Numerical analysis device and numerical analysis method

Abstract

To provide a numerical analysis device capable of predicting a flow field corresponding to an operation condition of air conditioning or the like at a high speed by using a small number of physical quantity sensors.SOLUTION: A numerical analysis device includes an ensemble creation unit 101 that creates an ensemble in which multiple analysis results are combined with boundary conditions including preset equipment operating conditions of an analysis target space, a feature vector set calculation unit 102 that divides the ensemble for each condition, applies singular value decomposition, and calculates a set of feature vectors, an observation data acquisition unit 103 that acquires observation data from a sensor that measures a physical quantity of at least a part of the analysis target space, an apparatus operation condition acquisition unit 104 that acquires an apparatus operation condition of an operation condition of an apparatus, a feature vector set selection unit 105 that selects a set of feature vectors according to the apparatus operation condition, a weight coefficient calculation unit 106 that calculates a weight coefficient of the feature vector from observation data, and a fluid field restoration unit 107 that multiplies the feature vector by the weight coefficient, adds the weight coefficients, and outputs an analysis result.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention provides a numerical analysis device and method that estimates the distribution of three-dimensional physical quantities, such as wind speed, indoors in a factory or other facility, and provides technology for visualizing areas where dust is likely to accumulate, ventilation conditions, etc., at low sensing costs. [Background technology]

[0002] To ensure stable factory operations and worker safety, it is necessary to understand the dust and ventilation conditions within a factory room. One way to understand the dust and ventilation conditions is to place wind speed sensors in the room and monitor whether the required wind speed is flowing. On the other hand, to understand the three-dimensional wind field, it is possible to place wind speed sensors in the room and interpolate from each measurement value and position. In this case, it is necessary to install many wind speed sensors in the room. In a factory with a network of piping and production lines, it is not easy to freely install many sensors, so a technology is needed to understand the conditions within the factory using as few sensors as possible.

[0003] It is also possible to simulate indoor environments using computational fluid analysis technology and evaluate three-dimensional flow fields. However, the more detailed the analytical model, the longer the simulation time required, making it difficult to apply to applications that require understanding the situation in real time. On the other hand, a technology has been developed in which a fluid analysis is performed in advance simulating the space to be estimated, the results are decomposed into spatial POD modes using proper orthogonal decomposition (POD) or singular value decomposition (SVD), and the flow field is reconstructed by adding up the modes.

[0004] Patent Document 1 discloses a method for correcting analysis results and identifying more likely analytical model parameters by incorporating the amount of strain on the surface of a structure obtained from an image using a parameter estimation device into structural analysis using a technique called data assimilation.

[0005] Non-Patent Document 1 discloses a method for applying SVD to the results of fluid analysis around a two-dimensional cylinder, and determining the sum coefficients of the POD modes using observed values ​​to restore the flow field. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2020-201146 [Non-patent literature]

[0007] [Non-Patent Document 1] Emily Clark, Travis Askham, Steven L. Brunton, and J.Nathan Kutz.: “Greedy Sensor Placement With Cost Constraints”, IEEE Sensors Journal, Vol. 19, No. 7, pp. 2642-2656. Summary of the Invention [Problem to be solved by the invention]

[0008] The technique described in Patent Document 1 makes it possible to obtain more plausible analysis results and correct analytical model parameters by assimilating two-dimensional observation data into structural analysis without deploying a large number of sensors. However, it is difficult to obtain wind speed data as an image, and it is not easy to apply a method similar to this document to estimating indoor flow fields.

[0009] Furthermore, the method described in Non-Patent Document 1 is effective for understanding the indoor ventilation status, etc. in real time, because if the POD mode is obtained by performing fluid analysis in advance, the flow field can be instantly restored by calculating the summation coefficient from the observation data. However, if the operating status of the indoor air conditioning, etc., differs, the accuracy of the flow field prediction may decrease.

[0010] The present invention has been made to solve the above-mentioned problems, and aims to provide a numerical analysis device and a numerical analysis method that can quickly predict a flow field according to the operating conditions of an air conditioning system or the like using a small number of physical quantity sensors. [Means for solving the problem]

[0011] To achieve the above object, the numerical analysis apparatus of the present invention is characterized by comprising: an ensemble creation unit that creates an ensemble consisting of a combination of boundary conditions, including preset equipment operating conditions, of a space to be analyzed, and corresponding analysis results; a feature vector set calculation unit that divides the ensemble into conditions and applies singular value decomposition to calculate a set of feature vectors; an observation data acquisition unit that acquires observation data at the time of the analysis from sensors that measure at least some physical quantities of the space to be analyzed; an equipment operating condition acquisition unit that acquires equipment operating conditions at the time of the analysis of the operating status of equipment included in the space to be analyzed; a feature vector set selection unit that selects a set of feature vectors according to the equipment operating conditions acquired by the equipment operating condition acquisition unit; a weight coefficient calculation unit that calculates weight coefficients for the feature vectors from the observation data; and a fluid field restoration unit that multiplies the feature vectors by the weight coefficients, adds them together, and outputs the analysis result. Other aspects of the present invention will be described in the embodiments described below. [Effects of the Invention]

[0012] According to the present invention, a flow field according to operating conditions of an air conditioner or the like can be predicted at high speed using a small number of physical quantity sensors. [Brief explanation of the drawings]

[0013] [Figure 1] 1 is a diagram illustrating a configuration of a numerical analysis system according to a first embodiment. [Figure 2] 1 is a flowchart showing a flow field reconstruction process according to the first embodiment. [Figure 3] FIG. 2 is a diagram showing an example of creating a numerical analysis ensemble according to the first embodiment. [Figure 4] FIG. 4 is a diagram showing a data matrix created for each device operating condition according to the first embodiment. [Figure 5] FIG. 3 is a diagram showing sensor positions according to the first embodiment. [Figure 6] FIG. 10 is a diagram illustrating the configuration of a numerical analysis system according to a second embodiment. [Figure 7] 10 is a flowchart showing a temperature field reconstruction process according to the second embodiment. [Figure 8] FIG. 10 is a diagram showing an example of creating a numerical analysis ensemble according to the second embodiment. [Figure 9] FIG. 10 is a diagram showing a thermal camera according to a second embodiment and the position of a window as an unnecessary region. [Figure 10] 10A and 10B are diagrams illustrating an example of an image captured by a thermal camera according to a second embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0014] Hereinafter, an embodiment of the numerical analysis according to the present invention will be described with reference to the drawings. In the following description and drawings, components having the same functional configuration are denoted by the same reference numerals, and redundant description will be omitted.

[0015] As described above, this embodiment provides a technology for estimating three-dimensional physical quantity distribution such as wind speed indoors in a factory or the like, and visualizing locations where dust is likely to accumulate, ventilation conditions, etc., at low sensing costs (for example, a small number of physical quantity sensors). This makes it possible to quickly predict a three-dimensional flow field using observation data acquired from a small number of physical quantity sensors and operation information of air conditioning equipment, etc.

[0016] First Embodiment Fig. 1 is a diagram showing the configuration of a numerical analysis system according to the first embodiment. The numerical analysis system includes a numerical analysis device 1000, an observation data acquisition unit 140, and an equipment operating condition acquisition unit 150. The numerical analysis device 1000 is an example of a computer device, and is configured by a CPU 100, an input / output unit 110, a storage 130, a communication unit 114, etc., as shown in Fig. 1.

[0017] The processing unit of CPU 100 has the functions of an ensemble creation unit 101, a feature vector set calculation unit 102, an observation data acquisition unit 103, an equipment operating condition acquisition unit 104, a feature vector set selection unit 105, a weighting coefficient calculation unit 106, and a fluid field restoration unit 107, and controls the operation of each of these components. Note that a GPU (Graphics Processing Unit) may be used instead of CPU 100, or the CPU 100 and a GPU may be used together.

[0018] The input / output unit 110 is composed of an input unit including a keyboard 111 and a mouse 112, etc., and an output unit including a display 113, etc. A user of the numerical analysis device 1000 can input commands from the keyboard 111 and the mouse 112 of the input unit, and visually grasp the results from the display 113 of the output unit.

[0019] The memory 120 stores a numerical analysis program 121 in the numerical analysis system of this embodiment, and temporarily stores information (data) necessary for various processes in each component of the CPU 100. The numerical analysis program 121 is, in other words, a program code of software that realizes the functions of each component of the CPU 100.

[0020] The storage 130 stores numerical analysis ensemble data 131, feature vector data 132, observation data 133, equipment operating condition data 134, etc., which are read out to the memory 120 and used as needed.

[0021] The numerical analysis ensemble data 131 is three-dimensional flow field data obtained by analyzing the state of the region where the flow field is to be predicted while varying boundary conditions such as the operating conditions of the air conditioning equipment, which are preset equipment operating conditions, and object placement. This data may be the result of a steady-state analysis or an unsteady-state analysis for each of the aforementioned conditions. Furthermore, to facilitate handling of differences in object placement, etc., the numerical analysis ensemble data 131 may be expressed using a three-dimensional orthogonal grid. However, even if the grid used during analysis is different, the data may be created by interpolating to a common grid when ensembling. Information such as flow velocity, pressure, temperature, and humidity is stored as the numerical analysis ensemble data 131.

[0022] The feature vector data 132 is eigenvector data obtained by applying POD (Proper Orthogonal Decomposition) to the numerical analysis ensemble data 131. Note that it is also possible to store and use modes obtained by applying Dynamic Mode Decomposition (DMD), a mode decomposition method other than POD. POD is performed on numerical analysis ensemble data that has been performed assuming the same operating conditions for the air conditioning equipment. In other words, the results of numerical analyses simulating different operating conditions for the air conditioning equipment are treated as separate data sets, and POD is applied to each data set. Therefore, the feature vector data 132 is obtained for each operating condition of the air conditioning equipment.

[0023] The observation data 133 is data acquired from a plurality of sensors 141 connected to the observation data acquisition unit 140. The observation data may include wind speed, pressure, temperature, humidity, etc. The acquired data is stored so that it can be identified for each position of the sensor 141 from which it was acquired.

[0024] The equipment operating condition data 134 is data acquired from a plurality of air conditioning equipment 151 connected to the equipment operating condition acquisition unit 150. The equipment operating conditions may include the strength and air volume of air conditioning, set temperature, and the like.

[0025] The data stored in the storage 130 can be input manually via the input / output unit 110, but can also be input from outside using a separate means.

[0026] Fig. 2 is a flowchart showing the flow field reconstruction process according to the first embodiment. That is, Fig. 2 is a flowchart of the process S200 when performing a numerical analysis.

[0027] (Ensemble creation process) The ensemble creation unit 101 executes the ensemble creation process S201. The ensemble creation unit 101 issues an instruction via the input / output unit 110 and loads the numerical analysis ensemble data 131 from the storage 130 into the memory 120. At this time, each piece of numerical analysis data is stored in association with the operating conditions of the air conditioning equipment that have been set in advance.

[0028] FIG. 3 is a diagram showing an example of creating a numerical analysis ensemble according to the first embodiment. FIG. 3 shows an example of creating an ensemble made up of multiple numerical analysis results. 301 is an indoor space region (space to be analyzed) that is the subject of numerical analysis. For the sake of explanation, it is shown two-dimensionally, but in reality it is a three-dimensional region. Multiple air conditioning devices 151a to 151c are arranged in the indoor space region 301 (space to be analyzed). The ensemble created in the ensemble creation process S201 is created for each operating condition of the air conditioning devices shown in FIG. 3.

[0029] In equipment operating condition combination 1, a large air volume is emitted from air conditioner 151a, a medium air volume is emitted from air conditioner 151b, and a small air volume is emitted from air conditioner 151c. Under this equipment operating condition combination 1, a computational fluid dynamics analysis is performed with the position of object 302 changed, as shown in Fig. 3. Note that 303 is an object that is constantly present in indoor space region 301, such as a factory production line.

[0030] In numerical analysis model 304a, object 302 is located in the upper left of indoor space region 301. In other numerical analysis models 304b and 304c, object 302 is located in the upper and upper right of indoor space region 301. In this way, numerical analysis is performed assuming that only the position of object 302 changes and that other structures and operating conditions, i.e., boundary conditions, do not change. This analysis may be a steady-state analysis or a non-steady-state analysis. A similar procedure is performed for equipment operating condition combination 2.

[0031] In equipment operating condition combination 2, it is assumed that only air conditioning equipment 151c is operating at high air volume, while 151a and 151b are stopped. Under these conditions, a numerical fluid analysis is performed with the position of object 302 changed. In this way, by performing numerical analysis on multiple air conditioning equipment 151 for multiple combinations of equipment operating conditions, an ensemble is created for each combination of equipment operating conditions.

[0032] (Calculation process of feature vector set) The feature vector set calculation unit 102 executes a calculation process S202 for a feature vector set. The feature vector set calculation unit 102 obtains a feature vector (POD mode) for the ensemble data created in the ensemble creation S201. An example is shown in FIG. 4.

[0033] FIG. 4 is a diagram showing a data matrix created for each equipment operating condition according to the first embodiment. Data matrix X401 is created by arranging the results of analysis performed under the same combination of operating conditions for the air conditioning equipment, and is expressed as Equation (1). That is, since data matrix X401 is created for each operating condition of the air conditioning equipment, multiple data matrices X401 are obtained. Here, column vectors 402a, 402b, 402c, etc. of the matrix are analysis results obtained for each different arrangement of the object 302 in FIG. 3, i.e., three-dimensional physical quantity data converted into one-dimensional vectors. Column vectors 402a, 402b, 402c, etc. store data such as flow velocity, pressure, temperature, and humidity. Furthermore, if a transient analysis is performed in advance, time-series data can be obtained for each arrangement of the object 302. Therefore, instead of column vector 402a, a matrix in which physical quantity data at multiple times along the time series are converted into one dimension and arranged can be used.

[0034] The feature vector set calculation unit 102 applies singular value decomposition (SVD) to the data matrix X 401 thus constructed to obtain a feature vector, that is, a POD mode. The POD mode is obtained as a POD mode U calculated by Equation (2).

number

[0035] Singular value decomposition is performed on multiple data matrices X401, i.e., for each combination of operating conditions of multiple air conditioning equipment. Therefore, the POD mode U is also obtained for each combination of equipment operating conditions, and is treated as a set of feature vectors. The POD mode U for each combination of equipment operating conditions obtained in this way, i.e., the set of feature vectors, is stored in storage 130 as feature vector data 132. As mentioned above, modes obtained by various mode decomposition methods such as DMD, in addition to SVD, can also be used as feature vectors.

[0036] The operations in the ensemble creation process S201 and the feature vector set calculation process S202 in FIG. 2 may be performed in advance before flow field estimation using observed values.

[0037] (Observation data acquisition process) The observation data acquisition unit 103 executes an observation data acquisition process S203. In the observation data acquisition process S203, the observation data acquired from multiple sensors 141 is integrated by the observation data acquisition unit 140 and input into the numerical analysis system. It is assumed that information on physical quantities such as wind speed, pressure, temperature, and humidity can be acquired as observation data. It is also assumed that the spatial coordinates of each sensor 141 are known. The acquired observation data is stored as observation data 133 in the storage 130 as needed. Note that, unlike the ensemble creation process S201, the acquired observation data is the observation data at the time of analysis.

[0038] (Device operating conditions acquisition process) The equipment operating condition acquisition unit 104 executes an equipment operating condition acquisition process S204. The equipment operating condition acquisition unit 104 imports data into the numerical analysis device 1000, which is obtained by integrating the equipment operating conditions at the time of analysis acquired from multiple air conditioning equipment 151 by the equipment operating condition acquisition unit 150. The acquired equipment operating condition data is stored as equipment operating condition data 134 in the storage 130 as necessary.

[0039] (Feature vector set selection process) The feature vector set selection unit 105 executes a feature vector set selection process S205. The feature vector set selection unit 105 selects a feature vector set to be used for fluid field reconstruction 206. At this time, the referenced feature vector data 132 is extracted using current equipment operating condition data 134 at the time of analysis. If the current equipment operating conditions at the time of analysis are that the air volume of air conditioner 151a is large, the air volume of air conditioner 151b is medium, and the air volume of air conditioner 151c is small, this combination of conditions corresponds to equipment operating condition combination 1 in FIG. 3. Therefore, the POD mode U obtained by singular value decomposition of the data matrix X401 corresponding to equipment operating condition combination 1 is extracted from the feature vector data 132 and used for flow field reconstruction.

[0040] On the other hand, there may be a situation where a data matrix X corresponding to the current equipment operating conditions does not exist. In such a case, an operation such as referencing the data matrix X with the most similar conditions can be performed. Furthermore, if the current equipment operating conditions can be reproduced by interpolating the combinations of multiple equipment operating conditions evaluated when extracting the feature vector data 132, multiple corresponding data matrices X can be extracted and used for flow field reconstruction.

[0041] That is, the weighting coefficient calculation unit 106 described later may calculate the weighting coefficient based on the feature vector calculated under boundary conditions similar to the device operating conditions. In other words, the POD mode U is obtained from the similar matrix X, and the weighting coefficient is calculated using the formulas (4) and (5) described later.

[0042] (Weighting coefficient calculation process for each feature vector) The weighting coefficient calculation unit 106 executes a weighting coefficient calculation process S206 for each feature vector. The weighting coefficient calculation unit 106 calculates a POD mode summation coefficient to be used for reconstructing a three-dimensional flow field using the observation data 133 and the feature vector data 132 selected by the feature vector set selection process S205.

[0043] Here, it is assumed that the data matrix X selected from the current equipment operating conditions can be approximated as shown in Equation (3). [Mathematics]

[0044] Here, the matrix U1:r is obtained by extracting the first r columns from the first column of the POD mode U, and r is assumed to be the number of modes that can approximate the original data matrix X with sufficient accuracy. When r is sufficiently small (r << m) with respect to the number of columns m of the POD mode U, which is the original matrix, the flow field is reduced to a low dimension with respect to the original data, and only r coefficients are required for the summation.

[0045] FIG. 5 is a diagram showing the sensor positions according to the first embodiment. FIG. 5 shows an example of restoring the fluid field under the condition that the device is operating under the combination of device operating conditions 1. The position of the object 302 is a condition not included in the conditions at the time of numerical analysis of the previously created ensemble. Also, it is assumed that the sensors 141a, 141b, and 141c are at the positions shown in FIG. 5. Further, it is assumed that the wind speed is measured by the sensors 141a, 141b, and 141c, the observation vector is y, and each observation value in the observation vector y is y , , 141c , , 141a , , 1:r , , , <00002​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​Here, the observation matrix H is a matrix that links the position of each sensor to a grid in numerical analysis. In this case, the coefficient vector ahat (weighting coefficient) can be estimated as shown in equation (5). Here, the matrix C is the product of the observation matrix H and the matrix U 1:r is the product of

[0048] (Restoration of fluid fields) The fluid field restoration unit 107 executes the fluid field restoration process S207. The fluid field restoration unit 107 reconstructs the current flow field using the coefficient vector ahat (weighting coefficient) calculated in the weighting coefficient calculation process S206 for each feature vector. Equation (6) is used for the reconstruction.

number

[0049] Here, the vector xhat is a flow field vector that represents the entire target space, and by converting it back to three-dimensional space, a three-dimensional flow field can be expressed. By visualizing the three-dimensional flow field reconstructed in this way on a display 113 or the like, the current flow field in the target space can be visualized quickly.

[0050] That is, the fluid field restoration unit 107 multiplies the feature vector by a weighting factor, adds them together, and outputs the analysis result. Regarding Equation (6), if ahat is considered as an r × 1 matrix as a coefficient vector, it becomes the product of the matrix of the feature vector and the coefficient vector.

[0051] The more sensors 141 there are, the more accurate the prediction of the flow field can be. Even in this case, the time required to calculate the coefficient vector ahat does not change significantly, so the flow field can be visualized quickly. In addition, by acquiring observed values ​​every moment, the flow field can be visualized in real time.

[0052] By using the numerical analysis device 1000 as shown in the first embodiment, it is possible to utilize data observed with a small number of sensors and quickly reconstruct and visualize a three-dimensional flow field in a target space according to the operating conditions of the equipment.

[0053] <Embodiment 2> The second embodiment aims to rapidly reconstruct and visualize the temperature distribution in space using two-dimensional temperature distribution observation values ​​obtained by a thermal camera or the like.

[0054] Fig. 6 is a diagram showing the configuration of a numerical analysis system according to the second embodiment. Compared to Fig. 1, Fig. 6 adds the functions of an unnecessary region designation unit 108 and a valid observation data extraction unit 109 to a CPU 100. In Fig. 6, the same functions as those in Fig. 1 of the first embodiment are denoted by the same reference numerals.

[0055] Fig. 7 is a flowchart showing the temperature field reconstruction process according to the second embodiment. Fig. 6 shows the process S600 for restoring the fluid field. This embodiment is intended for application to an indoor space in a data center where multiple server racks are installed. In Fig. 7, the same processes as those in Fig. 2 of the first embodiment are denoted by the same reference numerals.

[0056] (Ensemble creation process) The ensemble creating unit 101 executes the ensemble creating process S601. In the ensemble creation process S601, a numerical analysis such as that shown in Figure 8 is performed. A thermal fluid analysis is performed for each combination of operating conditions for the air conditioning equipment. In this case, assuming that multiple objects that can be heat sources exist in a common location, a thermal fluid analysis is performed with the position of the heat source 701 that actually generates heat changed, and the analysis results are created as an ensemble. For example, for the analysis target region 702 (analysis target space), in numerical analysis model 703a, the heat source 701 is the object in the upper left, but in numerical analysis models 703b and 703c, the heat source 701 is set to the object on the upper side and the object on the lower left, respectively, and analysis is performed. The temperatures of the space and wall surfaces are included in the ensemble as the results of the numerical analysis.

[0057] The calculation process S202 of the feature vector set is performed in the same manner as in embodiment 1. That is, singular value decomposition is applied to each operating condition of the air conditioner to determine the POD mode.

[0058] (Designation of unnecessary areas) The unneeded region designation unit 108 executes the unneeded region designation process S602. The unnecessary region designation unit 108 designates areas to be removed as unnecessary regions from the observation data acquired by the thermal camera. Here, an unnecessary region is an area where the reliability of the observation data from the thermal camera is assumed to be low. For example, an object with a glossy surface or an object not considered when calculating the ensemble is designated. The unnecessary region is designated by selecting from the object recognition labels that can be output by image recognition technology executed in the valid observation data extraction process S604 described below. As a specific example, the unnecessary region is designated by multiple texts such as a window in a room and a person.

[0059] In the observation data acquisition process S603, the temperature distribution in the space to be predicted is acquired using a thermal camera. At this time, the temperature data acquired as an image is linked to the data at which position in the results of the thermal fluid analysis performed in advance.

[0060] (Extraction of valid observation data) The valid observation data extraction unit 109 executes the process of extracting valid observation data S604. The valid observation data extraction unit 109 determines whether the unnecessary area specified in the unnecessary area designation process S602 is included in the observation data acquired in the observation data acquisition process S603, and if so, removes the data of the unnecessary area from the observation data and extracts only the valid data.

[0061] The order of the step 602 of specifying the unnecessary area and the step 603 of acquiring the observation data may be reversed.

[0062] FIG. 9 is a diagram showing a thermal camera according to the second embodiment and the position of a window as an unnecessary region. An example of determining an unnecessary region is shown in FIG. 9 . The camera set 801 includes a thermal camera 801a and a standard image capture camera 801b, each configured to capture the same area. The pixels of the images output by each camera are linked to each other. The thermal camera 801a is capable of acquiring wall surface temperature data within the area indicated by the dotted line. Assume that a window 802 is included in the image. Image recognition is performed on the image captured by the standard image capture camera 801b to determine whether it contains an object matching the recognition label of the unnecessary object previously specified in the unnecessary region specification 602. Note that objects 803 and 804 are placed in front of the thermal camera 801a in the indoor space region 301 (the space to be analyzed).

[0063] Fig. 10 is a diagram showing an example of imaging by a thermal camera according to the second embodiment. Fig. 10 is a diagram schematically showing an image captured by the normal image capturing camera 801b in Fig. 9. When a window 802 is recognized in the image through image recognition and removed as an unnecessary region, the observation data outside that region is deemed valid, and the value of the elements in the observation matrix is ​​set to 1. The values ​​of the observation matrix corresponding to the window 802, which is an unnecessary region in the image, and to regions not included in the image are set to 0. In other words, because the images captured by the thermal camera 801a and the normal image capturing camera 801b are linked on a pixel-by-pixel basis, pixels determined to be unnecessary by the normal image capturing camera 801b are also deemed unnecessary in the image data acquired by the thermal camera 801a, and the corresponding elements of the observation matrix are set to 0.

[0064] Specifically, since each pixel in the camera image is linked to the position of the analysis grid in the 3D fluid analysis results when the ensemble is created, the observation matrix can be configured as a matrix in which elements corresponding to the analysis grid positions corresponding to image pixels determined to be valid are equal to 1. The relationship between the observation data after removing unnecessary areas, the observation matrix, the spatial POD mode (feature vector), and the weighting coefficient vector ahat (weighting coefficient) is expressed by Equation (7). The weighting coefficient vector ahat is calculated in the same way as in the first embodiment. This operation removes areas of low reliability in the thermal camera observation data before calculating the weighting coefficient vector, enabling improved accuracy.

[0065]

number

[0066] To determine the unnecessary areas, image recognition technology using a neural network is used on images captured by a normal image capturing camera 801b. In some cases, it may be possible to determine the unnecessary areas from images captured by a thermal camera alone. In that case, the normal image capturing camera 801b may be eliminated, and the unnecessary areas may be determined and temperature data acquired using the thermal camera alone. Furthermore, when determining the unnecessary areas and acquiring temperature data using a thermal camera alone, it is also possible to configure the observation matrix described above without using image recognition by setting a temperature range or the like that is valid for data, and using only pixels with temperatures within that range as valid data.

[0067] That is, the numerical analysis device 1000 of the second embodiment includes an unnecessary area designation unit 108 that designates unnecessary areas from the observation data, and a valid observation data extraction unit 109 that deletes the data of the unnecessary areas from the observation data and extracts it as valid observation data. The weighting coefficient calculation unit 106 calculates weighting coefficients for the feature vectors from the valid observation data.

[0068] The observation data acquisition unit 103 acquires observation data from a thermal camera that measures the temperature distribution in the space to be analyzed, and the unnecessary region may be a region determined to correspond to an object corresponding to a preset recognition label in an image captured by a camera capable of capturing images similar to those of the thermal camera. Alternatively, the unnecessary region may be a region where the observation data from the thermal camera is not included in a preset data range.

[0069] The operations of the equipment operating condition acquisition process S204, the feature vector set selection process S205, the weight coefficient calculation process S206 for each feature vector, and the fluid field restoration process S207 are the same as those in the first embodiment, and will not be described further. By extracting only highly reliable thermo-camera observation data in the valid observation data extraction process S604, it becomes possible to more accurately estimate the weight coefficient vector ahat calculated in the weight coefficient calculation process S206 for each feature vector. Furthermore, when applying the second embodiment, not only thermo-camera images but also observation data from various sensors can be used as needed, i.e., by including them in the observation matrix and observation value vector, it becomes possible to reconstruct the temperature distribution with higher accuracy.

[0070] By using a numerical analysis device as shown in the second embodiment, it is possible to reconstruct a three-dimensional temperature distribution based on images from a thermal camera at low sensing cost.

[0071] The numerical analysis device of this embodiment has been described above. However, the numerical analysis method for the numerical analysis device is a numerical analysis method for analyzing the spatial distribution of physical quantities in a space to be analyzed, and is characterized by including: an ensemble creation step for creating ensembles consisting of multiple combinations of boundary conditions, including preset equipment operating conditions, and corresponding analysis results for the space to be analyzed; a feature vector set calculation step for dividing the ensembles into groups and applying singular value decomposition (SVD) to calculate a set of feature vectors; an observation data acquisition step for acquiring observation data from sensors that measure at least some of the physical quantities in the space to be analyzed; an equipment operating condition acquisition step for acquiring equipment operating conditions for the operating status of equipment included in the space to be analyzed; a feature vector set selection step for selecting a set of feature vectors corresponding to the equipment operating conditions acquired in the equipment operating condition acquisition step; a weight coefficient calculation step for calculating weight coefficients for the feature vectors from the observation data; and a fluid field reconstruction step for multiplying the feature vectors by the weight coefficients, adding them, and outputting the analysis results. This enables the use of data observed by a small number of sensors to quickly reconstruct and visualize a three-dimensional flow field in the space to be analyzed according to the equipment operating conditions.

[0072] As mentioned above, the fluid field reconstruction step multiplies the feature vector by a weighting factor, adds them together, and outputs the analysis result. Regarding Equation (6), if ahat is considered as an r × 1 matrix as a coefficient vector, it becomes the product of the feature vector and the coefficient vector matrix. [Explanation of symbols]

[0073] 100 CPU 101 Ensemble Creation Department 102 Feature vector set calculation unit 103 Observation data acquisition unit 104 Equipment operating condition acquisition unit 105 Feature Vector Set Selection Unit 106 Weighting coefficient calculation unit 107 Fluid field restoration section 108 Unnecessary area specification part 109 Valid observation data extraction section 110 Input / output section 111 keyboard 112 Mouse 113 Display 130 Storage 131 Numerical Analysis Ensemble Data 132 Feature Vector Data 133 Observation Data 134 Equipment operating condition data 140 Observation data acquisition unit 141 Sensors 150 Equipment operating condition acquisition unit 151 Air conditioning equipment 1000 Numerical Analysis Device 301 Indoor space area (space to be analyzed) 302 Object 304a, 304b, 304c Numerical analysis model 401 Data Matrix X 402a Column vector (analysis results of numerical analysis model 304a) 402b column vector (analysis results of numerical analysis model 304b) 402c column vector (analysis results of numerical analysis model 304c) 701 Heat Source 702 Analysis area (analysis space) 703a, 703b, 703c Numerical analysis model 801 Camera Set 801a Thermal Camera 801b Normal image capture camera 802 Window S201 Ensemble Creation Process S202 Calculation process of feature vector set S203 Observation data acquisition processing S204 Acquisition of equipment operating conditions S205 Feature vector set selection process S206 Calculation of weighting coefficient for each feature vector S207 Fluid field reconstruction processing S601 Ensemble Creation Process S602 Unnecessary area designation processing S603 Observation data acquisition processing S604 Extraction and processing of valid observation data

Claims

1. an ensemble creation unit that creates an ensemble by combining a plurality of boundary conditions, including preset equipment operating conditions, of the analysis target space and corresponding analysis results; a feature vector set calculation unit that divides the ensemble by condition and applies singular value decomposition to calculate a set of feature vectors; an observation data acquisition unit that acquires observation data at the time of analysis from a sensor that measures physical quantities of at least a part of the space to be analyzed; an equipment operating condition acquisition unit that acquires equipment operating conditions at the time of analysis of the operating status of the equipment included in the analysis target space; a feature vector set selection unit that selects a set of feature vectors according to the device operating conditions acquired by the device operating condition acquisition unit; a weighting coefficient calculation unit that calculates a weighting coefficient of the feature vector from the observation data; a fluid field reconstruction unit that multiplies the feature vectors by the weighting coefficients, adds them together, and outputs the analysis results. A numerical analysis device characterized by:

2. 2. The numerical analysis device according to claim 1, The weighting coefficient calculation unit calculates the weighting coefficient based on the feature vector calculated under boundary conditions similar to the device operating conditions. A numerical analysis device characterized by:

3. 2. The numerical analysis device according to claim 1, further comprising: an unnecessary region designation unit that designates an unnecessary region from the observation data; a valid observation data extraction unit that deletes data in the unnecessary region from the observation data and extracts it as valid observation data, The weighting coefficient calculation unit calculates a weighting coefficient of the feature vector from the valid observation data. A numerical analysis device characterized by:

4. 4. The numerical analysis device according to claim 3, the observation data acquisition unit acquires observation data from a thermal camera that measures the temperature distribution in the space to be analyzed; The unnecessary region is a region determined to correspond to an object corresponding to a preset recognition label in an image captured by a camera capable of capturing images similar to those of the thermal camera. A numerical analysis device characterized by:

5. 4. The numerical analysis device according to claim 3, the observation data acquisition unit acquires observation data from a thermal camera that measures the temperature distribution in the space to be analyzed; The unnecessary area is an area where the observation data from the thermal camera is not included in a preset data range. A numerical analysis device characterized by:

6. 2. The numerical analysis device according to claim 1, The ensemble creation unit creates an ensemble for each combination of operating conditions by performing a numerical analysis on a plurality of combinations of operating conditions of the equipment. A numerical analysis device characterized by:

7. 2. The numerical analysis device according to claim 1, The ensemble creation unit, when performing a thermal fluid analysis for each combination of operating conditions of equipment in the analysis target space, performs a thermal fluid analysis by changing the positions of the heat sources that actually generate heat, assuming that multiple heat sources exist in a common position, and creates the analysis results as the ensemble. A numerical analysis device characterized by:

8. A numerical analysis method for a numerical analysis device that analyzes a spatial distribution of a physical quantity in an analysis target space, comprising: an ensemble creation step of creating an ensemble configured by combining a plurality of boundary conditions, including preset equipment operating conditions, of the analysis target space and corresponding analysis results; a feature vector set calculation step of dividing the ensemble by condition and applying singular value decomposition to calculate a set of feature vectors; an observation data acquisition step of acquiring observation data at the time of analysis from a sensor that measures physical quantities of at least a part of the space to be analyzed; an equipment operating condition acquisition step of acquiring equipment operating conditions at the time of analysis of the operating status of the equipment included in the analysis target space; a feature vector set selection step of selecting a set of feature vectors according to the device operating conditions acquired in the device operating condition acquisition step; a weighting coefficient calculation step of calculating a weighting coefficient of the feature vector from the observed data; a fluid field reconstruction step of multiplying the feature vectors by the weighting coefficients, adding them up, and outputting an analysis result. A numerical analysis method characterized by:

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