## 1 Introduction  
With the development of society and economy, the demand of urban residents for electricity is growing, more and more substations are constructed near or even in residential areas, and the noise generated by the operation of power equipment in the substations has a serious impact on the daily life of the residents [1]. Noise generated by power equipment can be divided into transformer vibration radiation noise, transformer cooling system noise, corona discharge noise, and other mechanical noise from the operation of mechanical equipment [2; 3; 4]. And the transformer vibration radiation noise excited by electromagnetic forces can reach up to approximately 90 dBA, making it the primary noise source in substations [2; 5; 6; 7]. For a substation with multiple-transformer equipment, in order to realize vibration and noise reduction, we often need to develop vibration and noise reduction design projects (e.g., high-quality silicon steel sheets are used as the core material during manufacturing, and vibration damping bases or soundproof panels are installed after manufacturing) for transformers one by one, which can effectively reduce transformer radiation noise, but the cost is high [6; 8]. If we can separate the radiated noise of multiple transformers with the same spectral characteristics and clarify their noise contributions, we are able to develop vibration and noise reduction design only for the transformer that is the main source of noise, which greatly reduces the cost of substation environmental noise management and is of great significance for the management of substation environmental noise. At present, there have been many investigations on the separation of different types of substation noise. For example, [PERSON] et al. [9] realized the separation of transformer intrinsic vibration noise and other noises using a vibro-acoustic coherent analysis separation technique. [PERSON] et al. [3] used the wavelet packet analysis method combined with spectral subtraction speech enhancement technology to realize the separation of intrinsic noise, cooling device noise, and corona noise. [PERSON] et al. [10] developed a new method for measuring the noise emitted by substations, achieving the separation of substation noise from background noise. [PERSON] et al. [11] proposed a method for separating acoustic signals of Ultra-High Voltage (UHV) shunt reactors based on beamforming and uncertain blind source separation. However, the noises separated in the above investigations are noises with obvious spectral differences. The vibration noises generated by multiple transformers in a substation under the same electromagnetic excitation often have the same spectral characteristics, and the strong coherence of noises with the same frequency leads to difficulty in separating them. To our best knowledge, there have been rare papers that show how to separate the same type of noises with same frequency from different transformers. Phase conjugation (PC) in the frequency domain is equal to time reversal (TR) in the time domain, both of which can realize reverse propagation of acoustic waves and adaptive focusing of acoustic sources. PC or TR is used for acoustic field reconstruction and focusing imaging of acoustic sources [12]. The phase conjugation or time reversal process includes conjugating received frequency-domain signals or reversing received time-domain signals emitted from a source by a receive array and transmitting acoustic signals using the conjugate or time-reversed data as source excitations from a transmit array co-located with the receive array [13] (p. 191). Commonly used phase conjugations are monopolar phase conjugation (PC/M), which is based on sound pressure measurements and constructed with monopole sources; dipolar phase conjugation (PC/D), which is based on sound pressure gradient measurements and constructed with dipole sources; and perfect phase conjugation (PC/P), which is based on sound pressure and its gradient measurements and constructed with monopole and dipole sources [14].