CN-116798528-B - Electrochemical impedance spectrum parameter extraction method of heuristic global optimization algorithm

CN116798528BCN 116798528 BCN116798528 BCN 116798528BCN-116798528-B

Abstract

The invention discloses an electrochemical impedance spectrum parameter extraction method of heuristic global optimization algorithm, the method comprises the steps of firstly, collecting the impedance spectrum data of the escherichia coli by using an electrical impedance testing instrument, and preprocessing to obtain the effective impedance spectrum data. And secondly, selecting an equivalent circuit model from the effective impedance spectrum data, and describing by using a transfer function to obtain the transfer function of the equivalent circuit model. And rearranging the equivalent circuit model transfer functions to obtain the real part and the imaginary part of the equivalent circuit model transfer functions, and converting the real part and the imaginary part to obtain the multi-objective optimization model. And finally, carrying out heuristic global optimization algorithm solution on the multi-objective optimization model to obtain the optimal estimated parameters of the circuit model, namely electrochemical impedance spectrum parameters. The invention has good precision and convergence, can realize accurate EIS parameter estimation, reduces operation burden and accelerates experiment progress.

Inventors

XU YING
YU JUN
CHEN JUNTAO

Assignees

杭州电子科技大学

Dates

Publication Date: 20260505
Application Date: 20230330

Claims (7)

1. The electrochemical impedance spectrum parameter extraction method of the heuristic global optimization algorithm is characterized by comprising the following steps of: step 1, modifying escherichia coli in a culture dish to the surface of an electrode, then adding the electrode into a to-be-detected pond using potassium ferricyanide/potassium ferrocyanide solution as a redox probe, and acquiring escherichia coli impedance spectrum data by using an electrical impedance testing instrument And transmitted to a computer; Step 2, impedance spectrum data of the escherichia coli Preprocessing to obtain effective impedance spectrum data; step 3, selecting an equivalent circuit model for the effective impedance spectrum data to obtain the equivalent circuit model; step 4, describing the equivalent circuit model by using a transfer function to obtain an equivalent circuit model transfer function; Step 5, rearranging the equivalent circuit model transfer function to separate the real part and the imaginary part, so as to obtain the real part and the imaginary part of the equivalent circuit model transfer function, wherein the specific process is as follows: expanding the transfer function of the equivalent circuit model according to the complex operation theorem formula to obtain a real part And imaginary part : ; ; Wherein, the Is solution impedance; The impedance value coefficient of C in the nth parallel resistor R and the capacitor C; An index coefficient of C in the nth parallel resistor R and the capacitor C; is angular frequency; Step 6, converting the real part and the imaginary part of the transfer function of the equivalent circuit model to obtain a multi-objective optimization model; step 7, carrying out heuristic global optimization algorithm solution on the multi-objective optimization model to obtain the optimal estimated parameters of the circuit model, namely electrochemical impedance spectrum parameters; and 8, repeating the steps 1 to 7 every preset time to obtain electrochemical impedance spectrum parameters of the escherichia coli in different time periods.
2. The method for extracting electrochemical impedance spectrum parameters of heuristic global optimization algorithm according to claim 1, wherein in step 2, the specific process of preprocessing is as follows: 2-1 impedance Spectroscopy data of E.coli The real part and the imaginary part of the complex are respectively taken as dependent variables, the frequency is taken as independent variable, and the drawing is respectively carried out to obtain the real part-frequency Graph, imaginary part-frequency A figure; 2-2. Pair of A figure (C), The graph is subjected to smooth filtering operation by using Savitzky-Golay filters respectively, and the E.coli impedance spectrum data after smooth filtering is obtained ; 2-3, Impedance spectrum data of the Escherichia coli after smooth filtration And (5) performing Hilbert transform verification to obtain effective impedance spectrum data of the escherichia coli.
3. The method for extracting electrochemical impedance spectrum parameters of heuristic global optimization algorithm according to claim 2, wherein in step 3, the specific process of selecting the equivalent circuit model is as follows: 3-1 visualization of effective impedance Spectroscopy data of E.coli Using Nyquist plot, intersection of Nyquist plot with real axis of effective impedance Spectroscopy data if not at zero, determination of solution impedance Otherwise not having solution impedance ; 3-2, Determining the number of parallel resistors R and capacitors C according to a Nyquist diagram of effective impedance spectrum data and relaxation time distribution DRT transformation; 3-3. The Nyquist diagram of the effective impedance data determines the participation of the diffusion impedance if the effective impedance data has a 45-degree inclined straight line, otherwise, the equivalent circuit model does not have the diffusion impedance.
4. The method for extracting electrochemical impedance spectrum parameters of heuristic global optimization algorithm according to claim 3, wherein the specific process of determining the number of parallel resistors R and capacitors C in 3-2 is as follows: 3-2-1, obtaining the number of semicircles on the Nyquist diagram according to the Nyquist diagram of the effective impedance spectrum data; 3-2-2, performing DRT conversion on the effective impedance spectrum data to obtain the peak value number of a DRT conversion chart, and eliminating overlapped semicircle caused by similar electrochemical processes in the step 3-2-1; and 3-2-3. The maximum value of the number of semicircles and the number of peaks on the Nyquist diagram is the number of parallel resistors R and capacitors C in the impedance spectrum model.
5. The method for extracting electrochemical impedance spectrum parameters of heuristic global optimization algorithm according to claim 4, wherein the specific process of step4 is as follows: 4-1 impedance Using constant phase Angle element Describing the resistor R and the capacitor C obtained in the step 3-2; 4-2, describing according to a Warburg impedance formula if the equivalent circuit model obtained in the step 3-3 has diffusion impedance, otherwise, not describing; 4-3, calculating the total impedance of the equivalent circuit model according to the description and the series-parallel theorem of the circuit model elements obtained in the steps 4-1 to 4-2, and obtaining the electrochemical impedance spectrum EIS real dynamic description of the equivalent circuit model as follows, namely the transfer function of the equivalent circuit model: ; Wherein, the The device is solution impedance, N2 is the number of parallel resistors R and capacitors C, and N is the serial numbers of the parallel resistors R and the capacitors C; Is the resistance of the nth parallel resistor R and the resistance of R in the capacitor C, The impedance value of C in the nth parallel resistor R and the capacitor C.
6. The method for extracting electrochemical impedance spectrum parameters of heuristic global optimization algorithm according to claim 5, wherein the specific process of step 6 is as follows: 6-1, calculating to obtain an optimized objective function at the j-th term frequency point according to the following formula : ; ; Wherein, the The frequency point sequence number; Respectively the first E.coli impedance spectrum data, real part of E.coli impedance spectrum data and imaginary part of E.coli impedance spectrum data at the term frequency point; Respectively the first The equivalent circuit model impedance, the real part and the imaginary part of impedance at the term frequency point; Is the first Residual error of equivalent circuit model impedance and original effective impedance at term frequency point; 6-2, optimizing the objective function at a total of p frequency points obtained in the step 6-1 And (3) paralleling to obtain p rows of optimization objective function equation sets, namely the multi-objective optimization function of the equivalent circuit model.
7. The method of extracting electrochemical impedance spectrum parameters of a heuristic global optimization algorithm according to claim 6, wherein step 6 further comprises obtaining two objective functions, i.e., real optimal objective functions, at each frequency point in the multi-objective optimization function And an imaginary part optimal objective function ; Adding constraint conditions to the control parameters of the multi-objective optimization function obtained in the step 6-2, wherein the upper and lower limits of the resistance value are constrained in [ , In [ ], the upper and lower limits of the capacitance coefficient are constrained to [ , In [ ], the upper and lower limits of the exponent coefficients are constrained to [ [ In (1).

Description

Electrochemical impedance spectrum parameter extraction method of heuristic global optimization algorithm Technical Field The invention belongs to the field of bioelectrochemistry research, and mainly relates to an electrochemical impedance spectrum parameter extraction method of a heuristic global optimization algorithm. Background Electrochemical Impedance Spectroscopy (EIS) is a technique for characterizing the internal processes of an electrochemical system by measuring its electrical properties under an alternating electric field to obtain complex information about the electrochemical system. EIS is widely used in batteries, sensors, and biomedical fields. In the data processing of EIS, parameter estimation is an effective and practical way to fully understand the internal electrochemical process, as it can provide a quantitative description of the electrochemical reaction. However, the problem of parameter extraction in EIS has been a difficulty and bottleneck in this area. In recent years, many new algorithms have been developed that can extract impedance spectrum parameters more quickly and accurately, such as neural network-based methods, bayesian statistical methods, genetic algorithms, and the like. The traditional EIS parameter extraction method is mainly based on ideas such as model fitting or traditional mathematical solving, and because of the model fitting and the traditional mathematics, when solving the nonlinear problem of complex multi-parameters, the convergence result and the convergence speed are too dependent on initial values, are easy to sink into local optimum and overlong in execution time, the accuracy and the reliability are sometimes not ensured due to the wrong initial values, the problems of high complexity, poor precision, weak generalization capability and the like exist, and meanwhile, the learning cost and the threshold of experimenters are increased. Meanwhile, before any data extracted from equivalent circuit modeling is explained, a good characterization needs to be performed on the system, whether the system meets three requirements of stability, linearity and causality is verified, and verification of validity and reliability of EIS data is ignored by many experimenters, so that the result of experimental data is unreliable or incorrect. Disclosure of Invention The invention aims to provide an electrochemical impedance spectrum parameter extraction method of a heuristic global optimization algorithm. The method solves the technical problems that in the prior art, data validity screening, checking and evaluating indexes, convergence results and convergence speed are too dependent on initial values, are easy to fall into local optimum, are too long in execution time, and are not high in stability and accuracy. The electrochemical impedance spectrum parameter extraction method of the heuristic global optimization algorithm comprises the following specific steps: and step 1, acquiring escherichia coli impedance spectrum data by using an electrical impedance testing instrument. And 2, preprocessing the impedance spectrum data Z (omega) of the escherichia coli to obtain preprocessed effective impedance spectrum data. And 3, selecting an equivalent circuit model for the effective impedance spectrum data obtained in the step 2 to obtain the equivalent circuit model. And 4, describing the equivalent circuit model by using a transfer function to obtain the transfer function of the equivalent circuit model. And 5, rearranging the equivalent circuit model transfer function obtained in the step 4 to separate the real part and the imaginary part, so as to obtain the real part and the imaginary part of the equivalent circuit model transfer function. And step 6, converting the real part and the imaginary part of the transfer function of the equivalent circuit model to obtain a multi-objective optimization model. And 7, carrying out heuristic global optimization algorithm solution on the multi-objective optimization model to obtain the optimal estimation parameters of the circuit model. And 8, repeating the steps 1 to 7 every preset time length to obtain electrochemical impedance spectrum parameter extraction data of the escherichia coli in different time periods. Preferably, the specific process of acquiring the impedance spectrum data of the escherichia coli in the step 1 is as follows: 1-1 E.coli cultured for different growth periods was placed in a petri dish. 1-2. The E.coli obtained in the step 1-1 is modified on the surface of an electrode in a culture dish and added into a cell to be tested which uses a potassium ferricyanide/potassium ferrocyanide solution as a redox probe. And 1-3, carrying out electrochemical impedance spectrum measurement on the to-be-measured cell by using an electrical impedance test instrument to obtain escherichia coli impedance spectrum data. 1-4, Transmitting the E.coli impedance spectrum data Z (omega) obtained in the step 1-3 to a computer. Prefe