Method for accurately adjusting frequency of intelligent frequency modulation high-voltage power supply of electrostatic dust collector

Abstract

The invention relates to the technical field of electrostatic dust collection and discloses an accurate frequency adjustment method for an intelligent frequency modulation high-voltage power supply of an electrostatic dust collector. The method comprises the steps of collecting voltage signals with frequency fluctuation in operation of a high-voltage power supply to form a voltage sequence; dividing period segments by using wave crest distribution in the voltage sequence, and clustering to obtain adjustment subsequences; obtaining a trend fluctuation index based on local signal change trend fluctuation and signal differences of the adjustment subsequences, and obtaining an amplitude drop difference and an amplitude interval difference according to an amplitude change trend difference and an amplitude bit sequence change trend difference; obtaining a period stability coefficient by combining the difference, the average condition of the trend fluctuation index and the average condition of the sub-sequence similarity; constructing a Hankel matrix and performing singular value decomposition, and obtaining a main component proportion and a difference index based on a singular value condition; and according to the Hankel matrix line data correlation, the period stability coefficient, the main component proportion and the difference index, obtaining a signal stability index, and according to the signal stability index, accurately adjusting the high-voltage power supply frequency.

Description

Technical Field

[0001] This invention relates to the field of electrostatic dust removal technology, specifically a method for precisely adjusting the frequency of a high-voltage power supply for an intelligent frequency-modulated electrostatic dust collector. Background Technology

[0002] Electrostatic precipitators (ESPs) are key equipment for controlling dust emissions in industrial production, and their operating efficiency is closely related to the stability of the high-voltage power supply. As the core power unit of the ESP, the precise control of its output frequency directly affects the stability of the electric field strength, thus determining the effectiveness of dust charging, migration, and collection. In actual industrial environments, ESPs often face complex and variable operating conditions, such as fluctuations in flue gas flow, changes in dust concentration, and differences in temperature and humidity. These factors can cause irregular fluctuations in the operating state of the high-voltage power supply, causing the output frequency to deviate from the preset value, leading to problems such as electric field breakdown, increased energy consumption, and decreased dust removal efficiency.

[0003] Traditional high-voltage power supply frequency adjustment methods are mostly based on fixed-parameter PID control or simple feedback regulation mechanisms. These methods can play a certain role in dealing with linear and stable operating conditions, but when dealing with nonlinear and time-varying complex disturbances, they often exhibit shortcomings such as response lag, large overshoot, and insufficient stability. For example, when the dust concentration in flue gas suddenly increases, the space charge density in the electric field changes drastically, causing a nonlinear abrupt change in the load impedance of the high-voltage power supply. At this time, the fixed-parameter regulation algorithm is difficult to adapt to the impedance change quickly, which can easily lead to over- or under-frequency adjustment, affecting not only the dust removal effect but also potentially shortening the service life of the equipment.

[0004] Current technologies for monitoring frequency fluctuations largely rely on sampling single voltage or current signals, lacking in-depth analysis of the signal's intrinsic characteristics. In high-frequency fluctuation scenarios, the instantaneous value of a single signal often contains significant noise, making it difficult to accurately capture the trends and patterns of frequency changes through simple threshold judgments or averaging calculations. This results in a lack of precise data support for adjustment decisions. Furthermore, traditional methods do not consider the periodicity and correlation of voltage signals over time, failing to identify periodic interference components in the fluctuations. This leads to frequent ineffective adjustments, further exacerbating the instability of power supply operation.

[0005] With increasingly stringent environmental protection requirements in industrial production, emission standards for electrostatic precipitators are becoming increasingly stringent, placing higher demands on the precision of high-voltage power supply frequency control. Current technologies typically only allow frequency adjustment accuracy within ±1Hz, which is insufficient for handling low-concentration dust emissions. In energy-intensive industries such as power generation, metallurgy, and chemicals, reduced dust removal efficiency due to frequency fluctuations not only leads to excessive dust emissions but also increases the cost of subsequent exhaust gas treatment and may even pose production safety hazards. Therefore, developing a method that can adapt to complex operating conditions, accurately capture frequency fluctuation characteristics, and achieve dynamic adjustment has become an urgent need to improve the operational performance of electrostatic precipitators.

[0006] Some studies have attempted to introduce intelligent algorithms such as neural networks and fuzzy control for frequency regulation. However, these methods often rely on large amounts of historical data to train models. When operating conditions change drastically or data is insufficient, the model's generalization ability drops sharply, making it difficult to guarantee the accuracy of the adjustment. Furthermore, these methods often only extract signal features superficially, failing to deeply analyze the periodicity of the voltage sequence, the laws governing amplitude changes, and the inherent stability characteristics of the signal. This results in the adjustment strategy lacking a grasp of the signal's fundamental laws, making it difficult to achieve the desired control effect in practical applications. Summary of the Invention

[0007] The purpose of this invention is to provide a method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for electrostatic precipitators, so as to solve the problems mentioned in the background art.

[0008] To achieve the above objectives, the present invention provides a method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator, the method comprising:

[0009] A voltage sequence composed of voltage signals fluctuating at frequency during the operation of a high-voltage power supply;

[0010] The periodic segments are divided based on the distribution of peaks in the voltage sequence, and the periodic segments in the voltage sequence are clustered according to the distribution of periodic segments to obtain each adjustment subsequence;

[0011] Based on the fluctuation of local signal change trends in the adjusted subsequence and the differences between local signals, the trend fluctuation index of each adjusted subsequence is obtained.

[0012] Based on the differences in the changing trends of amplitude in the adjusted subsequences and the differences in the changing trends of amplitude in the order of amplitude in the adjusted subsequences, the differences in amplitude decrease and amplitude interval are obtained.

[0013] The periodic stability coefficient of the voltage sequence is obtained based on the difference in amplitude decrease, the difference in amplitude interval, the average trend fluctuation index of all adjusted subsequences, and the average similarity between adjusted subsequences.

[0014] Construct the Hankel matrix of the voltage sequence, perform singular value decomposition on the Hankel matrix to obtain each singular value, and obtain the main component proportion and difference index of the singular value sequence of the voltage sequence based on the distribution, average and difference of the singular values.

[0015] The signal stability index of the voltage sequence is obtained based on the correlation between data in each row of the Hankel matrix, the periodic stability coefficient, the proportion of main components, and the difference index; the high-voltage power supply frequency is precisely adjusted based on the signal stability index.

[0016] Preferably, the method for obtaining the adjusted subsequence is as follows:

[0017] The peak and valley detection algorithm is used to obtain all peaks and valleys in the voltage sequence. The voltage sequence is divided into subsequences from each peak. The range of elements in each subsequence is calculated. The range of all subsequences is used as the input of the clustering algorithm to output each cluster.

[0018] Calculate the mean of internal elements in each cluster, select the cluster with the largest mean of internal elements as the adjusted cluster, and select the voltage subsequence corresponding to the internal elements of the adjusted cluster as the adjusted subsequence.

[0019] Preferably, the method for obtaining the trend fluctuation index is as follows:

[0020] Based on the fluctuations in the local signal change trends and the differences between local signals in the adjusted subsequence, the oscillation coefficients and variation coefficients on both sides of each adjusted subsequence are obtained.

[0021] The trend fluctuation index of each adjusted subsequence is obtained by combining the oscillation coefficients and change coefficients on both sides.

[0022] Preferably, the method for obtaining the variation coefficients on both sides is as follows:

[0023] For each adjusted subsequence, obtain the minimum value in each adjusted subsequence, take the minimum value and the subsequence consisting of all elements to the left of the minimum value as the left subsequence of each adjusted subsequence, and take the subsequence consisting of all elements to the right of the minimum value as the right subsequence of each adjusted subsequence.

[0024] Obtain the first-order difference sequence of the left subsequence of each adjusted subsequence, and use the step function to process all elements in the first-order difference sequence to obtain the difference step sequence;

[0025] Calculate the absolute value of the difference between the sum of the elements in the difference step sequence and the length of the first difference sequence of the left subsequence, and use it as the oscillation index of the left subsequence of each adjustment subsequence;

[0026] Using the same method as for the left subsequence, obtain the oscillation index of the right subsequence of each adjusted subsequence; calculate the product of the absolute value of the difference between the oscillation indices of the left and right subsequences and the mean value as the oscillation coefficients of the two sides of each adjusted subsequence;

[0027] Calculate the variance of the elements in the left subsequence and the variance of the elements in the right subsequence of each adjusted subsequence, and use the mean of the variances of the left and right subsequences as the variation coefficients on both sides of each adjusted subsequence.

[0028] Preferably, the method for obtaining the amplitude interval difference is as follows:

[0029] Sort all amplitude values ​​in all adjustment subsequences according to their position in the voltage sequence to construct an amplitude sequence; sort all amplitude values ​​in the adjustment subsequences according to their magnitude to construct an amplitude position sequence.

[0030] Obtain the first-order difference sequences of the amplitude sequence and the amplitude position sequence. Use the variance of all elements in the first-order difference sequence of the amplitude sequence as the amplitude descent difference; use the variance of all elements in the first-order difference sequence of the amplitude position sequence as the amplitude interval difference.

[0031] Preferably, the method for obtaining the periodic stability coefficient is as follows:

[0032] Calculate the mean of the trend volatility indices of all adjusted subsequences as the average volatility index;

[0033] The mean of the Pearson similarity coefficients between each adjusted subsequence and all other adjusted subsequences is taken as the sequence similarity of each adjusted subsequence;

[0034] The periodic stability coefficient is calculated by combining the peak descent difference, peak interval difference, average volatility index, the mean of sequence similarity of all adjusted subsequences, and preset parameter tuning coefficients.

[0035] Preferably, the method for obtaining the proportion of the main components and the difference index is as follows:

[0036] Sorting all singular values ​​in descending order to construct a singular value sequence;

[0037] The singular value sequence is used as the input to Otsu's thresholding method, and the output of Otsu's thresholding method is the threshold. All singular values ​​greater than or equal to the threshold are considered important singular values, and all singular values ​​less than the threshold are considered minor singular values. The ratio of the number of important singular values ​​to the total number of all singular values ​​is used as the proportion of the principal components of the singular value sequence.

[0038] Calculate the mean and variance of all important singular values ​​in the singular value sequence, and use the product of the mean and variance as the volatility index of the important singular values. Using the same method as the volatility index of the important singular values, calculate the volatility index of the minor singular values, and use the absolute value of the difference between the volatility index of the important singular values ​​and the volatility index of the minor singular values ​​as the difference index of the singular value sequence.

[0039] Preferably, the method for obtaining the signal stability index is as follows:

[0040] Calculate the absolute value of the Pearson similarity coefficient between each row of data in the Hankel matrix and all other rows of data, and take the mean of the absolute values ​​of all the Pearson similarity coefficients of each row of data as the similarity coefficient of each row of data; take the mean of the similarity coefficients of all rows of data in the Hankel matrix as the self-similarity coefficient of the Hankel matrix.

[0041] The signal stability index is calculated by combining the proportion of the main components of the singular value sequence, the difference index of the singular value sequence, the self-similarity coefficient of the Hankel matrix, the periodic stability coefficient of the current sequence, and the preset parameter tuning factor.

[0042] Preferably, the precise adjustment of the high-voltage power supply frequency based on the signal stability index includes:

[0043] The default threshold for wavelet denoising is obtained based on the signal stability index of the voltage sequence.

[0044] The frequency fluctuation voltage signal is denoised based on the default threshold of wavelet denoising, and the target adjustment frequency of the high-voltage power supply is calculated using the frequency adjustment method.

[0045] Preferably, the step function is processed as follows: elements greater than zero in the first-order difference sequence are marked as positive changes, elements less than zero are marked as negative changes, and elements equal to zero are marked as no changes, forming a difference step sequence composed of positive, negative, and no-change markings.

[0046] Compared with the prior art, the beneficial effects of the present invention are:

[0047] This intelligent frequency-modulated high-voltage power supply method for electrostatic precipitators precisely adjusts the frequency by collecting voltage signals that fluctuate during the operation of the high-voltage power supply to form a voltage sequence. This provides a comprehensive and detailed raw data foundation for subsequent frequency adjustment. By dividing the voltage sequence into periodic segments based on the distribution of peaks and performing clustering to obtain each adjustment subsequence, the complex voltage signal can be decomposed into local sequences with similar characteristics. This makes the originally chaotic fluctuation information orderly and traceable, which helps to analyze the pattern of frequency change from the perspective of local features.

[0048] By obtaining the trend fluctuation index based on the fluctuation of local signal change trends and the differences between local signals in the adjusted subsequence, the dynamic change characteristics of the signals within each subsequence can be deeply characterized, identifying subtle fluctuations and abnormal changes in the signal, making frequency adjustment more targeted. Furthermore, by obtaining the amplitude decrease difference and amplitude interval difference through the differences in amplitude change trends and amplitude positional change trends of the adjusted subsequence, the intrinsic connections and differences between different subsequences can be explored from an amplitude perspective, providing a multi-dimensional analytical perspective for judging the amplitude and rhythm of frequency fluctuations.

[0049] By combining the differences in amplitude decrease, amplitude interval, average trend fluctuation index, and average similarity among adjusted subsequences to obtain the periodic stability coefficient, a quantitative assessment of the overall periodic stability of the voltage sequence is achieved, avoiding the one-sidedness of judging solely by a single indicator. Constructing a Hankel matrix and performing singular value decomposition, based on the distribution, average, and differences of singular values, yields the proportion of major components and the difference index, effectively extracting key feature components from the voltage sequence, filtering noise interference, and highlighting the essential characteristics of the signal.

[0050] The signal stability index is obtained by analyzing the correlation, periodic stability coefficient, proportion of main components, and difference index of data in each row of the Hankel matrix. This index comprehensively reflects the correlation, periodicity, main characteristics, and degree of difference of the signal, forming a quantitative indicator that fully reflects the stability of the voltage sequence. Adjusting the high-voltage power supply frequency based on this signal stability index allows the adjustment to closely match actual signal characteristic changes, maintaining precise frequency stability under complex operating conditions, reducing the occurrence of abnormal electric field phenomena, and improving the operating effect and equipment reliability of the electrostatic precipitator. Attached Figure Description

[0051] Figure 1 This is a schematic diagram illustrating the working principle of the intelligent frequency modulation high-voltage power supply frequency precise adjustment method for electrostatic precipitators described in this invention.

[0052] Figure 2 A flowchart for adjusting the method of obtaining subsequences;

[0053] Figure 3 A flowchart illustrating the method for obtaining the trend fluctuation index;

[0054] Figure 4 This is a flowchart illustrating the method for obtaining amplitude interval differences. Detailed Implementation

[0055] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0056] Please see Figures 1-4 This invention provides a method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator. The specific implementation steps are as follows:

[0057] A voltage sequence is formed by collecting voltage signals that fluctuate in frequency during the operation of a high-voltage power supply. During operation, voltage sensors collect voltage signals at the output terminal in real time. These signals reflect the characteristics of frequency fluctuations. The collected continuous voltage signals are arranged in chronological order to form a discrete voltage sequence.

[0058] The voltage sequence is divided into periodic segments based on the distribution of peaks. These periodic segments are then clustered to obtain adjustment subsequences. First, the peak positions in the voltage sequence are identified. Based on the peak intervals and distribution patterns, the voltage sequence is divided into multiple periodic segments. Then, a clustering algorithm is used to classify these periodic segments, selecting those with similar characteristics as adjustment subsequences.

[0059] Based on the fluctuations in local signal trends and the differences between local signals within the adjusted subsequence, a trend fluctuation index is obtained for each adjusted subsequence. The signal change trends in different local regions within each adjusted subsequence are analyzed, and the degree of fluctuation and the differences between local signals are calculated. These factors are then combined to obtain a trend fluctuation index that characterizes the overall fluctuation features of the adjusted subsequence.

[0060] Based on the differences in the amplitude trends of the adjusted subsequences and the differences in the amplitude order within the adjusted subsequences, amplitude decrease differences and amplitude interval differences are obtained. The differences in the amplitude decrease trends over time within the adjusted subsequences, as well as the differences in the amplitude order within the sequence, are studied separately. These differences are quantified into amplitude decrease differences and amplitude interval differences using specific calculation methods.

[0061] The periodic stability coefficient of the voltage series is obtained based on the amplitude decrease difference, amplitude interval difference, the average trend fluctuation index of all adjusted subsequences, and the average similarity among adjusted subsequences. The periodic stability coefficient, reflecting the periodic stability of the voltage series, is obtained by comprehensively calculating the amplitude decrease difference, amplitude interval difference, the average trend fluctuation index, and the average similarity among adjusted subsequences.

[0062] A Hankel matrix for the voltage sequence is constructed. Singular value decomposition (SVD) is performed on the Hankel matrix to obtain the singular values. Based on the distribution, average, and differences of the singular values, the proportion of principal components and the difference index of the singular value sequence of the voltage sequence are obtained. Following the construction rules of the Hankel matrix, the voltage sequence is converted into a Hankel matrix, and singular value decomposition is performed to obtain multiple singular values. Based on the magnitude distribution, average value, and differences between the singular values, the proportion of principal components and the difference index are calculated.

[0063] The signal stability index of the voltage sequence is obtained based on the correlation between data in each row of the Hankel matrix, the periodic stability coefficient, the proportion of principal components, and the difference index. The high-voltage power supply frequency is then precisely adjusted based on this signal stability index. The correlation between data in each row of the Hankel matrix is ​​calculated, and combined with the previously obtained periodic stability coefficient, principal component proportion, and difference index, the signal stability index is determined. Finally, the high-voltage power supply frequency is adjusted based on this index.

[0064] Example 1: The process of acquiring the adjusted subsequence involves several consecutive processing steps. First, the peaks and troughs of the acquired voltage sequence are identified, a process relying on a peak-trough detection algorithm. This algorithm analyzes the numerical changes of adjacent data points in the voltage sequence to determine the positions of peaks and troughs. Specifically, the algorithm compares each data point with its preceding and following data points one by one. When the value of a data point is simultaneously greater than the values ​​of its preceding and following data points, that point is identified as a peak; when the value of a data point is simultaneously less than the values ​​of its preceding and following data points, that point is identified as a trough. In this way, all peaks and troughs in the voltage sequence can be completely captured, providing accurate positional references for subsequent sequence segmentation.

[0065] After identifying peaks and troughs, the voltage sequence is segmented using each peak as a dividing point. Starting with the first peak, the voltage sequence is truncated at that peak to form the first subsequence; then, using the second peak as the dividing point, the remaining voltage sequence is truncated to form the second subsequence; and so on, until the entire voltage sequence is divided into several subsequences. Each subsequence contains all voltage data from one peak to the next. This segmentation method allows each subsequence to correspond to a complete fluctuation period of the voltage signal, thus facilitating independent analysis of the characteristics of each period.

[0066] After segmenting the data into subsequences, the range of each element in the subsequence needs to be calculated. The range is calculated as the difference between the maximum and minimum values ​​in the subsequence, reflecting the fluctuation range of the voltage signal within each subsequence. For each subsequence, all elements are iterated through to determine the specific values ​​of the maximum and minimum values. Then, the minimum value is subtracted from the maximum value to obtain the range of that subsequence. The ranges of all subsequences are then aggregated to form a dataset reflecting the fluctuation range of each subsequence. This dataset will serve as the input parameter for subsequent clustering operations.

[0067] Clustering algorithms aim to group subsequences with similar range characteristics into the same category. During clustering, the algorithm calculates the similarity between different subsequences based on the magnitude of their ranges, assigning subsequences with high similarity to the same cluster, ultimately forming multiple independent clusters. Each cluster contains multiple subsequences with similar range characteristics, while the subsequences in different clusters exhibit significant differences in their range characteristics.

[0068] After obtaining multiple clusters, further analysis of the internal characteristics of each cluster is required. The mean of the ranges of all subsequences within each cluster is calculated. This is achieved by summing the ranges of all subsequences within the cluster and dividing by the number of subsequences in that cluster. This mean reflects the overall fluctuation range of the subsequences contained in the cluster. By comparing the mean internal elements of all clusters, the cluster with the largest mean internal element is selected and defined as the adjustment cluster. The cluster with the largest mean internal element is chosen as the adjustment cluster because its subsequences have a relatively larger fluctuation range. These subsequences can more significantly reflect the frequency fluctuation characteristics in the voltage sequence, thus providing a more representative analytical object for subsequent frequency adjustment.

[0069] Finally, all subsequences contained within the adjusted clusters are extracted; these subsequences are the adjusted subsequences. These adjusted subsequences are the parts with significant fluctuation characteristics selected from the entire voltage sequence. They will serve as the basic data for subsequent calculations of parameters such as trend fluctuation index, amplitude decrease difference, and amplitude interval difference. Through in-depth analysis of these subsequences, the fluctuation patterns of the voltage sequence can be grasped more accurately, providing the necessary basis for subsequent precise frequency adjustment.

[0070] Example 2: Obtaining the trend volatility index requires multi-dimensional analysis of the local signal characteristics of the adjusted subsequence. First, for each adjusted subsequence, the oscillation coefficients and change coefficients on both sides are obtained separately. Then, these two coefficients are combined to obtain the trend volatility index.

[0071] The acquisition of the oscillation coefficients on both sides begins with identifying the minimum value in the adjusted subsequence. Within each adjusted subsequence, all elements are traversed to determine the element with the minimum value and its position. Using this minimum value as a boundary, the adjusted subsequence is divided into a left subsequence and a right subsequence. The left subsequence contains the minimum value and all elements to its left, while the right subsequence contains all elements to its right. This division method segments the adjusted subsequence into two continuous local regions based on the position of the minimum value, facilitating the separate analysis of the signal fluctuation characteristics on both sides.

[0072] For the left subsequence, its first-order difference sequence is calculated. The first-order difference sequence is obtained by subtracting the previous element from the next, reflecting the numerical changes between adjacent elements in the left subsequence. Then, a step function is used to process each element in the first-order difference sequence. During processing, if an element is greater than zero, it is marked as a positive change; if an element is less than zero, it is marked as a negative change; if an element is equal to zero, it is marked as no change. After this processing, the first-order difference sequence is transformed into a difference step sequence composed of positive, negative, and no-change labels, which visually represents the direction and state of change of elements in the left subsequence.

[0073] The oscillation index of the left subsequence is calculated based on the difference step sequence. Specifically, the absolute value of the sum of all elements in the difference step sequence is first calculated, and then the absolute value of the difference between this absolute value and the length of the first-order difference sequence of the left subsequence is calculated. This absolute value of the difference is the oscillation index of the left subsequence. The same process is used to process the right subsequence: first, the first-order difference sequence of the right subsequence is calculated, then it is converted into a difference step sequence using a step function, and finally the oscillation index of the right subsequence is calculated based on the difference step sequence and the length of the first-order difference sequence.

[0074] After obtaining the oscillation indices of the left and right subsequences, calculate the absolute value of their difference and their mean. Multiply the absolute value of the difference by the mean; the result is the oscillation coefficient of the adjusted subsequence. The oscillation coefficient reflects the degree of signal fluctuation difference in the local regions on both sides of the minimum value in the adjusted subsequence.

[0075] The determination of the two-sided variation coefficients begins with calculating the variances of the left and right subsequences. Variance is obtained by averaging the squared deviations of each element in the sequence from the sequence mean, reflecting the dispersion of the elements in the sequence. The variances of the left and right subsequences are calculated separately, then added together and divided by 2. The result is the two-sided variation coefficient of the adjusted subsequence. These two-sided variation coefficients reflect the signal dispersion differences in the local regions on either side of the minimum value in the adjusted subsequence.

[0076] The trend fluctuation index is obtained by combining the oscillation coefficients and the variation coefficients on both sides. In this combination, the different characteristics reflected by the two coefficients must be considered comprehensively. The oscillation coefficients emphasize the difference in the direction of signal fluctuations, while the variation coefficients emphasize the difference in the dispersion of signal values. The combination of the two comprehensively reflects the fluctuation of local signal trends and the differences between local signals within the adjusted subsequence. In this way, each adjusted subsequence can obtain a corresponding trend fluctuation index, which can be used for subsequent analysis of the overall fluctuation characteristics of the voltage sequence, providing a foundation for further calculation of parameters such as the periodic stability coefficient.

[0077] Example 3: Obtaining the differences in amplitude decrease and amplitude interval requires analyzing the amplitude and position of the adjusted subsequences. First, all amplitudes contained in all adjusted subsequences are collected. These amplitudes originally occupy different positions in the voltage sequence. They are arranged sequentially according to their position in the voltage sequence, forming a continuous amplitude sequence. The position refers to the time sequence or index position of each amplitude in the original voltage sequence. Through this sorting, the amplitude sequence can reflect the amplitude changes of the voltage signal over the entire time range. Simultaneously, the position of all amplitudes in each adjusted subsequence is extracted, and these positions are sorted according to their numerical value to construct an amplitude position sequence. The amplitude position sequence can reflect the interval characteristics of the amplitude distribution over time in different adjusted subsequences.

[0078] For a constructed amplitude sequence, its first-order difference sequence is calculated. The first-order difference sequence is generated by subtracting the previous element from the next element in the sequence, and the resulting difference forms a new sequence. The variance of all elements in this first-order difference sequence is calculated; this variance is the amplitude descent difference. The variance is calculated by averaging the squared deviations of each element in the first-order difference sequence from the mean of the sequence. Through this calculation, the amplitude descent difference can quantitatively reflect the dispersion of the amplitude's decrease during the overall change. Similarly, the first-order difference sequence is calculated for the amplitude position sequence, i.e., by subtracting the previous element from the next position to obtain the difference sequence, and then the variance of all elements in this difference sequence is calculated. This variance is defined as the amplitude interval difference, which reflects the dispersion of the amplitude's interval changes over time.

[0079] Obtaining the periodic stability coefficient requires calculation of multiple parameters. First, the average trend volatility index of all adjusted subsequences is calculated, and this average is used as the average volatility index. The average volatility index reflects the overall level of trend volatility across all adjusted subsequences. Next, for each adjusted subsequence, its Pearson similarity coefficient with all other adjusted subsequences is calculated. The Pearson similarity coefficient measures the degree of linear correlation between two sequences, and its value ranges from -1 to 1. The closer the value is to 1 or -1, the higher or lower the similarity between the two sequences. For each adjusted subsequence, its Pearson similarity coefficient with all other adjusted subsequences is averaged to obtain the sequence similarity of that adjusted subsequence. Then, the average of the sequence similarities of all adjusted subsequences is calculated as the overall average sequence similarity level.

[0080] The calculation of the periodic stability coefficient requires consideration of amplitude descent difference, amplitude interval difference, average fluctuation index, mean of sequence similarity, and preset parameter tuning coefficients. The preset parameter tuning coefficients are constants pre-set based on the actual application scenario and the characteristics of the voltage signal, used to adjust the weights of different parameters in the periodic stability coefficient calculation. The specific calculation formula is as follows:

[0081] S=α×A+β×B+γ×C+δ×D

[0082] Where S represents the periodic stability coefficient, A represents the amplitude decrease difference, B represents the amplitude interval difference, C represents the average fluctuation index, D represents the mean of sequence similarity among all adjusted subsequences, and α, β, γ, and δ represent the preset parameter tuning coefficients for their respective parameters. Calculated using this formula, the periodic stability coefficient comprehensively reflects the stability of the voltage sequence across multiple dimensions, including amplitude variation, positional interval, trend fluctuation, and subsequence similarity. This coefficient provides an important reference for the subsequent calculation of the signal stability index, making the assessment of voltage signal stability more comprehensive and accurate.

[0083] Example 4: Obtaining the proportion of principal components and the difference index begins with the singular value decomposition (SVD) of the Hankel matrix. The Hankel matrix is ​​a square matrix constructed from voltage sequences according to specific rules. Each row of data represents a continuous segment of the voltage sequence, and the next row is formed by shifting the previous row one position to the right. Singular value decomposition of the Hankel matrix yields a series of singular values, which reflect the energy or importance of different components in the matrix. Arranging all singular values ​​in descending order forms a singular value sequence. Through this ordering, the singular values ​​at the beginning of the sequence typically represent the principal components of the matrix, while those at the end represent the secondary components.

[0084] The singular value sequence is processed using the Otsu thresholding method. The Otsu thresholding method automatically determines a threshold by analyzing the gray-scale distribution characteristics of the data in the sequence. This threshold divides the data into two categories, maximizing the inter-class variance between the two classes. After processing with the Otsu thresholding method, a specific threshold value is obtained. All singular values ​​greater than or equal to this threshold are classified as major singular values, and all singular values ​​less than this threshold are classified as minor singular values. The number of major singular values ​​is counted, and the ratio of this number to the total number of singular values ​​is calculated. This ratio represents the proportion of the major components in the entire singular value sequence, reflecting the proportion of the major components within the entire sequence.

[0085] To calculate the volatility index of significant singular values, first calculate the mean of all significant singular values ​​(the sum of all significant singular values ​​divided by the number of significant singular values). Then calculate the variance of these significant singular values, which reflects the degree to which each significant singular value deviates from its mean. Multiplying the mean and variance of the significant singular values ​​gives the volatility index of the significant singular value. The same method is used for minor singular values. First calculate the mean and variance of the minor singular values, then multiply them to obtain the volatility index of the minor singular values. Calculate the difference between the volatility indices of the significant and minor singular values, and take its absolute value. This absolute value is the difference index of the singular value sequence, which reflects the degree of difference in volatility characteristics between the primary and secondary components.

[0086] Obtaining the signal stability index requires considering the self-similarity coefficient of the Hankel matrix. The Pearson similarity coefficient is calculated between each row of data in the Hankel matrix and all other rows. The Pearson similarity coefficient measures the linear correlation between two rows; a larger absolute value indicates a higher correlation. For each row, the average of the absolute values ​​of its Pearson similarity coefficients with all other rows is taken to obtain the similarity coefficient for that row. The average of the similarity coefficients for all rows in the Hankel matrix is ​​then calculated; this average is the self-similarity coefficient of the Hankel matrix, reflecting the overall correlation between the rows.

[0087] Obtaining the signal stability index requires a comprehensive consideration of the proportion of the main components of the singular value sequence, the difference index, the self-similarity coefficient of the Hankel matrix, the periodic stability coefficient of the voltage sequence, and a preset parameter tuning factor. The preset parameter tuning factor is a value pre-set based on the operating characteristics of the electrostatic precipitator's high-voltage power supply and the characteristics of the voltage signal, used to balance the influence of different parameters in the signal stability index calculation. By integrating these parameters in a specific way, the final signal stability index of the voltage sequence is obtained. This index comprehensively reflects the overall stability of the voltage signal in terms of periodic stability, component characteristics, and internal correlation, providing a comprehensive basis for subsequent frequency adjustment. The entire process, from processing singular values ​​to calculating correlation coefficients and integrating multiple parameters, forms a complete signal stability index acquisition workflow, ensuring that the assessment of voltage signal stability covers multiple key dimensions.

[0088] Example 5: Precise adjustment of high-voltage power supply frequency based on signal stability index. First, the default threshold for wavelet denoising needs to be determined based on the signal stability index of the voltage sequence. The signal stability index reflects the overall stability of the voltage sequence, and its value has a specific correlation with the wavelet denoising threshold. When the signal stability index is high, it indicates that the voltage sequence has small fluctuations and strong stability. In this case, the corresponding default threshold can be appropriately increased to avoid excessive denoising leading to the loss of useful signals. When the signal stability index is low, it means that there are more fluctuations and noise interference in the voltage sequence, and the default threshold needs to be lowered accordingly to more effectively filter out noise components. This correlation is derived through the characteristic analysis of the voltage signal and the principle of wavelet denoising, ensuring that the default threshold setting matches the actual stable state of the voltage sequence.

[0089] After determining the default threshold for wavelet denoising, this threshold is used to denoise the voltage signal exhibiting frequency fluctuations. The wavelet denoising process involves decomposing the voltage signal into wavelet coefficients of different frequency components. These coefficients are then processed according to the default threshold, with coefficients below the threshold considered noise and set to zero, while coefficients greater than or equal to the threshold are retained as useful signal components. Subsequently, the processed wavelet coefficients are reconstructed into the denoised voltage signal using inverse wavelet transform. After denoising, random noise and high-frequency interference in the voltage signal are effectively suppressed, improving signal smoothness while retaining the main components reflecting frequency fluctuation characteristics, providing a more reliable signal basis for subsequent frequency adjustment calculations.

[0090] After denoising, the target adjustment frequency of the high-voltage power supply is calculated using the frequency adjustment method. This method analyzes the periodic characteristics and fluctuation patterns of the denoised voltage signal to determine the deviation between the current frequency and the ideal stable frequency. First, effective periodic information, including period length and amplitude variations within the period, is extracted from the denoised voltage signal. These parameters are then compared with preset ideal operating parameters to calculate the required frequency deviation. Based on the magnitude and direction of the frequency deviation, and considering the regulation characteristics of the high-voltage power supply, the final target adjustment frequency is determined. Determining the target adjustment frequency requires considering the output capacity of the high-voltage power supply, the load characteristics of the electrostatic precipitator, and the response speed of the frequency adjustment to ensure that the adjusted frequency allows the high-voltage power supply to operate stably and minimizes the impact of frequency fluctuations on dust removal efficiency.

[0091] When processing first-order difference sequences, the step function follows a clear labeling rule. For each element in the first-order difference sequence, it is judged one by one: if the element's value is greater than zero, it indicates that the two adjacent signal points corresponding to that element show an upward trend, and it is marked as a positive change; if the element's value is less than zero, it indicates that the adjacent signal points show a downward trend, and it is marked as a negative change; if the element's value is equal to zero, it indicates that the values ​​of the adjacent signal points have not changed, and it is marked as no change. Through this labeling method, the original first-order difference sequence composed of numerical values ​​is transformed into a differential step sequence composed of three state labels: positive, negative, and no change. The differential step sequence can intuitively show the direction and trend of voltage signal changes within a local range, clearly reflecting the detailed characteristics of signal fluctuations. This processing method does not require complex calculations, but effectively transforms numerical changes into an easily analyzable state sequence, providing clear basic data for subsequent calculations of parameters such as the oscillation index, making the quantitative analysis of the local fluctuation characteristics of the signal more convenient and accurate.

[0092] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0093] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator, characterized in that, The method includes the following steps: A voltage sequence composed of voltage signals fluctuating at frequency during the operation of a high-voltage power supply; The periodic segments are divided based on the distribution of peaks in the voltage sequence, and the periodic segments in the voltage sequence are clustered according to the distribution of periodic segments to obtain each adjustment subsequence; Based on the fluctuation of local signal change trends in the adjusted subsequence and the differences between local signals, the trend fluctuation index of each adjusted subsequence is obtained. Based on the differences in the changing trends of amplitude in the adjusted subsequences and the differences in the changing trends of amplitude in the order of amplitude in the adjusted subsequences, the differences in amplitude decrease and amplitude interval are obtained. The periodic stability coefficient of the voltage sequence is obtained based on the difference in amplitude decrease, the difference in amplitude interval, the average trend fluctuation index of all adjusted subsequences, and the average similarity between adjusted subsequences. Construct the Hankel matrix of the voltage sequence, perform singular value decomposition on the Hankel matrix to obtain each singular value, and obtain the main component proportion and difference index of the singular value sequence of the voltage sequence based on the distribution, average and difference of the singular values. The signal stability index of the voltage sequence is obtained based on the correlation between data in each row of the Hankel matrix, the periodic stability coefficient, the proportion of main components, and the difference index; the high-voltage power supply frequency is precisely adjusted based on the signal stability index.

2. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 1, characterized in that, The method for obtaining the adjusted subsequence is as follows: The peak and valley detection algorithm is used to obtain all peaks and valleys in the voltage sequence. The voltage sequence is divided into subsequences from each peak. The range of elements in each subsequence is calculated. The range of all subsequences is used as the input of the clustering algorithm to output each cluster. Calculate the mean of internal elements in each cluster, select the cluster with the largest mean of internal elements as the adjusted cluster, and select the voltage subsequence corresponding to the internal elements of the adjusted cluster as the adjusted subsequence.

3. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 1, characterized in that, The method for obtaining the trend fluctuation index is as follows: Based on the fluctuations in the local signal change trends and the differences between local signals in the adjusted subsequence, the oscillation coefficients and variation coefficients on both sides of each adjusted subsequence are obtained. The trend fluctuation index of each adjusted subsequence is obtained by combining the oscillation coefficients and change coefficients on both sides.

4. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 3, characterized in that, The method for obtaining the variation coefficients on both sides is as follows: For each adjusted subsequence, obtain the minimum value in each adjusted subsequence, take the minimum value and the subsequence consisting of all elements to the left of the minimum value as the left subsequence of each adjusted subsequence, and take the subsequence consisting of all elements to the right of the minimum value as the right subsequence of each adjusted subsequence. Obtain the first-order difference sequence of the left subsequence of each adjusted subsequence, and use the step function to process all elements in the first-order difference sequence to obtain the difference step sequence; Calculate the absolute value of the difference between the sum of the elements in the difference step sequence and the length of the first difference sequence of the left subsequence, and use it as the oscillation index of the left subsequence of each adjustment subsequence; Using the same method as for the left subsequence, obtain the oscillation index of the right subsequence of each adjusted subsequence; calculate the product of the absolute value of the difference between the oscillation indices of the left and right subsequences and the mean value as the oscillation coefficients of the two sides of each adjusted subsequence; Calculate the variance of the elements in the left subsequence and the variance of the elements in the right subsequence of each adjusted subsequence, and use the mean of the variances of the left and right subsequences as the variation coefficients on both sides of each adjusted subsequence.

5. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 2, characterized in that, The method for obtaining the amplitude interval difference is as follows: Sort all amplitude values ​​in all adjustment subsequences according to their position in the voltage sequence to construct an amplitude sequence; sort all amplitude values ​​in the adjustment subsequences according to their magnitude to construct an amplitude position sequence. Obtain the first-order difference sequences of the amplitude sequence and the amplitude position sequence. Use the variance of all elements in the first-order difference sequence of the amplitude sequence as the amplitude descent difference; use the variance of all elements in the first-order difference sequence of the amplitude position sequence as the amplitude interval difference.

6. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 1, characterized in that, The method for obtaining the periodic stability coefficient is as follows: Calculate the mean of the trend volatility indices of all adjusted subsequences as the average volatility index; The mean of the Pearson similarity coefficients between each adjusted subsequence and all other adjusted subsequences is taken as the sequence similarity of each adjusted subsequence; The periodic stability coefficient is calculated by combining the peak descent difference, peak interval difference, average volatility index, the mean of sequence similarity of all adjusted subsequences, and preset parameter tuning coefficients.

7. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 1, characterized in that, The method for obtaining the proportion of the main components and the difference index is as follows: Sorting all singular values ​​in descending order to construct a singular value sequence; The singular value sequence is used as the input to Otsu's thresholding method, and the output of Otsu's thresholding method is the threshold. All singular values ​​greater than or equal to the threshold are considered important singular values, and all singular values ​​less than the threshold are considered minor singular values. The ratio of the number of important singular values ​​to the total number of all singular values ​​is used as the proportion of the principal components of the singular value sequence. Calculate the mean and variance of all important singular values ​​in the singular value sequence, and use the product of the mean and variance as the volatility index of the important singular values. Using the same method as the volatility index of the important singular values, calculate the volatility index of the minor singular values, and use the absolute value of the difference between the volatility index of the important singular values ​​and the volatility index of the minor singular values ​​as the difference index of the singular value sequence.

8. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 1, characterized in that, The method for obtaining the signal stability index is as follows: Calculate the absolute value of the Pearson similarity coefficient between each row of data in the Hankel matrix and all other rows of data, and take the mean of the absolute values ​​of all the Pearson similarity coefficients of each row of data as the similarity coefficient of each row of data; take the mean of the similarity coefficients of all rows of data in the Hankel matrix as the self-similarity coefficient of the Hankel matrix. The signal stability index is calculated by combining the proportion of the main components of the singular value sequence, the difference index of the singular value sequence, the self-similarity coefficient of the Hankel matrix, the periodic stability coefficient of the current sequence, and the preset parameter tuning factor.

9. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 1, characterized in that, The precise adjustment of the high-voltage power supply frequency based on the signal stability index includes: The default threshold for wavelet denoising is obtained based on the signal stability index of the voltage sequence. The frequency fluctuation voltage signal is denoised using the default threshold of wavelet denoising, and the target adjustment frequency of the high-voltage power supply is calculated using the frequency adjustment method.

10. The method for precisely adjusting the frequency of an intelligent frequency-modulated high-voltage power supply for an electrostatic precipitator as described in claim 4, characterized in that, The step function is processed as follows: elements greater than zero in the first-order difference sequence are marked as positive changes, elements less than zero are marked as negative changes, and elements equal to zero are marked as no changes, thus forming a difference step sequence composed of positive, negative, and no-change labels.

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