Similar to electric vehicles, electric bicycles are powered by batteries, widely known as nickel-metal hydride (NiMH) and lithium-ion (Li-ion) batteries, which require circulated energy supplement during reduplicated driving. As shown in Figure 1, the charger is essentially a single-phase AC/DC power supply with control voltage and current output capability.

Due to the rectification and chopping links, there are a large number of odd harmonics in its output direct current. Figure 2 shows the charging current waveform directly, with a typical triangular wave appearing. Accordingly, the ratios of harmonic content are presented in Figure 3, which are particularly obvious on odd harmonics such as three, five, and seven times.

The charging method directly impacts the safety, durability, and performance of batteries. An unscientific charging method can significantly reduce the life of batteries and cause danger. According to Young et al. (2013), there are three stages in common charging methods shown in the Figure 4.

1) Constant current stage. In the beginning, a large current should be applied to the battery to supply the energy at maximum speed. In order to maintain a constant current to the battery, controlled charging voltage is applied to the battery. However, the voltage of the grid side is basically unchanged, so the overall power is high and constant. In this scheme, the state of charge (SOC) will increase linearly and rapidly till the cut-off point constantly reaches the thermal or other chemical limits.

The V–I trajectory refers to the mutual trajectory of the instantaneous voltage and the current waveform of the electrical load (Hassan et al., 2013), which is mathematically manifested as a function of the sampling voltage and the current over a cycle. Baets proves that the V–I trajectories of household loads can be extracted from the delta of voltage and current samples before and after the start-up event (De Baets et al., 2018). Figure 5 shows the shapes of the V–I trajectories of two kinds of collected electric bicycles.

It is clear that the V–I trajectory exhibits distinct and easily distinguishable shape properties for electrical loads with different operating principles such as heating, motor driving, and electronic driving. At the same time, the voltage of the gird is relatively stable, and the voltage waveform of different loads is basically consistent. Therefore, the V–I trajectory can be equivalent to the current waveform characteristics of the reactive load device.

However, it should be noted that these V–I trajectories are drawn in the stable working state of the electric bicycles, without any other appliances working. When the electric bicycle load is started based on other appliances working, the steady-state current is the sum of the electric bike and other electric currents based on Kirchhoff laws. At this point, it is conceivable that the V–I trajectory of the mixed working state is severely distorted, as shown in Figure 6. The V–I trajectory under multiple appliances simultaneous operating cannot present the typical shape of electric bicycle load.

Considering that the load equipment startup is a very short transient process, assuming that the working waveform of already-on appliances is completely unchanged before and after the start event of another electric load on these background appliances is reasonable. Therefore, the difference vector (△I) of the current waveforms before and after the start of the electric bicycles will filter the effect caused by other working appliances. The V-△I trajectories calculated by the current differences and voltage will return to the situation with only one device working, where the voltage vector can take any cycle near the start event. Moreover, there are many event detection methods for NILM, such as generalized likelihood ratio (GLR) (Berges et al., 2011) and log-likelihood ratio (LLR) (Anderson et al., 2012a). In this study, a modified CUSUM algorithm (Fang et al., 2020) with a fast and accurate detection effect is adopted.

Finally, the V-△I trajectories of the electric bicycle devices are only approximated, not identical, which are just like the Arabic handwritten letters. Correspondingly, the identification of the electric bicycles, similar to the Arabic handwritten letter recognition, adopts image construction methods and an image recognition model.

In order to effectively handle the V-△I trajectories within the same category, this study proposes a three-step mapping algorithm, mapping the V-△I trajectory into a binary bitmap where each cell is assigned one binary number.

Given that the V-△I trajectory is drawn from current and voltage samples whose frequency may not match or meet the requirement, the first step is to perform the linear interpolation for the V-△I trajectory using the formulas given by Hart, (1992); Zoha et al., (2012). Assuming that the number of the original current or voltage samples during one cycle is n 0 , the formulas given by Hart (1992) and Zoha et al. (2012) expand the current or voltage samples sequence. i p q = q n 1 ( i p + 1 − i p ) + i p , q ∈ { 1,2 , ⋯ , n 1 } , p ∈ { 1,2 , ⋯ , n 0 − 1 } . (1) u p q = q n 1 ( u p + 1 − u p ) + u p , q ∈ { 1,2 , ⋯ , n 1 } , p ∈ { 1,2 , ⋯ , n 0 − 1 } . (2)

In the formula given by Hart (1992) and Zoha et al. (2012), n 1 is the number of interpolation points between the two original samples, i p is the p t h sample in the original current sequence, and i p q is the q t h interpolation point between sample i p and sample i p + 1 . Similarly, u p is the p t h sample in the original voltage sequence and u p q is the q t h interpolation point between sample u p and sample u p + 1 . The length of the expended current or voltage sequence is n 1 ∗ n 0 + n 0 − n 1 , also marked as n .

The second step is normalization. Changing the values of current and voltage expended sequence per unit which ranges from 0 to 1 is necessary by formula (Ruano et al., 2019) and (Li et al., 2021). i ′ k = i k − I min I max − I min , k ∈ { 1,2 , ⋯ , n } . (3) u ′ k = u k − U min U max − U min , k ∈ { 1,2 , ⋯ , n } . (4)

In the formula given by Ruano et al. (2019) and Li et al. (2021), i ′ k and i k are the k t h points in the current sequence before and after normalizing, respectively. I max and I min is the maximum and minimum value of the current sequence before normalizing, respectively. As for voltage, the u ′ k , u k , U max , and U min have the same computational properties.

The expended current and voltage sequences should be mapped into the bitmap in the third step, also called pixelization. Generally, the mapping process involves scanning each point in sequence and finding the location cell in the image which has m*m grid cells. The cells occupied by points in sequences will be colored in black, and unmatched cells will be white. A binary matrix, corresponding to a black-and-white bitmap, can be calculated by the formula given by Liu et al. (2022). x = ⌊ u ′ k ∗ ( m − 1 ) ⌋ . y = ⌊ i ′ k ∗ ( m − 1 ) ⌋ . M ( x , y ) = 1. (5)

In the formula given by Liu et al. (2022), x and y are row and column indexes of matrix M , respectively. ⌊ ⌋ is the symbol of the ceiling. All values in the bitmap are initialized as zero, and each point will be mapped to the corresponding cell.

It is noted that the parameter n 1 of linear interpolation in step 1 and the parameter m of the grid decide the degree of fuzziness of the bitmap. Under the same conditions, if the value of n 1 and m is less, the bitmap of the V − Δ I trajectory becomes more blurry. On the contrary, the bitmap is more close to the actual V − Δ I trajectory images with larger n 1 and n 1 . Figure 7 is a typical bitmap of the V − Δ I trajectory of electric bicycles.

Not surprisingly, the normalized V-△I trajectories lack information about active and reactive power. Therefore, the bitmap of the household with the same working principle but different working power, such as laptop and television, is not considered. In addition, harmonic amplitude and phase, as the effective harmonic features, are also not considered.

To solve the problem caused by the normalization and pixelization of the V-△I trajectory and improve the accuracy of load identification, supplementary features such as active power, reactive power, and harmonic current should be added to the bitmap. This study proposes the mixed feature bitmap, combining the V-△I trajectory, active power, reactive power, and high odd harmonic currents from 5 to 15.

Each supplementary feature is just one single value within the real number fields, differing from the two-dimensional images. It is necessary to change the single value into a special image that only has one column of pixels. Before transforming, the normalization of the supplementary feature should be executed. After all, the units vary across the supplementary parameters. Also, the formula given by Kelly and Knottenbelt (2015b) shows the calculating process during all samples of the supplementary feature. C ′ k = C k − C min C max − C min . (6)

In the formula given by Kelly and Knottenbelt (2015a), C ′ k and C k are the normalized and original values of the k t h supplementary feature, respectively, while C max and C min are the maximum and minimum values of the feature in all training samples, respectively.

After normalizing, the next step of gaining the hybrid feature bitmap is to encode and splice the image. First, each normalized feature, constantly within [0, 1], is expended to an integer within [ 0 , 2 m + 1 − 1 ] . The binary code of this integer is the one-column bitmap for the feature. Horizontal splicing of binary codes of multiple features yields the bitmap of supplementary features, whose matrix expression form is F m × a and a is the number of supplementary features. As shown in Figure 7, the hybrid feature bitmap M F m × ( a + m ) can be easily gained by combining the sub-bitmap of the V-△I trajectory and supplementary features.

The Transformer framework consists of an encoder and a decoder. The encoder comprises N identical encoder layers. Each encoder layer includes sub-modules such as multi-head attention, sum and norm layer, feed-forward neural network, etc. The decoder also comprises N identical decoder layers. In addition to including the same four sub-modules as the encoder, each decoder also adds a masked multi-head attention module to avoid subsequent information in the decoding process as known information to predict the current information.

The heavy use of the layer called self-attention is most special in Transformer. Also, the Attention mechanism imitates the internal process of biological observation behavior, and increasing the fineness of observation in some areas can quickly extract important features of sparse data. Self-attention is a variant of the attention mechanism, which reduces the dependence on external information and is better at capturing the internal correlation of data or features. The application of the self-attention mechanism in text mainly solves the problem of long-distance dependence by calculating the mutual influence between words. Multihead self-attention is the connection and mapping of multiple self-attention mechanisms. The purpose is to construct multiple sub-spaces and find correlations between input data from different angles so that multiple relationships and subtle differences can be encoded.

Compared with the traditional cyclic neural network, the Transformer network has no input sequence but adopts the idea of parallelization to speed up the operation so that the model can process the next sequence at the same time when the result of the previous sequence has not been revealed. Therefore, in order not to lose order, it is necessary to combine position embedding before inputting the sequence.

In order to convert the image into sequence data that can be processed by the Transformer structure, the two-dimensional image is first processed into blocks (sequence of flattened 2D patches), and then each image patch is flattened into a one-dimensional vector through a linear transformation (full connection layer). At the same time, position coding is introduced, and the position information of the sequence is added. In addition, a classification flag (class) is added before the input sequence data as a learnable embedding vector for outputting classification prediction.

The DeiT model uses distillation to guide ViT to learn from the teacher model, achieving better performance than the teacher model and spending less training overhead than the original ViT.

The method involves adding a distillation token after the input patch tokens. This token is used for computing the first loss function in the learned representation and the label of the teacher model. The representation and ground truth corresponding to the original class token are used for the second loss, and finally, the learning results of the two tokens are used. After linear transformation, they are used together as inferred embeddings.

There are two loss functions called soft loss and hard loss shown given in the formula by Le et al. (2015) and Nguyen et al. (2017), respectively. ℒ g l o b a l = ( 1 − λ ) ℒ C E ( ψ ( Z s ) , y ) + λ τ 2 K L ( ψ ( Z s / τ ) , ψ ( Z t / τ ) ) , (7) ℒ g l o b a l h a r d D i s t i l l = 1 2 ℒ C E ( ψ ( Z s ) , y ) + 1 2 ℒ C E ( ψ ( Z s ) , y t ) , (8) where Z s and Z t are the logits of the student model and teacher model, respectively; y is the ground truth label; y t is the value of the teacher prediction; ψ ( · ) presents the softmax function; ℒ C E presents the loss function of cross entropy; and K L ( · ) is the function calculating the KL divergence.

The overall flow of the electric bike recognition model based on DeiT presented here is shown in Figure 8. First, the high-frequency voltage and current data of all kinds of electrical appliances obtained are preprocessed. Subsequently, the trajectory image is generated, pixelated, and encoded to build a hybrid feature bitmap. Finally, the hybrid bitmap is used as an input to the image classifier, and the DeiT model is used for feature extraction and classification to complete the load recognition task.

Generally, the example verification of the nonintrusive load identification algorithm uses standard load datasets, such as BLUED and PLAID. The existing datasets released by European and American scientific research institutes mainly focus on households in these areas. Table 1 shows the main features of the household load datasets with more number of references.

Unfortunately, these datasets shown in the table are not well-suited for verification in this study. There are three main reasons for this. First, these existing load datasets lack the electric bicycle data. Second, the supply mode, voltage amplitude, and grid frequency for European and American users are quite different from those in China and Southeast Asia. Finally, the cases in which electric bicycle charging event happens under the ON-STATE appliances are also missed in these datasets, so the ability to identify the electric bicycles in more complex situations cannot be tested.

In order to solve the problem of lacking effective load data, a customized load data acquiring device which uses AD7685 from ADI as the core sampling chip, shown in Figure 9, is designed to use in this study. The schematic diagram of our device is shown in Figure 10. The collected data mainly include current, voltage, and active and reactive data at 1.6 kHz. Using this device, more than 507 pieces of data on electric bicycles and nearly 2,340 pieces of data on other household appliances under independent working were recorded separately. Meanwhile, 493 pieces of data on electric bicycles working with other appliances at the same time are also recorded.

The shortcomings of the load types of existing datasets and the amount of data on self-built datasets are both considered. This study adopts part data from UK-DALE which is most similar to the operation of the Chinese distribution network and combines the self-built datasets and UK-DALE as the training set, which contain the electric bicycles under single and superposition working condition. The detailed composition of the training set is shown in Table 2, and the division of the dataset is shown in Table 3. Focusing on identifying electric bicycles, the positive examples in the data set are electric bicycle data, including electric bicycle superposition with other electrical appliances. The counter-examples are various other electrical appliances, including air conditioners and hairdryers. The final DeiT algorithm is a binary classification model.

In this study, the ResNet18, ResNet50, and ViT models are selected as comparative experiments, and Table 4 shows the detailed characteristic of different models. ResNet18 and ResNet50 are deep convolutional neural networks. Compared with other fully connected neural networks, the CNN uses convolutional kernels to greatly reduce the training parameters and has high training efficiency.

It can be concluded from the aforementioned table that DeiT has more model parameters than the CNN but far less than ViT, and the speed of processing images is much faster than that of ViT, while Table 5 shows the training strategy and hyperparameter settings of the model. In addition, two hyper-parameters for DeiT are set as λ = 0.1 , τ = 3 .

Moreover, the hardware environment of the load identification case study is briefly explained. The cases are executed using a 64-bit computer with NVIDIA Quadro RTX 8000 graphics card, Intel(R) CoreTM i5-7300HQ CPU, and 6G DDR4 memory. Also, Windows 10, Python 3.6, and Keras comprise the software environment in this study.

The first case is executed using the testing dataset 1 in Table 3 to prove the effectiveness of this electric bicycle identification when other appliances are in off-state in one household. The results of case 1 are shown in Table 6. The results show that the DeiT model has an accuracy of 98.41% for the identification of electric bicycles without the interference of other electrical appliances, and the results are almost perfect.

Because the data set is relatively small, the loss function of the ViT model does not converge, the model fails completely, and the final accuracy rate approaches random probability. Compared with the traditional CNN deep learning model, the DeiT model has better performance in all four indicators.

Only focusing on monitoring the electric bicycles, the electric bicycle identification model based on DeiT is a binary classification model, explaining whether the turn-on device is an electric bicycle. It presents advantages in the accuracy of identifying compared with the multiclassification model. Figure 11 shows the accuracy bars of the DeiT classifier model with two to seven classes. Also, it is obvious that the accuracy of electric bicycles is decreasing with the increase in classification types.

The second case is executed using the testing dataset 2 in Table 3 to test the accuracy of the electric bicycle identification model when multiple appliances are working together. The results of the model on testing dataset 2 are shown in Table 7. The results show that the identification accuracy of the DeiT model under the superposition condition reaches 96.17%, which is lower than that of the single condition. The main reason is that the fluctuation of the superposition electrical appliance will still have a certain influence, but it still exceeds 95%, which can meet the requirements of NILM.

According to the results of case 2, the ViT model still fails completely, and the accuracy of the electric bicycles under the superposition state of other models is generally reduced, but the DeiT model still achieves the best performance, and the four indicators are better than the CNN.