of parameters having distributions. [Brief description of the drawings]

[0011] [Figure 1] 1 is a configuration diagram of an information processing device according to a first embodiment. [Diagram 2] 13 is a flowchart showing a calculation process. [Diagram 3] FIG. 11 is an explanatory diagram of an addition process. [Figure 4] FIG. 11 is an explanatory diagram of a calculation process when the input parameters are N-dimensional. [Diagram 5] FIG. 11 is an explanatory diagram of a calculation process when the input parameters are N-dimensional. [Figure 6] FIG. 13 is a diagram showing the relationship between the correlation coefficient and the input parameter range. [Figure 7] FIG. [Figure 8] FIG. [Figure 9] FIG. 11 is an explanatory diagram of multiplication when the input parameters are N-dimensional. [Figure 10] FIG. [Figure 11] FIG. 11 is an explanatory diagram of division when the input parameters are N-dimensional. [Figure 12]FIG. 11 is an explanatory diagram of an integral calculation process. [Figure 13] FIG. 11 is an explanatory diagram of an integral calculation process. [Figure 14] FIG. 11 is an explanatory diagram of a process for determining durability. [Figure 15] FIG. 13 is an explanatory diagram of a route simulation. [Figure 16] FIG. 13 is a diagram showing an example of a display screen. [Figure 17] FIG. 1 is an explanatory diagram of dimensional variations of parts. [Figure 18] FIG. 1 is an explanatory diagram of dimensional variations of parts. [Figure 19A] FIG. 1 is an explanatory diagram of a numerical calculation and a distribution calculation. [Figure 19B] FIG. 1 is an explanatory diagram of a numerical calculation and a distribution calculation. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Here, the embodiments will be described in the following order. (1) Numerical operations and probability distribution operations: (2) Configuration of the information processing device of the first embodiment: (3) Calculation processing: (4) Other embodiments:

[0013] (1) Numerical operations and probability distribution operations: Prior to describing the information processing device of the first embodiment, numerical calculation and probability distribution calculation will be described. In the calculation of parameters having a distribution in value, a correct calculation result cannot be obtained by calculation using numerical values ​​of the order of sample amount. For example, as shown in FIG. 17, consider a case where a first part having a dimension X and a second part having a dimension Y are combined to generate a third part having a dimension Z (Z=X+Y). Here, it is assumed that there are 10 first parts and 10 second parts, and there is a variation (distribution) of 0 to 3 between the individual parts. In this case, the dimension of the third part will have a variation of 0 to 6.

[0014] If the frequency values ​​on the vertical axis are replaced by blocks with a height of 0.1, the total area of ​​the 10 parts becomes 1.0, forming a probability distribution. The graph in the upper left of Fig. 17 is the probability distribution of the first part, and the graph in the upper right of Fig. 17 is the probability distribution of the second part. From these probability distributions, the graph in the lower part of Fig. 17 is obtained as the probability distribution of the third part. For example, the following three combinations will result in the dimension Z of the third part being +2. (X=0, Y=2) (X=1, Y=1) (X=2, Y=0)

[0015] As shown in (Equation 1), the sum of these three probabilities is the probability that the dimension Z of the third part will be +2. Note that it is assumed that the correlation coefficient can be considered to be zero. P(2)=3*0.1*0.1+4*0.1*3*0.1+2*0.1*1*0.1 …(Formula 1) By performing the above calculations for all values ​​of Z, we obtain the probability distribution of Z shown in the bottom of Figure 17. Note that the sum of the probability values ​​in this distribution is 1.0. This is the basic idea behind probability distribution calculations.

[0016] Next, a distribution is obtained by adding up the variability values ​​for various combinations of the first and second parts. The two graphs shown at the top of Figure 18 are probability distributions when X and Y are random, that is, when the correlation coefficient can be considered to be zero. The graph shown at the bottom of Figure 18 is the same as the graph shown at the bottom of Figure 17. The graph at the top left of Figure 18 and the graph at the top right of Figure 18 should both have the same probability distribution as the graph at the bottom of Figure 18, but they are different probability distributions. In this way, when calculations are performed on individual data, different probability distributions are obtained for each combination of data, and the distribution cannot be guaranteed.

[0017] Furthermore, we will explain the case where the number of data and calculations in the numerical calculation increases. Fig. 19A shows a case where the x-direction position and velocity (x, v) of a moving object are acquired n times by a recognition sensor, and n positions after t seconds are obtained by the calculation of (Equation 2). y=x+v*t ...(Equation 2) In FIG. 19A, one box indicates n data sets, and n arrows indicate that (Equation 3) is performed n times, with t=2. y=x+v+v …(Equation 3) As shown in (Equation 4), where i, j, and k are arbitrary values ​​from 1 to n, each arrow indicates a combination of a position, a velocity after 1 second, and a velocity after 2 seconds. (x(i),v(j),v(k)) (Equation 4)

[0018] In reality, for a position of x, there are some possibilities that are allowed by the correlation between v(1) to v(n), and in the calculation shown in Fig. 19A, some combinations of 0 to (n-1) are missing. Furthermore, at the position (x+v+v) one second after each (x+v), there are some possibilities of v that are allowed for each (x+v), and these combinations are missing.

[0019] FIG. 19B shows all the combinations that are missing in FIG. 19A. In this example, a maximum of n**3 combinations are required. The combinations are maximized when the correlation coefficient is close to 0, for example, when a vehicle located at x(i) with a speed v(k) varies in the range of speed v(0) to v(n) in the next second. In reality, the speed v(k) is unlikely to fluctuate significantly, and is presumably limited to a certain range around v(k).

[0020] Probability distribution calculation is a calculation method that obtains a result by incorporating the occurrence probability of these combinations as a probability distribution, reflecting the influence of correlation coefficients as necessary. In other words, probability distribution calculation is a method of interpolating information of combinations that are missing in numerical calculation of individual data. The more the number of calculations and the number of parameters increase, the larger the missing information becomes, which is thought to be the reason why Monte Carlo simulation and the like do not guarantee the probability value. For the above reasons, when performing calculations on multiple input parameters, the information processing device 100 of this embodiment performs calculations by dividing the range of the input parameter distribution. This makes it possible to obtain calculation results with high accuracy.

[0021] (2) Configuration of the information processing device of the first embodiment: The information processing device 100 of this embodiment will be described below. FIG. 1 is a block diagram showing the configuration of the information processing device 100 of this embodiment. The information processing device 100 includes a control unit 110, a storage unit 120, a UI unit 130, and a communication unit 140. The control unit 110 includes a CPU, a ROM, a RAM, etc. (not shown), and controls each unit of the information processing device 100 by the CPU executing various programs recorded in the ROM or the like using the RAM or the like. The control unit 110 may be configured with a single chip or may be configured with multiple chips. In addition, in the control unit 110, an ASIC may be adopted instead of the CPU. In addition, in the control unit 110, the CPU and other processing circuits such as an ASIC or a GPU may cooperate with each other to operate.

[0022] The storage unit 120 is, for example, a hard disk, and stores various information and various programs. The communication unit 140 includes a communication interface circuit for communicating with other devices connected to the information processing device 100 by wire or wirelessly according to various communication protocols. The UI unit 130 includes a touch panel display, various keys, switches, etc.

[0023] The control unit 110 of this embodiment performs an operation on two or more input parameters to obtain an output parameter. Here, the input parameters have a variation in value, that is, a distribution, and the output parameters also have a distribution in value. That is, the input parameters and output parameters each have a range of values, and a distribution value corresponding to the parameter is obtained in the parameter range. Here, the distribution value is a value whose integral value is a probability value. In this embodiment, an example will be described in which the distribution of the output parameter z is obtained from the input parameters x and y, x and y. Here, the distribution of x and the distribution of y are input distributions, and the distribution of z is an output distribution. In addition, the two or more input parameters are all one-dimensional parameters.

[0024] The control unit 110 processes parameters having such a distribution. Specifically, the control unit 110 executes a calculation program 111 to function as an acquisition unit 112, a setting unit 113, a generation unit 114, and an output processing unit 115 to perform the above-mentioned processing. In the following, the processing described as being performed by each functional unit is processing performed by the control unit 110 by executing the calculation program 111.

[0025] The acquisition unit 112 acquires two input parameters. Specifically, the acquisition unit 112 acquires the two input parameters via, for example, the communication unit 140. The setting unit 113 sets the distribution range of the output parameter based on the distribution range of each of the two input parameters. Then, the setting unit 113 sets each value of the output parameter within the distribution range of the output parameter as a processing target, and sets a first partial region for the value of the processing target. Here, the first partial region is a width of the output parameter that is set to obtain a probability value corresponding to the value of the output parameter. It is assumed that the first partial region is set in advance. The generation unit 114 obtains a probability value at each value of the output parameter based on the first partial region. The generation unit 114 obtains the distribution of the output parameter from the probability values ​​for all values ​​within the range of the output parameter. The output processing unit 115 outputs the distribution of the output parameter. The processing of each function will be described in detail later.

[0026] (3) Calculation processing: FIG. 2 is a flowchart showing the arithmetic processing executed by the control unit 110 of the information processing device 100. FIG. 3 is an explanatory diagram of the addition processing. Here, the arithmetic processing will be described taking as an example the case where the calculation is to obtain z by adding "x+y". As shown in FIG. 3, an xy plane with the horizontal axis being x and the vertical axis being y, that is, a two-dimensional plane, is considered. Furthermore, on the same plane as the two-dimensional plane, the z axis is set parallel to the x axis. Both x and y have distributions (variations) for the parameters shown on each axis. In this case, z obtained from x and y also has a distribution. Here, the distributions of x and y correspond to the input distribution, and the distribution of z corresponds to the output distribution.

[0027] In Figure 3, the distribution of x is shown as graph 201, which is perpendicular to the x-axis and positive in the opposite direction to the y-axis. The distribution of y is shown as graph 202, which is perpendicular to the y-axis and positive in the opposite direction to the z-axis. The distribution of z is shown as graph 203, which is perpendicular to the z-axis and positive in the opposite direction to the y-axis. The distribution of z extends to values ​​larger than the maximum value of the distribution of x. The distribution values ​​for x, y, and z are denoted as Px, Py, and Pz, respectively.

[0028] In the calculation process shown in FIG. 2, the distribution of z is obtained from the distribution of x and the distribution of y. In the calculation process, the acquisition unit 112 first acquires the distribution of input parameters, that is, the distribution of x and the distribution of y (step S100). Next, the setting unit 113 sets the range of combinations of x and y, that is, the input parameter range 220, based on the distribution range 211 of x and the distribution range 212 of y (step S102). The setting unit 113 sets a range including all combinations of x and y that are each value of z as the input parameter range. Note that the correlation coefficient is assumed to be zero here. In the example of FIG. 3, the range in the two-dimensional plane of x and y, which is the maximum area range determined by the distribution range of x and the distribution range of y, is set as the input parameter range 220.

[0029] Next, the setting unit 113 sets the distribution range 213 of z based on the distribution range 211 of x and the distribution range 212 of y (step S104). The value of "x+y" is a constant value on a line with a slope of "-1", and the value of x at the point where the line intersects with the x-axis is the value of z. That is, the value of x at the point where the line with a slope of "-1" intersects with the x-axis and a line tangent to the lower left point of the input parameter range 220 is the minimum value of z, and the value of x at the point where the line with a slope of "-1" intersects with the x-axis and a line tangent to the upper right point of the input parameter range is the maximum value of z. As a result, the distribution range 213 of z is set on the z-axis shown in parallel to the x-axis as shown in FIG. 3.

[0030] Next, the generation unit 114 calculates the value of z, z k(Step S106). Note that the process from step S106 to step S112 is a loop process, and in step S106, the generation unit 114 sets each value of z in order from the minimum value of z to the maximum value of z as the processing target value z k where z k is an equally spaced value obtained by dividing the minimum and maximum values ​​of z by a predetermined number. k may be a value according to the unit of z. For example, if z is a length, the value may be in units of 1 mm. Next, the generating unit 114 calculates z k A first partial region is set for (step S108). Here, the width (size) of the first partial region is a minute width of dzz, and the first partial region is set to z k In this embodiment, the generating unit 114 includes z k From z k+1 Width up to z k In other words, the width dz of the first partial region is the same width, i.e., the same length, regardless of the value of z.

[0031] Next, the generation unit 114 calculates z k The generation unit 114 first calculates the distribution value of the second partial region S corresponding to the width dz of the first partial region. ij Here, the second partial region S ij is a region in the xy plane, which corresponds to the first partial region.

[0032] First, the second sub-region S ij The value of "x+y", i.e. the value of z, is constant on a line with a slope of -1. k For (x,y)=(z k A straight line with a slope of -1 (z in Figure 3) passes through k The combination of x and y on the line connecting the dotted line extending from k The combination of x and y is as follows. i and y jIn addition, the widths of x and y corresponding to dz are dx and dy, respectively.

[0033] At the bottom of FIG. 3, the second partial region S ij The second partial region S ij As shown in the lower part of Figure 3, k A line with a slope of -1 corresponding to z k +dz" and the line with a slope of "-1" corresponding to (x i ,y j +dy) and a line with a slope of +1, (x i +dx,y j ) with a slope of +1. Here, (x i ,y j +dy) and a line with a slope of +1 that passes through (x i +dx,y j ) is a line with a slope of +1 that passes through the second subregion S ij In this way, the second partial area S ij is a region within the input parameter range 220, bounded by two straight lines with a slope of "-1" where the output parameter has a constant value, and two auxiliary lines that intersect with the straight lines and are parallel to each other.

[0034] z k The value Pz of the distribution in the first partial region dz and the second partial region S ij Area (size) a ij Using this, it can be expressed as (Equation 5).

number

number

[0035] Returning to FIG. 2 for explanation, after the process of step S110, the generation unit 114 k It is checked whether a distribution value is obtained for the unprocessed z k If there are any remaining z (N in step S112), the process returns to step S106. k The generation unit 114 sets all z k When the distribution value is obtained for each z k Based on the distribution value for each z, the generation unit 114 generates a distribution of z (step S114). k A continuous distribution of z is generated by using the least squares method or the like for the distribution values ​​corresponding to the value of z. Next, the output processing unit 115 outputs the distribution of z (step S116). Specifically, the output processing unit 115 displays the distribution of z on the display of the UI unit 130. As another example, the output processing unit 115 may transmit the distribution of z to an external device via a network.

[0036] As described above, the information processing device 100 of this embodiment can accurately obtain the calculation results of a plurality of parameters having distributions.

[0037] The distribution of the input parameters may be continuous or may be discrete like a histogram. When the control unit 110 acquires a parameter indicating a discrete value as an input parameter, it may interpolate the value of the distribution of the parameter, and obtain the distribution of the output parameter by using the parameter after the interpolation as a processing target. In this way, even when the input parameter is a discrete value, the information processing device 100 can accurately obtain the distribution of the output parameter by the calculation process described with reference to FIG. 2 etc.

[0038] Next, with reference to Figs. 4 and 5, a description will be given of the calculation process when both input parameters x and y are N-dimensional (N is an integer equal to or greater than 2). In this case, the one-dimensional case can be extended. Here, two dimensions will be described as an example. The two-dimensional parameters of x, i.e., the two parameters, will be denoted as x1 and x2. Similarly, the two-dimensional parameters of y will be denoted as y1 and y2, and the two-dimensional parameters of z will be denoted as z1 and z2. As described in the addition of one-dimensional parameters, the second partial region S ij is a rectangular area T ij Therefore, as shown in FIG. 5, the ranges of x, y, and z can be considered as rectangular regions. k The distribution of z is calculated based on the rectangular area defined by dz. z k =(z1(m),z2(n)) …(Equation 9) z k x corresponds to i ,y j are shown in (Equation 10) and (Equation 11), respectively. x i =(x1(s),x2(t)) …(Equation 10) y j =(y1(q),y2(r)) …(Eq. 11)

[0039] When (Equation 12) and (Equation 13) are satisfied, the distribution of z is expressed by (Equation 14). dz1=dx1=dy1 …(Equation 12) dz2=dx2=dy2 …(Equation 13)

number

[0040] In addition, when the input parameters are N-dimensional parameters, the widths dx and dy for parameters of corresponding dimensions in the calculation, such as x1 and y1, are assumed to be equal values. However, the widths dx and dy for parameters that do not correspond in the calculation, such as x1 and x2, may be different values.

[0041] Next, a calculation that takes the correlation coefficient into consideration will be described. In the above, an example was described in which the correlation coefficient can be considered to be zero, but there are cases in which a correlation coefficient other than zero is given. In this case, the generation unit 114 sets the input parameter range based on the correlation coefficient. More specifically, the closer the correlation coefficient is to "-1", the smaller the input parameter range is made.

[0042] FIG. 6 is a diagram showing the relationship between the correlation coefficient and the input parameter range. As shown in FIG. 6, when the correlation coefficient r is set to "-0.6", the input parameter range is the range 310 shown by the dashed line in the figure. When the correlation coefficient r is set to "+0.6", the input parameter range is the range 320 shown by the dashed line in the figure. Both ranges 310 and 320 are smaller than the maximum input parameter range 220. By making the input parameter range smaller in this way, the amount of calculation of the distribution value of z can be reduced. When the correlation coefficient is set to a negative value, the distribution 203 of z has a smaller range as shown by the distribution 311. When the correlation coefficient is set to a positive value, the range of the distribution 203 of z does not change as shown by the distribution 321.

[0043] In this embodiment, the generation unit 114 restricts the region range by transforming the input parameter range into a diamond shape. However, the generation unit 114 only needs to reduce the area of ​​the input parameter range according to the correlation coefficient, and the shape of the input parameter range after transformation is not limited to that of the embodiment. As another example, the generation unit 114 may restrict the input parameter range to an elliptical shape. The process of restricting the input parameter range according to the correlation coefficient in this manner can also be applied to subtraction, multiplication, and division, which will be described later.

[0044] The following describes subtraction, multiplication, and division. In the four arithmetic operations, z in S110 is k The process of calculating the probability of z is different, but the rest of the process is the same as in the case of addition. Therefore, in the following, we will consider the z k The process of calculating the probability will be described below.

[0045] FIG. 7 is an explanatory diagram of subtraction. Here, an example of a calculation to obtain z by subtracting "xy" is explained. In subtraction, the range from the minimum value to the maximum value of "xy" is the distribution range of z. Note that the input parameter range is the same for all four arithmetic operations.

[0046] The value of "zy" is constant on a straight line with a slope of "+1" on the xy plane. Therefore, as shown in Figure 7, k For z k The dotted line extending from and the line with a slope of "+1" that passes through the intersection with the x-axis are all points within the input parameter range, that is, all combinations of x and y are within the range of z k The combination of x and y is as follows. i ,y j Let dx and dy be the widths of x and y corresponding to dz.

[0047] 2nd partial area S ij As shown in Figure 7, z k The line with a slope of +1 corresponding to z k+dz" and the line with a slope of "+1" corresponding to (x i ,y j ) with a slope of -1, and (x i ,y j +dy) with a slope of +1. Here, (x i ,y j ) and a line with a slope of -1 that passes through (x i ,y j +dy) with a slope of +1 is the second partial region S ij In this way, the second partial area S ij is a region within the input parameter range, bounded by two straight lines with a slope of -1 where the output parameter is a constant value, and two auxiliary lines that intersect with the straight lines and are parallel to each other. ij Area a ij is a rectangular area T ij Area b ij The area is equal to z. k It can be seen that the distribution value Pz in can be obtained by (Equation 7). That is, the generation unit 114 also uses (Equation 7) in the subtraction to obtain z k Find the distribution value Pz at .

[0048] Next, multiplication will be described with reference to FIG. 8. Here, an example of a calculation to obtain z by multiplying "x*y" will be described. In multiplication, the distribution of z will also be in the range from the minimum value to the maximum value of "x*y". The value of "x*y" will be constant on a hyperbola. In multiplication, a straight line with a slope of "+1" is set as an auxiliary line, and the area surrounded by the two hyperbolae and the two auxiliary lines with a slope of "+1" is set as the second partial area. Here, the two hyperbolae are z k The hyperbola corresponding to z k+1 The two lines with a slope of +1 are the jth line and the j+1th line. These lines will be explained later.

[0049] When m auxiliary lines are set at equal intervals in the input parameter range 220, the following equation (15) holds. zmax-zmin=xmax*ymax-xmin*ymin =(m-1)*dz…(Equation 15)

[0050] The j-th auxiliary line is expressed by (Equation 16), where da is a constant value. y=x+ymax-xmin-j*da …(Eq. 16) The i-th hyperbola is expressed by (Equation 17). k The hyperbola corresponding to the minimum value of is a hyperbola passing through (xmin, ymin) in the input parameter range 220, and z k The hyperbola corresponding to the maximum value of is the hyperbola passing through (xmax, ymax) in the input parameter range 220. z=zmin+i*dz …(Eq. 17)

[0051] x i,j ,y i,j is expressed as (Equation 18). (x i,j ,y i,j )=((-(ymax-xmin-j*da)±((ymax-xmin-j*da)**2+4*(zmin+i*dz))**0.5) / 2, ((ymax-xmin-j*da)±((ymax-xmin-j*da)**2+4*(zmin+i*dz))**0.5) / 2) …(Formula 18) Where spx i,j and spy i,j is expressed by (Equation 19) and (Equation 20), and the second partial region S i,j Area a i,j spx i,j and spy i,j The second partial region S i,j Area a i,j is expressed as (Equation 21). spx i,j = x i+1,j+1 -x i,j …(Formula 19) spy i,j = y i+1,j -y i,j+1…(Formula 20) a i,j =(spx i,j *spy i,j ) / 2 …(Equation 21) In addition, the second partial region S i,j is the range enclosed by the i-th hyperbola, the "i+1"-th hyperbola, the j-th line, and the "j+1"-th line. i,j ,y i,j The value of is determined, and by interpolating the x and y obtained from the input parameters, px(x i,j ),Py(y i,j ) is obtained.

[0052] As shown in (Equation 22), the distribution of z can be found by summing up the distribution values ​​of the combination of i and j. Note that the right-hand side of (Equation 22) is the addition with respect to j.

number

[0053] Furthermore, if the origin exists within the z-plane, calculations can be performed by setting different auxiliary lines in the positive and negative regions.

[0054] Next, multiplication of an N-dimensional input parameter by a one-dimensional input parameter will be described. Here, with reference to FIG. 9, multiplication of a two-dimensional input parameter x by a one-dimensional input parameter y will be described as an example. In this case, a two-dimensional z-plane obtained by the calculation, that is, a two-dimensional plane with z1 and z2 as axes, is set. Furthermore, an origin O, an x-plane, is set. The x-plane is a two-dimensional plane with x1 and x2 as axes.

[0055] Here, the z plane is divided into a plurality of partial regions, and the partial region to be processed is designated as z(m,n). The generation unit 114 sets the straight line that overlaps the x plane among the straight lines connecting z(m,n) and the origin O as the s axis. That is, the value of s includes the components x1 and x2. Furthermore, the y axis is set perpendicular to the s axis, and a hyperbola that satisfies z(m,n) on the two-dimensional plane of s and y is set. Then, the generation unit 114 performs the calculation of (Equation 22) at the points on this hyperbola. This makes it possible to obtain the distribution value of z(m,n).

[0056] Next, division will be described with reference to FIG. 10. In FIG. 10, x is shown as the vertical axis and y is shown as the horizontal axis. Here, an example of a calculation to obtain z by dividing "x / y" will be described. In division, the distribution range of z is the range from the minimum value to the maximum value of "z / y". The value of "x / y" is constant on a straight line that passes through zero. In division, a straight line with a slope of "-1" is set as an auxiliary line, and the area surrounded by the two straight lines with a constant value of "x / y" and the two auxiliary lines with a slope of "-1" is set as a second partial area. The two straight lines with a constant value of "x / y" are z k , z k+1 The two lines with a slope of -1 are the jth line and the j+1th line. These lines will be explained later.

[0057] When m auxiliary lines are set at equal intervals in the input parameter range, Equation 23 holds, where da is a constant value. xmax+ymax-(xmin+ymin)=(m-1)*da ···(Equation 23)

[0058] The j-th auxiliary line is expressed by (Equation 24). x=-y+(ymin+xmin)+j*da =-y+(ymin+xmin)+j*(xmax+ymax-xmin-ymin) / (m-1) (Equation 24) The i-th straight line corresponding to "x / y" is expressed by (Equation 25). Here, z kis a value that is a unit of one of the n equal parts of the distribution range of z. dz is a constant value. In this embodiment, dz is defined as "z k+1 -z k " shall be of equal width. x=b(i)*y =(i*xmax / ymin+(n-1-i)*xmin / ymax) / (n-1)*y (Equation 25) Furthermore, if z=b(i), dz is expressed by (Equation 26). dz=b(i+1)-b(i) =-((i+1)*xmax / ymin+(n-1-(i+1))*xmin / ymax) / (n-1) +(i*xmax / ymin+(n-1-i)*xmin / ymax) / (n-1) =(xmax / ymin-xmin / ymax) / (n-1) ...(Formula 26)

[0059] From (equation 24), (equation 27) holds. b(i)*y=-y+(ymin+xmin)+j*da ···(Equation 27) x i,j ,y i,j are expressed by (Equation 28) and (Equation 29), respectively. y i,j =((ymin+xmin)+j*da) / (b(i)+1) =((ymin+xmin)+j*da) / ((i*xmax / ymin+(n-1-i)*xmin / ymax) / (n-1)+1) ...(Formula 28) x i,j =((ymin+xmin)+j*da) / (1+1 / b(i)) =((ymin+xmin)+j*da) / ((n-1) / (i*xmax / ymin+(n-1-i)*xmin / ymax)+1) ...(Formula 29) Where spx i,j and spy i,j is expressed by (Equation 30) and (Equation 31), and the second partial region S i,j Area ai,j spx i,j and spy i,j The second partial region S i,j Area a i,j It is expressed by (Equation 32). spxij=x(i+1,j+1)-x(i,j) …(Equation 30) spyij=y(i,j+1)-y(i+1,j)…(Equation 31) a i,j =(spx i,j *spy i,j ) / 2 …(Formula 32) From the above, z k It can be seen that the distribution value Pz in can be obtained by (Equation 22). That is, the generation unit 114 also uses (Equation 22) in the division to obtain z k Find the distribution value Pz at .

[0060] Next, division of an N-dimensional input parameter by a one-dimensional input parameter will be described. Here, division of a two-dimensional input parameter x by a one-dimensional input parameter y will be described as an example with reference to Fig. 11. In this case, a process similar to the multiplication of an N-dimensional input parameter by a one-dimensional input parameter may be performed.

[0061] As in the case of multiplication, the generation unit 114 sets the z-plane and the x-plane, and sets the partial region z(m,n) to be processed on the z-plane. The generation unit 114 sets the line that overlaps with the x-plane among the lines connecting z(m,n) and the origin O as the s-axis, and sets the y-axis perpendicular to the s-axis. The generation unit 114 sets a line that satisfies z(m,n) in the two-dimensional plane of s and y. Then, the generation unit 114 performs the calculation of (Equation 22) at a point on this line to obtain the probability of z(m,n). The above four arithmetic operations have been described in the case where the input parameter range 220 is in the first quadrant of the graph, but the inclination of the auxiliary line may be changed according to a line or curve with a constant z depending on the quadrant in which each input parameter range 220 is located.

[0062] Next, integration will be described with reference to FIG. 12. An example will be described in which acceleration a is integrated to obtain a velocity v. For example, it is considered that a distribution (infinite distribution) of infinitesimal multiples of acceleration a, such as 0.01 times and 0.001 times, can be created and added to the velocity v, thereby simulating the time change of the velocity v. However, a distribution of 0.01 times is one in which the original distribution is restored when 100 of these are added, but since the distribution calculation is a non-reversible calculation, such a distribution of infinitesimal multiples cannot be obtained. Therefore, the generation unit 114 of this embodiment obtains a post-infinite change distribution corresponding to an infinitesimal change time smaller than the unit change time, based on the velocity v1 and v2 after the unit change time of acceleration a has elapsed. Here, the unit change time is an example of a unit change amount.

[0063] As mentioned above, it is not possible to obtain a distribution of infinitesimal multiples, i.e., "a*dt". Therefore, the generation unit 114 first obtains v1 (v0+α) after a unit time of change of acceleration α has elapsed from v0. Here, the unit time of change is a unit of the amount of change, for example, if the unit of acceleration a is km / h, 2 In this case, one hour is the change unit time. In the integration to find position p from speed v, if the unit of speed v is m / s, one second is the change unit time. Then, the generation unit 114 obtains "v0+a*dt", i.e., the distribution after minute change 420, by taking a weighted average of peak value 401 of distribution 400 of speed v1 and peak value 411 of distribution 410 of speed v2. The generation unit 114 equally divides the range up to the peak value of the speed distribution before and after the change unit time has elapsed, and takes a weighted average of each point according to a 1:100 change unit time (for example, 1:100 when the minute distribution is 0.01 times).

[0064] As another example, the generating unit 114 may obtain a distribution after a small change by taking a weighted average of the parameter values ​​after division. In addition, in the present embodiment, the unit change amount is time, but the unit change amount is not limited to time as long as it is a value that can be used for integration.

[0065] Furthermore, in the integration, the generating unit 114 may perform the calculation by applying a negative correlation coefficient when performing feedback control, etc. This allows the calculation result to converge to a constant value.

[0066] Furthermore, the generation unit 114 can not only obtain the velocity from the acceleration by integration, but also obtain the position from the velocity, as shown in Fig. 13. The respective calculation expressions are expressed by (Equation 33) and (Equation 34). v = v0 + a * dt (Eq. 33) x=x0+v*dt (Formula 34) In this way, the generation unit 114 can also perform integration for parameters having a distribution.

[0067] Next, an example of calculation will be described. For example, as an example of multiplication, the control unit 110 of the information processing device 100 calculates the lifetime engine revolutions (revolutions) using (Equation 35) based on the distribution (statistical data) of the engine revolutions (revolutions / min) during the ship's voyage and the distribution (statistical data) of the lifetime sailing time. Lifetime engine revolutions (rpm) = Engine RPM during voyage × Lifetime voyage (hours) ... (Equation 35)

[0068] The control unit 110 further obtains the durability conditions of the engine based on the lifetime engine revolutions. Specifically, the durability conditions are obtained based on stress strength. FIG. 14 is an explanatory diagram of the process of obtaining durability. FIG. 14 shows lifetime revolutions distribution 500, Weibull cumulative distribution 510, and failure distribution 520. The horizontal axis of the graph indicates lifetime engine revolutions (times), the vertical axis shown on the left indicates the probability of engine revolutions, and the vertical axis shown on the right indicates the cumulative probability of strength. The lifetime revolutions distribution 500 obtained by the above (Equation 37) is set as stress, and the Weibull cumulative distribution 510 is set as strength. The failure distribution 520 is obtained by integrating these.

[0069] Since the area of ​​the failure distribution 520 is the failure rate, the Weibull distribution for achieving a certain failure rate can be determined by the above steps with the failure rate as the target. To guarantee the Weibull distribution, the durability conditions can be obtained as follows. For example, the engine speed at 60% is 5.0×10 9 Therefore, the engine speed is 5.0 x 10 9 In the case where there are three ships that do not break down within the first 1000 times, it can be seen from (Equation 36) that the failure distribution 520 is guaranteed with a reliability of 93·6%. In this way, the control unit 110 can determine the durability. 1 - (1 - 0.6) 3 =93.6%…(Formula 36)

[0070] As an example of division, the control unit 110 obtains the fuel efficiency of the engine based on the distribution of fuel consumption of the ship engine (statistical data) and the route distance (statistical data) using (Equation 37). Fuel efficiency = route distance / fuel consumption ... (Equation 37) The control unit 110 may refer to the fuel efficiency distribution thus obtained, determine a fuel efficiency threshold, and determine that an engine abnormality exists when the fuel efficiency is below the threshold, and may output, for example, a warning.

[0071] Next, the specific processing of arithmetic operations and integration will be described using an example of a ship route simulation. Fig. 15 is an explanatory diagram of the route simulation. Prior to the explanation, each parameter will be described. Each parameter is as follows. F: Propulsive force=36000tonmile / h 2 m:Weight=100ton a: Acceleration mile / h 2 (720=0.1m / s 2 ) v: Speed ​​mile / h (initial speed 10nt) g: Wind power = Direction x Wind power (2D distribution) 10m / s = 20mile / h

[0072] The force acting on a ship is expressed as in (Equation 38), where c represents resistance. F+g=m*a+c*v2 …(Formula 38) Therefore, the acceleration is expressed by (Equation 39). a(t)=(Fg(t)-c*v 2 ) / m …(Formula 39) Moreover, as shown in (Equation 40), the velocity can be found by integrating the acceleration with respect to time. v(t+1)=v(t)+a(t)*dt…(Equation 40)

[0073] As shown in FIG. 15, the control unit 110 calculates the square of the wind speed (Wx 2 ,Wy 2 The control unit 110 calculates a distribution 602 of the forces (Fx, Fy) acting on the ship using (Equation 41). Forces acting on the ship (Fx, Fy) = Area exposed to wind * Resistance area * Wind speed squared ... (Equation 41)

[0074] Furthermore, the control unit 110 adds the propulsive force and the resistance of the water to the distribution 604 to obtain a distribution 606 of the total force acting on the boat. Next, the control unit 110 obtains a distribution 608 of the acceleration (ax, ay) by dividing the distribution 606 by the mass. Next, the control unit 110 obtains a distribution 610 of the speed (vx(nt)+ax*dt,vy(nt)+ay*dt) after dt seconds by integration, and further obtains a distribution 612 of the speed (vx(nt),vy(nt)) after a unit time. The control unit 110 further obtains the distribution 610 of the next speed from the speed distribution 612. In this manner, the control unit 110 obtains the time series data of the speed by performing repeated calculations.

[0075] Control unit 110 also obtains distribution 614 of position after dt seconds (xx(mile)+vx*dt, xy(mile)+vy*dt) by integrating speed distribution 612, and further obtains distribution 616 of position after unit time (xx(mile), xy(mile)). Furthermore, control unit 110 obtains distribution 614 of the next position from distribution 616 of position. In this way, control unit 110 obtains time series data of position by performing repeated calculations.

[0076] The water resistance mentioned above is the square of the velocity (vx 2 ,vy 2 ) distribution 618, and the distribution 618 of the square of the speed is multiplied by the resistance coefficient to obtain the water resistance. This water resistance is used when calculating the distribution 606 of the total force. By repeating the above calculations, the control unit 110 can predict the time changes in speed and position on the route.

[0077] FIG. 16 is a diagram showing an example of a display screen displayed on the UI unit 130 by the control unit 110. The display screen 700 displays a graph 710 showing the time change in speed, and a graph 720 showing the horizontal position according to distance. The horizontal axis of the graph 710 indicates time, and the vertical axis indicates speed. The graph 710 shows the time change of the upper limit and the lower limit of the speed distribution obtained by the above calculation. The horizontal axis of the graph 720 indicates the route distance, and the vertical axis indicates the horizontal position. Here, the direction perpendicular to the traveling direction of the route is defined as the horizontal direction. The graph 720 shows the upper limit, the average, and the average of the position obtained by the above calculation.

[0078] Furthermore, when a predetermined time is selected in response to a user operation in graph 710, a 3D graph 730 showing the distribution of speeds at the selected time is displayed. In graph 730, the horizontal axis indicates the left-right direction and the front-back direction, and the vertical axis indicates the probability.

[0079] As described above, the control unit 110 can predict the speed and position on the route and display this information. Furthermore, since the control unit 110 performs these calculations using distributed calculations, it can display the calculation results having a distribution. As described above, the information processing device 100 of this embodiment can accurately obtain the calculation results of multiple parameters having a distribution.

[0080] (4) Other embodiments: The above embodiment is an example for implementing the present invention, and various other embodiments can be adopted. For example, the arithmetic processing may be executed by cooperation of a plurality of information processing devices. Furthermore, some of the configurations of the above embodiment may be omitted, and the order of processing may be changed or omitted.

[0081] In this embodiment, the distribution value of the first input parameter and the distribution value of the second input parameter are both values ​​whose integral value is a probability value. However, as another example, the distribution value of each input parameter itself may be a probability value. In this case, the control unit 110 can use (Equation 42) instead of (Equation 7).

number

[0082] As another example, the distribution value of each input parameter may be a frequency instead of a probability value. In this case, the control unit 110 can use (Equation 43) instead of (Equation 5). Here, n is the total number of times.

number

[0083] Furthermore, the control unit 110 calculates the cumulative probability value or the cumulative frequency Pz'(z k ) and output it. Here, the right-hand side is Pz(z k ) from 0 to k.

number

[0084] In this embodiment, the unit length of the output parameter is the width of the first partial region, but the width of the first partial region can be set arbitrarily. The width of the first partial region may be longer or shorter than the unit length of z. k The first subdomain of zk+1 A gap may be formed between the first partial regions of z k The first subdomain of z k+1 In any case where a first partial region is used, the area of ​​the first partial region z k For example, the probability value at z k Set the first subregion of 1 mm for z k+1 For example, set the first partial area to 2 mm. k A different first partial region may be set for each of the first partial regions z k Any width that includes z k It may be a width centered around.

[0085] In addition, in this embodiment, zk is set at equal intervals when obtaining the distribution of z, but the z value obtained to obtain the distribution does not have to be equal intervals. In this case, the control unit 110 can obtain the distribution of z by interpolating the probability value for each obtained z.

[0086] Also, for example, when the ratio between the distribution range of the first input parameter and the distribution range of the second input parameter exceeds a predetermined range, that is, when the ranges of the values ​​are significantly different, there is a high possibility that one distribution will not be reflected in the calculation result. In such a case, the control unit 110 performs calculations using the input parameter with the smaller ratio as a numerical value. Note that the numerical value in this case may be any value, and may be, for example, the average value, maximum value, or minimum value of the range of the input parameter.

[0087] In the present embodiment, the control unit 110 outputs the distribution of the output parameters. However, in another example, the control unit 110 may output a predetermined z k For example, the user can input z k When the value of z is input, the control unit 110 kAlternatively, only the probability value for may be calculated and output. Furthermore, the width dz of the first partial region in this case may be arbitrary, and may be set according to, for example, a user operation.

[0088] In the present embodiment, the first input parameter and the second input parameter are calculated as two orthogonal axes, but the calculation method is not limited to the embodiment. As another example, the first input parameter and the second input parameter may be two non-orthogonal axes. In this case, the input parameter range, the first partial region, and the second partial region may be expressed in the coordinate system.

[0089] Furthermore, the embodiments can be realized as a program or a method. The above-mentioned devices, programs, and methods may be realized as a single device or may be realized by using parts of multiple devices, and include various aspects. In addition, they can be modified as appropriate, such as being partly software and partly hardware. Furthermore, the invention can also be realized as a recording medium of a program that controls the system. Of course, the recording medium of the program may be a magnetic recording medium or a semiconductor memory, and any recording medium developed in the future can be considered in the same way. [Explanation of symbols]

[0090] 100 Information processing device 110 Control section 112 Acquisition Department 113 Setting section 114 Generation part 115 Output Processing Section

Claims

1. an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; a setting unit that sets a first partial region including a first value within an output distribution range of an output parameter obtained by performing an operation on the first input parameter and the second input parameter; a generation unit that calculates a distribution value for the first value based on a distribution value of the first input parameter corresponding to the first value and included in an input parameter range, the input parameter range being a range determined based on the first input distribution and the second input distribution within a range configured by the first input parameter and the second input parameter, a distribution value of the second input parameter on a line corresponding to the first value, a size of a second partial region that is included in the input parameter range and is a region surrounded by a line corresponding to the first partial region or a region having the same area as the first partial region, and a size of the first partial region; An information processing device comprising:

2. the value of the distribution of the first input parameter is a probability value of the first input parameter; The information processing apparatus according to claim 1 , wherein the value of the distribution of the second input parameter is a probability value of the second input parameter.

3. the distribution value of the first input parameter is a value whose integral value is a probability value of the first input parameter, The information processing apparatus according to claim 1 , wherein the distribution value of the second input parameter is a value whose integral value is a probability value for the second input parameter.

4. the value of the distribution of the first input parameter is a frequency of the first input parameter; The information processing apparatus according to claim 1 , wherein the distribution value of the second input parameter is a frequency in the second input parameter.

5. 5. The information processing device according to claim 1, wherein the generation unit sets as the second partial region an area that is bounded by a straight line or curve corresponding to the first value and the first partial region, and two auxiliary lines that intersect with the straight line or curve, and that is within the input parameter range.

6. 5 . The information processing device according to claim 1 , wherein when the operation is addition or subtraction, the generation unit sets a rectangular area obtained by dividing the first input parameter and the second input parameter at equal intervals as the second partial area.

7. 7. The information processing device according to claim 1, wherein the generation unit calculates the distribution value at the first value by dividing the sum of the product of the distribution value of the first input parameter, the distribution value of the second input parameter, and the size of the second partial region, which corresponds to each combination of the first input parameter and the second input parameter that results in the first value, by the size of the first partial region.

8. The information processing device according to claim 1 , wherein the setting unit divides a range of the output distribution into predetermined units, and sets the first partial regions of the same size for each value of the output parameter corresponding to the unit.

9. The information processing device according to claim 8 , wherein the generating unit determines a distribution value for each value of the unit, and generates the output distribution based on the distribution value for each value.

10. 10. The information processing device according to claim 1, wherein the generation unit sets the input parameter range to a range determined from a range of the first input distribution and a range of the second input distribution, or a range smaller than the range, based on a correlation coefficient between the first input parameter and the second input parameter.

11. 11. The information processing device according to claim 1, wherein when a ratio between a range of the first input distribution and a range of the second input distribution is outside a predetermined range, the generation unit determines a distribution value for the first value by setting an input parameter having a smaller value of the ratio as a predetermined value.

12. 12. The information processing device according to claim 1, wherein when the distribution values ​​are discrete in at least one of the range of the first input distribution and the range of the second input distribution, the generation unit interpolates the discrete distribution values ​​and determines the distribution value for the first value based on the interpolated distribution values.

13. 13. The information processing device according to claim 1, wherein the first input parameter and the second input parameter are N-dimensional (N is an integer greater than or equal to 2) values, and when an addition or subtraction operation is performed between the first input parameter and the second input parameter, the generation unit sets the first partial region of equal width for the two corresponding parameters in the operation.

14. 14. The information processing device of claim 1, wherein when the first input parameter is an N-dimensional (N is an integer equal to or greater than 2) value, the second input parameter is a one-dimensional value, and the generation unit performs the operation of multiplying or dividing the first input parameter by the second input parameter, the generation unit calculates a distribution value for the first value in an N-dimensional distribution of the first input parameter based on a distribution value of parameters on a straight line passing through the first value of the output parameter and the origin, and the second input distribution.

15. The information processing device according to claim 1 , wherein the generation unit sets the first partial regions of equal width for two corresponding parameters in the calculation.

16. an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; a generating unit that generates a post-change distribution by adding a unit change amount of the second input distribution to the first input distribution, and generates a post-increment change distribution corresponding to a small change amount smaller than the unit change amount based on the first input distribution and the post-change distribution; An information processing device comprising:

17. The information processing device according to claim 16 , wherein the generating unit generates the small change distribution by taking a weighted average of at least one of a parameter value and a distribution value at a point obtained by dividing the height of the peak of each of the first input distribution and the changed distribution and the height of the peak.

18. Computer, an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; a setting unit that sets a first partial region including a first value within a range of an output distribution of an output parameter obtained by performing an operation on the first input parameter and the second input parameter; and a generation unit that calculates a distribution value for the first value based on a distribution value of the first input parameter corresponding to the first value included in an input parameter range, the range being a range determined based on the first input distribution and the second input distribution within a range configured by the first input parameter and the second input parameter, a distribution value of the second input parameter on a line corresponding to the first value, a size of a second partial region that is included in the input parameter range and is a region surrounded by a line corresponding to the first partial region or a region having the same area as the first partial region, and a size of the first partial region. A program to function as a

19. Computer, an acquisition unit that acquires a first input distribution of a first input parameter and a second input distribution of a second input parameter; and a generation unit that generates a post-change distribution by adding a unit change amount of the second input distribution to the first input distribution, and generates a post-change distribution corresponding to a small change amount smaller than the unit change amount based on the first input distribution and the post-change distribution. A program to function as a

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