A method for detecting signal denoising based on an electrochemical workstation

Abstract

The application discloses a detection signal denoising method based on an electrochemical workstation and relates to the technical field of signal processing. The detection signal denoising method provided by the application can generate corresponding reverse noise randomly according to the normal distribution law of thermal noise generated by the electrochemical workstation during work and the independent analysis and processing of each group of electrochemical experimental data, independently denoises each group of electrochemical experimental data by using the similar normal distribution law, and displays the experimental data after denoising in real time. The method can realize real-time and efficient denoising processing of the electrochemical experimental data, greatly retains the real characteristics of the original collected signal and noise signal, and thus enhances the electrochemical measurement precision and reliability.

Description

Technical Field

[0001] This invention relates to the field of signal processing technology, and in particular to a method for noise reduction of detection signals based on an electrochemical workstation. Background Technology

[0002] The signal characteristics of an electrochemical workstation typically consist of a superposition of low-frequency signals and high-frequency noise. These two components are independent and do not affect each other. The low-frequency signal, ranging from millihertz to kilohertz, represents useful information generated during the electrochemical reaction and reflects the electrochemical characteristics of the electrode reactions, such as changes in parameters like current and voltage. On the other hand, the high-frequency noise primarily originates from external environmental interference and the electronic noise inherent in the equipment itself. Its frequency is high, generally exceeding megahertz, surpassing the instrument's maximum sampling frequency. This signal characteristic necessitates effective noise reduction methods during signal detection and data analysis to enhance signal identifiability and accuracy while preserving the integrity of the original signal, i.e., improving the signal-to-noise ratio of the electrochemical workstation.

[0003] In the application scenarios of electrochemical workstations, real-time data display is crucial. It empowers researchers to monitor the dynamic progress of electrochemical reactions in real time, ensuring keen detection and timely adjustments to changes in experimental conditions. Given this requirement, the noise reduction strategies offered by related technologies—that is, performing noise reduction processing centrally after complete data acquisition—clearly conflict with the stringent real-time requirements of electrochemical workstations. These technologies, limited by their inherent post-processing computational complexity, often consume significant time resources, making it difficult to achieve the goal of immediate processing and feedback, thus weakening the timeliness of data-guided experiments. Furthermore, smoothed data loses the characteristics of noise, and comparing the characteristics of noise signals with those of real signals is often an important means of determining the authenticity of a signal. Summary of the Invention

[0004] To address the aforementioned problems in existing technologies, this invention provides a noise reduction method for detection signals based on an electrochemical workstation. By performing real-time independent noise identification and reduction processing on each data point collected by the electrochemical workstation, the method reduces the level of randomly distributed thermal noise and white noise while ensuring the effective preservation of the inherent characteristics of the noise. This significantly improves the signal-to-noise ratio, thereby enhancing the accuracy and reliability of electrochemical measurements. The technical solution provided by this invention is as follows:

[0005] According to one aspect of the present invention, a method for denoising detection signals based on an electrochemical workstation is provided, characterized in that the method includes:

[0006] S10: Obtain the original independent and dependent variables corresponding to the first n sets of electrochemical experimental data. Calculate the standard deviation σ based on the original dependent variable of the first n sets of electrochemical experimental data. The value of n increases dynamically and is automatically updated as the number of electrochemical experimental data acquisitions increases.

[0007] S20: Perform linear regression fitting on the first n sets of electrochemical experimental data, calculate the slope a and intercept b of the linear regression equation, and predict the corresponding dependent variable y using the original independent variables of the (n+1)th set of electrochemical experimental data based on the linear regression equation. predicted Predict the dependent variable y predicted The expression is as shown in Equation 1:

[0008] y predicted =a·x n+1 +b Equation 1 Where, x n+1 For the (n+1)th group of electrochemical experimental data, the original independent variable is denoted as .

[0009] S30: Randomly generate noise value z corresponding to the reverse noise within the range [-5σ, 5σ], wherein the generation rule of the noise value z follows a normal distribution.

[0010] S40: Calculate the probability density f(z) corresponding to the noise value z and the maximum probability density f(x) based on the probability density function f(x). max The ratio r between the two is calculated; the probability density function f(x) is expressed as Equation 2:

[0011]

[0012] Where μ = 0;

[0013] Maximum probability density f max Let f(x) be the value of f(x) when x = μ = 0;

[0014] The expression for the ratio r is shown in Equation 3:

[0015]

[0016] S50: Generate a random number within the range [0, 1]. If the random number is less than r, the noise value z is determined to be valid noise. If the random number is greater than r, the step of generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] in S30 is repeated.

[0017] S60: Add the noise value z, which is determined to be effective noise, to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new Noise reduction dependent variable y newThe expression is as shown in Equation 4:

[0018] y new =y measured +z Equation 4;

[0019] S70: Calculate the original dependent variable y measured With the prediction of the dependent variable y predicted The first absolute distance, and the noise reduction dependent variable y new With the prediction of the dependent variable y predicted If the second absolute distance is less than the first absolute distance, then the noise reduction dependent variable y will be... new The true dependent variable corresponding to the original independent variable of the (n+1)th group of electrochemical experimental data is determined, output and displayed, and then the value of n is updated. The step of obtaining the original independent variable and original dependent variable corresponding to the first n groups of electrochemical experimental data described in S10 is executed again. If the second absolute distance is greater than the first absolute distance, the step of randomly generating the noise value z corresponding to the reverse noise in the range [-5σ, 5σ] described in S30 is executed again.

[0020] Preferably, the initial value of n is a fixed preset value m, where m and n are both positive integers greater than 1.

[0021] Preferably, the method includes:

[0022] After outputting and displaying the true dependent variable corresponding to the original independent variable of each group of electrochemical experimental data after the m-th group, for each group of electrochemical experimental data, the true dependent variable corresponding to the electrochemical experimental data is updated to the original dependent variable ymeasured, n is updated to m, and steps S10 to S70 are executed again to achieve successive noise reduction of each group of electrochemical experimental data.

[0023] Preferably, the method includes:

[0024] When the absolute value of the difference between the standard deviation σ corresponding to the first n-2 groups of electrochemical experimental data and the standard deviation σ corresponding to the first n-1 groups of electrochemical experimental data is less than the preset difference, after performing the step of obtaining the original independent variable and original dependent variable corresponding to the first n groups of electrochemical experimental data as described in S10, the standard deviation σ corresponding to the first n-1 groups of electrochemical experimental data is directly determined as the standard deviation σ corresponding to the first n groups of electrochemical experimental data.

[0025] Preferably, the noise value z corresponding to the reverse noise is similar in amplitude and opposite in phase to the noise value corresponding to the original thermal noise generated when the electrochemical workstation is working.

[0026] Preferably, the method further includes:

[0027] Analyze other noise types present during the operation of the electrochemical workstation;

[0028] For each other noise type, determine the distribution characteristics corresponding to the other noise type, and generate the corresponding effective reverse noise based on the distribution characteristics corresponding to the other noise type;

[0029] In execution S60, the noise value z, which is determined to be effective noise, is added to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new During the step, the noise value of the effective reverse noise corresponding to each noise type is added to the noise reduction dependent variable y. new And update the noise reduction dependent variable y new .

[0030] Preferably, the linear regression fitting algorithm uses the least squares method.

[0031] Preferably, the detection signal noise reduction method is terminated when the electrochemical workstation fails to acquire the latest set of electrochemical experimental data.

[0032] Preferably, the successive noise reduction step is performed at least three times.

[0033] Preferably, the original independent variable is the x-axis corresponding to the electrochemical experimental data before noise reduction, and the original dependent variable is the y-axis corresponding to the electrochemical experimental data before noise reduction.

[0034] Compared with existing technologies, the detection signal noise reduction method based on an electrochemical workstation provided by this invention has the following advantages:

[0035] This invention provides a method for noise reduction of detection signals based on an electrochemical workstation, which includes acquiring the original independent and dependent variables corresponding to the first n sets of electrochemical experimental data; calculating the standard deviation σ based on the original dependent variable of the first n sets of electrochemical experimental data; performing linear regression fitting on the first n sets of electrochemical experimental data; and calculating the slope of the linear regression equation.

[0036] And the intercept b, and based on the linear regression equation, using the original independent variables of the (n+1)th group of electrochemical experimental data, predict the corresponding dependent variable y. predicted Randomly generate noise values ​​z corresponding to the reverse noise within the range [-5σ, 5σ], where the generation rule of the noise values ​​z follows a normal distribution. Calculate the probability density f(z) and the maximum probability density f(x) corresponding to the noise values ​​z based on the probability density function f(x). maxThe ratio r between the two is calculated; a random number is generated within the range [0, 1]. If the random number is less than r, the noise value z is determined as valid noise; if the random number is greater than r, the step of randomly generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] is repeated; the noise value z determined as valid noise is added to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new ; Calculate the original dependent variable y measured With the prediction of the dependent variable y predicted The first absolute distance, and the noise reduction dependent variable y new With the prediction of the dependent variable y predicted If the second absolute distance is less than the first absolute distance, then the noise reduction dependent variable y will be reduced. new The true dependent variable corresponding to the original independent variable of the (n+1)th group of electrochemical experimental data is output and displayed. Then, the value of n is updated, and the step of obtaining the original independent and dependent variables corresponding to the first n groups of electrochemical experimental data is executed. If the second absolute distance is greater than the first absolute distance, the step of randomly generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] is executed again. According to the normal distribution law of the thermal noise generated when the electrochemical workstation is working, and the independent analysis and processing of each group of electrochemical experimental data, the present invention uses a similar normal distribution law to randomly generate the corresponding reverse noise to independently reduce the noise of each group of electrochemical experimental data and display the noise-reduced experimental data in real time. While realizing the real-time and efficient noise reduction processing of electrochemical experimental data, it greatly preserves the true characteristics of the original acquisition signal and noise signal, thereby enhancing the accuracy and reliability of electrochemical measurement. Attached Figure Description

[0037] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with the invention and, together with the description, serve to explain the principles of the invention.

[0038] Figure 1 This is a flowchart illustrating a method for noise reduction of detection signals based on an electrochemical workstation according to an exemplary embodiment of the present invention.

[0039] Figure 2 This is a schematic diagram illustrating the distribution of generated noise values ​​according to an exemplary embodiment of the present invention.

[0040] Figure 3 This is a schematic diagram of the initial cyclic voltammetry curve corresponding to Embodiment 1 of the present invention.

[0041] Figure 4 This is a schematic diagram of the change in the cyclic volt-ampere characteristic curve after noise reduction corresponding to Embodiment 1 of the present invention.

[0042] Figure 5 This is a schematic diagram of the initial noise curve corresponding to Embodiment 1 of the present invention.

[0043] Figure 6 This is a schematic diagram of the noise curve change after noise reduction corresponding to Embodiment 1 of the present invention.

[0044] Figure 7 This is a schematic diagram of the change in noise standard deviation with the number of noise reduction cycles corresponding to Embodiment 1 of the present invention.

[0045] Figure 8 This is a schematic diagram of the initial timing current curve corresponding to Embodiment 2 of the present invention.

[0046] Figure 9 This is a schematic diagram of the initial curve change of the timing current after noise reduction corresponding to Embodiment 2 of the present invention.

[0047] Figure 10 This is a schematic diagram of the initial noise curve corresponding to Embodiment 2 of the present invention.

[0048] Figure 11 This is a schematic diagram of the noise curve change after noise reduction corresponding to Embodiment 2 of the present invention.

[0049] Figure 12 This is a schematic diagram of the change in noise standard deviation with the number of noise reduction cycles corresponding to Embodiment 2 of the present invention.

[0050] Figure 13 This is a schematic diagram of the initial cyclic voltammetry curve corresponding to Embodiment 3 of the present invention.

[0051] Figure 14 This is a schematic diagram of the change in the cyclic volt-ampere characteristic curve after noise reduction corresponding to Embodiment 3 of the present invention.

[0052] Figure 15 This is a schematic diagram of the initial noise curve corresponding to Embodiment 3 of the present invention.

[0053] Figure 16 This is a schematic diagram of the noise curve change after noise reduction corresponding to Embodiment 3 of the present invention.

[0054] Figure 17 This is a schematic diagram of the change in noise standard deviation with the number of noise reduction cycles corresponding to Embodiment 3 of the present invention. Detailed Implementation

[0055] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0056] Figure 1 This is a flowchart illustrating a method for noise reduction of detection signals based on an electrochemical workstation according to an exemplary embodiment of the present invention. Figure 1 As shown, this method for denoising detection signals includes:

[0057] S10: Obtain the original independent and dependent variables corresponding to the first n sets of electrochemical experimental data. Calculate the standard deviation σ based on the original dependent variable of the first n sets of electrochemical experimental data. The value of n increases dynamically and is automatically updated as the number of electrochemical experimental data acquisitions increases.

[0058] In S10, the timing for acquiring and calculating the standard deviation σ corresponding to the first n sets of electrochemical experimental data can be: when acquiring the (n+1)th set of the latest electrochemical experimental data. That is, when acquiring a new set of electrochemical experimental data, this invention performs fine noise reduction processing on the currently acquired (n+1)th set of electrochemical experimental data based on the signal characteristics presented by the previous n sets of electrochemical experimental data, thereby achieving real-time dynamic noise reduction of the detection signal.

[0059] The value of n increases dynamically and is self-updated as the number of electrochemical experimental data acquisitions increases; that is, the value of n is automatically updated to n+1 each time new electrochemical experimental data is acquired.

[0060] Preferably, the original independent variable is the x-axis corresponding to the electrochemical experimental data before noise reduction, and the original dependent variable is the y-axis corresponding to the electrochemical experimental data before noise reduction.

[0061] For example, the horizontal axis represents time or voltage, and the vertical axis represents the measured analog quantity. When a potential is applied in the electrochemical workstation, the current is measured, and when a current is applied, the potential is measured.

[0062] For example, to facilitate understanding, when n is 4, the electrochemical experimental data of each group shown in Example A are as follows:

[0063] The data for the first group of electrochemical experiments were (6.01650 × 10⁻⁶). -1 7.73106×10 -6 );

[0064] The data for the second group of electrochemical experiments were (6.01339 × 10⁻⁶). -1 7.75108×10 -6 );

[0065] The electrochemical experimental data for group 3 is (6.01171×10). -1 3.91377×10 -6 );

[0066] The data for the fourth group of electrochemical experiments were (6.00784 × 10⁻⁶). -11.96271×10 -6 );

[0067] The data for the fifth group of electrochemical experiments were (6.00289 × 10⁻⁶). -1 1.45374×10 -6 ).

[0068] After obtaining the first four sets of electrochemical experimental data, the standard deviation σ was calculated based on the original dependent variable, i.e., the ordinate value, and the standard deviation σ was found to be: σ = 2.885 × 10⁻⁶. -6 .

[0069] S20: Perform linear regression fitting on the first n sets of electrochemical experimental data, calculate the slope a and intercept b of the linear regression equation, and predict the corresponding dependent variable y using the original independent variables of the (n+1)th set of electrochemical experimental data based on the linear regression equation. predicted .

[0070] Predict the dependent variable y predicted The expression is as shown in Equation 1:

[0071] y predicted =a·x n+1 +b Equation 1

[0072] Where, x n+1 is the original independent variable corresponding to the (n+1)th group of electrochemical experimental data.

[0073] Preferably, the linear regression fitting algorithm uses the least squares method.

[0074] Preferably, the initial value of n is a fixed preset value m, where m and n are both positive integers greater than 1.

[0075] Here, m is a preset standard parameter used to define the starting point for calculating the predicted dependent variable, beginning with the m-th set of electrochemical experimental data. This setting means that the first m-1 sets of electrochemical experimental data are used as the reference set for performing the linear fitting process. Due to the inherent logic of linear fitting, the first m-1 sets of electrochemical experimental data do not participate in the direct generation of the predicted value, thus resulting in a blank in the noise reduction process for this data segment; that is, the noise reduction step is naturally bypassed.

[0076] In one feasible implementation, when using cyclic voltammetry experiments, given the characteristics of curve retracement, the first set of data in the retracement period can be used as the starting point of the new sequence. Subsequently, linear fitting is performed using the following m-1 sets of data to accurately predict the values ​​of subsequent data points. It should be noted that during the retracement stage, the first m-1 sets of data in this sequence are used as the basis for fitting and are not subject to noise reduction processing.

[0077] Continuing with the explanation using the electrochemical experimental data from Example A above, a linear regression was performed based on the x-axis and y-axis values ​​of the first four sets of electrochemical experimental data in Example A. The resulting linear regression equation has a slope of a = 0.0073 and an intercept of b = -0.0044. Therefore, the linear regression equation is:

[0078] y predicted =0.0073·x n+1 -0.0044

[0079] The current value of n is 4, so the x-axis value of the fifth group of electrochemical experimental data is 6.00289 × 10. -1 Substituting into the linear regression equation above, we obtain the current predicted dependent variable y. predicted For: y predicted = -1.589 × 10 -6 .

[0080] S30: Randomly generate noise values ​​z corresponding to the reverse noise within the range [-5σ, 5σ], wherein the generation rule of the noise values ​​z follows a normal distribution.

[0081] The distribution diagram of the noise values ​​generated by the above scheme is shown in the figure below. Figure 2 As shown, by Figure 2 It can be seen that the generated noise follows a normal distribution, which is consistent with the basic characteristics of noise.

[0082] This invention conducts an in-depth analysis of various noises generated during electrochemical experiments at an electrochemical workstation, discovering that thermal noise strictly follows a normal distribution. Based on this law, an inverse noise model that conforms to a normal distribution is designed to perform targeted noise reduction on the thermal noise in the detection signal.

[0083] Continuing with the explanation using the electrochemical experimental data from Example A above, the standard deviation σ corresponding to the first four sets of electrochemical experimental data in Example A, calculated as described above, is 2.885 × 10⁻⁶. -6 Then, in the range [-1.4425×10] -5 1.4425×10 -5 A random inverse noise value z = -2.274983 × 10⁻⁶, following a normal distribution, is generated within the [internal area]. -7 .

[0084] S40: Calculate the probability density f(z) corresponding to the noise value z and the maximum probability density f(x) based on the probability density function f(x). max And calculate the ratio r between the two.

[0085] The probability density function f(x) is expressed as shown in Equation 2:

[0086]

[0087] Where μ = 0;

[0088] Maximum probability density f max Let f(x) be the value of f(x) when x = μ = 0;

[0089] The expression for the ratio r is shown in Equation 3:

[0090]

[0091] Continuing with the explanation using the electrochemical experimental data from Example A above, the standard deviation σ corresponding to the first four sets of electrochemical experimental data in Example A, calculated as described above, is 2.885 × 10⁻⁶. -6 The randomly generated reverse noise value z = -2.274983 × 10 -7 Then, according to the expression of the probability density function f(x) shown in Equation 2, the previously calculated μ = 0 and σ = 2.885 × 10 -6 z = x = -2.274983 × 10 -7 Substituting into Equation 2, we calculate the probability density f(z) corresponding to the current noise value z = 137852.29. Then, setting x = μ = 0 in Equation 2, we obtain the maximum probability density f. max =138281.55, then according to Equation 3, divide the probability density f(z) corresponding to the current noise value z by the maximum probability density f max The calculated ratio r is 0.9969.

[0092] It should be noted that further experimental investigations revealed that white noise also exhibits the same distribution pattern, therefore this method can also be used to reduce white noise in the detection signal.

[0093] S50: Generate a random number within the range [0, 1]. If the random number is less than r, the noise value z is determined to be valid noise. If the random number is greater than r, the step of generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] in S30 is repeated.

[0094] Continuing with the explanation using the electrochemical experimental data from Example A above, the calculated ratio r corresponding to the current noise value z is 0.9969. A random number of 0.702839 is generated within the range [0, 1]. Since the random number is less than the ratio r, the noise value z is set to -2.274983 × 10⁻⁶. -7 It has been determined to be valid noise.

[0095] S60: Add the noise value z, which is determined to be effective noise, to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new.

[0096] Noise reduction dependent variable y new The expression is as shown in Equation 4:

[0097] y new =y measured +z Formula 4.

[0098] Original dependent variable y measured These are unprocessed electrochemical experimental data obtained from measurements taken at an electrochemical workstation.

[0099] Continuing with the electrochemical experimental data shown in Example A above, the effective noise value z, determined earlier, is calculated according to Equation 4 as -2.274983 × 10⁻⁶. -7 Added to the original dependent variable y corresponding to the electrochemical experimental data of group 5. measured =1.45374×10 -6 The noise reduction dependent variable y is obtained. new =1.2262417×10 -6 .

[0100] S70: Calculate the original dependent variable y measured With the prediction of the dependent variable y predicted The first absolute distance, and the noise reduction dependent variable y new With the prediction of the dependent variable y predicted If the second absolute distance is less than the first absolute distance, then the noise reduction dependent variable y will be... new The true dependent variable corresponding to the original independent variable of the (n+1)th group of electrochemical experimental data is determined, output and displayed, and then the value of n is updated. The step of obtaining the original independent variable and original dependent variable corresponding to the first n groups of electrochemical experimental data described in S10 is executed again. If the second absolute distance is greater than the first absolute distance, the step of randomly generating the noise value z corresponding to the reverse noise in the range [-5σ, 5σ] described in S30 is executed again.

[0101] Through the steps S10 to S70 described above, the present invention dynamically adjusts the intensity and phase of the generated noise according to the characteristics of the noise, thereby ensuring that the introduced noise and the original noise are added together and processed to approximate the true value.

[0102] Continuing with the explanation using the electrochemical experimental data shown in Example A above, the original dependent variable y corresponding to the fifth set of electrochemical experimental data has already been obtained. measured =1.45374×10 -6 The current predictor of the dependent variable y predicted = -1.589 × 10 -6 Noise reduction dependent variable y new =1.2262417×10 -6Then the original dependent variable y is calculated. measured With the prediction of the dependent variable y predicted The first absolute distance Δy1 = 3.04274 × 10 -6 Noise reduction dependent variable y new With the prediction of the dependent variable y predicted The second absolute distance Δy2 = 2.8152417 × 10 -6 The second absolute distance Δy2 was detected to be 2.8152417 × 10⁻⁶. -6 Less than the first absolute distance Δy1 = 3.04274 × 10 -6 That is, the noise reduction dependent variable y new The value is closer to the value of the predictor of the dependent variable y. predicted The value of y will then reduce the noise reduction dependent variable y. new =1.2262417×10 -6 The true dependent variable corresponding to the independent variable of the 5th group of electrochemical experimental data is determined and output and displayed on the screen. Then, the value of n is updated to 5, and the steps in S10 to obtain the original independent and original dependent variables corresponding to the first 5 groups of electrochemical experimental data are continued.

[0103] Preferably, the method includes:

[0104] After outputting and displaying the true dependent variable corresponding to the original independent variable of each group of electrochemical experimental data after the m-th group, for each group of electrochemical experimental data, the true dependent variable corresponding to the electrochemical experimental data is updated to the original dependent variable y. measured Then update n to m and repeat steps S10 to S70 to achieve successive noise reduction of the electrochemical experimental data for each group.

[0105] It should be noted that m is a fixed preset value, and the value of n increases dynamically with the number of times electrochemical experimental data is acquired. When the original independent variables corresponding to the true dependent variables of each group of electrochemical experimental data after the m-th group are all output and displayed, that is, when each group of electrochemical experimental data acquired in this round of electrochemical experiment has been denoised once by the detection signal denoising method provided by this invention, the electrochemical experimental data after one denoising process can be used as a benchmark, and the detection signal denoising method provided by this invention can be used again to perform multiple rounds of denoising processing on the electrochemical experimental data after one denoising process.

[0106] The above method enables multiple noise reduction of the detection signal, maximizing the purity and accuracy of the signal. It should be noted that the first m-1 sets of electrochemical experimental data serve as the baseline set for linear fitting. Due to the inherent logic of linear fitting, the first m-1 sets of electrochemical experimental data do not directly participate in the generation of the predicted value, and therefore do not require noise reduction processing during the successive noise reduction process.

[0107] Preferably, the method includes:

[0108] When the absolute value of the difference between the standard deviation σ corresponding to the first n-2 groups of electrochemical experimental data and the standard deviation σ corresponding to the first n-1 groups of electrochemical experimental data is less than the preset difference, after performing the step of obtaining the original independent variable and original dependent variable corresponding to the first n groups of electrochemical experimental data as described in S10, the standard deviation σ corresponding to the first n-1 groups of electrochemical experimental data is directly determined as the standard deviation σ corresponding to the first n groups of electrochemical experimental data.

[0109] That is, when the absolute value of the difference between the standard deviation σ corresponding to the first n-2 sets of electrochemical experimental data and the standard deviation σ corresponding to the first n-1 sets of electrochemical experimental data is less than the preset difference, it is determined that the characteristics of the noise have been fully acquired, and the corresponding reverse noise can be generated based on the standard deviation σ corresponding to the first n-1 sets of electrochemical experimental data for noise reduction.

[0110] Preferably, the noise value z corresponding to the reverse noise is similar in amplitude and opposite in phase to the noise value corresponding to the original thermal noise generated when the electrochemical workstation is working.

[0111] The noise value z corresponding to the reverse noise has a similar amplitude and opposite phase to the noise value corresponding to the original thermal noise, so as to achieve the best noise suppression effect.

[0112] Preferably, the method further includes:

[0113] Analyze other noise types present during the operation of the electrochemical workstation;

[0114] For each other noise type, determine the distribution characteristics corresponding to the other noise type, and generate the corresponding effective reverse noise based on the distribution characteristics corresponding to the other noise type;

[0115] In execution S60, the noise value z, which is determined to be effective noise, is added to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new During the step, the noise value of the effective reverse noise corresponding to each noise type is added to the noise reduction dependent variable y. new And update the noise reduction dependent variable y new .

[0116] The preceding section explained how to improve the purity and accuracy of detection signals by performing multiple rounds of single-noise-type denoising on electrochemical experimental data. The above section describes how to further improve the purity and accuracy of detection signals by performing multiple rounds of multi-noise-type denoising on electrochemical experimental data. It should be noted that each generation of reverse noise is adjusted based on the residual noise characteristics after the previous denoising, and different description and processing methods are required to simulate and generate reverse noise for different types of noise distributions.

[0117] Preferably, the detection signal noise reduction method is terminated when the electrochemical workstation fails to acquire the latest set of electrochemical experimental data.

[0118] Furthermore, as a specific termination condition, the operation of the detection signal noise reduction method can be terminated if the electrochemical workstation fails to acquire the latest set of electrochemical experimental data within a preset time period.

[0119] Preferably, the successive noise reduction step is performed at least three times.

[0120] To better illustrate the beneficial effects of the detection signal noise reduction method based on an electrochemical workstation provided by the present invention, the following Examples 1-3 are shown for illustrative purposes:

[0121] Example 1

[0122] Cyclic voltammetry experiments were conducted using a glassy carbon electrode in a 1 mmol / L K3Fe(CN)6+ 0.1 mol / L KCl system, with a sampling frequency of 1 kHz. The initial cyclic voltammetry curves obtained using the electrochemical workstation are shown in the diagram below. Figure 3 As shown.

[0123] Through observation Figure 3 It can be seen that the initial curve of cyclic voltammetry is significantly affected by noise, which directly hinders the accurate reading of redox peak current and peak potential.

[0124] The detection signal denoising method based on an electrochemical workstation provided by this invention was used to perform six rounds of continuous denoising on the electrochemical experimental data in this cyclic voltammetry experiment scenario. The resulting schematic diagram of the cyclic voltammetry characteristic curve changes after denoising is shown in the figure. Figure 4 As shown, in Figure 4 In the diagram, a is a schematic diagram of the cyclic volt-ampere characteristic curve after the first round of noise reduction, b is a schematic diagram of the cyclic volt-ampere characteristic curve after the second round of noise reduction, c is a schematic diagram of the cyclic volt-ampere characteristic curve after the third round of noise reduction, d is a schematic diagram of the cyclic volt-ampere characteristic curve after the fourth round of noise reduction, e is a schematic diagram of the cyclic volt-ampere characteristic curve after the fifth round of noise reduction, and f is a schematic diagram of the cyclic volt-ampere characteristic curve after the sixth round of noise reduction.

[0125] according to Figure 4 It can be seen that by using the detection signal noise reduction method provided by the present invention to perform one to six consecutive noise reduction processes, each round of noise reduction process has achieved significant suppression of noise.

[0126] It is important to emphasize that the number of noise reduction processes should not be increased indefinitely. While excessive noise reduction can greatly smooth the curve, it may also lead to the loss of the original noise characteristics of the curve due to over-processing, resulting in information distortion. Therefore, while pursuing better noise reduction effects, the number of noise reduction processes must be carefully controlled to ensure the integrity and accuracy of the curve information.

[0127] To further demonstrate the beneficial effects of the detection signal noise reduction method based on an electrochemical workstation provided by this invention, Figure 3 The schematic diagram of the initial noise curve corresponding to the initial cyclic voltammetry curve shown is presented separately. Figure 5 ,exist Figure 5 In the figure, the noise characteristics of the initial cyclic voltammetry curve are presented separately, and its distribution range is clearly defined around zero, specifically in the range of -12.5 μA to 10 μA.

[0128] After the aforementioned six rounds of continuous noise reduction processing, the change in the noise curve after noise reduction is shown in the diagram below. Figure 6 As shown, in Figure 6 In the diagram, a is a schematic diagram of the noise curve after the first round of noise reduction, b is a schematic diagram of the noise curve after the second round of noise reduction, c is a schematic diagram of the noise curve after the third round of noise reduction, d is a schematic diagram of the noise curve after the fourth round of noise reduction, e is a schematic diagram of the noise curve after the fifth round of noise reduction, and f is a schematic diagram of the noise curve after the sixth round of noise reduction.

[0129] according to Figure 6 As can be seen, by gradually increasing the number of times random reverse noise is introduced, the resulting image clearly demonstrates the noise suppression effect. Although the noise is still concentrated near zero, its amplitude has been significantly reduced. In particular, after the sixth round of reverse noise introduction, the original noise range was significantly reduced to the -2μA to 2μA range, indicating that the present invention effectively suppresses noise while successfully preserving the original characteristics of the noise, avoiding excessive distortion of information. Obviously, the detection signal noise reduction method based on an electrochemical workstation provided by the present invention is an effective means to reduce the noise of cyclic voltammetry curves and improve the quality of electrochemical experimental data.

[0130] Furthermore, a schematic diagram showing the change in noise standard deviation with the number of noise reduction cycles using the detection signal denoising method provided by this invention in this cyclic voltammetry experiment scenario is shown below. Figure 7 .exist Figure 7The correlation between the number of noise reduction operations and the noise standard deviation is clearly demonstrated. As the number of noise reduction operations increases, the noise standard deviation tends to decrease, but this process does not follow a strictly linear pattern. Specifically, as noise reduction operations continue, the rate of decrease in the noise standard deviation gradually flattens out. After the first noise reduction, the standard deviation is reduced to approximately 54.7% of its initial value; the second noise reduction further reduces it to 58.6% of the standard deviation after the first noise reduction; and by the sixth noise reduction, the standard deviation is only about 28.3% lower than that after the fifth noise reduction, meaning that approximately 71.7% of the standard deviation after the fifth noise reduction remains. This trend clearly indicates that as the number of noise reduction operations accumulates, its noise suppression effect gradually weakens. Therefore, in practical applications, it is necessary to reasonably control the number of noise reduction operations to balance the noise reduction effect with computational costs.

[0131] Example 2

[0132] The chronoamperometry experiment using a glassy carbon electrode in a 2 mmol / L K3Fe(CN)6+ 0.1 mol / L KCl system, with a sampling frequency of 1 kHz, is illustrated in the schematic diagram of the initial chronoamperometry curve obtained by the electrochemical workstation. Figure 8 As shown.

[0133] Through observation Figure 8 It can be seen that the initial curve of the timing current is significantly affected by noise, which directly hinders the accurate reading of data at specific points.

[0134] The detection signal denoising method based on the electrochemical workstation provided by this invention was used to perform six rounds of continuous denoising on the electrochemical experimental data in the chronoamperometry experiment scenario. The resulting schematic diagram of the cyclic voltammetric characteristic curve after denoising is shown below. Figure 9 As shown, in Figure 9 In the diagram, a is a schematic diagram of the timing current curve after the first round of noise reduction, b is a schematic diagram of the timing current curve after the second round of noise reduction, c is a schematic diagram of the timing current curve after the third round of noise reduction, d is a schematic diagram of the timing current curve after the fourth round of noise reduction, e is a schematic diagram of the timing current curve after the fifth round of noise reduction, and f is a schematic diagram of the timing current curve after the sixth round of noise reduction.

[0135] according to Figure 9 As shown, by implementing one to six consecutive noise reduction processes using the detection signal noise reduction method provided by the present invention, each noise reduction process achieves significant suppression of noise. In particular, when the number of noise reduction processes reaches six, the curve shows an extremely smooth state, which fully verifies the effectiveness and superiority of the noise reduction method provided by the present invention.

[0136] To further demonstrate the beneficial effects of the detection signal noise reduction method based on an electrochemical workstation provided by this invention, Figure 8 The schematic diagram of the initial noise curve corresponding to the initial timing current curve shown is presented separately. Figure 10,exist Figure 10 In the figure, the noise characteristics of the initial curve of the timing current are presented separately, and its distribution range is clearly defined around zero, specifically in the range of -0.09μA to 0.08μA.

[0137] After the aforementioned six rounds of continuous noise reduction processing, the change in the noise curve after noise reduction is shown in the diagram below. Figure 11 As shown, in Figure 11 In the diagram, a is a schematic diagram of the noise curve after the first round of noise reduction, b is a schematic diagram of the noise curve after the second round of noise reduction, c is a schematic diagram of the noise curve after the third round of noise reduction, d is a schematic diagram of the noise curve after the fourth round of noise reduction, e is a schematic diagram of the noise curve after the fifth round of noise reduction, and f is a schematic diagram of the noise curve after the sixth round of noise reduction.

[0138] according to Figure 11 As can be seen, by gradually increasing the number of times random reverse noise is introduced, the resulting image clearly demonstrates the noise suppression effect. Although the noise is still concentrated near zero, its amplitude has been significantly reduced. In particular, after the sixth round of reverse noise introduction, the original noise range was significantly reduced to -0.015μA to 0.01μA, indicating that the present invention not only significantly reduces the noise level of the chronocurrent curve, but also cleverly preserves the original characteristics of the noise, ensuring the authenticity and integrity of the data and providing a solid foundation for subsequent accurate analysis.

[0139] Furthermore, a schematic diagram is shown illustrating the variation of the noise standard deviation with the number of noise reduction cycles under the detection signal denoising method provided by this invention in the context of this chronocurrent experiment. Figure 12 .exist Figure 12 The correlation between the number of noise reduction operations and the noise standard deviation is clearly demonstrated. Both the chronoamperometry and cyclic voltammetry methods show a similar trend: the noise standard deviation gradually decreases with each additional noise reduction operation. However, this process does not follow a simple linear law. Specifically, the rate of decrease in the noise standard deviation gradually slows down as noise reduction operations continue. Specifically, after the first noise reduction, the standard deviation is reduced to approximately 54.8% of its initial value; the second noise reduction further reduces it to 57.8% of the standard deviation after the first noise reduction; and by the sixth noise reduction, the reduction in standard deviation compared to the fifth noise reduction is only 33.5% of the remaining standard deviation, i.e., approximately 66.5% of the standard deviation after the fifth noise reduction. This phenomenon also indicates that the noise reduction effect gradually weakens with each additional noise reduction operation.

[0140] Example 3

[0141] A cyclic voltammetry experiment was conducted with a 6800μF capacitor and a sampling frequency of 2kHz. The schematic diagram of the initial cyclic voltammetry curve obtained by the electrochemical workstation is shown below. Figure 13 As shown.

[0142] Through observation Figure 13 It can be seen that the initial curve of the cyclic voltammetry is significantly affected by noise.

[0143] The detection signal denoising method based on an electrochemical workstation provided by this invention was used to perform six rounds of continuous denoising on the electrochemical experimental data in this cyclic voltammetry experiment scenario. The resulting schematic diagram of the cyclic voltammetry characteristic curve changes after denoising is shown below. Figure 14 As shown, in Figure 14 In the diagram, a is a schematic diagram of the cyclic current-voltage characteristic curve after the first round of noise reduction, b is a schematic diagram of the cyclic current-voltage characteristic curve after the second round of noise reduction, c is a schematic diagram of the cyclic current-voltage characteristic curve after the third round of noise reduction, d is a schematic diagram of the cyclic current-voltage characteristic curve after the fourth round of noise reduction, e is a schematic diagram of the cyclic current-voltage characteristic curve after the fifth round of noise reduction, and f is a schematic diagram of the cyclic current-voltage characteristic curve after the sixth round of noise reduction.

[0144] according to Figure 14 It can be seen that by using the detection signal denoising method provided by the present invention to perform one to six consecutive denoising processes, each denoising process achieves further significant suppression of noise.

[0145] To further demonstrate the beneficial effects of the detection signal noise reduction method based on an electrochemical workstation provided by this invention, Figure 13 The schematic diagram of the initial noise curve corresponding to the initial cyclic voltammetry curve shown is presented separately. Figure 15 ,exist Figure 15 In the figure, the noise characteristics of the initial cyclic voltammetry curve are presented separately, and its distribution range is also clearly defined around zero, specifically in the range of -3μA to 3μA.

[0146] After the aforementioned six rounds of continuous noise reduction processing, the change in the noise curve after noise reduction is shown in the diagram below. Figure 16 As shown, in Figure 16 In the diagram, a is a schematic diagram of the noise curve after the first round of noise reduction, b is a schematic diagram of the noise curve after the second round of noise reduction, c is a schematic diagram of the noise curve after the third round of noise reduction, d is a schematic diagram of the noise curve after the fourth round of noise reduction, e is a schematic diagram of the noise curve after the fifth round of noise reduction, and f is a schematic diagram of the noise curve after the sixth round of noise reduction.

[0147] according to Figure 16 As can be seen, after gradually increasing the number of times random inverse noise is introduced, the noise curve after each round of noise reduction clearly shows the effective noise suppression effect brought by the detection signal noise reduction method. Although the noise is still concentrated near zero, its amplitude has been significantly reduced. In particular, after implementing six rounds of inverse noise introduction, the original noise range is greatly reduced to the range of -0.3μA to 0.2μA. This indicates that the detection signal noise reduction method provided by the present invention can effectively suppress noise while also preserving the original characteristics of the noise to a great extent, thus avoiding excessive distortion of the acquired detection signal.

[0148] Furthermore, a schematic diagram showing the change in noise standard deviation with the number of noise reduction cycles using the detection signal denoising method provided by this invention in this cyclic voltammetry experiment scenario is shown below. Figure 17 .exist Figure 17 The correlation between the number of noise reduction cycles and the noise standard deviation is clearly demonstrated. As the number of noise reduction cycles increases, the noise standard deviation tends to decrease, but this process does not follow a strictly linear pattern. With continuous noise reduction operations, the rate of reduction in the noise standard deviation gradually flattens out. Specifically, after the first round of noise reduction, the standard deviation is reduced to approximately 56.6% of its initial value; the second round further reduces it to 59.1% of the standard deviation after the first round; and by the sixth round, the standard deviation is only about 8.0% lower than the fifth round, meaning it remains approximately 92.0% of the standard deviation after the fifth round. This trend also indicates that the noise suppression effect gradually weakens with the accumulation of noise reduction cycles.

[0149] Comparative analysis of Examples 1 and 3 reveals that although different sampling frequencies were used for the same experimental method and detection signal denoising method, the noise reduction effects exhibited by the noise curves after each round of detection signal denoising were not significantly different. This comparative experiment strongly demonstrates that the detection signal denoising method based on an electrochemical workstation provided by this invention possesses high versatility and adaptability. Its application efficiency is not limited by the specific value of the sampling frequency and it can preserve the frequency characteristics of the noise. Clearly, the detection signal denoising method provided by this invention has strong independence and stability, achieving efficient and stable noise reduction effects under different sampling conditions.

[0150] In summary, the present invention provides a method for noise reduction of detection signals based on an electrochemical workstation, which includes acquiring the original independent and dependent variables corresponding to the first n sets of electrochemical experimental data; calculating the standard deviation σ based on the original dependent variable of the first n sets of electrochemical experimental data; performing linear regression fitting on the first n sets of electrochemical experimental data; calculating the slope a and intercept b of the linear regression equation; and predicting the corresponding predicted dependent variable y using the original independent variable of the (n+1)th set of electrochemical experimental data based on the linear regression equation. predicted Randomly generate noise values ​​z corresponding to the reverse noise within the range [-5σ, 5σ], where the generation rule of the noise values ​​z follows a normal distribution. Calculate the probability density f(z) and the maximum probability density f(x) corresponding to the noise values ​​z based on the probability density function f(x). maxThe ratio r between the two is calculated; a random number is generated within the range [0, 1]. If the random number is less than r, the noise value z is determined as valid noise; if the random number is greater than r, the step of randomly generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] is repeated; the noise value z determined as valid noise is added to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new ; Calculate the original dependent variable y measured With the prediction of the dependent variable y predicted The first absolute distance, and the noise reduction dependent variable y new With the prediction of the dependent variable y predicted If the second absolute distance is less than the first absolute distance, then the noise reduction dependent variable y will be reduced. new The true dependent variable corresponding to the original independent variable of the (n+1)th group of electrochemical experimental data is output and displayed. Then, the value of n is updated, and the step of obtaining the original independent and dependent variables corresponding to the first n groups of electrochemical experimental data is executed. If the second absolute distance is greater than the first absolute distance, the step of randomly generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] is executed again. According to the normal distribution law of the thermal noise generated when the electrochemical workstation is working, and the independent analysis and processing of each group of electrochemical experimental data, the present invention uses a similar normal distribution law to randomly generate the corresponding reverse noise to independently reduce the noise of each group of electrochemical experimental data and display the noise-reduced experimental data in real time. While realizing the real-time and efficient noise reduction processing of electrochemical experimental data, it greatly preserves the true characteristics of the original acquisition signal and noise signal, thereby enhancing the accuracy and reliability of electrochemical measurement.

[0151] Although the present invention has been described in detail above with general descriptions, specific embodiments, and experiments, modifications or improvements can be made to it, which will be obvious to those skilled in the art. Therefore, all such modifications or improvements made without departing from the spirit of the present invention fall within the scope of protection claimed by the present invention.

[0152] Other embodiments of the invention will readily occur to those skilled in the art upon consideration of the specification and practice of the invention herein. This invention is intended to cover any variations, uses, or adaptations of the invention that follow the general principles of the invention and include common knowledge or customary techniques in the art not disclosed herein. It should be understood that the invention is not limited to the precise structures described above and shown in the accompanying drawings, and various modifications and changes can be made without departing from its scope.

Claims

1. A method for noise reduction of detection signals based on an electrochemical workstation, characterized in that, The detection signal noise reduction method includes: Si0: Obtain the original independent and dependent variables corresponding to the first n sets of electrochemical experimental data. Calculate the standard deviation σ based on the original dependent variable of the first n sets of electrochemical experimental data. The value of n increases dynamically and is self-updated as the number of electrochemical experimental data acquisitions increases. S20: Perform linear regression fitting on the first n groups of electrochemical experimental data, calculate the slope α and intercept b of the linear regression equation, and predict the corresponding dependent variable y using the original independent variables of the (n+1)th group of electrochemical experimental data based on the linear regression equation. predicted Predict the dependent variable y predicted The expression is as shown in Equation 1: y predicted =a·x n+1 +b Equation 1 Where, x n+1 For the (n+1)th group of electrochemical experimental data, the original independent variable is denoted as . S30: Randomly generate noise value z corresponding to the reverse noise within the range [-5σ, 5σ], wherein the generation rule of the noise value z follows a normal distribution. S40: Calculate the probability density f(z) corresponding to the noise value z and the maximum probability density f(x) based on the probability density function f(x). max The ratio r between the two is calculated; the probability density function f(x) is expressed as Equation 2: Where μ = 0; Maximum probability density f max Let f(x) be the value of f(x) when x = μ = 0; The expression for the ratio r is shown in Equation 3: S50: Generate a random number within the range [0, 1]. If the random number is less than r, the noise value z is determined to be valid noise. If the random number is greater than r, the step of generating the noise value z corresponding to the reverse noise within the range [-5σ, 5σ] in S30 is repeated. S60: Add the noise value z, which is determined to be effective noise, to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new Noise reduction dependent variable y new The expression is as shown in Equation 4: y new = y measured + z Equation 4; S70: Calculate the original dependent variable y measured With the prediction of the dependent variable y predicted The first absolute distance, and the noise reduction dependent variable y new With the prediction of the dependent variable y predicted If the second absolute distance is less than the first absolute distance, then the noise reduction dependent variable y will be... new The true dependent variable corresponding to the original independent variable of the (n+1)th group of electrochemical experimental data is determined, output and displayed, and then the value of n is updated. The step of obtaining the original independent variable and original dependent variable corresponding to the first n groups of electrochemical experimental data described in S10 is executed again. If the second absolute distance is greater than the first absolute distance, the step of randomly generating the noise value z corresponding to the reverse noise in the range [-5σ, 5σ] described in S30 is executed again.

2. The detection signal noise reduction method according to claim 1, characterized in that, The initial value of n is a fixed preset value m, where m and n are both positive integers greater than 1.

3. The detection signal noise reduction method according to claim 2, characterized in that, The method includes: After outputting and displaying the true dependent variable corresponding to the original independent variable of each group of electrochemical experimental data after the m-th group, for each group of electrochemical experimental data, the true dependent variable corresponding to the electrochemical experimental data is updated to the original dependent variable y. measured Then, update n to m and repeat steps S10 to S70 to achieve successive noise reduction of the electrochemical experimental data for each group.

4. The detection signal noise reduction method according to claim 1, characterized in that, The method includes: When the absolute value of the difference between the standard deviation σ corresponding to the first n-2 groups of electrochemical experimental data and the standard deviation σ corresponding to the first n-1 groups of electrochemical experimental data is less than the preset difference, after performing the step of obtaining the original independent variable and original dependent variable corresponding to the first n groups of electrochemical experimental data as described in S10, the standard deviation σ corresponding to the first n-1 groups of electrochemical experimental data is directly determined as the standard deviation σ corresponding to the first n groups of electrochemical experimental data.

5. The detection signal noise reduction method according to claim 1, characterized in that, The noise value z corresponding to the reverse noise is similar in amplitude and opposite in phase to the noise value corresponding to the original thermal noise generated when the electrochemical workstation is working.

6. The method for denoising detection signals according to claim 1, characterized in that, The method further includes: Analyze other noise types present during the operation of the electrochemical workstation; For each other noise type, determine the distribution characteristics corresponding to the other noise type, and generate the corresponding effective reverse noise based on the distribution characteristics corresponding to the other noise type; In execution S60, the noise value z, which is determined to be effective noise, is added to the original dependent variable y corresponding to the (n+1)th group of electrochemical experimental data. measured The noise reduction dependent variable y is obtained. new During the step, the noise value of the effective reverse noise corresponding to each noise type is added to the noise reduction dependent variable y. new And update the noise reduction dependent variable y new .

7. The method for denoising detection signals according to claim 1, characterized in that, The linear regression fitting algorithm uses the least squares method.

8. The method for denoising detection signals according to claim 1, characterized in that, When the electrochemical workstation fails to acquire the latest set of electrochemical experimental data, the operation of the detection signal noise reduction method is terminated.

9. The detection signal noise reduction method according to claim 3, characterized in that, The successive noise reduction steps should be performed at least three times.

10. The method for denoising detection signals according to claim 1, characterized in that, The original independent variable is the x-axis corresponding to the electrochemical experimental data before noise reduction, and the original dependent variable is the y-axis corresponding to the electrochemical experimental data before noise reduction.

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