JP5467929B2 - Function generating apparatus and function generating method - Google Patents

Description

  The present invention relates to a function generation device and a function generation method, and more particularly to a function generation device and a function generation method for generating an approximate objective function that approximates an objective function for optimally controlling a control model, for example.

  Conventionally, in the process optimum operation of a building air conditioning system or a petrochemical plant, a method for obtaining a set value that minimizes the running cost on a simulation model has been used. For example, Patent Document 1 is an example of a central air conditioning system. This method requires a simulation model in which the physical behavior of the target is precisely expressed in advance, and it is necessary to adjust the simulation model over a long time each time the device configuration and operating conditions change.

  As a method for coping with the above problem, a method of obtaining a model function corresponding to a simulation model from operation data has been devised (Patent Document 1). The input variables of such a model are, for example, “non-control variables” corresponding to environmental conditions that are factors that fluctuate the air conditioning characteristics but cannot be used to operate the air conditioning characteristics, such as the outside air temperature for the air conditioning system. For example, “control variables” that can be controlled (or operated) to optimize the air conditioning characteristics are included.

  In this case, the range of the input variable value that is desired to be handled at a specific time point is the value of the control variable that gives an optimum state corresponding to the value of the non-control variable (that is, environmental condition) at that time point. Therefore, the value of the non-control variable can be selected arbitrarily according to the environmental conditions, and the value of the control variable is functionalized over the entire possible numerical range of the entire variable space so that it can be freely changed for optimal solution search. It is desirable that the model is complete. When the input / output relationship is obtained as an approximate function from the operation data for the purpose of optimization, this model function is particularly referred to as an “approximate objective function”.

JP 2004-293844 A JP-A-6-332506

  As described above, if a function is approximated over the entire numerical range that can be taken by all variables, the function becomes a function having a higher dimension by the number of input variables, and the amount of calculation becomes enormous when the amount of data increases. In this case, it is not particularly suitable for a sequential update type online system.

  On the other hand, if the value of a non-control variable is fixed at a specific representative value to reduce the amount of computation and only the data that falls within that representative value is extracted to create an approximate objective function, the non-control variable itself is no longer a variable. Therefore, the dimension can be lowered and the amount of calculation can be reduced. However, since the data is inevitably limited, an area where the data is sparse is likely to occur. Therefore, the reliability in that region is lowered, and an inappropriate approximate objective function is created, so that it cannot be optimized correctly.

For example, for ease of explanation, the following fictitious 12 sets of data (hereinafter referred to as P _{1 to} P ₁₂ ) are assumed. First, X is an input variable and a control variable, Y is an input variable and a non-control variable, and Z is an output variable and a target variable. The notation of a set of data is (X, Y, Z) as follows.

P ₁ (1.0, 1.0, 2.0), P ₂ (1.5, 1.0, 1.5),
P ₃ (2.0, 1.0, 2.0), P ₄ (3.0, 1.0, 3.0),
P ₅ (2.0, 1.1, 2.0), P ₆ (2.1, 1.1, 2.1),
P ₇ (2.2, 1.1, 2.2), P ₈ (2.3, 1.1, 2.3),
P ₉ (0.9, 1.3, 2.1), P ₁₀ (1.4, 1.3, 1.6),
P ₁₁ (1.9, 1.3, 1.9), P ₁₂ (2.9, 1.3, 2.9)

  At this time, if an input two-dimensional approximate objective function is created using both X and Y as input variables, X should use all data as a data group distributed between 0.9 and 3.0. become. In this case, if the control variable X is manipulated to X = 1.5, the objective variable Z can be estimated to be the minimum value 1.5 (optimization). This means that the correct optimization has been achieved.

On the other hand, a non-control variable Y that cannot be used in the optimization operation is fixed as a representative value, and a simple one-dimensional input objective function is created. For this reason, if only the data corresponding to Y = 1.1 is extracted with the intention of being near the median value of Y in the obtained data group, the data of P _{5 to} P ₈ are extracted. In this case, if the control variable X is manipulated to X = 2.0, the target variable Z must be estimated to be the minimum value 2.0 (optimization). In other words, the data becomes a sparse area in the vicinity of X = 1.5, which can be optimized, and cannot be optimized correctly. As described above, the conventional method has a problem that it is difficult to appropriately calculate an approximate objective function that approximates an objective function for performing optimal control.

  An object of the present invention is to provide a function calculation device and a function calculation method that reduce the probability that an inappropriate approximate objective function will be created while reducing the amount of calculation.

  The function generation device according to the first aspect of the present invention is an approximate objective function that approximates an objective function for optimal control of the control model using analysis data given to update the control model to be controlled. A non-control variable that is a non-control target among a plurality of input variables included in the objective function, and the analysis data is projected to a low-dimensional space Based on the low-dimensional space projection unit, a distance index calculation unit that calculates a distance index according to the distance from the spatial point of the analysis data to the spatial point representative of the non-control variable, based on the distance index, A function generation processing unit that generates an approximate objective function using the control variable to be controlled as an input variable. As a result, it is possible to reduce the probability that an inappropriate approximate objective function will be created while reducing the amount of calculation.

  A function generation device according to a second aspect of the present invention is the function generation device described above, wherein the plurality of input variables are normalized, and the discrete spatial points when the non-control variables are fixed to representative values. The normalized distance from the spatial point of analysis data to the shortest is used as a distance index. Thereby, a more appropriate approximate objective function can be generated.

  A function generation device according to a third aspect of the present invention is the function generation device described above, wherein the shortest distance from a set of spatial points to a spatial point of the analysis data when the non-control variable is fixed to a representative value. The distance is used as a distance index. Thereby, the approximate objective function can be generated more easily.

  A function generation device according to a fourth aspect of the present invention is the function generation device described above, wherein the approximate objective function is calculated by a weighted least square method using a weight corresponding to the distance index. Thereby, the approximate objective function can be generated more easily.

  The function generation method according to the fifth aspect of the present invention is an approximate objective function that approximates an objective function for optimal control of the control model using analysis data given to update the control model to be controlled. A non-control variable that is a non-control target among a plurality of input variables included in the objective function, and the non-control variable from the spatial point of the analysis data Calculating a distance index according to a distance to a spatial point having a control variable as a representative value; generating an approximate objective function using the control variable to be controlled as an input variable based on the distance index; , With. As a result, it is possible to reduce the probability that an inappropriate approximate objective function will be created while reducing the amount of calculation.

  A function generation method according to a sixth aspect of the present invention is the function generation method described above, wherein the plurality of input variables are normalized and the shortest analysis is performed from discrete spatial points when fixed to the representative value. The normalized distance to the spatial point of the business data is used as a distance index. Thereby, a more appropriate approximate objective function can be generated.

  A function generation method according to a seventh aspect of the present invention is the function generation method described above, wherein the shortest distance from the set of spatial points to the spatial point of the analysis data when the non-control variable is fixed to a representative value. The distance is used as a distance index. Thereby, the approximate objective function can be generated more easily.

  A function generation method according to an eighth aspect of the present invention is the function generation method described above, wherein the approximate objective function is calculated by a weighted least square method using a weight corresponding to the distance index. Thereby, the approximate objective function can be generated more easily.

  According to the present invention, it is possible to provide a function calculation device and a function calculation method that reduce the probability of creating an inappropriate approximate objective function while reducing the amount of calculation.

The block diagram which shows the whole structure of an air conditioning system. The figure which shows an example of a structure of a heat source system. The functional block diagram of a control model update apparatus. It is a graph which shows the relationship of the output parameter with respect to an input parameter. It is a graph which shows distribution of the data for analysis. FIG. 6 is a diagram illustrating an example of calculating a distance index according to the first embodiment. 6 is a graph showing an approximate objective function generated by the function generation method according to the first embodiment. FIG. 10 is a diagram illustrating a calculation example of a distance index according to the second embodiment. 10 is a graph showing an approximate objective function generated by the function generation method according to the second embodiment.

(Principle of the invention)
When the value of a non-control variable is fixed at a specific representative value, data other than the data that falls under that representative value can be used as relatively reliable data as long as the data is close to the representative value. The inventor is able to use even if the data is far from the representative value by recognizing that it is far from the representative value and treating the data with a reduced weight. I focused on.

  Then, the target variable value in the non-control variable value fixed to a specific representative value is interpreted as data that can be estimated even if it cannot be given accurately, and the distance index from the representative value of the non-control variable Data is weighted according to this distance index, and data that does not apply to the representative value is conceptually projected onto the input space fixed (or limited) to the representative value, and the approximate objective function is used. I came up with making it. The distance index corresponds to a projection distance. As a result, it is possible to reduce the probability that an inappropriate approximate objective function will be created while reducing the amount of calculation by reducing the number of dimensions.

For example, regarding the above-described fictitious 12 sets of data P _{1 to} P ₁₂ , the data P _{5 to} P ₈ are assigned the minimum distance index and the weight because the non-control variable Y is Y = 1.1 which is the representative value itself. Is available as a maximum of 1.0. Since the data P _{1 to} P ₄ are Y = 1.0 where the non-control variable Y is 0.1 away from the representative value 1.1, the weight is set to about 0.8, for example, as a sufficiently usable data although it is a slightly larger distance index. Available. Since the data P _{9 to} P ₁₂ are Y = 1.3 where the non-control variable Y is 0.2 away from the representative value 1.1, the data P _{9 to} P ₁₂ can be used as data that can be used even with a large distance index, for example, with a weight of about 0.6. As a result, data in the vicinity of X = 1.5 is also included, and the probability that an inappropriate approximate objective function will be created is reduced. In addition, since the number of dimensions is reduced, the amount of calculation can be reduced. Note that the method of defining the distance index is not necessarily one, and can be designed as appropriate. In the embodiments described later, two typical methods are shown as Embodiments 1 and 2.

In the following description of the first embodiment, the objective variable values of the analytical data different from the representative values, such as the data P _{1 to} P ₄ and the data P _{9 to} P ₁₂ , are referred to as objective variable estimated values. To do. The essence of this is the meaning that “the target variable value of the data that can be used for estimation even for reference” although the non-control variable value does not apply to a specific representative value.
(Control model)
Control that aims to save energy by setting the water supply temperature of the refrigerator optimally is generally referred to as VWT (Variable Water Temperature) control. The transport energy of the pump increases. On the contrary, if the water supply temperature is lowered, the efficiency of the refrigerator becomes worse and more energy is used. However, since the necessary cold water flow rate is reduced, the conveyance energy is reduced. Usually, since such a trade-off relationship exists, there exists an optimum water supply temperature with the lowest energy consumption of the entire air conditioning system. In addition, the efficiency of the refrigerator and the characteristics of the chilled water pump are greatly affected by uncontrollable external factors such as the indoor load and the outside air temperature. Therefore, the optimum water supply temperature also changes due to these external factors. In this example, the control variable corresponds to the refrigerator water supply temperature, and the non-control variable corresponds to the indoor load / outside temperature.

  In this case, fixing the non-control variable value to a specific representative value is fixed at the latest indoor load / outside temperature at the timing at which control is desired. Even if it is not the latest, the maximum value, minimum value, average value, etc. within a certain period may be used as appropriate. In the following description, among the functions representing the update model that optimally controls the control model, a function having all variables (input parameters) including control variables and non-control variables as input variables is defined as an objective function, and at least one or more A function when the non-control variable of is fixed at a representative value is an approximate objective function. The number of input variables included in the approximate objective function is smaller than the number of input variables included in the objective function.

  DESCRIPTION OF EMBODIMENTS Hereinafter, embodiments of the present invention will be illustrated and described with reference to reference numerals attached to respective elements in the drawings. The function generation device and method according to the present embodiment are particularly effective for an air conditioning system that needs to consider the influence of environmental conditions, but the application target is not limited to the air conditioning system.

(Embodiment 1)
A first embodiment according to the present invention will be described.
FIG. 1 is a block diagram showing an overall configuration of an air conditioning system using the objective function calculation apparatus according to the present embodiment.
The air conditioning system 100 includes a heat source system 110 to be controlled, an optimal control unit 120 that optimally controls the heat source system 110, a monitoring device 130 that monitors the entire air conditioning system, and a control model used in the optimal control unit 120. And a control model update device 200 that performs the update.

The heat source system 110 adjusts the temperature of the room (load) 101.
FIG. 2 is a diagram showing an example of the configuration of the heat source system 110. As shown in FIG.
The heat source system 110 includes a refrigerator 111 that generates cold water, a pump 112 that circulates cold water, and an air conditioner 113 that circulates air.

The refrigerator 111 can change the control target value of the chilled water outlet temperature according to a command from the outside. For example, the temperature of cold water can be variably controlled in the range of 6 ° C to 12 ° C.
The pump 112 circulates cold water generated by the refrigerator 111.
The air conditioner 113 brings the air in the room 101 into contact with cold water and circulates the cooled air to the room 101.

Here, when the temperature of the room 101 is controlled to a predetermined temperature, the operating cost of the heat source system changes when the chilled water outlet temperature is changed.
For example, if the cold water outlet temperature is raised (for example, 12 ° C.), the operating cost of the refrigerator 111 is lowered.
However, since the air in the room 101 has to be cooled with cold water having a high temperature, the cold water flow rate of the pump 112 increases. Therefore, the operating cost of the pump 112 increases.

Further, when the cold water outlet temperature is lowered (for example, 6 ° C.), the operating cost of the refrigerator 111 increases.
On the other hand, since the room air can be cooled with cold water having a low temperature, the flow rate of cold water may be small. Therefore, in this case, the operating cost of the pump 112 is reduced.

  Thus, in controlling the temperature of the room 101 to a predetermined temperature, the operating cost of the refrigerator 111 and the operating cost of the pump 112 are in a trade-off relationship. Therefore, the temperature can be adjusted efficiently by optimally controlling the operating cost of the entire heat source system. Further, the optimum operating condition varies depending on external environmental factors such as the outside air temperature.

  The optimal control unit 120 optimally controls the heat source system 110 so that the operation cost is minimized. The optimal control unit 120 is given a control model of the heat source system 110 from the control model update device 200. The optimal control unit 120 calculates an optimal control target value using this control model, and controls the operation of the refrigerator 111 and the pump 112 according to the optimal control target value.

The monitoring device 130 monitors the operation status of the heat source system 110 and acquires data by various sensors (not shown).
The acquired data includes, for example, the outside air temperature, the cold water outlet temperature, the cold water flow rate, the cooling water temperature, the cooling water flow rate, the pump pressure, the room temperature, and the like. These values are input variables for the approximate objective function and objective function. The amount of energy consumed (electricity, gas) and the like are output variables.
The input variables include control variables that can be controlled and non-control variables that are not controlled. That is, the input variables include, for example, “non-control variables” corresponding to environmental conditions that are factors that fluctuate the air conditioning characteristics but cannot be used for operating the air conditioning characteristics, such as the outside air temperature for the air conditioning system. “Control variables” that can be controlled (or manipulated) to optimize properties are included. The control variable is an adjustable parameter such as a cold water flow rate, and the optimum control is executed by adjusting the control variable. Both the control variable and the non-control variable are monitored by the monitoring device 130.
Further, the monitoring device 130 stores a set temperature of the room set in units of time / day of the week / month, etc., in addition to the amount of heat of load, indoor enthalpy, electricity bill, gas bill, and the like.

The monitoring device 130 periodically provides the control model update device 200 with the data listed above as analysis data necessary for constructing the control model of the heat source system 110.
In addition, the monitoring device 130 gives data necessary for the operation of the heat source system 110 to the optimum control unit 120, and causes the optimum control unit 120 to perform optimum control of the heat source system 110.
The data required for operation includes, for example, electric bills, gas bills, etc., control set values (target values) such as room set temperatures set in units of time / day of the week / month, and cold water outlet temperature, for example Control variable values such as cooling water temperature.

Next, the control model update device 200 that is a function generation device will be described.
FIG. 3 is a functional block diagram of the control model update device 200.
The control model update device 200 includes an analysis data storage unit 210, a control model calculation unit 220, a control model update unit 230, and a control model storage unit 240.

The analysis data storage unit 210 is a buffer memory that temporarily stores analysis data given from the monitoring device 130.
The data buffered in the analysis data storage unit 210 is output to the control model calculation unit 220.

The control model calculation unit 220 calculates a control model of the heat source system 110 that is a control target based on the analysis data.
The control model is a functional expression that approximates the behavior of the heat source system 110.
Here, the operation of the heat source system 110 varies depending on changes in characteristics of the refrigerator 111 and the pump 112 as well as external factors such as environmental temperature, cooling water temperature, and room temperature. Therefore, the control model calculation unit 220 calculates a control model of the heat source system 110 that reflects the current operation state using analysis data that is periodically provided. That is, the control model calculation unit 220 generates an approximate objective function that approximates an objective function for optimal control of the control model.

The control model update unit 230 takes in the control model calculated by the control model calculation unit 220 and overwrites the control model storage unit 240 in the subsequent stage. That is, the control model update unit 230 updates the approximate objective function. The control model storage unit 240 always stores the latest control model and gives it to the optimal control unit 120. The control model storage unit 240 stores the latest approximate objective function. The optimal control unit 120 controls the heat source system 110 to perform optimal control of the air conditioning system 100.

The control model calculation unit 220 will be described in detail. The control model calculation unit 220 includes a low-dimensional space projection unit 221, a distance index calculation unit 222, and a function generation processing unit 223.
The control model calculation unit 220 is a function calculation device that calculates an approximate objective function that approximates an objective function for optimal control of the control model, using analysis data given to update the control model to be controlled. .

  The low-dimensional space projection unit 221 projects the objective function to the low-dimensional space by fixing the non-control variable that is the non-control target to the representative value among the plurality of input variables included in the objective function. The distance index calculation unit 222 calculates a distance index corresponding to the distance from the spatial point of the analysis data to the set of spatial points with the non-control variable fixed as a representative value. The function generation processing unit 223 generates an approximate objective function using the control variable to be controlled as an input variable based on the distance index. This approximate objective function shows the behavior of the control model. Therefore, by using the approximate objective function, it is possible to perform optimal control that minimizes the operating cost. For example, the function generation processing unit 223 weights each analysis data according to the distance index. That is, for analysis data with a short projection distance, the weight is increased, and for analysis data with a large distance, the weight is decreased.

According to the above “principle of the invention”, it is shown as the simplest embodiment.
Although it is a distance index, the distance between the representative value of the non-control variable and the non-control variable value of the specific analysis data is adopted as the distance index. That is, if the representative value of the non-control variable Y is, for example, Y = 0.5, and the value of the non-control variable Y of specific data is Y = 0.8, the value of the distance index is set to 0.3 (= 0.8−0.5). If = 0.4, the value of the distance index is 0.1 (= 0.5-0.4). In this case, the data operation is as if the data to be adopted is projected in a limited input space fixed to the representative value of the non-control variable.

  In order to facilitate understanding of a specific processing method, a fictitious input / output relationship that is mathematically simple will be set and described. First, an input / output relationship as shown in Expression (1) and FIG. 4 is assumed.

Z = 1.5X ⁴ + X ³ -X ² + Y ² -X + 1 (1)

  In the formula (1), if the control variable is X, the non-control variable Y, the objective variable is Z, and the non-control variable Y is fixed to 0.5, the minimum value of the objective variable Z is about 0.7. Is about 0.58. FIG. 4 is a graph showing the relationship between the input variables X and Y and the objective variable Z.

  Here, the value of the output parameter Z corresponding to the value of 15 sets (A to O) of the input parameters X and Y is obtained as analysis data (X, Y, Z) (first collected data) Shall.

A (-0.1, 0.8, 1.73), B (-1.0, -0.7, 1.99), C (-0.4, 0.6, 1.57), D (-0.7, 0.0, 1.23),
E (0.5, 0.9, 1.28), F (-0.4, -0.9, 2.02), G (-0.5, -1.0, 2.21), H (0.3, 0.4, 0.81),
I (0.3, 0.6, 1.01), J (0.4, 0.7, 1.03), K (-0.1, -0.9, 1.90), L (-0.9, -0.3, 1.44),
M (1.0, -1.0, 2.50), N (1.0, 1.0, 2.50), O (-1.0, 0.55, 1.80)

  Note that the analysis data acquired by the monitoring device 130 is stored in the analysis data storage unit 210. The distribution of analytical data is shown in FIG. These are all accurate data on the curved surface given by the quartic equation of Equation (1).

When the low-dimensional space projection unit 221 projects the above analysis data into a low-dimensional space with the non-control variable Y fixed to the representative value 0.5, the following data A _{1 to} O ₁ are obtained.

A ₁ (-0.1, 0.5, 1.73), B ₁ (-1.0, 0.5, 1.99), C ₁ (-0.4, 0.5, 1.57), D ₁ (-0.7, 0.5, 1.23),
E ₁ (0.5, 0.5, 1.28), F ₁ (-0.4, 0.5, 2.02), G ₁ (-0.5, 0.5, 2.21), H ₁ (0.3, 0.5, 0.81),
I ₁ (0.3, 0.5, 1.01), J ₁ (0.4, 0.5, 1.03), K ₁ (-0.1, 0.5, 1.90), L ₁ (-0.9, 0.5, 1.44),
M ₁ (1.0, 0.5, 2.50), N ₁ (1.0, 0.5, 2.50), O ₁ (-1.0, 0.5, 1.80)

However, as described above, if the objective variable value Z of the data after projection is used as it is, an inappropriate approximate objective function is created, and therefore the distance index of each data is calculated. Here, as shown in FIG. 6, the distance index defined by the absolute value of the difference between the fixed non-control variable value 0.5 and the non-control variable value Y of each acquired data is used. When the distance index calculation unit 222 calculates the distance index, the following distance index data A _{2 to} O ₂ are obtained.

A ₂ (0.3), B ₂ (1.2), C ₂ (0.1), D ₂ (0.5), E ₂ (0.4), F ₂ (1.4), G ₂ (1.5), H ₂ (0.1),
I ₂ (0.1), J ₂ (0.2), K ₂ (1.4), L ₂ (0.8), M ₂ (1.5), N ₂ (0.5), O ₂ (0.05)

Here, the distance index data A _{2 to} O ₂ are absolute values of the difference between the non-control variable Y values of A to O and the fixed non-control variable value 0.5. Therefore, as shown in FIG. 6, the shortest distance between the straight line with the non-control variable as a representative value and the spatial point of the analysis data is the distance index. That is, the distance index is a linear distance in the Y direction from a spatial point having a non-control variable as a representative value to a spatial point of the analysis data A to O.
In the present embodiment, since a description is given in a two-dimensional space composed of two input variables, a set of spatial points with non-control variables as representative values, that is, continuous spatial points are straight lines. However, as the number of dimensions increases, the set of spatial points with non-control variables as representative values may not be straight.
For example, in the case of a two-input variable, the input variable space is two-dimensional. If one non-control variable is fixed (because one dimension is dropped), the set of spatial points is a straight line.
In the case of three input variables, the input variable space will be three-dimensional, and if you fix one uncontrolled variable (because one dimension drops), the set of spatial points will be a plane.
In the case of three input variables, the input variable space is three-dimensional. If two non-control variables are fixed (because two dimensions drop), the set of spatial points is a straight line.

Uncontrolled variable value becomes smaller distance index O ₂ data close to the fixed value 0.5, distance index data inverse to the data G, uncontrolled variable values such as M is separated from the fixed value 0.5 as data O G ₂ and M ₂ increase. Using the weighted least-squares method with the reciprocal of this distance index as the weight for each control variable value, the data with a small distance index has a high effect on the approximation of the objective function, and conversely for the data with a large distance index Can lower the impact. Here, the weighted least square method is a method for obtaining a function that minimizes the sum of weights of error squares for each data and can be expressed by the following equation (2).

In Expression (2), w _i is a weight, X _i is a control variable value collected, Z _i is an objective variable value collected, n is the number of collected data, and f is an approximate objective function. If f is an approximate objective function of a quartic expression, Expression (3) and the function shown in FIG. 4 are obtained based on the 15 sets of data.

The function generation processing unit 223 generates an approximate objective function by the weighted least square method. In this way, the approximate objective function can be calculated by performing regression analysis on the post-projection data A _{1 to} O ₁ using the weighted least square method based on the distance index. Since the analysis data is projected onto the low-dimensional space, the amount of calculation can be reduced. Also, an appropriate approximate objective function can be obtained by considering the distance index as a weight.
In this way, by changing the strength of the influence on the approximate objective function according to the distance from the fixed non-control variable, an inappropriate approximate objective function is created along with a reduction in the amount of calculation due to the reduction in dimensions. Probability can be reduced.

  In the above description, Y is the only non-control variable fixed to the representative value, but the above method can be applied even when the number of input variables increases and the number of non-control variables is increased. However, in this case, different distance indices are calculated for a set of data as many as the number of non-control variables fixed to the representative value, but the average value, minimum value, maximum value, and center of all distance indices are calculated. What is necessary is just to summarize suitably by a value etc. When there are a plurality of non-control variables, all non-control variables may be fixed with representative values, or only some non-control variables may be fixed with representative values.

  Note that the approximate objective function may be generated using a method other than the weighted least square method. For example, a support vector regression method can be used to derive the approximate objective function. Here, an error band for each data may be set based on the distance index. For example, for data with a small distance index, the allowable error (error band) may be reduced, and for data with a large distance index, the allowable error may be increased. Then, an approximate objective function that satisfies the tolerance of all data may be calculated.

(Embodiment 2)
According to the above “principle of the invention”, another embodiment is shown. In addition, about the content which overlaps with Embodiment 1, description is abbreviate | omitted suitably.
Assuming a specific value of a distance index, but a representative value of a non-control variable and any other input variable (which can be a control variable or non-control variable), its assumed input Data in the vicinity of the space point α is searched, and the distance between the input space point of the searched data and the assumed input space point α is adopted as a distance index.

First, differences in technical significance from the second embodiment will be described.
In the first embodiment, since the objective variable estimated value is obtained by a simple projection, the search is substantially a straight line search (see FIG. 6) instead of the neighborhood search for the assumed input space point α. ing. Accordingly, in the case of the first embodiment, the processing procedure is simple, but data at a position slightly deviated from the straight line is not selected as the objective variable estimated value. Therefore, it cannot be said that the data that should have high reliability can be efficiently and effectively utilized.

  In the method of the second embodiment described below, the processing is more complicated than in the first embodiment, but the data can be used efficiently and effectively. However, the method of defining the distance index is different, and the embodiment is based on the principle of the invention. It is not a simple projection, but can be said to be a projection from many directions, and as a superordinate concept, it is a projection.

The same fictitious input / output relationship (data A to O) as in the first embodiment is set and described.
First, each input variable is normalized in advance from the upper / lower limit range, variation, strength of correlation with the objective function, etc. for each input variable. For example, normalization is performed according to the following equation (4), where μ _X and μ _Y are the average values for the control variable X and the non-control variable Y, and the standard deviations are σ _X and σ _Y.

  The data normalized by Expression (4) is stored in the analysis data storage unit 210. By performing normalization, almost all data in X and Y can be within ± 3 (within 3 times the standard deviation).

  The vicinity of each control variable value X when the non-control variable Y is fixed to the representative value 0.5 is searched for the normalized data. The neighborhood search method is performed by searching for data that minimizes the distance between normalized variables as follows.

  In Expression (5), d (X) is a distance index. In equation (5), it means that the distance to the nearest analysis data for a given value of X is a distance index to the spatial point for that value. Here, the distance from the spatial point where Y is the representative value (0.5) to the spatial point of the nearest analysis data is used as a distance index. That is, as shown in FIG. 8, the distance index is a distance between spatial points discretely present on a straight line Y = 0.5 (every 0.25 in FIG. 8) and the spatial points of the analysis data. Nine spatial points (−1.0,0.5), (−0.75,0.5), (−0.5,0.5), (−0.25,0.5), (0,0.5) Normal from (0.25,0.5), (0.5,0.5), (0.75,0.5), (1.0,0.5) to the spatial point of the nearest analytical data among the spatial points of analytical data A to O Euclidean distance. For example, the spatial point of the analytical data closest to (0,0.5) is the spatial point of the analytical data A, and the distance index (normalized Euclidean distance) is 0.40.

  As described above, in the neighborhood data search process, a data distance that minimizes the normalized distance is used as a distance index. As shown in FIG. 8, a distance index defined by a fixed non-control variable value 0.5 and a minimum normalized Euclidean distance of all input variables of each acquired data is used. The distance index calculation unit 222 calculates the distance index. Note that when there are n input variables, the Euclidean distance in the n-dimensional space is a distance index.

As in the first embodiment, the reciprocal of this distance index is used as the weight of the weighted least square method. As a result, an approximate objective function can be generated according to the distance of the neighborhood data. Assuming a quadratic approximate objective function, a function represented by Expression (6) is obtained from the analysis data A to O.

  Note that the function generation processing unit 223 generates an approximate objective function. Even when there are a plurality of input variables, highly reliable data can be used for estimation by appropriately setting the distance. Further, in the present embodiment, the spatial point of the analytical data nearest to the discrete spatial point with the non-control variable as a representative value is extracted from among a plurality of spatial points of the analytical data. Thereby, the uneven distribution of analysis data in the space can be eliminated, and a more appropriate approximate objective function can be generated. For example, the spatial points for generating the approximate objective function are uniformly distributed by setting the discrete spatial points at equal intervals. Furthermore, a distance index is defined according to a distance from a spatial point with a non-control variable as a representative value. Therefore, a more appropriate approximate objective function can be generated and optimal control can be performed. Further, similarly to the first embodiment, since the non-control variables determined by the environmental conditions are fixed as representative values, the number of input variables (the number of dimensions) is reduced. Thereby, the calculation amount for generating the approximate objective function can be reduced.

  In the above, we have normalized from the average value and standard deviation by assuming that each input variable of the acquired data was generated based on an independent normal distribution, but we used the upper and lower limit average value and the upper and lower limit range. Or normalization based on a more complicated probability distribution (such as a multivariate normal distribution) may be performed.

  In the above embodiment, the heat source system that cools the room temperature is exemplified as the control target. However, as a heat source system, the room temperature may be warmed as a matter of course.

  In addition, the present invention is effective not only for controlling an air conditioner but also for controlling various devices having optimal control points. Further, the distance index may be defined using a method other than the above-described first and second embodiments.

100 ... Air conditioning system, 101 ... Room, 110 ... Heat source system, 111 ... Refrigerator, 112 ... Pump, 113 ... Air conditioner, 120 ... Optimal control unit, 130 ... Monitoring device, 200 ... Control model update device, 210 ... Analysis Data storage unit, 220 ... Control model calculation unit, 221 ... Low-dimensional space projection unit, 222 ... Distance index calculation unit, 223 ... Function generation processing unit, 230 ... Control model update unit, 240 ... Control model storage unit,

Claims (8)

A function calculation device that calculates an approximate objective function that approximates an objective function for optimally controlling the control model, using analysis data provided to update a control model of a control target,
Of the plurality of input variables included in the objective function, by fixing a non-control variable that is a non-control target to a representative value, a low-dimensional space projection unit that projects analysis data to a low-dimensional space;
A distance index calculation unit that calculates a distance index according to a distance from a spatial point of the analysis data to a spatial point with the non-control variable as a representative value;
A function calculation apparatus comprising: a function generation processing unit that generates an approximate objective function using the control variable to be controlled as an input variable based on the distance index. Normalize the plurality of input variables,
The function calculation device according to claim 1, wherein a normalized distance from a discrete spatial point to a spatial point of the shortest analysis data when the non-control variable is fixed to a representative value is used as a distance index. .   2. The function calculation device according to claim 1, wherein the shortest distance from a set of spatial points to the spatial point of the analysis data when the non-control variable is fixed to a representative value is used as a distance index.   The function calculation apparatus according to claim 1, wherein the approximate objective function is calculated by a weighted least square method using a weight corresponding to the distance index. A function calculation method for calculating an approximate objective function that approximates an objective function for optimal control of the control model, using analysis data given to update a control model of a controlled object,
Of the plurality of input variables included in the objective function, fixing a non-control variable that is a non-control target to a representative value;
Calculating a distance index according to a distance from a spatial point of the analysis data to a spatial point having the non-control variable as a representative value;
Generating an approximate objective function using the control variable to be controlled as an input variable based on the distance index. Normalize the plurality of input variables,
6. The function calculation method according to claim 5, wherein a normalized distance from a discrete spatial point to a spatial point of the shortest analysis data when fixed to the representative value is used as a distance index.   The function calculation method according to claim 6, wherein the shortest distance from a set of spatial points when the non-control variable is fixed to a representative value to the spatial point of the analysis data is used as a distance index.   The function calculation method according to claim 5, wherein the approximate objective function is calculated by a weighted least square method using a weight corresponding to the distance index.

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