Numerical analysis device and numerical analysis method

Abstract

This numerical analysis device comprises: an ensemble creation unit (101) that creates an ensemble by combining a plurality of boundary conditions, which include preset equipment operating conditions for a space being analyzed, and analysis results; a feature vector set calculation unit (102) that partitions the ensemble by condition and applies singular value decomposition to calculate a set of feature vectors; an observation data acquisition unit (103) that acquires observation data from a sensor that measures a physical quantity in at least a part of the space being analyzed; an equipment operating condition acquisition unit (104) that acquires equipment operating conditions for an operation status of equipment; a feature vector set selection unit (105) that selects a set of feature vectors corresponding to the equipment operating conditions; a weighting coefficient calculation unit (106) that calculates weighting coefficients for the feature vectors from the observation data; and a fluid field reconstruction unit (107) that outputs an analysis result by multiplying the feature vectors by the weighting coefficients and summing the weighted vectors.

Description

Numerical analysis device and numerical analysis method

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

[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 and evaluate three-dimensional flow fields using computational fluid analysis technology. However, the more detailed the analytical model, the longer the simulation time required, making it difficult to apply to applications where the situation needs to be grasped in real time. On the other hand, a technology has been developed in which a fluid analysis is performed in advance to simulate 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 summing 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 coefficient of the POD mode using observed values ​​to restore the flow field.

[0006] Japanese Patent Application Laid-Open No. 2020-201146

[0007] 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.

[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 technique similar to this document to estimating flow fields indoors.

[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 determined in advance by performing fluid analysis, 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.

[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.

[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.

[0013] FIG. 1 is a diagram illustrating the configuration of a numerical analysis system according to the first embodiment. FIG. 2 is a flowchart illustrating the process of flow field reconstruction according to the first embodiment. FIG. 3 is a diagram illustrating an example of creating a numerical analysis ensemble according to the first embodiment. FIG. 4 is a diagram illustrating a data matrix created for each equipment operating condition according to the first embodiment. FIG. 5 is a diagram illustrating sensor positions according to the first embodiment. FIG. 6 is a diagram illustrating the configuration of a numerical analysis system according to the second embodiment. FIG. 7 is a flowchart illustrating the process of temperature field reconstruction according to the second embodiment. FIG. 8 is a diagram illustrating an example of creating a numerical analysis ensemble according to the second embodiment. FIG. 9 is a diagram illustrating a thermal camera according to the second embodiment, and the position of a window as an unnecessary region. FIG. 10 is a diagram illustrating an example of imaging by a thermal camera according to the second embodiment.

[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 distributions, such as wind speed, and visualizing locations where dust is likely to accumulate, ventilation conditions, etc., indoors in a factory or the like, at low sensing costs (for example, using a small number of physical quantity sensors). This makes it possible to quickly predict three-dimensional flow fields using observation data acquired from a small number of physical quantity sensors and operation information on 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 the 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 the CPU 100, or the CPU 100 and a GPU may be used together.

[0018] Input / output unit 110 is composed of an input unit including keyboard 111 and mouse 112, etc., and an output unit including display 113, etc. A user of numerical analysis device 1000 can input commands from keyboard 111 and mouse 112 of the input unit, and visually grasp the results from 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. The numerical analysis ensemble data 131 stores information such as flow velocity, pressure, temperature, and humidity.

[0022] The feature vector data 132 is eigenvector data obtained by applying POD (proper orthogonal decomposition) to the numerical analysis ensemble data 131. 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 was run 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, the 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 output from air conditioning equipment 151a, a medium air volume is output from air conditioning equipment 151b, and a small air volume is output from air conditioning equipment 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 Figure 3. Note that 303 is an object that is constantly present in the indoor space region 301, such as a factory production line.

[0030] In the numerical analysis model 304a, the object 302 is located in the upper left of the indoor space region 301. In the other numerical analysis models 304b and 304c, the position of the object 302 is located on the upper side and upper right of the indoor space region 301. In this way, the numerical analysis is performed assuming that only the position of the object 302 changes and that the other structures and operating conditions, i.e., boundary conditions, remain unchanged. This analysis may be a steady-state analysis or a non-steady-state analysis. A similar procedure is performed for the 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 air conditioning equipment 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 calculation process S202 of feature vector set. The feature vector set calculation unit 102 obtains feature vectors (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, because 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-dimensional data 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, i.e., a POD mode. The POD mode is obtained as a POD mode U calculated by Equation (2).

[0035] Singular value decomposition is performed on the multiple data matrices X401, i.e., for each combination of operating conditions of the multiple air conditioning devices. 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 the 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 observation data acquisition process S203. In observation data acquisition process S203, observation data acquired from multiple sensors 141 is integrated by the observation data acquisition unit 140 and input into the numerical analysis system. As observation data, information on physical quantities such as wind speed, pressure, temperature, and humidity can be acquired. Also, the spatial coordinates of each sensor 141 are assumed to be 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 observation data at the time of analysis.

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

[0039] (Feature Vector Set Selection Process) The feature vector set selection unit 105 executes 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 a large air volume for air conditioning equipment 151a, a medium air volume for air conditioning equipment 151b, and a small air volume for air conditioning equipment 151c, this combination of conditions corresponds to equipment operating condition combination 1 in FIG. 3. Therefore, a 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 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 device operating conditions can be approximated as shown in Equation (3).

[0044] Here, the matrix U1:r is obtained by extracting the first to r-th columns of the POD mode U, and r is 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 original matrix POD mode U, the flow field is reduced in dimension relative to the original data, and only r coefficients are required for addition.

[0045] Fig. 5 is a diagram showing sensor positions according to the first embodiment. Fig. 5 shows an example of restoring a fluid field under the condition that the equipment is operating under equipment operating condition combination 1. The position of the object 302 is a condition that is not included in the conditions for the numerical analysis of the ensemble created in advance. Also, it is assumed that the sensors 141a, 141b, and 141c are positioned as shown in Fig. 5. It is also assumed that the sensors 141a, 141b, and 141c measure wind speed, and the observation vector is y, and each observation value in the observation vector y is y. １４１ａ , y １４１ｂ , y １４１ｃ Let's say.

[0046]

[0047] Here, the current flow field is expressed as a matrix U １：ｒ If it is possible to reconstruct it by adding up the POD mode U, which is multiplied by a certain coefficient vector a (weighting coefficient) and added up as shown in Equation (4), １：ｒ The observation data extracted from the observation matrix H is y １４１ａ , y １４１ｂ , y １４１ｃ 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 sum of the observation matrix H and the matrix U １：ｒ is the product of

[0048] (Restoration process of fluid field) The fluid field restoration unit 107 executes the restoration process S207 of the fluid field. 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. For the reconstruction, Equation (6) is used.

[0049] Here, the vector x 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 represented. By visualizing the reconstructed three-dimensional flow field 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 a 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] Second Embodiment The second embodiment aims to rapidly reconstruct and visualize the temperature distribution in space using temperature distribution observation values ​​obtained two-dimensionally 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 a 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 creation unit 101 executes an ensemble creation process S601. In the ensemble creation process S601, a numerical analysis such as that shown in FIG. 8 is performed. A thermal fluid analysis is performed for each combination of operating conditions of 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 actual heat source 701 positioned differently, and the analysis results are created as an ensemble. For example, for an analysis target region 702 (analysis target space), in the numerical analysis model 703a, the heat source 701 is the object in the upper left, while in the 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. Note that the temperatures of the space and wall surfaces are included in the ensemble as numerical analysis results.

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

[0058] (Unnecessary Region Designation Processing) The unnecessary region designation unit 108 executes the unnecessary region designation processing S602. The unnecessary region designation unit 108 designates an object to be removed as an unnecessary region 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 designation method is selected from the object recognition labels that can be output by image recognition technology, which is executed in the valid observation data extraction processing S604 described below. As a specific example, the unnecessary region is designated using 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 a thermal fluid analysis performed in advance.

[0060] (Valid observation data extraction process) The valid observation data extraction unit 109 executes valid observation data extraction process S604. The valid observation data extraction unit 109 determines whether the unnecessary area specified in the unnecessary area specification 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 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 using 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. It is also assumed that 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. It is assumed 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 the image 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. If 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, since 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 three-dimensional 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 method for determining the weighting coefficient vector ahat is the same as in the first embodiment. This operation allows the weighting coefficient vector to be determined after excluding areas of low reliability in the thermal camera observation data, thereby improving accuracy.

[0065]

[0066] To determine the unnecessary area, image recognition technology using a neural network is used on images captured by a normal image capturing camera 801b. In some cases, conditions may exist where the unnecessary area can be determined from images captured by a thermal camera alone. In such cases, the normal image capturing camera 801b may be eliminated, and the unnecessary area determination and temperature data acquisition may be performed using the thermal camera alone. Furthermore, when determining the unnecessary area 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 in advance, and using only pixels with temperatures within that range as valid data.

[0067] That is, the numerical analysis apparatus 1000 of the second embodiment includes an unnecessary region designation unit 108 that designates unnecessary regions from the observation data, and a valid observation data extraction unit 109 that deletes the data of the unnecessary regions 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 thermocamera 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 thermocamera 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 is a numerical analysis method for a numerical analysis device that analyzes the spatial distribution of physical quantities in an analysis target space, and is characterized by including: an ensemble creation step of creating ensembles consisting of multiple combinations of boundary conditions, including preset equipment operating conditions, and corresponding analysis results for the analysis target space; a feature vector set calculation step of dividing the ensemble into conditions and applying singular value decomposition (SVD) to calculate a set of feature vectors; an observation data acquisition step of acquiring observation data from sensors that measure at least some of the physical quantities in the analysis target space; an equipment operating condition acquisition step of acquiring equipment operating conditions for the operating status of equipment included in the analysis target space; a feature vector set selection step of 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 of calculating weight coefficients for the feature vectors from the observation data; and a fluid field reconstruction step of multiplying the feature vectors by the weight coefficients, adding them, and outputting the analysis result. This makes it possible to quickly reconstruct and visualize a three-dimensional flow field in the target space according to the equipment operating conditions by utilizing data observed by a small number of sensors.

[0072] As described 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 a 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.

[0073] 100 CPU 101 Ensemble creation unit 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 unit 108 Unnecessary area designation unit 109 Valid observation data extraction unit 110 Input / output unit 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 Sensor 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 result of numerical analysis model 304a) 402b Column vector (analysis result of numerical analysis model 304b) 402c Column vector (analysis result of numerical analysis model 304c) 701 Heat source 702 Analysis target area (analysis target space) 703a, 703b, 703c Numerical analysis model 801 Camera set 801a Thermo camera 801b Ordinary image capturing camera 802 Window S201 Ensemble creation process S202 Feature vector set calculation process S203 Observation data acquisition process S204 Equipment operating condition acquisition process S205 Feature vector set selection process S206 Weight coefficient calculation process for each feature vector S207 Fluid field restoration process S601 Ensemble creation process S602 Unnecessary area designation process S603 Observation data acquisition process S604 Extraction and processing of valid observation data

Claims

1. A numerical analysis device comprising: an ensemble creation unit that creates an ensemble composed 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 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 the analysis from sensors that measure at least some of the physical quantities of the space to be analyzed; an equipment operating condition acquisition unit that acquires the 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 results.

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

3. A numerical analysis device according to claim 1, further comprising: an unnecessary area designation unit that designates unnecessary areas from the observation data; and a valid observation data extraction unit that deletes data from the unnecessary areas from the observation data and extracts it as valid observation data, wherein the weighting coefficient calculation unit calculates a weighting coefficient for the feature vector from the valid observation data.

4. A numerical analysis device according to claim 3, wherein the observation data acquisition unit acquires observation data from a thermal camera that measures the temperature distribution in the space to be analyzed, and the unnecessary region is a region that is determined to correspond to an object that corresponds to a predetermined recognition label in an image taken by a camera that can take images similar to that of the thermal camera.

5. A numerical analysis device according to claim 3, wherein the observation data acquisition unit acquires observation data from a thermo camera that measures the temperature distribution in the space to be analyzed, and the unnecessary region is a region where the observation data from the thermo camera is not included in a predetermined data range.

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

7. A numerical analysis device according to claim 1, wherein the ensemble creation unit, when performing a thermal fluid analysis for each combination of operating conditions of equipment in the space to be analyzed, assumes that multiple heat sources are present in a common position, performs a thermal fluid analysis by changing the position of the heat source that actually generates heat, and creates the results of these analyses as the ensemble.

8. A numerical analysis method for a numerical analysis device that analyzes the spatial distribution of physical quantities in a space to be analyzed, comprising: an ensemble creation step of creating an ensemble consisting of a combination of boundary conditions, including preset equipment operating conditions, of the space to be analyzed and analysis results corresponding thereto; 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 sensors that measure at least some of the physical quantities 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 equipment included in the space to be analyzed; a feature vector set selection step of selecting a set of feature vectors according to the equipment operating conditions acquired in the equipment operating condition acquisition step; a weight coefficient calculation step of calculating weight coefficients for the feature vectors from the observation data; and a fluid field restoration step of multiplying the feature vectors by the weight coefficients, adding them up, and outputting the analysis results.

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