JP6097200B2 - Data estimation method and apparatus - Google Patents

Description

  The present invention relates to a data estimation method and apparatus, and more particularly, to a data estimation method and apparatus applied to monitoring, image sensing, and the like in a real environment in the power field, energy field, communication field, and sensing field.

  Various sensors are used to measure the characteristics of natural phenomena in real space. For the output from each sensor, noise is removed to obtain a highly accurate measurement value, or a prediction process is performed to utilize the measurement result. However, since many prediction methods perform prediction calculation by applying a linear model or a nonlinear model independently for each sensor, physical phenomena in real space cannot be sufficiently expressed.

  For example, measuring and knowing the characteristics of airflow in real space is necessary and important in reducing energy consumption in air conditioners, communication devices, server computers and the like in a communication device room. In an actual operation system, in order to construct an optimal control system for energy saving, it is required to predict time-series temperature changes. For physical phenomena such as temperature changes, not only a single point in space but also the influence of its vicinity should be considered.

  However, as described above, since the prediction calculation is performed for each sensor, the physical phenomenon is not sufficiently expressed. In conventional methods, it is difficult to interpolate physical phenomena at intermediate positions between sensors as numerical values, and complicated physical system equations are solved simultaneously, resulting in a time delay that is not suitable for online control. It was. In addition, since mathematical equations that differ for each physical quantity are introduced, there is a problem that the memory capacity of the entire system becomes enormous.

http://hil.t.u-tokyo.ac.jp/~sagayama/enshu3/Enshu2010s1-LPC.pdf http://www.caero.mech.tohoku.ac.jp/publicData/Daiguji/Chapter5.pdf http://opencv.jp/sample/optical_flow.html

  Conventionally, as a method of interpolating physical quantities at intermediate positions between sensors using measurement data from sensors or predicting future physical quantities from measurement data acquired in time series, data is applied to appropriate physical equations such as diffusion equations. A method of interpolation and prediction was known by substituting and determining parameters of the equation. However, in the diffusion equation, the diffusion coefficient is often a constant value, and there is a problem that it is difficult to accurately estimate a non-uniform physical quantity distribution due to a deviation from an actual physical phenomenon. It was.

  An object of the present invention is to provide a data estimation method and apparatus capable of estimating spatial interpolation and temporal prediction with high accuracy for a physical variable in a two-dimensional plane or a three-dimensional space. It is in.

One embodiment of the data estimation method according to the present invention is a data estimation method for estimating a physical quantity of a physical phenomenon in a two-dimensional plane or a three-dimensional space in a data estimation apparatus connected to a plurality of sensors, The measurement data output from the sensor is acquired in time series and stored in the data storage means, and the measurement data stored in the data storage means is read out, and at any given time, one two-dimensional plane or A step of mapping measurement data in a three-dimensional space, a velocity vector is estimated from the mapped measurement data based on a spatial distribution and a time series change, and an advection diffusion equation in which the velocity vector is substituted is used. recursively calculated Te, characterized by comprising the step of outputting the estimated data by performing a spatial interpolation and temporal prediction

Wherein said step of outputting the estimated data, the advection diffusion equation obtained by substituting the velocity vector is discretized by finite difference method, time and space to be proportional to the diffusion coefficient of the advection-diffusion equation to the reciprocal of the speed from the speed vector It is also possible to calculate spatial interpolation and temporal prediction by changing according to.

  As described above, according to the present invention, a velocity vector is obtained from discrete measurement data, and a physical quantity in a two-dimensional plane or a three-dimensional space is obtained by spatial interpolation and temporal analysis using a diffusion equation using a diffusion coefficient. Accurate prediction can be estimated with higher accuracy. As a result, it is possible to perform spatial interpolation and temporal prediction with higher accuracy from measurement data having a spatially coarse distribution regardless of the type of the measured physical quantity.

It is a figure which shows the data estimation apparatus concerning one Embodiment of this invention. It is a figure which shows the example which performs temporal prediction from the measurement data of a sensor. It is a figure which shows the example which performs spatial interpolation from the measurement data of a sensor. It is a figure which shows the example using the diffusion equation concerning one Embodiment of this invention.

  Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings. In this embodiment, measurement data of physical quantities such as temperature, speed, pressure, etc. is acquired from discretely arranged sensors, and a velocity vector is obtained by an optical flow method based on a spatial distribution and a time series change. . By calculating recursively using the advection-diffusion equation into which the obtained velocity vector is substituted, spatial interpolation and temporal prediction are estimated with high accuracy.

  FIG. 1 shows a data estimation apparatus according to an embodiment of the present invention. For example, a plurality of sensors 180 installed in the communication equipment room are connected to the data estimation apparatus 100. Measurement data output from the sensor 180 is taken in time series by the data measuring means 110 and accumulated in the data accumulating means 120. The data synthesizing unit 130 reads the measurement data stored in the data storage unit 120 and maps the measurement data to one two-dimensional plane or three-dimensional space for each arbitrary time.

  The speed estimation unit 140 estimates a speed vector from the mapped measurement data based on a spatial distribution and a time-series change, for example, estimates an airflow speed. The diffusion coefficient varying means 150 changes the diffusion coefficient according to time and space so as to be proportional to the reciprocal of the speed. The data interpolation / prediction means 160 uses the estimated velocity vector and the diffusion coefficient to interpolate / predict in a spatio-temporal manner using a physical equation (convection-diffusion equation) based on measurement data at a certain time, and estimate data Is generated. The measurement data and the estimation data are displayed by the display unit 170.

  With reference to FIG. 2, an example of performing temporal prediction from sensor measurement data will be described. The data measurement unit 110 acquires measurement data 200 about temperature, wind speed, and atmospheric pressure as different physical quantities from a plurality of different sensors 180. The plurality of sensors 180 are arranged, for example, on a two-dimensional surface or a three-dimensional space in the communication device room.

  Conventionally, future prediction data 210 has been predicted using a linear model or a nonlinear model (see, for example, Non-Patent Document 1). The prediction method is made one-dimensionally for each physical quantity. However, since thermal fluid (air) is interposed between the sensors, there is a certain correlation between the measurement data of adjacent sensors.

  FIG. 3 shows an example in which spatial interpolation is performed from sensor measurement data. In FIG. 3A, four temperature sensors 181 to 184 are arranged in a certain two-dimensional plane 300, and the data estimation apparatus 100 acquires temperature measurement data from each temperature sensor. This measurement data represents the temperature of the space closest to the temperature sensors 181 to 184. That is, only the temperature in the range of the small circle shown in FIG. 3A is shown, and the temperature at the intermediate position between the temperature sensors is not directly known.

  Therefore, the temperature at the intermediate position can be interpolated by a geometric interpolation method as described in Non-Patent Document 2. As shown in FIG. 3B, the temperature at an intermediate position is calculated from the measurement data of the adjacent temperature sensors, and estimated data representing the temperature of the space away from the temperature sensors 181 to 184 can be obtained. . Note that FIG. 3 shows a range where estimated data can be obtained, and does not show a temperature distribution. The intervals of the temperature sensors do not need to be equal, and can be interpolated using measurement data from sensors at arbitrary positions. However, this method cannot perform interpolation / prediction on time-series data.

  FIG. 4 shows an example using a diffusion equation according to an embodiment of the present invention. It is known that the accuracy can be improved by using a physical equation for interpolation and prediction when a physical phenomenon is involved. Therefore, the advection diffusion equation is used in this embodiment. The three-dimensional advection-diffusion equation uses a diffusion coefficient λ, where S (t) is a physical quantity such as temperature, velocity, and atmospheric pressure at a certain time t.

It is expressed. However,

And u is a velocity vector. Equation (1) expresses a phenomenon in which the change in value per unit time depends on λ, and the initial density becomes thinner with time. There are a case where the spatial position of S (t) is constant and a case where it moves, but the present embodiment deals with the former case where the spatial position of S (t) is constant. The left side of Equation (1) is a first derivative with respect to time, and the right side is a second derivative with respect to space. The diffusion prediction can be easily calculated by the finite difference method to spread isotropically and uniformly. When equation (1) is discretized by the finite difference method,

It becomes. In Equation (2), S is a general-purpose variable that is not limited to a specific physical quantity. However, in order to simplify the expression, the two-dimensional plane 400 is divided into a lattice shape, and the lattice width is set to 1 for x and y. The velocity vector u = (u, v). (I, j) indicates a discrete position in the analysis region, and n indicates a discrete time. Hereinafter, Δt = 1. The obtained solution has an apparently smooth change in a shorter time as the diffusion coefficient λ is larger.

  The velocity vector u can be obtained based on the spatial distribution of the acquired measurement data and the time series change (for example, Non-Patent Document 3). The motion estimation methods are roughly classified into a pattern matching method and a gradient method, which are called apparent velocity and optical flow obtained by these methods. FIG. 4B shows the result of obtaining the velocity vector in the analysis region by the optical flow method.

  The obtained velocity vector 410 (FIG. 4B) is substituted into equation (2). In Expression (2), after substituting the value of S at n = 1 as an initial condition, S is recursively calculated (with the values of time n and n + 1 switched) in the entire analysis region. As a result, the estimation result 420 of the advection phenomenon shown in FIG. 4C is obtained from the estimation data shown in FIG.

  The diffusion phenomenon becomes prominent when the moving speed of an air current or the like is slow. On the other hand, when the moving speed is fast, the advection phenomenon becomes strong, so that it can be assumed that the diffusion effect becomes thin. Here, it is assumed that the diffusion coefficient is constant and constant regardless of the concentration gradient. Even if the influence of the diffusion phenomenon is constant, if the speed due to the advection phenomenon is not zero, the concentration always changes. Therefore, the equation (2) is effective when the advection phenomenon is stronger than the diffusion phenomenon. From this, even if the diffusion coefficient is a constant value, spatial interpolation and temporal prediction can be estimated with high accuracy. Note that FIG. 4 shows the range in which the estimated data can be obtained, as in FIG. 3, and does not show the temperature distribution.

  In the present embodiment, the diffusion coefficient λ is basically constant. However, if necessary, the diffusion coefficient λ can be given in proportion to the reciprocal of the magnitude of the speed. Diffusion coefficient

Becomes different for each time and space, and the estimation accuracy can be improved.

  The general setting method of the diffusion coefficient can be simplified and empirically determined to be a partial differential equation with only a diffusion term and a time term, except for special cases. For example, if the average flow velocity (average advection speed) of the air current in the communication equipment room is 1 m / sec and the average temperature gradient is 1 degree / m, the diffusion coefficient is the temperature gradient per unit time, and diffusion When the phenomenon is slower than the advection phenomenon, the diffusion coefficient λ is 0.7.

  According to this embodiment, a velocity vector is obtained from discrete measurement data, and spatial interpolation and temporal prediction are performed on a physical quantity in a two-dimensional plane or a three-dimensional space by a diffusion equation using a diffusion coefficient. It can be estimated with higher accuracy.

  This makes it possible to perform spatial interpolation and temporal prediction with higher accuracy from measured data with a spatially coarse distribution regardless of the type of physical quantity measured, and control physical quantities in various facilities. Can be implemented more appropriately and efficiently.

100 Data Estimator 180-184 Sensor

Claims (4)

A data estimation method for estimating a physical quantity of a physical phenomenon in a two-dimensional plane or a three-dimensional space in a data estimation device connected to a plurality of sensors,
Acquiring measurement data output from the plurality of sensors in time series and storing the data in a data storage unit;
Reading the measurement data stored in the data storage means, and mapping the measurement data to one two-dimensional plane or three-dimensional space for each arbitrary time;
From the mapped measurement data, a velocity vector is estimated based on a spatial distribution and a change in time series, recursively calculated using an advection diffusion equation with the velocity vector substituted, and spatial interpolation and And a step of performing temporal prediction and outputting estimated data. A data estimation method for estimating a physical quantity of a physical phenomenon in a two-dimensional plane or a three-dimensional space in a data estimation device connected to a plurality of sensors,
Acquiring measurement data output from the plurality of sensors in time series and storing the data in a data storage unit;
Reading the measurement data stored in the data storage means, and mapping the measurement data to one two-dimensional plane or three-dimensional space for each arbitrary time;
From the mapped measurement data, the velocity vector is estimated based on the spatial distribution and the change in time series, and the advection diffusion equation into which the velocity vector is substituted is discretized by the finite difference method, and the diffusion coefficient of the advection diffusion equation is calculated. And calculating a spatial interpolation and a temporal prediction by changing the speed vector according to time and space so as to be proportional to the reciprocal of the speed from the speed vector, and outputting estimated data. Characteristic data estimation method. A data estimation device that is connected to a plurality of sensors and estimates a physical quantity of a physical phenomenon in a two-dimensional plane or a three-dimensional space,
Data measurement means for acquiring measurement data output from the plurality of sensors in time series;
Data storage means for storing the acquired measurement data;
Data combining means for reading the measurement data stored in the data storage means and mapping the measurement data to one two-dimensional plane or three-dimensional space for each arbitrary time;
A velocity estimation means for estimating a velocity vector from the mapped measurement data based on a spatial distribution and a time-series change;
And wherein the velocity vector recursively calculated using the convection-diffusion equation obtained by substituting, and a data interpolation and prediction means for outputting the estimated data by performing a spatial interpolation and temporal prediction Data estimation device. A data estimation device that is connected to a plurality of sensors and estimates a physical quantity of a physical phenomenon in a two-dimensional plane or a three-dimensional space,
Data measurement means for acquiring measurement data output from the plurality of sensors in time series;
Data storage means for storing the acquired measurement data;
Data combining means for reading the measurement data stored in the data storage means and mapping the measurement data to one two-dimensional plane or three-dimensional space for each arbitrary time;
A velocity estimation means for estimating a velocity vector from the mapped measurement data based on a spatial distribution and a time-series change;
The advection diffusion equation into which the velocity vector is substituted is discretized by a finite difference method, and the diffusion coefficient of the advection diffusion equation is changed according to time and space so as to be proportional to the reciprocal of velocity from the velocity vector. A data estimation apparatus comprising: a data interpolation / prediction unit that calculates simple interpolation and temporal prediction and outputs estimated data.