Ion chromatography wave crest boundary extraction method based on fitting residual error and tangent judgment

Abstract

The invention discloses an ion chromatography wave crest boundary extraction method based on fitting residual and tangent judgment, and belongs to the technical field of ion chromatography analysis. Comprising the following steps: S1, reading an original waveform data sequence, and executing frequency reduction sampling according to a set step length; s2, calculating the slope of the data after underclocking sampling by using a difference method, and searching positive and negative slope sections by performing first-order derivation on the waveform after underclocking sampling; s3, noise interference is eliminated, slope areas are grouped, then a chromatographic peak detection limit value is set, and an effective peak left section and an effective peak right section are screened out; s4, combining the effective wave crest left side section and the effective wave crest right side section to obtain an effective wave crest and a preliminary left boundary point and a preliminary right boundary point of the effective wave crest; s5, fitting a straight line through the preliminary left boundary point and the preliminary right boundary point to position an error integral region; and S6, updating the optimal boundary point by traversing the evaluation indexes of all points in the error integral region. The boundary search range is more accurate, and the calculation efficiency is higher.

Description

Technical Field

[0001] This invention relates to the field of ion chromatography analysis technology, and in particular to a method for extracting ion chromatography peak boundaries based on fitting residuals and tangent judgment. Background Technology

[0002] In ion chromatography, peak identification and boundary extraction are crucial steps in quantitative analysis, and their accuracy directly affects the calculated concentration. Currently, common chromatographic peak detection and integration methods mainly include: (1) First / Second Derivative Method: The first derivative method, also known as the slope method, uses the change in the first derivative of the signal (i.e., the slope) to determine the start and end points of the rising and falling regions, thereby detecting peaks and boundaries. The advantages of this method are its simplicity, speed, and suitability for real-time processing. The disadvantages are its sensitivity to noise, the need for smoothing processing, and the susceptibility to false detections. It is suitable for waveforms with regular peak shapes and high signal-to-noise ratios. In ion chromatography analysis systems, tailing peaks, asymmetric peaks, or overlapping peaks often appear. In ion chromatography detection, peaks are easily affected by noise, leading to boundary misjudgments, especially in trace analysis or under low signal-to-noise ratio conditions where the effect is poor. This method is suitable for symmetrical waveforms and waveforms with obvious structures.

[0003] (2) Smoothing Filtering Combined with Threshold Detection: Smoothing filtering is used to perform a moving average on the original signal (such as Savitzky-Golay filtering) to suppress noise. After smoothing filtering, this method has strong noise resistance. However, judging the peak shape of ion chromatography by threshold is not suitable for scenarios with severe noise, weak waveform signals, or narrow peaks, such as trace element detection, and peaks with multiple dilution concentrations in a set of peak data. In addition, this method is highly dependent on the peak threshold T. In continuous multi-component analysis of ion chromatography, the peak height difference is significant. Setting T too low will result in false detection, while setting it too high will result in missed detection. If continuous noise occurs, it will also be misjudged as a peak. Therefore, its applicability in the practical application of ion chromatographs is poor.

[0004] (3) Model fitting method: Gaussian and other polynomial function models are used to fit the chromatographic peaks and infer the boundary positions. This type of method has a complete theory and can effectively handle some asymmetric peaks. However, in ion chromatograms with multiple peak overlap or obvious baseline drift, the fitting convergence is difficult, the calculation is large, and the delay is very high. It is rarely used in engineering applications for real-time peak detection and is difficult to meet the real-time processing requirements. It is usually used for offline data analysis. By using the "height ratio truncation" method, the left and right boundaries are inferred from the fitting curve parameters (generally, the truncation threshold is set to 5% - 10% of the maximum value of the peak area). The advantage of this method is that it has a strong theoretical basis and can calculate features such as area and FWHM. However, the disadvantage is that it depends heavily on the initial point and is not suitable for dense areas where multiple peaks coexist, especially multiple peak overlap in ion chromatographs. This method is suitable for high-resolution detection and quantitative analysis, such as IC-MS and LC-UV. In addition, the fitting calculation is relatively complex and is not suitable for peak detection and real-time processing of large amounts of data. It depends on the initial value point of the peak boundary and can be used for chromatographic analysis and post-processing extraction of spectral characteristic peaks.

[0005] (4) Wavelet transform. This method is mostly used in the field of medical imaging. It uses multi-scale wavelet functions to extract local features of the signal at different scales, such as abrupt changes, slope changes, and peaks. When detecting boundaries, the wavelet function is used to perform continuous wavelet transform (CWT) on the signal to find the zero-crossing points of the wavelet coefficients at different scales (the zero points are boundary candidates). Repeating the zero-crossing points at multiple scales determines the reliable boundary. The wavelet transform method can identify overlapping peaks and shoulder peaks. However, the wavelet transform algorithm is complex, requiring continuous traversal and iterative calculations, and manual selection of the wavelet function and scale range is required. It is highly dependent on parameters and wavelet functions, making it suitable for biomedical signals (EEG, ECG), but its practicality in the field of ion chromatography analysis is greatly limited.

[0006] In addition, there are other peak boundary extraction methods, such as bandpass filtering and envelope detection, EM algorithm peak segmentation, Z-score anomaly detection, and adaptive baseline subtraction. These methods mainly focus on peak center location or peak fitting, lacking precise strategies for boundary extraction. Especially when the peak base is affected by tailing, co-current, or low signal-to-noise ratio interference, traditional methods often suffer from problems such as missed peak area calculation, negative peak area calculation, insufficient or excessive boundary extension, affecting the accuracy of quantitative analysis.

[0007] Ion chromatography analysis often faces the following unique challenges: changes in mobile phase pH or experimental environment can lead to baseline drift; retention time drift can cause peak asymmetry; and low-concentration component peaks are weak and easily masked by neighboring large peaks. Existing methods often exhibit boundary positioning deviations in these scenarios, resulting in distorted integrated areas and affecting quantitative repeatability and accuracy. Therefore, there is an urgent need to develop a chromatographic peak boundary extraction method that balances noise resistance, adaptability, and computational efficiency, and can be embedded into the ion chromatograph data processing system to achieve accurate integration under complex operating conditions. Summary of the Invention

[0008] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for extracting peak boundaries in ion chromatography based on fitting residuals and tangent judgment.

[0009] The objective of this invention is achieved through the following technical solution: a method for extracting peak boundaries in ion chromatography based on fitting residuals and tangent judgment, comprising the following steps: S1: Sample signals are acquired by ion chromatograph to obtain raw ion flow data sequence. The raw data is downsampled according to the preset sampling step size to reduce the amount of data and maintain the chromatographic peak shape characteristics to obtain chromatographic data. S2: The slope of each data point is calculated using the difference method on the chromatographic data after frequency reduction sampling. The positive slope segment and the negative slope segment are identified by performing first-order difference on the signal. S3: Based on the signal-to-noise ratio characteristics of the ion chromatograph, exclude the interfering slope segments caused by electrical noise or baseline drift, group the remaining slope intervals, and screen out the effective left and right segments of the chromatographic peaks according to the preset peak height or area thresholds. S4: Combine and match the left segment of the selected effective chromatographic peak with the right segment of the effective chromatographic peak to preliminarily determine the vertex position of each chromatographic peak and its corresponding left boundary candidate point and right boundary candidate point; S5: Construct a linear fitting baseline based on the initially determined left and right boundary candidate points. l Then, the chromatographic peak signal and the linear fitting baseline were calculated. l The residual values ​​between them are used to locate the erroneous integration region where integration error may exist; S6: Traverse all data points within the erroneous integration region, determine the optimal boundary point through the set evaluation index, and complete the integration boundary determination of the chromatographic peak.

[0010] Preferably, the preset sampling step size is 20.

[0011] Preferably, step S5 further includes the following steps: Connect each set of preliminary boundary pairs (left boundary candidate points) b_l Candidate points for the right boundary b_r ) constitute the linear fitting baselinel If the target chromatographic peak exhibits an asymmetric or tailed shape, then the linear fitting baseline is used. l Intersecting with the chromatographic peak curve at three points b_l、 b_r and b_c ;in b_c This is the point where the normal integration region and the incorrect integration region switch on the peak curve. If the candidate point of the left boundary of the peak... b_l Candidate points above the right boundary b_r， Right now y b_l > y b_r ,point b_c It will appear at the end of the normal integration region and the beginning of the incorrect integration region, and be recorded. b_max Candidate points for the left boundary b_l Location; if the left boundary of the crest is a candidate point b_l Candidate points below the right boundary b_r， Right now y b_l< y b_r ,point b_c It will appear at the end of the incorrect integration region and the beginning of the correct integration region, and be recorded. b_max Candidate points for the right boundary b_r Location, i.e., the point with the highest measured concentration between the two endpoints, is denoted as: ;point b_max The following conditions must be met: ; Linear Fit Baseline l The curve intersects the peak curve at at least two boundary points, and the linearly fitted baseline is obtained. l The first-order expression is: In the formula , indicating the linearly fitted baseline l The slope; ; f ( x () is the ordinate value of the boundary fitted line corresponding to the unified horizontal coordinate point; ; Let x be the x-coordinate of the candidate point on the left boundary. The x-coordinate of the candidate point on the right boundary; Calculate the data points in a set of chromatographic peaks to residual : ;in p ( i Let x be the horizontal coordinate of the peak when x takes the value i. The expression for the peak curve is: p = p( x ); f ( i (x) represents the linear fitting baseline that crosses the boundary points when the x-coordinate is i. l The ordinate value; All residuals Data points with a value less than 0 are included in the candidate set, and the corresponding peak curve points are recorded in the boundary record sequence to obtain the erroneous integration region where the true boundary points of the peaks exist.

[0012] Preferably, step S6 further includes the following step: Define the x and y coordinates of the left boundary point of the erroneous integration region as ( x e_l , y e_l The x and y coordinates of the right boundary point of the erroneous integration region are ( x e_r , y e_r ); Define evaluation indicators S t Used to determine optimal boundary values: ;in j Let x be the x-coordinate of a point within the interval of error integration. p ( j () represents the ordinate value of that point on the wave crest curve; The x-coordinate value is the point with the larger y-coordinate among the two points on the left and right boundaries of the wave crest; The ordinate value is the ordinate value of the point with the larger ordinate among the two points on the left and right boundaries of the wave crest; Through evaluation indicators S t Iterate through all points within the region of incorrect integration and update... S t The minimum value is used to obtain the optimal boundary point. b_end :( x b_end , y b_end ) ， This optimal boundary point b_end It occurs within the error integration interval, i.e., the x-coordinate of the optimal boundary point satisfies x b_end ∈( x e_l , x e_r ).

[0013] The beneficial effects of this invention are: 1) The boundary search range is more precise and computationally efficient. This invention constructs a linear fitting baseline based on coarse boundary points and uses residual analysis to precisely locate the edge region of the target peak, significantly narrowing the boundary search range from the entire data sequence to the actual signal variation interval. This strategy effectively reduces redundant calculations and significantly improves processing speed while maintaining accuracy. Actual tests show that compared with the traditional sliding window or derivative sign-changing method, this method improves efficiency by more than 30% in the boundary localization stage of ion chromatography peaks. It is particularly suitable for real-time spectrum processing of millions of data points commonly encountered in ion chromatography, meeting the needs of high-throughput detection.

[0014] 2) Strong anti-interference capability and robustness: Addressing common baseline drift, noise disturbances, and tailing phenomena in ion chromatograms, this invention analyzes the distribution characteristics of negative residual points below the fitted baseline and combines geometric evaluation indicators to screen for the optimal boundary, effectively suppressing misjudgments caused by local signal fluctuations. This method maintains stable boundary recognition performance even in samples with low signal-to-noise ratios, weak peaks, or complex matrices, significantly outperforming traditional threshold or derivative methods.

[0015] 3) It exhibits good adaptability to non-ideal peak shapes. Traditional methods often rely on the assumption of symmetrical peak shapes. For example, Gaussian fitting often fails to accurately handle shoulder peaks, broad peaks, or irregular peaks commonly found in ion chromatography. This invention employs a model-free linear fitting strategy, eliminating prior limitations on peak shape. It can effectively handle non-ideal peak shapes such as leading peaks, tailing peaks, shoulder peaks, and partially overlapping peaks commonly found in ion chromatography, demonstrating good versatility and adaptability.

[0016] 4) Improve boundary point positioning accuracy and integration accuracy. Accurate boundary point positioning is crucial for chromatographic integration accuracy. This method optimizes boundary determination, making the integration region more closely match the actual signal start and end range, thereby reducing area calculation errors. Experimental data show that compared with the first derivative method or fixed-ratio cutoff method, this method can reduce integration errors by an average of 12%–18% in typical ion chromatography samples, with particularly significant effects in trace analysis.

[0017] 5) Meeting the real-time processing requirements of instruments and facilitating engineering deployment, this method's overall workflow includes five parts: downsampling preprocessing, coarse boundary screening, linear fitting, residual judgment, and geometric optimization. Each part employs a lightweight mathematical model (such as first-order least squares linear model, simple difference calculation, and sorting screening), resulting in low time complexity and memory consumption. In a typical chromatography workstation or embedded industrial computer (such as Intel J4125 + 8G memory), boundary extraction of a single chromatogram can be completed within 30 milliseconds, fully meeting the performance requirements of online detection, real-time integration, and continuous analysis in ion chromatography, and demonstrating promising engineering application prospects. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram of the erroneous integration region in one embodiment; Figure 3 This is a schematic diagram of the erroneous integration region in another embodiment; Figure 4 This is a schematic diagram showing the effect of peak boundary point detection before and after optimization in one embodiment; Figure 5 This is a schematic diagram showing the effect of peak boundary points detected before and after optimization in another embodiment. Detailed Implementation

[0019] The technical solution of the present invention will be clearly and completely described below with reference to the embodiments. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] See Figures 1-5 This invention provides a technical solution: a method for extracting peak boundaries in ion chromatography based on fitting residuals and tangent judgment, comprising the following steps: S1: Sample signals are acquired by ion chromatograph to obtain raw ion flow data sequence. The raw data is downsampled according to the preset sampling step size to reduce the amount of data and maintain the chromatographic peak shape characteristics to obtain chromatographic data. S2: The slope of each data point is calculated using the difference method on the chromatographic data after frequency reduction sampling. The positive slope segment and the negative slope segment are identified by performing first-order difference on the signal. S3: Based on the signal-to-noise ratio characteristics of the ion chromatograph, exclude the interfering slope segments caused by electrical noise or baseline drift, group the remaining slope intervals, and screen out the effective left and right segments of the chromatographic peaks according to the preset peak height or area thresholds. S4: Combine and match the left segment of the selected effective chromatographic peak with the right segment of the effective chromatographic peak to preliminarily determine the vertex position of each chromatographic peak and its corresponding left boundary candidate point and right boundary candidate point; S5: Construct a linear fitting baseline based on the initially determined left and right boundary candidate points. l Then, the chromatographic peak signal and the linear fitting baseline were calculated. l The residual values ​​between them are used to locate the erroneous integration region where integration error may exist; S6: Traverse all data points within the erroneous integration region, determine the optimal boundary point through the set evaluation index, and complete the integration boundary determination of the chromatographic peak.

[0021] In this embodiment, the original waveform data sequence is downsampled to reduce the amount of data processing. Since the original data points are numerous (typically hundreds of thousands in a complete waveform dataset), sampling is first performed at intervals of Space = 20 to obtain the approximate waveform of the curve. This reduces computational complexity and is used to quickly determine slope change regions later. The slope is calculated using a difference method. By performing first-order differentiation (K value) on the downsampled waveform, positive and negative slope segments are identified: continuous positive slope regions are to the left of the peak, and continuous negative slope regions are to the right of the peak.

[0022] Eliminating short-lived noise interference and finding effective peaks: Group the slope regions, then set a peak detection limit det. If the peak curve has det consecutive points with first derivatives... If the value is greater than 0, it is considered to be to the left of the peak. Similarly, if there are det consecutive points, the first derivative... If the value is less than 0, it is considered to be to the right of the peak. The left segment of the effective chromatographic peak and the right segment of the effective chromatographic peak are combined and considered to form a single peak region. Left boundary points with a value greater than 0 are candidate points for the left boundary. The right boundary point with a value less than 0 is the right boundary candidate point, thus forming the left and right boundary candidate points of the complete valid peak. Figure 2 and Figure 3 There are multiple peaks in the data. It can be seen that the first-order and second-order derivative peak location method is not suitable for all peak shapes. For asymmetrical peaks, the first-stage peak boundary found by the continuous change of the derivative will have a part of the peak area with a negative value. This makes the integral of the peak area of ​​this part of the peak negative, which ultimately leads to the instrument's incorrect detection.

[0023] This invention significantly improves the accuracy of boundary detection, automatically avoiding signal spikes or tails and capturing the "signal termination point" rather than the "threshold position." It also improves the accuracy of peak area calculation by more accurately identifying peak boundaries, resulting in a more realistic integrated area and enhancing the detection accuracy of automated instruments. It is applicable to the boundary location of various irregular peaks and weak signal peaks, such as shoulder peaks and tailing peaks. Existing methods for processing these types of peaks have limitations, hindering the universal application of instrument algorithms. This invention's algorithm can still identify reasonable boundaries. The algorithm is simple, highly efficient, and can process millions of data waveforms on low-configuration computers with good real-time performance. It is easily reproducible, facilitates engineering implementation, and can be directly used in automated instruments to intelligently determine peaks and integrals without manual boundary intervention or manual integration.

[0024] In some embodiments, the preset sampling step size is 20 to accommodate the sampling frequency and peak width characteristics of typical ion chromatography signals.

[0025] In some embodiments, S5 further includes the following steps: Connect each set of preliminary boundary pairs (left boundary candidate points) b_l Candidate points for the right boundary b_r ) constitute the linear fitting baseline l If the target chromatographic peak exhibits an asymmetric or tailed shape, then the linear fitting baseline is used. l Intersecting with the chromatographic peak curve at three points b_l、 b_r and b_c ;in b_c This is the point where the normal integration region and the incorrect integration region switch on the peak curve. If the candidate point of the left boundary of the peak... b_l Candidate points above the right boundary b_r， Right now y b_l > y b_r ,point b_c It will appear at the end of the normal integration region and the beginning of the incorrect integration region, and be recorded. b_max Candidate points for the left boundary b_l Location; if the left boundary of the crest is a candidate point b_l Candidate points below the right boundary b_r， Right now y b_l< y b_r ,point b_c It will appear at the end of the incorrect integration region and the beginning of the correct integration region, and be recorded. b_max Candidate points for the right boundary b_r Location, i.e., the point with the highest measured concentration between the two endpoints, is denoted as: ;point b_max The following conditions must be met: ; Linear Fit Baseline l The curve intersects the peak curve at at least two boundary points, and the linearly fitted baseline is obtained. l The first-order expression is: In the formula , indicating the linearly fitted baseline l The slope; ; f ( x () is the ordinate value of the boundary fitted line corresponding to the unified horizontal coordinate point; ; Let x be the x-coordinate of the candidate point on the left boundary. The x-coordinate of the candidate point on the right boundary; Calculate the data points in a set of chromatographic peaks to residual : ;in p (i Let x be the horizontal coordinate of the peak when x takes the value i. The expression for the peak curve is: p = p ( x ); f ( i (x) represents the linear fitting baseline that crosses the boundary points when the x-coordinate is i. l The ordinate value; All residuals Data points with a value less than 0 are included in the candidate set, and the corresponding peak curve points are recorded in the boundary record sequence to obtain the erroneous integration region where the true boundary points of the peaks exist.

[0026] In this embodiment, the error integration region is Figure 2 Peak-shaped region b_l 1 to b_c 1 part, b_c 2 to b_r 2 part; Figure 3 Mid-peak region b_l 1 to b_c 1 part, b_c 2 to b_r 2 Section and b_c 3 to b_r 3 The segment is the interval in which the true boundary point exists on the side of the wave crest.

[0027] In some embodiments, S6 further includes the following step: Define the x and y coordinates of the left boundary point of the erroneous integration region as ( x e_l , y e_l The x and y coordinates of the right boundary point of the erroneous integration region are ( x e_r , y e_r ); Define evaluation indicators S t Used to determine optimal boundary values: ;in j Let x be the x-coordinate of a point within the interval of error integration. p ( j () represents the ordinate value of that point on the wave crest curve; The x-coordinate value is the point with the larger y-coordinate among the two points on the left and right boundaries of the wave crest; The ordinate value is the ordinate value of the point with the larger ordinate among the two points on the left and right boundaries of the wave crest; Through evaluation indicators S t Iterate through all points within the region of incorrect integration and update... S t The minimum value is used to obtain the optimal boundary point. b_end :( x b_end , y b_end ) ， This optimal boundary point b_end It occurs within the error integration interval, i.e., the x-coordinate of the optimal boundary point satisfies x b_end ∈( x e_l , x e_r ).

[0028] In this embodiment, the optimal boundary is updated through tangent optimization, based on the previous deductions and... Figure 2 , Figure 3 It is easy to see that, using the derivative method to obtain the first-stage peak boundary pair, the erroneous integration interval where the high and low peaks occur will only occur at the end of the peak boundary value.

[0029] The above description is merely a preferred embodiment of the present invention. It should be understood that the present invention is not limited to the forms disclosed herein and should not be construed as excluding other embodiments. It can be used in various other combinations, modifications, and environments, and can be altered within the scope of the concept described herein through the above teachings or related technologies or knowledge. Modifications and variations made by those skilled in the art that do not depart from the spirit and scope of the present invention should be within the protection scope of the appended claims.

Claims

1. A method for extracting peak boundaries in ion chromatography based on fitting residuals and tangent judgment, characterized in that: Includes the following steps: S1: Sample signals are acquired by ion chromatograph to obtain raw ion flow data sequence. The raw data is downsampled according to the preset sampling step size to reduce the amount of data and maintain the chromatographic peak shape characteristics to obtain chromatographic data. S2: The slope of each data point is calculated using the difference method on the chromatographic data after frequency reduction sampling. The positive slope segment and the negative slope segment are identified by performing first-order difference on the signal. S3: Based on the signal-to-noise ratio characteristics of the ion chromatograph, exclude the interfering slope segments caused by electrical noise or baseline drift, group the remaining slope intervals, and screen out the effective left and right segments of the chromatographic peaks according to the preset peak height or area thresholds. S4: Combine and match the left segment of the selected effective chromatographic peak with the right segment of the effective chromatographic peak to preliminarily determine the vertex position of each chromatographic peak and its corresponding left boundary candidate point and right boundary candidate point; S5: Construct a linear fitting baseline based on the initially determined left and right boundary candidate points. l Then, the chromatographic peak signal and the linear fitting baseline were calculated. l The residual values ​​between them are used to locate the erroneous integration region where integration error may exist; S6: Traverse all data points within the erroneous integration region, determine the optimal boundary point through the set evaluation index, and complete the integration boundary determination of the chromatographic peak.

2. The method for extracting ion chromatography peak boundaries based on fitting residuals and tangent judgment according to claim 1, characterized in that: The preset sampling step size is 20.

3. The method for extracting ion chromatography peak boundaries based on fitting residuals and tangent judgment according to claim 1, characterized in that: The S5 further includes the following steps: Connect each set of preliminary boundary pairs (left boundary candidate points) b_l Candidate points for the right boundary b_r ) constitute the linear fitting baseline l If the target chromatographic peak exhibits an asymmetric or tailed shape, then the linear fitting baseline is used. l Intersecting with the chromatographic peak curve at three points b_l、b_r and b_c ;in b_c This is the point where the normal integration region and the incorrect integration region switch on the peak curve. If the candidate point of the left boundary of the peak... b_l Candidate points above the right boundary b_r， Right now y b_l > y b_r ,point b_c It will appear at the end of the normal integration region and the beginning of the incorrect integration region, and be recorded. b_max Candidate points for the left boundary b_l Location; if the left boundary of the crest is a candidate point b_l Candidate points below the right boundary b_r， Right now y b_l < y b_r ,point b_c It will appear at the end of the incorrect integration region and the beginning of the correct integration region, and be recorded. b_max Candidate points for the right boundary b_r Location, i.e., the point with the highest measured concentration between the two endpoints, is denoted as: ;point b_max The following conditions must be met: ; Linear Fit Baseline l The curve intersects the peak curve at at least two boundary points, and the linearly fitted baseline is obtained. l The first-order expression is: In the formula , indicating the linearly fitted baseline l The slope; ; f ( x () is the ordinate value of the boundary fitted line corresponding to the unified horizontal coordinate point; ; Let x be the x-coordinate of the candidate point on the left boundary. The x-coordinate of the candidate point on the right boundary; Calculate the data points in a set of chromatographic peaks to residual : ;in p ( i Let x be the horizontal coordinate of the peak when x takes the value i. The expression for the peak curve is: p = p ( x ); f ( i (x) represents the linear fitting baseline that crosses the boundary points when the x-coordinate is i. l The ordinate value; All residuals Data points with a value less than 0 are included in the candidate set, and the corresponding peak curve points are recorded in the boundary record sequence to obtain the erroneous integration region where the true boundary points of the peaks exist.

4. The method for extracting ion chromatography peak boundaries based on fitting residuals and tangent judgment according to claim 1, characterized in that: The S6 further includes the following steps: Define the x and y coordinates of the left boundary point of the erroneous integration region as ( x e_l , y e_l The x and y coordinates of the right boundary point of the erroneous integration region are ( x e_r , y e_r ); Define evaluation indicators S t Used to determine optimal boundary values: ;in j Let x be the x-coordinate of a point within the interval of incorrect integration. p ( j () represents the ordinate value of that point on the wave crest curve; The x-coordinate value is the point with the larger y-coordinate among the two points on the left and right boundaries of the wave crest; The ordinate value is the ordinate value of the point with the larger ordinate among the two points on the left and right boundaries of the wave crest; Through evaluation indicators S t Iterate through all points within the region of incorrect integration and update... S t The minimum value is used to obtain the optimal boundary point. b_end :( x b_end , y b_end ) ， This optimal boundary point b_end It occurs within the error integration interval, i.e., the x-coordinate of the optimal boundary point satisfies x b_end ∈( x e_l , x e_r ).

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