Photovoltaic panel vibration monitoring method based on heterogeneous fusion network communication
By introducing a frequency domain correction method based on local relative timestamps and relative transmission delay differences into photovoltaic power plants, the problem of asynchronous vibration data from sensor nodes in photovoltaic power plants is solved, enabling efficient and accurate vibration anomaly localization, and making it suitable for online monitoring of large-scale photovoltaic power plants.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- ZHUHAI HUACHENG ELECTRIC POWER DESIGN INST CO LTD
- Filing Date
- 2026-04-16
- Publication Date
- 2026-06-19
AI Technical Summary
In large-scale photovoltaic power plant scenarios, the number of sensor nodes is large and widely distributed. The time synchronization problem of vibration data in heterogeneous communication networks leads to inaccurate frequency domain analysis results. Existing time domain interpolation resampling methods have a large computational load and are prone to introducing errors, making it difficult to balance real-time performance, accuracy and engineering deployment costs.
By introducing local relative timestamps and relative transmission delay differences, a frequency domain phase correction factor is constructed to perform cross-spectral density correction. Combined with coherence function values, vibration abnormality areas are located on the photovoltaic array topology, and data is transmitted using LoRa and Wi-Fi heterogeneous communication protocols.
It enables efficient and reliable joint analysis of vibration data in heterogeneous networks, improves analysis accuracy and stability, reduces computational burden, and is suitable for online monitoring of large-scale photovoltaic power plants.
Smart Images

Figure CN122026618B_ABST
Abstract
Description
Technical Field
[0001] This application relates to the field of cloud-edge collaborative technology, and more specifically, to a method for monitoring the vibration of photovoltaic panels based on heterogeneous fusion network communication. Background Technology
[0002] As the installed capacity of photovoltaic power plants continues to expand, photovoltaic arrays are subjected to complex operating conditions such as wind loads, temperature differences, and equipment operation disturbances. This can easily lead to problems such as loosening, fatigue, and deformation of the photovoltaic panels, their supports, and connectors. If these problems are not detected in time, they may further cause abnormal stress on the modules, reduced power generation efficiency, and even localized structural damage. Therefore, vibration monitoring of photovoltaic panels and the identification of abnormal areas have become important technical directions in the structural health monitoring of photovoltaic power plants. In existing technologies, multiple vibration sensors are typically deployed on the surface of the photovoltaic panels or at key locations on the supports. Vibration signals are collected by a terminal and uploaded to a gateway or backend system. The data from multiple nodes are then jointly analyzed to determine whether there are abnormal vibration locations within the array.
[0003] However, in large-scale photovoltaic power plant scenarios, the number of sensor nodes is large and their distribution is wide. Low-power, long-range wireless links are often used to transmit data between the terminal and the gateway, while a broadband link is used for backhaul between the gateway and the backend. Under such heterogeneous communication network conditions, data from different nodes is easily affected by factors such as channel access contention, transmission delay differences, and local clock frequency deviations during the upload process, making it difficult to maintain accurate time alignment of vibration data from multiple nodes. For applications requiring joint frequency domain analysis such as cross-spectral density and coherence, time asynchrony directly affects the accuracy of the analysis results, thereby reducing the reliability of anomaly localization.
[0004] Existing methods typically use time-domain interpolation and resampling to align data from different nodes before performing frequency-domain analysis. However, this method is not only computationally intensive and requires high embedded processing resources on the gateway side, but it may also introduce problems such as spectrum leakage and truncation errors during interpolation and resampling, making it difficult to balance real-time performance, accuracy, and engineering deployment costs.
[0005] Therefore, there is an urgent need for a technical solution that is suitable for multi-node vibration monitoring of photovoltaic panels and can achieve efficient and reliable joint analysis under heterogeneous integrated network communication conditions. Summary of the Invention
[0006] This application provides a photovoltaic panel vibration monitoring method based on heterogeneous converged network communication, which at least solves some of the technical problems existing in the related technologies described above.
[0007] According to a first aspect of the embodiments of this application, a method for monitoring the vibration of photovoltaic panels based on heterogeneous converged network communication is provided, including:
[0008] After each sensor terminal completes vibration data acquisition and processing within the same acquisition cycle, it reads the count difference between the start time and the current time of the free-running timer in its microcontroller unit as a local relative timestamp, and sends the local relative timestamp to the gateway base station along with the uplink data packet.
[0009] The gateway base station receives uplink data packets from each sensor terminal within the same acquisition period and the same logical group, records the reception time of each uplink data packet and extracts the local relative timestamp; for any node pair, the relative transmission delay difference of the node pair is obtained by subtracting the difference between their local relative timestamps from the difference between their reception times.
[0010] Based on the relative transmission delay difference, a frequency domain phase correction factor is constructed at each discrete frequency point. The phase angle of the frequency domain phase correction factor at each discrete frequency point is the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference.
[0011] The frequency domain phase correction factor is multiplied at each frequency point by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair to obtain the corrected cross-spectral density.
[0012] Based on the corrected cross-spectral density and the autospectral density of each node in the node pair, the coherence function value of the node pair is calculated, and the vibration anomaly region is located according to the spatial distribution of the coherence function value on the photovoltaic array topology.
[0013] As an optional solution, each sensor terminal transmits the uplink data packets with the gateway base station using the LoRa communication protocol, and the gateway base station transmits the corrected cross-spectral density or the coherence function value with the cloud server via WIFI.
[0014] As an optional approach, the gateway base station records the relative transmission delay difference of the same node pair in multiple consecutive acquisition cycles. A linear regression is performed using the cumulative running time corresponding to each acquisition cycle as the independent variable and the corresponding relative transmission delay difference as the dependent variable to obtain the slope. The slope represents the crystal oscillator frequency offset between the two nodes in the node pair. In subsequent acquisition cycles, the relative transmission delay difference of the current acquisition cycle is subtracted from the product of the crystal oscillator frequency offset and the current cumulative running time to obtain the frequency offset-compensated relative transmission delay difference. The frequency domain phase correction factor is constructed using the frequency offset-compensated relative transmission delay difference.
[0015] As an optional approach, the data collected during the linear regression fitting is taken from a sliding window consisting of the most recent collection periods; when the residual of the linear regression fitting exceeds a preset range, the historical data in the sliding window is cleared and the accumulation of new collection period data is restarted.
[0016] As an optional approach, the average cross-spectral density is obtained by performing arithmetic mean on a frequency-by-frequency basis on the corrected cross-spectral density obtained for the same node in multiple consecutive acquisition cycles; the average cross-spectral density is then used to replace the corrected cross-spectral density of a single acquisition cycle to calculate the coherence function value.
[0017] As an optional approach, the corrected cross-spectral density of each of the multiple consecutive acquisition cycles is obtained by multiplying the frequency domain phase correction factor by the uncorrected cross-spectral density at each frequency point. The frequency domain phase correction factor corresponding to each acquisition cycle is independently constructed based on the relative transmission delay difference estimated in its respective acquisition cycle.
[0018] As an optional approach, the calculation of the coherence function value of the node pair includes: calculating the ratio of the square of the magnitude of the corrected cross-spectral density to the product of the autospectral densities of the two nodes in the node pair at each discrete frequency point corresponding to the frequency band of interest, to obtain the coherence function value at each discrete frequency point; taking the arithmetic mean of the coherence function values at each discrete frequency point within the frequency band of interest to obtain the in-band average coherence index, and using the in-band average coherence index as the coherence function value in subsequent vibration anomaly area localization.
[0019] As an optional approach, the upper limit frequency of the band of interest is consistent with the cutoff frequency of the digital low-pass filter in each sensor terminal, and the lower limit frequency of the band of interest is consistent with the starting frequency of the environmental vibration energy distribution of the photovoltaic panel.
[0020] As an optional approach, locating the vibration anomaly region based on the spatial distribution of the coherence function values on the photovoltaic array topology includes: comparing the coherence function values of each node pair with the statistical baseline values of that node pair under historical normal operating conditions; when the current coherence function value deviates from the statistical baseline value by more than the fluctuation range determined based on historical statistics, the node pair is marked as an abnormal node pair; in the photovoltaic array topology, when a node and its multiple adjacent nodes are all marked as abnormal node pairs, the location of the photovoltaic panel corresponding to that node is determined as the vibration anomaly region.
[0021] According to a second aspect of the embodiments of this application, a photovoltaic panel vibration monitoring system based on heterogeneous converged network communication is also provided, comprising:
[0022] Includes multiple sensor terminals and gateway base stations; among which:
[0023] Each of the aforementioned sensor terminals is used to complete vibration data acquisition and processing within the same acquisition cycle, and then read the count difference between the start time and the current time of the free-running timer in its microcontroller unit as a local relative timestamp, and send the local relative timestamp to the gateway base station along with the uplink data packet;
[0024] The gateway base station is used to receive uplink data packets from each sensor terminal within the same acquisition period and the same logical group, record the reception time of each uplink data packet and extract the local relative timestamp; for any node pair, the relative transmission delay difference of the node pair is obtained by subtracting the difference between their local relative timestamps from the difference between their reception times.
[0025] The gateway base station is also used to construct a frequency domain phase correction factor at each discrete frequency point based on the relative transmission delay difference. The phase angle of the frequency domain phase correction factor at each discrete frequency point is the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference.
[0026] The gateway base station is also used to multiply the frequency domain phase correction factor by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair at each frequency point to obtain the corrected cross-spectral density.
[0027] The gateway base station is also used to calculate the coherence function value of the node pair based on the corrected cross-spectral density and the self-spectral density of each node in the node pair, and to locate the vibration anomaly area based on the spatial distribution of the coherence function value on the photovoltaic array topology.
[0028] This application introduces local relative timestamps, estimates relative transmission delay differences, and performs frequency offset compensation to perform phase correction on cross-spectral density in the frequency domain. This avoids the spectral leakage, truncation errors, and high computational overhead caused by existing time-domain interpolation resampling methods, making it more suitable for real-time deployment on gateway-side embedded platforms. Simultaneously, by averaging the corrected cross-spectral density across multiple acquisition cycles and combining it with the node's self-spectral density to calculate coherence function values, the stability and anti-interference capability of multi-node joint analysis can be effectively improved. Furthermore, based on the spatial distribution of the coherence function in the photovoltaic array topology, abnormal vibration areas can be located more accurately. This approach offers advantages such as low time alignment requirements, high analysis accuracy, low computational burden, and suitability for online monitoring of large-scale photovoltaic power plants.
[0029] It should be understood that the foregoing general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this disclosure. Furthermore, no embodiment in this disclosure is required to achieve all the effects described above. Attached Figure Description
[0030] The accompanying drawings, which are incorporated in and form a part of this specification, illustrate embodiments consistent with this disclosure and, together with the description, serve to explain the principles of this disclosure.
[0031] Figure 1 This is a schematic diagram of a photovoltaic panel vibration monitoring method based on heterogeneous fusion network communication, provided in an embodiment of this disclosure.
[0032] Figure 2 This is a schematic diagram of the cross-spectral density correction process provided in an embodiment of this disclosure.
[0033] Figure 3 This is a schematic diagram of the vibration anomaly localization process provided in an embodiment of this disclosure.
[0034] Figure 4 This is a schematic diagram of a photovoltaic panel vibration monitoring system based on heterogeneous converged network communication, provided as an embodiment of this disclosure.
[0035] Figure 5 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this disclosure. Detailed Implementation
[0036] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort should fall within the scope of protection of the present application.
[0037] This disclosure provides a photovoltaic panel vibration monitoring method based on heterogeneous converged network communication. This method is applicable to scenarios involving online monitoring of the structural health of photovoltaic arrays in large-scale grid-connected photovoltaic power plants. Under typical deployment conditions, a photovoltaic power plant comprises several photovoltaic arrays, each array consisting of multiple photovoltaic panels assembled via supports and connectors. Vibration sensor terminals are installed on the surface of each photovoltaic panel or at key locations on the supports. Each sensor terminal integrates a microcontroller unit (MCU), a triaxial accelerometer, and a low-power wide-area network communication module, enabling it to locally acquire vibration acceleration signals from the photovoltaic panels, perform preliminary processing, and then send data packets to the gateway base station.
[0038] Gateway base stations are typically located in combiner boxes or management boxes near the photovoltaic array. They are responsible for receiving uplink data from multiple sensor terminals, aggregating and converting the data according to protocols, and then uploading it via a broadband network link to a remote cloud server or local edge computing platform for subsequent joint analysis and anomaly detection. In this heterogeneous network architecture, when the cloud or gateway side performs joint frequency domain analysis on the vibration data of multiple nodes within the same photovoltaic array, the data from each node has an accurate time alignment relationship.
[0039] The implementation process of the method described in this application will be described in detail below with reference to specific embodiments. It should be noted that this embodiment is only used to explain this application and is not intended to limit the scope of protection of this application. Conventional adjustments or substitutions of each step by those skilled in the art without departing from the concept of this application should be included in the scope of protection of this application.
[0040] Please see Figure 1 , Figure 1 This is a flowchart of a photovoltaic panel vibration monitoring method based on heterogeneous converged network communication according to an embodiment of the present invention, as shown below. Figure 1 As shown, the method includes steps S1-S5:
[0041] In step S1, after each sensor terminal completes vibration data acquisition and processing within the same acquisition cycle, it reads the count difference between the start time and the current time of the free-running timer in its microcontroller unit as a local relative timestamp, and sends the local relative timestamp to the gateway base station along with the uplink data packet.
[0042] Each sensor terminal and the gateway base station transmit uplink data packets using the LoRa long-range radio communication protocol. The LoRa protocol falls under the category of Low Power Wide Area Network (LPWAN), featuring long transmission distances and low power consumption, making it suitable for scenarios like photovoltaic power plants where sensor terminals are widely distributed and the data volume per node is moderate. The gateway base station and the cloud server communicate via Wi-Fi to transmit aggregated and processed data, including analysis results such as corrected cross-spectral density or coherence function values.
[0043] These two communication links constitute a heterogeneous converged network architecture. The front end uses LoRa to achieve low-power long-distance coverage from the sensor terminal to the gateway, while the back end uses Wi-Fi to achieve high-bandwidth data backhaul from the gateway to the cloud. Protocol conversion and data format adaptation are completed at the gateway base station.
[0044] Each sensor terminal samples the vibration acceleration of the photovoltaic panel using its built-in triaxial accelerometer during each acquisition cycle, obtaining acceleration time series in three orthogonal directions. After acquisition, the terminal MCU performs vector synthesis on the triaxial acceleration data, for example, by calculating the square root of the sum of the squares of the three-axis components to obtain a scalar vibration amplitude sequence. Subsequently, a digital low-pass filter is used to filter out noise components above the frequency band of interest, and the filtered vibration characteristic quantity sequence is output.
[0045] This digital low-pass filter can be configured as a finite impulse response (FIR) filter, with its cutoff frequency set according to the environmental vibration energy distribution characteristics of the photovoltaic panel. For example, it can be appropriately extended beyond the coverage range of the photovoltaic panel's natural frequency and wind load excitation frequency to retain effective vibration information while suppressing out-of-band noise. The length of the acquisition period is determined comprehensively based on the required frequency resolution and data transmission bandwidth.
[0046] After completing the vibration data acquisition and processing, the terminal MCU reads the current count value of its internal free-running timer and uses this count value as a local relative timestamp. The free-running timer is a general-purpose hardware peripheral on the MCU chip, which continuously increments its count from the time the MCU is powered on or reset, using the MCU system clock or its divided clock as the counting reference.
[0047] This local relative timestamp is not synchronized with any external clock source, and there is no requirement for a unified absolute time base among the nodes. Its only function is to mark the position of the time when the data packet is generated at the terminal side relative to the start time of the current acquisition cycle of the terminal. The terminal MCU appends the local relative timestamp as a field to the LoRa uplink data packet and sends it to the gateway base station along with the vibration characteristic sequence. The data length of the timestamp field depends on the timer bit width; for example, for a 32-bit timer, this field occupies 4 bytes.
[0048] In step S2, the gateway base station receives uplink data packets from each sensor terminal within the same acquisition period and the same logical group, records the reception time of each uplink data packet and extracts the local relative timestamp; for any node pair, the difference between their reception times and the difference between their local relative timestamps are subtracted to obtain the relative transmission delay difference of the node pair.
[0049] The gateway base station receives uplink data packets from sensor terminals within the same logical group. A logical group refers to the gateway grouping multiple sensor terminals belonging to the same photovoltaic array or monitoring area into the same group based on the sensor terminal's device identifier and array location information, enabling joint analysis of data from nodes within the group. Each time the gateway MCU completes the reception and demodulation of a LoRa message, it immediately reads the count value of the local timer on the gateway side and records it as the reception time of the message; simultaneously, it extracts the local relative timestamp embedded on the terminal side from the message data frame.
[0050] The local timer on the gateway side is similar in principle to the free-running timer on the terminal side. It also does not need to be synchronized with an external clock; it only needs to run continuously during the processing of messages within the same logical group, providing a unified reference for the reception time of each message within the same group. For any two sensor terminals forming a node pair within the same logical group, the gateway MCU performs differential calculations based on their reception times and local relative timestamps to estimate the relative transmission delay difference between the node pair.
[0051] Specifically, the relative transmission delay difference of the node pair is obtained by subtracting the difference in their local relative timestamps from the difference in their reception times. The principle is that the time difference between two messages arriving at the gateway contains two components: the difference in the time when the two terminals generate the messages within the same acquisition period, and the differentiated transmission delay experienced by the two messages in the LoRa channel. By subtracting the time difference generated by the terminals from the reception time difference, the delay difference introduced by the transmission link can be separated. Since each terminal's local timer is based on the clock of its own MCU crystal oscillator, there are slight deviations in the crystal oscillator frequencies of different nodes. However, within the time scale of a single acquisition period, the cumulative timing error introduced by this deviation is on the order of microseconds, far less than the millisecond-level random fluctuations caused by the LoRa channel access contention delay and the differences in air interface transmission duration caused by different spreading factors. Therefore, the influence of crystal oscillator frequency offset can be ignored in single-cycle delay difference estimation.
[0052] Optionally, when the same logical group contains three or more sensor terminals, one node is selected as the reference node, and the remaining nodes form node pairs with the reference node. Each node pair independently performs the calculation of the relative transmission delay difference, the subsequent construction of the frequency domain phase correction factor, and the acquisition of the corrected cross-spectral density. The selection of the reference node can be determined based on its communication link quality or the stability of message arrival, for example, selecting the node with the lowest packet loss rate or the most stable signal reception strength.
[0053] Although the impact of crystal oscillator frequency offset on delay difference estimation is negligible within a single acquisition cycle, the cumulative deviation between local timers of each node gradually increases over long-term continuous system operation. Without compensation, this will lead to a trend-like shift in the estimated delay difference over a considerable timescale. To ensure the long-term accuracy of delay difference estimation, the gateway base station records the relative transmission delay difference of the same node pair within multiple consecutive acquisition cycles and uses a linear regression fitting method to estimate the crystal oscillator frequency offset rate between the node pairs.
[0054] Specifically, the cumulative running time corresponding to each acquisition cycle is used as the independent variable, i.e., the time span from system startup to that acquisition cycle, and the estimated relative transmission delay difference within that acquisition cycle is used as the dependent variable. Linear regression fitting is performed on data points from multiple cycles to obtain the slope. The slope characterizes the crystal oscillator frequency offset between the two nodes in the node pair, and its physical meaning is the timing deviation generated by the local timers of the two nodes per unit time. Linear regression fitting can employ the least squares method, which determines the optimal slope by minimizing the sum of the squares of the distances from each observed data point to the fitted line.
[0055] In subsequent acquisition cycles, the gateway MCU uses the estimated crystal oscillator frequency offset to compensate for the relative transmission delay difference of the current acquisition cycle: the relative transmission delay difference of the current acquisition cycle is subtracted from the product of the crystal oscillator frequency offset and the current accumulated running time to obtain the frequency offset-compensated relative transmission delay difference. The product of the frequency offset and the accumulated running time represents the total timing deviation accumulated by the local timers of the two nodes from system startup to the current moment. After subtracting this deviation from the original delay difference estimate, the remaining part is the true delay difference introduced only by the transmission link difference. The subsequent construction of the frequency domain phase correction factor is based on this frequency offset-compensated relative transmission delay difference.
[0056] In some embodiments, the acquisition period data used for linear regression fitting is taken from a sliding window consisting of the most recent acquisition periods, and the window length can be configured, for example, to be the most recent 20 to 50 acquisition periods. Because the frequency characteristics of the crystal oscillator are affected by ambient temperature, under the outdoor operating conditions of a photovoltaic power plant, diurnal temperature differences and seasonal temperature changes may cause the crystal oscillator frequency offset to change slowly over a longer time scale. The sliding window allows the frequency offset estimate to track this slow change without being dragged down by premature historical data.
[0057] When the residuals of the linear regression fit exceed the preset range, it indicates that the crystal oscillator characteristics of the node pair may have abruptly changed or that there is abnormal interference. At this time, the gateway clears the historical data within the sliding window and restarts the accumulation of new acquisition cycle data to avoid abnormal data points causing continuous interference to subsequent frequency offset estimation. The preset range can be determined based on statistical data during the system debugging phase, for example, taking a certain multiple of the standard deviation of the residual distribution of the node pair during normal operation as the judgment boundary.
[0058] In step S3, based on the relative transmission delay difference, a frequency domain phase correction factor is constructed at each discrete frequency point. The phase angle of the frequency domain phase correction factor at each discrete frequency point is the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference.
[0059] In existing multi-node vibration monitoring technologies, the conventional approach to addressing time asynchrony between nodes is to interpolate and resample the acquired data from each node in the time domain, aligning the data from each node to a unified time axis before performing frequency domain analysis. Time-domain interpolation typically requires upsampling and low-pass filtering of the original data. This process itself introduces spectral leakage and truncation errors, and the computational load increases significantly with the upsampling factor.
[0060] To address the aforementioned issues, this method recognizes that in this application scenario, the ultimate goal of time alignment is to ensure the accuracy and reliability of the joint frequency domain analysis results of multiple nodes, particularly the calculation results of cross-spectral density. Based on the time-shift property of Fourier transform, when a signal undergoes a time shift in the time domain, its spectral amplitude remains unchanged, while its phase rotates proportional to the product of the frequency value and the time shift. Based on this deterministic analytical relationship, the impact of transmission delay difference on cross-spectral density can be precisely described by a frequency-dependent phase rotation factor. Therefore, the time-domain interpolation alignment step can be skipped, and a reverse phase rotation factor can be directly constructed and applied for correction during the cross-spectral calculation stage. This avoids time-domain interpolation errors while reducing computational complexity to accommodate the limited computing resources of the gateway-side embedded platform.
[0061] Suppose a gateway base station receives filtered vibration feature sequences from two nodes in the same logical packet. Under ideal time synchronization conditions, the data from the two nodes are strictly aligned on the time axis, and the calculated cross-spectral density can accurately reflect the frequency domain cross-correlation characteristics of the vibration signals between the two nodes. However, because the messages from the two nodes experience different transmission delays, the data from one node has an offset on the time axis relative to the data from the other node, which is the relative transmission delay difference after frequency offset compensation.
[0062] Based on the time-shift property of Fourier transform, this time shift causes a frequency-varying phase rotation in the calculated cross-spectral density relative to the true cross-spectral density. The rotation angle at each frequency point is equal to the product of twice pi, the frequency value, and the time delay difference. In the low-frequency range, this phase shift is small and has a limited impact on the cross-spectral results. As the frequency increases, the phase shift gradually increases. When the frequency approaches the upper limit of the band of interest, the accumulated phase shift may reach a level sufficient to cause significant distortion in the cross-spectral results, thereby affecting subsequent anomaly judgments based on cross-spectral analysis.
[0063] Therefore, the effect of time delay difference in cross-spectral density has a definite analytical form, which is a phase rotation factor that depends only on the frequency and the time delay difference. Unlike the difficulty in accurately compensating for non-integer sampling point offsets in the time domain, phase rotation correction in the frequency domain can handle time delay difference with arbitrary precision, regardless of whether the time delay difference is an integer multiple of the sampling interval.
[0064] Therefore, the gateway MCU constructs a frequency domain phase correction factor at each discrete frequency point to address the relative transmission delay difference after frequency offset compensation. The phase angle of this frequency domain phase correction factor at each discrete frequency point is equal to the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference, expressed as:
[0065]
[0066] in
[0067] For the first
[0068] The frequency value of each discrete frequency point is determined by the number of data points in the vibration characteristic quantity sequence and the sampling frequency. For nodes With nodes The relative transmission delay difference between them after frequency offset compensation; It is the imaginary unit.
[0069] This correction factor applies an equal-magnitude, opposite-direction reverse rotation to the phase rotation introduced by the time delay difference in the cross-spectrum, thereby eliminating the frequency-dependent phase offset caused by the time delay difference on a frequency-by-frequency basis. Specifically, for each discrete frequency point, the correction factor is a complex number with a modulus of 1, where its real and imaginary parts are the cosine and sine values of the corresponding phase angle, respectively. For each pair of nodes requiring cross-spectrum calculation, the gateway MCU independently constructs the corresponding phase correction factor based on the node's estimated time delay difference after frequency offset compensation.
[0070] In step S4, the frequency domain phase correction factor is multiplied at each frequency point by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair to obtain the corrected cross-spectral density.
[0071] Please see Figure 2 , Figure 2 This is a schematic diagram of the cross-spectral density correction process provided in an embodiment of this disclosure. Figure 2 As shown, in step S201, the frequency domain phase correction factor is multiplied at each frequency point by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair to obtain the corrected cross-spectral density.
[0072] The process of obtaining the uncorrected cross-spectral density includes performing a Discrete Fourier Transform (DFT) on the vibrational characteristic sequences of the two nodes, where the DFT maps the finite-length time-domain sequence to spectral coefficients at equally spaced discrete frequency points. The product of the complex conjugate of the spectral coefficient of one node and the spectral coefficient of the other node at the same frequency point yields the uncorrected cross-spectral density value at that frequency. Based on this, a correction operation performs a complex multiplication at each discrete frequency point, multiplying the uncorrected cross-spectral density value by the phase correction factor at the corresponding frequency point to obtain the corrected cross-spectral density.
[0073] for Each discrete frequency point requires the entire correction process to... The computational load of complex multiplication is linearly related to the data length. Each complex multiplication involves four real multiplications and two real addition / subtraction operations. For embedded MCUs, this computational load is far lower than the convolution operations required in time-domain interpolation alignment. Compared to the multiple steps of upsampling, low-passband-limited filtering, and resampling required by time-domain interpolation alignment, frequency-domain phase correction has a simpler computational process. It does not involve the design of interpolation filters or convolution operations, thus avoiding the inherent spectral leakage and truncation errors of time-domain interpolation. Its computational cost is also lower, making it more suitable for real-time execution on embedded MCU platforms used in gateway base stations.
[0074] In some embodiments, the calculation of cross-spectral density and phase correction can be performed only on discrete frequency points within the band of interest to further reduce the computational load. In another embodiment, the gateway base station can also upload the spectrum data of each node and the corresponding estimated time delay difference to a cloud server, where the cloud performs frequency domain correction and subsequent analysis. In this case, the gateway base station undertakes the functions of time delay difference estimation and data forwarding.
[0075] In step S202, the corrected cross-spectral density obtained from the same node pair in multiple consecutive acquisition cycles is arithmetically averaged at each frequency point to obtain the average cross-spectral density.
[0076] In real-world operating environments, the estimated cross-spectral density within a single acquisition cycle is affected by factors such as measurement noise, random environmental vibration components, and minor errors introduced by LoRa channel transmission, resulting in high estimation variance. Using single-cycle results for anomaly detection can easily lead to misjudgments. To improve the statistical reliability of cross-spectral estimation, the corrected cross-spectral densities obtained from multiple consecutive acquisition cycles for the same node are arithmetically averaged at each frequency point to obtain the average cross-spectral density. This average cross-spectral density is then used to replace the corrected cross-spectral density of a single acquisition cycle for subsequent coherence function value calculations.
[0077] In each acquisition period involved in averaging, the corrected cross-spectral density of each period is obtained by multiplying the frequency-domain phase correction factor corresponding to that period by the uncorrected cross-spectral density of that period at each frequency point. The frequency-domain phase correction factor for each acquisition period is independently constructed based on the relative transmission delay difference estimated in its respective acquisition period. The access contention results and air interface transmission conditions of the LoRa channel differ across acquisition periods, resulting in variations in the transmission delay difference between periods. Therefore, delay difference estimation and correction factor construction must be performed independently for each period; a uniform delay difference from a fixed period cannot be used as a substitute.
[0078] The prerequisite for multi-period averaging to effectively reduce cross-spectral estimation variance and improve statistical reliability is that the corrected cross-spectral density remains consistent in phase across each period. If phase correction is not performed period by period and multi-period averaging is directly applied to the uncorrected cross-spectrum, the phase of the uncorrected cross-spectrum will exhibit random fluctuations due to the random variation in transmission delay differences between periods. While suppressing noise variance, the averaging operation will also attenuate the amplitude of the effective signal components, resulting in an incoherent averaging effect.
[0079] After phase correction is performed independently cycle by cycle, the cross-spectrum of each cycle after correction has eliminated the random offset caused by the time delay difference in phase. The multi-cycle averaging constitutes coherent averaging, which reduces noise variance while maintaining unbiased estimation of signal amplitude. The number of acquisition cycles used for averaging can be configured according to the balance requirements of signal-to-noise ratio and real-time data update in the actual application scenario. For example, the most recent 8 to 16 acquisition cycles can be selected.
[0080] In step S5, based on the corrected cross-spectral density and the autospectral density of each node in the node pair, the coherence function value of the node pair is calculated, and the vibration anomaly region is located according to the spatial distribution of the coherence function value on the photovoltaic array topology.
[0081] Please see Figure 3 , Figure 3 A schematic diagram of the vibration anomaly localization process provided in an embodiment of this disclosure is shown. Figure 3 As shown, in step S301, based on the obtained corrected cross-spectral density or the average cross-spectral density after multi-period averaging, and combined with the autospectral density of each node in the node pair, the coherence function value of the node pair is calculated.
[0082] The self-spectral density is the power spectral density of a single node's vibration characteristic sequence, reflecting the energy distribution of the node's vibration signal at each frequency component. It is calculated by performing a DFT on the node's vibration characteristic sequence and then taking the square of the magnitude of the spectral coefficients.
[0083] At each discrete frequency point corresponding to the band of interest, the ratio of the square of the magnitude of the corrected cross-spectral density to the product of the autospectral densities of the two nodes in that node pair is calculated to obtain the coherence function value at each discrete frequency point:
[0084]
[0085] in This refers to the corrected cross-spectral density or average cross-spectral density. and They are nodes and nodes The coherence function value ranges from 0 to 1. A value closer to 1 indicates a stronger correlation between the vibration signals of the two nodes at that frequency; a value closer to 0 indicates almost no linear correlation between the vibration signals of the two nodes at that frequency. In the calculation of the coherence function, the product of the self-spectral densities in the denominator acts as a normalization factor, ensuring that the coherence function value is not affected by the absolute amplitude of the vibration signals of each node, but only reflects the similarity in phase and waveform between the vibration signals of the two nodes.
[0086] The arithmetic mean of the coherence function values at each discrete frequency point within the band of interest is taken to obtain the average coherence index within the band. This average coherence index is then used as the coherence function value for that node pair in subsequent vibration anomaly area localization. The upper limit frequency of the band of interest is consistent with the cutoff frequency of the digital low-pass filter in each sensor terminal, and the lower limit frequency is consistent with the starting frequency of the environmental vibration energy distribution of the photovoltaic panel.
[0087] Because vibration energy is extremely weak and the signal-to-noise ratio is too low in frequency bands below the starting frequency, the coherence function values calculated in these bands are dominated by noise and have no physical meaning. Similarly, signals in frequency bands above the filter cutoff frequency are significantly attenuated by the terminal-side filter and are also unsuitable for coherence assessment. Calculating the average coherence only within the frequency range covered by the effective vibration signal provides a reliable measure of the vibration correlation between two nodes.
[0088] In step S302, the vibration anomaly area is located based on the spatial distribution of coherence function values on the photovoltaic array topology. Under normal operating conditions, the environmental vibration experienced by adjacent panels on the same photovoltaic array mainly originates from the uniform action of wind load on the array panel and the combined transmission of foundation vibration and mechanical operation vibration by the support structure. It has a high spatial correlation, and the in-band average coherence index between adjacent node pairs is maintained at a high level accordingly.
[0089] When a plate changes its local vibration transmission characteristics due to structural anomalies such as loose fasteners, fatigue fracture of connectors, or deformation and warping of the plate surface, the vibration response mode of the plate will differ from that of its adjacent plates. The abnormal plate may exhibit characteristics such as increased vibration amplitude, shift in natural frequency, or change in damping characteristics, and the coherence function value of the corresponding node pair will decrease accordingly.
[0090] When locating abnormal vibration areas based on the spatial distribution of coherence function values on the photovoltaic array topology, the coherence function values of each node pair are first compared with the statistical baseline values of that node pair under historical normal operating conditions. The statistical baseline values are obtained during the initial system deployment or periodic calibration phase by continuously collecting coherence function values for multiple cycles under normal operating conditions with known structural integrity, and then performing statistical analysis on their mean and standard deviation.
[0091] When the current coherence function value deviates from the statistical baseline value by more than the fluctuation range determined based on historical statistics, the node pair is marked as an abnormal node pair. The fluctuation range can be a multiple of the historical statistical standard deviation, such as 2 to 3 times the standard deviation. This multiple serves as a detection sensitivity parameter and can be adjusted according to the on-site requirements for balancing false alarm and false negative rates. The smaller the multiple, the more sensitive it is to abnormal changes, but the higher the risk of false alarms; the larger the multiple, the opposite is true.
[0092] Furthermore, in the photovoltaic array topology, when a node and its multiple adjacent nodes are all marked as abnormal node pairs, the location of the photovoltaic panel corresponding to that node is determined as a vibration anomaly region. If a photovoltaic panel experiences a local structural anomaly, the vibration correlation between the sensor nodes installed on that panel and their adjacent nodes in all directions will decrease simultaneously, rather than only exhibiting occasional coherent fluctuations with a specific adjacent node. By requiring node pairs in multiple directions to simultaneously meet the anomaly conditions, the systemic coherence decrease caused by panel structural anomalies can be effectively distinguished from local random fluctuations caused by environmental disturbances or measurement noise, thereby improving the accuracy and reliability of anomaly localization.
[0093] In practical applications, the definition of adjacent nodes depends on the physical topology of the photovoltaic array and the deployment scheme of the sensor nodes. For example, in a row-and-column photovoltaic array, the sensor nodes of a certain panel are usually adjacent to the sensor nodes of the panels immediately above, below, left, and right in the four directions. For nodes located at the edge or corner of the array, the number of adjacent nodes is less than that of internal nodes. When making a judgment, the number of adjacent node pairs that need to meet the abnormal conditions can be appropriately reduced to ensure that anomalies in the edge area can also be detected in a timely manner. The anomaly location results can be reported to the cloud server via the gateway base station through the Wi-Fi link. The operation and maintenance management system will then present the results in a visual manner on the array topology map to help operation and maintenance personnel quickly locate the panel that needs to be inspected on-site.
[0094] In some embodiments, the cloud server can also introduce an artificial intelligence model to assist in the determination of the identification results of abnormal node pairs. Specifically, the in-band average coherence index, the amplitude and phase characteristics of the corrected cross-spectral density in the frequency band of interest, the phase dispersion, the historical baseline deviation, and the array topological adjacency relationship of each node pair are used as feature inputs to train a classification or regression model, which outputs the abnormal risk score or abnormal type of each photovoltaic panel. The output result is then cross-validated with the aforementioned determination results based on statistical baseline and spatial distribution. When the two are consistent or the risk score exceeds a preset threshold, the corresponding location is confirmed as a vibration abnormality area, and an early warning information is generated and uploaded to the operation and maintenance management system.
[0095] In some embodiments, to continuously monitor the actual effect of frequency domain phase correction during system operation, this method further includes a correction effectiveness verification step. For the same node pair, the standard deviation of the phase angle of the uncorrected cross-spectral density at each frequency point within the band of interest before applying the frequency domain phase correction factor is calculated as the phase dispersion before correction, and the standard deviation of the phase angle of the corrected cross-spectral density at each frequency point within the same band is calculated as the phase dispersion after correction.
[0096] Under ideal conditions where there is no time delay difference, the cross-spectral phase of adjacent nodes is relatively stable within the band of interest during normal operation, corresponding to a small phase dispersion. When a transmission time delay difference exists, the cross-spectral phase exhibits an approximately linear trend along the frequency axis, meaning that there is a systematic increasing or decreasing relationship between the phase values at different points on the frequency axis, leading to a significant increase in phase dispersion. Therefore, if frequency domain phase correction effectively eliminates the influence of the time delay difference, the corrected phase dispersion should be significantly smaller than the uncorrected value.
[0097] In actual execution, the gateway or cloud calculates the phase dispersion before and after each phase correction and then calculates the ratio between the two. When the ratio of the phase dispersion after correction to the phase dispersion before correction is higher than the preset verification pass condition, it means that the phase dispersion after correction has not been sufficiently reduced. This indicates that the node may have other sources of phase mismatch besides the time delay difference, such as additional phase noise caused by loose sensor installation, or frequency-selective phase distortion caused by LoRa channel multipath effects. At this time, the gateway or cloud generates a prompt message to instruct the maintenance personnel to investigate the node.
[0098] The preset investigation trigger threshold can be determined based on the theoretical performance of the correction algorithm and on-site measured data. For example, it can be configured to trigger an investigation when the ratio of the phase dispersion after correction to that before correction exceeds a certain threshold. This threshold can be determined during the system debugging phase by running the correction algorithm under known normal conditions. The execution frequency of verification can be configured according to operation and maintenance needs, such as executing it once every few collection cycles, or triggering it after the system detects an abnormal event. The verification results can be uploaded to the cloud server as operation and maintenance logs for long-term trend monitoring and statistical analysis by the operation and maintenance management system.
[0099] Therefore, this method transfers the multi-node time alignment problem from traditional time-domain interpolation to frequency-domain cross-spectral correction. By utilizing the deterministic analytical relationship between time delay and frequency-domain phase rotation, the accuracy of multi-node joint frequency-domain analysis is restored without introducing time-domain interpolation errors. At the same time, the computational complexity is reduced to adapt to the computing power constraints of the gateway-side embedded platform, providing a reliable technical means for the health monitoring of array-level structures in large-scale photovoltaic power plants.
[0100] In some embodiments, see Figure 4 , Figure 4 This is a schematic diagram of a photovoltaic panel vibration monitoring system based on heterogeneous converged network communication, provided in an embodiment of this application. Figure 4 As shown, the system includes:
[0101] Includes multiple sensor terminals and gateway base stations; among which:
[0102] Each of the aforementioned sensor terminals is used to complete vibration data acquisition and processing within the same acquisition cycle, and then read the count difference between the start time and the current time of the free-running timer in its microcontroller unit as a local relative timestamp, and send the local relative timestamp to the gateway base station along with the uplink data packet;
[0103] The gateway base station is used to receive uplink data packets from each sensor terminal within the same acquisition period and the same logical group, record the reception time of each uplink data packet and extract the local relative timestamp; for any node pair, the relative transmission delay difference of the node pair is obtained by subtracting the difference between their local relative timestamps from the difference between their reception times.
[0104] The gateway base station is also used to construct a frequency domain phase correction factor at each discrete frequency point based on the relative transmission delay difference. The phase angle of the frequency domain phase correction factor at each discrete frequency point is the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference.
[0105] The gateway base station is also used to multiply the frequency domain phase correction factor by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair at each frequency point to obtain the corrected cross-spectral density.
[0106] The gateway base station is also used to calculate the coherence function value of the node pair based on the corrected cross-spectral density and the self-spectral density of each node in the node pair, and to locate the vibration anomaly area based on the spatial distribution of the coherence function value on the photovoltaic array topology.
[0107] Those skilled in the art will clearly understand that the technical solutions of the embodiments of this application can be implemented by means of software and / or hardware. In this specification, "unit" and "module" refer to software and / or hardware that can independently complete or cooperate with other components to complete a specific function, wherein the hardware may be, for example, a field-programmable gate array (FPGA), an integrated circuit (IC), etc.
[0108] Each processing unit and / or module in the embodiments of this application can be implemented by an analog circuit that implements the functions described in the embodiments of this application, or by software that executes the functions described in the embodiments of this application.
[0109] Based on the same inventive concept, this application also provides an electronic device, the method corresponding to which can be the method in the foregoing embodiments, and its problem-solving principle is similar to that method. For example... Figure 5 As shown, Figure 5 This is a schematic diagram of an electronic device structure provided in an embodiment of the present disclosure. The device includes: at least one processor; and a memory communicatively connected to the at least one processor; wherein the memory stores instructions executable by the at least one processor, and the instructions are executed by the at least one processor to enable the at least one processor to perform the methods and / or technical solutions of the foregoing embodiments of the present application.
[0110] In particular, the methods and / or embodiments in this application can be implemented as computer software programs. For example, the embodiments disclosed in this application include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowchart. When the computer program is executed by a processor, it performs the functions defined in the methods of this application.
[0111] Another embodiment of this application provides a storage medium storing computer program instructions thereon, which can be executed by a processor to implement the methods and / or technical solutions of any one or more embodiments of this application.
[0112] In the above embodiments, the descriptions of each embodiment have different focuses. Parts not described in detail in a certain embodiment can be referred to in the relevant descriptions of other embodiments. The above descriptions are merely preferred embodiments of this application and explanations of the technical principles used. Those skilled in the art should understand that the scope of the invention involved in this application is not limited to the technical solutions formed by specific combinations of the above technical features, but should also cover other technical solutions formed by arbitrary combinations of the above technical features or their equivalent features without departing from the inventive concept.
Claims
1. A method for monitoring the vibration of photovoltaic panels based on heterogeneous converged network communication, characterized in that, include: After each sensor terminal completes vibration data acquisition and processing within the same acquisition cycle, it reads the count difference between the start time and the current time of the free-running timer in its microcontroller unit as a local relative timestamp, and sends the local relative timestamp to the gateway base station along with the uplink data packet. The gateway base station receives uplink data packets from each sensor terminal within the same acquisition period and the same logical group, records the reception time of each uplink data packet and extracts the local relative timestamp; for any node pair, the relative transmission delay difference of the node pair is obtained by subtracting the difference between their local relative timestamps from the difference between their reception times. Based on the relative transmission delay difference, a frequency domain phase correction factor is constructed at each discrete frequency point. The phase angle of the frequency domain phase correction factor at each discrete frequency point is the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference. The gateway base station records the relative transmission delay difference of the same node pair in multiple consecutive acquisition cycles. A linear regression is performed with the cumulative running time corresponding to each acquisition cycle as the independent variable and the corresponding relative transmission delay difference as the dependent variable to obtain the slope. The slope represents the crystal oscillator frequency offset between the two nodes in the node pair. In subsequent acquisition cycles, the relative transmission delay difference of the current acquisition cycle is subtracted from the product of the crystal oscillator frequency offset and the current cumulative running time to obtain the frequency offset-compensated relative transmission delay difference. The frequency domain phase correction factor is constructed using the frequency offset-compensated relative transmission delay difference. The frequency domain phase correction factor is multiplied at each frequency point by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair to obtain the corrected cross-spectral density. Based on the corrected cross-spectral density and the autospectral density of each node in the node pair, the coherence function value of the node pair is calculated, and the vibration anomaly region is located according to the spatial distribution of the coherence function value on the photovoltaic array topology.
2. The method of claim 1, wherein, Each sensor terminal transmits uplink data packets with the gateway base station using the LoRa communication protocol, and the gateway base station transmits the corrected cross-spectral density or the coherence function value with the cloud server using WIFI.
3. The method of claim 2, wherein, The data collected during the linear regression fitting is taken from a sliding window consisting of the most recent collection periods. When the residual of the linear regression fitting exceeds a preset range, the historical data in the sliding window is cleared and the accumulation of new collection period data begins again.
4. The method of claim 1, wherein, The average cross-spectral density is obtained by performing arithmetic mean on a frequency-by-frequency basis for the corrected cross-spectral density obtained for the same node in multiple consecutive acquisition cycles; the coherence function value is calculated by replacing the corrected cross-spectral density of a single acquisition cycle with the average cross-spectral density.
5. The method of claim 4, wherein, The corrected cross-spectral density of each of the multiple consecutive acquisition cycles is obtained by multiplying the frequency domain phase correction factor by the uncorrected cross-spectral density at each frequency point. The frequency domain phase correction factor corresponding to each acquisition cycle is independently constructed based on the relative transmission delay difference estimated in its respective acquisition cycle.
6. The method of claim 1, wherein, The calculation of the coherence function value of the node pair includes: calculating the ratio of the square of the magnitude of the corrected cross-spectral density to the product of the autospectral densities of the two nodes in the node pair at each discrete frequency point corresponding to the frequency band of interest, to obtain the coherence function value at each discrete frequency point; taking the arithmetic mean of the coherence function values at each discrete frequency point within the frequency band of interest to obtain the in-band average coherence index, and using the in-band average coherence index as the coherence function value to participate in the subsequent vibration anomaly area localization.
7. The method of claim 6, wherein, The upper limit frequency of the band of interest is consistent with the cutoff frequency of the digital low-pass filter in each sensor terminal, and the lower limit frequency of the band of interest is consistent with the starting frequency of the environmental vibration energy distribution of the photovoltaic panel.
8. The method of claim 1, wherein, The method of locating the vibration anomaly region based on the spatial distribution of the coherence function value on the photovoltaic array topology includes: comparing the coherence function value of each node pair with the statistical baseline value of the node pair under historical normal operating conditions; when the current coherence function value deviates from the statistical baseline value by more than the fluctuation range determined based on historical statistics, the node pair is marked as an abnormal node pair; in the photovoltaic array topology, when a node and its multiple adjacent nodes are all marked as abnormal node pairs, the location of the photovoltaic panel corresponding to the node is determined as the vibration anomaly region.
9. A photovoltaic panel vibration monitoring system based on heterogeneous converged network communication for performing the method of any one of claims 1-8, characterized in that, include: Multiple sensor terminals and gateway base stations; among which: Each of the aforementioned sensor terminals is used to complete vibration data acquisition and processing within the same acquisition cycle, and then read the count difference between the start time and the current time of the free-running timer in its microcontroller unit as a local relative timestamp, and send the local relative timestamp to the gateway base station along with the uplink data packet; The gateway base station is used to receive uplink data packets from each sensor terminal within the same acquisition period and the same logical group, record the reception time of each uplink data packet and extract the local relative timestamp; for any node pair, the relative transmission delay difference of the node pair is obtained by subtracting the difference between their local relative timestamps from the difference between their reception times. The gateway base station is further configured to construct a frequency domain phase correction factor at each discrete frequency point based on the relative transmission delay difference. The phase angle of the frequency domain phase correction factor at each discrete frequency point is the product of twice pi, the frequency value at that frequency point, and the relative transmission delay difference. Specifically, the gateway base station records the relative transmission delay difference of the same node pair in multiple consecutive acquisition cycles. A linear regression is performed using the cumulative running time corresponding to each acquisition cycle as the independent variable and the corresponding relative transmission delay difference as the dependent variable to obtain the slope. The slope represents the crystal oscillator frequency offset between the two nodes in the node pair. In subsequent acquisition cycles, the relative transmission delay difference of the current acquisition cycle is subtracted from the product of the crystal oscillator frequency offset and the current cumulative running time to obtain the frequency offset-compensated relative transmission delay difference. The frequency domain phase correction factor is constructed using the frequency offset-compensated relative transmission delay difference. The gateway base station is also used to multiply the frequency domain phase correction factor by the uncorrected cross-spectral density calculated from the vibration characteristic sequence of the two nodes in the node pair at each frequency point to obtain the corrected cross-spectral density. The gateway base station is also used to calculate the coherence function value of the node pair based on the corrected cross-spectral density and the self-spectral density of each node in the node pair, and to locate the vibration anomaly area based on the spatial distribution of the coherence function value on the photovoltaic array topology.