Enhancing the performance of smart electrical grids using data mining and fuzzy inference engine

Abstract

This paper is about enhancing the smart grid by proposing a new hybrid feature-selection method called feature selection-based ranking (FSBR). In general, feature selection is to exclude non-promising features out from the collected data at Fog. This could be achieved using filter methods, wrapper methods, or a hybrid. Our proposed method consists of two phases: filter and wrapper phases. In the filter phase, the whole data go through different ranking techniques (i.e., relative weight ranking, effectiveness ranking, and information gain ranking) The results of these ranks are sent to a fuzzy inference engine to generate the final ranks. In the wrapper phase, data is being selected based on the final ranks and passed on three different classifiers (i.e., Naive Bayes, Support Vector Machine, and neural network) to select the best set of the features based on the performance of the classifiers. This process can enhance the smart grid by reducing the amount of data being sent to the cloud, decreasing computation time, and decreasing data complexity. Thus, the FSBR methodology enables the user load forecasting (ULF) to take a fast decision, the fast reaction in short-term load forecasting, and to provide a high prediction accuracy. The authors explain the suggested approach via numerical examples. Two datasets are used in the applied experiments. The first dataset reported that the proposed method was compared with six other methods, and the proposed method was represented the best accuracy of 91%. The second data set, the generalization data set, reported 90% accuracy of the proposed method compared to fourteen different methods.

1 Introduction

A smart grid has become a global trend due to its usage mechanism of information and communication technologies [14]. Smart grids had a simple architecture of two levels in which data are sent from devices directly to the cloud to be processed and the results are sent back. This could not be possible without the Internet of Things (IoT) which is the infrastructure of the whole architecture [11, 32]. IoT made it possible for such systems to be maintainable, secure, flexible, and interactive [36]. Unfortunately, this two-level architecture had many problems such as latency as the whole data is sent to the cloud directly and no control over location as all devices at different locations end to pour in the same cloud [11]. To overcome the previous problems, a new architecture of three levels came to the light. This new level is called fog and it is the second level or the intermediate medium between devices and the cloud.

Fog is responsible to receive data from devices, apply data pre-processing, remove unnecessary (or noisy) data, and apply computations on data based on rules received from the cloud. These rules are responsible to represent the data in an appropriate form; so it can be stored in a local server inside the fog to provide a quick response for real-time applications [51]. Periodically, data is being sent from the local server inside the fog to a larger server managed by the cloud called Cloud Computing Data Center (C2DC). After that, then the data is removed from the local server so it is ready to receive a bunch of new data from devices. Fog succeeded to reduce the load on the cloud and the amount of data being sent to it [12, 33, 51].

Smart grid made it easy and possible to ensure stability in the electrical network by monitoring the relationship between supplies and demands of all users at once and tracking the users’ behaviors for different hours, days, or maybe any sudden events. So that, the user is an essential part of the network to maintain its stability and control the required energy size from the stations [19, 52]. However, this shows up as a problem as many of these events or data is unnecessary and unhelpful that may affect the whole system negatively or maybe lead the system to unrequired behavior [41, 57]. Fortunately, we can eliminate them inside the fogs before being sent to the mining algorithms in the cloud. This can be done by using feature selection algorithms.

1.1 Feature selection (FS) methods

Feature selection (FS) is to decide which features are more relevant and useful and which to drop without affecting the overall performance of the system [1, 54]. In electric power systems, extreme values are represented as bad records that can have an unexpected effect on loads. For example, the presence of public holidays that occurs once or twice a year in winters or summers. The demand for electrical energy will be higher than normal loads in normal times as a result of this event [58]. Because this event is not repeated, it is therefore not reliable in the learning system. Extreme values from data sets must be eliminated before applying any further processing. Whereas, these extreme values can cause noise during many data mining algorithms [22].

FS is implemented in many tasks in diverse fields including Machine Learning (ML) [34], Pattern Recognition (PR), Image Processing (IP), and multimedia. FS is a process concerning selecting relevant and informative features, so, redundant information can be avoided and ignored [1]. It majorly focuses on selecting a subset of features from the input dataset, which could effectively describe the input dataset. FS can significantly minimize the detrimental effects of noise and irrelevant characteristics on data [13, 22]. Some of the dependent features may supply no additional information. In other words, the majority of the critical information could be achieved via a few unique features that provide class discriminative information. As a result, removing the dependent features in some cases that do not correlate with the classes is essential.

There are two mainstream categories for FS and the associated taxonomy are illustrated in Table 1. They are label information and search strategy FS algorithms can be categorized concerning the search strategy into three categories (1) filter, (2) wrapper, or (3) hybrid. Filter methods depend on applying different statistical tests on each feature and ranking the features based on the score [22] and selecting the subset of features as a pre-processing step before a classification [62]. Wrapper methods select a set of features and pass them to a classifier to check the accuracy, and repeat the same process with different sets of features until the maximum accuracy is reached [10]. They also use a learning algorithm to evaluate the subsets of features according to their predictive power and accuracy [18]. A hybrid method is a mixture of filter and wrapper methods. First, features are ranked using filter methods, and then only the top scores’ features are passed to the wrapper [22].

Table 1 Categorization of the feature selections techniques

Moreover, the FS methods can be categorized into three types according to the class label information (1) supervised FS, (2) unsupervised FS, and (3) semi-supervised FS. Supervised FS methods employ labeled data for feature selection and measure the correlation of the features with the class label to determine the feature significance. To evaluate feature relevance, semi-supervised FS algorithms leverage label information from labeled data as well as the data distribution structure of both labeled and unlabeled data. Unsupervised FS methods assess feature relevance by the capability of keeping specific attributes of the data [27].

The objective of the current study is to filter the collected data selecting only the effective features of the collected data from Fogs to the cloud for the next load prediction phase. Where a perfect feature selection methodology not only improves the model prediction efficiency but also speeds up the forecasting process by considering fewer features. The main contribution of this paper is to present a new effective hybrid feature selection technique named FSBR. Figure 1 represents the framework for the proposed method which contains two phases. The first phase is the ranking phase. The features go through three different ranking methods: (1) relative weight ranking (R_FRW), (2) effectiveness ranking(R_FE), and (3) information gain ranking(R_IG). Then, the three ranks are passed to a fuzzy inference system to generate the final ranks based on a set of rules. The second phase is the wrapper phase, different sets of top-ranked features are passed through three different classifiers: (1) Naïve Bayes, (2) Support Vector Machine (SVM), and Neural Network (NN), only one set of features is chosen based on the performances of the three classifiers.

Fig. 1

The framework for the proposed method feature selection-based ranking

The contributions of the current study can be summarized as follows:

• Proposing a hybrid technique in the feature selection field called FSBR.

• FSBR is to present two phases [feature ranking phase, and feature selection phase]

• feature ranking phase is to present three different ranking methods[relative weight ranking, effectiveness ranking, and information gain ranking].

• feature selection phase Combining different machine learning classification algorithms(Naive Bayes, Support Vector Machine, and neural network).

• Apply the proposed method to two types of datasets.

• Comparing the current study with a set of state-of-the-art studies.

1.2 Paper organization

This paper is organized as follows: Section 2 discusses the previous efforts concerning the feature selection strategy. Section 3 presents the proposed user load forecasting strategy. Section 4 shows the experimental results. The conclusions and future work are discussed in Section 5.

2 Literature review

Initially, this section introduces a set of the previous efforts in the field of FS generally. Then, it introduces the previous efforts in the smart grid system and FS methods. Currently, there are many related works related to the concept of fog computing that discusses the difference between cloud computing [37] and edge computing technologies, its applications, emerging key technologies (i.e., communication and storage technologies), and various challenges involved in fog technology [17, 48].

Bellavista et al. [8] presented a survey on fog computing for the IoT. They illustrated the architecture of fog and some of the applications based on fog. Javadzadeh et al. [25] provided a systematic survey with a different analytical evaluation of fog computing applications in smart cities. They presented a differential approach of evolution that incorporates filter and wrapper methods into an enhanced local knowledge computational search process that is based on fuzziness principles to cope with both continuous and discrete data sets [22]. Another study by Mafarja et al. proposed an approach to solve problems in the FS using two incremental hill-climbing techniques (i.e., quick reduce and CEBARKCC). They are hybridized with the binary ant lion optimizer in a model called HBALO [29]. Sayed et al. [44] suggested a metaheuristic optimizer, namely a chaotic crow search algorithm, to find an optimal feature subset that maximizes the classification performance and minimizes the number of selected features.

Mafarja et al. [30] presented a binary grasshopper optimization algorithm for FS problems. Binary variants were recommended and used to select the best feature subset within a wrapper-based system for classification purposes. Cilia et al. [9] presented a ranking-based approach related to the FS for handwritten character recognition. Zhu et al. [63] suggested a supervised FS algorithm to simultaneously preserve the local structure (i.e., through adaptive structure learning in a low-dimensional feature space of the original data) and the global structure (i.e., through a low-rank constraint) of the data at the same time. Bassine et al. [7] proposed an improved Arabic text classification system that used the Chi-square FS, called ImpCHI, to improve the efficiency of the classification. Verma et al. [53] applied a new hybrid approach using three FS techniques Chi-Square, Information Gain, and Principle Component Analysis, and then merged them to select the best available subset of the collected data for skin disease [60].

Ahmed et al. [3] suggested a supervised machine learning-based approach to detect a covert cyber deception assault in the state estimate with a genetic algorithm-based feature selection to improve detection accuracy. Hafeez et al. [20] provided two modules: FS like random forests and Relief-F. They were merged to create a hybrid FS algorithm to reduce the. Ahmad et al. [2] presented an artificial neural network-based day-ahead load forecasting model for smart grids, with is made up of three modules; the data preparation module, FS, and the forecast module. The data preparation module made the historical load curve compatible with the FS module to predict the future load based on the selected features. Niu et al. [35] developed a practical machine learning model based on FS using binary-valued cooperation search algorithm and parameter optimization for short-term load prediction using support vector machine. The related studies are summarized in Table 2 according to the publication year in ascending order.

Table 2 Related Studies Summarization

Based on what was mentioned in this section, there have been researches that work only on the filtering method, while others work on the wrapper. In addition, more than one other way to feature selection was mentioned, but it had limitations such as the time, as well as computationally complex. In our proposed method, we collected the filtering method and the cover, and this gave a higher accuracy when implementing and compared to other methods, and we used easy-to-implement equations. In addition, to using equations that are easy to implement in our method.

3 The suggested feature selection strategy

An efficient forecasting model makes acceptable use of the electric loads-based data with all characteristics and also reduces its dimensionality of it. Load forecasting is classified into three types based on the time intervals. First is the short-term load forecasting that forecasts the load from a period of 24 h to one week. Short-term load forecasting makes great progress recently concerning the large data collected from smart meters [40]. The second is Medium-Term Load Forecasting, which anticipates load for a week to a year. The third is Long Term Load Forecasting, which forecasts the load from a period of one year to more than two years. With the presence of fog and the development of the centralized computing topology, we can train the load forecasting models and forecast the workloads to distributed smart meters so that consumers’ raw data is handled locally and forwarded. The data to a central cloud [46].

The suggested forecasting model [59] is built in an architectural manner that consists of three tiers. The first tier contains the IoT devices such as sensors, smart meters, monitoring systems, wireless communication devices, and demand response [6, 26]. The data is collected and sent to the fog computing layer, where it is the second tire. Fog is responsible to take data from devices such as smart meters. In the fog layer, two operations are carried out, (1) a pre-processing layer and (2) a short-term prediction model layer as shown in Fig. 2. The third tire is the cloud that contains a set of integrated data that can be used in long-term prediction Thus, we can obtain an improved electrical grid for accurate load prediction [38].

Fig. 2

User load forecasting strategy

In this paper, we focus on the fog first layer. In summary, the current study works in the data pre-processing layer using the suggested FSBR approach. In this section, we will go through the proposed feature selector in detail. It consists of two phases. First, the feature ranking phase (filter methods) using the proposed methods [relative weight ranking, effectiveness ranking, and information gain ranking]. Second, the feature selection phase (wrapper method) uses the different machine learning classification [Naive Bayes, Support Vector Machine, and neural network]. As shown in Fig. 3, data is collected from smart devices and sent to fog to start the execution of the feature selection algorithm.

Fig. 3

The proposed feature selection phases

3.1 Feature ranking phase (FRP)

FSBR starts with the ranking phase using three different filter methods (1) Feature Relative Weight Ranking (R_FRW), (2) Feature Effectiveness Ranking (R_FE), and (3) information gain (IG) [49]. Each of the previous methods produces a different ranking for the priority and importance of the feature; so to have only one ranking for the feature, a fuzzy inference system is used. Fuzzy will take these ranks in and produce a final ranking from the three methods to give us the best features in order. so it can be used in the second phase. The feature selection phase is about determining the best set of top-ranked features. This is done by determining different sets of the top-ranked features and passing them to a classifier. Based on the results of the classifier, the best set is selected. This is represented graphically in Fig. 3.

3.1.1 Feature relative weight ranking (R_FRW)

The first-ranking method depends on the greatest feature’s impact on the output. Where the number of unique states in each feature affects the priority of the feature and the bond’s strength of output. The bond between the inputs’ features and output is a true metric to measure the importance of each feature concerning the strength of the bond. This reflects the greatest feature’s impact on the output. To achieve this, we followed an assumption that, each data column including input and output, consists of a finite number of unique states. Assume a feature F_i consists of n unique states as follows: S₁, S₂, …, S_n, and the output consists of m unique states as follows: O₁, O₂, …, O_m, where n and m are finite numbers. S₁ is repeated k times inside the feature’s column, which means the corresponding output, could be any state of output’s states and the same applies for other states. To measure the bond’s strength, we have to calculate the probability of the different output states occurring inside S₁ on its own and then for S₂, S₃, and so on. The formulas used for this method are presented in Eqs. (1) and (2).

$$ \mathrm{FRW}\left({F}_i,{O}_j\right)=P\left({S}_1,{O}_j\right)+P\left({S}_2,{O}_j\right)+\dots +P\left({S}_n,{O}_j\right) $$

(1)

$$ {\mathrm{R}}_{\mathrm{FRW}}\left({F}_i\right)=\left|\mathrm{diff}\ \left(\mathrm{FRW}\left({F}_i,{O}_1\right),\mathrm{FRW}\left({F}_i,{O}_2\right),\dots, \mathrm{FRW}\left({F}_i,{O}_m\right)\right)\right|\times n $$

(2)

where i is the feature’s index, j is the output’s state’s index, P(S_n, O_j) is the probability of the output O_j to occur when the input’s state is S_n. where R_FRW(F_i) is the feature relative weight ranking for feature F_i.

The R_FRW is calculation is presented in Algorithm 1 (Fig. 4). To simplify the illustration of this method, a sample dataset (Table 3) of 15 items (6 features and 1 output) is used for the explanation where T1 indicates (Saturday, Sunday, Monday), T2 indicates; (Tuesday, Wednesday, Thursday), and T3 indicates (Friday) are respectively. The employed states of the features are presented in Table 4. illustrates how to execute the R_FRW method on Table 5.

Fig. 4

Algorithm1: Features Ranking using R_FRW Algorithm

Table 3 A Sample Dataset with 15 Records

Table 4 The Employed States of the Features of the Sample Dataset

Table 5 Illustration of the Relative Weight Ranking Method on an Example

3.1.2 Feature effectiveness ranking

The second-ranking method is driven by the popular Naïve Bayes classifier that has presented in Eq. (3).

$$ P\left(O\ \right|\ F\Big)=\frac{P\left(F\ \right|\ O\Big)\times P(O)}{P(F)} $$

(3)

The newly proposed ranking technique inherits the same formula but instead of applying it once, using only one state of each feature to get the probability of output, we used it on each feature’s state to get The effect of the feature over other features. Where P(O | F) is the probability of target O to happen if given attribute F, P(F | O) is the conditional probability of F given O, P(O) is the probability of the class, and P(F) is the probability of the attribute. It is used as a classifier by giving attributes as input and getting a probability as an output. The higher probability we get, the higher chance the output to occur. We have driven a new ranking technique using this probability based on the different states of each feature as mentioned in the first ranking method.

The newly proposed ranking technique inherits the same previous formula but instead of applying it once, using only one state of each feature to get the probability of output, we used it on each feature’s state to get the probability of each output’s state as presented in Eq. (4).

$$ P\left({O}_j|{F}_i\right)=\sum \limits_{i=1}^nP\left({O}_j|{S}_i\right) $$

(4)

where P(O_j| F_i) is the probability to get output state O_j if given feature F_i, P(O_j| S_i) is the probability to get output state O_j if given feature’s state S_i, n is the number of feature’s states, and O_j is the required output’s state. Then the following formula is used to get a final rank that represents the whole feature’s column as presented in Eq. (5).

$$ {R}_{FE}\left({F}_i\right)=\mathrm{diff}\left(P\left({O}_1\ \right|\ {F}_i\Big),P\left({O}_2\ \right|\ {F}_i\Big),\dots, P\left({O}_m\ \right|\ {F}_i\Big)\right) $$

(5)

where R_FE(F_i) is the feature effectiveness of the feature’s column F_i, and P(O₁ | F_i) is the probability to get output state O₁ if given feature F_i. Rank Feature Effectiveness is illustrated in Algorithm 2 (Fig. 5). To simplify the previous formulas and the ranking technique, the dataset shown in Table 3 is used a gain to simplify the illustration as show in Table 6.

Fig. 5

Algorithm 2: Features Ranking Using R_FE Algorithm

Table 6 The Followed Steps of Rank Feature Effectiveness

3.1.3 Information gain

Information gain [15] is used as a third-ranking method with the previous two methods where it measures the mutual dependence between two variables such as the dependence between an input’s feature and the output. From our context, the higher information gain, the strongest relation between input’s feature and the output. Hence, we aim to find which features have the highest values with the output. Equation 6 shows the used formula to calculate IG.

$$ IG\ \left(y,X\right)=E(y)\hbox{--} E\ \left(X\ |\ y\right) $$

(6)

where E(y) is the target’s entropy and E (X | y) is the measure of the entropy of target y given variable X. The term Entropy represents the measure of uncertainty or disorder, which has the formula shown in Eq. 7.

$$ E(y)=-\sum \limits_{i=1}^mP\left({y}_i\right)\times {Log}_2\left(P\left({y}_i\right)\right) $$

(7)

where m is the number of target’s classes, P(y_i) is the probability of class y_i, and Log₂(P(y_i)) is the logarithmic value of the class’s probability. E (X | y) can be calculated from:

$$ E\left(X\ |\ y\right)=\sum \limits_{i=1}^mP\left({y}_i\right)\times \sum \limits_{j=1}^nP\left({X}_j\ |\ {y}_i\right)\times {Log}_2\left(P\left({X}_j\ |\ {y}_i\right)\right) $$

(8)

To measure a feature’s IG first, we measure the whole dataset’s output entropy. Then, we measure the entropy of the output but for a given input’s feature. Finally, we subtract both values to get the final value of the IG. Table 7 shows the values of IG for each feature from the dataset presented in Table 3. Thus, we have obtained the third and final rank of the proposed types of ranks.

Table 7 Third Rank Values using the IG Method

3.2 Fuzzy Interface engine

The previous ranking methods will lead to three different ranking tables. Hence, somehow it is necessary to merge them into only one. A fuzzy inference system is the best among alternatives to do that. Fuzzy is based only on simple IF-THEN rules merged with fuzzy logic operators (e.g., AND and OR) to enhance the decision-making which is much similar to humans’ reasoning. Fuzzy inference is a process to map the input into an output using fuzzy logic [43]. The previous process goes as follows (1) the input of crisp values is converted into fuzzy quantities, (2) then it goes through the fuzzy rules and fuzzy memberships to generate an output, and (3) the output is in a form of a fuzzy set that needs to be defuzzified to get the output of crisp values once again.

The input to the fuzzy system is the crisp values as shown in Table 8. They need to be converted into fuzzy sets using the memberships shown in Fig. 6. To generate the corresponding memberships for the three ranking methods, we need to determine the α, β, and ϒ values as presented in Eqs. 9 to 11 [43].

Table 8 Crisp Input Values of the Fuzzy Inference Engine

Fig. 6

The Membership Function

$$ \upalpha =\frac{0.5\times {\sum}_{x=1}^n{(value)}_x}{n} $$

(9)

$$ \beta =\upalpha \times 2 $$

(10)

$$ \Upsilon =\upalpha \times 3 $$

(11)

After calculating the three values of α, β, and ϒ, each value from each ranking is converted into fuzzy input that can be small (S), medium (M), or large (L) by using the Eqs. 12 to 14.

$$ \mu {(x)}_{small}=\left\{\begin{array}{c}1\ x\le \alpha\ \\ {}\frac{\beta -x}{\beta -\alpha }\ \upalpha <\mathrm{x}\le \upbeta \\ {}0\ x>\beta\ \end{array}\right. $$

(12)

$$ \mu {(x)}_{medium}=\left\{\ \begin{array}{c}\ 0\ x\le \alpha\ \\ {}\frac{x-\alpha }{\beta -\alpha }\ \upalpha <\mathrm{x}\le \upbeta \\ {}\frac{\Upsilon -x}{\Upsilon -\beta }\ \beta <x\le \gamma \\ {}0\ x>\gamma \end{array}\right. $$

(13)

$$ \mu {(x)}_{large}=\left\{\begin{array}{c}0\ x\le \beta \\ {}\frac{x-\beta }{\Upsilon -\beta }\ \beta <x\le \gamma \\ {}1\ x>\gamma\ \end{array}\right. $$

(14)

where n is the number of the input values for the methods, value is the ranking of the feature x related to a particular method.

Consequently, the fuzzy rule-based input is the fuzzification process’ output. A set of rules are considered here in the form; if (X is A) AND (Y is B) THEN (Z is C), where A, B, and C represent input variables (R_FRW, R_FE, and R_IG) and A, B, and C represent the corresponding linguistic variables (e.g., small, medium, and large). The first part of the rule (before THEN) is called “antecedent”. The second part (after THEN) is called “consequent”. These input fuzzy sets go through if-then rules to determine the output. In this paper, there are 27 different rules used to determine the output as shown in Table 9. Then the output goes into a defuzzify process to get crisp values back representing the final ranking.

Table 9 The Used Fuzzy Rules

Defuzzification can be applied using different methods such as max-min, max criterion, center-of-gravity (COG), and the mean of maxima [5, 39, 43]. The max-min depends on choosing a min operator for the conjunction in the premise of the rule as well as for the implication function and the max aggregation operator [5]. Consider a simple case of two elements of evidence per rule, the corresponding rules will be:

(15)

This yields to:

$$ {\mu}_M=\max \left(\min \left({\mu}_{k_{11}},{\mu}_{k_{12}}\right),\min \left({\mu}_{k_{21}},{\mu}_{k_{22}}\right),\dots, \min \left({\mu}_{k_{N1}},{\mu}_{k_{N2}}\right)\right) $$

(16)

The COG is the most popular one [5] and this is the used method in the current study. This method is identical to the formula for calculating the center of gravity in physics. The membership function, In our case, is bounded by the weighted average of the membership function or the COG of the area. Defuzzification can be accomplished by the output membership function shown in step 3 in Table 10. Assuming α = 3, β = 6, and ϒ = 9 related to Eqs. 9 to 11. In Algorithm 3 (Fig. 7), the final ranking using the fuzzy interface engine of the fuzzy rank is used to get results of the implemented fuzzy rank (R) method. An example is illustrated in Table 10.

Table 10 The Followed Steps of the Fuzzy Rank Method

Fig. 7

Algorithm 3: final ranking using fuzzy interface engine

3.3 Feature selection phase (FSP)

The results of the previous phase are the ranks of all features ranked from the most effective features to the least ones. This is suitable as we can drop the least effective ones to reduce the computations and complexity, ending with the most effective features but they could be many, for big systems they could be hundreds or thousands. Therefore, the question is; What is the least amount of the most effective features that could be enough to operate as if we had used every feature from the features set? this question will be answered in this section. A wrapper phase is a tray-and-error phase where we use different classifiers with a different number of top-ranked features to end with the least number of features that could do the same job as the whole features set.

In this work, we have used three different classifiers (1) Simple Neural Network, (2) Naïve Bayes, and (3) Support Vector Machine. First, we have to determine the accuracy of each classifier to compare the results with the different combinations of top-ranked features. Then, we determine the average accuracy in each combination, and only one set of these features is chosen based on the highest average accuracy. As an explanation, the dataset described in Table 3 is divided into 15 items for training and 10 items for testing.

First, it is time to test the top-ranked sets. The top-ranked features for this sample are [Season, Weather, Time, Weekday, Holidays, and Events]. Five different sets were made, Top 1 to Top 6, where Top 1 contains only the first top-ranked feature, which is the Season, and Top 5 contains top-five-ranked features. Results are shown in Table 11. Nevertheless, for the sake of simplicity, fewer computations, and faster decision-making; Top 3 is better than Top 5, as only three features could do the same job as the whole features set.

Table 11 The Accuracy Results

During our work, as a summary, we discussed the first phase that is called the feature ranking phase (FRP) by applying the filter feature selection methods. The final features ranking are the outputs of the fuzzy method. Illustrative calculations are performed on a sample dataset (Table 3). The second stage is called the feature selection phase (FSP) will apply a wrapper methodology feature selection method to select the best features from x feature ranking according to three classifiers (1) neural network, (2) naive Bayes, and (3) support vector machine. Based on the output fuzzy, the order of features is [Season, Weather, Time, Holidays, Events, Weekday]. First, we will test each classifier on the data multiple times. The first experiment calculates the accuracy from the first feature TOP1 [Season] then calculates the accuracy by adding the following feature TOP2 [Season, Weather]. Thus, We continue to add the features gradually, then find six results in each classifier. With the imposition of the values as shown in Table 11, we find that at the TOP3 and TOP5 features. We have the average accuracy of TOP3 is 89.66% and of TOP5 is 88.33%. When calculating the average accuracy, we found that TOP3 features are the best for sake of simplicity.

4 Evaluation and results

The current section shows the experiments, reported results, and the corresponding discussions. The experiments are performed on Windows 10 using the Python programming language. The used packages are NumPy, Pandas, Keras, and Scikit-Learn. The environment had an Intel Core i7 processor with a RAM of 6 GB.

4.1 Datasets

The current study uses two datasets. The first is the EUNITE dataset while the second is the USPS dataset.

4.1.1 EUNITE dataset

European Network on Intelligent Technologies or EUNITE [15] is a dataset that contains electrical loads for Eastern Slovakian Electricity Corporation during the period between January 1, 1997, and December 31, 1998. It was in the form of four columns that contain daily information as follows (1) date, (2) temperature, (3) holiday, and (4) load. The holiday column represents if the corresponding day meets an annual holiday or not (e.g., Christmas and Easter). The first three columns are the features while the last one (load) is the desired output, but for a complete test and representation of our proposed method, we have added three more columns based on the day’s date. These columns are (1) weekday, (2) event, and (3) season. The event represents if there any occasional events happened. The resultant modified dataset consists of 730 samples and seven columns (i.e., six columns as features and one column as the desired output). Samples from the modified dataset are shown in Table 12.

Table 12 Samples from the Modified EUNITE Dataset

The data in its current form cannot be used, neither for the filter phase nor for the selection phase, because there are different forms for each column and a wide range for numerical columns temperature and load. Hence, it is necessary to go through a preprocessing stage to reform the data in an appropriate numerical form. This stage converts the date column into a number that represents a day in the week. It also converts the holiday, weekday, and events columns into 1 or 0 where 1 is Yes or 0 is No. Finally, it normalizes the temperature and load columns. The temperature range is set to [−1, 1] and the load range is set to [0, 1]. Table 13 shows the results after the preprocessing stage.

Table 13 Samples from the Preprocessed Modified EUNITE Dataset

4.1.2 USPS dataset

The handwritten digits USPS dataset [23] is a digital dataset created by the United States by scanning envelopes automatically. Postal Service contains 9298 images divided into 7291 images for training and 2007 images for testing which is 80%:20% divisions. There are 256 features. The images here have been deslanted and the size is normalized, resulting in (16, 16) grayscale images.

4.2 Performance metrics

The used performance metrics are (1) accuracy, (2) precision, (3) recall, and (4) F1-score. They, and their equations, are represented in Table 14.

Table 14 The used Performance Metrics

where TP (True Positive) is the number of samples classified positive correctly, TN (True Negative) is the number of samples classified negative correctly, FP (False Positive) is the number of samples wrongly classified positive, and FN (False Negative) is the number of samples wrongly classified negative.

4.3 Evaluation of EUNITE

The current subsection shows a comparison between the proposed method and others filters methods (1) CHI square [7], (2) mutual information [7], (3) Feature Importance [56], (4) ACC2 [42], and (5) AACC2 [42]. The results are shown in Table 15.

Table 15 Filter phase results using different methods

Table 15 shows the top-ranked feature up to top-5. As shown, the top-1 is the same for all methods whereas the other top-k differs from one method to another. To prove that the proposed method accurately ranks the features, each method is tested separately during the second phase. Figures 8, 9, and 10 show the accuracy for each method using the Neural Network, Naïve Bayes, and Support vector machine respectively. The results of this comparison are shown in Table 16. where The accuracy in different feature selection techniques for all features with classifiers We find in the NN classifier given the highest accuracy 0.97 among other classification in NB classifier given 0.79 and in SVM classifier given 0.92, in Top 3 the NN classifier given the highest accuracy 0.97 among other classification in NB classifier given 0.82 and in SVM classifier given 0.95, and Top 4 the NN classifier given the highest accuracy 0.97 among other classification in NB classifier given 0.81 and in SVM classifier given 0.95, they present values close to Top 5, which shows the highest value using all the features and our proposed method is of the highest values. From the results and to take advantage of the values of the different classifiers in each method and get the best values from merging them. we can calculate the average to each top to the proposed filter method and the other different feature selection techniques for each Top with classifiers, In Fig. 11 illustrated the average result in each top.

Fig. 8

Accuracy for different methods using Neural Network classifier

Fig. 9

Accuracy for different methods using Naïve Bayes classifier

Fig. 10

Accuracy for different methods using SVM classifier

Table 16 The result of the FSBR and other methods with different classifiers on the EUNITE dataset

Fig. 11

The average Accuracy for the different methods

From previous figures, we can conclude that the top 3, top 4, and top 5 ranked features are the best to use but for the sake of simplicity and less time and hardware computation, the top 3 is chosen to continue our comparisons between the proposed filter method and other different filters. The implementation of these different features selection techniques provides a different subset of the selected features. However, the Chi-square, mutual information, and feature importance techniques provide the same features subset. For this reason, Chi-square, mutual information, and feature importance have the same “Accuracy”,” Precision”,” Recall”, and “F1-score “values based on the average classifier. On the other hand, the other techniques which are; Most correlated features, ACC2, AACC2, and FSBR have different results of the measurements as shown in Table 17.

Table 17 The performance metrics of FSBR compared to other methods on the EUNITE dataset

According to the obvious results and Figs. 12, 13, 14, 15, it is noticed that the proposed features selection method represented in FSBR demonstrates the “Accuracy”, “Precision”, “Recall”, and “F1-score”. Thus, It has been proven that FSBR is the most efficient methodology. On the other hand, it is found that Most correlated features introduce the worst performance in terms of “Accuracy”, “Precision”, “Recall”, and “F1-score”. For Most correlated features and FSBR, the error reaches 22% and 9% respectively. FSBR is better than Most correlated features because FSBR is based on using a hybrid technique that combines filter and wrapper methods. Firstly, the hybrid technique composes of three filter methods called FRW, FE, and IG which are cooperated for providing the best rank of features by the fuzzy method. Finally, using NN, NB, and SVM to Combine them to get the best value is applied as a wrapper method to determine exactly the most significant subset of features. On the other hand, Most correlated features are based only on the filter selection method, so it provides a less accurate subset of features.

Fig. 12

Accuracy for Top 3 ranked features for different filter methods

Fig. 13

Precision for Top 3 ranked features for different filter methods

Fig. 14

Recall for Top 3 ranked features for different filter methods

Fig. 15

F1-score for Top 3 ranked features for different filter methods

Finally, FSBR is better than other techniques to select the best subset of features that is improving the performance of the classifier or the prediction model using only three features.

4.4 Generalization using USPS

The USPS dataset is used to prove the applicability of our proposal on a big dataset. Table 18 shows a comparison between our proposed method for feature ranking and selection with different feature selection algorithms in [31]. Comparison criterion is made as follows, the whole number of features go through each feature selection algorithm including the proposed one then the top-ranked features are used to train a Neural Network, and finally, the test results are used to decide which method is the best. Figure 16 illustrates the result accuracy, precision, and recall of the proposed method and the different feature selection algorithms in Table 18. From that, our proposed method has reported the best result.

Table 18 The performance metrics of FSBR compared to other methods on the USPS dataset

Fig. 16

The result to accuracy, precision, and sensitivity

As shown in Table 18, the least amount of features to gain the maximum accuracy were 10 features, the number is the same for each method but each method chooses its features based on their ranks. The proposed method succeeded to get the highest accuracy compared to 12 methods and is very close to the others. Also, it got the highest precision among others. The recall was better than 10 methods.

5 Conclusions and future work

As a recap, the proposed method is a feature selection method based on filter and wrapper techniques. The filter phase consists of three different filters: relative weight ranking, effectiveness ranking, and information gain ranking. In the wrapper phase, we used three different classifiers to select the least amount of top-ranked features (from the previous phase) without affecting the performance. The used were classifiers Neural Network, Naïve Bayes, and Support Vector Machine. Hence, our main contribution was to improve the smart electrical grid by optimizing the data being sent to fog and cloud. However, only important data is selected while any other repetitive and irrelevant data is dropped, maintaining the performance of the system. Therefore, we have proposed a new feature selection method that could successfully choose only important data with proving its correctness by applying it on two different datasets. EUNITE, which is related to the electrical field, and USPS, which is not related to the electrical field but is about images. In both cases, results were satisfying enough to put our proposed method in a comparison with other methods. Experimental results have shown that the proposed feature selection technique provides more accurate results than the existing methods in terms of accuracy, precision, recall, and F1-score. FSBR provide accuracy, precision, recall, and F1-score values that reached 91%, 0.90%, 0.91%, and 0.90% respectively in EUNITE 90%, 93%, and 88% were the best accuracy, precision, and recall respectively use the USPS dataset. In future work, we will work on the second layer, the user load forecasting strategy, and the possibility of saving on electricity consumption by predicting the load per user in the short-term and long term.