Frequency Synchronization and Signal Acquisition
When using an acoustic camera, its PRPD detection frequency must first be set to match that of the equipment under test.
The equipment being tested is typically in operation within the power grid, and its fundamental frequencies are predominantly 60 Hz, 50 Hz, or 16.7 Hz (railway systems).
An acoustic camera detects the spatial distribution of ultrasonic intensity and plots the acoustic intensity signal across time and frequency. Methods such as circular mean, von Mises distribution, and phase histograms are used for central phase estimation. Meanwhile, the PRPD pattern is constructed using maximum likelihood estimation to obtain a probabilistic model of the energy distribution, yielding a maximum log-likelihood value that can be used for subsequent classification or thresholding.
Mathematical Method: Maximum Likelihood Phase Alignment
Assume a set of partial discharge pulses has been collected:
where:
If the power frequency is (e.g., 50 Hz), the phase corresponding to each pulse can be written as:
The key unknown quantity here Δϕ is , i.e., the phase offset.
Consider a certain class of PRPD patterns as a probability distribution , , which represents the probability of a PD pulse occurring near phase and amplitude . Given a specific phase offset Δϕ , the joint probability of all observed pulses is:
In practice, the logarithm is taken to avoid numerical underflow:
Maximum likelihood estimation seeks the that maximizes this log-likelihood:
Intuitive Understanding
The PRPD pattern is continuously cyclically shifted along the phase axis. The shift angle that makes the current pulses best match the reference distribution is taken as the optimal phase alignment.
Probabilistic Modeling of Partial Discharge Patterns
Phase Distribution with von Mises Mixture
Common types of partial discharge include positive corona, negative corona, surface discharge, and floating discharge. Their discharge characteristics are well defined and typically concentrated around two phase regions, conforming to the von Mises distribution—that is, their discharge models follow a normal distribution on a circular variable.
Hence, the phase distribution can be expressed as:
Noise Separation and Clean Energy Map
By combining field data with the two-dimensional probability histogram of the PRPD, a standard energy distribution map can be obtained, effectively filtering out impulsive noise and yielding a clean distribution probability for the measurement point:
where:
Bayesian Estimation and Defect Classification
Prior Distribution
P(μ)
In further signal processing, a Bayesian estimation method with prior information is introduced to reduce systematic bias. The PRPD recognition algorithm thus becomes a probability estimation problem during measurement.
Bayesian estimation is a statistical inference method. Its core concept is not to find a single fixed parameter value, but to treat the parameter to be estimated as a random variable, using a probability distribution to describe the knowledge about that parameter.
This method relies on a core formula: Bayes' theorem.
represents the parameter to be estimated (e.g., the average height of a population).
D represents the observed data.
P() is the Prior Distribution: The initial probability assessment of the parameter before observing any data.
is the Likelihood Function: The probability of observing the data D given the parameter . It describes how much the data supports different parameter values.
P(|D) is the Posterior Distribution: The updated probability assessment of the parameter after combining the prior knowledge with the new observational data. This is the final output of Bayesian estimation.
Here is the estimation visualization for a cse like observed mean as 1, prior mean as 1.4, Prior Std Dev as 1, and with a 10 samples size. 
Here is the estimation visualization for a cse like observed mean as 1, prior mean as 1.4, Prior Std Dev as 1, and with a 80 samples size. 
With sample numbers increase the ratio of currenction will be increased. so a circle, the camera gathering more than 50 times, so it can recognize the PRPD with a high accurrancy.
The algorithm assumes four defect categories: corona discharge, surface discharge, floating discharge, and noise (particle discharge). Each category has its own PRPD distribution, so a standard probability distribution can be used as the likelihood function for modeling, and the final detection result is obtained through Bayesian estimation.
Why Positive and Negative Corona Cannot Be Separated
It should be noted that while positive and negative corona can be physically distinguished, the acoustic camera lacks a voltage polarity reference and cannot determine the absolute voltage zero-crossing. Therefore, in the practical recognition algorithm, positive and negative corona are unified into a single “corona discharge” class. This is precisely why an acoustic camera cannot differentiate between negative and positive corona. Nevertheless, even with this merging, the acoustic camera can still provide high-confidence results for the overall detection of corona-type discharges.
AI-Based Robust Alignment and Anomaly Identification
To further enhance system robustness in complex field environments, artificial intelligence is introduced to handle challenges such as noise interference, multi-source discharge superposition, sensor variability, and unstable phase references. The AI model can directly output the phase offset Δϕ , a confidence score, the defect category, and an indication of whether multi-source superposition is present.
Retaining the “Uncertain” State
The system retains an “uncertain” state: when the PRPD pattern is too sparse, the noise level is excessively high, the defect type is unknown, or multi-source superposition is evident, the model does not force an alignment. Instead, it returns a low confidence or rejects the judgment, thereby avoiding misclassification.
Self-Supervised Learning for Phase Restoration
During the training phase, a self-supervised learning strategy is adopted to automatically construct large-scale samples: artificial random cyclic shifts (e.g., , , ) are applied to the PRPD patterns, and the model is tasked with predicting this offset. This provides abundant training data without manual labeling and enables the model to learn to recover the true phase from perturbations.
Differentiable Phase Shift Layer
In terms of model architecture, a differentiable phase shift layer (analogous to a circular shift structure in a spatial transformer network) can be embedded, allowing the network to automatically search for the optimal phase translation during forward propagation so that the input pattern best matches the internal reference template, thereby achieving end-to-end phase alignment.
Phase-Invariant Classification
When the objective is only to identify the defect type and not to recover the absolute phase, a phase-invariant classification strategy can be employed. During data augmentation, the PRPD patterns are randomly rotated, forcing the model to learn “shape features” that are independent of absolute phase position. This yields a classifier insensitive to phase rotation, capable of accurately distinguishing defect types even without precise alignment.
