A Non-Invasive Circuit Breaker Arc Duration Measurement Method with Improved Robustness Based on Vibration–Sound Fusion and Convolutional Neural Network

Abstract

Previous studies have shown that the contact wear estimation of circuit breakers can be based on the accumulative arc duration. However, one problem that remains unresolved is how to reliably measure the arc duration. Existing methods encounter difficulties in implementation and suffer from limited accuracy owing to the impact of the substation environment. To overcome these issues, this article presents a novel, non-invasive method for measuring arc duration that combines vibration–sound fusion and convolutional neural network. The proposed method demonstrates excellent performance, achieving errors below 0.1 ms under expected noise conditions and less than 1 ms in the presence of various forms of noise, transient interference, and even sensor failure. Its advantages include its ability to accurately measure arc duration and its robustness against noise and interference with unknown patterns and varying intensity as well as sensor failure. These features make it highly suitable for practical deployment in substation environments.

1. Introduction

Circuit breakers are critical elements of substations because they are responsible for controlling and protecting the power grid. The increasing integration of distributed generation has led to a higher frequency of switching operations and a greater susceptibility of this equipment to contact erosion and reduced life. To ensure the reliable operation of circuit breakers, the traditional time-based maintenance schedule is gradually shifting to a condition-based maintenance (CBM) schedule due to its lower maintenance cost and higher reliability [1].

The efficacy of CBM strategies is highly dependent on the ability to continuously monitor the condition of switchgear, with particular emphasis on the condition of contact wear in this paper. Common approaches for measuring the contact erosion of circuit breakers include dynamic resistance measurement (DRM) and arc duration/energy-based contact erosion analysis [2]. DRM is a highly effective technique for evaluating the condition of the circuit breaker’s main and arcing contacts [3,4,5,6,7,8]. Specifically, a direct current is applied, and the voltage between contacts during the opening operation is recorded to determine the resistance profile versus separation movement. While DRM provides valuable information on the condition of arcing and main contacts without dismantling, it is limited to off-line deployment. Furthermore, it has been demonstrated recently that contact erosion cannot be reflected in the dynamic resistance curves until the whole contact surface is eroded [7].

The arc duration/energy-based contact erosion analysis is based on the concept that the arcing time [9,10,11,12,13], transferred electric charge [11,13], and arc energy [12,13,14,15,16,17] can be used to ascertain the contact mass loss in each current interruption event. This approach offers a significant advantage over DRM since it can be implemented online, making it more suitable for CBM. The determination of total transferred charge and arc energy relies on the arc voltage, arc current, and arc duration. Typically, the arc current is the line current, which can be obtained from a current transformer (CT), and the arc voltage in a circuit breaker can be simulated using various arc models [18,19,20]. Thereby, the arc duration becomes the essential parameter that must be determined for contact erosion analysis.

A variety of techniques have been developed to measure the arcing time of circuit breakers. The most direct method is to determine the arc initiation time using arc voltage and measure the arc extinction time based on arc current [21]. The arcing time measurement can also solely rely on arc voltage, as proposed in [22]. However, the measurement of arc voltage is challenging to implement in practice due to the introduction of electromagnetic noise from transient recovery voltage (TRV) and the difficulty of accurately measuring arc voltage while withstanding severe TRV [2,17,21,23]. An alternative approach involves using the travel curve and arc current to determine the start and end of an arc, as employed in [11,24]. However, this approach is subject to severe vibration interference during circuit breaker operations, which makes it difficult to achieve satisfactory accuracy [21]. Non-invasive methods for measuring arcing time have gained popularity in recent years due to their ease of integration into the power grid [23]. These means use electric and magnetic fields at very-high-frequency (VHF) and ultra-high-frequency (UHF) bands [21,25] and auxiliary contact timing [23]. Non-invasive arcing detection and contact separation detection using infrared [26] and acoustics [26,27] can also be used to measure the arc duration. However, these techniques have limited applicability in the actual substation environment. For instance, installing infrared and other optical sensors can be challenging [21], and acoustic-based methods can be prone to interference from ambient noise from surrounding power equipment operation [28]. In addition, corona discharge in substations can generate strong electromagnetic interference in the VHF and UHF bands [29,30], and the auxiliary contact timing method requires the installation of auxiliary contacts for obtaining measurements. In summary, existing techniques for measuring arc duration encounter challenges in implementation and often lack adequate consideration of noise and interference present in the substation environment. This highlights the need for the development of a more reliable and robust method for accurately measuring arc duration.

In recent years, the effectiveness of machine learning-based sensor fusion has been demonstrated in circuit breaker fault detection and classification. Recent studies have combined various signals for diagnosis, including vibration and sound [31], coil current and angular displacement [32], coil current and sound [33], vibration, temperature, and travel curve [34], and vibration and coil current [35]. The success of sensor fusion in circuit breaker fault detection and its robustness against noise [36] suggest its potential application to the arc duration measurement in the substation environment, which is largely unexplored. This article presents a non-invasive arc duration measurement method, with a focus on the arc initiation time detection leveraging a convolutional neural network and fusion of vibration and sound. Given the widespread use of wavelet transform in circuit breaker vibration analysis [37,38,39], it is used as an initial step to fuse the vibration and sound at the data level. Based on the current, vibration, and acoustic signals, the method enables accurate and robust arc duration determination in the presence of both noise and transient interference in the vibration and acoustic signals. Furthermore, since the strong electromagnetic interference present in substations can have a detrimental effect on sensor lifespan, the capacity of the proposed method to tolerate sensor failure is also discussed in this paper.

The remaining sections of the paper are structured as follows. In Section 2, the wavelet transform and convolutional neural network utilized in the proposed method are introduced. Section 3 provides a comprehensive overview of the proposed arc duration measurement method. The detailed procedures and results of the experimental validation are presented in Section 4 and Section 5. Section 6 discusses the advantages and limitations of the proposed method, and the contributions of the paper are summarized in Section 7.

2. Wavelet Transform and Convolutional Neural Network

2.1. Wavelet Transform

Wavelet transform (WT) is a powerful mathematical tool used for analyzing signals and images. It is one of the most common time-frequency representations utilized in signal analysis [40]. The main advantage of WT lies in its ability to adjust the time-frequency resolution based on the frequency components present in the signal, enabling a more accurate time-frequency representation [41]. The fundament of WT is the use of wavelets. The formation of orthonormal wavelet functions involves the dilations and translations of a prototype or mother function ψ(t) [42]. The wavelet function can be represented as shown in Equation (1), where a represents the scale parameter and b represents the time parameter. By varying these parameters, the wavelet function can adapt to different scales and positions, allowing for a multi-resolution analysis of the signal [42].

$${\psi }_{ab}(t)=\frac{1}{\sqrt{a}}\psi (\frac{t-b}{a})$$

(1)

The WT then performs signal decomposition by convolving the input signal with a set of wavelet functions, as described in Equation (2). This convolution operation generates a matrix of wavelet coefficients, known as a scalogram [41], which provides valuable information about the distribution of frequencies present in the signal at various temporal locations. By analyzing the scalogram, one can gain insights into the time-varying behavior and spectral characteristics of the signal [42].

$$W_f(a,b)={\int }_{-\mathrm{\infty }}^{\mathrm{\infty }}{\psi }_{ab}(t)f(t)$$

(2)

The choices of prototype function vary and include Morlet, Morse, Meyer, Shannon, and Hermitian wavelets. The determination of an optimal wavelet for specific applications lacks a standardized methodology [43]. To address this issue, a Morse wavelet is proposed and shows the ability to effectively unify a wide range of wavelet types [44]; thereby, it is used in this paper.

2.2. Convolutional Neural Network

A Convolutional Neural Network (CNN) is a deep learning architecture that is specifically designed for image processing tasks. It can automatically learn hierarchical features from images, capturing local patterns and spatial relationships.

A CNN usually consists of several layers, including the convolutional, pooling, dropout, and fully connected layers. In the convolutional layer, the input image is convolved with a set of learnable filters to extract relevant features. Specifically, when a filter is applied to a subarea of an image, it computes a dot product between the filter weights and the corresponding pixels. By scanning the entire image using a sliding window, each filter produces one feature map that captures a distinctive pattern such as edge, texture, and shape. The value at location (i, j) in the kth feature map of the lth layer, denoted as $z_{i,j,k}^l$, is computed by Equation (3) [45]. In these equations, ${\mathit{w}}_k^l$ and $b_k^l$ are the weight vector and bias term of the kth filter of the lth layer, respectively, and ${\mathit{x}}_{i,j}^l$ refers to the input patch centered at location (i, j) of the lth layer [45].

$$z_{i,j,k}^l={{\mathit{w}}_k^l}^T{\mathit{x}}_{i,j}^l+b_k^l$$

(3)

$$a_{i,j,k}^l=ReLU\left(z_{i,j,k}^l\right)=\mathrm{m}\mathrm{a}\mathrm{x}(0,z_{i,j,k}^l)$$

(4)

All feature maps extracted by multiple different filters then undergo non-linear transformation through the application of an activation function. The activation function introduces non-linearities into the CNN, enabling it to learn the complex relationship between the input data and the extracted features. A popular choice for the activation function in CNNs is the Rectified Linear Unit (ReLU), which is shown in Equation (4).

In addition to the convolutional layer, other layers also serve important purposes. Pooling layers perform down-sampling on feature maps while preserving key information. Dropout layers are a regularization technique by randomly dropping out a fraction of the input to zero, which forces the network to learn more robust features and reduces the reliance on individual neurons. Fully connected layers are traditional neural network layers where each neuron is connected to every neuron in the previous layer. They are typically placed at the end of the network (after several convolutional, dropout and pooling layers) and are responsible for making the final predictions.

In recent years, CNNs have gained significant popularity for analyzing time-frequency images, particularly in the domain of vibration and sound analysis [40,41,46,47]. This increasing trend can be attributed to the capability of CNN to effectively address the challenges in time-frequency domain analysis [40]. Specifically, a signal can exhibit a complex distribution in its time-frequency diagram. Relying solely on features extracted based on expert knowledge may result in information loss. Moreover, the presence of noise often leads to the inclusion of irrelevant features alongside the signal-related features in the scalogram. Separating signal-related features becomes impractical when there is a significant overlap between signal-related and noise-related features. CNNs offer a solution by automatically and intelligently identifying features that are relevant to the signal, even in cases where these features are weak and overlapped with noise features. This ability makes it a promising approach for time-frequency analysis. In this study, CNN is employed to process the vibration-sound scalogram and detect the arc initiation time.

3. Arc Duration Measurement

3.1. Problem Analysis

Accurately measuring the arc duration necessitates the precise identification of arc initiation and arc extinction. Detecting the current interruption is the most straightforward approach to determine the arc extinction time [21]. Given the accuracy requirements stipulated in standards such as IEEE C57.13-2016, the current signal measured by CTs is also least affected by the noise and interference. Therefore, the method primarily focuses on detecting the arc initiation time under challenging conditions.

In this study, it is assumed that the arc initiates immediately after the contact separates, and thus, the contact separation time is interpreted as the arc initiation time. The contact separation of the circuit breaker is achieved by the operating mechanism (OM). The primary types of Oms employed include a hydraulic-driven mechanism, pneumatic-driven mechanism, and spring-driven mechanism [48]. To achieve fast switching, regardless of the type of OM used or model of circuit breaker, a substantial amount of energy is required to be stored in advance, such as pressurizing the accumulator or charging the spring. Upon receiving the signal to open, the stored energy is rapidly released, which can lead to a significant vibration and sound. Thus, the arc initiation (contact separation) time can be detected based on the corresponding vibration and sound signals. Figure 1 illustrates the distinct increase in the intensity of aligned vibration and sound signals during a load-switching experiment.

Unlike current signals, vibration and sound signals are more susceptible to significant levels of noise and interference in the substation environment. Additionally, unlike today’s highly reliable CTs, the vibration and acoustic sensors are more prone to sensor failure. These factors present a challenge for accurate arc initiation detection using vibration and sound signals. In this study, the noise in the substation refers to the signals continuously emitted by the monitored circuit breaker, surrounding power equipment, or earth, and the transient interference refers to the emissions generated by adjacent circuit breakers during their load-switching operations. Sensor failure in this context is defined as a fail-stop failure, where a sensor completely ceases to respond and produces zero output, and only one sensor (either vibration or acoustic sensor) will fail.

To achieve an optimal signal-to-noise ratio (SNR) in such a challenging environment, strategic sensor placement is crucial. The vibration sensor can be installed on the enclosure of OM of the monitored circuit breaker, and the acoustic sensor can also be deployed closer to the OM. Furthermore, highly directional sensors like shotgun microphones can be used to suppress noise from side directions.

3.2. General Principle of the Proposed Method

The proposed arc duration measurement method is depicted in Figure 2. Initially, the method remains in a standby state until the supervisory control and data acquisition (SCADA) system requests the circuit breaker monitored by the method to execute a load-switching operation. Upon triggering, the method will analyze the current signal from the CT to determine the current interruption time. It then extracts the vibration and sound data segments preceding this time.

In AC systems, the arc extinguishes at the next current zero-crossing point after the separation of contacts [48]. Therefore, the arc initiation time is expected to be between the previous current zero-crossing point and the current interruption point. Based on this principle, the length of the vibration and acoustic data segment extracted for analysis is set as half of a cycle, for simplicity, 8.5 ms in this study. However, considering that the propagation speeds of vibration and sound are much slower than those of electrical signals, the vibration and sound signals captured in the same period are not synchronized with the current signal. Hence, delays are introduced when extracting the vibration and sound data segment to ensure their alignments with the current signal.

Next, the aligned vibration and sound data undergo data-level fusion using the WT and signal averaging, resulting in the averaged vibration–sound scalogram. This scalogram is then fed into CNN for arc initiation time detection. Finally, according to the arc extinction time determined by the current interruption, the arc duration can be measured.

3.3. Determination of Delays during Data Alignment

The delays of vibration and sound signals are determined by their respective propagation speeds. As electrical signals travel at the speed of light, this study posited that the propagation delay in signal cable is negligible. In cases where the vibration sensor is situated on the enclosure of the OM, the delay is in the order of microseconds, as sound waves travel at km/s in metal. The velocity of the vibration can be calculated utilizing Equation (5), where E represents the Young’s modulus of the material and ρ indicates the material’s density. In contrast, sound travels significantly slower in air. When the sensor is located within 1 m from the circuit breaker, the propagation delay is in the order of milliseconds. Although the speed of sound in air is influenced by the temperature, the variation is negligible for short distances. For instance, if the actual temperature around the circuit breaker is 30 °C while the sound velocity at 20 °C is used to calculate the delay, the error induced by a 1 m distance is only 0.04 ms. Moreover, the error can be further reduced if the temperature error is not such significant or the distance is even closer. Therefore, this study does not consider the error resulting from the data alignment. Figure 1 illustrates the aligned vibration and sound signals during load switching.

$$v=\sqrt{\raisebox{1ex}{$E$}\!\left/ \!\raisebox{-1ex}{$\rho $}\right.}$$

(5)

3.4. Arc Initiation Time Determination

The arc initiation detection process involves multiple steps. Initially, the WT is employed to generate the time-frequency representation of the aligned vibration and sound signals. The utilization of WT allows for signal separation in the frequency domain while preserving essential time domain information. This separation further enables the effective differentiation between the circuit breaker load-switching signal and various forms of noise and interference with different time and frequency characteristics.

Next, the average of the two normalized time-frequency scalograms is computed. This data-level fusion technique can enhance the signal-related features in the two scalograms and suppress the uncorrelated noise and interference. Specifically, the vibration and sound signals are aligned and originate from the same source: namely, the vibration of the monitored circuit breaker. Thus, they possess temporal consistency and a similar frequency spectrum, resulting in a similar distribution in their respective time-frequency images. However, the random noises in vibration and sound signals are uncorrelated, leading to inconsistent distributions within the scalograms. By performing signal averaging, correlated regions remain almost unchanged, while inconsistent regions are suppressed. Figure 3 demonstrates the scalograms and the averaged scalogram of the two aligned signals shown in Figure 1. It can be observed that the signal averaging maintains the intensity of the regions where both vibration and sound signals are stronger in their scalograms, specifically after the contact separation (0 ms) and within the frequency range of 3 to 5 kHz. Meanwhile, the remaining areas with less consistency, which can be considered as noise-related features, are blurred because of the signal averaging.

Ultimately, the averaged vibration–sound scalogram is input into the pre-trained CNN to determine the arc initiation time, even in the presence of noise, transient interference caused by the load-switching of adjacent circuit breakers, and sensor failures.

3.5. General Training Process of CNN in the Proposed Method

The CNN model needs to be trained strategically before it can effectively perform the arc initiation time determination task in challenging conditions, and the designed training process is outlined in Figure 4. First, the measurements of circuit breaker load-switching tests in a clean environment, such as a lab or testing factory, are used as the original data. In cases where load-switching tests are difficult to conduct, no-load testing can be performed as an alternative. This option is viable because the appearance of the arc has little impact on the vibration patterns of the OM [49], and the arc noise is typically much less significant compared to the sound of the OM during load-switching operations. Even if the arc noise is not negligible, it will be attenuated during the data-level fusion process since the arc noise does not appear in the vibration scalogram.

To simulate the specific working environment, the original data are then contaminated by adding noise. Access to noise data is straightforward, as continuous measurements can be conducted directly within the substation. The study recommends carrying out continuous noise measurements after the circuit breaker monitored by the method is put into operation in the substation, spanning a duration of one day or one week. The noise acquired in the substation before the method starts running is referred to as pre-measured noise. Although this approach may introduce a delay in implementing the method, the noise signal obtained during this period can accurately represent the noise present in the actual working condition. Moreover, since noise data are more abundant, multiple sets of noise signals can be respectively superimposed on a single set of original signals to generate several new data, effectively increasing the data volume. This approach, with the subsequent data augmentation step, largely reduces the reliance on a huge volume of original data, thereby minimizing the experiment efforts of the method. However, it is important to note that there is no guarantee that the actual noise level in the substation after the method starts operating will perfectly align with the pre-measured noise level. Furthermore, the appearance of new noise patterns (not seen in pre-measured noise) should be considered. These facets shall be explored in greater detail in the subsequent sections.

Moreover, incorporating interference data into the training process is also crucial. The optimal situation is those signals are already present in the pre-measured noise, as nearby circuit breakers may switch during the measurement period. Noise can still be collected after the method’s deployment, which is referred to as post-measured noise. Once interference data are captured, the entire training process can be re-executed using the updated noise. One another potential approach is to simulate the interference data using the original data, taking advantage of the fact that adjacent circuit breakers are usually of the same model. But it is essential to note that the interference signal could appear different from the original data due to frequency-dependent attenuation during propagation in real-world scenarios.

With the availability of the O, N and I-data, datasets required for training the CNN can be generated through the signal contamination and data augmentation, and the training of the CNN can be completed. The specifics of each step in the training process are introduced in the following Experimental Validation section.

4. Experimental Validation: Dataset Generation and Model Training

To evaluate the method, it is necessary to first build the method (train a CNN model). Therefore, this section provides a detailed example of the dataset generation and model training processes shown in Figure 4. These procedures will slightly differ from the actual application of the method, as they are tailored specifically for evaluation purposes. The specific differences will be mentioned.

4.1. Original Data

A synthetic test circuit is constructed to obtain the current, vibration, and sound during the circuit breaker load-switching operations. The circuit diagram of the test circuit is shown in Figure 5a. To interrupt the alternating current generated by the LC circuit, an EATON medium-voltage vacuum circuit breaker (rated voltage: 7.2 kV) is utilized with S₁ serving as the making switch. The procedure for the load-switching experiment is as follows. Initially, the circuit breaker is in the closed state, while S₁ remains open. Upon closing S₁, the current starts following through the circuit, and after a few milliseconds, the circuit breaker opens to interrupt the current. During the load-switching experiment, the current at node 1 (I₁), the contact voltage difference (V₁₂), the vibration, and the sound are measured using a Rogowski coil, a differential voltage meter, an accelerometer (0–27 kHz) and a shotgun condenser microphone (0–20 kHz), respectively. Figure 5b shows that both the accelerometer and microphone are secured on the aluminum frame to ensure the accurate relative location to the circuit breaker. Additionally, the microphone is mounted on the rail using a shock mount to decouple the vibration wave from the sound wave, as the former arrives earlier due to the greater speed of sound in the metal rails compared to the surrounding air.

The Original Dataset used in this study comprises a total of 100 load-switching experimental data, which serves as the basis for multiple Contaminated datasets. This dataset not only ensures that there is enough information regarding the vibration and sound characteristics during load switching of the circuit breaker but also simulates the scenario where the available data volume is relatively small (dozens of points). For the sake of simplicity, the vibration and sound signals in the Original Dataset are aligned before mixing with the noise and interference, so that the newly generated datasets based on the Original Dataset do not need to be aligned again in the data alignment step of the proposed method. As discussed earlier, raw vibration and acoustic signals are aligned with the current and voltage signals based on their propagation speeds and sensor locations. In this study, the sound speed at 20 °C (343.21 m/s) is used for all experiments, and the speed of vibration is computed using Equation (5). Figure 6 showcases a group of aligned signals, namely I₁, V₁₂, vibration, and sound signals, arranged from top to bottom. The transition of V₁₂ from 0 to 12 V at 4 ms signifies the separation of the contacts (arc initiation), while the subsequent current interruption at approximately 7.4 ms indicates the arc extinction.

4.2. Noise Data

In practice, collecting noise data directly from the substation would be ideal. However, the authors did not have direct access to perform measurements within the substation, so artificial noise is used in this paper as a substitute. To ensure that the artificial noise closely resembles the real noise in the substation, the following analysis on noise characteristics is conducted.

In the case where the vibration sensor is installed on the enclosure of the OM, the OM itself contributes significantly to the overall noise. As reported in the literature, the vibrating frequencies of circuit breakers range from 0 to 0.7 kHz and 1.2 to 3 kHz [50], and spiking noise can also be observed in vibration signals [49]. By carefully selecting the sensor’s placement on the OM, it is possible to reduce the noise impact [51]. In addition to the noise from the OM, vibrations originating from surrounding equipment and busbar can also be captured by the sensor. Their frequencies could fall below 3 kHz, since the frequencies focused by prior studies on the vibration of different power equipment, such as transformer [52], capacitor bank [53], and busbar [54], are all below 3 kHz. Moreover, it is worth noting that seismic waves may introduce noise as well, typically with frequencies below 100 Hz [55].

Acoustic noise is also diverse in the substation. Given that transformers are typically the noisiest equipment in substations [56,57,58], and circuit breakers are often situated near them, the sound of a transformer is considered as the main source of noise. Transformer noise typically falls below 1 kHz [56,57,58]. Another significant source of noise is corona discharge activity, which includes high-frequency components [58] and could overlap with the frequency range of the sound emitted by the circuit breaker during load switching. Finally, the Gaussian noise (also known as “white noise”) is commonly observed in both vibration and sound signals.

Based on the analysis, artificial noise is produced in various ways. For vibration, previous studies have employed Gaussian noise [59] and the combination sets of sine waves at different frequencies [60] to simulate the noise of the circuit breaker vibration signals. In this paper, three types of noises are injected into the vibration signal: (1) a synthetic noise composed of 20 sine waves with random frequencies (under 3 kHz), amplitudes, and phase delays; (2) Gaussian noise; and (3) random spiking noise. For sound, publicly available datasets like https://pixabay.com/ (accessed on 25 April 2023) are utilized. Specifically, the substation sound effect and corona discharge sound effect form the main components of artificial sound noises, and Gaussian noise is also introduced into the signal then. The frequency spectrums of the two sound effects and measured signal are shown in Figure 7. It is shown that the frequency of the substation sound effect is concentrated below 1 kHz, which could be mainly contributed by the transformer, and the corona discharge has higher frequency components.

4.3. Interference Data

Artificial interference is generated by randomly selecting the vibration and sound data from the Original Dataset. However, a distinction arises due to the different spatial distances between the nearby circuit breaker and sensors in comparison to the ones between the monitored circuit breaker and sensors. As shown in Figure 8a, the time required for the vibration and sound emitted by the two circuit breakers to reach the respective sensors differs. Due to the data alignment, the vibration and sound data are advanced by t₁₁ and t₁₂. In this way, the signals from circuit breaker 1 are aligned, but there is still a delay of (t₂₁–t₁₁)–(t₂₂–t₁₂) between the vibration and sound interference from circuit breaker 2. To replicate this delay, a random delay is injected into the vibration and sound signals that are used as interference. Furthermore, the amplitude of the interference signal should be lower than that of the original data due to the substantial power loss of vibration when propagating in the ground, as studied in [61], and the attenuation of the shotgun microphone on the sound coming from the side direction, as depicted in Figure 8b. In the paper, the amplitude of the interference signal is set to be below 30% (specifically, 10%, 20%, and 30%) of the original signal.

4.4. Signal Contamination and Data Augmentation

In practical scenarios, the pre-measured noise data can be directly added to the original data. However, since the paper uses artificial noise, a different signal contamination approach is employed. A previous study [62] mixed the vibration signal and artificial noise according to the SNR with a range from +10 to −4 dB. In this paper, both the vibration and sound signals are mixed with different artificial noise based on Equations (6) and (7). In these equations, V and A represent the vibration and acoustic signals, while S and N represent the original signal and noise, respectively. The coefficient a_ndB denotes the factor by which the noise signal is multiplied when mixing the signal and noise at an SNR of n dB. The Gaussian and spiking noise are consistently mixed with the signal at an SNR of 10 dB, whereas the synthetic vibration noise, substation noise, and corona discharge noise are mixed at varying SNRs. The chosen SNR values include 5 dB, 2 dB, 1 dB, −1 dB, −2 dB, and −5 dB. As mentioned earlier, there is a possibility that the actual noise level encountered after the method starts working exceeds the level of pre-measured noise. Therefore, in this paper, the 5 dB case is used to simulate the pre-measured noise or N-data, while the remaining cases are used to assess the performance of the method when the noise level significantly surpasses the expectation. Figure 9a,b illustrate several instances of vibration and sound noise as well as the resulting contaminated vibration and sound signals when the SNR is −1 dB.

$$V_{contaminated-n\mathrm{d}\mathrm{B}}=S_V+a_{n\mathrm{d}\mathrm{B}}^{\left(1\right)}*N_{synthetic}+a_{10\mathrm{d}\mathrm{B}}^{\left(2\right)}*N_{gaussian}+a_{10\mathrm{d}\mathrm{B}}^{\left(3\right)}*N_{spiking}$$

(6)

$$A_{contaminated-n\mathrm{d}\mathrm{B}}=S_A+a_{n\mathrm{d}\mathrm{B}}^{\left(1\right)}*N_{substation}+a_{n\mathrm{d}\mathrm{B}}^{\left(2\right)}*N_{corona}+a_{10\mathrm{d}\mathrm{B}}^{\left(3\right)}*N_{gaussian}$$

(7)

Artificial interference is introduced into the original signals by directly injecting it at a random time point. Figure 9c depicts the signals before and after the introduction of the interference, where their amplitudes are set at 30% of the original signals. It is noticed that the interference initiates earlier than the original signals, and there is a delay between the vibration and sound interference.

According to the signal contamination rules detailed above, each pair of vibration and sound signals (vib-sound pair) from the Original Dataset is first split into three subsets: the training set, validation set, and testing set, with a ratio of 60%:20%:20%, respectively, and then mixed with different levels of artificial noise and interference data to produce multiple Contaminated Datasets. This data splitting is only needed for evaluation. In practice, a testing set is not required.

All datasets generated in this study are listed in

Table 1. List of all datasets.

Dataset		Total Number of Injected Artificial Noise and Transient Interference	Total Number of the Vib-Sound Pair in the Dataset	Total Number of the Vib-Sound Pair after Data Augmentation
Original Dataset		N/A	100	100 × 200 = 20,000
Contaminated Datasets	Noise Dataset (5 dB)	400 × (5 dB artificial noise)	100 × 400 = 40,000	40,000 × 2 = 80,000
	Noise Dataset (2 dB to −5 dB)	20 × (ndB artificial noise), n = 2, 1, −1, −2, −5	Each dataset: 100 × 20 = 2000, training set (60%), validation set (20%), testing set (20%)	Each dataset: 2000 × 2 = 4000, training set (60%), validation set (20%), testing set (20%)
	10% Interf. * Dataset (5 dB, 1 dB, −5 dB)	20 × (ndB artificial noise + 10% artificial interf. *), n = 5, −1, −5
	20% Interf. * Dataset (5 dB, 1 dB, −5 dB)	20 × (ndB artificial noise + 20% artificial interf. *), n = 5, −1, −5
	30% Interf. * Dataset (5 dB, 1 dB, −5 dB)	20 × (ndB artificial noise + 30% artificial interf. *), n = 5, −1, −5

* Interf. is the abbreviation for interference.

. For example, to generate the 20% Interference Dataset (5 dB), each vib-sound pair from the Original Dataset is added with 20 different 5 dB artificial noise sources and 20 different 20% interference data. This results in a total of 100 × 20 = 2000 contaminated vib-sound pairs. A dedicated signal contamination program is developed to guarantee that each vibration–sound pair within each Contaminated Dataset possesses unique noise and interference components. Finally, data augmentation is performed using an 8.5 ms random extraction window, as shown in Figure 10. This window randomly selects multiple 8.5 ms data segments, and the arc initiation time is required to be within this window. In addition to increasing data volume, this random data extraction can also simulate the real-world scenario where contact separation may occur at any time point within the input data. The total number of vib-sound pairs in each dataset after data augmentation is also summarized in Table 1.

4.5. Model Training

This method utilizes a two-dimensional three-layer CNN to ascertain the arc initiation time based on the averaged vibration–sound scalogram. Its architecture is shown in

Table 2. Architecture of the CNN model.

Layer Name	Characteristic Description
Input layer	Input size (55, 340, 1)
Convolutional layer 1	4 convolutional (5, 40) filters
Pooling layer 1	maxpooling
Dropout layer 1	0.1 dropout rate
Batch normalization layer 1
Convolutional layer 2	8 convolutional (5, 20) filters
Pooling layer 2	maxpooling
Dropout layer 2	0.1 dropout rate
Batch normalization layer 2
Convolutional layer 3	16 convolutional (5, 10) filters
Pooling layer 3	maxpooling
Dropout layer 3	0.1 dropout rate
Batch normalization layer 3
Flatten layer
Fully connected layer	Layer size (128, 1)
Output layer	Output size (1, 1)

. The adoption of wide filters in CNN can mitigate the noise impact, as reported in prior research [62]. Moreover, batch normalization is applied after each convolutional layer, leading to an improved training performance [63].

As mentioned earlier, each dataset is split into three subsets: the training set, validation set, and testing set. To mitigate the impact of random variations in the data splitting on the method’s performance, five different train–validation–test splits are used to ensure that training and testing processes are reliable and statistically sound.

Table 3. Final training, validation, and testing sets of the CNN model.

Final Training Set	Final Validation Set	Final Testing Set
training set of Original Dataset + training set of Noise Dataset (5 dB)	validation set of Original Dataset + validation set of Noise Dataset (5 dB)	testing set of all Contaminated Datasets

highlights the composition of the final training and validation sets, which exclusively consists of data from the Original Dataset and Noise Dataset (5 dB). The final testing set, on the other hand, is comprised of testing sets from all Contaminated Datasets. The Original Dataset and Noise Dataset (5 dB) correspond to O and N, respectively, in Figure 4. However, the I-data (interference) are not included in the training set of the model. This modification is made specifically in this study to enable a comprehensive evaluation of the method. As discussed earlier, new noise patterns may emerge in real-world situations. Since the interference data can be considered as a new noise pattern, it is utilized to not only evaluate the robustness of the method to the interference but also assess the effectiveness of the method in dealing with new noise. Once the training and validation sets are determined, the vib-sound pairs in each set are used to generate the averaged vibration–sound scalograms, which are the input data for the CNN. The label assigned to each input scalogram is its arc initiation time, which is determined based on its corresponding V₁₂.

5. Experimental Validation: Case Studies

In this study, the assumption is made that there is no error in determining the arc extinction time using the current signal. Therefore, any errors that arise are specifically related to the arc initiation detection process. To evaluate the performance of the proposed method under various conditions, different testing sets are input to the method.

Since each vib-sound pair in the testing sets is already aligned, they are directly used to generate the averaged vibration–sound scalogram, which is then fed into the CNN. The calculated arc initiation time by the method is compared with the true value, which is determined based on the corresponding V₁₂. To quantify the accuracy of the method, the root mean squared error (RMSE) is computed by Equation (8), where $y_i$ represents the actual arc initiation time of the ith vib-sound pair in the testing set, and ${\widehat{y}}_i$ refers to the arc initiation time estimated by the method based on the ith input. Since five different splits are used, the training and testing processes are repeated five times.

$$\mathrm{R}\mathrm{M}\mathrm{S}\mathrm{E}=\sqrt{\frac{1}{N}{\sum }_{I=1}^N{(y_i-{\widehat{y}}_i)}^2}$$

(8)

5.1. Expected Noise Case

The proposed method is initially tested using the testing set of the Noise Dataset (5 dB). The results, as shown in

Table 4. RMSE of the method in expected noise cases.

No. of Split	1	2	3	4	5
Error (ms)	0.069	0.077	0.065	0.071	0.069

, indicate that the errors of the method (each is trained and tested with different splits) are all below 0.1 ms. Upon further analysis, it has been observed that the average error is 0.0702 ms. Considering that half of a cycle in a 60 Hz power system is around 8.33 ms, the percentage error is less than 1%. This indicates that the proposed method achieves a millisecond-level accuracy, making it highly suitable for the precise arc duration measurement. Since the CNN model is trained on the training set of the Original Dataset and Noise Dataset (5 dB), it is not surprising that the error is low. However, it also means that if the pre-measured noise contains sufficient knowledge (time and frequency characteristics) of the actual noise in the substation, the proposed method can measure the arc duration with extremely high accuracy.

5.2. Strong Noise Case

The performance of the proposed method is then evaluated using the testing sets of datasets with stronger artificial noise.

Table 5. RMSE of the method in strong noise cases.

SNR (dB)		2	1	–1	–2	–5
Error (ms)	No.1	0.094	0.104	0.143	0.162	0.297
	No.2	0.094	0.103	0.122	0.138	0.275
	No.3	0.078	0.092	0.106	0.13	0.291
	No.4	0.075	0.073	0.109	0.102	0.275
	No.5	0.077	0.111	0.13	0.196	0.296
	Mean	0.0836	0.0966	0.122	0.1456	0.2868

summarizes the error of the method when tested by Noise Datasets with varying SNRs, ranging from 2 to –5 dB. The results demonstrate that the method can still maintain extremely high accuracy when the noise level is slightly higher than expected (the level of pre-measured noise), and even under the most severe condition (–5 dB), the error remains below 0.3 ms. It is worth mentioning that incorporating the datasets with higher noise levels in the training process can lead to an improvement in accuracy. However, it is crucial to consider the possibility of encountering stronger noise in real-world scenarios. Since the noise energy in the –5 dB case is already 10 times higher than the energy in the 5 dB case, the results prove the robustness of the proposed method in accurately detecting the arc duration, even when the noise level is beyond expectations.

This satisfied performance can be attributed to the training of CNN on the Noise Dataset (5 dB). Because, even if the noise waveform used to generate Noise Dataset (5 dB) are distinct from and weaker than the noise waveform generating other Contaminated Datasets, they still share a similar frequency spectrum as they originate from the same source, such as the transformer and corona discharge. Training on the Noise Dataset (5 dB) allows the CNN model to recognize the underlying noise patterns, even if the patterns are weak. Therefore, the method can still maintain accuracy when facing datasets with stronger noise. Moreover, the suppression on the noise-related features due to the vibration–sound fusion also contributes to this result, as the vibration and sound noise are uncorrelated.

5.3. Transient Interference Case

Table 6. RMSE of the method in cases with both interference and noise.

SNR (dB)		5			−1			−5
Intensity		10%	20%	30%	10%	20%	30%	10%	20%	30%
Error (ms)	No.1	0.08	0.339	0.666	0.152	0.412	0.858	0.379	0.549	0.902
	No.2	0.093	0.346	0.665	0.194	0.36	0.98	0.318	0.543	0.891
	No.3	0.089	0.316	0.911	0.204	0.35	0.755	0.356	0.7	1.094
	No.4	0.061	0.279	0.548	0.19	0.396	0.882	0.271	0.614	0.902
	No.5	0.082	0.265	0.756	0.158	0.38	0.729	0.322	0.512	1.006
	mean	0.081	0.309	0.7092	0.1796	0.3796	0.8408	0.3292	0.5836	0.959

presents the average error of the method under varying noise levels and interference intensities. The results demonstrate that when the interference intensity is low or the noise level is not beyond expectation too much, the method achieves an error below 0.4 ms, which is less than 5% of a half of a cycle. Moreover, even in scenarios characterized by strong interference intensity or severe noise levels, the method maintains an error around 0.95 ms. These results show the robustness of the method in detecting the arc duration in the presence of interference from nearby circuit breakers. More importantly, it should be emphasized that the datasets containing both artificial noise and interference are not used in the training process. This simulates real-world situations where previously unobserved interference or noise and observed noise emerge together. In this case, the method still exhibits a reasonable accuracy, demonstrating its robustness in accurately measuring the arc initiation time even in the presence of novel interference or noise as well as the noise which is already learned but much stronger.

In practical applications, it is beneficial to include both N and I-data in the training process to enhance the performance of the method. Moreover, the results highlight that as long as the intensity of interference is carefully controlled, even if the I-data are not present in the pre-measured noise, the method can still accurately measure arc duration in the presence of interference. Considering the distances between circuit breakers, achieving a 30% attenuation due to the power loss of vibration in the ground is relatively feasible [57]. In the case of sound signals, a 30% amplitude attenuation corresponds to a reduction of –10 dB. Consequently, the utilization of a sound probe with strong directivity becomes imperative.

5.4. Sensor Failure Case

The robustness of the proposed method to sensor failures is examined with modified testing sets. The modification involves randomly replacing either the vibration or sound signal with zero for each vib-sound pair in the testing sets, and the probability of replacing the vibration signal is set at 50%. The outcomes of the evaluation are listed in

Table 7. RMSE of the method in sensor failure cases.

SNR (dB)		5	2	1	−1	−2	−5
Error (ms)	No.1	0.255	0.41	0.341	0.515	0.689	0.931
	No.2	0.297	0.379	0.426	0.572	0.626	0.872
	No.3	0.208	0.277	0.4	0.557	0.64	0.903
	No.4	0.23	0.304	0.422	0.511	0.596	0.941
	No.5	0.27	0.432	0.404	0.467	0.632	0.87
	Mean	0.252	0.3604	0.3986	0.5244	0.6366	0.9034

. For the Noise Dataset (5dB), the error increases to approximately 0.25 ms due to sensor failures. When the noise level does not surpass the expectation a lot (2 dB and 1 dB), the method still manages to maintain an error within 0.4 ms. Under the most severe condition (SNR = –5 dB), the error remains within 1.0 ms. Despite the apparent degradation in accuracy due to sensor failures, the method retains its ability to measure the arc duration and maintain a reasonable level of precision when the noise level is not significantly higher than expected. This performance renders it suitable for deployment in the substation environment where sensor reliability may be an issue.

6. Discussion

6.1. Result Evaluations

The above results demonstrate the ability of the proposed method to accurately detect the arc duration while being robust to various sources of noise, transient interferences from nearby circuit breakers, and sensor failures. Specifically, the results can be categorized into four distinct scenarios:

Full knowledge of noise: in this scenario, a systematic understanding of the noise characteristics in the working environment is offered by the pre-measured noise or post-measured noise. The method demonstrates exceptional ability in accurate arc duration measurement with the error being less than 0.1 ms.

Full knowledge of noise patterns but not noise level: in this situation, the actual noise patterns, such as the frequency spectra, match the pre-measured noise, but the actual noise level can significantly exceed expectations. The method can still maintain a high level of accuracy, with the error being less than 0.3 ms, demonstrating robustness in handling more substantial levels of noise.

Incomplete knowledge of noise and interference: in this case, unencountered noise or interference can appear with the noise with well-known patterns together. If the original noise level is not significantly beyond expectation or the intensity of new noise or interference is well controlled, the error of less than 0.4 ms can be achieved. Even if the observed noise is much stronger than expected and the high-intensity noise or interference with new patterns appear, the method can still detect the arcing time with an error of around 0.95 ms. The results prove the robustness of the method against new noise or interference patterns, which is particularly valuable as it eliminates the need for extensive knowledge about the specific operating environment.

Sensor failure: Even in the event of a sensor failure where the actual noise level is notably higher than expected, the method remains capable of measuring the arc duration with the error being less than 1.0 ms.

The authors believe that the integration of data-level fusion and CNN plays a crucial role in the accuracy and robustness exhibited by the proposed method. Firstly, the use of an averaged vibration–sound scalogram in the data fusion process effectively preserves signal-related features while attenuating noise- and interference-related features. This step significantly facilitates the identification of signal-related features. Secondly, the training process of the CNN also contributes to an accurate recognition of signal-related features. This is because the training dataset comprises not only the original data but also the contaminated data. The Original Dataset allows the CNN model to learn the complete set of signal features. Additionally, the Noise Dataset (5 dB) enables the CNN model to distinguish between the signal-related features that remain constant among inputs and the noise-related features that keep changing among inputs. This enables the method to understand the difference between signal and noise and thus gain resistance to stronger noise with unknown patterns.

6.2. Potential Capabilities of the Proposed Method

An additional advantage of the proposed method is its potential for performance improvement. Specifically, the collection of noise data can continue, and the post-measured noise can be used to continually update the Contaminated Datasets. Subsequently, the CNN model can be periodically fine-tuned using the new datasets, thereby enhancing the knowledge of the working environment. This approach is also valuable when changes in the substation environment happen, such as the replacement of surrounding equipment, as the method can adapt to the new noise characteristics due to the environment changes.

Furthermore, the proposed method can be adapted to detect the closing time of the circuit breaker given that both the closing and opening actions of the circuit breaker generate significant vibration and sound signals. The closing time also holds crucial significance in the condition monitoring of circuit breakers, as it enables the assessment of parameters such as closing simultaneity, closing duration, and closing speed [59].

6.3. Limitations of the Proposed Method

The authors acknowledge that the proposed method is associated with some limitations. Potential solutions are proposed, aiming to inspire and guide future research endeavors to address the challenges in this field.

First, the method is reliant on the availability of original data of the circuit breaker. The paper proves the applicability of the method with a small data volume, but conducting dozens of tests for each circuit breaker can still be complex and time-consuming. Fortunately, recent advancements in artificial intelligence provide promising avenues to address this limitation. One solution is the utilization of various data augmentation methods to increase the data volume. In this study, the data volume has been considerably expanded by using noise superposition and random window extraction. Additionally, for time series, decomposition-based methods, statistical generative models, and learning-based methods can generate a significant amount of realistic data [64]. By leveraging such techniques, the requirement for a large volume of original data can be reduced effectively. Furthermore, transfer learning can be employed to mitigate the data volume requirements, which is a machine learning technique that allows knowledge acquired from one task to be utilized in a related task. For example, in image classification, the knowledge gained while recognizing cars can be applied to recognize trucks. Similarly, the knowledge from one circuit breaker can be used to determine the arc initiation time for other similar circuit breakers (e.g., of the same type). Specifically, the proposed method is first built based on the data of one source circuit breaker. Then, for each target circuit breaker, the pre-trained CNN can be fine-tuned using the limited data specific to that target circuit breaker. This approach allows the method to adapt its knowledge to the new target, enabling arc duration measurement with limited data availability. Previous studies have demonstrated the successful application of transfer learning through fine tuning with limited data [65].

Second, a dedicated set of sensors is required for each circuit breaker, which is not cost-effective for wide applications. To mitigate the cost issue, blind source separation algorithms like Overcomplete Independent Component Analysis (ICA) [66] can disentangle the signals from multiple circuit breakers in distinct locations using a fewer number of sensors. Furthermore, the CNN model can be trained to accurately ascertain the arc duration for each circuit breaker based on the separated signals. This approach is a potential way to effectively reduce the number of sensors required for multiple circuit breakers.

Third, arc reignition is not considered in this method. Since the method can be modified to detect contact closing/reclosing time and the arc restrike time can also be determined by analyzing the current waveform, the additional arc duration can be determined by (contact reclosing time–arc restrike time). A more comprehensive scheme will be required in the future to address this case.

7. Conclusions

This article presents a non-invasive arc duration measurement method based on vibration–sound fusion and convolutional neural network. The proposed approach can accurately determine the arc duration in the challenging substation environment. The performance of the method is summarized as follows. (1) When the CNN model of the method obtains complete characteristics of substation noise, the error of the method remains below 0.1 ms. (2) In scenarios where the CNN model only obtains the noise patterns while the intensity of actual noise surpasses expectations, the error remains under 0.3 ms. (3) When severe unknown noise or interference from nearby circuit breakers appear and the intensity of known noise patterns surpasses expectations, the method still maintains an error below 1.0 ms. (4) In the event of sensor failure where the known noise patterns are stronger than expectations, the error is below 1.0 ms. These capabilities demonstrate the suitability of the method for deployment in the substation environment.

The main contributions of this paper include the following. (1) It introduces the use of sensor fusion in arc duration measurement, which had not been explored in previous studies. (2) It considers the impact of the substation environment on the performance of non-invasive arc duration measurement methods, filling a research gap in this area. (3) It proposes a method exhibiting robustness to noise, interference, and sensor failure, setting it apart from existing arc duration measurement means.

Finally, the authors elaborate on the limitations of the proposed method, and promising solutions are proposed.

8. Patents

One PCT application [67] and one U.S. provisional patent [68] are associated with this paper.