Patent Publication Number: US-10325214-B2

Title: Physical quantities prediction apparatus and method

Description:
CROSS-REFERENCE TO RELATED APPLICATION 
     This application is based upon and claims the benefit of priority of the prior Japanese Patent Application No. 2015-044798, filed on Mar. 6, 2015, the entire contents of which are incorporated herein by reference. 
     FIELD 
     The embodiments discussed herein are related to a physical quantities prediction apparatus and method. 
     BACKGROUND 
     In recent years, with an arrival of high-level information society, computers have come to deal with a large quantity of data. A facility instanced by a data center and other equivalent facilities has increasingly and collectively managed a multiplicity of computers installed indoors. For example, the data center installs a multiplicity of server racks into a computer room, and the multiplicity of computers (servers) is stored in the respective server racks. A large amount of jobs are organically distributed to the computers, corresponding to operation statuses of the plurality of computers, and thus efficiently processed. 
     By the way, the computer generates heat as being operated. A rise of temperature within the computer causes a malfunction and a failure, and therefore the computer uses a built-in fan. The built-in fan takes cool air into the computer of the server rack, and the heat generated in the computer is discharged outside the computer. Generally, the built-in fan of the computer is operated under map table control based on an exothermic temperature of the computer in many cases. 
     On the other hand, an operator sets target values of a blowout temperature and a blowout airflow volume in a cooling system of an air conditioner so that a temperature of suction air sucked into each of the computer of every rack satisfies a value equal to or lower than the predetermined temperature. It is herein considered to assist the operator in operating the air conditioner through a prediction result by predicting a state of a future temperature of the suction air based on a prediction model. For example, a model prediction control method frequently uses a transfer function in the prediction model. 
     PATENT DOCUMENT 
     [Patent document 1] Japanese Laid-Open Patent Publication No. 2009-76037 
     [Patent document 2] Japanese Laid-Open Patent Publication No. 2011-258620 
     SUMMARY 
     One aspect of the embodiments is exemplified by an information processing apparatus described below. To be specific, the information processing apparatus includes a database configured to store a plurality of physical quantities acquired in time-series together with time. 
     The information processing apparatus further includes a processor and a memory storing a program causing the processor to execute acquiring the plurality of physical quantities in time-series, extracting, as one or more explanatory variates, one or more physical quantities becoming factors for variations of one or more objective variates with respect to the one or more objective variates set from one or more prediction target physical quantities in the plurality of physical quantities, selecting such one or more first explanatory variates as to minimize errors between actual values of the physical quantities set in the one or more objective variates and prediction values of a first model based on the one or more objective variates when presuming the first model from the one or more explanatory variates, selecting such one or more second explanatory variates as to minimize errors between the actual values of the physical quantities set in the one or more objective variates and prediction values of a second model based on one or more objective variates when presuming the second model added to the first model by setting, as the explanatory variates, the physical quantities other than the physical quantities selected as the one or more first explanatory variates in the plurality of physical quantities, generating past case data by acquiring, from the database, the physical quantities corresponding to the one or more objective variates and an input variate group of the first explanatory variates and the second explanatory variates, setting, when the prediction is requested, the current physical quantities corresponding to the input variate group in the input vectors for predicting the one or more objective variates, calculating inter-vector distances between the input vectors and the input variate group in the past case data, searching for predetermined pieces of past case data in the sequence from the shortest of the inter-vector distances, building up the second model from the input variate group in the predetermined pieces of searched past case data and from the one or more objective variates, predicting values of the one or more objective variates from the second model, and indicating the predicted values of the one or more objective variates. 
     The object and advantages of the invention will be realized and attained by means of the elements and combinations particularly pointed out in the claims. It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory and are not restrictive of the invention. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  is a schematic side view illustrating one example of a data center to which a temperature management system is applied; 
         FIG. 2  is a schematic plan view of the data center; 
         FIG. 3  is a block diagram illustrating a configuration of a temperature management system; 
         FIG. 4  is a diagram of a configuration of an input vector update unit; 
         FIG. 5  is a diagram of a configuration of a prediction processing unit; 
         FIG. 6  is a flowchart illustrating processes of the input vector update unit; 
         FIG. 7  is a diagram of a processing example of equally segmenting a suction surface of a server rack; 
         FIG. 8  is a diagram illustrating an example of data stored in a large-scale database; 
         FIG. 9  is a diagram illustrating an example of generating a variable with time being delayed; 
         FIG. 10  is a flowchart illustrating details of a process based on a stepwise procedure; 
         FIG. 11  is a flowchart illustrating details of a process of a modified stepwise procedure processing unit; 
         FIG. 12  is a diagram illustrating an example of storing data in an I/O vector database; 
         FIG. 13A  is a diagram of another data example (time base) of the I/O vector database; 
         FIG. 13B  is a diagram of still another data example (data number) of the I/O vector database; 
         FIG. 14  is a flowchart illustrating a process of a prediction processing unit; 
         FIG. 15  is a diagram illustrating a hardware configuration of an information processing apparatus applied to the temperature management system; 
         FIG. 16  is a diagram illustrating an example of segmenting an area of the data center; 
         FIG. 17  is a diagram illustrating a conventional example of selecting an input variable; 
         FIG. 18  is a diagram illustrating a combination of variables selected based on a result of the stepwise procedure; 
         FIG. 19  is a diagram illustrating a combination of variables selected based on a result of a modified stepwise procedure; 
         FIG. 20  is a diagram illustrating an equipment operating state; 
         FIG. 21  is a diagram illustrating comparative results about prediction results by the temperature management system according to an embodiment and by a conventional procedure 1; 
         FIG. 22  is a diagram illustrating comparative results about prediction results by the temperature management system according to the embodiment and by a conventional procedure 2; 
         FIG. 23  is a diagram illustrating a prediction example of the temperature management system according to the embodiment; and 
         FIG. 24  is a diagram illustrating a prediction value of operation of a tile fan in relation to a prediction value of an air suction temperature. 
     
    
    
     DESCRIPTION OP EMBODIMENTS 
     In the actual facility instanced by the data center and other equivalent facilities, an equipment layout and server installation positions are changed on a daily basis in the facility. When a prediction target configuration instanced by the equipment layout and the server installation positions varies, an error between the prediction value of the prediction model and an actual value occurs in the conventional prediction model of the transfer function. This error results in a problem that temperature prediction performance is insufficient for the control using the prediction value and for the control assistance according to conventional technologies. It does not, however, mean that this type of problem is limited to the temperature prediction of the computer and other equivalent apparatuses, and the problem may also arise in predicting a variety of physical quantities. 
     A temperature management system according to one embodiment will hereinafter be described with reference to the drawings.  FIG. 1  is a schematic side view illustrating one example of a data center to which the temperature management system according to the embodiment is applied, and  FIG. 2  is a schematic plan view that likewise illustrates this data center. Note that cool air of an air conditioner, e.g., flows under a floor and further flows to an air suction side of a computer from under the floor to cool down the computer, a server and other equivalent equipment in the data center according to the embodiment. Herein, the “air suction side of the computer” indicates a chassis surface side on which internal fans of the computer suck the cool air. Warmed exhaust air is discharged by the internal fans of the computer from another chassis surface opposite to the air suction side of the computer. The chassis surface from which the warmed air is discharged is called an “exhaust side”. 
     As in  FIG. 1 , in the data center according to the embodiment, a server room  10  is separated into a server room upper section  10   a , a server room under-floor section  10   b , and a roof-space hot aisle  15 . A server rack  11 , a plurality of servers  12  stored in the server rack  11 , and an air conditioner  13  are installed in the server room upper section  10   a.    
     A grill panel  14  (vent holes) having a plurality of air gaps to let the cool air under the floor through to the server room upper section  10   a  is provided between the server room upper section  10   a  and the server room under-floor section  10   b . A tile fan  17  including a built-in blower fan is provided in the server room under-floor section  10   b , the tile fan serving to blast the cool air under the floor to the upper section of the server room via the grill panel  14 . 
     The cool air blasted by the air conditioner  13  flows through the server room under-floor section  10   b  and is supplied to the suction side of the servers  12  in the server room upper section  10   a  via the grill panel  14 . The tile fan  17  blasts the cool air toward the server room upper section  10   a  from the server room under-floor section  10   b . The tile fan  17  is capable of switching over an airflow volume at four stages instanced by, “strong”, “intermediate”, “weak” and “OFF”. The servers  12  suck the cool air fed via the grill panel  14  from one side surface of the chassis, and discharge the warmed exhaust air toward an opposite side surface. The warmed exhaust air is returned to the air conditioner  13  via the roof-space hot aisle  15 . Note that the servers  12  are stored in the server rack  11 . One chassis is configured to include the server rack  11  and the servers  12  stored in the server rack  11  on the whole. 
     As illustrated in  FIG. 2 , e.g., a rack row  11   a  and a rack row  11   b  of the server racks  11  are installed in parallel, while the grill panel  14  is interposed therebetween. The respective servers  12  of the rack rows  11   a ,  11   b  suck the cool air flowing from the tile fan  17 . To be specific, the servers  12  of the rack rows  11   a ,  11   b  suck the cool air from the side surface face-to-face to each other, and discharge the warmed exhaust air from side surfaces on opposite sides thereof. In other words, in the example of  FIG. 2 , the servers  12  of the rack row  11   a  of the server racks  11  are arranged so that the exhaust sides correspond to front sides of the servers  12 , while the suction sides correspond to back sides of the servers  12 . While on the other hand, the servers  12  of the rack row  11   b  of the server racks  11  are arranged so that the suction sides correspond to the front sides of the servers  12 , while the exhaust sides correspond to the back sides of the servers  12 . Note that the suction side of the chassis for the servers  12  is also simply referred to as the suction side of the server rack  11 . The embodiment is described on the assumption that the servers  12  are aggregated per server rack  11  and deemed to be one chassis, and the server rack  11  appears to suck the cool air. 
       FIG. 3  is a block diagram illustrating a configuration of the temperature management system for an electronic equipment according to a first embodiment of the present invention. The temperature management system includes a prediction unit  20 , a suction air temperature distribution detecting unit  21 , each of air conditioner blowout temperature detecting units  22 , each of air conditioner fan airflow volume detecting units  23 , each of tile fan airflow volume detecting units  24 , a parameter setting unit  25 , a prediction result indicating unit  26 , and an alarm output unit  27 . The suction air temperature distribution detecting unit  21 , each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , and each of the tile fan airflow volume detecting units  24  illustrate an “acquiring unit”. 
     The prediction unit  20  calculates prediction values of physical quantities of a temperature of the suction air and other equivalent quantities, based on items of information given from the suction air temperature distribution detecting unit  21 , each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , each of the tile fan airflow volume detecting units  24  and other equivalent units. 
     The suction air temperature distribution detecting unit  21  acquires temperatures on the suction side of the server rack  11  by measuring the temperatures at a plurality of points. For example, one or a plurality of temperature sensors is provided on a suction-sided wall surface of the chassis for each of the servers  12  in the server rack  11 . The suction air temperature distribution detecting unit  21  acquires, as digital data, the temperatures measured by the temperature sensors on the suction-sided wall surfaces of the chassis for the respective server racks  11 . 
     Each of the air conditioner blowout temperature detecting units  22  acquires a setting value of blowout temperature of the air conditioner  13  from a control unit within the air conditioner  13 . Each of the air conditioner fan airflow volume detecting units  23  acquires a setting value of fan airflow volume of the air conditioner  13  from the control unit within the air conditioner  13 . Each of the tile fan airflow volume detecting units  24  acquires a setting value of fan airflow volume of the tile fan  17  from the control unit of the tile fan  17 . Note that a large-scale database  43  illustrated in  FIG. 4  accumulates detected values given from the suction air temperature distribution detecting unit  21 , each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , each of the tile fan airflow volume detecting units  24  and other equivalent units. 
     The parameter setting unit  25  acquires parameters used in the respective units within the temperature management system. The parameters are parameters for designating, e.g., a resolution, to be processed by the prediction unit  20 , of a temperature distribution of the server rack  11 , and are instanced by a segment count of a suction surface area of the server rack  11 , a determination value for determining whether a temperature predicted by the prediction unit  20  is normal or abnormal, a threshold value used for determining whether an alarm is to be output, a threshold value of contribution ratio of an explanatory variable to be selected for a regression model, and other equivalent values. 
     The prediction result indicating unit  26  indicates a predicted value given from the prediction unit  20 . The alarm output unit  27  outputs an alarm based on the predicted value given from the prediction unit  20 . The alarm is instanced by a sound, a message and other equivalent elements. 
     The prediction unit  20  includes an input vector update unit  31 , I/O vector database  32 , and a prediction processing unit  33 . The input vector update unit  31  generates the I/O vector database  32 . The input vector is a combination of the detected values largely contributing to a prediction target output vector of the prediction unit  20  in the detected values accumulated in the large-scale database  43  of  FIG. 4 . The output vector is a combination of prediction target values of the prediction unit  20 . The output vector is a future value associated with the detected values accumulated in the large-scale database  43  of  FIG. 4 , and is designated by, e.g., a user. However, the output vector may also be one variable, i.e., a scalar value. 
     The input vector update unit  31  defines, as the input vector, a combination of input variables x for expressing a prediction target output variable y or the output vector defined as a combination of output variables y. The prediction unit  20  stores, in the I/O vector database  32 , the input vectors and the output vectors (output variables) as past case data by being associated with each other with respect to the detected values detected in the past and accumulated in the large-scale database  43  of  FIG. 4 . Accordingly, the I/O vector database  32  is a database that stores the defined input vectors and output vectors by being associated with each other as the past case data. The input variable is one example of an “input variate”. 
     The prediction processing unit  33  acquires the past case data similar to a current system status from the I/O vector database  32 . The prediction processing unit  33  builds up a local model based on the past case data, and makes a prediction by using the local model. The local model connotes, e.g., a model generated based on specified and partially limited items of data in the past case data, e.g., based on the past case data similar to the current system status. 
       FIG. 4  is a diagram of a configuration of the input vector update unit  31  of the temperature management system. The input vector update unit  31  includes an area segmenting unit  40 , a respective area maximum temperature calculation unit  41 , a data storage unit  42 , the large-scale database  43 , a time delay variable generating unit  44 , a stepwise procedure processing unit  45 , a modified stepwise procedure processing unit  46 , and a past case data storage unit  47 . The area segmenting unit  40 , the respective area maximum temperature calculation unit  41  and the data storage unit  42  illustrate the “acquiring unit”. The large-scale database  43  is one example of a “database”. The stepwise procedure processing unit  45  is one example of a “first selection unit”. The modified stepwise procedure processing unit  46  is one example of a “second selection unit”. The past case data storage unit  47  is one example of a “generating unit”. 
     The area segmenting unit  40  acquires a segment count from the parameter setting unit  25 , and segments data of the suction temperature distribution detected by the suction air temperature distribution detecting unit  21  into data per segment area segmented by the segment count. For example, the area segmenting unit  40  laterally segments the suction surface of the server rack  11  equally by two into a right surface and a left surface, and further vertically segments the right and left surfaces equally by four into totally eight segment areas. 
     The respective area maximum temperature calculation unit  41  calculates a maximum temperature per segment area into which the suction surface is segmented by the area segmenting unit  40 . The use of the maximum temperature is for specifying a variation range containing a worst case of a high temperature value of the server rack  11 , i.e., the server  12 . 
     The data storage unit  42  sequentially accumulates, per sampling period in the large-scale database  43 , the detected values detected by each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23  and each of the tile fan airflow volume detecting units  24 , and each segment area maximum temperature data given from the respective area maximum temperature calculation unit  41  respectively. The thus-accumulated detected values and the maximum temperature data of the segment areas become time-series data. The time-series data is also called variable data. The large-scale database  43  stores the variable data on a per time basis from the present down to the past. 
     The time delay variable generating unit  44  generates a variable with the time being delayed with respect to the variable data stored in the large-scale database  43 . The time delay variable generating unit  44  acquires a count of the times (periods) to be delayed from the parameter setting unit  25 . Note that the temperature management system deals with the measured values, which are of the same type of physical quantity but are different in time delay, as different variables. For example, a temperature tx(t) in a position x and a temperature tx(t−T 1 ) having a time delay T are dealt with as the different variables. With respect to these two variables, the time delay variable generating unit  44  generates variables with the time being delayed, respectively. The variables with the time being delayed are, e.g., tx(t 1 ), tx(t 2 ), . . . and tx(t 1 −T 1 ), tx(t 2 −T 1 ), . . . . 
     The stepwise procedure processing unit  45  presumes the regression model for predicting a prediction target from the variables becoming control factors in the variables generated by the time delay variable generating unit  44 , and selects such a combination of explanatory variables as to minimize an error between the predicted value of the model and an actual value. The variable becoming the control factor represents a variable of the factor (control quantity) to control a controlled quantity that is to be controlled under the control. For example, the variable in flow rate control is a variable of physical quantity instanced by a valve opening for controlling the flow rate. The regression model is one example of a “first model”. Herein, the regression model includes models based on a multiple regression analysis. The combination of explanatory variables is one example of a “first explanatory variate”. 
     The stepwise procedure processing unit  45 , when using a stepwise procedure, acquires the threshold value of the contribution ratio in the stepwise procedure from the parameter setting unit  25 , and selects the variable larger than the contribution ratio. The contribution ratio, which is also called an F-value, a t-value and a variance ratio, is a scale for measuring how much a residual sum of squares of the calculated value of the model and the actual value decreases, e.g., in the regression model, and is also a numerical value indicating a degree of how much each variable contributes to an object variable (predicted value). The contribution ratio is calculated per variable from the residual sum of squares based on the model when each variable is added to the model and from the residual sum of squares based on the model when not added. An implication is that the variable having a higher contribution ratio contributes to accuracy of the object variable (predicted value) at a higher rate. 
     The modified stepwise procedure processing unit  46 , in addition to the control variable selected by the stepwise procedure processing unit  45 , adds a variable other than the control variable. The modified stepwise procedure processing unit  46 , when adding the variable, presumes the regression model for predicting the prediction target, selects such a combination of explanatory variables as to minimize the error value between the predicted value of the model and the actual value, and defines the selected variable group as the input vectors. Hence, the final input vectors include the control variable selected by the stepwise procedure processing unit  45  and the variable added by the modified stepwise procedure processing unit  46 . For example, in the modified stepwise procedure into which the stepwise procedure is modified, the modified stepwise procedure processing unit  46  acquires the threshold value of the contribution ratio in the modified stepwise procedure from the parameter setting unit  25 , and selects the variable larger than the contribution ratio. The variable to be added by the modified stepwise procedure processing unit  46  is one example of a “second explanatory variate”. 
     The past case data storage unit  47  generates the past case data by associating the detected values of the prediction target output vectors with the detected values of the input vectors selected by the modified stepwise procedure processing unit  46 . The past case data storage unit  47  stores the generated past case data on the per time basis in the I/O vector database  32 . 
       FIG. 5  is a diagram of a configuration of the prediction processing unit  33  in the temperature management system according to the first embodiment of the present invention. The prediction processing unit  33  includes the area segmenting unit  40 , the respective area maximum temperature calculation unit  41 , a request point data generating unit  51 , an inter-vector distance calculation unit  52 , a request point vicinal data searching unit  53 , a local model build-up unit  54 , a predicted value calculation unit  55 , and an alarm determining unit  56 . The area segmenting unit  40  and the respective area maximum temperature calculation unit  41  in  FIG. 5  are the same as those in  FIG. 4 . The request point data generating unit  51  is one example of an “input setting unit”. The inter-vector distance calculation unit  52  and the request point vicinal data searching unit  53  illustrate a “data searching unit”. The local model build-up unit  54  is one example of a “build-up unit”. 
     The request point data generating unit  51  generates the input vector at a latest time from the data detected by each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23  and each of the tile fan airflow volume detecting units  24  and from the respective area maximum temperature data given by the respective area maximum temperature calculation unit  41  in accordance with the definitions of variables of the input vectors. Note that each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23  and each of the tile fan airflow volume detecting units  24  may temporarily output the detected values and other equivalent values to the large-scale database  43  in  FIG. 4 , while the request point data generating unit  51  may generate the input vector at the latest time from the large-scale database  43 . The request point data generating unit  51  stores the input vector at the latest time in the I/O vector database  32 . The input vector at the latest time is called request point data. 
     The inter-vector distance calculation unit  52  calculates the inter-vector distance between the request point data and the respective input vectors in the I/O vector database  32 . The request point vicinal data searching unit  53  acquires a setting count of the past cases to be searched for from the parameter setting unit  25 . The request point vicinal data searching unit  53  searches for the past case data based on the distances calculated by the inter-vector distance calculation unit  52 , thus acquiring the past case data by the setting count in the sequence from the smallest distance. 
     The local model build-up unit  54  builds up the model from the input vectors and the output vectors of the acquired past case data. The model to be built up is a model based on the past case data acquired by the predetermined count in the sequence from the smallest distance, and this model is called a local model. The local model is one example of a “second model”. 
     The predicted value calculation unit  55  calculates the predicted value by use of the model built up by the local model build-up unit  54 , and may display the calculated predicted value on a display unit and other equivalent displays. The alarm determining unit  56  acquires a threshold value for the alarm from the parameter setting unit  25 . The alarm determining unit  56  instructs the alarm output unit  27  to output the alarm when the predicted value of the predicted value calculation unit  55  exceeds the threshold value. 
       FIG. 6  is a flowchart illustrating processes of the input vector update unit  31  according to the embodiment. The processes of the input vector update unit  31  are also called an input vector update method. The input vector update unit  31  executes a series of processes illustrated in  FIG. 6  at an interval of a fixed period of time (e.g., once a day). 
     To start with, in step  11 , the input vector update unit  31  acquires the detected values from each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , each of the tile fan airflow volume detecting units  24  and the suction air temperature distribution detecting unit  21 . The input vector update unit  31  serving as one example of an “acquiring unit” executes the process in S 11 . 
     Next, in step S 12 , the area segmenting unit  40  of the input vector update unit  31  segments the suction surface of every server rack  11  into a predetermined number of segment areas. For example, the area segmenting unit  40  segments, as illustrated in  FIG. 7 , the suction surface of the single server rack  11  equally into eight segment areas. The area segmenting unit  40  executes the same process as in  FIG. 7  with respect to the respective server racks. 
     Next, in step S 13 , the respective area maximum temperature calculation unit  41  of the input vector update unit  31  calculates the maximum temperatures of the respective segment areas. For example, the large-scale database  43  saves position coordinates per temperature sensor provided in each server within the server rack  11 . The large-scale database  43  saves also the detected values per temperature sensor. Such being the case, it may be sufficient that the respective area maximum temperature calculation unit  41  acquires the maximum temperature in the detected values of the temperature sensor, which are contained in the respective segment areas. 
     Subsequently, in step S 14 , the data storage unit  42  of the input vector update unit  31  sequentially accumulates, in the large-scale database  43 , the detected values detected by each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , each of the tile fan airflow volume detecting units  24  and the respective area maximum temperature data given from the respective area maximum temperature calculation unit  41  on a per data item basis and a per sampling period basis. As a result of the process in S 14 , the detected values per data item and the respective area maximum temperature data are dealt with as the variable data in time-series.  FIG. 8  illustrates an example of the data stored in the large-scale database  43 . As illustrated in  FIG. 8 , the large-scale database  43  stores the data at respective dates &amp; times from time t 1  to time tM for every set of N-number of variables zn(t). 
     Next, in step S 15 , the time delay variable generating unit  44  of the input vector update unit  31  generates variables with the time being delayed in the variables in the large-scale database  43 .  FIG. 9  depicts an example of generating the variables with the time being delayed with respect to a variable  1  (z 1  (t) in the table). Generated are a value of the variable  1  before one period with the time for one period being delayed, a value of the variable  1  before two periods with the time for two periods being delayed, and a value of the variable  1  before three periods with the time for three periods being delayed with respect to the variable  1 . 
     Next, in step S 16 , the stepwise procedure processing unit  45  presumes the regression model for predicting the prediction target from the variables (control variables) of the control factors in the variables with the time being delayed, which are generated in step S 15 . An in-depth description of a way of selecting the explanatory variables adopted for the regression model will be made in  FIG. 10 . The stepwise procedure processing unit  45  selects such a combination of explanatory variables as to minimize the error between the predicted value of the model and the actual value. Note that the explanatory variable is selected also from the detected values with the time being delayed (before a predetermined period) in step S 16  in addition to the detected values of the respective variables illustrated in  FIG. 8 . This is because such an instance may arise that the detected value before the predetermined period from the present has a higher contribution ratio than the current detected value of each variable. For example, with respect to the variable affecting the output vector after a delay of the predetermined time, the detected value before the time being delayed from the present is assumed to have the large contribution ratio. 
     Note that in addition to the stepwise procedure, a method and other equivalent techniques using Akaike&#39;s Information Criterion are available as methods for selecting such a combination of explanatory variables as to minimize the error between the predicted value of the mode and the actual value on the presumption of using the regression model for predicting the prediction target. 
       FIG. 10  is a flowchart illustrating details of the process (S 16  in  FIG. 6 ) based on the stepwise procedure. In  FIG. 10 , a symbol P represents a first set explanatory variable group containing the control variables, np represents a number of variables of the first set explanatory variable group, Q denotes an adopted explanatory variable group fetched from the explanatory variable group P, and nq indicates a number of variables of the fetched adopted explanatory variable group Q. An initial value of the adopted explanatory variable group Q is, e.g., a null set. The stepwise procedure processing unit  45  serving as one example of a “first selection unit” executes processes in  FIG. 10 . 
     The stepwise procedure processing unit  45  substitutes “0” into np in S 41 . In S 42 , the stepwise procedure processing unit  45  determines whether a relationship of nq&lt;np is established or not. When determined to be “Yes” in S 42 , the stepwise procedure processing unit  45  advances to the process in S 43 . Whereas when determined to be “No”, the stepwise procedure processing unit  45  terminates the processing. A reason for the termination is that the entire variables of the explanatory variable group P have been fetched into the adopted explanatory variable group Q. 
     The stepwise procedure processing unit  45  performs regression analyses for an np-number of Cases by sequentially replacing and adopting the variables one by one from within the remaining explanatory variable group P in S 43  in addition to the adopted explanatory variable group Q. The stepwise procedure processing unit  45  obtains an F-value of the variable adopted in each Case. Herein, the F-value connotes the contribution ratio to a result of the regression analysis of the adopted variable. The contribution ratio is calculated based on, e.g., the residual sum of squares of the predicted value and the actual value in each Case to increase the contribution ratio of the variable adopted in the Case having a small error. 
     In S 44 , the stepwise procedure processing unit  45  obtains the maximum F-value by making a comparison with the F-value of an (np+1)th variable in each Case. The stepwise procedure processing unit  45  notates the maximum F-value by F max . In other words, what is obtained is the maximum F-value in the F-values of the variables added and adopted in the respective Cases in S 43 . 
     The stepwise procedure processing unit  45  acquires, from the parameter setting unit  25 , and retains F in  defined as the F-value of a criterion for determination when adopting the explanatory variable. The stepwise procedure processing unit  45  determines whether a relationship of F max &gt;F in  is established in S 45 . When determined to be “Yes” in S 45 , the stepwise procedure processing unit  45  advances to the process in S 46 . Whereas when determined to be “No” in S 45 , the stepwise procedure processing unit  45  terminates the processing. A reason for the termination is that the set explanatory variable group P does not contain any variable having a contribution ratio F exceeding the criterion value F in . 
     In S 46 , the stepwise procedure processing unit  45  fetches, into the adopted explanatory variable group Q, the variable having the contribution ratio F max  as the adopted explanatory variable in the explanatory variable group P. The stepwise procedure processing unit  45  performs counting to establish nq=nq+1 and np=np−1. 
     In S 47 , the stepwise procedure processing unit  45  sets, as processing targets, the remaining variables from which to exclude each one variable fetched into the adopted explanatory variable group Q in the process of S 46 . With respect to the Case of excluding one by one the remaining variables of the adopted explanatory variable group Q, the regression analyses are performed sequentially for the np-number of Cases (by the number of variables before being counted up), thereby obtaining the F-values of the variables excluded in the respective Cases. In the process of S 47 , the stepwise procedure processing unit  45  searches for the variable that is desirable for being excluded from the explanatory variable group Q in place of the variable fetched into Q in S 46 . 
     In S 48 , the stepwise procedure processing unit  45  obtains the minimum F-value by making the comparison between the respective F-values of the variables excluded in the respective Cases. The stepwise procedure processing unit  45  notates the obtained minimum F-value by F min . 
     The stepwise procedure processing unit  45  acquires, from the parameter setting unit  25 , and retains an F-value F out  of the criterion for determination when excluding the explanatory variables. The stepwise procedure processing unit  45  determines whether a relationship of F min &lt;F out  is established. When determined to be “Yes” in S 49 , the stepwise procedure processing unit  45  diverts to the process in S 50 . Whereas when determined to be “No” in S 49 , the stepwise procedure processing unit  45  advances to the process in S 51 . 
     The stepwise procedure processing unit  45  returns, to the explanatory variable group P, the explanatory variable with the contribution ratio becoming F min  in the explanatory variables contained in the explanatory variable group Q. The stepwise procedure processing unit  45  performs counting to establish q=q−1 and p=p+1, and loops back to the process in S 47 . In other words, the stepwise procedure processing unit  45  iterates the process of further excluding the explanatory variables. Thus, the stepwise procedure processing unit  45  iterates the processes in S 46  through S 50  till the explanatory variables with the contribution ratio being smaller than F min  disappear. 
     The stepwise procedure processing unit  45  determines in S 51  whether a relationship of nq=0 is established. When determined to be “Yes”, the processing is finished. This is because the existing explanatory variable group Q remains to be the null set, and consequently the iteration of the processes has no meaning. Whereas when determined to be “No”, the stepwise procedure processing unit  45  loops back to the process in S 42 . The stepwise procedure processing unit  45  continues the process of adding the explanatory variable next. To be specific, the stepwise procedure processing unit  45  repeats the processes in S 42  through S 49  for the remaining explanatory variable group P with respect to the adopted explanatory variable group Q to which the variable is newly added. The explanatory variable selected by the stepwise procedure processing unit  45  is one example of a “first explanatory variate”. 
     Next, in step S 17  of  FIG. 6 , the modified stepwise procedure processing unit  46  tries to add the explanatory variable other than the control variable in addition to the adopted explanatory variable based on the control variable selected by the stepwise procedure processing unit  45 . The modified stepwise procedure processing unit  46 , when adding the variable, presumes the regression model for predicting the prediction target. The modified stepwise procedure processing unit  46  selects the explanatory variable to be added so as to minimize the error value between the predicted value of the regression model and the actual value. Accordingly, the final input vectors are set as the adopted explanatory variable group selected by the modified stepwise procedure processing unit  46 . 
       FIG. 11  is a flowchart illustrating details of the process (S 17  in  FIG. 6 ) by the modified stepwise procedure processing unit  46 . In S 61 , the modified stepwise procedure processing unit  46  adopts, as an initial value of the adopted explanatory variable group Q, the variable or the variable group based on the control variable selected by the stepwise procedure in S 16  of  FIG. 6 . In  FIG. 11 , processes in S 41  through S 48  are the same as the processes in  FIG. 10  except a point that the initial value of the adopted explanatory variable group Q is set in S 61 . Such being the case, a detailed description of S 41  through S 48  is omitted. The modified stepwise procedure processing unit  46  serving as one example of a “second selection unit” executes the processes in  FIG. 11 . 
     In the processes of S 41  through S 48 , the modified stepwise procedure processing unit  46  determines whether the explanatory variable can be further added in addition to the adopted explanatory variable group Q set in S 61 , and tries to add the explanatory variable. Note that the variable count nq initially set in S 42 , counted up in S 46  and counted down in S 50  is defined as a counter to count the number of variables to be added by the modified stepwise procedure processing unit  46 . The F-value and F max  to be calculated in S 44  are calculated by using an nq-number of variables added in the processes of S 41  through  662  in addition to the initial value (the explanatory variable group set in S 61 ) of the adopted explanatory variable group Q. 
     The modified stepwise procedure processing unit  46  determines whether it is satisfied that the variable having the relationship of F min &lt;F out  in  662  and having the contribution ratio becoming F min  is not the control variable selected by the stepwise procedure in S 16 . When determined to be “Yes”, the modified stepwise procedure processing unit  46  diverts to the process in S 50 . Whereas when determined to be “No”, the modified stepwise procedure processing unit  46  advances to the process in S 51 . The modified stepwise procedure processing unit  46  executes the process in S 62  as one example of “excluding a second explanatory variate having a contribution ratio not reaching a reference value”. 
     In S 50 , the modified stepwise procedure processing unit  46  returns the explanatory variable having F min  in the explanatory variable group Q to the remaining explanatory variable group P. the modified stepwise procedure processing unit  46  performs counting to establish nq=nq−1 and np=np+1, and loops back to the process in S 47 . On the other hand, the modified stepwise procedure processing unit  46  determines in S 51  whether a relationship of nq=0 is established. When determined to be “Yes” in S 51 , the modified stepwise procedure processing unit  46  terminates the processing. Note that when determined to be “No” in S 51 , the modified stepwise procedure processing unit  46  loops back to the process in S 42 , and repeats the processes for further adding the explanatory variables. The explanatory variable added by the modified stepwise procedure processing unit  46  is one example of a “second explanatory variate”. 
     Next, in step S 18  of  FIG. 6 , the modified stepwise procedure processing unit  46  defines the selected combination of variables as the input vectors. Subsequently, in step S 19 , the past case data storage unit  47  generates the past case data by associating the prediction target output vectors with the input vectors selected by the modified stepwise procedure processing unit  46 . The past case data storage unit  47  stores the past case data at every point of time in the E/O vector database  32 . The past case data storage unit  47  serving as one example of a “generating unit” executes the process in S 19 . 
       FIG. 12  illustrates an example how the data are stored in the I/O vector database  32 . In  FIG. 12 , the input vectors each containing I-number of input variables selected by the modified stepwise procedure processing unit  46  and the prediction target output vectors are stored by being associated with each other. In the embodiment, the temperature management system can also store a plurality of output variables desired to be predicted. Note that the date &amp; time tm in  FIG. 8  is replaced by a data number km in  FIG. 12 . 
       FIG. 13A  depicts another data example of the I/O vector database  32 . In  FIG. 13A , a horizontal direction in the table corresponds to a row arrangement per variable. A vertical direction in the table corresponds to a column arrangement per time. In the example of  FIG. 13A , the variables of the input vectors are a variable of Area  23  at present, a variable of Area  68  before 210 sec, a variable of Area  61  before 300 sec, . . . , and a variable of FanB before 300 sec. The output vectors are variables of Area  31  after 30 sec. The time elapses such as t 1 , t 2 , t 3 , and the present time is notated by tq. In this case, the request point data are set with respect to the input vectors such as Z 23  (tq), Z 68  (tq−210), Z 61  (tq−300), . . . , ZFanB(tq−300). As depicted in  FIG. 13A , it does not mean that the variable value of the input vector is limited to the value of present time (tq), and the time values tracing back from the present time are also selectable. 
       FIG. 13B  illustrates a data example of changing the variable in  FIG. 13A  to “x” from “z” and also replacing the time by the data number. Note that the variable z can be considered to be a variable representing, e.g., the data in the large-scale database  43 , while the variable x can be considered to be a variable representing the input vector in the I/O vector database  32 . To be specific, in  FIG. 13B , data numbers k 1 , k 2 , k 3 , . . . are adopted in place of the times t 1 , t 2 , t 3 , . . . . . In  FIG. 13B , x 1  (k 1 ), x 2  (k 2 ), x 3  (k 3 ), . . . , XI(kI) are used in place of Z 23  (tq), Z 68  (tq−210), Z 61  (tq−300), . . . , ZFanB(tq−300) as the variable of Area  23  at present, the variable of Area  68  before 210 sec, the variable of Area  61  before 300 sec, . . . , and the variable of FanB before 300 sec. The variables specified by the data number kq are set as the input vectors. In other words, the temperature management system determines each variable by a combination of a type of physical quantity (a temperature per Area or a setting value of the fan and other equivalent elements) and a time delay of each physical quantity. The request point data becomes the vector of the physical quantity determined from the present time and the time delay of each variable. 
       FIG. 14  is a flowchart illustrating processes of the prediction processing unit  33  according to the embodiment. The prediction processing unit  33  executes a series of processes exemplified in  FIG. 14  at an interval of a fixed period of time (e.g., once every 30 sec). To begin with, in step S 31 , the prediction processing unit  33  acquires the respective items of data from each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , each of the tile fan airflow volume detecting units  24  and the suction air temperature distribution detecting unit  21 . Next, in step S 32 , the area segmenting unit  40  of the prediction processing unit  33  segments the suction surface of each server rack  11  into a predetermined number of segment areas. Subsequently, in step S 33 , the respective area maximum temperature calculation unit  41  of the prediction processing unit  33  calculates the area maximum temperature. 
     Next, in step S 34 , the request point data generating unit  51  of the prediction processing unit  33  acquires the data in accordance with the definitions of variables of the input vectors. Specifically, the request point data generating unit  51  acquires the current detected values detected by each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23  and each of the fan airflow volume detecting units  24 . The request point data generating unit  51  acquires the current maximum temperature data of each segment area from the respective area maximum temperature calculation unit  41 . The request point data generating unit  51  acquires the past detected values corresponding to the variables with the time being delayed from the past case data in the I/O vector database  32 . The request point data generating unit  51  generates the request point data by setting the acquired detected values as the input vectors at the latest time. The request point data generating unit  51  serving as an “input setting unit” executes the process in S 34 . 
     Next, in step S 35 , the inter-vector distance calculation unit  52  of the prediction processing unit  33  calculates an inter-vector distance between the request point data and each of the respective input vectors in the I/O vector database  32 . 
     For example, when using a Euclidean distance, the inter-vector distance between a km-th input vector in the I/O vector database  32  and a request point vector xkq at request point time kq is calculated by a Mathematical Expression 1. The inter-vector distance calculation unit  52  serving as a “data searching unit” executes the process in S 35 . 
     
       
         
           
             
               
                 
                   
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     Next, in step S 36 , the request point vicinal data searching unit  53  of the prediction processing unit  33  searches for the past case data based on the distances calculated by the inter-vector distance calculation unit  52 , thus acquiring the past case data in the sequence from the smallest distance. The request point vicinal data searching unit  53  serving as the “data searching unit” executes the process in S 36 . 
     Subsequently, in step S 37 , the local model build-up unit  54  of the prediction processing unit  33  builds up the local model from the input vectors and the output vectors of the acquired past case data. The local model build-up unit  54  serving as one example of a “build-up unit” executes the process in S 37 . 
     Note that when the input variables of the input vectors contain the predicted variable designated by the user, it may be sufficient that the prediction processing unit  33  adds the output vector by advancing the time of the variable desired to be predicted to the time desired to be predicted. 
     For example, when using the multiple regression model, i.e., such a model is built up that a predicted value ykq at the request point time kq is calculated from the request point vector xkq by a Mathematical Expression 2. 
     
       
         
           
             
               
                 
                   
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     Herein, regression moduli β0, β1, β2, . . . , βI are estimated by a least-squares method from the input vectors and the output vectors of the acquired past case data. A symbol “I” represents a number of input variables. A symbol xikq denotes an i-th input variable in the definitions of the input vectors at the request point time kq. Next, in step S 38 , the predicted value calculation unit  55  of the prediction processing unit  33  calculates the predicted value by use of the model built up by the local model build-up unit  54 , and displays the predicted value on a display unit  114 . For example, air suction temperatures at the plurality of points on the suction surface of each of the plurality of chassis are designated as the predicted values, in which case the respective air suction temperatures are displayed. The predicted value calculation unit  55  executes the process in S 38  as one example of “indicating air suction temperatures at a plurality of points on a suction surface of each of a plurality of chassis”. 
     Subsequently, in step S 39 , the alarm determining unit  56  of the prediction processing unit  33  instructs the alarm unit  27  to output an alarm when the predicted value of the predicted value calculation unit  55  exceeds the threshold value. 
       FIG. 15  is a diagram illustrating a hardware configuration of an information processing apparatus applied to the temperature management system. The information processing apparatus includes a CPU  111 , a main storage device  112  and external units connected to the main storage device  112  via an interface (I/F), and executes information processes through programs. The external units can be exemplified by an external storage unit  113 , a display unit  114 , an operation unit  115  and a communication unit  116 . 
     The CPU  111  (which will hereinafter be termed also a processor) runs computer programs deployed in an executable manner on the main storage device  112 , thereby providing functions of the information processing apparatus. The CPU  111  runs the programs in the main storage device  112  as the prediction unit  20 , the suction air temperature distribution detecting unit  21 , each of the air conditioner blowout temperature detecting units  22 , each of the air conditioner fan airflow volume detecting units  23 , each of the tile fan airflow volume detecting units  24 , the parameter setting unit  25 , the prediction result indicating unit  26 , and the alarm output unit  27 , which are illustrated in, e.g.,  FIG. 3 . The CPU  111  runs the programs in the main storage device  112  as the area segmenting unit  40 , the respective area maximum temperature calculation unit  41 , the data storage unit  42 , the time delay variable generating unit  44 , the stepwise procedure processing unit  45 , the modified stepwise procedure processing unit  46 , and the past case data storage unit  47 , which are illustrated in, e.g.,  FIG. 4 . 
     The main storage device  112  (which will hereinafter be termed also a memory) stores the computer programs run by the CPU  111  and the data or other equivalent information processed by the CPU  111 . The main storage device  112  is exemplified by a DRAM (Dynamic Random Access Memory), an SRAM (Static Random Access Memory), a ROM (Read Only Memory), and other equivalent storages. The external storage unit  113  is used as a storage area for assisting, e.g., the main storage device  112 , and stores the computer programs run by the CPU  111  and the data or other equivalent information processed by the CPU  111 . The external storage unit  113  is exemplified by a hard disk drive, an SSD (Solid State Drive or Disk) and other equivalent drives. The information processing apparatus may be provided with a drive for a non-transitory detachable storage medium. The non-transitory detachable storage medium is exemplified by Blu-ray disc, a DVD (Digital Versatile Disk), a CD (Compact Disc), a flash memory and other equivalent mediums. 
     The information processing apparatus includes the display unit  114 , the operation unit  115  and the communication unit  116 . The display unit  114  is exemplified by a liquid crystal display, an electroluminescence panel and other equivalent displays. The prediction result indicating unit  26  displays a prediction result on the display unit  114 . The operation unit  115  is exemplified by a keyboard, a pointing device and other equivalent devices. The embodiment exemplifies a mouse as the pointing device. The communication unit  116  transfers and receives the data to and from other devices on the network. For example, it may be sufficient that the CPU  111  acquires the air suction temperature, the setting values of the air conditioner  13 , an installation value of the tile fan  17  and other equivalent values via the communication unit  116 . It may also be sufficient that the CPU  111  transmits the alarm of the alarm unit  27  to a remote apparatus via the communication unit  116 . 
     In the embodiment, as described above, the temperature management system accumulates, in the I/O vector database  32 , the past case data organized to associate the output vectors containing the prediction target output variables with the input vectors containing the input variable group for expressing the prediction target by the model. The temperature management system searches the I/O vector database  32  for the past case data having a near inter-vector distance between the input vector of the past case data and the request point data defined as the current input vector. The temperature management system performs modeling by using the searched past case data, thereby executing a prediction process. Through the processes described above, the temperature management system can indicate, to the operator, the result of the future prediction that provides flexible handling about a variation of an equipment configuration, and can assist the operator for a rational operation. 
     In the temperature management system according to the embodiment, in addition to selecting the explanatory variable of the control factor by the stepwise procedure processing unit  45 , the modified stepwise procedure processing unit  46  adds the explanatory variable other than the control factor. It is therefore feasible to build up the model while improving the accuracy to a greater degree than hitherto. 
     In the temperature management system according to the embodiment, the modified stepwise procedure processing unit  46 , when adding the explanatory variable, maintains the control variable selected by the stepwise procedure processing unit  45  as the initial value. In other words, the process of the modified stepwise procedure processing unit  46  prevents the control variable selected by the stepwise procedure processing unit  45  from being excluded to enable modification of the explanatory variable having a less side effect. 
     The temperature management system according to the embodiment uses, as the input vectors, the physical quantities of the different acquisition targets at the predetermined time and the physical quantities of the same acquisition target at different points of time. In other words, owing to the process (the time delay variable generating unit  44 ) of generating the variable group of the time-series data with the sampling time being delayed at which the physical quantities are acquired, the physical quantities of the same acquisition target, which are acquired at different points of time, can be dealt with as the variables. The processes described above enable the temperature management system to build up the model by using the data at the time exhibiting the high contribution ratio for the output vectors. 
     In the temperature management system according to the embodiment, the area segmenting unit  40  segments the suction surface of the server rack  11  into the predetermined segment areas. The respective area maximum temperature calculation unit  41  calculates the maximum temperature of each segmented area. As a result of these processes, the operator can be safely guided based on the highest state (the worst value) of the temperature. 
     EXAMPLE 
     An arithmetic example using the temperature management system according to the embodiment will hereinafter be described.  FIG. 16  illustrates an example in which the temperature management system according to the embodiment segments the area of the data center in  FIG. 2 . In  FIG. 16 , each of the server racks  11  is segmented into eight segment areas. In the Example, the prediction target temperature is to be an air suction temperature of the Area  31  after 5 min. 
     This Example uses the time-series data when varying the tile fans FanA and FanB. Herein, the blowout temperature and the blowout airflow volume of the air conditioner are to take fixed values. 
       FIG. 17  illustrates results of selecting the input variables from all the variables by the normal stepwise procedure, as a conventional input variable selection instance. The FanA (the airflow volume thereof) is herein selected for the control variable, while the FanB (the airflow volume thereof) is not selected. However, the prediction target Area  31  is an area that is physically affected by the FanB. Thus, it happened in the conventional selection of the variable that both of the FanA and the FanB having a causal relationship in a physical sense were not necessarily selected with respect to the control variable. In other words, the model did not necessarily sufficiently take account of the influence of the control variable in the conventional selection of the variable. It is desirable for conducting the control assistance to build up the local model enabled to take account of the influence of the control variable. 
     Such being the case, the temperature management system in the Example implements the normal stepwise procedure about the control variable defined as the variable becoming the operation factor.  FIG. 18  illustrates a combination of variables selected based on the results thereof. Herein, it is recognized that the FanA at the present, the FanB at the present, the FanA before 30 sec and the FanB before 300 sec have a high relevancy with the prediction target. Subsequently, the temperature management system selects a combination of variable other than the control variable by the modified stepwise procedure in addition to the four selected control variables. 
     Incidentally, the normal stepwise procedure has a function of excluding the selected variable with the contribution ratio being conversely decreased by continuously adding the variables on the presumption of using the regression model. This function is exemplified by the processes in S 47 -S 50  of  FIG. 10 . Such an excluding function excludes the control variable from the final combination of variables as the case may be. The modified stepwise procedure processing unit  46  modifies a determination condition not to exclude the previously added control variable as instanced in S 62  of  FIG. 11 .  FIG. 19  illustrates the combination of variables selected based on the results by the modified stepwise procedure. In  FIG. 19 , Area  23  at the present, Area  68  at 210 sec and other equivalent Areas are selected, thereby obtaining the results different from those in  FIG. 15 . Thus, the modified stepwise procedure processing unit  46  has an enhanced possibility of building up the input vectors by combining the variables containing the control variables having the causal relationship in the physical sense. 
     For making a comparative evaluation of prediction performance against variations of the equipment configuration, an evaluation of post-varying prediction is made by varying an operating state of the equipment.  FIG. 20  illustrates the operating state of the equipment. 
       FIG. 20  is the diagram of arrangement of the server racks  11 , in which values of loads on the computers are indicated on the unit of kW. The loads on the computers are indicated in separation into upper parts and a lower parts of the server racks  11 . In  FIG. 20 , a left side represents the values before being varied, while a right side represents the values after being varied. In  FIG. 20 , a numeral “0” indicates power-OFF, and the numerals 1, 2, 3 indicate power consumptions on the unit of kW. In the instance of  FIG. 20 , there is a variation of the operating state of the server rack  11  specified by No. 10. 
     A conventional procedure 1 predicts a temperature of Area 31 from the airflow volume of the FanA and the airflow volume of the FanB by using a transfer function in Mathematical Expression 3. 
     
       
         
           
             
               
                 
                   
                     
                       
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       FIG. 21  illustrates comparative results about the prediction results by the temperature management system and by the conventional procedure  1 .  FIG. 21  indicates the results of performing the predictions after 30 sec at an interval of 30 sec. The actual values contain noises, and hence a window width 6, i.e., a moving average for six pieces of sample data is conducted in  FIG. 21 . Note that setting values of the FanA and the FanB are given in a lower part of  FIG. 21 . In other words, it is illustrated that both of the FanA and the FanB vary at three stages. 
     The actual value decreases from after a period of time “1800 sec” in a proposal procedure but increases in the conventional procedure  1 . On the other hand, it is recognized that the proposal procedure can attain recurrence of the descent at the same point of time as the actual value decreases. A root mean square error (RMSE) is 0.757 in the conventional procedure  1  and 0.116 in the proposal procedure. The proposal procedure according to the Example enables this prediction to be made on condition that the post-varying operation data of the operating state of the equipment is acquired even once. 
     Another set of comparative results with a conventional procedure  2  will be illustrated. The conventional procedure  2  calculates a prediction value YTF by Mathematical Expression 4 from a prediction value yest(k) of the transfer function at the present, a prediction value yest(k−1) before one period and an actual value yactual(k−1) before one period.
 
 YTF=yest ( k )+( y actual( k− 1)− yest ( k− 1))  [Mathematical expression 4]
 
     Mathematical Expression 4 modifies the prediction value yest(k) at the present by a difference (offset) between the actual value before one period and the prediction value before one period. 
       FIG. 22  illustrates a diagram for comparing the prediction results by the conventional procedure  2  with the prediction results by the temperature management system according to the embodiment. In  FIG. 22 , the setting values of the FanA and the FanB are the same as in the case of  FIG. 21 . It is understood that the prediction value by the conventional procedure  2  follows after a past actual value with a time delay (a primary delay). It is also recognized that the prediction results in the embodiment do not exhibit any primary delay but attain the high prediction accuracy. Herein, the root mean square error (RMSE) is 0.144 in the conventional procedure  2  and 0.116 in the proposal procedure of the Example. 
       FIG. 23  illustrates a prediction instance by the temperature management system according to the embodiment.  FIG. 23  illustrates the instance of making the prediction after 5 min at an interval of 5 min. A threshold temperature for causing the alarm unit  27  to output the alarm is set at 30° C. When the threshold temperature is 30° C., it is predicted that the temperature will be over 30° C. after 300 sec at a point of the time “300 sec”, in which case the temperature management system can perform the control assistance to prompt the operator to take an action by previously sounding the alarm to notify the operator. 
       FIG. 24  illustrates a prediction value of the operation of the tile fan in relation to the prediction value of the air suction temperature.  FIG. 24  illustrates an instance of performing the prediction after 5 min at the interval, of 5 min. As indicated by the prediction value of the airflow volume of the tile fan, it is recognized that the temperature management system can predict a tendency, which is substantially approximate to the actual value. In the Example, however, the airflow volume of the tile fan, which is a control factor and is also a factor that can be varied by the operator or the controller without any restriction, is not therefore necessarily a proper airflow volume as the prediction target. However, the airflow volume of the tile fan can be understood as information of the control value when becoming a value of the future air suction temperature, and the temperature management system can provide the operator with the information of the control value when becoming the value of the future air suction temperature. 
     A conventional prediction model based on the transfer function has occurrence of an error between the prediction value of the prediction model and the actual value and occurrence of a problem of decreased prediction performance for the control assistance when the configuration of the equipment varies. The temperature management system according to the embodiment accumulates, in the I/O vector database  32 , the past case data organized to associate the output vectors containing the prediction target variables with the input vectors containing the input variable group for expressing the prediction targets. The temperature management system searches the I/O vector database  32  for the past case data having the near inter-vector distance between the input vector of the past case data and the current input vector (request point data). The temperature management system performs modeling to build up the local model by using the searched past case data. The result of the future prediction, which provides the flexible handling about the variation of the equipment configuration, can be indicated to the operator, thus making it possible to assist the operator in performing the rational operation. 
     Modified Example 
     The embodiment discussed above has applied the stepwise procedure and the modified stepwise procedure to the temperature management system. The air suction temperatures and other equivalent values of the servers  12  mounted in the server racks  11  at, e.g., the data center have been predicted. It does not, however, mean that the processes exemplified in the embodiment are limited to the temperature management system applied to the servers and other equivalent apparatuses at the data center. The temperature management system according to the embodiment can be applied to, e.g., apparatuses generating the heat and a general type of cooling systems thereof. 
     For instance, the processes of calculating the prediction value in the embodiment, which encompasses the stepwise procedure and the modified stepwise procedure, can be applied to a system in which to measure a given physical quantity and to acquire another physical quantity affecting the former physical quantity or a control quantity by a control apparatus, a setting value and other equivalent values. The processes according to the embodiment can be applied to systems in which a gas having a target concentration is introduced into the equipment. To be specific, the exemplified system acquires measured values of concentrations in respective positions, a setting value of blowout quantity of the gas when introducing the gas, a setting value of discharge pressure of the gas, a setting value of airflow volume of a fan to circulate the gas or a setting value of driving quantity of a compressor, and other equivalent values within the equipment. It may be sufficient that this system predicts the gas concentration in a desired position in the same procedure as by the temperature management system according to the embodiment. 
     According to the present invention, it is feasible to restrain the decrease in prediction performance of the physical quantities even when the configuration and the state of the prediction target vary because of enabling a model to be built up by selecting a proper input variate group. 
     &lt;Non-Transitory Recording Medium&gt; 
     A program for making a computer, other machines and apparatuses (which will hereinafter be referred to as the computer and other equivalent apparatuses) attain any one of the functions, can be recorded on a non-transitory recording medium readable by the computer and other equivalent apparatuses. The computer and other equivalent apparatuses are made to read and execute the program on this non-transitory recording medium, whereby the function thereof can be provided. 
     Herein, the non-transitory recording medium readable by the computer and other equivalent apparatuses connotes a non-transitory recording medium capable of accumulating information instanced by data, programs and other equivalent information electrically, magnetically, optically, mechanically or by chemical action, which can be read from the computer and other equivalent apparatuses. Among these non-transitory recording mediums, the mediums removable from the computer and other equivalent apparatuses are exemplified by a flexible disc, a magneto-optic disc, a CD-ROM (Compact Disc-Read Only Memory), a CD-R (Recordable), a DVD (Digital Versatile Disk), a Blu-ray disc, a DAT (Digital Audio Tape), an 8 mm tape, and a memory card like a flash memory. A hard disc, a ROM (Read-Only Memory) and other equivalent recording mediums are given as the non-transitory recording mediums fixed within the computer and other equivalent apparatuses. Still further, a solid state drive (SSD) is also available as the non-transitory recording medium removable from the computer and other equivalent apparatuses and also as the non-transitory recording medium fixed within the computer and other equivalent apparatuses. 
     All examples and conditional language provided herein are intended for the pedagogical purposes of aiding the reader in understanding the invention and the concepts contributed by the inventor to further the art, and are not to be construed as limitations to such specifically recited examples and conditions, nor does the organization of such examples in the specification relate to a showing of the superiority and inferiority of the invention. Although one or more embodiments of the present invention have been described in detail, it should be understood that the various changes, substitutions, and alterations could be made hereto without departing from the spirit and scope of the invention.