Method for detecting thickness uniformity of liquid-cooled server copper bar electroplating layer

Abstract

The present application relates to the field of electroplating layer detection, and particularly relates to a liquid-cooled server copper bar electroplating layer thickness uniformity detection method, which comprises: recording impedance sequence by eddy current full-length scanning on the surface of the copper bar to be detected; calculating the first-order difference standard deviation of the amplitude sequence in each local window as the oscillation strength; calculating the absolute value of the normalized correlation coefficient between the amplitude sequence in each local window and the lagging one rolling wave spatial period version thereof as the period correlation degree; performing normalization processing on the oscillation strength and the period correlation degree and taking the product to obtain the lift-off dominance of each local window; determining the adaptive regularization parameter corresponding to each local window according to the lift-off dominance, performing low-rank sparse decomposition on the Hankel matrix constructed by the normalized amplitude sequence, and restoring the electroplating layer thickness distribution sequence of the copper bar to evaluate the electroplating layer thickness uniformity. The present application can reduce the missed detection rate of the end electroplating layer thin area.

Description

Technical Field

[0001] This invention relates to the field of electroplating layer inspection, and more particularly to a method for inspecting the uniformity of electroplating layer thickness on copper busbars of liquid-cooled servers. Background Technology

[0002] The method for testing the uniformity of electroplated coating thickness of copper busbars in liquid-cooled servers is an incoming quality inspection technique for critical conductive and thermally conductive components in data centers. Copper busbars in liquid-cooled servers are responsible for high-current transmission and heat dissipation between modules. Their surface electroplated coating must ensure contact stability during long-term current flow and resist corrosion in the liquid cooling environment. Therefore, thickness uniformity testing is necessary to control the quality of incoming copper busbars before installation.

[0003] As data centers evolve towards higher power densities, the power of a single rack has increased from tens of kilowatts to hundreds of kilowatts or even higher. Consequently, the current density and temperature gradient experienced by copper busbars are rising in tandem, leading to increasingly stringent requirements for their long-term reliability. Early methods for coating inspection primarily employed magnetic thickness measurement or X-ray fluorescence. The former is ill-suited for non-ferromagnetic substrates, while the latter suffers from high equipment costs and limited scanning efficiency. Eddy current scanning, due to its fast detection speed and non-contact operation, has become the mainstream method for scanning the electroplated thickness of copper busbars.

[0004] Chinese patent document CN109345563B discloses a moving target detection method based on low-rank sparse decomposition, comprising the following steps: First, constructing a structured sparse induced norm expression with overlapping block structure based on the structured distributed sparse signal; Second, extending the above structured sparse induced norm expression to obtain the final structured sparse induced norm expression applied to video; Third, further dividing the sparse part S in the low-rank sparse decomposition algorithm into dynamic background E and foreground moving target F; Fourth, combining the above structured sparse induced norm expression and the further division of the sparse part to obtain the final low-rank sparse decomposition model; Fifth, solving the obtained low-rank sparse decomposition model to obtain the foreground target based on the solution.

[0005] In the eddy current signal processing stage, the low-rank sparse decomposition method separates the low-rank components and sparse components after constructing the measurement sequence into a Hankel matrix. It has been widely adopted because it does not depend on a preset frequency band and is suitable for processing aliasing components.

[0006] However, in actual testing scenarios for copper busbars in liquid-cooled servers, the surface of the copper busbar substrate after rolling has microscopic ripples. Due to the lateral constraints and springback differences of the material, the amplitude of the ripples exhibits a spatial distribution that is strong at both ends and weak in the middle along the length of the copper busbar. Consequently, the lift-off noise oscillation intensity generated during probe scanning shows obvious spatial non-uniformity. Existing low-rank sparse decomposition methods control component distribution with uniform regularization parameters along the entire length, which is difficult to match with this spatial non-uniform oscillation. This results in a systematic deviation between the thickness distribution obtained from the test and the actual service performance of the copper busbar. That is, the thinner end plating that should have been detected is masked by noise and judged as qualified. After the copper busbar is installed in the liquid-cooled server and put into operation, corrosion and leakage and contact heating occur from the ends under the long-term action of the liquid cooling medium, causing rack-level failures and downtime, resulting in decreased data center availability and increased operation and maintenance costs. Summary of the Invention

[0007] To address the problem that existing low-rank sparse decomposition methods, which use globally uniform regularization parameters, cannot adapt to the uneven spatial distribution of lift-off noise intensity along the length of the copper busbar surface, which is strong at both ends and weak in the middle, resulting in the thinner plating at the ends being masked by noise and thus missed, this invention provides a method for detecting the uniformity of electroplating thickness of copper busbars in liquid-cooled servers.

[0008] This invention provides a method for detecting the uniformity of electroplating thickness on copper busbars in liquid-cooled servers, employing the following technical solution: S1: Perform a full-length eddy current scan on the surface of the copper busbar to be tested to record the impedance sequence, and extract the impedance amplitude for standardization to obtain a standardized amplitude sequence. S2: Calculate the rolling ripple spatial period of the normalized amplitude sequence, and divide the normalized amplitude sequence into multiple local windows according to the rolling ripple spatial period. Calculate the first-order difference standard deviation of the amplitude sequence in each local window as the oscillation intensity. S3: Calculate the absolute value of the normalized correlation coefficient between the amplitude sequence within each local window and its version lagged by one rolling corrugation spatial cycle, as the periodic correlation. S4: Normalize the correlation between oscillation intensity and period and multiply them to obtain the lift-off dominance of each local window; S5: Determine the adaptive regularization parameters corresponding to each local window based on the lift-off dominance. Use the adaptive regularization parameters to perform low-rank sparse decomposition on the Hankel matrix constructed from the normalized amplitude sequence to restore the coating thickness distribution sequence of the copper busbar. Then, evaluate the coating thickness uniformity based on the range and coefficient of variation.

[0009] The technical effect of this invention is as follows: by calculating the correlation between oscillation intensity and period through a local window and fusing them into the lift-off dominance, and then adaptively adjusting the regularization parameters to perform low-rank sparse decomposition, it can adaptively separate noise from the true thickness signal for the uneven spatial distribution of lift-off noise intensity along the length direction of the copper busbar, which is strong at both ends and weak in the middle. This effectively avoids the thinner plating area at the end being masked by noise and thus missed detection, thereby improving the accuracy of plating thickness uniformity detection.

[0010] Preferably, the specific steps for performing a full-length eddy current scan of the copper busbar surface to be tested to record the impedance sequence and extract the impedance amplitude for standardization to obtain a standardized amplitude sequence are as follows: control the eddy current probe to move at a constant speed along the length of the copper busbar, and record the real and imaginary parts of the eddy current impedance at each sampling position in real time; take the magnitude of the vector formed by the real and imaginary parts of the eddy current impedance at each sampling position as the eddy current impedance amplitude at that position, and arrange the eddy current impedance amplitudes of all sampling positions in sequence to form an amplitude sequence; calculate the global mean and standard deviation of the amplitude sequence, subtract the global mean from the amplitude at each sampling position, and then process it by using the global standard deviation as the divisor to obtain the standardized amplitude sequence.

[0011] The technical effect of this invention is as follows: by taking the modulus of the real and imaginary parts of the eddy current impedance to obtain the amplitude sequence and performing Z-score normalization, the DC bias and dimensional differences of the amplitude sequence can be eliminated, so that the amplitude fluctuations of different local regions are at a uniform amplitude scale, providing a reliable standardized input for the subsequent horizontal comparison of indicators such as oscillation intensity and period correlation between local windows.

[0012] Preferably, the specific steps for calculating the rolling ripple spatial period of the standardized amplitude sequence are as follows: calculate the autocorrelation coefficients of the standardized amplitude sequence under different integer lags; traverse all integer values ​​with lags greater than zero, and determine the lag at the position of the first local maximum in the corresponding autocorrelation coefficient sequence as the rolling ripple spatial period.

[0013] The technical effect of this invention is that by calculating the autocorrelation coefficient under different integer hysteresis values ​​for the standardized amplitude sequence, and determining the hysteresis value at the location of the first local maximum as the rolling ripple spatial period, the ripple period can be automatically estimated from the signal without prior acquisition of process parameters such as roll diameter and feed speed, thus adapting to the process differences of different batches of copper busbars.

[0014] Preferably, the specific steps for dividing the standardized amplitude sequence into multiple local windows based on the spatial period of the rolling ripples are as follows: Based on the rolling ripple spatial period, the standardized amplitude sequence is divided into multiple non-overlapping local windows; the length of each local window is uniformly set to three rolling ripple spatial periods to ensure that each local window covers more than three complete oscillation periods.

[0015] The technical effect of this invention is as follows: the standardized amplitude sequence is divided into non-overlapping local windows based on the rolling ripple spatial period, and the window length is uniformly set to three rolling ripple spatial periods, ensuring that each local window covers more than three complete oscillation periods. At the same time, the window length is greater than one period, providing a sufficient sample size for subsequent calculation of oscillation intensity and period correlation. Moreover, each window is independent of the others, which facilitates local feature extraction.

[0016] Preferably, the specific steps for calculating the first-order difference standard deviation of the amplitude sequence within each local window as the oscillation intensity are as follows: Within each local window, the amplitude differences of adjacent sampling points are arranged sequentially to form the first-order difference sequence of the corresponding local window; the standard deviation of the first-order difference sequence within each local window is calculated and used as the oscillation intensity of the corresponding local window.

[0017] The technical effect of this invention is that by calculating the standard deviation of the first-order difference sequence as the oscillation intensity within each local window, the severity of amplitude fluctuations in the local area can be directly quantified. This index maintains a monotonically positive correlation with the oscillation intensity of the lift-off noise, providing a reliable first-dimensional basis for subsequently distinguishing the lift-off noise intensity of different regions.

[0018] Preferably, the specific steps for calculating the absolute value of the normalized correlation coefficient between the amplitude sequence within each local window and its version lagged by one rolling corrugation spatial cycle, as the periodic correlation, are as follows: Within each local window, extract the local amplitude sequence within that window; obtain the amplitude sequence version corresponding to the local amplitude sequence lagged by one rolling wave space cycle; calculate the normalized correlation coefficient between the local amplitude sequence and the version lagged by one rolling wave space cycle, and use the absolute value of the normalized correlation coefficient as the periodic correlation of that local window.

[0019] The technical effect of this invention is that by calculating the absolute value of the normalized correlation coefficient between the local amplitude sequence and its lagging version of the rolling ripple spatial cycle in each local window as the periodic correlation, the spatial quasi-periodicity of the local signal can be effectively quantified, thereby distinguishing periodic lift-off noise from non-periodic coating thickness anomalies, and making up for the deficiency that the source of oscillation cannot be determined by oscillation intensity alone.

[0020] Preferably, the specific steps for normalizing the correlation between oscillation intensity and period and multiplying them to obtain the lift-off dominance of each local window are as follows: Max-min normalization is applied to the oscillation intensity of all local windows to obtain the normalized oscillation intensity; max-min normalization is applied to the periodic correlation of all local windows to obtain the normalized periodic correlation; the normalized oscillation intensity of each local window is multiplied by the normalized periodic correlation to obtain the lift-off dominance of that local window.

[0021] The technical effect of this invention is as follows: after performing maximum and minimum normalization on the oscillation intensity and periodic correlation of all local windows, the product is taken to obtain the lift-off dominance. The normalized oscillation intensity and periodic correlation are both dimensionless confidence indices in the range of 0 to 1. The product of the two is the joint confidence obtained by performing a fuzzy logic "logical AND" fusion on the two independent pieces of evidence, namely, the high oscillation amplitude and the high quasi-periodic regularity. This ensures that the lift-off dominance only takes a large value when both the oscillation intensity and quasi-periodicity are high. If either one is low, the lift-off dominance will be significantly reduced. This allows the large adjustment of the regularization parameter to be precisely limited to the lift-off noise dominance region, avoiding erroneous adjustments to the true thickness anomaly region.

[0022] Preferably, the specific steps for constructing the Hankel matrix from the standardized amplitude sequence are as follows: set the number of rows of the Hankel matrix to half of the total number of sampling points after rounding down; extract the corresponding elements from the standardized amplitude sequence to construct the Hankel matrix according to the rule of subtracting the amplitude at the corresponding sampling point from the sum of the row number and column number of the matrix.

[0023] The technical effect of this invention is as follows: the standardized amplitude sequence is constructed into a Hankel matrix, the number of rows is half of the total number of sampling points rounded down, and the elements are filled in such a way that the sum of the row number and column number minus one corresponds to the sampling point position. This ensures that all elements on the same anti-diagonal line in the matrix correspond to the same sampling position of the original signal, providing a structural basis for the subsequent low-rank sparse decomposition and restoration to a one-dimensional sequence along the anti-diagonal line.

[0024] Preferably, the specific steps for performing low-rank sparse decomposition on the Hankel matrix constructed from the standardized amplitude sequence using adaptive regularization parameters are as follows: The Hankel matrix is ​​sequentially updated using the alternating direction multiplier method framework, performing low-rank component matrix updates, sparse component matrix updates, and dual variable updates until the residuals satisfy the convergence condition. Specifically, in the sparse component matrix update, the anti-diagonal index p+q-1 corresponding to the element in the p-th row and q-th column of the Hankel matrix is ​​divided by the local window length and rounded up to obtain the number of the local window to which the element belongs. The adaptive regularization parameter of the local window corresponding to this index is then used as a soft threshold to perform soft threshold shrinkage on the element.

[0025] The technical effects of this invention are as follows: Under the framework of the alternating direction multiplier method, the globally unified soft threshold in the sparse component update is replaced with an adaptive threshold assigned according to the local window to which the element belongs; since the elements on the same anti-diagonal in the Hankel matrix correspond to the same sampling position of the original signal, the number of the local window to which the element belongs is determined according to the anti-diagonal index and a soft threshold is applied to each element, avoiding the phase distortion caused by the same sampling point being given different penalty strengths on different anti-diagonals when dividing the window by column. This allows different local regions to obtain a matching sparse contraction intensity according to their own lift-off noise intensity. The stronger the lift-off noise, the larger the threshold, thereby achieving adaptive suppression of spatially non-uniform lift-off noise, while avoiding over-processing of weak noise regions.

[0026] Preferably, the steps for restoring the copper busbar plating thickness distribution sequence and evaluating the plating thickness uniformity based on the range and coefficient of variation are as follows: The mean values ​​of the low-rank component matrix and sparse component matrix obtained from the decomposition are taken along the anti-diagonal direction, and the mean values ​​of the elements on each anti-diagonal line are arranged sequentially to restore the macroscopic thickness sequence and the local thickness deviation sequence, respectively; the macroscopic thickness sequence and the local thickness deviation sequence are superimposed after conversion using calibration curves to obtain the copper busbar plating thickness distribution sequence; the maximum and minimum values ​​in the plating thickness distribution sequence are extracted to calculate the range, and the ratio of the standard deviation to the mean is calculated to obtain the coefficient of variation; if both the range and the coefficient of variation are within the preset acceptable threshold, the copper busbar electroplating thickness uniformity is deemed acceptable; otherwise, it is deemed unacceptable, and the locations where the thickness deviation exceeds the threshold are marked as process re-inspection areas.

[0027] The technical effect of this invention is as follows: by taking the average of the low-rank component matrix and sparse component matrix obtained by decomposition along the anti-diagonal and restoring them, and then superimposing them after calibration curve conversion, a coating thickness distribution sequence is obtained. The range and coefficient of variation are used for quantitative evaluation, which can comprehensively reflect the maximum deviation range and relative fluctuation level of coating thickness over the entire length range. When the coating is unqualified, the position where the thickness deviation exceeds the threshold is automatically marked, providing clear guidance for subsequent process review.

[0028] The present invention has the following technical effects: By constructing a lift-off dominance index that integrates oscillation intensity and periodic correlation, and adaptively adjusting the regularization parameters of each local window in the low-rank sparse decomposition accordingly, it is possible to accurately match the spatially uneven distribution of lift-off noise on the copper busbar surface, which is strong at both ends and weak in the middle along the length direction. This effectively separates periodic lift-off noise from the actual coating thickness anomaly, reduces the false negative rate in the thinner coating area at the end, and improves the accuracy and reliability of coating thickness uniformity detection. Attached Figure Description

[0029] Figure 1This is a flowchart of a method for detecting the uniformity of electroplating thickness of copper busbars in liquid-cooled servers according to the present invention.

[0030] Figure 2 This is a schematic diagram showing the spatial distribution of the three indicators of the present invention along the length of the copper busbar.

[0031] Figure 3 This is a schematic diagram of the low-rank sparse decomposition results of the eddy current signal in this invention. Detailed Implementation

[0032] 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, not all, of the embodiments of the present invention. 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.

[0033] This invention discloses a method for detecting the uniformity of electroplating thickness on copper busbars in liquid-cooled servers, referring to... Figure 1 This includes the following steps: S1: Eddy current scanning and signal normalization.

[0034] The testing system consists of an impedance-type eddy current probe, a single-axis linear scanning mechanism, and an impedance analyzer. Before testing, the copper busbar to be tested is horizontally fixed on the testing stage to ensure that the copper busbar does not shift or deform during the scanning process.

[0035] After the test begins, the eddy current probe moves at a constant speed along the length of the copper busbar. Throughout the entire scanning stroke, the lift-off value between the probe's bottom surface and the copper busbar surface remains stable under ideal conditions. The impedance analyzer records the real and imaginary parts of the eddy current impedance in real time at each sampling location using a fixed sampling frequency, and sequentially numbers the sampling locations. , where N is the total number of sampling points. After the scan is completed, a complete impedance sequence containing the real and imaginary parts of each sampling position is obtained.

[0036] After obtaining the impedance sequence, the magnitude of the vector formed by the real and imaginary parts of the eddy current impedance at each sampling location is used as the eddy current impedance amplitude at that location. The eddy current impedance amplitudes at all sampling locations are arranged sequentially to form an amplitude sequence. Z-score standardization is then performed on the amplitude sequence: the global mean and standard deviation of the amplitude sequence are calculated, and the global mean is subtracted from the amplitude at each location, with the global standard deviation as the divisor, to obtain the standardized amplitude sequence. Standardization eliminates the DC bias in the amplitude sequence, ensuring that the amplitude fluctuations in different local regions are on a uniform amplitude scale, facilitating subsequent horizontal comparisons of indicators between different local windows.

[0037] S2: Calculation of local oscillation intensity.

[0038] The copper busbar substrate is formed by rolling. The contact surface between the rolls and the substrate leaves periodic ripples on the surface of the copper busbar along the rolling direction. The spatial period of the ripples is determined by the roll diameter and feed speed. Under the same batch and rolling process parameters, this spatial period remains stable throughout the entire length of the copper busbar. However, due to the influence of differences in the tool path and material springback, the ripple amplitude at various locations on the copper busbar exhibits systematic variations along its length. At the two ends of the copper busbar, due to the weakened lateral constraint of the material and greater rolling springback, the peak-to-valley difference of the surface ripples is higher than that in the middle section. In the middle section, constrained by adjacent material, the deformation is more uniform, and the ripple amplitude is relatively lower. Taking a 500mm long copper busbar as an example, the peak-to-valley difference of the surface ripples within a 200mm range in the middle section is approximately 3μm to 5μm, while the peak-to-valley difference within a 50mm range at each end can reach 8μm to 12μm.

[0039] During eddy current scanning, the actual lift-off value varies periodically with the ripple fluctuations, forming an oscillating component in the eddy current amplitude signal with the same spatial period as the ripples—this is lift-off noise. The ripple amplitudes at both ends of the copper busbar are larger, corresponding to higher lift-off noise oscillation intensities; the ripple amplitudes in the middle section are smaller, corresponding to lower lift-off noise oscillation intensities. Fixed regularization parameters cannot adaptively adjust to this spatial distribution of lift-off noise intensity. Therefore, it is necessary to first construct an index that reflects the lift-off noise oscillation intensity in each local area, providing a basis for subsequent spatially differentiated adjustments of the regularization parameters.

[0040] The autocorrelation coefficients of the standardized amplitude sequence under different integer lags τ are calculated. Iterating through all integer values ​​of τ greater than zero, the lag at the location of the first local maximum in the corresponding autocorrelation coefficient sequence is determined as the estimated value of the rolling ripple spatial period, denoted as b, with units of sampling points. Based on b, the standardized amplitude sequence is divided into non-overlapping local windows, each with a uniform length of 3b sampling points. This ensures that each local window covers more than three complete oscillation cycles and satisfies the condition that the window length is greater than b, guaranteeing sufficient sample size for subsequent autocorrelation coefficient calculations. The i-th local window covers the sampling positions. to The standardized amplitude sequence within the window is denoted as the local amplitude sequence.

[0041] Calculate the first-order difference for the local amplitude sequence within each local window. This involves arranging the differences in amplitude between adjacent sampling points within the local window sequentially to form the first-order difference sequence for that window. Use the standard deviation of the first-order difference sequence for each local window as the oscillation intensity of that window. By traversing all local windows, the oscillation intensity sequence is obtained.

[0042] The larger the amplitude of the lift-off noise oscillation, the more frequent the amplitude jumps between adjacent sampling points, the higher the dispersion of the first-order difference sequence, and the greater the corresponding oscillation intensity. Conversely, regions with smaller ripple amplitudes exhibit weaker lift-off noise oscillations, with smoother amplitude changes between adjacent sampling points, lower dispersion of the first-order difference sequence, and corresponding smaller oscillation intensity. The oscillation intensity maintains a monotonically positive correlation with the lift-off noise oscillation intensity of each local region, which can serve as the first dimension for subsequent spatial differentiation adjustments of the regularization parameter.

[0043] Step S3: Identification of oscillation periodicity.

[0044] Oscillation intensity directly measures the amplitude fluctuation of a local region, but local anomalies in coating thickness can also cause significant jumps in eddy current amplitude at their locations. When the amplitude of anomalies in thickness in a local region is comparable to that of lift-off noise oscillations, their contributions to oscillation intensity are similar, making it impossible to determine whether the oscillation originates from lift-off noise or a genuine coating thickness anomaly based solely on oscillation intensity. If the regularization parameter is adjusted only based on oscillation intensity, locations with larger thickness anomaly amplitudes also correspond to higher oscillation intensities. The algorithm misclassifies these areas as high-noise regions and increases the sparsity threshold, causing genuine anomalies to be included in low-rank components, resulting in missed detections. Therefore, it is necessary to construct an index reflecting the quasi-periodicity of local signals, used in conjunction with oscillation intensity, to limit the adjustment of regularization parameters to regions where oscillations originate from lift-off noise.

[0045] The surface ripples of the copper busbar substrate are formed by the rolling process. The roll diameter and feed speed of the same batch of copper busbars are kept consistent, and the spatial period of the ripples is stable over the entire length of the copper busbar. The lift-off value fluctuates with the same spatial period as the ripples, and the corresponding lift-off noise exhibits stable spatial quasi-periodic characteristics in the eddy current signal: the distance between adjacent peaks and valleys of the lift-off noise at each location is always close to b. This characteristic is determined by the periodic physical mechanism of the rolling process and does not disappear with local changes in the intensity of the lift-off noise oscillation.

[0046] Local anomalies in coating thickness are formed by local current density deviations or disturbances in the plating solution flow field. They are randomly distributed on the copper busbar surface, with no fixed spacing between adjacent anomalies, and do not exhibit quasi-periodic characteristics. When lift-off noise dominates within a local window, the two signal segments at a lag of b sampling points are in close phase with a high degree of linear correlation. When thickness anomalies dominate within a local window, there is no regular correlation between signal amplitudes at different locations, and the normalized correlation coefficient at a lag of b is low. Taking measured data as an example, the absolute value of the normalized correlation coefficient at a lag of b in the lift-off noise-dominated region can reach above 0.7, while that in the thickness anomaly-dominated region is usually below 0.2.

[0047] Within each local window, the normalized correlation coefficient between the local amplitude sequence and its version lagged by b sampling points is calculated. The absolute value of this correlation coefficient is taken as the periodic correlation of that local window. This process is repeated across all local windows to obtain the periodic correlation sequence. The more significant the quasi-periodicity of the local signal, the higher the linear correlation between the two signals at lag b, and the greater the periodic correlation. When the window is dominated by randomly distributed thickness anomalies, the two signals have no systematic correlation, and the periodic correlation is low. The periodic correlation distinguishes the contribution of lift-off noise and thickness anomalies to the signal from the perspective of the spatial regularity of oscillations, making up for the insufficiency of judging the signal source solely by amplitude fluctuations of oscillation intensity, and providing a second dimension of information for the subsequent construction of lift-off dominance.

[0048] Step S4: Calculate the degree of dominance.

[0049] Oscillation intensity reflects the oscillation amplitude of a local area, while periodicity reflects the spatial quasi-periodicity of the local oscillation. Lift-off noise is caused by rolling ripples and is characterized by both high oscillation intensity and significant spatial quasi-periodicity; both are indispensable. Regions with strong oscillations but no quasi-periodic pattern correspond to predominantly abnormal coating thickness. In this case, increasing the regularization parameter will push the true anomalies into low-rank components, causing missed detections. Regions with significant quasi-periodicity but extremely weak oscillation amplitude have low lift-off noise levels and do not require significant adjustment of the regularization parameter. Only when both oscillation intensity and quasi-periodicity are high do they correspond to regions dominated by lift-off noise, requiring an increase in the regularization parameter to strengthen the suppression of lift-off noise.

[0050] In extreme cases, a localized area of ​​the copper busbar may simultaneously exhibit lift-off noise of comparable amplitude and plating thickness anomalies. In this scenario, the oscillation intensity is high, and the period correlation falls between the range dominated by pure noise and the range dominated by pure anomalies. If the regularization parameter is adjusted solely based on the oscillation intensity, increasing the regularization parameter will suppress both lift-off noise and genuine anomalies, leading to missed detections in this area. By incorporating the period correlation into the index multiplicatively, the lift-off dominance is set at an intermediate value in this mixed region. This corresponds to a moderate adjustment range for the regularization parameter, which suppresses lift-off noise to a certain extent while allowing for the retention of genuine anomalies.

[0051] Oscillation intensity and periodicity correlation characterize the oscillation amplitude and quasi-periodic regularity of the signal in a local region, respectively. First, the oscillation intensity of all local windows is subjected to max-min normalization, which converts it into a dimensionless confidence score representing the degree to which the oscillation amplitude of that window is high, with a value ranging from 0 to 1. Then, the periodicity correlation of all local windows is subjected to max-min normalization, which converts it into a dimensionless confidence score representing the degree to which the quasi-periodic regularity of that window is high, also with a value ranging from 0 to 1. Multiplying the two is equivalent to performing a fuzzy logic "logical AND" fusion of two independent pieces of evidence: high oscillation amplitude and high quasi-periodic regularity, to obtain a joint confidence score where both are true. The product is close to 1 only when both confidence scores are high; a low score for either one will significantly reduce the product. This yields the lift-off dominance of that local window. Traversing all local windows yields a lift-off dominance sequence.

[0052] The lift-off dominance value ranges from 0 to 1: when both the oscillation intensity and quasi-periodicity are high in the local region, the lift-off dominance value approaches 1, corresponding to the lift-off noise-dominated region; when the oscillation is strong but the quasi-periodicity is low, the lift-off dominance value is significantly lower than 1 due to the low correlation of the normalized period, corresponding to the thickness anomaly-dominated region; when both are low, the lift-off dominance value approaches zero, and the regularization parameter remains at the baseline level. Combining the two indicators in a product form, the lift-off dominance value takes a larger value only when both the oscillation intensity and quasi-periodicity are high. A low value for either one significantly reduces the lift-off dominance value, thus precisely limiting the adjustment of the regularization parameter to the lift-off noise-dominated region, providing a complete basis for the calculation of the adaptive regularization parameters for each local window in step S5.

[0053] Step S5: Adaptive decomposition and uniformity assessment.

[0054] The adaptive regularization parameters for each local window are calculated based on the lift-off dominance sequence: the first-order difference standard deviation of the amplitude sequence within each local window (i.e., the oscillation intensity calculated in step S2) is used as the noise intensity metric for that window. The minimum noise intensity metric of all local windows is taken as the reference noise intensity. The ratio of the noise intensity metric of each local window to the reference noise intensity is recorded as the upper limit of the regularization gain for that window. Based on the preset reference regularization parameter, the product of the lift-off dominance of each local window, the reference regularization parameter, and the upper limit of the regularization gain is superimposed on the reference regularization parameter to obtain the adaptive regularization parameters for each local window. When the lift-off dominance is 0, the adaptive regularization parameter is equal to the baseline regularization parameter; when the lift-off dominance is 1, the adaptive regularization parameter is the product of the baseline regularization parameter and the upper limit of the regularization gain. The higher the noise intensity metric of the window, the larger the upper limit of the regularization gain. The adaptive regularization parameter in the middle region changes linearly with the lift-off dominance between the baseline value and the above product value. The region with stronger lift-off noise corresponds to a larger sparse contraction threshold.

[0055] The normalized amplitude sequence is constructed as a Hankel matrix, with the number of rows taken as half the total number of sampling points N, rounded down. The construction rule is that the element in the p-th row and q-th column of the matrix is ​​taken from the amplitude at the (p+q-1)-th sampling point of the normalized amplitude sequence. From this construction rule, it can be seen that all elements on the same anti-diagonal line in the Hankel matrix correspond to the same sampling position in the normalized amplitude sequence. This property is directly utilized in the subsequent signal reconstruction step.

[0056] The Hankel matrix is ​​decomposed into a low-rank sparse matrix using the alternating direction multiplier method framework. The Hankel matrix is ​​decomposed into the sum of low-rank component matrices and sparse component matrices. The iterative process executes three sub-steps in sequence: the low-rank component matrix is ​​updated using singular value thresholding shrinkage, and the dual variable is updated using the standard steps of the alternating direction multiplier method. Both are consistent with the original algorithm.

[0057] The original algorithm applied the same soft threshold to all elements of the Hankel matrix for shrinkage. This method replaces the globally uniform threshold with an adaptive threshold assigned according to the local window to which the element belongs. Elements on the same anti-diagonal of the Hankel matrix correspond to the same sampling position of the original signal. If windows are divided by column and the same threshold is applied to all elements in the column, elements on the same anti-diagonal will be assigned to window numbers corresponding to different columns, resulting in different penalty strengths for the same sampling point on different anti-diagonals, causing phase distortion. To address this, for the element in the p-th row and q-th column of the Hankel matrix, its anti-diagonal index p+q-1 is taken. p+q-1 is divided by the local window length and rounded up to obtain the number of the local window to which the element belongs. The adaptive regularization parameter of the local window corresponding to this number is used as the soft threshold to perform soft threshold shrinkage on the element. This process is repeated for all elements in the matrix to complete the soft threshold shrinkage of the sparse component matrix. This improvement only modifies the threshold allocation method in the sparse component update; the update structure of the low-rank components and dual variables remains unchanged. The three sub-steps are iterated repeatedly until the residuals meet the convergence condition, and the low-rank component matrix and sparse component matrix are output.

[0058] Since the elements on the same anti-diagonal of the Hankel matrix correspond to the same sampling position of the original signal, after decomposition, the average values ​​of the low-rank component matrix and the sparse component matrix are taken along the anti-diagonal direction, and the average values ​​of the elements on each anti-diagonal are arranged in sequence to restore two one-dimensional sequences. The former corresponds to the macroscopic distribution of the coating thickness on the copper busbar surface, and the latter corresponds to the local abnormal component of the coating thickness after noise separation.

[0059] Before testing, a calibration curve between eddy current amplitude and coating thickness is pre-established using a standard test piece. The two one-dimensional sequences are converted into a macro thickness sequence and a thickness deviation sequence respectively through the calibration curve. The two are then superimposed to obtain a complete coating thickness distribution sequence along the length of the copper busbar surface.

[0060] Taking the range and coefficient of variation of the thickness distribution sequence as the uniformity evaluation indicators, the range is the difference between the maximum value and the minimum value in the thickness distribution sequence, which reflects the maximum deviation amplitude of the coating thickness within the full length range; the coefficient of variation is the ratio of the standard deviation to the mean of the thickness distribution sequence, which reflects the relative level of fluctuation of the coating thickness. The range and the coefficient of variation are respectively compared with the preset qualification thresholds in the inspection standard. If both are within the qualification thresholds, it is determined that the thickness uniformity of the electroplated coating of the copper bar is qualified; otherwise, it is determined as unqualified, and the thickness distribution diagram along the length direction of the copper bar is output, and the positions where the thickness deviation exceeds the threshold are marked as process recheck areas.

[0061] Figure 2 is a schematic diagram of the spatial distribution of the three indicators of the present invention along the length direction of the copper bar, and the spatial distribution curves of the oscillation intensity, the periodic correlation and the lift-off dominance along the length direction of the copper bar are shown in the figure. All three curves show higher values in the two end regions of the copper bar and lower values in the middle region, which is consistent with the rule that the amplitude of the surface ripple at the two ends of the copper bar caused by rolling springback is higher than that in the middle section; the peak value of the lift-off dominance curve in the two end regions is significantly higher than the respective peak values of the oscillation intensity and the periodic correlation, which verifies that the product form can precisely limit the adjustment of the regularization parameters to the region dominated by lift-off noise.

[0062] Figure 3 is a schematic diagram of the low-rank and sparse decomposition result of the eddy current signal according to the present invention, in which the distribution curves of the normalized original eddy current amplitude signal, the low-rank component and the sparse component along the length direction of the copper bar are presented. The low-rank component curve is smooth, reflecting the macroscopic distribution trend of the coating thickness on the surface of the copper bar; the sparse component shows obvious peaks at two positions, corresponding to the locally too-thin and too-thick regions of the coating, and the values at the other positions are close to zero, indicating that the lift-off noise has been effectively separated by the low-rank component, and the positions and amplitudes of the local abnormal components are clearly distinguishable.

[0063] The above are all preferred embodiments of the present invention, which are not intended to limit the protection scope of the present invention. Therefore, all equivalent changes made according to the structure, shape and principle of the present invention shall be covered within the protection scope of the present invention.

Claims

1. A method for detecting the uniformity of electroplated layer thickness on copper busbars of liquid-cooled servers, characterized in that, Includes the following steps: S1: Perform a full-length eddy current scan on the surface of the copper busbar to be tested to record the impedance sequence, and extract the impedance amplitude for standardization to obtain a standardized amplitude sequence. S2: Calculate the rolling ripple spatial period of the normalized amplitude sequence, and divide the normalized amplitude sequence into multiple local windows according to the rolling ripple spatial period. Calculate the first-order difference standard deviation of the amplitude sequence in each local window as the oscillation intensity. S3: Calculate the absolute value of the normalized correlation coefficient between the amplitude sequence within each local window and its version lagged by one rolling corrugation spatial cycle, as the periodic correlation. S4: Normalize the correlation between oscillation intensity and period and multiply them to obtain the lift-off dominance of each local window; S5: Determine the adaptive regularization parameters corresponding to each local window based on the lift-off dominance. Use the adaptive regularization parameters to perform low-rank sparse decomposition on the Hankel matrix constructed from the normalized amplitude sequence to restore the coating thickness distribution sequence of the copper busbar. Then, evaluate the coating thickness uniformity based on the range and coefficient of variation.

2. The method for detecting the uniformity of copper busbar plating thickness in a liquid-cooled server according to claim 1, characterized in that, The specific steps for performing a full-length eddy current scan on the surface of the copper busbar under test to record the impedance sequence and extract the impedance amplitude for standardization to obtain the standardized amplitude sequence are as follows: control the eddy current probe to move at a constant speed along the length of the copper busbar, and record the real and imaginary parts of the eddy current impedance at each sampling position in real time; take the magnitude of the vector formed by the real and imaginary parts of the eddy current impedance at each sampling position as the eddy current impedance amplitude at that position, and arrange the eddy current impedance amplitudes of all sampling positions in sequence to form an amplitude sequence; calculate the global mean and standard deviation of the amplitude sequence, subtract the global mean from the amplitude at each sampling position, and then process it by using the global standard deviation as the divisor to obtain the standardized amplitude sequence.

3. The method for detecting the uniformity of electroplated layer thickness of copper busbar in a liquid-cooled server according to claim 1, characterized in that, The specific steps for calculating the rolling ripple spatial period of the standardized amplitude sequence are as follows: calculate the autocorrelation coefficients of the standardized amplitude sequence under different integer lags; traverse all integer values ​​with lags greater than zero, and determine the lag at the position of the first local maximum in the corresponding autocorrelation coefficient sequence as the rolling ripple spatial period.

4. The method for detecting the uniformity of copper busbar plating thickness in a liquid-cooled server according to claim 1, characterized in that, The specific steps for dividing the standardized amplitude sequence into multiple local windows based on the spatial period of the rolling ripples are as follows: Based on the rolling ripple spatial period, the standardized amplitude sequence is divided into multiple non-overlapping local windows; the length of each local window is uniformly set to three rolling ripple spatial periods to ensure that each local window covers more than three complete oscillation periods.

5. The method for detecting the uniformity of copper busbar plating thickness in a liquid-cooled server according to claim 1, characterized in that, The specific steps for calculating the first-order difference standard deviation of the amplitude sequence within each local window as the oscillation intensity are as follows: Within each local window, the amplitude differences of adjacent sampling points are arranged sequentially to form the first-order difference sequence of the corresponding local window; the standard deviation of the first-order difference sequence within each local window is calculated and used as the oscillation intensity of the corresponding local window.

6. The method for detecting the uniformity of electroplating thickness of copper busbars in liquid-cooled servers according to claim 1, characterized in that, The specific steps for calculating the absolute value of the normalized correlation coefficient between the amplitude sequence within each local window and its version lagged by one rolling corrugation spatial cycle, as a measure of the periodic correlation, are as follows: Within each local window, extract the local amplitude sequence within that window; obtain the amplitude sequence version corresponding to the local amplitude sequence lagged by one rolling wave space cycle; calculate the normalized correlation coefficient between the local amplitude sequence and the version lagged by one rolling wave space cycle, and use the absolute value of the normalized correlation coefficient as the periodic correlation of that local window.

7. The method for detecting the uniformity of copper busbar plating thickness in a liquid-cooled server according to claim 1, characterized in that, The specific steps for normalizing the correlation between oscillation intensity and period and multiplying them to obtain the lift-off dominance of each local window are as follows: Max-min normalization is applied to the oscillation intensity of all local windows to obtain the normalized oscillation intensity; max-min normalization is applied to the periodic correlation of all local windows to obtain the normalized periodic correlation; the normalized oscillation intensity of each local window is multiplied by the normalized periodic correlation to obtain the lift-off dominance of that local window.

8. The method for detecting the uniformity of copper busbar plating thickness in a liquid-cooled server according to claim 1, characterized in that, The specific steps for constructing the Hankel matrix from the normalized amplitude sequence are as follows: set the number of rows of the Hankel matrix to half of the total number of sampling points after rounding down; extract the corresponding elements from the normalized amplitude sequence to construct the Hankel matrix according to the rule of subtracting the amplitude at the corresponding sampling point from the sum of the row number and column number of the matrix.

9. The method for detecting the uniformity of copper busbar plating thickness in a liquid-cooled server according to claim 1, characterized in that, The specific steps for performing low-rank sparse decomposition on the Hankel matrix constructed from the standardized amplitude sequence using adaptive regularization parameters are as follows: The Hankel matrix is ​​sequentially updated using the alternating direction multiplier method framework, including low-rank component matrix updates, sparse component matrix updates, and dual variable updates, until the residuals meet the convergence condition. Specifically, in the sparse component matrix update, the anti-diagonal index p+q-1 corresponding to the element in the p-th row and q-th column of the Hankel matrix is ​​divided by the local window length and rounded up to obtain the local window number to which the element belongs. The adaptive regularization parameter of the local window corresponding to this index is then used as a soft threshold to perform soft threshold shrinkage on the element.

10. The method for detecting the uniformity of electroplating thickness of copper busbars in a liquid-cooled server according to claim 1, characterized in that, The steps for restoring the copper busbar plating thickness distribution sequence and evaluating the plating thickness uniformity based on the range and coefficient of variation are as follows: The mean values ​​of the low-rank component matrix and sparse component matrix obtained from the decomposition are taken along the anti-diagonal direction, and the mean values ​​of the elements on each anti-diagonal line are arranged sequentially to restore the macroscopic thickness sequence and the local thickness deviation sequence, respectively. The macroscopic thickness sequence and the local thickness deviation sequence are converted using calibration curves and then superimposed to obtain the copper busbar plating thickness distribution sequence. The maximum and minimum values ​​in the plating thickness distribution sequence are extracted to calculate the range, and the ratio of the standard deviation to the mean is calculated to obtain the coefficient of variation. If both the range and the coefficient of variation are within the preset acceptable threshold, the copper busbar electroplating thickness uniformity is deemed acceptable; otherwise, it is deemed unacceptable, and the locations where the thickness deviation exceeds the threshold are marked as process re-inspection areas.

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