Fusion filtering method, system, equipment and medium for monitoring winding state of power transformer

Abstract

The invention discloses a fusion filtering method, system, equipment and medium for power transformer winding state monitoring, and belongs to the technical field of power equipment state monitoring, and the method comprises the steps: obtaining an original state monitoring signal of a transformer winding; performing multi-scale decomposition on the original state monitoring signal by adopting self-adaptive wavelet transform; an improved particle filter is embedded, and a suggested distribution function of relative entropy optimization and a dynamic weight updating mechanism are combined; the filtered sub-signals are reconstructed through inverse wavelet transformation; weight parameters are adjusted in a self-adaptive mode; and outputting the key state parameters for transformer winding health assessment. Under the complex electromagnetic environment and the dynamic load fluctuation working condition, the signal-to-noise ratio of the state data of the transformer winding can be remarkably improved, the comprehensive accuracy rate of state evaluation is improved, and reliable data support is provided for health management and preventive maintenance of the transformer winding. And the operation reliability of the transformer and the intelligent level of state evaluation can be obviously improved.

Description

Technical Field

[0001] The present invention relates to the technical field of power equipment state monitoring, and in particular to a fusion filtering method, system, equipment and medium for power transformer winding state monitoring. Background Art

[0002] With the increasing complexity of power grids and load fluctuations, transformer windings face increasingly severe operating environments. They are susceptible to electromagnetic interference, multi-source noise, and complex operating conditions, resulting in a decline in the quality of condition monitoring data. Traditional data acquisition and signal processing technologies are unable to cope with these challenges. Existing transformer winding condition monitoring technologies, especially in complex electromagnetic environments, generally have the following problems:

[0003] 1. The electromagnetic interference in the transformer winding operating environment is complex. Traditional filtering methods are difficult to effectively suppress the composite interference from multiple sources and multiple frequency bands, resulting in a decrease in the signal-to-noise ratio.

[0004] 2. The operating state of the transformer changes dynamically. Traditional fixed parameter filtering methods are difficult to adapt to the non-stationary characteristics of signals caused by load fluctuations, harmonic interference, etc., and the filtering performance is limited.

[0005] 3. The state evolution of transformer windings is the result of the coupling of electromagnetic, thermal and mechanical multi-physical fields. Traditional methods are difficult to fully consider these coupling characteristics, which affects the accuracy of state assessment. Summary of the Invention

[0006] In order to solve the above technical problems, a fusion filtering method for power transformer winding state monitoring is proposed, including obtaining the original state monitoring signal of the transformer winding;

[0007] Adaptive wavelet transform is used to perform multi-scale decomposition of the original state monitoring signal, extract characteristic sub-signals of different frequency bands, and adaptively adjust the number of decomposition layers according to the signal bandwidth;

[0008] For each scale sub-signal, an improved particle filter is embedded, combining the relative entropy optimized proposed distribution function with a dynamic weight update mechanism to perform adaptive filtering on multi-source noise.

[0009] The filtered sub-signal is reconstructed by inverse wavelet transform to obtain the purified signal;

[0010] By constructing a signal energy entropy model, a signal-to-noise ratio evaluation index, and a weight control function, the dynamic fusion weight coefficients corresponding to the multi-scale signal components in the fusion filtering process are adaptively optimized and adjusted;

[0011] Key status parameters are output and used for transformer winding health assessment, supporting the accuracy and robustness of condition monitoring in complex electromagnetic environments.

[0012] As a preferred solution of the fusion filtering method for monitoring the state of the power transformer winding according to the present invention, the adaptive wavelet transform is expressed as:

[0013]

[0014] in, represents the j-th layer wavelet decomposition operator, X filter The signal after filtering is represented by matrix, X raw Represents the original state monitoring signal matrix of the transformer winding, represents the inverse wavelet transform operator, which is used to reconstruct the sub-signals of different scales after filtering, restore them from the frequency domain to the time domain, and achieve complete recovery of the signal. J represents the number of wavelet decomposition layers, and α j represents the dynamic weight coefficient, Φ IPF (·,Θ j ) represents the wavelet operator of the fused improved particle filter, where Θ j Represents the weight corresponding to the k-th wavelet basis function of the j-th layer.

[0015] As a preferred solution of the fusion filtering method for monitoring the state of the power transformer winding according to the present invention, the number of decomposition layers is determined by the adaptive signal bandwidth, which is expressed as:

[0016]

[0017] Among them, J represents the number of decomposition layers, log2 represents the logarithm with base 2, and f s Indicates the sampling frequency, f min is the lowest frequency component of the effective signal.

[0018] As a preferred solution of the fusion filtering method for monitoring the state of the power transformer windings according to the present invention, the dynamic weight updating mechanism is expressed as follows:

[0019]

[0020] Among them, D KL Represents the relative entropy divergence; q is the state transition suggestion distribution to be optimized; Q is the function set consisting of all feasible suggestion distributions, q * The asterisk * in (·) indicates the best recommended distribution function obtained through optimization, q * (x t ∣x t-1 ,z t ) represents the known previous state x t-1 and the current observation z t Under the condition of , the optimized state transition suggestion distribution function, || is the separation mark of the divergence operator, p(xt |x t-1 ) represents the conditional probability distribution of the real state transition; p(z t |x t ) represents the observation probability distribution of the observation model under a given state; q(x t ) represents the proposed distribution.

[0021] As a preferred solution of the fusion filtering method for monitoring the state of the power transformer windings according to the present invention, the adaptive adjustment of the weight parameters includes:

[0022] Aiming at the time-varying characteristics of the non-stationary vibration signal of the transformer winding, a dynamic weight optimization model with parameter self-correction capability is established;

[0023] The dynamic weight optimization model includes defining a real-time signal-to-noise ratio index, constructing weight space constraints based on signal energy entropy characteristics, and optimizing the objective function of the dynamic weight matrix.

[0024] As a preferred solution of the fusion filtering method for monitoring the state of the power transformer winding according to the present invention, the real-time signal-to-noise ratio index is expressed as:

[0025]

[0026] Among them, SNR(t) represents the signal-to-noise ratio, log 10 represents the base 10 logarithm, represents the square of the norm of the signal, s(t) and n(t) represent the effective signal component and noise component after wavelet packet decomposition, respectively;

[0027] Construct weight space constraints based on signal energy entropy characteristics:

[0028]

[0029] Among them, Φ(X raw ) represents the signal energy entropy characteristic function; X raw is the original state monitoring signal; E k is the energy proportion of the kth frequency band;

[0030] The energy proportion of the k-th frequency band is expressed as:

[0031]

[0032] Among them, x k represents the kth subband signal obtained by wavelet decomposition; N represents the total number of subbands obtained by wavelet decomposition; Indicates signal energy; E k Indicates the proportion of the kth frequency band in the total energy, which is used for dynamic weight evaluation;

[0033] The optimization objective function of the dynamic weight matrix W(t) is expressed as:

[0034]

[0035] Among them, x j (t) represents the filtered sub-signal of the jth scale; ω j (t) represents the corresponding dynamic fusion weight (real-valued function); represents the ideal reference signal; W i (t) represents the dynamic weight matrix under different signal channels; represents the Euclidean norm, used for error evaluation; represents the Frobenius norm, which serves as a regularization term; λ represents the regularization coefficient, which adjusts the model complexity; N is the number of signal fusion channels; and M represents the number of signal scale decomposition layers.

[0036] As a preferred solution of the fusion filtering method for monitoring the state of the power transformer windings described in the present invention, the wavelet basis function selection mechanism of the adaptive wavelet transform is optimized taking into account the time-frequency coupling characteristics of the winding vibration and temperature signals, which is expressed as:

[0037]

[0038] Among them, opt represents the optimal selection strategy of wavelet basis function obtained through optimization, Indicates the independent variable corresponding to the maximum value of the function, W f (a i ,b i ) indicates that the wavelet basis function has a scale parameter a i and displacement parameter b i The continuous wavelet transform coefficients under i represents the i-th scale parameter of the wavelet basis function, M represents the number of candidate wavelet basis functions or the number of wavelet parameter combinations, b i Represents the i-th displacement parameter of the wavelet basis function; I A-T (τ c ) represents the delay τ c The mutual information value between the vibration signal and the temperature signal at φ is used to quantify the time domain coupling strength between the two.

[0039] Another object of the present invention is to provide a fusion filtering system for monitoring the winding status of power transformers. The present invention combines the energy distribution and noise characteristics of the current signal to dynamically update the contribution ratio of sub-signals of different scales in the final reconstructed signal to improve the robustness and signal-to-noise ratio of the filtering output.

[0040] As a preferred solution of the fusion filtering system for monitoring the state of the power transformer winding described in the present invention, it is characterized by comprising: a data acquisition module for acquiring transformer winding state data; a data preprocessing module for performing denoising and formatting preprocessing on the acquired data; an adaptive wavelet transform optimization module for optimizing the wavelet basis function selection of the adaptive wavelet transform; an improved particle filter optimization module for optimizing the state transition equation of the improved particle filter; a multi-scale signal decomposition module for performing multi-scale signal decomposition; an improved particle filter noise suppression module for performing noise suppression using the improved particle filter algorithm; an inverse wavelet transform reconstruction module for performing inverse wavelet transform to reconstruct the filtered signal; a signal quality evaluation module for evaluating signal quality; a dynamic weight adaptive adjustment module for performing dynamic weight adaptive adjustment when the signal quality does not meet the requirements; a fusion filter output module for performing fusion filter output when the signal quality meets the requirements; an adaptive learning rate adjustment module for performing adaptive learning rate adjustment; a performance evaluation module for using the MEPTI indicator (Maximum Energy to Mean Power Time Index, The module is used to perform performance evaluation based on the performance evaluation index; the parameter fine-tuning module is used to perform parameter fine-tuning when the performance evaluation does not meet the standards; and the output module is used to output the optimized transformer winding status data.

[0041] A computer device includes a memory and a processor, wherein the memory stores a computer program and the processor implements the steps of the fusion filtering method for monitoring the state of a power transformer winding when executing the computer program.

[0042] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements the steps of the fusion filtering method for monitoring the state of a power transformer winding.

[0043] The beneficial effects of the present invention are as follows: By analyzing the electromagnetic environment complexity and multi-physical field coupling characteristics of transformer winding status data, an improved particle filter-adaptive wavelet transform fusion filtering framework is constructed, and a dynamic weight adaptation mechanism and algorithm optimization strategy are introduced, which effectively solves the problems of low signal filtering accuracy and insufficient adaptability of traditional filtering methods in complex electromagnetic environments and dynamic working conditions. Experimental results show that the method and device proposed in the embodiment of the present invention can significantly improve the signal-to-noise ratio and quality of transformer winding status monitoring data, improve the accuracy and reliability of status assessment, provide reliable technical support for transformer winding health management and preventive maintenance, and are of great significance to ensuring the safe and stable operation of the power system.

[0044] The embodiments of the present invention aim to provide a more effective and reliable power transformer winding condition monitoring technology to address the challenges faced by existing technologies in complex electromagnetic environments and dynamic operating conditions, improve the intelligence level of power equipment condition monitoring, and ensure the safe and stable operation of the power system. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0046] Figure 1 The present invention provides an overall flow chart of a fusion filtering method for monitoring the winding status of a power transformer according to an embodiment of the present invention.

[0047] Figure 2 A schematic structural diagram of an improved particle filter-adaptive wavelet transform fusion filter framework of a fusion filtering method for power transformer winding condition monitoring provided by an embodiment of the present invention.

[0048] Figure 3 A schematic diagram of the principle of a dynamic weight adaptive parameter adjustment mechanism of a fusion filtering method for power transformer winding state monitoring provided by an embodiment of the present invention.

[0049] Figure 4 This is a performance comparison diagram of an improved particle filter-adaptive wavelet transform fusion filtering algorithm and a traditional filtering algorithm of a fusion filtering method for power transformer winding condition monitoring provided by an embodiment of the present invention.

[0050] Figure 5 This is a signal comparison diagram of the fusion filtering method for power transformer winding status monitoring provided by one embodiment of the present invention. DETAILED DESCRIPTION

[0051] To make the above-mentioned objects, features, and advantages of the present invention more clearly understood, the following detailed description of the specific embodiments of the present invention is given in conjunction with the accompanying drawings. It is obvious that the described embodiments are only part of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by ordinary persons in this field without creative work should fall within the scope of protection of the present invention.

[0052] Example 1, reference Figure 1 , which is the first embodiment of the present invention, provides a fusion filtering method for monitoring the state of a power transformer winding, comprising:

[0053] Step 101: obtaining an original monitoring signal of a transformer winding;

[0054] Step 102: using adaptive wavelet transform to perform multi-scale decomposition on the original signal to obtain multiple decomposition levels;

[0055] Step 103: In each decomposition level, an improved particle filter algorithm is embedded, and the particle weights are dynamically adjusted in combination with the relative entropy optimization criterion to achieve non-stationary noise suppression;

[0056] Step 104: performing inverse wavelet transform on the filtered sub-signal to restore it to a time-domain purified signal;

[0057] Step 105: Extract features from the reconstructed time domain signal and analyze indicators such as frequency band energy and mutual information;

[0058] Step 106: Based on the multi-source interference modeling results, perform signal-to-noise ratio evaluation and dynamic weight update on the reconstructed signal;

[0059] Step 107: Output transformer winding state parameters for operation state judgment and abnormality identification;

[0060] Step 108: The temperature-shape variable adaptive weight adjustment mechanism can be introduced to further enhance the generalization ability of the model;

[0061] Step 109: Finally, high-precision acquisition of transformer status signals in a complex working environment under the fusion filtering architecture is achieved.

[0062] It should be noted that with the continuous advancement of smart grids and the intelligence of power equipment, power transformers, as critical components in the power grid, face significant challenges in terms of operational reliability, directly impacting the safe and stable operation of the entire grid. However, monitoring the winding condition of power transformers during actual operation presents significant challenges. Traditional monitoring methods and data processing technologies, particularly in complex electromagnetic environments and under dynamic operating conditions, have exposed numerous limitations. First, the electromagnetic interference (EMI) in the operating environment of power transformer windings is highly complex. The coexistence of multiple interference sources, including high-frequency pulse trains, power frequency harmonics, and non-stationary noise, results in a low signal-to-noise ratio (SNR) in the collected condition monitoring signals, easily obscuring valid information. Traditional filtering methods often struggle to balance signal fidelity and noise suppression when suppressing these complex interferences, resulting in low filtering accuracy.

[0063] Secondly, power transformer operating conditions are dynamic. Factors such as load fluctuations and changes in system operating mode can cause dynamic changes in transformer winding vibration, temperature, and other state parameters, making the condition monitoring signal non-stationary. Traditional fixed-parameter filtering methods are difficult to adapt to these dynamic changes. Filtering performance degrades with changing operating conditions, making it difficult to ensure monitoring accuracy and reliability.

[0064] Furthermore, the evolution of power transformer winding conditions is a multi-physics coupling process. Electromagnetic, thermal, and force fields couple and influence each other. Changes in winding state parameters such as vibration and temperature are not the result of a single physical field, but rather a comprehensive reflection of the effects of multi-physics coupling. Traditional monitoring methods and data processing technologies often focus on a single physical quantity, making it difficult to effectively extract and utilize multi-physics coupling information, resulting in incomplete and in-depth condition assessments.

[0065] Furthermore, advanced persistent threats (APTs) also warrant attention in the field of power equipment condition monitoring. While APT attacks primarily target network security, APT attacks against condition monitoring systems can indirectly threaten the safe operation of power systems by tampering with or interfering with monitoring data, misleading operators about equipment status. Traditional rule-based detection methods struggle to effectively identify and protect against these advanced threats.

[0066] Therefore, existing research methods have significant limitations in addressing the signal processing challenges faced by power transformer winding condition monitoring in complex electromagnetic environments and dynamic operating conditions. Traditional filtering methods struggle to meet the demands of high-precision and high-reliability condition monitoring. As power monitoring systems face increasingly complex operating environments and potential threats, new technical solutions are urgently needed to improve the data quality and intelligence level of condition monitoring.

[0067] In order to solve the technical problems existing in the above-mentioned existing methods, the method of this embodiment constructs an improved particle filter-adaptive wavelet transform fusion filtering framework that integrates the improved particle filter and the adaptive wavelet transform, and combines the dynamic weight adaptive adjustment mechanism and algorithm optimization strategy, so as to effectively improve the filtering accuracy and quality of the transformer winding status monitoring signal under complex electromagnetic environments and dynamic working conditions, and provide a more reliable data basis for subsequent status assessment, fault diagnosis and early warning.

[0068] Example 2, reference Figure 1 , which is the first embodiment of the present invention, provides a fusion filtering method for monitoring the state of a power transformer winding, comprising:

[0069] To address the problem of decreased acquisition accuracy caused by multi-source interference in transformer winding signals under complex working conditions, this embodiment proposes a fusion filtering method for power transformer winding condition monitoring that combines adaptive wavelet transform (AWT) and improved particle filter (IPF). The steps are as follows:

[0070] Step 201: obtaining an original monitoring signal of a transformer winding;

[0071] Step 202: using adaptive wavelet transform to perform multi-scale decomposition on the original signal to obtain multiple decomposition levels;

[0072] Step 203: In each decomposition level, an improved particle filter algorithm is embedded, and particle weights are dynamically adjusted in combination with the relative entropy optimization criterion to achieve non-stationary noise suppression;

[0073] Step 204: Perform an inverse wavelet transform on the filtered sub-signals to restore them to the time-domain purified signal. This inverse wavelet transform, as the reconstruction process of wavelet analysis, utilizes the wavelet basis functions and scaling functions corresponding to the decomposition process to restore the sub-signals at each scale after frequency domain denoising to the time-domain signal, achieving complete signal reconstruction. This process, used in the present invention to synthesize the filtered multi-scale characteristic signals into the purified original monitoring signal, is a standard process in current wavelet analysis methods and offers excellent signal fidelity and reconstruction stability.

[0074] Step 205: For the inverse-transformed time-domain purified signal, a signal energy entropy model and a signal-to-noise ratio evaluation index are constructed. Based on the multi-source interference modeling results, dynamic weight adaptive adjustment is achieved through a weight control function. The above indicators are used to evaluate signal quality and provide feedback to optimize the particle filtering and wavelet decomposition processes to improve the overall filtering performance.

[0075] Step 206: Output transformer winding state parameters for operation state judgment and abnormality identification;

[0076] Step 207: A temperature-shape variable adaptive weight adjustment mechanism can be introduced to further enhance the generalization capability of the model;

[0077] Step 208: Finally, high-precision acquisition of transformer status signals in a complex working environment under the fusion filtering architecture is achieved.

[0078] Specifically, the process of improving the signal filtering accuracy under complex working conditions in the method proposed in step 202 is as follows:

[0079] In an embodiment of the present invention, when the transformer winding operates in a complex electromagnetic environment, its state monitoring signal exhibits significant non-stationary characteristics, manifested as the time-frequency coupling effect of multiple interference sources such as high-frequency noise, transient disturbances and load fluctuations. In order to resolve the contradiction between signal fidelity and noise suppression in traditional filtering methods, the present invention example constructs a dynamic collaborative filtering architecture that integrates improved particle filtering (improved particle filtering) and adaptive wavelet transform. The core mathematical expression of this architecture is defined as:

[0080]

[0081] in, represents the j-th layer wavelet decomposition operator, X filter The signal after filtering is represented by matrix, X raw Represents the original state monitoring signal matrix of the transformer winding, represents the inverse wavelet transform operator, which is used to reconstruct the sub-signals of different scales after filtering, restore them from the frequency domain to the time domain, and achieve complete recovery of the signal. J represents the number of wavelet decomposition layers, and α j represents the dynamic weight coefficient, Φ IPF (·,Θ j ) represents the wavelet operator of the fused improved particle filter, where Θ j Represents the weight corresponding to the k-th wavelet basis function of the j-th layer.

[0082] It should be noted that the number of wavelet decomposition layers J is determined adaptively by the signal bandwidth:

[0083]

[0084] Among them, J represents the number of wavelet decomposition layers, f s Indicates the sampling frequency, f min is the lowest frequency component of the effective signal.

[0085] In the layered filtering process, the weight update mechanism of the improved particle filter adopts the suggestion distribution optimized by relative entropy:

[0086]

[0087] Among them, D KL represents the relative entropy (Kullback-Leibler, KL) divergence, which is used to measure the difference between two probability distributions; q is the state transition suggestion distribution to be optimized; Q is the function set consisting of all feasible suggestion distributions. * The asterisk * in (·) indicates the best recommended distribution function obtained through optimization, q * (x t ∣x t-1 ,z t ) represents the known previous state x t-1 and the current observation z t Under the condition of , the optimized state transition suggestion distribution function is used, where || is the separation identifier of the divergence operator. p(x t |x t-1 ) represents the conditional probability distribution of the real state transition; p(z t |x t ) represents the observation probability distribution of the observation model under a given state; q(x t ) represents the proposal distribution, which is the approximate posterior distribution used for sampling.

[0088] Dynamic weight coefficient α j The generation of is based on real-time working condition evaluation:

[0089] The optimized standard expression is:

[0090]

[0091] Among them, αj represents the dynamic weight of the j-th layer signal component in the final fusion result; is the energy value of the layer signal in the Teager energy domain, reflecting its instantaneous energy intensity; η j It represents the noise suppression factor or energy compression coefficient of the signal, which is used to enhance the signal significance; J is the total number of layers of wavelet decomposition; this ratio structure reflects the dynamic adjustment ability of the relative contribution of each layer of signal under the noise suppression mechanism.

[0092] The mathematical expression of the Teager energy operator is: Used to extract the instantaneous energy of the signal; where x represents the input signal; and Represent the first-order derivative and second-order derivative of the input signal respectively; satisfy the tight support condition, and its support interval supp is defined as:

[0093]

[0094] in, represents the kth wavelet basis function of the jth layer; Represents the support interval of the wavelet basis function in the time domain; the non-zero area (support) of the j-th layer and k-th wavelet basis function is in the time period This corresponds to the multi-scale and multi-position characteristics of wavelet. The energy normalization condition of wavelet basis function is as follows:

[0095]

[0096] Among them, ∫ is the energy normalization factor of the wavelet basis function, η j Represents the noise energy or scale signal-to-noise ratio weight coefficient of the j-th layer wavelet decomposition signal, which is often used to construct an inverse weight relationship, that is, η j -1 The larger the value, the smaller the noise level and the higher the signal reliability. Strictly define the kth wavelet basis atom in the jth layer The local support and energy specifications make the above formula (ie with all The coefficient matrix obtained by doing the inner product) can be traced back to its source. represents the frequency domain intensity of the jth layer, E j is the wavelet energy of this layer, and the two are used to characterize the scale signal-to-noise ratio.

[0097] Specifically, the key mechanism of the dynamic weight adjustment method described in the present invention is as follows:

[0098] In the embodiment of the present invention, a dynamic weight optimization model with parameter self-correction capability is established based on the time-varying characteristics of the non-stationary vibration signal of the transformer winding. The real-time signal-to-noise ratio index is defined as:

[0099]

[0100] Among them, SNR(t) represents the signal-to-noise ratio, which is the power ratio of the effective signal to the noise at time t; log 10 Represents the logarithm with base 10, which is used to convert the magnitude of a ratio into decibel units; Represents the square of the signal norm, which is used to measure signal power. s(t) and n(t) represent the effective signal component and noise component after wavelet packet decomposition, respectively. The weight space constraint condition is constructed based on the signal energy entropy feature:

[0101]

[0102] Among them, Φ(X raw ) represents the signal energy entropy characteristic function, reflecting the complexity of energy distribution in different frequency bands; X raw is the original state monitoring signal; E k is the energy proportion of the kth frequency band, defined as:

[0103]

[0104] Among them, x k represents the kth subband signal obtained by wavelet decomposition; N represents the total number of subbands obtained by wavelet decomposition; Indicates signal energy; E k Indicates the proportion of the kth frequency band in the total energy and is used for dynamic weight evaluation.

[0105] The optimization objective function of the dynamic weight matrix W(t) is expressed as:

[0106]

[0107] Among them, x j (t) represents the filtered sub-signal of the jth scale; ω j (t) represents the corresponding dynamic fusion weight (real-valued function); represents the ideal reference signal; W i (t) represents the dynamic weight matrix under different signal channels; represents the Euclidean norm, used for error evaluation; represents the Frobenius norm, which serves as a regularization term; λ represents the regularization coefficient, which adjusts the model complexity; N is the number of signal fusion channels; and M represents the number of signal scale decomposition layers.

[0108] Specifically, the optimization process of the improved particle filter-adaptive wavelet transform fusion filter algorithm for transformer winding condition monitoring in the method proposed in the present invention is as follows:

[0109] In this embodiment of the present invention, based on a transformer winding multi-physics coupling model and a mechanical-electrical parameter transfer characteristic model, an improved particle filter-adaptive wavelet transform fusion filtering algorithm is specifically optimized to better meet the specific needs of transformer winding condition monitoring. This optimized algorithm fully considers the time-frequency coupling characteristics of winding vibration and temperature signals, as well as the influence of mechanical deformation on electrical parameters, thereby improving the algorithm's adaptability to multi-physics coupling effects.

[0110] Specifically, considering the time-frequency coupling characteristics of the winding vibration and temperature signals, the wavelet basis function selection mechanism of the adaptive wavelet transform is optimized. The new selection criterion is expressed as:

[0111]

[0112] Among them, opt It represents the optimal selection strategy of wavelet basis function obtained through optimization, which is the best one in the candidate set. Indicates the independent variable (optimization target) corresponding to when the function reaches its maximum value, W f (a i ,b i ) indicates that the wavelet basis function has a scale parameter a i and displacement parameter b i The continuous wavelet transform coefficients under i represents the i-th scale parameter of the wavelet basis function (M represents the number of candidate wavelet basis functions or the number of wavelet parameter combinations, which is used to evaluate the energy distribution characteristics of the wavelet basis at different scales and displacements), controls the scaling characteristics of the wavelet function, b i Represents the i-th displacement parameter of the wavelet basis function, which controls the position characteristics of the wavelet function. A-T (τ c ) represents the delay τ c The mutual information value between the vibration signal and the temperature signal at φ is used to quantify the time domain coupling strength between the two.

[0113] In this paper, traditional particle filtering algorithms, based on state transitions and observation updates, suffer from problems such as particle degradation and accumulated sampling errors. To address this, we propose an improved particle filtering algorithm that optimizes the algorithm by embedding a mechanical-electrical coupling model and a dynamic parameter control mechanism. This optimized algorithm is collectively referred to herein as the "improved particle filter."

[0114] Based on the mechanical-electrical parameter transfer characteristic model, the state transfer equation of the improved particle filter is modified:

[0115] x t =f(x t-1 )+g(||ε|| F )+w t

[0116] Among them, f represents the state transfer function, which is the core definition of the state space model; x t Represents the state vector of the current particle, x t-1 is its state at the previous moment, g(||ε|| F ) represents the nonlinear deformation function constructed based on the Frobenius norm, which is used to characterize the influence of the strain tensor ε on the state transition, w t is the process noise of the particle.

[0117] Accordingly, the particle weight update formula is adjusted to:

[0118]

[0119] in, is the weight of the i-th particle at time t, is the weight of the i-th particle at the previous moment t-1, represents the current state of the i-th particle, y t is the observed value, ε is the strain tensor, and its Frobenius norm ||ε|| F Characterizes the overall magnitude of the deformation variable. P(·) is the joint probability distribution of the true state and the observation, q(·) is the proposed distribution, considering the optimal path for sampling the current state under multi-source disturbances, and t-1 represents the previous moment. t is the current observation value, which represents the observation signal received by the system at time t, Observation likelihood function, which means that in a given state The next observation is y t The probability of The true prior distribution of state transition, taking deformation factors into account, Proposed distribution function,for particle sampling, taking into account the current state, historical state and,perturbations.

[0120] In terms of fusion strategy, the fusion filter output formula is improved by taking into account the multi-physics field coupling effect:

[0121]

[0122] Among them, α j (t,T,||ε|| F ) represents the dynamic fusion weight corresponding to the j-th layer wavelet decomposition signal, which depends on time t, temperature T and strain intensity; W j(·) is the j-th layer wavelet transform operator, Φ IPF To improve the particle filter output mapping function, it reflects the characteristic components of the signal after denoising and reconstruction. This fusion method improves the credibility and time-frequency consistency of the output signal under complex working conditions.

[0123] In addition, based on the electromagnetic-thermal-mechanical coupling model, the adaptive learning rate adjustment mechanism is optimized:

[0124] η(t)=η0·exp(-βt)+γ·sigmoid(SNR(t))+δ·H(ω,t)

[0125] Where η(t) represents the current learning rate, η0 is the initial value of the learning rate, β is the time decay factor, and the sigmoid function is used to adjust the current signal-to-noise ratio's response to the learning rate. H(ω,t) represents the high-frequency perturbation response function, reflecting the impact of frequency-domain energy changes on state sampling perturbations. ω is the frequency component. This mechanism ensures the dynamic stability of parameter updates and prevents overshoot during filtering. γ is the strain-related regulation function, and δ is the dynamic scaling factor.

[0126] Specifically, through the aforementioned optimization, the improved particle filter-adaptive wavelet transform fusion filtering algorithm better incorporates the physical model characteristics of the transformer winding, improving not only the filtering accuracy but also the physical interpretability of the algorithm results. This approach, combining research object modeling with advanced algorithms, provides a more reliable data foundation for transformer winding condition assessment and is of great significance for improving the performance of transformer winding online monitoring systems. This optimization algorithm is suitable for transformer winding health management and preventive maintenance and is expected to play a significant role in the field of power equipment monitoring and diagnosis technology.

[0127] In summary, by constructing an improved particle filter-adaptive wavelet transform fusion filtering framework, designing a dynamic weight adaptation mechanism, and performing algorithm optimization, this present invention has established a comprehensive and efficient signal processing solution for transformer winding condition monitoring, significantly improving signal quality and the reliability of condition assessment under complex operating conditions. Specifically, the system effectively combines the advantages of adaptive wavelet transform in time-frequency analysis with the dynamic noise suppression capabilities of improved particle filtering through the improved particle filter-adaptive wavelet transform fusion filtering algorithm.

[0128] Example 3, reference Figure 2-Figure 5 , which is the third embodiment of the present invention, provides a fusion filtering method for monitoring the state of power transformer windings. In order to verify the beneficial effects of the present invention, scientific demonstration is carried out through experiments.

[0129] To verify the application effect of the present invention in the transformer winding online monitoring system, tests and verification based on specific embodiments were conducted. The test environment includes hardware configuration and software tools to ensure the comprehensiveness and accuracy of the test.

[0130] Table 1 shows the specific parameter settings of the simulation model and algorithm. These parameter settings ensure that the simulation environment can fully test and verify the performance and effects of the present invention in different scenarios, providing reliable data support and theoretical basis for practical applications.

[0131] Table 1 Simulation model and algorithm parameter settings

[0132]

[0133]

[0134] Figure 2 Comparative signal-to-noise ratio (SNR) results for three filtering algorithms—the improved particle filter-adaptive wavelet transform, the improved particle filter, and the adaptive wavelet transform—are presented. The figure clearly shows that the improved particle filter-adaptive wavelet transform algorithm achieves the best SNR, reaching 32.18 dB, significantly higher than the 16.98 dB of the improved particle filter and the 21.48 dB of the adaptive wavelet transform. The improved particle filter-adaptive wavelet transform algorithm improves by 15.20 dB compared to the improved particle filter and by 10.70 dB compared to the adaptive wavelet transform, demonstrating significant performance advantages. Furthermore, the standard deviation of the improved particle filter-adaptive wavelet transform algorithm is 2.37 dB, slightly higher than the 1.85 dB of the improved particle filter and the 2.12 dB of the adaptive wavelet transform, indicating room for improvement in its stability under various operating conditions. The results show that the improved particle filter-adaptive wavelet transform fusion filtering algorithm effectively combines the nonlinear processing capabilities of the improved particle filter with the time-frequency analysis advantages of the adaptive wavelet transform, demonstrating enhanced anti-interference capabilities in complex electromagnetic environments. Compared with either the improved particle filter or the adaptive wavelet transform alone, the improved particle filter-adaptive wavelet transform algorithm can better handle the time-frequency coupling characteristics of multi-source and multi-type signals in transformer winding condition monitoring, achieving a significant improvement in signal filtering accuracy. This result validates the superiority of the improved particle filter-adaptive wavelet transform algorithm in processing multi-physics field coupled transformer winding models and provides more reliable technical support for online monitoring of transformer winding conditions.

[0135] Figure 3 This is a schematic diagram of the dynamic weight adaptive parameter adjustment mechanism proposed in the present invention, showing the feedback control relationship between signal energy entropy, signal-to-noise ratio, and dynamic learning rate, which is used to dynamically adjust the weight parameters of each sub-signal in a complex environment. Figure 3(a) shows the mean square error (MSE) trends of the three algorithms during the iterative convergence process, using a logarithmic coordinate system to intuitively demonstrate the convergence characteristics of the algorithms. It can be observed that the improved particle filter-adaptive wavelet transform fusion algorithm (red curve) exhibits superior convergence characteristics: the initial MSE value is approximately 80, which drops below 0.5 after approximately 150 iterations. The improved particle filter algorithm alone (blue dashed line) remains around 5 after 200 iterations. Although the adaptive wavelet transform algorithm (green dotted line) eventually drops to around 1, its convergence speed is significantly slower than that of the fusion algorithm. Notably, the improved particle filter-adaptive wavelet transform algorithm breaks through the convergence threshold (MSE = 1.0) at approximately 120 iterations, reaching convergence approximately 80 iterations earlier than the improved particle filter algorithm, demonstrating a significant computational efficiency advantage. Figure 3 (b) The robustness of the fusion algorithm under varying electromagnetic interference intensities was further verified, demonstrating a comparison of the signal-to-noise ratio (SNR) performance of the three algorithms. Under weak interference conditions, the improved particle filter-adaptive wavelet transform (IPF-AWT) achieved an SNR of 35.5 dB, 7.0 dB higher than the improved particle filter and 3.5 dB higher than the adaptive wavelet transform. Even under extremely strong interference, the IPF-AWT maintained an SNR of 18.5 dB, exceeding the acceptable performance threshold (15 dB), while the IPF achieved only 7.5 dB under these conditions, which no longer meets practical application requirements. Data analysis shows that the IPF-AWT algorithm has the most significant performance advantage under moderate interference conditions, achieving a 10.5 dB (62%) improvement over the improved particle filter and a 5.5 dB (25%) improvement over the adaptive wavelet transform. This result fully demonstrates the adaptability of the proposed fusion filter architecture in complex electromagnetic environments. By effectively combining the global search capability of the improved particle filter with the local feature extraction advantages of the adaptive wavelet transform, a significant improvement in filtering performance is achieved. The experimental results reveal the combined advantages of the improved particle filter-adaptive wavelet transform fusion algorithm in terms of convergence speed, stability, and anti-interference ability, providing an efficient and reliable technical solution for signal processing in transformer winding condition monitoring.

[0136] The fusion filtering algorithm based on improved particle filter and adaptive wavelet transform (improved particle filter-adaptive wavelet transform) shows significant advantages in many aspects. Figure 4 (a) Shows the signal-to-noise ratio comparison results of the improved particle filter-adaptive wavelet transform fusion algorithm under different interference conditions. Its memory usage, CPU utilization, and delay resource index are 23.15%, 24.73%, and 12.89%, respectively, which are 15.27%, 10.94%, and 13.02% lower than those of the traditional scheme. Figure 4(b) Shows the changing trends of the minimum mean square error (MSE) of different algorithms in a strong interference environment, demonstrating the superiority of the improved particle filter-adaptive wavelet transform in the delay-accuracy trade-off. Its average delay is 49.83ms and the accuracy is 94.87%, while the traditional solution has a delay of 208.45ms and an accuracy of 92.47%. Figure 4 (c) The performance of each algorithm under the delay-accuracy trade-off is demonstrated, and the resource consumption of each component is detailed. The standardized resource consumption index of the improved particle filter-adaptive wavelet transform in computing engine, data transmission and model inference are 45.36, 32.18 and 28.95, respectively, which are all lower than the traditional solution. Figure 4 (d) shows a comparative analysis of system resource usage (CPU, memory), highlighting the consistency advantage of the improved particle filter-adaptive wavelet transform across different test points. Its latency ranged from 38.45ms to 61.23ms, while the traditional solution fluctuated between 169.35ms and 241.78ms. These data fully demonstrate the significant effectiveness of the improved particle filter-adaptive wavelet transform algorithm in resource utilization, performance balance, and multi-dimensional optimization, providing strong support for efficient data processing in edge computing environments.

[0137] Figure 5 This is a comparison diagram of the signal waveforms before and after filtering. The figure shows the matching of the original signal, the superimposed noise signal, and the filtered reconstructed signal in the time domain, which intuitively reflects the denoising performance and signal fidelity of the algorithm of the present invention. Figure 5 (a) shows a direct comparison between the original signal (blue) and the noise signal (red). It can be seen that while the noise signal retains the main frequency characteristics of the original signal, it also superimposes a significant high-frequency interference component. The peak noise amplitude reaches ±1.8, which seriously affects the signal quality. Figure 5 The lower middle sub-figure (b) shows the precise match between the reconstructed signal (green) and the original signal (blue) after processing using the improved particle filter-adaptive wavelet transform algorithm. Quantitative analysis shows that the reconstructed signal not only fully preserves the periodic characteristics of the original signal (approximately 50Hz fundamental frequency), but also effectively suppresses high-frequency noise components. The reconstructed waveform closely matches the original waveform, improving waveform fidelity by approximately 87.3%. Particularly noteworthy is that in time periods such as 0.2s to 0.4s and 0.6s to 0.8s, despite relatively high noise interference, the reconstructed signal still accurately restores the amplitude characteristics of the original signal, demonstrating the robustness of the algorithm in non-stationary noise environments.

[0138] Example 4 is the fourth embodiment of the present invention, which differs from the first three embodiments in that:

[0139] If the functions are implemented in the form of software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes several instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present invention. The aforementioned storage medium includes various media that can store program codes, such as a USB flash drive, a mobile hard disk, a read-only memory (ROM), a random access memory (RAM), a magnetic disk, or an optical disk.

[0140] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as an ordered list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0141] More specific examples (a non-exhaustive list) of computer-readable media include the following: an electrical connection with one or more wires (electronic devices), a portable computer disk cartridge (magnetic devices), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program is printed, since the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, deciphering, or processing in another suitable manner as necessary, and then stored in a computer memory.

[0142] It should be understood that various parts of the present invention can be implemented using hardware, software, firmware, or a combination thereof. In the above-described embodiments, multiple steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, it can be implemented using a combination of any of the following technologies known in the art: a discrete logic circuit having logic gate circuits for implementing logic functions on data signals, an application-specific integrated circuit having suitable combinational logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0143] Embodiment 5, the fifth embodiment of the present invention, provides a fusion filtering system for monitoring the state of a power transformer winding, comprising:

[0144] A data acquisition module is used to obtain transformer winding status data;

[0145] Data preprocessing module, used for denoising and formatting the acquired data;

[0146] Adaptive wavelet transform optimization module, used to optimize the selection of wavelet basis functions for adaptive wavelet transform;

[0147] Improved particle filter optimization module, used to optimize the state transfer equation of the improved particle filter;

[0148] Multi-scale signal decomposition module, used for multi-scale signal decomposition;

[0149] Improved particle filter noise suppression module, used to suppress noise using improved particle filter algorithm;

[0150] An inverse wavelet transform reconstruction module is used to perform inverse wavelet transform to reconstruct the filtered signal;

[0151] A signal quality evaluation module, used for evaluating signal quality;

[0152] Dynamic weight adaptive adjustment module, used for dynamic weight adaptive adjustment when signal quality does not meet the requirements;

[0153] Fusion filter output module, used for fusion filter output when the signal quality meets the requirements;

[0154] Adaptive learning rate adjustment module, used for adaptive learning rate adjustment;

[0155] Performance evaluation module, used to perform performance evaluation using the MEPTI indicator;

[0156] Parameter fine-tuning module, used to fine-tune parameters when performance evaluation does not meet the standards;

[0157] The output module is used to output optimized transformer winding status data.

[0158] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that the technical solutions of the present invention may be modified or replaced by equivalents without departing from the spirit and scope of the technical solutions of the present invention, which should all be included in the scope of the claims of the present invention.

Claims

1. A fusion filtering method for monitoring the winding condition of a power transformer, characterized by: include, Obtaining the original status monitoring signal of the transformer winding; Adaptive wavelet transform is used to perform multi-scale decomposition of the original state monitoring signal, extract characteristic sub-signals of different frequency bands, and adaptively adjust the number of decomposition layers according to the signal bandwidth; For each scale sub-signal, an improved particle filter is embedded, combining the relative entropy optimized proposed distribution function with a dynamic weight update mechanism to perform adaptive filtering on multi-source noise. The filtered sub-signal is reconstructed by inverse wavelet transform to obtain the purified signal; By constructing a signal energy entropy model, a signal-to-noise ratio evaluation index, and a weight control function, the dynamic fusion weight coefficients corresponding to the multi-scale signal components in the fusion filtering process are adaptively optimized and adjusted; Key status parameters are output and used for transformer winding health assessment, supporting the accuracy and robustness of condition monitoring in complex electromagnetic environments.

2. The fusion filtering method for monitoring the state of a power transformer winding according to claim 1, characterized in that: The adaptive wavelet transform is expressed as, in, represents the j-th layer wavelet decomposition operator, X filter The signal after filtering is represented by matrix, X raw Represents the original state monitoring signal matrix of the transformer winding, represents the inverse wavelet transform operator, which is used to reconstruct the sub-signals of different scales after filtering, restore them from the frequency domain to the time domain, and achieve complete recovery of the signal. J represents the number of wavelet decomposition layers, and α j represents the dynamic weight coefficient, Φ IPF (·,Θ j ) represents the wavelet operator of the fused improved particle filter, where Θ j Represents the weight corresponding to the k-th wavelet basis function of the j-th layer.

3. The fusion filtering method for monitoring the state of a power transformer winding according to claim 2, characterized in that: The number of decomposition layers is determined by the signal bandwidth adaptively, which is expressed as, Among them, J represents the number of decomposition layers, log2 represents the logarithm with base 2, and f s Indicates the sampling frequency, f min is the lowest frequency component of the effective signal.

4. The fusion filtering method for monitoring the state of a power transformer winding according to claim 3, characterized in that: The dynamic weight update mechanism is expressed as, Among them, D KL Represents the relative entropy divergence; q is the state transition suggestion distribution to be optimized; Q is the function set consisting of all feasible suggestion distributions, q * The asterisk * in (·) indicates the best recommended distribution function obtained through optimization, q * (x t ∣x t-1 ,z t ) represents the known previous state x t-1 and the current observation z t Under the condition of , the optimized state transition suggestion distribution function, || is the separation mark of the divergence operator, p(x t |x t-1 ) represents the conditional probability distribution of the real state transition; p(z t |x t ) represents the observation probability distribution of the observation model under a given state; q(x t ) represents the proposed distribution.

5. The fusion filtering method for monitoring the state of a power transformer winding according to claim 4, characterized in that: Adaptive adjustment of weight parameters includes, Aiming at the time-varying characteristics of the non-stationary vibration signal of the transformer winding, a dynamic weight optimization model with parameter self-correction capability is established; The dynamic weight optimization model includes defining a real-time signal-to-noise ratio index, constructing weight space constraints based on signal energy entropy characteristics, and optimizing the objective function of the dynamic weight matrix.

6. The fusion filtering method for monitoring the state of a power transformer winding according to claim 5, characterized in that: The real-time signal-to-noise ratio indicator is expressed as, Among them, SNR(t) represents the signal-to-noise ratio, log 10 represents the base 10 logarithm, represents the square of the norm of the signal, s(t) and n(t) represent the effective signal component and noise component after wavelet packet decomposition, respectively; Construct weight space constraints based on signal energy entropy characteristics: Among them, Φ(X raw ) represents the signal energy entropy characteristic function; X raw is the original state monitoring signal; E k is the energy proportion of the kth frequency band; The energy proportion of the k-th frequency band is expressed as: Among them, x k represents the kth subband signal obtained by wavelet decomposition; N represents the total number of subbands obtained by wavelet decomposition; Indicates signal energy; E k Indicates the proportion of the kth frequency band in the total energy, which is used for dynamic weight evaluation; The optimization objective function of the dynamic weight matrix W(t) is expressed as: Among them, x j (t) represents the filtered sub-signal of the jth scale; ω j (t) represents the corresponding dynamic fusion weight (real-valued function); represents the ideal reference signal; W i (t) represents the dynamic weight matrix under different signal channels; represents the Euclidean norm, used for error evaluation; represents the Frobenius norm, which serves as a regularization term; λ represents the regularization coefficient, which adjusts the model complexity; N is the number of signal fusion channels; and M represents the number of signal scale decomposition layers.

7. The fusion filtering method for monitoring the state of a power transformer winding according to claim 6, characterized in that: Considering the time-frequency coupling characteristics of winding vibration and temperature signals, the wavelet basis function selection mechanism of adaptive wavelet transform is optimized and expressed as: Among them, opt represents the optimal selection strategy of wavelet basis function obtained through optimization, Indicates the independent variable corresponding to the maximum value of the function, W f (a i ,b i ) indicates that the wavelet basis function has a scale parameter a i and displacement parameter b i The continuous wavelet transform coefficients under i represents the i-th scale parameter of the wavelet basis function, M represents the number of candidate wavelet basis functions or the number of wavelet parameter combinations, b i Represents the i-th displacement parameter of the wavelet basis function; I A-T (τ c ) represents the delay τ c The mutual information value between the vibration signal and the temperature signal at φ is used to quantify the time domain coupling strength between the two.

8. A fusion filtering system for monitoring the winding state of a power transformer, applying the fusion filtering method for monitoring the winding state of a power transformer as claimed in any one of claims 1 to 7, characterized in that: include: A data acquisition module is used to obtain transformer winding status data; Data preprocessing module, used for denoising and formatting the acquired data; Adaptive wavelet transform optimization module, used to optimize the selection of wavelet basis functions for adaptive wavelet transform; Improved particle filter optimization module, used to optimize the state transfer equation of the improved particle filter; Multi-scale signal decomposition module, used for multi-scale signal decomposition; Improved particle filter noise suppression module, used to suppress noise using improved particle filter algorithm; An inverse wavelet transform reconstruction module is used to perform inverse wavelet transform to reconstruct the filtered signal; A signal quality evaluation module, used for evaluating signal quality; Dynamic weight adaptive adjustment module, used for dynamic weight adaptive adjustment when signal quality does not meet the requirements; Fusion filter output module, used for fusion filter output when the signal quality meets the requirements; Adaptive learning rate adjustment module, used for adaptive learning rate adjustment; Performance evaluation module, used to perform performance evaluation using the MEPTI indicator; Parameter fine-tuning module, used to fine-tune parameters when performance evaluation does not meet the standards; The output module is used to output optimized transformer winding status data.

9. A computer device comprising a memory and a processor, wherein the memory stores a computer program, wherein: When the processor executes the computer program, the steps of the fusion filtering method for monitoring the state of a power transformer winding are implemented as described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the fusion filtering method for monitoring the state of a power transformer winding are implemented as described in any one of claims 1 to 7.

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