Patent Publication Number: US-2022237544-A1

Title: Method and system for graph signal processing based energy modelling and forecasting

Description:
PRIORITY CLAIM 
     This U.S. patent application claims priority under 35 U.S.C. § 119 to: Indian Patent Application No. 202121003901, filed on Jan. 28, 2021. The entire contents of the aforementioned application are incorporated herein by reference. 
     TECHNICAL FIELD 
     The disclosure herein generally relates to energy forecasting, and, more particularly, to a method and system for graph signal processing energy modelling and forecasting. 
     BACKGROUND 
     Building load forecasting is useful in several applications like electricity purchase, budget planning, and to address demand-response programs. In many scenarios, governing bodies of many places may have to purchase energy from energy markets so as to meet energy requirements of people. Such energy requirements may be from homes, commercial buildings, industries and so on. There are various factors which affect energy consumption in buildings. For example, if energy consumption in an office building is considered, corresponding pattern would indicate that energy consumption is maximum on weekdays (i.e. office working days) and is minimum over weekends/holidays (office non-functioning days). Likewise, at homes energy consumption would be less over weekdays as kids and parents are likely to be at school and offices respectively, and the energy consumption would be higher on holidays if the family is at home. Considering such usage patterns while procuring energy can help plan expenses wisely. 
     Energy forecasting helps estimate the energy requirements, by considering such usage patterns, so that the purchase and other activities can be planned accordingly. Machine learning based approaches are available for such forecasting purpose. However, disadvantage/limitation of the state of the art techniques which employ the machine learning algorithms for prediction is that they tend to rely on an assumption that incoming data is independent and is identically distributed, which may not be always true for time series data collected as input. Another disadvantage is that these systems fail when there is a concept drift in input data. Some other state of the art systems which rely on deep learning models can address the aforementioned limitations of the machine learning based models. However, they are computationally heavy. 
     SUMMARY 
     Embodiments of the present disclosure present technological improvements as solutions to one or more of the above-mentioned technical problems recognized by the inventors in conventional systems. For example, in one embodiment, a processor implemented method of building energy forecasting is provided. Initially, data on energy consumption in a building for a pre-defined time window, and a plurality of corresponding energy consumption parameters, as input, via one or more hardware processors. Further, a building energy consumption model is generated by processing the plurality of energy consumption parameters via the one or more hardware processors, using a Graph Signal Processing (GSP) modelling. The GSP modelling includes constructing a graph for a measured energy value of the building, using the following method. In this approach, a weighted adjacent matrix of the GSP is built using the plurality of energy consumption parameters. Further, samples of the measured energy value are used as nodes of the graph, and then weight of edge between each set of nodes of a graph for each sample of the measured energy value is determined based on a) vector difference between energy consumption parameters, and b) a co-variance matrix of the plurality of energy consumption parameters, wherein the weight of each edge is calculated for a pre-defined time window. Post the GSP modelling, a smooth signal is generated by minimizing variation of the graph by performing total variation minimization on the graph, via the one or more hardware processors, and then a forecast is generated using the smooth signal, via the one or more hardware processors. The generated forecast is then used to fill a plurality of missing values in the graph, via the one or more hardware processors. 
     In another aspect, a system for building energy forecasting is provided. The system includes one or more hardware processors, a communication interface, and a memory storing a plurality of instructions. The plurality of instructions when executed, cause the one or more hardware processors to initially collect data on energy consumption in a building for a pre-defined time window and a plurality of corresponding energy consumption parameters, as input. The system then generates a building energy consumption model by processing the plurality of energy consumption parameters, using a Graph Signal Processing (GSP) modelling. The GSP modelling includes constructing a graph for a measured energy value of the building, using the following method. In this approach, a weighted adjacent matrix of the GSP is built using the plurality of energy consumption parameters. Further, samples of the measured energy value are used as nodes of the graph, and then weight of edge between each set of nodes of a graph for each sample of the measured energy value is determined based on a) vector difference between energy consumption parameters, and b) a co-variance matrix of the plurality of energy consumption parameters, wherein the weight of each edge is calculated for a pre-defined time window. Post the GSP modelling, the system generates a smooth signal by minimizing variation of the graph by performing total variation minimization on the graph, and then generates a forecast using the smooth signal. The system then uses the generated forecast to fill a plurality of missing values in the graph. 
     In yet another aspect, a non-transitory computer readable medium for building energy forecasting is provided. Initially, data on energy consumption in a building for a pre-defined time window, and a plurality of corresponding energy consumption parameters, as input, via one or more hardware processors. Further, a building energy consumption model is generated by processing the plurality of energy consumption parameters via the one or more hardware processors, using a Graph Signal Processing (GSP) modelling. The GSP modelling includes constructing a graph for a measured energy value of the building, using the following method. In this approach, a weighted adjacent matrix of the GSP is built using the plurality of energy consumption parameters. Further, samples of the measured energy value are used as nodes of the graph, and then weight of edge between each set of nodes of a graph for each sample of the measured energy value is determined based on a) vector difference between energy consumption parameters, and b) a co-variance matrix of the plurality of energy consumption parameters, wherein the weight of each edge is calculated for a pre-defined time window. Post the GSP modelling, a smooth signal is generated by minimizing variation of the graph by performing total variation minimization on the graph, via the one or more hardware processors, and then a forecast is generated using the smooth signal, via the one or more hardware processors. The generated forecast is then used to fill a plurality of missing values in the graph, via the one or more hardware processors. 
     It is to be understood that both the foregoing general description and the following detailed description are exemplary and explanatory only and are not restrictive of the invention, as claimed. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The accompanying drawings, which are incorporated in and constitute a part of this disclosure, illustrate exemplary embodiments and, together with the description, serve to explain the disclosed principles: 
         FIG. 1  illustrates an exemplary system for energy model generation and forecasting, according to some embodiments of the present disclosure. 
         FIG. 2  is a flow diagram depicting steps involved in the process of performing energy forecasting, by the system of  FIG. 1 , according to some embodiments of the present disclosure. 
         FIG. 3  is a flow diagram depicting steps involved in the process of constructing a graph by processing the energy consumption parameters using the GSP, by the system of  FIG. 1 , in accordance with some embodiments of the present disclosure. 
         FIG. 4A  is an example of graphical representations depicting missing value estimation by the system of  FIG. 1 , and comparison with a few state of the art techniques, in accordance with some embodiments of the present disclosure. 
         FIG. 4B  is an example of graphical representations depicting day ahead forecast by the system of  FIG. 1 , and comparison with a few state of the art techniques, in accordance with some embodiments of the present disclosure. 
         FIG. 4C  is an example of graphical representations depicting quarter ahead forecast by the system of  FIG. 1 , and comparison with a few state of the art techniques, in accordance with some embodiments of the present disclosure. 
         FIG. 4D  is an example of graphical representations depicting month ahead forecast by the system of  FIG. 1 , and comparison with a few state of the art techniques, in accordance with some embodiments of the present disclosure. 
     
    
    
     DETAILED DESCRIPTION 
     Exemplary embodiments are described with reference to the accompanying drawings. In the figures, the left-most digit(s) of a reference number identifies the figure in which the reference number first appears. Wherever convenient, the same reference numbers are used throughout the drawings to refer to the same or like parts. While examples and features of disclosed principles are described herein, modifications, adaptations, and other implementations are possible without departing from the scope of the disclosed embodiments. It is intended that the following detailed description be considered as exemplary only, with the true scope being indicated by the following claims. 
     Referring now to the drawings, and more particularly to  FIG. 1  through  FIG. 4D , where similar reference characters denote corresponding features consistently throughout the figures, there are shown preferred embodiments and these embodiments are described in the context of the following exemplary system and/or method. 
       FIG. 1  illustrates an exemplary system for energy model generation and forecasting, according to some embodiments of the present disclosure. The system  100  includes one or more hardware processors  102 , communication interface(s) or input/output (I/O) interface(s)  103 , and one or more data storage devices or memory  101  operatively coupled to the one or more hardware processors  102 . The one or more hardware processors  102  can be implemented as one or more microprocessors, microcomputers, microcontrollers, digital signal processors, central processing units, state machines, graphics controllers, logic circuitries, and/or any devices that manipulate signals based on operational instructions. Among other capabilities, the processor(s) are configured to fetch and execute computer-readable instructions stored in the memory. In an embodiment, the system  100  can be implemented in a variety of computing systems, such as laptop computers, notebooks, hand-held devices, workstations, mainframe computers, servers, a network cloud and the like. 
     The communication interface(s)  103  can include a variety of software and hardware interfaces, for example, a web interface, a graphical user interface, and the like and can facilitate multiple communications within a wide variety of networks N/W and protocol types, including wired networks, for example, LAN, cable, etc., and wireless networks, such as WLAN, cellular, or satellite. In an embodiment, the communication interface(s)  103  can include one or more ports for connecting a number of devices to one another or to another server. 
     The memory  101  may include any computer-readable medium known in the art including, for example, volatile memory, such as static random access memory (SRAM) and dynamic random access memory (DRAM), and/or non-volatile memory, such as read only memory (ROM), erasable programmable ROM, flash memories, hard disks, optical disks, and magnetic tapes. In an embodiment, one or more components (not shown) of the system  100  can be stored in the memory  101 . The memory  101  is configured to store a plurality of operational instructions (or ‘instructions’) which when executed cause one or more of the hardware processor(s)  102  to perform various actions associated with the process of energy forecasting being performed by the system  100 . The system  100  can be implemented in a variety of ways as per requirements. Various steps involved in the process of the energy forecasting being performed by the system  100  of  FIG. 1  are depicted in  FIG. 2  and  FIG. 3 , and are explained with reference to the hardware components depicted in  FIG. 1 . 
       FIG. 2  is a flow diagram depicting steps involved in the process of performing energy forecasting, by the system of  FIG. 1 , according to some embodiments of the present disclosure. 
     At step  202 , the system  100  collects information such as but not limited to energy consumption in a building being monitored, and corresponding energy consumption parameters as input. The energy consumption parameters may include, but not limited to, occupancy of the building, weather information of the region in which the building being monitored is located, and other contextual information like time of the day, day of the week, and holiday information, which impact the energy consumption of the building. 
     Further, at step  204 , a building energy consumption model is generated, which involves constructing a graph representing the energy consumption at the building, by processing the energy consumption parameters (also referred to as “parameters”) using a Graph Signal Processing (GSP) approach, which is explained below: 
     Let p(t i ) be the measured energy value of the building at time instance t i . An N-length graph G=(V,A) is constructed such that each vertex of the graph is associated to one sample of p(t i ). A is the adjacency matrix defining the edges between the vertices. The system  100  defines the weighted adjacency matrix using the energy consumption parameters. Nodes with similar input parameters have an edge with larger weight. A Gaussian kernel density function is used to define the weights of the edges between the nodes of the graph. The weights of an existing edge connecting vertices (i; j) is expressed as in equation 1. 
     
       
         
           
             
               
                 
                   
                     A 
                     ⁡ 
                     ( 
                     
                       i 
                       , 
                       j 
                     
                     ) 
                   
                   = 
                   
                     exp 
                     ⁢ 
                     
                       { 
                       
                         
                           - 
                           
                             
                               ( 
                               
                                 
                                   s 
                                   i 
                                 
                                 - 
                                 
                                   s 
                                   j 
                                 
                               
                               ) 
                             
                             2 
                           
                         
                         
                           σ 
                           2 
                         
                       
                       } 
                     
                   
                 
               
               
                 
                   ( 
                   1 
                   ) 
                 
               
             
           
         
       
     
     Where s i  and s j  are signal values at nodes i and j respectively. 
     In the GSP based approach used by the system  100 , the system  100  builds the adjacency matrix using the energy consumption parameters, wherein a set (c) the energy consumption parameters used are, a) temperature (T), b) occupancy (O), c) day of the week (D), and d) time of the day(t). c at node i is defined as a vector: 
       c i =[T i ,O i ,D i ,t i ]  (2)
 
     The weight of the edge between nodes i and j is defined as follows: 
         A ( i,j )=exp(Δ c   i,j   T Σ −1   Δc   i,j )   (3)
         where Δc i,j =c i −c j  is the vector difference between the input parameters at nodes i and j and Σ −1  is the co-variance matrix of all the energy consumption parameters and is a symmetric matrix in which all the diagonal elements represent the variance of the respective input parameters and off-diagonal elements represent the co-variances between the energy consumption parameters.       

     In the graph constructed using the aforementioned approach, each vertex represents one sample of the energy value. Energy values are taken as the graph signal on these vertices and the weight of the edges between any two vertices are calculated using the equation 3 in such a way that they represent the similarity between the two instances of energy consumption. The constructed graph satisfies property of piece-wise smoothness, i.e. the value of the graph signal does not abruptly change in its neighbourhood i.e. at similar nodes. 
     Further, at step  206 , the system  100  generates a smooth signal by minimizing variation in the graph by performing a total variation minimization on the constructed graph. The step of performing the total variation minimization is explained below: 
     Consider that energy values for n time instants are available and for rest of the instances the energy values need to be forecasted. The system  100  uses the known values for training of the graph, and then to forecast next (N−n) values. For this purpose, N-length graph signal s is defined as: 
     
       
         
           
             
               
                 
                   s 
                   = 
                   
                     { 
                     
                       
                         
                           
                             p 
                             i 
                           
                         
                         
                           
                             
                               if 
                               ⁢ 
                                   
                               i 
                             
                             ≤ 
                             n 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
     Second part of this signal is to be computed, as it gives estimate of energy consumption in the building. 
     For this purpose, the system  100  then creates a weighted adjacency matrix A for the graph such that the weight of the edge between the two vertices describe their correlation. As weight matrix plays an important role in the GSP technique used, the weights of the edges are determined by the system  100  as explained below. The system  100  determines Degree matrix D and Laplacian matrix L, and then applies the total variation minimization on the graph signal. Due to this intrinsic nature of graph construction, true values of energy usage forms a low-frequency graph signal (alternately referred to as ‘smooth signal’) s, having a small value of the total variation s T Ls. Hence the system  100  finds the smooth signal by minimizing the total variation. Labelled training samples for i≤n are close in value to the unknown samples, i&gt;n, for the similar nodes as they have large edge weights A(i, j). Smooth graph signal prior ensure that the testing samples have similar values as that of training samples. 
     The second part of this smooth signal by minimizing the total variation of the graph signal i.e. 
     
       
         
           
             
               
                 
                   
                     
                       
                         min 
                       
                     
                     
                       
                         s 
                       
                     
                   
                   ⁢ 
                   
                     
                        
                       
                         
                           s 
                           T 
                         
                         ⁢ 
                         L 
                         ⁢ 
                         s 
                       
                        
                     
                     2 
                     2 
                   
                 
               
               
                 
                   ( 
                   5 
                   ) 
                 
               
             
           
         
       
     
     As value of s 1:n  is known, (5) can be rewritten as: 
     
       
         
           
             
               
                 
                   
                     
                       s 
                       T 
                     
                     ⁢ 
                     L 
                     ⁢ 
                     s 
                   
                   = 
                   
                     
                       
                         [ 
                         
                           
                             S 
                             A 
                           
                           ⁢ 
                             
                           
                             S 
                             B 
                           
                         
                         ] 
                       
                       [ 
                       
                         
                           
                             
                               L 
                               
                                 A 
                                 ⁢ 
                                 A 
                               
                             
                           
                           
                             
                               L 
                               
                                 A 
                                 ⁢ 
                                 B 
                               
                             
                           
                         
                         
                           
                             
                               L 
                               
                                 B 
                                 ⁢ 
                                 A 
                               
                             
                           
                           
                             
                               L 
                               
                                 B 
                                 ⁢ 
                                 B 
                               
                             
                           
                         
                       
                       ] 
                     
                     [ 
                     
                       
                         
                           
                             s 
                             A 
                           
                         
                       
                       
                         
                           
                             s 
                             B 
                           
                         
                       
                     
                     ] 
                   
                 
               
               
                 
                   ( 
                   6 
                   ) 
                 
               
             
           
         
       
         
         
           
             Where s A  is labeled training samples of the graph signal for i≤n and s A =s 1:n , s B  is the signal value that is to be estimated for i=n+1:N, and s B =s n+1:N , L AA  is top left sub-matrix of the Laplacian matrix for indexes 1:n, 1:n (rows, columns), L AB  is top right sub-matrix of the Laplacian matrix for indexes 1:n, n+1:N, L BA  is bottom left sub-matrix of the Laplacian matrix for indexes n+1: N, 1:n, and L BB  is bottom right sub-matrix of the Laplacian matrix for indexes n+1:N, 1:n:N. 
           
         
       
    
     All the sub-matrices are conformable for matrix multiplication and the above matrix multiplication results when expanded, is represented as: 
         s   T   Ls=s   A   T   L   AA   s   A   +s   A   T   L   AB   s   B   +s   B   T   L   BA   s   A   +s   B   T   L   BB   s   B    (7)
 
     As the Adjacency matrix A is symmetric and D is diagonal, the Laplacian matrix L is symmetric, hence 
       s A   T L AB s B =s B   T L BA s A    (8)
 
     As s A  is constant in (7), the first term does not affect minimization, hence the Total Variation Minimization can be rewritten as: 
       arg min∥ s   T   Ls ∥ 2   2 =arg min{2 s   B   T   L   BA   s   A   +s   B   T   L   BB   s   B }  (9)
 
     A closed form solution for (9) is provided as: 
         s*   B   =L   BB   + *(− s   A   T )* L   AB   T    (10)
         Where L BB   +  is pseudo inverse of the matrix L BB  and s* B  is estimate of S n+1:N , and hence is forecast of energy usage for the period t n+1  to t N , generated at step  208 . The forecasted data may be provided as output to a user of the system  100 .       

     Further, at step  210 , the system  100  may fill missing values in the graph constructed at step  204 , using the forecasted data, thereby fine-tuning the building energy consumption model. 
     In various embodiments, the steps in method  200  may be performed in the same order as depicted in  FIG. 2  or in any alternate order that is technically feasible. In another embodiment, one or more steps of the method  200  may be omitted if required. 
     Applications of the Forecasting Method and the Building Energy Consumption Model 
     The building energy consumption model generated by the system  100  may be used for various forecasting applications such as, but not limited to:
         Day-ahead forecast where hourly consumption data is used as input and requires to predict 24 values.   Month ahead and Quarter ahead forecast where day-wise energy consumption is used for building the models.       

     a) Day-Ahead Forecast: 
     The Day-ahead forecasting is required for purchasing of energy (bidding), addressing demand response and energy benchmarking. In day-ahead forecast, hourly consumption data is used for building energy modelling. The graph is constructed using the hourly consumption data and the remaining inputs are considered as follows
         Occupancy—Average occupancy of the day is used for modelling and so typically this remains constant across the day and varies depending on day of the week, working day or holiday.   Temperature—Hourly temperature values.   day of the week (Sunday to Saturday).   working day or holiday.       

     Missing values in smart meter data are quite common due to many reasons like smart meter failures, communication failures etc. Treating missing values is very important to build good models for forecasting and so it is essential to treat the missing values before we use these models for forecasting. The proposed model is used to estimate the energy consumption at those time instants where energy data is missing by tweaking the model. Unlike forecasting, missing values could be anywhere in the data series, so it is solved by considering the missing instants at the end of the graph signal and similar approach (used for forecasting) is used to estimate the missing values. Hence, missing values are estimated using both preceding and succeeding values, so it is comparatively more accurate than forecasting. Example values obtained via the missing value estimation are depicted in  FIG. 4A . 
     Day-ahead forecasting consists of building the N length graph with the last 24 values as zeros and use the steps in method  200  to estimate the hourly consumption values. The forecasting results are compared with the ARIMAX and ANN.  FIG. 4B  shows that the forecasting accuracy of system  100  is better than ARIMAX and almost same as ANN. The performance of the method  200  was validated using four actual buildings data from varied climatic zones of India and the performance was compared using Mean Average Percentage Error (MAPE) and Normalized Root Mean Square Deviation (NRMSD) as mentioned in the Tables 1 and 2 respectively. MAPE and NRMSD values are computed by taking the average over 10 days of day-ahead forecast for all the buildings. 
     b) Month and Quarter Ahead Forecast 
     Month and Quarter ahead forecasting involves forecasting day-wise energy consumption for the next one month and three months respectively. Month and Quarter ahead energy forecasting is required mainly for planning and budgeting reasons. The smart meter data is aggregated day-wise to create the day-wise energy consumption series. Unlike day ahead forecast, month and quarter ahead forecasts are challenging as it requires to forecast the independent parameters like temperature, occupancy for the period of the forecast horizon. Comparison of month ahead and quarter ahead forecasts generated by the system  100  and state of the art techniques (i.e., ARIMAX and ANN), and actual values, are depicted in  FIG. 4C  and  FIG. 4D  respectively. 
     Temperature: Maximum and minimum day-wise temperatures are used. Temperature Forecasts for the period of forecast horizon were extracted from weather websites. 
     Occupancy Forecasting: Day-wise average occupancy was used to build the models. Occupancy for the forecast horizon was predicted using the disclosed GSP based approach. Occupancy is taken as the graph signal and the weight matrix is calculated using day of the week, working day or holiday as the input parameters. Let O i  be the average occupancy of the i th  day and assumption is that occupancy values for the first n time instants are available and that estimate for next h time instants are required. A similar graph G=(V, Ao) is constructed, where each vertex is associated to the average occupancy value of a particular day. N=n+h−length graph signal s 0  similar to the energy usage graph signal is generated as: 
     
       
         
           
             
               
                 
                   
                     s 
                     0 
                   
                   = 
                   
                     { 
                     
                       
                         
                           
                             O 
                             i 
                           
                         
                         
                           
                             
                               if 
                               ⁢ 
                                   
                               i 
                             
                             ≤ 
                             n 
                           
                         
                       
                       
                         
                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   11 
                   ) 
                 
               
             
           
         
       
     
     Second part of the signal represented by equation (11) is computed to get estimate of average occupancy of the building. 
     The system  100  creates a weight matrix A 0  for this graph, which is created such that the weights of the edges between the two vertices describe their correlation. In general, office buildings&#39; average occupancy varies largely for working days, weekends and holidays. So, the weight of the edge between a vertex representing a weekday, and a vertex representing either a weekend or a holiday is considered as 0 (i.e., no edge between these two vertices). The average occupancy on two different weekdays also varies to some extent. Hence, an edge should exist between two vertices representing the same day of the week. Weights of all the existing edges can be taken as 1. Then the smooth signal is generated using the total variation minimization approach and minimizing the total variation. Thereby the estimated occupancy values to generate the forecast on energy usage on the building are obtained. Day of the week and Holidays information for the period of forecast horizon are extracted from the calendar and location-specific holidays list. 
     All these input parameters are then used for graph construction by the system  100 . The covariance matrix is generated such that it captures the interactions among the impacting variables like temperature, occupancy, day of the week etc. The N-length graph signal is generated using energy data s as follows: 
     
       
         
           
             
               
                 
                   s 
                   = 
                   
                     { 
                     
                       
                         
                           
                             e 
                             i 
                           
                         
                         
                           
                             
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                             ≤ 
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                           0 
                         
                         
                           otherwise 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   12 
                   ) 
                 
               
             
           
         
       
     
     The weight adjacenary matrix is calculated as: 
     
       
         
           
             
               
                 
                   
                     A 
                     ⁡ 
                     ( 
                     
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                       , 
                       j 
                     
                     ) 
                   
                   = 
                   
                     exp 
                     ⁢ 
                        
                     
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                           c 
                           
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                     and 
                   
                 
               
               
                 
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                   13 
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                     [ 
                     
                       
                         
                           
                             σ 
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                   14 
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             Where, the elements σ tt , σ oo , and σ dd  are variances of temperature, occupancy, and day of the week respectively. Other elements such as σ to  represent covariance between temperature and occupancy data and a similar explanation goes for other elements in the matrix. The above-mentioned graph signal and covariance matrix are further used in the total variation minimization equations i.e., equations 4 through 10, to estimate the energy consumption. 
           
         
       
    
     Edge weights obtained through covariance matrix further dictates the inter-relationship between the nodes, providing useful strength for GSP framework for building energy modelling and forecasting. The models developed are validated using the data from four buildings and comparisons were carried out with ARIMAX and ANN algorithms. 
     In  FIG. 4C , it can be seen that GSP based proposed formulation outperformed ARIMAX and is on par with ANNs. The metrics comparison is given only for Quarter ahead forecast in Tables 1 and 2 as the performance for month ahead forecast were also similar. 
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 1 
               
               
                   
                   
               
               
                   
                 BUILDING 
                 GSP 
                 ARIMAX 
                 ANN 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 A 
                 6.5 
                 7.5 
                 5 
               
               
                   
                 B 
                 8 
                 10 
                 7.5 
               
               
                   
                 C 
                 7 
                 9 
                 8 
               
               
                   
                 D 
                 9.5 
                 13 
                 10 
               
               
                   
                   
               
            
           
         
       
     
     
       
         
           
               
               
               
               
               
             
               
                   
                 TABLE 2 
               
               
                   
                   
               
               
                   
                 BUILDING 
                 GSP 
                 ARIMAX 
                 ANN 
               
               
                   
                   
               
             
            
               
                   
               
            
           
           
               
               
               
               
               
            
               
                   
                 A 
                 0.09 
                 0.107 
                 0.07 
               
               
                   
                 B 
                 0.10 
                 0.12 
                 0.09 
               
               
                   
                 C 
                 0.09 
                 0.11 
                 0.09 
               
               
                   
                 D 
                 0.09 
                 0.15 
                 0.13 
               
               
                   
                   
               
            
           
         
       
     
     The written description describes the subject matter herein to enable any person skilled in the art to make and use the embodiments. The scope of the subject matter embodiments is defined by the claims and may include other modifications that occur to those skilled in the art. Such other modifications are intended to be within the scope of the claims if they have similar elements that do not differ from the literal language of the claims or if they include equivalent elements with insubstantial differences from the literal language of the claims. 
     The embodiments of present disclosure herein address unresolved problem of Graph Signal Processing (GSP) based energy consumption forecasting for buildings. The embodiment thus provides a mechanism to model the energy consumption of a building by processing energy consumption related data and associated energy consumption parameters using the GSP. 
     It is to be understood that the scope of the protection is extended to such a program and in addition to a computer-readable means having a message therein; such computer-readable storage means contain program-code means for implementation of one or more steps of the method, when the program runs on a server or mobile device or any suitable programmable device. The hardware device can be any kind of device which can be programmed including e.g. any kind of computer like a server or a personal computer, or the like, or any combination thereof. The device may also include means which could be e.g. hardware means like e.g. an application-specific integrated circuit (ASIC), a field-programmable gate array (FPGA), or a combination of hardware and software means, e.g. an ASIC and an FPGA, or at least one microprocessor and at least one memory with software processing components located therein. Thus, the means can include both hardware means and software means. The method embodiments described herein could be implemented in hardware and software. The device may also include software means. Alternatively, the embodiments may be implemented on different hardware devices, e.g. using a plurality of CPUs. 
     The embodiments herein can comprise hardware and software elements. The embodiments that are implemented in software include but are not limited to, firmware, resident software, microcode, etc. The functions performed by various components described herein may be implemented in other components or combinations of other components. For the purposes of this description, a computer-usable or computer readable medium can be any apparatus that can comprise, store, communicate, propagate, or transport the program for use by or in connection with the instruction execution system, apparatus, or device. 
     The illustrated steps are set out to explain the exemplary embodiments shown, and it should be anticipated that ongoing technological development will change the manner in which particular functions are performed. These examples are presented herein for purposes of illustration, and not limitation. Further, the boundaries of the functional building blocks have been arbitrarily defined herein for the convenience of the description. Alternative boundaries can be defined so long as the specified functions and relationships thereof are appropriately performed. Alternatives (including equivalents, extensions, variations, deviations, etc., of those described herein) will be apparent to persons skilled in the relevant art(s) based on the teachings contained herein. Such alternatives fall within the scope of the disclosed embodiments. Also, the words “comprising,” “having,” “containing,” and “including,” and other similar forms are intended to be equivalent in meaning and be open ended in that an item or items following any one of these words is not meant to be an exhaustive listing of such item or items, or meant to be limited to only the listed item or items. It must also be noted that as used herein and in the appended claims, the singular forms “a,” “an,” and “the” include plural references unless the context clearly dictates otherwise. 
     Furthermore, one or more computer-readable storage media may be utilized in implementing embodiments consistent with the present disclosure. A computer-readable storage medium refers to any type of physical memory on which information or data readable by a processor may be stored. Thus, a computer-readable storage medium may store instructions for execution by one or more processors, including instructions for causing the processor(s) to perform steps or stages consistent with the embodiments described herein. The term “computer-readable medium” should be understood to include tangible items and exclude carrier waves and transient signals, i.e., be non-transitory. Examples include random access memory (RAM), read-only memory (ROM), volatile memory, non-volatile memory, hard drives, CD ROMs, DVDs, flash drives, disks, and any other known physical storage media. 
     It is intended that the disclosure and examples be considered as exemplary only, with a true scope of disclosed embodiments being indicated by the following claims.