Non-intrusive load monitoring is a method that disaggregates the overall energy consumption of a building to estimate the electric power usage and operating status of each appliance individually. Prior studies have mostly concentrated on the identification of high-power appliances like HVAC systems while overlooking the existence of low-power appliances. Low-power consumer appliances have comparable power consumption patterns, which can complicate the detection task and can be mistaken as noise. This research tackles the problem of classification of low-power appliances and uses turn-on current transients to extract novel features and develop unique appliance signatures. A hybrid feature extraction method based on mono-fractal and multi-fractal analysis is proposed for identifying low-power appliances. Fractal dimension, Hurst exponent, multifractal spectrum and the Hölder exponents of switching current transient signals are extracted to develop various ‘turn-on’ appliance signatures for classification. Four classifiers, i.e., deep neural network, support vector machine, decision trees, and K-nearest neighbours have been optimized using Bayesian optimization and trained using the extracted features. The simulated results showed that the proposed method consistently outperforms state-of-the-art feature extraction methods across all optimized classifiers, achieving an accuracy of up to 96 % in classifying low-power appliances.

Monitoring the electrical system at individual load levels often enables condition-based diagnostics and forecasts that can minimize the impact of equipment malfunctions or system failures [

Nonintrusive Load Monitoring (NILM) is a low-cost solution to the load monitoring problem and it provides the necessary information in real-time to formulate various energy management schemes [

Fractal analysis is a powerful technique that mathematically defines patterns in apparently random and complex figures [

The concept of NILM was first introduced by MIT researcher Hart in the 1980s [

Earlier techniques of feature extraction focused on “steady-state” features like active and reactive powers and V-I trajectories [

Several hybrid and unconventional techniques also exist in the literature with a range of performance efficiencies [

Based on the above literature review, there is still a void in the NILM research space for an effective feature extraction solution that works well with low-power appliance classification. Particularly, there is very little literature that deals with switching transient signals of low-power (less than 50 W) appliances with non-linear characteristics. The challenges include the difficulty in characterizing transient signals due to their short duration and wide frequency content. Existing methods such as spectrogram and wavelet decomposition have limitations in discriminating near similar transients. Additionally, the turn-on transient current of electrical appliances tends to decay to a steady state that is different from the one preceding it. To address these challenges, this research work has made the following research contributions:

Mono- and Multi-Fractal Analysis is used for appliance classification in NILM research.

The proposed fractal-based novel feature extraction method is compared with four other feature extraction methods, i.e., different variants of Scattering Transform and multi-level DWT.

The proposed mono- and multi-fractal analysis method outshined all other feature extraction methods, achieving an accuracy of up to 96% with superior precision, recall, and F1-score values of up to 97.3%.

Successfully used fractal analysis for low-power (less than 50 W) appliances.

The paper is organized as follows:

The selection of a suitable mathematical technique for time series analysis is based on its adaptability and practical applicability to real-world signals. Several real signals demonstrate nonlinear power-law characteristics, which are dependent upon higher-order moments and scale. In certain instances, the dynamic attributes of these processes exhibit multifractal as well as monofractal characteristics. This paper proposes to use the Wavelet Leaders Multifractal Formalism (WLMF) method, Higuchi’s method, and monofractal detrended fluctuation analysis (DFA) to extract multifractal and monofractal features of current switching transient for automatic classification of low-power electrical appliances.

Fractal processes can be categorized into two types: Monofractal and multifractal [

The Wavelet Leaders Multifractal Formalism (WLMF) method builds on wavelet coefficients obtained through the DWT following the Mallat pyramid scheme [

Wavelet leaders are identified as space- or time-localized maxima of discrete wavelet coefficients. To achieve time localization of the maxima, it is necessary to derive the wavelet coefficients utilising a compactly supported wavelet. The Hölder exponents, which quantify the local regularity, are computed from these maxima. The size of the set of Hölder exponents in the time series is referred to as the singularity spectrum. Wavelet leaders are defined at any given scale as [

The multi-resolution structure-function

The scaling exponent

The monofractal structure of a time series is characterized by the Hurst exponent

Let

Next, create an approximate geometric progression

The value of

A Hurst exponent

Higuchi’s technique is used to estimate the fractal dimension of the start-up transient in the current waveform [

The total average length of

If the series under consideration exhibits non-linear behaviour and has fractal-like properties, then:

Graph of

This paper proposes to extract fractal dimension

The power spectral density (PSD) estimates shown in

Hölder exponents classify singularity strength by indicating their degree of differentiability. A Holder exponent equal to or less than 0 signifies a discontinuity at that specific location. Conversely, Holder exponents equal to or greater than 1 indicate differentiability at those locations. Holder values falling between 0 and 1 signify continuity but not differentiability at specific locations, revealing how closely the signal at that sample approaches differentiability. Holder exponents nearing 0 points to signal locations with lower differentiability compared to those with exponents closer to 1, suggesting a smoother signal at locations featuring higher local Holder exponents.

In^{st}-order statistical moments, the scaling exponents exhibit a linear relationship. This linearity suggests monofractality in the current signals for these specific moments. However, when considering moments from the 2^{nd} order onwards, the scaling exponents deviate from linearity. This departure is likened to the behaviour of a multifractal process, which is characterized by a nonlinear scaling law. This observation suggests that the switching transient signals from the charger and CFL exhibit both monofractal and multifractal features. Therefore, this characteristic of mono- and multi-fractality in the transient signals is explored by extracting

This study employs the WHITED dataset as its primary data source. This dataset offers individual appliance current and voltage information for 5 s concurrently measured at a sampling rate of 44.1 kHz across eight distinct zones and under three distinct power supply standards [

Appliance | Label | Samples | Power (W) |
---|---|---|---|

Charger | Chager | 70 | 7 to 28 |

Compact fluorescent lamp | CFL | 20 | 13.9 |

Game console | GameC | 30 | 13.7 to 33.9 |

Hi-Fi speaker | Hi-Fi | 10 | 41.6 |

Laser printer | LP | 10 | 18.1 |

Massager | Mass | 30 | 26.9 to 37.6 |

Mosquito repellent | Mosquito | 10 | 7.7 |

Power supply | PS | 40 | 9.5 to 47.5 |

Shoe warmer | ShoeW | 20 | 16.5 to 22.2 |

Washing machine | WM | 10 | 26.8 |

For each switching current transient of low-power devices in the WHITED dataset, the current transient is pre-processed,

To assess the efficacy of the proposed feature extraction methodology, the study conducts a series of comprehensive comparative experiments. Different strategies are employed to select features derived from Scattering Transform, multi-level DWT, and the proposed feature extraction method for low-power NILM signals. The features matrix is determined through five distinct strategies, outlined briefly below:

The performance of all five strategies is assessed using the commonly employed evaluation indices: Precision, recall,

The performance of the proposed method (scenario 5) is tested using four optimized classifiers, i.e., deep neural network (DNN), SVM, decision trees, and KNN.

The results of the Bayesian optimization with the proposed feature extraction method are shown in

DNN | SVM | KNN | Decision trees | ||||
---|---|---|---|---|---|---|---|

Hyperparameter | Value | Hyperparameter | Value | Hyperparameter | Value | Hyperparameter | Value |

No. of layers | 3 | Multiclass method | One-vs-One | No. of neighbours | 1 | Max no. of splits | 52 |

Regularization strength | 5.96e-6 | Box constraint level | 888.463 | Distance metric | Correlation | Split criterion | Max deviance reduction |

First layer neurons | 9 | Kernel scale | 5.36 | Distance weight | Inverse | ||

Second layer neurons | 147 | Kernel function | Gaussian | Standardize data | True | ||

Third layer neurons | 14 | Standardize data | True | ||||

Activation Function | ReLU |

The SVM optimization model focuses on optimizing the multiclass technique, box constraint level, kernel scale, and kernel function. The selection of a multiclass technique is crucial in deciding its strategy for dealing with classification problems that involve more than two classes. The box constraint parameter plays a crucial role in striking a balance between accurately classifying training points and achieving a smooth decision boundary. The kernel scale parameter assumes significance in shaping the decision boundary by dictating the extent of influence wielded by each data point. Manipulating the kernel scale introduces variations in the boundary’s flexibility. The optimized configuration consists of a one-vs-one multiclass method, a box constraint level of 888.463, a kernel scale of 5.36, and a Gaussian kernel function. In one-vs-one, each class is treated as a binary classification problem against the rest. Additionally, data standardization was deemed beneficial for this SVM setup.

The KNN classifier was optimized by adjusting the number of neighbours, selecting an appropriate distance metric, and assigning weights to the distances. The number of neighbours indicates the degree to which nearby data points have an impact on the classification of a given point. The distance metric is used to calculate the distance between data points in the KNN algorithm, which determines the level of similarity or dissimilarity. In addition, the distance weight assigns different weights to surrounding points based on their distance from the query point. The complexity of this situation is essential in controlling the importance of each neighbour’s input in determining the final classification result. The optimized configuration dictated one neighbour, a correlation-based distance metric, and inverse distance weighting.

In the case of Decision Trees, the optimization targeted the maximum number of splits and the split criterion. This maximum number of splits establishes an upper limit on the depth of the decision tree. By limiting the maximum number of splits, the algorithm avoids creating an excessively deep tree, which could lead to overfitting the training data

Moreover, the split criterion determines the metric used to evaluate the quality of a split at each node. The resulting configuration included a maximum of 52 splits and the use of the “Max Deviance Reduction” criterion. Standardization of data was identified as advantageous for this Decision Trees setup.

Optimized DNN | Optimized SVM | Optimized KNN | Optimized decision trees | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Label | Precision | Recall | F1-score | Precision | Recall | F1-score | Precision | Recall | F1-score | Precision | Recall | F1-score |

Charger | 1 | 1 | 1 | 1 | 0.857 | 0.923 | 0.923 | 0.857 | 0.889 | 0.909 | 0.714 | 0.80 |

CFL | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.75 | 0.857 | 1 | 1 | 1 |

GameC | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.833 | 0.833 | 0.833 |

Hi-Fi | 1 | 0.5 | 0.667 | 1 | 1 | 1 | 0.667 | 1 | 0.80 | 1 | 1 | 1 |

LP | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.667 | 1 | 0.80 |

Mass | 857 | 1 | 0.923 | 0.667 | 1 | 0.80 | 0.75 | 1 | 0.857 | 0.50 | 0.833 | 0.625 |

Mosquito | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

PS | 0.875 | 0.875 | 0.875 | 1 | 0.875 | 0.933 | 1 | 0.875 | 0.933 | 1 | 0.625 | 0.77 |

ShoeW | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

WM | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0.667 | 1 | 0.80 |

Furthermore,

The SVM classifier also exhibited robust classification capabilities, yielding high precision and recall for most appliances. Similarly, the KNN classifier performed commendably, demonstrating good precision, recall, and F1-score values for various appliances The Decision Trees classifier also displayed reliable performance, with consistently high scores in precision, recall, and F1-score for multiple appliances. Nevertheless, appliances such as the Hi-Fi Speaker System and Massager exhibited slightly lower F1-scores, indicating potential areas for further optimization using advanced optimization techniques [

To provide a more holistic view, we complemented accuracy, F1-score, precision, and recall with the AUC metric. The value of AUC can vary from 0 to 1, with a value of 1.0 representing flawless classification and a value below 0.5 indicating quasi-random guessing.

Classifiers | Charger | CFL | GameC | Hi-Fi | LP | Mass | Mosquito | PS | ShoeW | WM |
---|---|---|---|---|---|---|---|---|---|---|

DNN | 1 | 1 | 1 | 0.9896 | 1 | 1 | 1 | 0.9911 | 1 | 1 |

SVM | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |

Decision tree | 0.9742 | 1 | 0.9754 | 1 | 0.9896 | 0.9242 | 1 | 0.7946 | 1 | 0.9896 |

KNN | 0.9147 | 0.875 | 1 | 0.9896 | 1 | 0.9773 | 1 | 0.9375 | 1 | 1 |

Considering all the discussed performance metrics, DNN was found to be the model that achieved the best classification results. These variations in performance metrics across classifiers underscore the importance of considering the specific characteristics of each appliance when choosing an optimal classifier.

Classifier | Feature extraction method | Accuracy (%) | Precision (%) | Recall (%) | F1-score (%) |
---|---|---|---|---|---|

Optimized | ST all orders | 82 | 80.07 | 83.57 | 81.78 |

DNN | ST 1st order | 88 | 92.74 | 90.36 | 91.54 |

ST 2nd order | 70 | 73.0 | 69.64 | 71.28 | |

Multi-level DWT | 84 | 85.1 | 79.7 | 82.3 | |

Proposed multi-fractal analysis | 96 | 97.3 | 93.75 | 95.5 | |

Optimized | ST all orders | 80 | 83.42 | 83.69 | 83.56 |

SVM | ST 1st order | 82 | 74.41 | 73.57 | 73.99 |

ST 2nd order | 76 | 69.8 | 72.86 | 71.3 | |

Multi-level DWT | 78 | 70.91 | 71.25 | 71.1 | |

Proposed multi-fractal analysis | 94 | 96.67 | 97.32 | 97.0 | |

Optimized | ST all orders | 82 | 81.68 | 78.57 | 80.1 |

decision trees | ST 1st order | 76 | 74.78 | 72.14 | 73.44 |

ST 2nd order | 70 | 74.38 | 70.36 | 72.31 | |

Multi-level DWT | 72 | 69.92 | 64.7 | 67.21 | |

Proposed multi-fractal analysis | 82 | 85.76 | 90.05 | 87.85 | |

Optimized | ST all orders | 92 | 91.67 | 90.0 | 90.83 |

KNN | ST 1st order | 92 | 88.81 | 90.0 | 89.4 |

ST 2nd order | 82 | 82.46 | 81.8 | 82.12 | |

Multi-level DWT | 80 | 69.46 | 69.16 | 69.31 | |

Proposed multi-fractal analysis | 92 | 93.4 | 94.82 | 94.10 |

Using the optimized DNN classifier, the method employing ST coefficients of all orders achieves an accuracy of 82% with similar levels of precision, recall, and F1-score. The approach focusing solely on first-order ST coefficients demonstrates an improved accuracy at 88%, showing improvement in capturing primary signal characteristics. However, the method considering second-order ST coefficients experiences a decrease in accuracy to 70%, indicating challenges in capturing more complex patterns.

The multi-level DWT method attains an accuracy of 84%, offering a balanced trade-off between precision and recall. Notably, the proposed mono- and multi-fractal analysis method outshines all other feature extraction methods, achieving an impressive accuracy of 96% with superior precision, recall, and F1-score values of 97.3%, 93.75%, and 95.5%, respectively.

Moving to the Support Vector Machine (SVM) classifier, the feature extraction methods display consistent performance across various metrics. The ST coefficients of all orders method achieves a low accuracy of 80%, with low precision, recall, and F1-score values. The ST coefficients of the first order show a slight increase in accuracy to 82% but lower values of precision, recall, and F1-score. Similarly, the second-order ST coefficients method records an even lower accuracy of 76% and similar smaller values of other performance metrics. The multi-level DWT method attains an accuracy of 78%, displaying a balanced performance. Once again, the proposed multi-fractal analysis method stands out, achieving a remarkable accuracy of 94%, emphasizing its effectiveness in optimizing SVM classification.

Different feature extraction approaches demonstrate varied performances for the Decision Trees classifier. The approach using ST coefficients of all orders as features produces a relatively low accuracy of 82% while maintaining a balanced performance in terms of precision, recall, and F1-score. The approach that uses only first-order ST coefficients achieves a marginally lower accuracy rate of 76% and considerably low precision and recall. The approach using second-order ST coefficients demonstrates a precision of 70%, suggesting difficulties in capturing intricate patterns. The Multi-level DWT approach produces a 72% accuracy and very low precision and recall values. The suggested multi-fractal analysis method once again demonstrates exceptional performance, obtaining an accuracy of 82% along with high precision, recall, and F1-score values, i.e., 85.76%, 90.05%, and 87.85%, respectively.

Lastly, in the evaluation of the KNN classifier, the feature extraction methods demonstrate robust performances. The ST coefficients of all orders achieves an accuracy of 92%, maintaining a balance between precision, recall, and F1-score. The first-order ST coefficients method maintains consistent accuracy at 92%, with balanced precision and recall. The second-order ST coefficients method records an accuracy of 82%, showcasing a solid performance. The multi-level DWT method attains a low accuracy level of 80% with poor precision, recall, and F1-score values. The proposed multi-fractal analysis method once again stands out, achieving an accuracy of 92%, precision of 93.4%, recall of 94.82%, and F1-score of 94.10, emphasizing its effectiveness in enhancing KNN classification accuracy.

The coefficients in scattering transform (ST) in the first three scenarios are determined analytically and do not need to be learned. The ST also has time-shifting and small time-warping invariance, reducing the need for precise temporal localization for classification. It has shown promising results for classifying high-power level appliances such as vacuum cleaners [

In the proposed hybrid mono- and multi-fractal analysis method, the fractal dimension captures the complexity of the signal, the Hurst exponent characterizes long-term dependencies, the multifractal spectrum describes the distribution of singularities, and the Hölder exponents provide information about local regularities. The hybrid approach integrated both mono- and multi-fractal features to optimize classification accuracy. When employing only mono-fractal features, specifically the Hurst exponent and Fractal dimension, the accuracy achieved was 64%. Similarly, employing only multi-fractal analysis resulted in an accuracy of 84%. However, the combination of these features proved highly effective with an accuracy of up to 96%. The synergistic combination of mono- and multi-fractal features evidently enhanced the overall classification performance, showcasing the robustness of the hybrid method in achieving superior accuracy compared to individual feature sets.

In general, the suggested method exhibited exceptional efficacy in categorizing low-power level appliances, a task that is frequently problematic for alternative algorithms that may erroneously classify such signals as background noise. It can manage the intricacy and lack of linearity that is inherent in low-power appliance signatures. The versatility of fractal-based techniques in handling signals with different levels of complexity enables an efficient differentiation between noise and real appliance patterns in the low-power range. It is intrinsically well-suited to deal with the lack of density in signals, emphasizing important features and enabling the reduction of dimensions. This is especially beneficial in situations with weak signals, as extraneous data might obscure the real characteristics of the devices. The utilization of a hierarchical representation provided by fractal analysis enhances the effectiveness of the procedure. On the contrary, other methods, such as ST coefficients or multi-level DWT have struggled to adapt to the intricacies of low-power appliance signals. Their representations have failed to adequately distinguish between noise and genuine appliance signatures in the low-power range.

For the comparative assessment of computational efficiency, the performance of the proposed multi-fractal and mono-fractal analysis methods is evaluated against established state-of-the-art techniques as shown in

Total execution time (s) | Self-time (s) | Child functions time (s) | |
---|---|---|---|

Proposed multi-fractal analysis | 1.364 | 0.008 | 1.36 |

Proposed mono-fractal analysis | 3.456 | 1.442 | 2.01 |

Multi-level DWT | 153.84 | 153.04 | 0.80 |

ST all orders | 81.41 | 1.165 | 80.25 |

The multi-level DWT predominantly consumed time within the algorithm itself (153.04 s), while ST analysis distributed its computational load more evenly between self-time (1.165 s) and child functions’ time (80.25 s). This analysis underscores the efficiency of the proposed multi- and mono-fractal analysis, particularly in optimizing child functions time, highlighting its potential as a competitive alternative to existing methodologies.

Furthermore, the WHITED dataset contains appliance data from various regions across the world. For instance, the start-up transients of the charger are collected from three different regions of the world. The performance of the proposed algorithms suggests that fractal analysis can capture unique features from start-up transients of low-power nonlinear appliances regardless of their underlying circuit connection with the power mains. However, isolation of the switching transients plays an important role in the implementation of this methodology and event detection is very critical as this step directly determines the upper limit of the identification performance. Furthermore, this method needs to be tested for multi-switching of appliances and that is to be included as part of future work of this project.

This research work addresses a significant gap in NILM research by proposing a novel hybrid feature extraction method based on mono-fractal and multi-fractal approaches. While prior studies have focused on high-power appliances, our work specifically targets the challenging domain of low-power appliances, where distinguishing between devices with similar power profiles poses a considerable obstacle. The utilization of fractal dimension, Hurst exponent, multifractal spectrum, and Hölder exponents in the analysis of switching current transient signals has proven to be a robust approach, achieving superior performance compared to state-of-the-art methods. The comprehensive evaluation using precision, recall, F1-score, and accuracy consistently demonstrates the superiority of our mono- and multi-fractal analysis, achieving an outstanding accuracy of up to 96%.

This work not only advances the understanding of low-power appliance identification but also introduces a valuable methodology for feature extraction in NILM research. The successful application of fractal analysis in this context enhances the accuracy and efficiency of NILM, paving the way for more effective energy management strategies and increased awareness among consumers. These findings underscore the potential of fractal-based approaches in improving the performance of appliance recognition algorithms.

For future work, we plan to test this algorithm on aggregated measurements and develop a complete NILM solution that fuses various methods of appliance signature development to encompass low and medium-power appliances as well as energy-intensive appliances.

The authors are grateful to the University of Engineering and Technology Lahore for providing a platform to conduct this research.

The authors received no specific funding for this study except from the regular research fund of the university.

Anam Mughees: Conceptualization, Methodology, Software, Data curation, Validation, Writing-original draft preparation, Formal analysis. Muhammad Kamran: Conceptualization, Formal analysis, Supervision, Project administration, Validation.

Data is openly available in a public repository. The data that support the findings of this study are openly available at

The authors declare that they have no conflicts of interest to report regarding the present study.