JP7014394B2 - Temperature measurement method and equipment - Google Patents

Description

The present invention relates to a temperature measuring method and an apparatus for measuring a temperature distribution in a building or an urban space using a thermal infrared spectroradiometer.

When measuring the temperature distribution in a building space or an urban space, there is a method of installing a thermometer at each place where the temperature is to be measured. By such a method, many thermometers are required to measure the temperature distribution, and it may be difficult to install a thermometer depending on the restrictions of actual measurement. In addition, since the thermometer has a heat capacity, the time constant may be a problem, and there is a problem that an error due to the influence of radiation is likely to be mixed due to the measurement principle.

In Japanese Patent Application Laid-Open No. 63-100309 (Patent Document 1), a detection plate made of a material having a small heat capacity is installed in a space where a temperature distribution should be measured, and an infrared radiation temperature for measuring the temperature of the detection plate. The meter discloses a device for measuring the temperature distribution inside the building.

Further, in Japanese Patent Application Laid-Open No. 10-318844 (Patent Document 2), the temperature at which the sea surface temperature is estimated based on the thermal infrared image data obtained by photographing the sea surface from an artificial satellite and the atmospheric state information at the time of photographing. The estimation device is disclosed. Further, in the field of remote sensing, a method of observing the vertical distribution of air temperature from an artificial satellite or the ground with a spectroradiometer has been put into practical use. For example, in Kaplan, LD; Opt.Soc.Am .: 49 (10), 1959, p.1004. (Non-Patent Document 1), Kaplan (1959) observes multiple wavelengths with different gas absorption coefficients. It is disclosed that it is possible to obtain a vertical distribution of temperature in. In addition, Wark, D.Q .; Hilleary, D.T .; Science.165 (3899), 1969, p.1256. (Non-Patent Document 2) discloses that the vertical distribution of temperature can be observed by an artificial satellite. Further, Japanese Patent Application Laid-Open No. 2007-3308 (Patent Document 3) describes a ground surface temperature estimation method and a program for accurately estimating the ground surface temperature based on the observed values of a thermal infrared sensor mounted on an aircraft or the like. It has been disclosed. Further, when estimating the ground surface temperature of the observation target region based on the radiation transmission calculation for evaluating the influence of the atmosphere, a method of estimating the ground surface brightness temperature using a radiation transmission equation including atmospheric parameters is disclosed. As described above, in the field of remote sensing, it is disclosed to measure the vertical distribution of air temperature (temperature distribution along the vertical direction of the earth's surface).

Here, the outline of the conventional radiation transmission process and the formulation of the observation equation will be described.

Regarding the radiation transmission process, it is generally known that radiation is absorbed or scattered by substances in the air and attenuated while propagating in the air, and is amplified by scattering from other directions or radiation from the air. There is. The general solution of the radiation transfer equation that describes the radiation transfer process can be expressed as the following equation 1 as an observation equation when the boundary surface is a blackbody and the local thermodynamic equilibrium state is set.

数１について説明すると、数１の左辺は分光放射計に入射するエネルギー、数１における右辺第１項は境界面からの寄与、第２項は空気からの寄与を表している。なお、

であり、熱赤外光は波長が可視光線より長く、散乱の影響が殆どないので、散乱を無視できる。このため、光の放射伝達方程式による

は、数１のように近似することができる。

Explaining the number 1, the left side of the number 1 represents the energy incident on the spectroradiometer, the first term on the right side of the number 1 represents the contribution from the interface, and the second term represents the contribution from the air. note that,

Therefore, since the wavelength of thermal infrared light is longer than that of visible light and there is almost no influence of scattering, scattering can be ignored. Therefore, it depends on the radiation transmission equation of light.

Can be approximated as in equation 1.

FIG. 1 is a schematic diagram showing how radiation from a boundary surface is incident on an observation aircraft (for example, a thermal infrared spectroradiometer). In FIG. 1, the contribution from the air layer divided into n layers to the observation aircraft is shown, and the thickness of the arrow indicates that the closer the air layer is to the observation aircraft, the greater the contribution to the observation aircraft. Here, the integral of the second term in Equation 1 is calculated as an air layer discretized into n layers. Then, for efficient programming and simplification of understanding, the observed value measured by the observer is y, the true value of the temperature in each air layer (true temperature distribution) is x, and the error ε is explicitly expressed. However, I promise that the observation equation of Equation 1 can be simply expressed as Equation 2 below. It should be noted that T (s') of Eq. 1 corresponds to x of Eq. 2 and Iv (s) of Eq. 1 corresponds to y of Eq. 2.

各空気層における気温（真の気温分布）ｘが、観測値ｙに対して寄与する程度については、数３のように表すことができ、ヤコビアン（Jacobian matrix）と呼ばれる。

The degree to which the air temperature (true air temperature distribution) x in each air layer contributes to the observed value y can be expressed as in Equation 3, and is called the Jacobian matrix.

観測値ｙの数値計算をするため、数２について真の気温分布ｘの近傍ｘ₀において、数３のヤコビアンを用いて、数２をテイラー展開することができる。数２のテイラー展開は下記数４として表せる。

In order to perform the numerical calculation of the observed value y, the number 2 can be Taylor-expanded by using the Jacobian of the number 3 in the neighborhood x ₀ of the true temperature distribution x for the number 2. The Taylor expansion of the number 2 can be expressed as the following number 4.

水平方向から観測機に入射されるエネルギーを計算した例を図２に示し、ヤコビアン（Jacobian matrix）を計算した例を図３に示す。図３に示されるように、ヤコビアンは境界面と観測機との距離の増加するにつれて単調に減少する。つまり、観測機から離れた位置の空気からの寄与が小さくなる。このようなヤコビアンの特性は、人工衛星からの鉛直方向の観測と異なり、水平方向の観測に特有なものである。

An example of calculating the energy incident on the observation aircraft from the horizontal direction is shown in FIG. 2, and an example of calculating the Jacobian matrix is shown in FIG. As shown in FIG. 3, the Jacobian decreases monotonically as the distance between the interface and the observation aircraft increases. That is, the contribution from the air at a position far from the observation aircraft becomes small. Such characteristics of Jacobian are peculiar to horizontal observation, unlike vertical observation from artificial satellites.

To obtain the temperature distribution is to calculate the true temperature distribution x from the observed value y of Equation 2. The premise is that the concentration of gas (air) is known, and the temperature and reflectance of the interface are known.

With such a premise, by dividing the air into n layers and setting the number of observation channels to m, it is possible to obtain m simultaneous equations having n unknowns. By measuring using an observer (thermal infrared spectroradiometer) that can observe with m channels, the number m of simultaneous equations is set to n or more (n <m). By solving the simultaneous equations, the temperature (air temperature distribution x) in each air layer can be calculated.

Japanese Unexamined Patent Publication No. 63-100309 Japanese Unexamined Patent Publication No. 10-318844 Japanese Unexamined Patent Publication No. 2007-3308

Kaplan, L.D .; Opt.Soc.Am .: 49 (10), 1959, p.1004. Wark, D.Q .; Hilleary, D.T .; Science.165 (3899), 1969, p.1256.

However, as shown by the equations 2 and 4, the error ε is added to the actual observed value y. The solution then responds sensitively to the error ε. It is known that such agility becomes a problem, and in actual observations, it is not possible to obtain a sufficiently meaningful and credible solution of simultaneous equations.

Against this background, in the field of remote sensing, there is no disclosure regarding the measurement of the temperature distribution in the horizontal direction with respect to the ground surface and the distance between the boundary surface and the observation aircraft. Then, in the measurement of the temperature distribution in the vertical direction with respect to the earth's surface from an artificial satellite, it is possible to utilize the property that the gas component decreases as the altitude rises. On the other hand, such a property cannot be used when measuring the horizontal distribution of air temperature.

The present invention has been made based on the above circumstances, and an object of the present invention is to reversely estimate the temperature distribution mainly in the horizontal direction with respect to the ground surface in the field of construction by using a thermal spectroradiometer. It is an object of the present invention to provide a method and an apparatus for measuring a temperature.

The present invention estimates the temperature distribution of air from the building or urban space to the observation point by observing infrared rays emitted from the building or urban space and analyzing the observed infrared observed values. The object of the present invention is to set the temperature as x, the infrared observed value as y, the prior probability distribution related to the temperature distribution as P (x), and the probability density function of the observed error of the infrared observed value. P (y | x), the posterior probability distribution related to the temperature distribution is P (x | y), and the posterior probability distribution P (x) and the probability density function P (y | x) are used as the posterior probability distribution. It is achieved by estimating the posterior temperature distribution that maximizes the probability distribution P (x | y).

前記（１）式の右辺を最大とする前記事後の気温分布を推定することにより、或いはガウス・ニュートン法を用いて、前記事後の気温分布を最大にするＭＡＰ解を算出することにより、より効果的に達成される。 Further, the object of the temperature measuring method according to the present invention is that the relationship between the prior probability distribution P (x), the probability density function P (y | x) and the posterior probability distribution P (x | y) is established. Expressed by equation (1)

By estimating the ex post facto temperature distribution that maximizes the right side of equation (1), or by calculating the MAP solution that maximizes the ex post facto temperature distribution using the Gauss-Newton method . Achieved more effectively.

Further, the object of the temperature measuring device according to the present invention is an observation means for observing infrared rays emitted from a building or an urban space, and the building or the above based on the infrared observation values observed by the observation means. It has a calculation means for calculating and measuring the temperature distribution of air between the urban space and the observation means, and the calculation means has x for the temperature, y for the infrared observation value, and a prior probability distribution for the temperature distribution. Is P (x), the probability density function of the observation error of the infrared observation value is P (y | x), the posterior probability distribution related to the temperature distribution is P (x | y), and the prior probability distribution P (x). And, based on the probability density function P (y | x), it is achieved by calculating the posterior temperature distribution that maximizes the posterior probability distribution P (x | y) .

前記演算手段は、前記（１）式の右辺を最大とする前記事後の気温分布を推定することにより、或いはガウス・ニュートン法を用いて、前記事後の気温分布を最大にするＭＡＰ解を算出することにより、より効果的に達成される。
Further, the object of the temperature measuring apparatus according to the present invention is that the relationship between the prior probability distribution P (x), the probability density function P (y | x) and the posterior probability distribution P (x | y) is established. Expressed by equation (1)

The calculation means obtains a MAP solution that maximizes the ex post facto temperature distribution by estimating the ex post facto temperature distribution that maximizes the right side of the equation (1) or by using the Gauss-Newton method. By calculating, it is achieved more effectively.

According to the present invention, an observer (for example, a thermal infrared spectroradiometer) can be used to reverse-estimate the temperature distribution in a building, building space or urban space. It is also effective in obtaining the average value of the temperature in the architectural space and the urban space, and it is also possible to obtain a representative temperature. In addition, this method does not require many thermometers, and it is not necessary to consider the influence of errors due to the heat capacity and radiation of the thermometer.

It is a schematic diagram which shows the energy incident on a thermal infrared spectroradiometer. This is an example of calculating the energy incident on the observation aircraft (thermal infrared spectroradiometer) from the horizontal direction. It is a characteristic diagram which shows the example which calculated the Jacobian matrix. It is a block diagram which shows the structural example of this invention. It is a block diagram which shows the structure of the spectroradiometer of this invention. It is a block diagram which shows the structure of the arithmetic part of this invention. It is a flowchart which shows the specific operation of a sensitivity analysis. It is a schematic diagram of a standard case. It is a figure which shows AK (averaging kernel) and AKarea of a standard case. It is a figure which shows the MAP solution of a standard case. It is a figure which shows the MAP solution when the prior probability distribution is 11 ± 5 ° C. It is a figure which shows the MAP solution when the temperature is not uniform (when the temperature of the 4th to 5th layers decreases). It is a figure which shows the MAP solution when the distance between an observation aircraft and a boundary plane is 10 m. It is a figure which shows the MAP solution when the distance between an observation aircraft and a boundary plane is 1000 m. It is a figure which shows the MAP solution when the number of divisions of an air layer is 3 (discretized into three layers). It is a figure which shows the MAP solution when the number of divisions of an air layer is 10 (discretized into 10 layers). It is a figure which shows the MAP solution in the case of 30 [cm ^-1 ]) which is 1/2 times the resolution (FWHM) of a standard case. It is a figure which shows the MAP solution in the case of 5 [cm ^-1 ]) that the resolution (FWHM) of an observer is 3 times that of a standard case. It is a figure which shows the MAP solution when there is an estimation error of -5% rh in water vapor. It is a figure which shows the MAP solution when there is an estimation error of + 5% rh in water vapor. It is a figure which shows the plan view of the space of an outdoor experiment. It is a figure which shows the plan view of the space of an indoor experiment. It is a photograph of the spectroradiometer used in the experiment. It is a photograph of the plane blackbody furnace used in the experiment. It is a figure which shows the MAP solution and the measured temperature in an indoor experiment. It is a figure which shows the MAP solution and the measured temperature in an outdoor experiment. It is a figure which shows AK (averaging kernel) and AKarea in an indoor experiment. It is a figure which shows AK (averaging kernel) and AKarea in an outdoor experiment.

In the present invention, a maximum a posteriori estimation method (hereinafter referred to as MAP (Maximum A Posteriori) method) is used in order to eliminate the sensitivity due to the above-mentioned error. The MAP method is a method for estimating posterior probability distributions using Bayes' theorem.

Hereinafter, the principle of a method of reversely estimating the temperature distribution in the horizontal direction with respect to the ground surface using a spectroradiometer in a building space will be described.

Here, first, Bayes' theorem will be briefly explained.

The probabilities of the temperature x and the observed value (data: observation result) y are expressed as P (x) and P (y), respectively. In particular, the probability P (x) of the temperature x represents the prior probability distribution with respect to the temperature x. Further, the conditional probability of the temperature x (event x) under the condition of the observed value y is expressed as P (x | y) and is called a posterior probability distribution. The conditional probability of the observed value y under the condition of the temperature x (event x) is expressed as P (y | x), and is called the probability density function or the likelihood of the observation error. In the present invention, a normal distribution is assumed for the probabilities P (x) and P (y | x). Moreover, the Bayesian formula used in the MAP method of the embodiment of the present invention is expressed as Equation 5.

なお、Ｐ（ｙ）は、観測データｙが生起する確率であり、ＭＡＰ推定においては、計算する必要はない。即ち、観測値ｙが定数であることを考慮し、数５の右辺定数項Ｐ（ｙ）を無視すると、数６のようなベイズの定理（「事後確率分布∝尤度×事前確率分布」）になる。

Note that P (y) is the probability that the observation data y will occur, and does not need to be calculated in the MAP estimation. That is, considering that the observed value y is a constant, if the right-hand side constant term P (y) of the equation 5 is ignored, Bayes' theorem such as the equation 6 (“posterior probability distribution ∝ likelihood × prior probability distribution”). become.

ＭＡＰ法においては、数６のベイズの定理によって与えられた事後確率分布Ｐ（ｘ｜ｙ）が最大となるような気温分布ｘをＭＡＰ解x_MAPとして求める。

In the MAP method, the temperature distribution x that maximizes the posterior probability distribution P (x | y) given by Bayes' theorem of equation 6 is obtained as the MAP solution x _MAP .

Further, when obtaining the MAP solution x _MAP , the MAP method uses the prior probability distribution P (x) (stochastic information) regarding the temperature x, which can be known before the observation.

In the MAP method, x is obtained so that P (y | x) P (x) is maximized, and the found x is the MAP solution x _MAP .

On the other hand, x that maximizes the posterior probability distribution P (x | y) coincides with x that maximizes the logarithmic log (P (x | y)).

Further, since the probability distributions related to the likelihood P (y | x) and P (x) all assume a normal distribution, the likelihood P (y | x) can be expressed as the equation 7. In particular, the covariance matrix related to the observation error is represented by _Sε , the variance of the _MAP solution is represented by SMAP, and the variance of the prior probability distribution is represented by Sa.

したがって、尤度Ｐ（ｙ｜ｘ）に関して、数８のようになる。また、事前確率分布Ｐ（ｘ）に関して、数９のようになる。

Therefore, with respect to the likelihood P (y | x), it becomes like the equation 8. Further, with respect to the prior probability distribution P (x), it becomes as in Eq. 9.

そして、数８及び数９におけるconstは定数である。そのため、Ｐ（ｙ｜ｘ）Ｐ（ｘ）は、数１０のように表される。

And the const in the equation 8 and the equation 9 is a constant. Therefore, P (y | x) P (x) is expressed as the number tens.

本発明における目的は、Ｐ（ｙ｜ｘ）Ｐ（ｘ）を最大にするｘを見つけることである。それは数１０の右辺である、

を最小にするようなｘを見つけることで達成される。そのためには、一般的にガウス・ニュートン法を用いることができる。

An object of the present invention is to find x that maximizes P (y | x) P (x). It is the right side of the number tens,

It is achieved by finding x that minimizes. For that purpose, the Gauss-Newton method can generally be used.

On the other hand, since the MAP solution x _MAP includes the influence from the prior probability distribution, it is dangerous to evaluate only by the difference from the true value. Therefore, in order to evaluate the effect of the prior probability distribution P (x) on the MAP solution x _MAP , as will be described later, a Root Mean Squared Error (hereinafter referred to as RMSE), an averaging kernel (hereinafter referred to as AK, or “A””. ), AKarea, and Degree Of Freedom for Signal (hereinafter referred to as DOFS) are used. (X _a represents the expected value (mean) of the prior probability distribution P (x).)
First, the averaging kernel will be described. The MAP solution x _MAP can be expressed as Equation 11 by using the true value (true temperature distribution) x, the averaging kernel A, the expected value x _a of the prior probability distribution, and the identity matrix I.

Ａ≡ＧＫ

により定義されるＡをアベレージングカーネル（Averaging kernel）と呼ぶ。

A≡GK

A defined by is called an averaging kernel.

According to Eq. 11, the MAP solution x _MAP weights the true temperature distribution x and the prior probability distribution x _a by the average kernel A and the identity matrix I minus the average kernel A, respectively. It shows that it is an average. In other words, the closer A is to the identity matrix, the more correctly the MAP solution x _MAP reflects the temperature distribution. By calculating A by A≡GK, the MAP solution x _MAP can be evaluated. The covariance matrix S (also referred to as a variance-covariance matrix) is a matrix obtained by extending the concept of variance (an index showing the degree of dispersion) to multidimensional stochastic variables. The covariance matrix is a collection of information such as the degree of dispersion and correlation of variables (prior probability distribution, observed values).

Next, RMSE and DOFS will be described.

RMSE is the root mean square error calculated based on the MAP solution x _MAP and the true temperature distribution x. The trace tr (A) of the averaging kernel A is a number called DOFS, which represents an unknown number revealed by observation. The addition of the averaging kernel A in the row direction is called AKarea, which indicates the degree to which the observation data at each position contributes. These are indicators of the effectiveness of the MAP solution x _MAP .

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.

FIG. 4 is a block diagram showing a configuration example of the temperature measuring device 10 of the present invention. The temperature measuring device 10 includes a spectroradiometer 12 for observing the spectrum of infrared rays emitted from a heat source 11 (for example, a blackbody furnace), and a calculation unit 13 for calculating a temperature distribution based on the observed values.

FIG. 5 is a block diagram showing the configuration of the spectroradiometer 12 of the present invention. The spectroradiometer 12 can perform spectroscopic measurement of light rays in a wide wavelength range from ultraviolet to far infrared. In FIG. 5, the spectroradiometer 12 has an incident unit 120, a condensing unit 121, a half mirror 122, a CCD camera 123, a chopper 125, an internal blackbody 126, a continuously variable filter (hereinafter referred to as CVF) 127, and a detection unit 128. This is an example configured using.

First, the light beam emitted from the blackbody furnace 11 is incident on the condensing unit 121 via the incident unit 120. The light collecting unit 121 collects light rays and emits the light rays to the half mirror 122. The light rays that have passed through the half mirror 122 are incident on the CCD camera 123. The CCD camera 123 converts the image of the incident light beam into a video signal. The video signal may be output to the controller 124, and the controller 124 may convert the video signal into a digital signal that can be input to the display unit 13b described later.

Further, the light rays reflected by the half mirror 122 are incident on the chopper 125. Then, when the chopper 125 closes and blocks the light beam, the radiation of the internal blackbody 126 is emitted to the detection unit 128 via the CVF 127 described later. On the other hand, when the chopper 25 opens and passes the light beam, the light beam from the condensing unit 121 is incident on the detection unit 128 via the CVF 127.

In CVF127, filters having different spectral characteristics are arranged on the circumference. The CVF 127 is configured to rotate about a predetermined axis. For example, the CVF 127 may be rotated by a motor (not shown), and the light rays can pass through filters having different spectral characteristics depending on the rotation angle of the motor. By doing so, the observed value y (for example, spectroscopic data) can be acquired every time the CVF 127 is rotated once.

A control line and a data line are arranged between the chopper 125, the CVF 127, and the detection unit 128 in the controller 124, and control or data can be input / output. Thereby, for example, the rotational angular velocities of the chopper 125 and the CVF 127 can be controlled by using the controller 124. Further, the detection unit 128 can convert to a digital signal according to the luminance value of the light beam, and the controller 124 can select the timing of conversion by the detection unit 128 and the format of the digital signal.

By changing the characteristics of the optical system (incident unit 120, condensing unit 121, half mirror 122), CVF127, and detection unit 128 in the spectroradiometer 12, the range of the measurement wavelength or the viewing angle to be measured is changed. can do. Further, when CVF127 is fixedly used at an arbitrary wavelength, the change over time in the amount of radiation at that wavelength can be measured. As described above, the spectroradiometer 12 has a different configuration from a general spectrophotometer (for example, FTIR), and is not a type in which a measurement sample is placed inside the apparatus. Therefore, there is a feature that a large measurement object, a heated / cooled measurement object, or a distant object can be measured.

Further, the observed value y (for example, spectroscopic data) measured by the spectroradiometer 12 can be variously analyzed by dedicated software. As an example, since it can be output in CSV format, it is also possible to analyze using general spreadsheet software and numerical calculation.

Next, FIG. 6 is a block diagram showing a configuration of a calculation unit 13 that reversely estimates the temperature distribution using the MAP method of the present invention.

The calculation unit 13 is composed of a CPU 13a and a display unit 13b, and the CPU 13a includes a radiation transmission calculation unit 1, a Jacobian storage unit 2, a control unit 3, an input unit 4, an optimum solution processing unit 5, a mean square error calculation unit 6, and a prior. It is composed of a probability distribution storage unit 7. The relationship, function and operation with each configuration will be described in order.

First, the parameters for the radiation transmission calculation (distance, temperature of the boundary surface, layer width (division width) for discretization (division number), gas (air) concentration) are input to the radiation transmission calculation unit 1. Will be done.

Next, the radiation transmission calculation unit 1 performs radiation transmission calculation using MODERate resolution TRANsmission (hereinafter referred to as MODETRAN) based on the parameters, and calculates Jacobian K.

Then, the radiation transmission calculation unit 1 outputs the Jacobian K to the Jacobian storage unit 2, and the Jacobian storage unit 2 stores the Jacobian K.

Further, the control unit 3 inputs and outputs control signals to and controls each of the input unit 4, the optimum solution processing unit 5, and the mean square error calculation unit 6.

Specifically, the Jacobian storage unit 2 corresponding to the control signal from the control unit 3 via the input unit 4 outputs the Jacobian K to the input unit 4. On the other hand, the observed value y (observed data) from the spectroradiometer 12 is input to the input unit 4, and the observed value y is converted into a data format suitable for processing inside the arithmetic unit 13 (for example, a computer). .. Further, the prior probability distribution P (x) is input to the optimum solution processing unit 5 from the prior probability distribution storage unit 7 according to the control signal from the control unit 3. Further, the observed value y and the Jacobian K are input to the optimum solution processing unit 5 from the input unit 4 in response to the control signal from the control unit 3.

Then, according to the control signal from the control unit 3, the optimum solution processing unit 5 performs the optimum solution processing by the Gauss-Newton method based on the prior probability distribution P (x), the observed value y, and the Jacobian K. The control unit 3 outputs the control signal to the optimum solution processing unit 5 a predetermined number of times, and causes the MAP solution x _MAP to be calculated. Then, the MAP solution x _MAP and the variance can be calculated so that the posterior probability distribution P (x | y) is maximized by the iterative calculation a predetermined number of times.

Then, when the optimum solution processing unit 5 outputs a control signal indicating that the predetermined plurality of iterative calculations have been completed to the control unit 3, the control unit 3 has the mean square error calculation unit with respect to the optimum solution processing unit 5. Outputs a control signal instructing 6 to output the MAP solution x _MAP and the distributed S _MAP . Then, the mean square error calculation unit 6 executes the calculation of RMSE and DOFS based on the MAP solution x _MAP .

Finally, statistical data such as MAP solution x _MAP , variance, RMSE and DOFS are displayed on the display unit 13b (for example, a computer monitor) of the calculation unit 13.

Next, the method of accuracy verification and sensitivity analysis of inverse estimation by numerical simulation using the MAP method will be described.

The specific operation of the sensitivity analysis will be described with reference to the flowchart shown in FIG. First, parameters (distance, interface temperature, layer width (division width) for discretization (division number), true temperature distribution and gas (air) concentration) are input to the system (step S10). .. Using MODTRAN, which is a program for calculating the radiation transmission process, the radiation transmission calculation is performed, and the true observation value and the Jacobian K are calculated and stored (step S20). MODTRAN calculates the transmittance of the atmosphere and the radiance with respect to the wave number. Next, the true observation value y and the Jacobian K are read from a file or the like (step S30). Next, the observed value y + ε and the Jacobian K with a random error following a normal distribution are input to the true observed value y (step S40). Here, the prior probability distribution (prior information) P (x) regarding the temperature is read (step S41). The Gauss-Newton method is used to calculate the MAP solution x _MAP that maximizes the posterior probability distribution P (x | y) for the observed value to which the prior probability distribution and the error are added (step S50). Output the MAP solution x _MAP and the variance S _MAP for the temperature (step 60). It is determined whether or not the MAP solution x _MAP has been calculated 1000 times (step S70). If the number of repeated calculations is less than 1000, the process returns to step S40, and if the number of repeated calculations is 1000, the process proceeds to step S80. Based on the calculation result, DOFS which is a trace of RMSE (RMS _error ) and AK for the MAP solution x _MAP is calculated (step S80).

Next, numerical simulations will clarify the feasibility of reverse estimation of horizontal temperature distribution on an architectural scale. In addition, the results of sensitivity analysis to investigate the relationship between the changes in the parameters that affect the inverse estimation and the effects on the MAP solution x _MAP will be described. Therefore, as shown in Table 1 and FIG. 8, the target of the numerical simulation using the MAP method is a block scale (hereinafter, standard) in which the distance from the observation aircraft to the boundary surface is 100 m and the temperature is uniformly set at 15 ° C. Let's assume a case.) Further, as shown in Table 2, the prior probability distribution in the standard case is 17 ± 5 ° C. Further, AK and AK area of the standard case are shown in FIG. In FIG. 9, since the AK area of the first layer exceeds “1”, it is considered that the contribution from the observation is large. It is shown that the AK area decreases monotonically as the distance from the observation aircraft increases, and the contribution of the prior probability distribution P (x) to the MAP solution x _MAP increases.

また、標準ケースにおけるＭＡＰ法の入力条件を、下記表２に示す。

The input conditions of the MAP method in the standard case are shown in Table 2 below.

そして、標準ケースにおけるＭＡＰ解x_MAPを図１０に示す。標準ケースにおける1層目のＭＡＰ解x_MAPは真値に近かった。しかし、観測機からの距離が大きくなるにつれ，ＭＡＰ解x_MAPは事前確率分布に近づく。１層目におけるＭＡＰ解x_MAPの標準偏差は最小である。一方、２層目のＭＡＰ解x_MAPの標準偏差は最大であり、さらに距離が大きくなるにつれて、２層目以降のＭＡＰ解x_MAPの標準偏差は減少する。このような傾向によって、気温の水平分布の逆推定は特徴付けられる。結果的に、ＭＡＰ解x_MAPのＲＭＳＥである１．２±０．６℃は、事前確率分布のＲＭＳＥである２．０℃より小さいから、標準ケースにおけるＲＭＳＥは減少している。結論的に、気温分布の逆推定に対して、ＭＡＰ法が有効であることが示された。なお、標準ケースにおける、ＲＭＳＥ、ＤＯＦＳは、それぞれ１．２、１．７であり、後述するパラメータ（条件）の影響の調査の際に基準となる数値である。

Then, the MAP solution x _MAP in the standard case is shown in FIG. The MAP solution x _MAP of the first layer in the standard case was close to the true value. However, as the distance from the observation aircraft increases, the MAP solution x _MAP approaches the prior probability distribution. The standard deviation of the MAP solution x _MAP in the first layer is the smallest. On the other hand, the standard deviation of the MAP solution x _MAP of the second layer is the maximum, and the standard deviation of the MAP solution x _MAP of the second and subsequent layers decreases as the distance increases. This tendency characterizes the inverse estimation of the horizontal distribution of temperature. As a result, the RMSE of the MAP solution x _MAP , 1.2 ± 0.6 ° C., is smaller than the RMSE of the prior probability distribution, 2.0 ° C., so that the RMSE in the standard case is reduced. In conclusion, it was shown that the MAP method is effective for the inverse estimation of the temperature distribution. In the standard case, RMSE and DOFS are 1.2 and 1.7, respectively, which are reference values when investigating the influence of parameters (conditions) described later.

Next, the effect of parameters (conditions) on the inverse estimation of the temperature distribution will be investigated. Parameters (conditions) include prior probability distribution, non-uniform temperature (true temperature distribution is not uniform), distance (distance between the interface and the observer), and layer division n (number of divisions of the air layer). ), The resolution of the observer (hereinafter referred to as FWHM (Full Width at Half Maximum) [cm ^-1 ])), and the estimation error of water vapor.

First, as shown in FIG. 11, the accuracy of the MAP solution x _MAP when the prior probability distribution is changed from 17 ± 5 ° C to 11 ± 5 ° C does not change significantly in the vicinity of the observed value.

Next, reverse estimation is applied to the temperature distribution in which the true temperature is not uniform (the temperature distribution in the third layer is relatively high and the temperatures in the first and second layers and the fourth to fifth layers are relatively low). As a result of the above, as shown in FIG. 12, although the increase in temperature in the 1st to 3rd layers could be reversely estimated, the decrease in temperature in the 4th to 5th layers could not be estimated. From these results, it was shown that the method of inverse estimation of the temperature distribution of the present invention tends to reduce the influence of the prior probability distribution and improve the accuracy of the estimated temperature as it approaches the observation aircraft. ..

Next, FIGS. 13 and 14 show the results of reverse estimation of the temperature distribution for the air layer in which the distance between the boundary surface and the observation aircraft is set to 10 m and 1000 m, respectively. As shown in FIGS. 13 and 14, RMSE and DOFS did not change significantly in either case. Therefore, it was shown that the method of inverse estimation of the temperature distribution of the present invention can obtain the same accuracy on both the building scale and the block scale.

Next, FIG. 15 shows the result of reverse estimation of the temperature distribution for the air layer in which the number of divisions of the air layer is 3. As shown in FIG. 15, the DOFS was 1.7. On the other hand, the RMSE was 1.3 ± 0.8 ° C, which was slightly worse than the RMSE of 1.2 ± 0.6 ° C in the standard case. Further, FIG. 16 shows the result of reverse estimation of the temperature distribution for the air layer in which the number of divisions of the air layer is 10. As shown in FIG. 16, the DOFS was 1.7. In contrast, RMSE slightly improved to 1.1 ° C. For such results, the contribution of the observed value increases as the DOFS improves. Therefore, it is considered that the influence of the random error ε of the observed value became large.

Next, FIG. 17 shows the result of reverse estimation of the temperature distribution by increasing the resolution (FWHM) of the observation aircraft by 1/2 times to 30 [cm ^-1 ]. As shown in FIG. 17, DOFS was reduced to 1.6 and RMSE remained unchanged at 1.2 ± 0.6 ° C. Further, FIG. 18 shows the result of reverse estimation of the temperature distribution by triple the resolution (FWHM) of the observation aircraft to 5 [cm ^-1 ]. As shown in FIG. 18, DOFS increased to 2.1 and RMSE improved to 1.1 ± 0.5 ° C. In addition, the accuracy of temperature estimation in the air layer away from the observation aircraft could be improved on average. As a result, the accuracy could be improved by increasing the resolution of the observation aircraft.

Next, FIGS. 19 and 20 show the results of reverse estimation of the air temperature distribution for an air layer having an estimation error in the relative humidity of water vapor. When creating the Jacobian as described above, if the water vapor has an estimation error of -5% rh, the RMSE will be 2.0 ± 0.6 ° C to 2.0 ± in the standard case, as shown in FIG. It changed (worse) to 0.9 ° C and tended to give a biased estimation result. Further, when the relative humidity rh of the water vapor had an estimation error of + 5% rh, the RMSE changed (worse) to 1.5 ± 0.8 ° C. as shown in FIG.

In summary, in the sensitivity analysis for the inverse estimation of the temperature distribution in the embodiment, it was shown that the RMSE of the MAP solution x _MAP is improved from the RMSE of the prior probability distribution.

Next, the reverse estimation of the horizontal temperature distribution of the building scale in the embodiment will be described.

In the embodiment of the present invention, the reverse estimation of the horizontal air temperature distribution was performed for two rooms having different temperatures (existing temperature distribution) (indoor experiment). Furthermore, the reverse estimation of the horizontal temperature distribution was performed for the building space with the temperature difference between indoors and outdoors (outdoor experiment). The plan views of the indoor experiment space and the outdoor experiment space are shown in FIGS. 21 and 22. The specifications of the spectroradiometer and the flat blackbody furnace used in the experiment are shown in Tables 3 and 4, respectively, and the photographs shown in FIGS. 23 and 24, respectively. The temperature of the blackbody furnace at the boundary surface between the indoor experiment and the outdoor experiment was set to 50 ° C.

また、ＭＡＰ法に用いた条件を表５に示す。

Table 5 shows the conditions used in the MAP method.

温湿度計で実際に測定した値より２℃高い事前確率分布（Case 1）、及び温湿度計で実際に測定した値より２℃低い事前確率分布（Case 2）を用いて、屋内実験及び屋外実験を行った。なお、ヤコビアン（Jacobian matrix）計算のため、水蒸気濃度として温湿度計で測定した値が用いられた。また、無用なノイズを避けられるように、全チャンネルの内から相互情報量の多い１０チャンネルが、ＭＡＰ解x_MAPを計算するために用いられた。

Indoor experiments and outdoors using prior probability distribution 2 ° C higher than the value actually measured by the thermo-hygrometer (Case 1) and prior probability distribution 2 ° C lower than the value actually measured by the thermo-hygrometer (Case 2). An experiment was conducted. For the Jacobian matrix calculation, the value measured with a thermo-hygrometer was used as the water vapor concentration. In addition, 10 channels with a large amount of mutual information were used to calculate the MAP solution x _MAP from all the channels so as to avoid unnecessary noise.

Figures 25 to 28 show the MAP solution x _MAP , the distribution of the measured temperature (measured value of the thermometer), and the AK area in the indoor and outdoor experiments. As shown in FIGS. 25 to 28, the temperature distribution could be reproduced in the indoor experiment and the outdoor experiment. The prior probability distribution had a significant effect on the second and subsequent layers. Further, as shown in FIG. 27, since the AK area of the first layer is about 0.8, the observed value contributed predominantly to the MAP solution x _MAP . On the other hand, as shown in FIG. 27, since the AK area of the fourth layer is about 0.2, the prior probability distribution predominantly contributes to the MAP solution x _MAP . Table 6 shows the prior probability distribution and the RMSE of the MAP solution x _MAP . As shown in Table 6, except for Case 2 in the indoor experiment, the RMSE of the MAP solution x _MAP could be reduced (improved) from the RMSE of the prior probability distribution. It is considered that the reason why the RMSE of the prior probability distribution is not 2.0 is that the positions are linearly interpolated.

以上の説明によって、本発明によれば、建築空間における観測対象となる気温について観測前に分かっている確率的な情報（事前確率分布）に基づいて、分光放射計を用いた水平気温分布を逆推定することが可能である。

According to the above description, according to the present invention, the horizontal temperature distribution using the spectroradiometer is reversed based on the stochastic information (prior probability distribution) known before the observation about the temperature to be observed in the building space. It is possible to estimate.

It should be noted that all of the above-described embodiments of the present invention are examples of embodiment of the present invention (for example, the number of divisions of the air layer, whether or not the true temperature distribution is uniform, the boundary surface and observation. It only shows the distance to the machine, the resolution of the observation machine, the specific weight of water vapor in the air, etc.), and the technical scope of the present invention should not be interpreted in a limited manner by these. That is, the present invention can be implemented in various forms without departing from the technical idea or its main features.

Further, regarding P (x) and P (y | x), a normal distribution is assumed in the embodiment of the present invention, but the distribution is not limited to the normal distribution, for example, a gamma (γ) distribution. , Poisson distribution may be used. However, in that case, the Gauss-Newton method cannot be used, so it is necessary to use the Markov chain Monte Carlo method.

Further, although the Gauss-Newton method is mentioned as a method for nonlinear optimization, for example, the Levenberg-Marquardt method may be used depending on the balance between the amount of calculation and the accuracy.

1 Radiation transmission calculation unit 2 Jacobian storage unit 3 Control unit 4 Input unit 5 Optimal solution processing unit 6 Mean square error calculation unit 7 Prior probability distribution storage unit 10 Temperature measuring device 11 Heat source (blackbody furnace)
12 Spectroradiometer 13 Calculation unit 13a CPU
13b Display unit 120 Incident unit 121 Condensing unit 122 Half mirror 123 CCD camera 124 Controller 125 Chopper 126 Internal blackbody 127 Continuously variable filter (CVF)
128 detector

Claims (6)

A temperature measurement method that estimates the temperature distribution of air from the building or urban space to the observation point by observing infrared rays emitted from the building or urban space and analyzing the observed infrared observation values. And
The temperature is x, the infrared observation value is y, the prior probability distribution related to the temperature distribution is P (x), the probability density function of the observation error of the infrared observation value is P (y | x), and the posterior probability distribution related to the temperature distribution. Let P (x | y)
It is characterized in that the posterior temperature distribution that maximizes the posterior probability distribution P (x | y) is estimated based on the prior probability distribution P (x) and the probability density function P (y | x). Temperature measurement method. The relationship between the prior probability distribution P (x), the probability density function P (y | x), and the posterior probability distribution P (x | y) is expressed by the equation (1).

The temperature measurement method according to claim 1, wherein the temperature distribution after the fact is estimated with the right side of the equation (1) as the maximum. The temperature measuring method according to claim 2, wherein a MAP solution that maximizes the subsequent temperature distribution is calculated by using the Gauss-Newton method. The temperature distribution of air between the building or the urban space and the observation means based on the observation means for observing the infrared rays emitted from the building or the urban space and the infrared observation values observed by the observation means. Has a calculation means to calculate and measure
The calculation means is
The temperature is x, the infrared observation value is y, the prior probability distribution related to the temperature distribution is P (x), the probability density function of the observation error of the infrared observation value is P (y | x), and the posterior probability distribution related to the temperature distribution. Let P (x | y)
It is characterized in that the posterior temperature distribution that maximizes the posterior probability distribution P (x | y) is calculated based on the prior probability distribution P (x) and the probability density function P (y | x). Temperature measuring device. The relationship between the prior probability distribution P (x), the probability density function P (y | x), and the posterior probability distribution P (x | y) is expressed by the equation (1).

The temperature measuring device according to claim 4, wherein the calculation means estimates the subsequent temperature distribution with the right side of the equation (1) as the maximum. The temperature measuring device according to claim 5, wherein a MAP solution that maximizes the temperature distribution after the fact is calculated by using the Gauss-Newton method.

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