JP2015153230A - Wattage estimating method, wattage estimating apparatus, and program - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enhance the accuracy of forecasting the peak wattage of electric power consumption.SOLUTION: A wattage estimating apparatus 10 figures out a forecasting formula for wattage consumed by regression analysis on the basis of an observed wattage consumed corresponding to a value of performance information of a wattage estimation object device 1, calculates a density function 14a of the residual between a forecast wattage obtained by the forecasting formula and the observed wattage, extracts from data represented by the density function 14a on an area of the density function 14a (data extraction area 14h) containing a maximum point 14d having the largest residual out of maximum points 14b, 14c and 14d of the density function 14a, and figures out the forecasting formula of the peak level of wattage consumed on the basis of the extracted data.

Description

  The present invention relates to a power estimation method, a power estimation device, and a program.

  When designing an integrated circuit, an information device, or the like, power consumption is estimated in advance. For example, a power model that abstracts power consumption is created using the performance information (MIPS (Million Instruction Per Second) value, etc.) of the device that is the target of power estimation. There is a method for estimating power. The power model is expressed in a linear format using the sum of products of performance information and coefficients, and each coefficient is obtained using regression analysis or the like.

JP 2007-293542 A JP2013-45328A

  When predicting the peak value of power consumption in order to select the package performance (heat dissipation performance, etc.) when designing, linear programming and regression analysis using the observed power consumption of the device It is conceivable to obtain a peak value prediction formula by the above.

  However, it is difficult to obtain an accurate peak value prediction formula. For example, in the case of linear programming, an accurate prediction formula cannot be obtained if there are outliers in the observed value, and when using regression analysis, even when multiple trends are shown for changes in performance information with power consumption. An accurate prediction formula cannot be obtained. Therefore, the prediction accuracy of the peak value of power consumption becomes low.

  According to an aspect of the invention, the power estimation device calculates a prediction formula of the power consumption by regression analysis based on the observed value of power consumption according to the performance information value of the power estimation target device, and the prediction formula A density function of a residual between the predicted value obtained and the observed value is calculated, and from the data represented by the density function, a region of the density function including a maximum point where the residual is the maximum among the maximum points of the density function And a power estimation method for calculating a prediction formula for the peak value of the power consumption based on the extracted data.

  According to the disclosed power estimation method, power estimation apparatus, and program, it is possible to improve the prediction accuracy of the peak value of power consumption.

It is a figure which shows an example of the power estimation method and power estimation apparatus of 1st Embodiment. It is a figure which shows the hardware example of the electric power estimation apparatus used for 2nd Embodiment. It is a flowchart which shows the flow of an example of an electric power estimation method. It is a figure which shows an example of the correlation of a MIPS value and power consumption. It is an example of the look-up table holding the density function value of a residual. It is a figure which shows an example of the density function of the residual obtained using the Gaussian kernel. It is a flowchart which shows the flow of an example of extraction of an observed value and a MIPS value. It is a flowchart which shows an example of the process which excludes specific data. It is a figure which shows an example of the area division of the definition area of a residual density function. It is a flowchart which shows the other example of the process which excludes specific data. It is a flowchart which shows the 1st example of a data extraction method. It is a flowchart which shows the flow of an example of the detection method of a maximum point. It is a flowchart which shows the 2nd example of a data extraction method. It is a figure explaining an example of the range of the data extracted. It is a flowchart which shows the 3rd example of a data extraction method. It is a flowchart which shows the 4th example of a data extraction method. It is a flowchart which shows the flow of an example of the detection method of a minimum point. It is a figure which shows an example of the density function of the extracted residual. It is a figure which shows the correlation between the extracted MIPS value and the observed value of power consumption. It is a table | surface which shows the example of prediction of peak electric power.

Hereinafter, embodiments for carrying out the invention will be described with reference to the drawings.
(First embodiment)
FIG. 1 is a diagram illustrating an example of a power estimation method and a power estimation apparatus according to the first embodiment.

The power estimation apparatus 10 includes a processor 11 and a storage unit 12.
The processor 11 executes power estimation processing based on data and programs stored in the storage unit 12.

  The storage unit 12 stores programs executed by the processor 11 and various data. For example, the storage unit 12 stores power information D1 and performance information D2 used for power estimation processing described below.

  The power information D1 includes an observed value of power consumption (hereinafter simply referred to as an observed value) according to the value of the performance information D2 of the power estimation target device 1 (processor, LSI (Large Scale Integrate circuit), electrical equipment, etc.). It is out. The observed value can be obtained, for example, by simulation based on design information or actual machine measurement for a device having the same performance as the power estimation target device 1.

The performance information D2 is information including an index (MIPS (Million Instructions Per Second) value, throughput, etc.) for evaluating the performance of the power estimation target apparatus 1.
Hereinafter, an example of the power estimation method according to the first embodiment will be described.

  First, the processor 11 reads the power information D1 and the performance information D2 stored in the storage unit 12, and calculates a prediction formula for power consumption by regression analysis based on the observed value corresponding to the value of the performance information D2 (step S1). S1).

  For example, a linear format representing power consumption as MIPS values is used as the regression equation. The processor 11 calculates a prediction formula for power consumption by obtaining a linear coefficient by a least square method or the like. FIG. 1 shows a correlation diagram showing the relationship between the MIPS value and power consumption, and shows an example of a regression line 13a representing a prediction formula for power consumption. In the correlation diagram, the vertical axis indicates the power consumption, and the horizontal axis indicates the MIPS value. A square plot (for example, plot 13b) indicates the observed value.

  Next, the processor 11 calculates a density function of a residual between the predicted value obtained from the power consumption prediction formula and the observed value (step S2). For example, the processor 11 subtracts a predicted value of power consumption calculated by a power consumption prediction formula from each observed value to calculate the residual. For example, the residual calculated from the observed value indicated by the plot 13b shown in FIG. 1 is d1. Note that the residual may be calculated in advance in step S1. The density function of the residual can be obtained by a kernel density estimation method as described later, for example.

  FIG. 1 shows an example of a density function distribution, and an example of a residual density function 14a. In the distribution diagram of the density function, the vertical axis indicates the residual density, and the horizontal axis indicates the residual. In the example of FIG. 1, the density function 14a has a plurality of maximum points 14b, 14c, and 14d.

  This is because it is considered that the power consumption shows a plurality of trends with respect to the value of performance information (MIPS value in the case of FIG. 1). For example, in a semiconductor integrated circuit including a processor, an instruction of a processor includes an instruction dominant in integer arithmetic and an instruction dominant in floating point arithmetic, and power consumption differs in a circuit executing each instruction. It is possible. Therefore, if the power consumption is simply predicted by a linear expression using the MIPS value, good accuracy cannot be obtained.

  The peak value of power consumption (hereinafter referred to as peak power) is the peak power predicted value = the predicted value of power consumption by regression analysis + 3 if the density function is close to a normal distribution having a maximum value when the residual = 0. X Standard deviation of residual may be used. At this time, the power consumption is about 99.8%, which is below the predicted peak power value.

However, when a plurality of maximum points 14b, 14c, and 14d are included as in the density function 14a in FIG. 1, it is not appropriate to predict the peak power using the above formula.
Therefore, in the power estimation method of the present embodiment, the following processing is further performed.

The processor 11 extracts, from the data represented by the density function, data of the density function region including the maximum point having the maximum residual among the maximum points of the density function (step S3).
In the example of the distribution diagram of the density function 14a in FIG. 1, since the maximum point 14d is the maximum residual among the maximum points 14b, 14c, and 14d, data of the region of the density function 14a including the maximum point 14d is extracted. Is done.

  The peak power is used to determine the package performance (heat dissipation performance, etc.), etc., so that the power consumption is larger than the predicted power consumption value (ie, the residual value is larger). This is because it is desirable to make a prediction based on this.

  As the data extraction area, for example, a method of determining the residual of the maximum point 14d to be an average value can be considered. For example, the processor 11 calculates the average of the residuals while expanding the range of the residuals from the highest residual to the lower one of the residuals calculated from the observed values. The residual range in which the average value is equivalent to the residual of the maximum point 14d is determined as the data extraction region. In the example of FIG. 1, the average of the residual is calculated while expanding the range of the residual from the maximum residual value 14e to the lower residual, and the calculated average of the residual is the maximum point 14d. The range of the residual that is equivalent to the residual is determined as the data extraction area 14h.

Other data extraction methods will be described later.
The data to be extracted includes a residual in the data extraction area or an observation value of power consumption corresponding to the residual.

After the processing in step S3, the processor 11 calculates a prediction formula for peak power based on the extracted data (step S4), and estimates the peak power (step S5).
The processor 11 adds, for example, a value obtained by multiplying the standard deviation of the residual in the data extraction area by 3 to the power consumption prediction formula obtained in step S1 as a design margin, and obtains a peak power prediction formula. calculate.

  Further, the processor 11 adds the value obtained by multiplying the standard deviation of the residual in the data extraction region by 3 and the average value as a design margin to the power consumption prediction formula obtained in the process of step S1, and calculates the peak power. A prediction formula may be calculated. Further, the processor 11 may perform the regression analysis and the residual calculation again using the observed value of the power consumption corresponding to the residual in the data extraction area and the value of the performance information D2 corresponding to the observed value. Then, the processor 11 calculates a peak power prediction formula by adding, as a design margin, a value obtained by multiplying the standard deviation of the residual obtained again by 3 to the power consumption prediction formula obtained by the regression analysis. You may do it.

  As described above, in the power estimation method and the power estimation apparatus 10 according to the present embodiment, the density function of the residual value between the predicted value of power consumption and the observed value by regression analysis is calculated, and the residual among the plurality of maximum points is calculated. Data of the density function region including the maximum maximum point is extracted, and the peak value is predicted.

  As a result, even when there are outliers in the observed values or when the power consumption shows multiple trends with respect to changes in performance information, it is possible to prevent the peak power from being estimated too much or too little, and the peak power prediction accuracy Can be improved.

Hereinafter, an example of the power estimation apparatus and the power estimation method according to the second embodiment will be described.
(Example of power estimation device)
FIG. 2 is a diagram illustrating a hardware example of the power estimation apparatus used in the second embodiment.

  The power estimation apparatus can be realized by a computer 20 as shown in FIG. The entire computer 20 is controlled by a processor 21. The processor 21 is connected to a RAM (Random Access Memory) 22 and a plurality of peripheral devices via a bus 29. The processor 21 may be a multiprocessor. The processor 21 is, for example, a central processing unit (CPU), a micro processing unit (MPU), a digital signal processor (DSP), an application specific integrated circuit (ASIC), or a programmable logic device (PLD). The processor 21 may be a combination of two or more elements among CPU, MPU, DSP, ASIC, and PLD.

  The RAM 22 is used as a main storage device of the computer 20. The RAM 22 temporarily stores at least part of an OS (Operating System) program and application programs to be executed by the processor 21. The RAM 22 stores various data necessary for processing by the processor 21.

  Peripheral devices connected to the bus 29 include an HDD (Hard Disk Drive) 23, a graphic processing device 24, an input interface 25, an optical drive device 26, a device connection interface 27, and a network interface 28.

  The HDD 23 magnetically writes and reads data to and from the built-in disk. The HDD 23 is used as an auxiliary storage device of the computer 20. The HDD 23 stores an OS program, application programs, and various data. As the auxiliary storage device, a semiconductor storage device such as a flash memory can be used.

  A monitor 24 a is connected to the graphic processing device 24. The graphic processing device 24 displays an image on the screen of the monitor 24a in accordance with a command from the processor 21. Examples of the monitor 24a include a display device using a CRT (Cathode Ray Tube) and a liquid crystal display device.

  A keyboard 25 a and a mouse 25 b are connected to the input interface 25. The input interface 25 transmits a signal sent from the keyboard 25a and the mouse 25b to the processor 21. The mouse 25b is an example of a pointing device, and other pointing devices can also be used. Examples of other pointing devices include a touch panel, a tablet, a touch pad, and a trackball.

  The optical drive device 26 reads data recorded on the optical disc 26a using a laser beam or the like. The optical disk 26a is a portable recording medium on which data is recorded so that it can be read by reflection of light. The optical disk 26a includes a DVD (Digital Versatile Disc), a DVD-RAM, a CD-ROM (Compact Disc Read Only Memory), a CD-R (Recordable) / RW (ReWritable), and the like.

  The device connection interface 27 is a communication interface for connecting peripheral devices to the computer 20. For example, the device connection interface 27 can be connected to a memory device 27a and a memory reader / writer 27b. The memory device 27 a is a recording medium equipped with a communication function with the device connection interface 27. The memory reader / writer 27b is a device that writes data to the memory card 27c or reads data from the memory card 27c. The memory card 27c is a card-type recording medium.

  The network interface 28 is connected to the network 28a. The network interface 28 transmits / receives data to / from other computers or communication devices via the network 28a.

  With the hardware configuration described above, the processing functions of the second embodiment can be realized. The power estimation apparatus 10 shown in the first embodiment can also be realized by the same hardware as the computer 20 shown in FIG.

  The computer 20 implements the processing functions of the second embodiment by executing a program recorded on a computer-readable recording medium, for example. A program describing the processing contents to be executed by the computer 20 can be recorded in various recording media. For example, a program to be executed by the computer 20 can be stored in the HDD 23. The processor 21 loads at least a part of the program in the HDD 23 into the RAM 22 and executes the program. A program to be executed by the computer 20 can also be recorded on a portable recording medium such as the optical disk 26a, the memory device 27a, and the memory card 27c. The program stored in the portable recording medium becomes executable after being installed in the HDD 23 under the control of the processor 21, for example. The processor 21 can also read and execute the program directly from the portable recording medium.

(Example of power estimation method)
FIG. 3 is a flowchart showing a flow of an example of the power estimation method.
Data generated in the middle of each process described below may be held in the RAM 22 or the HDD 23 as appropriate. In the example shown below, a MIPS value is used as performance information, but the present invention is not limited to this, and throughput or the like may be used.

  For example, the processor 21 acquires the input data In1 including the observed value and the MIPS value stored in the HDD 23 (step S10), and performs regression analysis (step S11). In the regression analysis, a linear form as shown by the following formula (1) is used as a regression equation.

In equation (1), the explanatory variable x represents the MIPS value, and the target variable y represents the predicted value of power consumption. For the equation (1), the processor 21 substitutes each observed value acquired in the process of step S10 for the objective variable y, substitutes the MIPS value at each observed value for the explanatory variable x, and uses the least square method. Etc. are used to find the coefficients a ₀ and a ₁ . Thereby, the prediction formula of power consumption is obtained.

  Furthermore, in the process of step S11, the processor 21 subtracts the predicted value given by Expression (1) from each observed value, and calculates a residual indicating the error of the observed value from the predicted value. The residual is calculated by the following equation (2).

In equation (2), a residual e _i indicates a residual from a predicted value of the i-th observed value among a plurality of observed power consumption values.
FIG. 4 is a diagram illustrating an example of the correlation between the MIPS value and the power consumption.

  The horizontal axis indicates the MIPS value, and the vertical axis indicates the power consumption. In addition, a plot (for example, plot plt1) indicated by a square, a triangle, a cross, and an x mark indicates an observation value. Observation values with different plot shapes mean, for example, that the operation (program) of the power estimation target device at the time of observation is different. For example, since the observation value at the time of execution of an instruction dominated by integer arithmetic and the observation value at the time of execution of an instruction dominated by floating-point arithmetic may have different correlation magnitudes for different MIPS values, Observed values during operation are used.

  A straight line ln1 illustrated in FIG. 4 is an example of a regression line calculated by the processor 21 from Expression (1), and is represented by a power consumption prediction expression such as Expression (3).

  The residual calculated from the observed value above the straight line ln1 by the formula (2) is a positive value, and the residual calculated by the formula (2) from the observed value below the straight line ln1 is a negative value. . For example, the residual d11 of the plot plt1 is a positive value.

  As shown in FIG. 4, the power consumption and the MIPS value show a relatively good correlation, but the residual calculated by the equation (2) with respect to the observed value, that is, the predicted value and the observed value by regression analysis It can be seen that the error from the value has a width and is not uniform.

  Next, the processor 21 calculates a residual density function from the residual calculated in step S11 (step S12). The density function of the residual can be calculated using Equation (4) by, for example, a kernel density estimation method.

In the formula (4), e _i is the residual of the i-th observation value calculated by Equation (2), h is the bandwidth, n represents the number of observations, K is a kernel function. As the kernel function, for example, the following equations (5), (6), and (7) are used.

Equation (5) is a Gaussian kernel, Equation (6) is an Epanechnikov kernel, and Equation (7) is a Rectangular kernel.
Further, the bandwidth h in the formula (4) is obtained by, for example, the following formula (8).

In equation (8), n is the number of observation values, and σ is the standard deviation of the residual.
In the process described later, since a process such as definite integration is performed on the residual density function, the function value of the residual density function is held in the form of a lookup table. Below, an example of the data structure expressing a lookup table is shown.

In the formula (9), e _m is the minimum value of t, the maximum value of e _M is t, delta represents an incremental width of t.
e _m and e _M are, for example, the maximum point and the minimum point at which the function value of the density function is 0 when the Epanechnikov kernel or the Rectangular kernel is used as the kernel function, and these points are integers of the increment increment Δ. Can be given to double. As an example, equations for obtaining e _m and e _M are shown below.

Equation (10), (11) is e _m, equation for e _M of Epanechnikov kernel, formula (12), (13) is e _m, equation for e _M of Rectangular kernel. Further, min e _i and max e _i indicate the minimum value and the maximum value of the residual e _i obtained by the equation (2), respectively.

When the Gaussian kernel is used as the kernel function, the function value of the density function does not become 0, so it is difficult to explicitly give e _m and e _M as described above. Therefore, for example, e _m and e _M can be obtained by the following equations (14) and (15).

When the Gaussian kernel is used as the kernel function, the processor 21 first sets ε (for example, ε = 0.001) having a predetermined value. Next, the processor 21 calculates a value ξ _e (t) of the residual density function at t and t for j = 0, 1, 2,... In the equation (14), and ξ _e (t) < the maximum t that the epsilon, obtained as e _m. Further, the processor 21 calculates the value ξ _e (t) of the residual density function at t and t for j = 0, 1, 2,... In the equation (15), and ξ _e (t)> ε Is determined as e _M.

  Hereinafter, a method for estimating peak power using a Gaussian kernel as a kernel function will be described. Note that the kernel function is not limited to the Gaussian kernel, and the peak power can be estimated by the same method as described below even if another kernel function is used.

An example of a look-up table and a residual density function used when a Gaussian kernel is used is shown below.
FIG. 5 is an example of a look-up table that holds the density function value of the residual. 5, the increment width Δ of t 0.1, the minimum value e _m of t -780, the maximum value e _M of t is 420.

FIG. 6 is a diagram illustrating an example of a residual density function obtained using a Gaussian kernel.
The horizontal axis indicates the residual, and the vertical axis indicates the density of the residual. As shown in FIG. 6, the density function of the residual is not symmetric with respect to the absolute value of the residual. For example, as described above, due to the difference in the magnitude of the correlation with the observed MIPS value due to the difference in operation, It has multiple extreme values.

  Therefore, simply performing regression analysis with a linear expression using MIPS values, and adding the standard deviation of the residual as a design margin to the obtained regression equation (power consumption prediction formula), predicting the peak power, It is an underestimation and there is a possibility that a reasonable value cannot be obtained. It is also conceivable that the observed value when the power estimation target device is in a peculiar state (a state that hardly occurs) deteriorates the peak power prediction accuracy.

  In the present embodiment, the processor 21 first excludes data determined as data when the power estimation target device is in a unique state (hereinafter referred to as unique data). Then, the processor 21 extracts data of the density function region including the maximum point having the maximum residual among the plurality of maximum points (step S13).

The process of step S13 is demonstrated using the flowchart of FIG.
FIG. 7 is a flowchart showing an exemplary flow of extracting observed values and MIPS values.
First, the processor 21 sorts the observed values and the MIPS values corresponding to the observed values in ascending order of the residual e _i calculated by the equation (2) (step S131). This is because, when the power values and MIPS values are sorted in the ascending order of the residuals as shown in the following equation (16), processing such as data extraction described later becomes easy.

In the following, the k-th residual in the sort order is set to e _{s (k)} (1 ≦ k ≦ n) (n is the number of residuals (= number of observed values)), and observations corresponding to e _{s (k)} The value and the MIPS value are represented by y _{s (k)} and x _{s (k)} .

  Next, the processor 21 excludes singular data (step S132). For example, the processor 21 divides the density function of the residual into a plurality of sections based on the magnitude of the residual density, calculates the area for each section by integrating the density function for each section, and prioritizes the section with a large area. The data is extracted within the selected section. The singular data is generated, for example, when the power estimation target device is in a singular state, so that the frequency of occurrence is small and the residual density of the singular data is a small value. By making it difficult to select a section having a small area (a section where there is a high possibility that unique data exists) by the above method, the possibility that specific data can be excluded increases.

Hereinafter, two examples of a method for preferentially selecting a section having a large area and excluding specific data will be described.
(Specific data exclusion method 1)
FIG. 8 is a flowchart illustrating an example of processing for excluding specific data.

First, in order to perform definite integration of the density function ξ _e (t) of the residual, the processor 21 divides the domain of the definite integration domain (step S21). The domain segmentation is preferably performed at each t giving a residual density function ξ _e (t) = 0, but the residual density function using a Gaussian kernel does not take a value of 0. The section division is performed as follows.

FIG. 9 is a diagram illustrating an example of sectioning the domain of the residual density function.
The horizontal axis indicates the residual, and the vertical axis indicates the density of the residual.
First, ε having a predetermined value (for example, ε = 0.001) is set. Next, a look-up table as shown in FIG. 5 is referred to, and t (residual) satisfying ξ _e (t) <ε is searched. The t is, for example, the residual I _{a1 at} the boundary of the section, I _a2 (I _b1 ), I _a3 (I _b2 ), I _a4 (I _b3 ), I _a5 (I _b4 ), I _a6 (I _b5 ). This gives a set of sections I = {(I _a1 , I _b1 ), (I _a2 , I _b2 ) _,. Here, for example, the section (I _a1 , I _b1 ) indicates a section between the residuals I _a1 and I _b1 .

In the section where the width of the section matches the increment width Δ of t, ξ _e (t) in the section is smaller than ε (for example, the sections (I _a3 , I _b3 ) and (I _a4 , I _b4 ) in FIG. )), It is unlikely that the data in that section will be used, so it is desirable to exclude it in order to reduce the amount of calculation of the definite integral.

Next, the processor 21 divides e _{s (k)} , y _{s (k)} , and x _{s (k)} sorted in the process of step S131 so as to correspond to the section determined in the process of step S21 ₍ step S21 _). S22). Such a process is performed in order to easily perform the process of step S24 described later.

For example, the data corresponding to the j-th interval (I _aj , I _bj ) has a minimum k satisfying I _aj < _{es (k)} as kaj and a maximum k satisfying e _{s (k)} <I _bj as kbj. Then, the sort order is from the kajth data to the kbjth data.

The following formulas (17), (18), and (19) show the residual column e _j , the observed value column y _j , and the MIPS value column x _j in the section (I _aj , I _bj ).

Next, the processor 21 calculates a definite integral of the density function ξ _e (t) of the residual for the section obtained by the process of step S21 (step S23). The definite integration in the j-th interval (I _aj , I _bj ) is performed by, for example, a piecewise quadrature method in which the value of the lookup table as shown in FIG. Is called.

In the example shown in FIG. 9, definite integration is performed for each of the sections (I _a1 , I _b1 ), (I _a2 , I _b2 ), (I _a5 , I _b5 ), and the areas SA1 and SA2 indicated by hatched portions. , SA3 is calculated.
After that, the processor 21 extracts data (observation value, MIPS value, residual) corresponding to the section where the area calculated in the process of step S23 is maximum (step S24). In the example shown in FIG. 9, the section with the largest area is (I _a5 , I _b5 ). Therefore, the processor 21 extracts the data in the section (I _a5 , I _b5 ) from the data divided in the process of step S22. The processor 21 performs the subsequent process of step S133 using the extracted data.

As a result, data in a section having a small area (a section in which there is a high possibility that singular data exists) is not used, so that the possibility that singular data can be excluded increases.
(Specific data removal method 2)
In the singular data removal method described below, the processor 21 performs segmentation of the domain and definite integration of the density function in the same manner as described above. From the obtained domain, data of a certain segment is obtained according to a specific condition. By removing, singular data is excluded. Hereinafter, this method will be described with reference to FIG.

FIG. 10 is a flowchart illustrating another example of processing for excluding specific data.
First, the processor 21 divides an interval into the domain of the residual density function ξ _e (t) (step S31) and sorts e _{s (k)} , y sorted in S131 so as to correspond to the interval. _{s (k)} and x _{s (k)} are divided (step S32). Thereafter, the processor 21 calculates a definite integral of ξ _e (t) for the section obtained by the process of step S31 (step S33). The processes in steps S31, S32, and S33 are the same as the processes in steps S21, S22, and S23.

Next, the processor 21 selects and removes any of the divided sections (step S34).
The section to be removed is selected based on preset section removal conditions. For example, when the number of sections not to be removed is determined as the section removal condition, the area calculated in the process of step S33 is preferentially removed from the smallest section. In addition, when the section removal condition is set to remove the average value of the residual in the section where the area is the maximum and the section outside the variance, the section where the average value of the residual in the section is the maximum area The interval farthest from the average value of the residuals is preferentially selected and removed.

  After the process of step S34, the processor 21 determines whether or not there is a section that satisfies the section removal condition (step S35). The processor 21 repeats the process from step S34 when there is a section that satisfies the section removal condition, and performs the process of step S36 when there is no section that satisfies the section removal condition.

In the process of step S36, the processor 21 extracts data (residual, observed value, MIPS value) of the remaining section from the data divided in the process of step S32.
Through the processing as described above, data in a section having a small area (a section in which there is a high possibility that singular data exists) is not used, so that the possibility that singular data can be excluded increases.

As illustrated in FIG. 7, when the singular data exclusion process ends, the processor 21 extracts data in the density function region including the maximum point of the maximum residual (step S133).
When only one local maximum point is included in the remaining section, the peak power prediction formula may be calculated based on the data in that section.

Hereinafter, four examples of the data extraction method in the process of step S133 will be described.
Note that data (residuals, observed values, MIPS values) handled in the following are also sorted in the ascending order of the residuals by the process of step S131 described above.

(Data extraction method (1))
FIG. 11 is a flowchart illustrating a first example of the data extraction method.
In the example of the data extraction method shown in FIG. 11, the data extraction area is set so that the residual that becomes the maximum point becomes the average value in the residual to be extracted.

First, the processor 21 detects the maximum point of the density function of the residual on the side with the highest residual (step S51). In the following, it is assumed that the sort order of the local maximum data is pMth.
FIG. 12 is a flowchart illustrating a flow of an example of a maximum point detection method.

  First, the processor 21 acquires data after the singular data exclusion process (step S132) (step S41), and sets n, which is the maximum value in the sort order of the residual data, to the variable i (step S42). It is assumed that the data acquired in the process of step S41 is the mth (1 ≦ m) to nth data in the sort order (the same applies to the following). However, when the nth data (maximum residual) in the sort order is deleted in the singular data exclusion process in step S132, n is the maximum value in the sort order of the data after the singular data exclusion process. To do.

Thereafter, the processor 21 calculates ξ _e ( _{es (i} −1 ₎ )> ξ _e ( _{es (i)} ) from the relationship between the density of the i-th residual and the density of the i−1th residual. In addition, it is determined whether m <i (step S43). When ξ _e (e _{s (i} -1 ₎ )> ξ _e (e _{s (i)} ) and m <i, the processor 21 subtracts 1 from i (step S44), and the processing from step S42 repeat. When ξ _e (es _(i −1 ₎ )> ξ _e ( _{es (i)} ) and m <i is not satisfied, the processor 21 determines the value of the variable i at that time. It is set to pM which is the sort order of the local maximum data (step S45).

Returning to the description of FIG.
When pM is obtained, the processor 21 determines the residuals from the residual with the sort order kth (m ≦ k <pM) to the residual with the sort order n (corresponding to the number of data n described above). Calculate the average value of. Then, the processor 21 acquires, as ks, the maximum k whose average value is equal to or less than _{es (pM)} (step S52). The reason why m ≦ k <pM is that the residual data is sorted in ascending order. Therefore, if the average value is calculated for the residuals from k to n that are equal to or greater than pM, e _{s (pM)} is calculated. It is because it exceeds.

  After the process of step S52, the processor 21 extracts the data having the sort order from ks + 1 to nth from the data after the removal of the unique data (step S53). As a result, as data of the density function region including the maximum point of the maximum residual, data in the range of the residual in which the residual of the maximum point becomes an average value can be extracted.

Of the extracted data, the residual column can be _{expressed as (es (ks + 1)} , _{es (ks + 2)} ,..., _{Es (n)} ). The MIPS value column is (x _{s (ks + 1)} , x _{s (ks + 2)} ,..., X _{s (n)} ), and the observed value column is (y _{s (ks + 1)} , Y _{s (ks + 2)} ,..., Y _{s (n)} ).

When all the residuals are 0, even if the average of all the residuals is taken, it does not become smaller than _{es (pM)} which is the residual value of the maximum point. In this case, the processor 21 extracts all the data acquired in the process of step S41.

(Data extraction method (2))
FIG. 13 is a flowchart showing a second example of the data extraction method.
In the example of the data extraction method illustrated in FIG. 13, the data extraction area is set so that the sorting order of the residuals that are the maximum points is the center in the data extraction area.

The process of step S61 is the same as the process of step S51 shown in FIG. 11, the residual that becomes the maximum point is detected, and pM that is the sort order of the residual data that becomes the maximum point is obtained.
Next, the processor 21 sets 2pM-n or m which is larger as ks which determines the data extraction range (step S62). An example of determining ks will be described below with reference to FIG.

FIG. 14 is a diagram for explaining an example of the range of data to be extracted.
The horizontal axis indicates the sort order of data by the process of step S131, and the sort order of the first to nth data is shown.

  As described above, the residual that becomes the local maximum becomes the pMth data in the sort order, but when counted from the larger side (n side), it becomes the n−pM + 1th data. In order to extract data from the residual of the highest value so that the sorting order of the residual that becomes the maximum point becomes the center in the data extraction area, counting from the n side, 2 (n−pM + 1) −1. What is necessary is just to extract the data. This is because the number of residual data from the pMth to the nth is n−pM + 1 as shown in FIG.

This is equivalent to extracting the nth residual data from the 2pM-nth residual data in the sort order.
Therefore, the processor 21 sets 2pM-n to ks so that the lower limit of the data extraction range is 2pM-nth data.

However, when 2pM−n ≦ m−1, the 2pM−nth data cannot be set as the lower limit of the data extraction range, and therefore the lower limit is set as the mth data and m is set to ks.
Since 2pM-nth data can be set as the lower limit of the data extraction range when 2pM-n ≧ m, 2pM-n or the larger of m may be set in ks (2pM-1 When m = m, k is set to m).

Returning to the description of the flow in FIG.
After the process of step S62, the processor 21 extracts the data with the sort order from the ksth to the nth from the data after the removal of the unique data (step S63). As a result, data in the data extraction region can be extracted as the data in the density function region including the maximum point of the residual difference, such that the sort order (pM) of the residuals that are the maximum point is in the center of the data extraction region. Of the extracted data, the residual column can be _{expressed as (es (ks)} , _{es (ks + 1)} ,..., _{Es (n)} ). The MIPS value column is (x _{s (ks)} , x _{s (ks + 1)} ,..., X _{s (n)} ), and the observed value column is (y _{s (ks)} , y _{s ( ks + 1)} ,..., y _{s (n)} ).

(Data extraction method (part 3))
FIG. 15 is a flowchart illustrating a third example of the data extraction method.
In the example of the data extraction method shown in FIG. 15, the data extraction area is set so that the residual that becomes the maximum point becomes the value of the middle point in the residual of the data extraction area.

The process of step S71 is the same as the process of step S51 shown in FIG. 11, the residual that becomes the maximum point is detected, and pM that is the sort order of the residual data that becomes the maximum point is obtained.
Next, the processor 21 determines the data extraction region so that the maximum residual value is set as the upper limit of the residual of the data extraction region and the residual having the maximum point becomes the midpoint of the residual of the data extraction region. Is determined (step S72).

In order to set the maximum value of the residual as the upper limit of the residual in the data extraction region and the residual as the maximum point as the midpoint of the residual in the data extraction region, the lower limit residual in the data extraction region is set to e _{s ( n)} -2 ( _{es (n)} -es _(pM) ). Therefore, the processor 21 sets the maximum k satisfying _{es (k)} < _{es (n)} -2 _{(es (n)} −es _(pM) ) as ks.

After the process of step S72, the processor 21 extracts the data having the sort order from ks + 1 to nth from the data after the removal of the unique data (step S73). As a result, as data in the density function region including the maximum residual maximum point, data in the data extraction region can be extracted so that the residual that becomes the maximum point becomes the midpoint of the residual in the data extraction region. Of the extracted data, the residual column can be _{expressed as (es (ks + 1)} , _{es (ks + 2)} ,..., _{Es (n)} ). The MIPS value column is (x _{s (ks + 1)} , x _{s (ks + 2)} ,..., X _{s (n)} ), and the observed value column is (y _{s (ks + 1)} , Y _{s (ks + 2)} ,..., Y _{s (n)} ).

(Data extraction method (4))
FIG. 16 is a flowchart illustrating a fourth example of the data extraction method.
In the example of the data extraction method shown in FIG. 16, in the density function, when the residual from the highest value is scanned to the side where the residual is smaller, the residual that becomes the minimum point detected first is extracted. The data extraction area is set so as to be a residual at the lower limit of the area.

The process of step S81 is the same as the process of step S51 shown in FIG. 11, and the residual that becomes the maximum point is detected, and pM that is the sort order of the residual data that becomes the maximum point is obtained.
Next, the processor 21 scans from the residual of the highest value to the side of smaller residual, and detects the minimum point of the density function of the residual (step S82). In the following, the sort order of the local minimum data is pm.

A method for detecting the minimum point number pm of the density function of the residual will be described below with reference to FIG.
FIG. 17 is a flowchart showing a flow of an example of a minimum point detection method.

First, the processor 21 acquires residual data after the singular data exclusion process (step S132) (step S91), and sets pM-1 to the variable i (step S92).
Thereafter, the processor 21 calculates ξ _e (e _{s (i)} ) <ξ _e (e _{s (i + 1)} ) from the relationship between the density of the i-th residual and the density of the i + 1-th residual. , M <i is determined (step S93). When ξ _e (e _{s (i)} ) <ξ _e (e _{s (i + 1)} ) and m <i, the processor 21 subtracts 1 from i (step S94), and performs the processing from step S92. repeat. If neither of the following conditions is satisfied, ξ _e (e _{s (i)} ) <ξ _e (e _{s (i + 1)} ) and m <i, the processor 21 determines the value of the variable i at that time. It is set to pm which is the sort order of the minimum points (step S95).

Returning to the description of FIG.
After the process of step S95, the processor 21 extracts the data with the sort order from the pmth to the nth from the data after the removal of the unique data (step S83). As a result, as the density function area data including the maximum residual maximum point, the minimum point detected next to the maximum point detected when scanning from the highest residual to the smaller residual side. Can be extracted from the data extraction area so as to be the residual of the lower limit of the data extraction area.

Of the extracted data, the residual column can be expressed as _{(es (pm)} , _{es (pm + 1)} ,..., _{Es (n)} ). Further, the MIPS value column is (x _{s (pm)} , x _{s (pm + 1)} ,..., X _{s (n)} ), and the observed value column is (y _{s (pm)} , y _{s ( pm + 1)} ,..., y _{s (n)} ).

  When the data extraction process as described above is completed, the process of step S14 is performed in the flow shown in FIG. In the process of step S14, the processor 21 calculates a peak power prediction formula using the data extracted in the process of step S13. Then, the processor 21 predicts the peak power based on the peak power prediction formula (step S15).

Three examples of peak power prediction formula calculation methods will be described below.
(Example of calculation method of peak power prediction formula (1))
FIG. 18 is a diagram illustrating an example of an extracted residual density function.

The horizontal axis indicates the residual, and the vertical axis indicates the residual density. In the example of FIG. 18, the standard deviation σ of the extracted residual is 54 and the average value μ is 170.
In the first example of the peak power prediction formula calculation method, the processor 21 calculates the standard deviation as described above from the extracted residual, and obtains the peak power prediction formula using the standard deviation. For example, the processor 21 calculates a standard deviation from the extracted residual, adds a value obtained by multiplying the standard deviation by 3 as a design margin to the power consumption prediction formula obtained in the process of step S11, and calculates the peak power. Find the prediction formula. The peak power prediction formula obtained by adding the value obtained by multiplying the standard deviation σ = 54 by 3 to the power consumption prediction formula shown in Formula (3) is as shown in Formula (21) below. (Significant figures are shown in two digits).

(Example of calculation method of peak power prediction formula (2))
In the second example of the peak power prediction formula calculation method, the processor 21 calculates a standard deviation and an average value from the extracted residual, and obtains a peak power prediction formula using the standard deviation and the average value. For example, the processor 21 calculates the standard deviation and the average value from the extracted residuals, and uses the value obtained by adding the standard deviation multiplied by 3 and the average value as the design margin as the power consumption obtained in the process of step S11. To obtain a peak power prediction formula. The peak power prediction obtained by adding the value obtained by multiplying the standard deviation σ = 54 shown in FIG. 18 by 3 and the average value μ = 170 of the residuals to the power consumption prediction formula shown in Expression (3). The formula is as shown in the following formula (22) (significant figures are shown in two digits).

(Example of calculation method of peak power prediction formula (3))
In the third example of the peak power prediction formula calculation method, the processor 21 performs regression analysis and residual calculation using the observed power consumption value and MIPS value extracted in step S13. A peak power prediction formula is obtained from the prediction formula of power consumption and the standard deviation of the residual.

First, similarly to the process of step S11 described above, the processor 21 performs regression analysis using the extracted observation values and MIPS values and calculates a residual.
FIG. 19 is a diagram illustrating the correlation between the extracted MIPS value and the observed power consumption value.

  The horizontal axis indicates the MIPS value, and the vertical axis indicates the power consumption. Plots (for example, plot plt2) indicated by squares and triangles indicate observed values extracted by the process of step S13. A straight line ln2 shown in FIG. 19 represents the power consumption prediction formula calculated by the processor 21 based on the formula (1) and the extracted MIPS value and the observed value as a regression line. The power consumption prediction formula is, for example, the formula (23) (significant figures are shown in two digits).

The residual is calculated by the above-described equation (2). For example, the residual from the predicted value of the observed value of the plot plt2 is d12.
Since the data shown in FIG. 19 is data after the singular data removal and data extraction processing, it can be seen that the observed power consumption value and the MIPS value show a good correlation.

The processor 21 obtains the standard deviation of the residual.
Thereafter, for example, the processor 21 adds a value obtained by multiplying the standard deviation of the residual by 3 to the power consumption prediction formula represented by Expression (23) as a design margin to obtain a peak power prediction formula. For example, assuming that the standard deviation σ of the residual obtained from the relationship between the observed value and the power consumption prediction formula shown in FIG. 19 is 51, the peak power prediction formula is as shown in the following formula (24) (effective Numbers are shown in two digits).

(Example of peak power prediction)
FIG. 20 is a table showing an example of peak power prediction.
In FIG. 20, for example, when the peak power prediction formula calculated by the following five methods (1) to (5) is used based on the observed value correlated with the MIPS value as shown in FIG. An example of peak power prediction is shown.

  The peak power prediction formula obtained by each method, the ratio of the observed value exceeding the predicted value obtained by the peak power prediction formula, the peak power prediction value when x = 0 (that is, the MIPS value is 0), x = 6000 (that is, The peak power prediction value when the MIPS value is 6000) is shown.

  In the method (1), a peak power prediction formula is obtained using linear programming. In the method (2), the peak power prediction formula is obtained by adding a value obtained by multiplying the standard deviation of the residual by 3 to the power consumption prediction formula obtained in step S11.

  In the method (3), the peak power prediction formula shown in the formula (21) is obtained by the first method of the above-described calculation method of the peak power prediction formula. In the method (4), the peak power prediction formula shown by the formula (22) is obtained by the second method of the calculation method of the peak power prediction formula. In the method (5), the peak power prediction formula shown in the formula (24) is obtained by the third method of the calculation method of the peak power prediction formula.

  In the methods (1) and (2), there is no observed value exceeding the predicted value obtained by the peak power prediction formula. In the method (3), the observed value exceeding the predicted value obtained by the peak power prediction formula is 21%. In the methods (4) and (5), the observed value exceeding the predicted value obtained by the peak power prediction formula is 0.6%.

  It can be seen that the peak power predicted value is larger in the methods (1) and (2) than in the methods (3) to (5) when x = 0. When x = 6000, it can be seen that the peak power predicted value is larger in the method (2) than in any of (3) to (5).

  For example, when x = 0, the peak power predicted value in the method (2) is 1500 mW, which is about 36% compared with the peak power predicted value (1100 mW) obtained by the methods (4) and (5). Is also big. Further, for example, when x = 6000, the peak power predicted value in the method (2) is 2300 mW, which is 21% larger than the peak power predicted value (1900 mW) obtained in (4) and (5). .

  In the methods (1) and (2), the peak power is predicted without considering the tendency of the power consumption with respect to the change of the MIPS value by using all the observation values including the observation value that may be peculiar data. Therefore, it is considered that the peak power prediction value is overestimated.

  On the other hand, in the methods (3) to (5), the density function of the residual value between the predicted value of power consumption and the observed value by regression analysis is calculated, and the maximum point having the maximum residual among the plurality of maximum points is calculated. The peak power is predicted based on the data of the density function region that includes it. Thereby, even when there is an outlier in the observed value or when the power consumption shows a plurality of trends with respect to the change in performance information, the peak power of the apparatus can be estimated accurately.

  Further, in the present embodiment, since the data that is considered to be in a unique state of the power estimation target device is removed before data extraction, the peak power of the device can be estimated with higher accuracy.

  As described above, one aspect of the power estimation method, the power estimation apparatus, and the program according to the present invention has been described based on the embodiments, but these are merely examples and are not limited to the above description.

  For example, the case where the performance information is of one type (for example, MIPS value) has been described above, but each process in the above embodiment can be similarly applied even when there are a plurality of types of performance information. When considering a plurality of performance information, the number of explanatory variables in Equation (1) is increased, and a coefficient to be multiplied by the explanatory variables is calculated by regression analysis to obtain a prediction formula for power consumption. Thereafter, the density function of the residual is similarly calculated, data extraction processing is performed, and a peak power prediction formula is calculated.

DESCRIPTION OF SYMBOLS 1 Power estimation object apparatus 10 Power estimation apparatus 11 Processor 12 Storage part 13a Regression line 13b Plot 14a Density function 14b, c, d Maximum point 14e Maximum value 14h Data extraction area D1 Power information D2 Performance information

Claims (6)

The power estimation device
Based on the observed value of power consumption according to the performance information value of the power estimation target device, calculate the prediction formula of the power consumption by regression analysis,
Calculating the density function of the residual between the predicted value obtained by the prediction formula and the observed value;
From the data represented by the density function, the data of the area of the density function including the maximum point where the residual is the maximum among the maximum points of the density function is extracted,
Based on the extracted data, a prediction formula for the peak value of the power consumption is calculated.
A power estimation method characterized by the above.   The power estimation method according to claim 1, wherein the extracted data includes the residual included in the region or the observation value corresponding to the residual. Dividing the density function into a plurality of intervals based on the magnitude of the residual density;
Integrate the density function for each interval to calculate the area for each interval,
3. The power estimation method according to claim 1, wherein, among the plurality of sections, a section having the large area is preferentially selected, and the data is extracted within the selected section.   The power estimation method according to claim 3, wherein the plurality of sections are deleted in order from the section having the smallest area. Have a processor,
The processor is
Based on the observed value of power consumption according to the performance information value of the power estimation target device, calculate the prediction formula of the power consumption by regression analysis,
Calculating the density function of the residual between the predicted value obtained by the prediction formula and the observed value;
From the data represented by the density function, the data of the area of the density function including the maximum point where the residual is the maximum among the maximum points of the density function is extracted,
Based on the extracted data, a prediction formula for the peak value of the power consumption is calculated.
A power estimation device. Based on the observed value of power consumption according to the performance information value of the power estimation target device, calculate the prediction formula of the power consumption by regression analysis,
Calculating the density function of the residual between the predicted value obtained by the prediction formula and the observed value;
From the data represented by the density function, the data of the area of the density function including the maximum point where the residual is the maximum among the maximum points of the density function is extracted,
Based on the extracted data, a prediction formula for the peak value of the power consumption is calculated.
A program that causes a computer to execute processing.

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