A method and system for classifying simulated electrochemical impedance spectroscopy (EIS) data from various electrochemical circuits

Abstract

The present invention relates to system for electrochemical impedance spectroscopy (EIS) for EIS data analysis with a ML based tool. The tool automates the manual analysis and provide fast and efficient analysis of the data. The system also reduces the errors in estimation and enable a continuous, in-situ EIS data analysis.

Description

[0001] A METHOD AND SYSTEM FOR CLASSIFYING SIMULATED

[0002] ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY (EIS) DATA FROM VARIOUS ELECTROCHEMICAL CIRCUITS

[0003] FIELD OF THE INVENTION:

[0004] The invention relates to a system to identify the equivalent circuit using ML and further estimate the values for individual circuit elements. Particualrly, the invention provides a method and system for classifying simulated Electrochemical Impedance Spectroscopy (EIS) data from various electrochemical circuits

[0005] BACKGROUND OF THE INVENTION:

[0006] The following background discussion includes information that may be useful in understanding the present invention. It is not an admission that any of the information provided herein is prior art or relevant to the presently claimed invention, or that any publication specifically or implicitly referenced is prior art.

[0007] Electrochemical impedance spectroscopy (EIS) is a widely used technique in various applications like batteries, supercapacitors, fuel cells and sensors. This technique uses a small alternating current (AC) signal to study the impedance of a cell. The AC signal is applied over a wide range of frequencies to create an impedance spectrum for the cell. Circuit identification and estimation of component values for the identified circuits are essential in the EIS analysis.

[0008] Predicting an Equivalent Circuit Model (ECM) from Electrical Impedance Spectroscopy (EIS) data is crucial in many scientific and engineering domains, particularly in battery diagnostics, corrosion analysis, fuel cells, supercapacitors, and biological systems.

[0009] This frequency dependent impedance data from the EIS is used to analyze interfacial properties in corrosion, biosensors, battery development, fuel cell development, paint characterization, sensor development.

[0010] The estimation of these interfacial data is a two step process that involves:

[0011] 1 : Assigning an equivalent circuit to the impedance data

[0012] 2: Based on the assigned equivalent circuit, extract the component values for the circuit can co-relate them with the change in the interface This 2-step procedure is a manual process and needs to be done several times in iteration. The entire procedure is manual and is prone to humane error resulting in poor estimation of the data. There are existing processes and literature which estimate the equivalent circuits of the EIS for example CN111095008B discloses an electrical architecture for Electrochemical Impedance Spectroscopy (EIS) analysis. The EIS circuit includes at least two current regulators and an electrical energy storage device connected to one or more electrochemical cells in a configuration that decouples power flowing into the respective current regulators. The presence of the electrical energy storage device enables each regulator to operate simultaneously at lower power levels while inducing the desired EIS perturbation current. Operating at low power allows for smaller volume and lower cost than either dissipative or non-dissipative current regulators alone for the same current. Further, the electrical energy storage device allows the power flowing through the current regulator to be independently varied to achieve the desired EIS perturbation current while generating a minimum amount of heat in the circuit, thereby allowing the circuit to occupy a minimum size and produce a minimum cost.

[0013] Further, US9461320B2 discloses Systems, methods, and devices of the various embodiments enable electrochemical impedance spectroscopy (“EIS”) to be performed on electrochemical devices, such as fuel cell stack segments, by power electronics connecting the electrochemical devices in parallel to a common load and / or bus. In an embodiment, the power electronics may compensate for any ripple generated during EIS such that no ripple is realized at the common load and / or bus.

[0014] However, the existing process is not able to provide in-situ EIS analysis and this can provide vital data about the system for example health of the battery and supercapacitors in EV, extent of corrosion in aircrafts and electrochemical biosensors.

[0015] Thus, to address the above-mentioned challenges, the present invention provides a system to identify the equivalent circuit using ML and further estimate the values for individual circuit elements.

[0016] OBJECTIVE OF THE INVENTION:

[0017] The primary object of the present invention is to overcome the drawbacks associated with prior art.

[0018] Another object of the present invention provides a system to identify the equivalent circuit using ML and further estimate the values for individual circuit elements. Another object of the present invention provides a system to identify the equivalent circuit using ML and further estimate the values for individual circuit elements, this will reduce the manual load and the errors in estimation and enable a continuous, in-situ EIS data analysis.

[0019] SUMMARY OF THE INVENTION:

[0020] The invention provides a machine learning method and system for classifying simulated Electrochemical Impedance Spectroscopy (EIS) data from various electrochemical circuits comprising steps of: a) Generating a customised EIS dataset for each circuit by mathematical equation / s for equivalent impedance for each circuit wherein the values for each component of the circuit are varied to generate 10000 combination for each circuit; b) Normalising the dataset for each circuit individually to eliminate the potential biases introduced by features with varying scales; c) Filtering the data based on absolute difference by comparing the datasets of different circuits; and for each comparison between the two EIS spectra, the absolute differences between corresponding data points was determined; wherein if more than 80% of these differences fell below a 3% threshold, the corresponding EIS spectra was removed to achieve a more diverse dataset for training.

[0021] The method of the present invention, comprises the steps of: a) feeding an input data by the user to a program which processes the data and filters non-physical and causal data sets; b) the data is then fed to the first set of ML model which predicts the circuit type; which is further confirmed by the user about the circuit type; c) Thereafter, the input data and user approved circuit type is fed to the second model which predicts the values of each circuit element for the provided data set. DETAILED DESCRIPTION OF THE DRAWINGS:

[0022] To further clarify the advantages and features of the present invention, a more particular description of the invention will be rendered by reference to specific embodiments thereof, which are illustrated in the appended drawings. It is appreciated that these drawings depict only typical embodiments of the invention and are therefore not to be considered limiting in their scope. The invention will be described and explained with additional specificity and detail with the accompanying drawings in which:

[0023] Figure 1 : illustrates the overall workflow of the program. Wherein an input data from the user is fed to the program. The program processes the data and filters non-physical and causal data sets. Then the data is fed to the first set of ML model which predicts the circuit type. The user confirms the circuit type (user can modify the circuit type as well) and then the input data and user approved circuit type is fed to the second model which predicts the values of each circuit element for the provided data set.

[0024] Figure 2: illustrates Equivalent circuits selected for the present invention

[0025] Figure 3: illustrates Raw datasets for each circuit ((A-G) for circuit 1-7 respectively)

[0026] Figure 4: illustrates Datasets for each circuit after normalization ((A-G) for circuit 1-7 respectively)

[0027] Figure 5: illustrates Test-train accuracy comparison for Decision Tree, Light GBM and CatBoost model

[0028] Figure 6: illustrates Comparison of Models accuracy for different cases of datasets in (A) training and (B) testing

[0029] Figure 7: illustrates Comparison of testing accuracy before and after data filtration

[0030] Figure 8: illustrates Confusion matrix for CatBoost model

[0031] Figure 9: illustrates steps involved in the process of the present invention

[0032] DETAILED DESCRIPTION:

[0033] For the purpose of promoting an understanding of the principles of the invention, reference will now be made to the embodiment illustrated in the drawings and specific language will be used to describe the same. It will nevertheless be understood that no limitation of the scope of the invention is thereby intended, such alterations and further modifications in the illustrated system, and such further applications of the principles of the invention as illustrated therein being contemplated as would normally occur to one skilled in the art to which the invention relates.

[0034] It will be understood by those skilled in the art that the foregoing general description and the following detailed description are exemplary and explanatory of the invention and are not intended to be restrictive thereof.

[0035] In an embodiment, the present invention provides a method and system to identify the equivalent circuit using classification based machine learning (ML) and further estimate the values for individual circuit elements.

[0036] In an embodiment, the present invention provides a method and system to identify the equivalent circuit using ML and further estimate the values for individual circuit elements, this will reduce the manual load and the errors in estimation and enable a continuous, in-situ EIS data analysis. In the present method, the data processing, circuit prediction and parameter estimation is done manually. By the present method, the user can directly feed the experimental data to the model which can immediately do the analysis, hence making the system in-situ.

[0037] In an embodiment, the present invention uses electrochemical impedance spectroscopy (EIS) data from the EIS to analyze interfacial properties in corrosion, biosensors, battery development, fuel cell development, paint characterization, sensor development. The present invention uses a ML based tool is developed for EIS data analysis. The tool will automate the manual analysis and provide fast and efficient analysis of the data.

[0038] In an embodiment, the data from EIS has several vital information about the electrochemical interface. This information can be used in several electrochemical applications like supercapacitors, EV batteries, corrosion and biosensors. The method of the present invention enables an on-site and real time analysis of EIS data which can be instrumental in several applications like health of the battery and supercapacitors in EV, extent of corrosion in several structures and aircrafts and electrochemical biosensors.

[0039] In an embodiment, the present invention provides a method and system to identify the equivalent circuit using ML and further estimate the values for individual circuit elements. This reduces the manual load and the errors in estimation and enable a continuous, in-situ EIS data analysis. In an embodiment, as shown in figure 1, the workflow of the system is shown, the data recorded from the EIS measuring instrument would be fed to the model, and it will estimate the circuit type. Further, the values for circuit elements will also be calculated and displayed to the user.

[0040] In an embodiment, the use of physics-based approaches in data filtration and model training, make the model / system of the present invention more efficient. This, combined with parameter extraction tool, makes our tool a complete EIS analysis solution.

[0041] In an embodiment, the invention provides a machine learning method for classifying simulated Electrochemical Impedance Spectroscopy (EIS) data from various electrochemical circuits. The method comprises the steps of a) Generating a customised EIS dataset for each circuit by mathematical equation / s for equivalent impedance for each circuit wherein the values for each component of the circuit are varied to generate 10000 combination for each circuit; b) Normalising the dataset for each circuit individually to eliminate the potential biases introduced by features with varying scales; c) Filtering the data based on absolute difference by comparing the datasets of different circuits; and for each comparison between the two EIS spectra, the absolute differences between corresponding data points was determined; wherein if more than 80% of these differences fell below a 3% threshold, the corresponding EIS spectra was removed to achieve a more diverse dataset for training.

[0042] In an embodiment, for each combination of the component values, impedance of the circuit across a frequency range spanning from 0.001 Hz to 1 MHz, encompassing a total of 50 logarithmically spaced frequencies was determined.

[0043] In an embodiment, during the data normalization process, each feature is transformed within the EIS dataset to have a mean of zero and a standard deviation of one, to ensure all features contribute equally during the machine learning model training process.

[0044] In an embodiment, the method further comprises the step of a) optimizing the hyperparameters for each model, ensuring they are fine-tuned for the specific characteristics of the EIS data; b) Following hyperparameter optimization, each model was trained on the pre- processed dataset, and their performance was evaluated using standard metrics like accuracy.

[0045] Particularly, the method of the present invention includes feeding an input data by the user to a program which processes the data and filters non-physical and causal data sets; a) the data is then fed to the first set of ML model which predicts the circuit type; which is further confirmed by the user about the circuit type; b) Thereafter, the input data and user approved circuit type is fed to the second model which predicts the values of each circuit element for the provided data set.

[0046] The Invention also provides a system for classifying simulated Electrochemical Impedance Spectroscopy (EIS) data from various electrochemical circuits comprises a processor to perform the steps of: a) Generating a customised EIS dataset for each circuit by mathematical equation / s for equivalent impedance for each circuit wherein the values for each component of the circuit are varied to generate 10000 combination for each circuit; b) Normalising the dataset for each circuit individually to eliminate the potential biases introduced by features with varying scales; c) Filtering the data based on absolute difference by comparing the datasets of different circuits; and for each comparison between the two EIS spectra, the absolute differences between corresponding data points was determined; wherein if more than 80% of these differences fell below a 3% threshold, the corresponding EIS spectra was removed to achieve a more diverse dataset for training.

[0047] The Invention is further described with the help of various experiments, presented by the way of following examples:

[0048] The below examples are described in terms of 7 circuits, however, the present invention can be applied and will be useful for more than 7 or less than 7 circuits. The application of the present invention is not limited to a specific number of the circuits. 1: a) Data Generation:

[0049] Seven typical ECM for batteries, biosensors, corrosion, and supercapacitors application were identified (figure 2). In the figure 2, circuit 1 and 2 are the Randles circuit with and without Warburg element respectively. It is the most basic circuit and is widely used as Equivalent Circuit Model (ECM) to model various applications like sensors, supercapacitors, characterisation of electrodeposited layers etc. The circuit 4 and 7 shown in figure 2 are widely used as ECM for preventive coatings for corrosion and corrosion mechanism of metals. The circuit 5 and 6 shown in figure 2 are widely used as Equivalent Circuit Model (ECM) to model batteries and fuel cells.

[0050] To train and evaluate the ML model by the process of the present invention, a simulated EIS dataset was generated for each circuit. This dataset was computed using mathematical equations for equivalent impedance for each circuit. The mathematical expression for each circuit element is tabulated in Figure 2. The values for each component of the circuit were varied to generate 10000 combination for each circuit. The component values were selected based on the reported EIS spectra in the literature as tabulated in Figure 2.

[0051] For each combination of the component values, impedance of the circuit across a frequency range spanning from 0.001 Hz to 1 MHz, encompassing a total of 50 logarithmically spaced frequencies was calculated.

[0052] The variables Rl, R2 and R3, dominates the features of Nyquist plot. The ML models accuracy should have a minimum effect of these for better applicability in real world. To study the effect of these parameters, three different datasets were generated by changing the ranges of Rl, R2 and R3 as per Table 3-2. imple 2:

[0053] Data Normalization:

[0054] To address potential biases introduced by features with varying scales, the dataset for each circuit was normalised individually. The dataset was normalised using Standard Seal er feature of SciKit in Python 3. This technique transforms each feature within the EIS dataset to have a mean of zero and a standard deviation of one. This ensures all features contribute equally during the machine learning model training process. StandardScaler achieves this by subtracting the mean of each feature from all data points within that feature and then dividing by the feature's standard deviation. This normalization step helps mitigate the influence of features with inherently larger scales, preventing them from dominating the model's learning process. Example 3:

[0055] Data Filtration:

[0056] To promote model generalizability and reduce overfitting, the inventors implemented a data filtering strategy based on absolute difference. This process compared datasets of different circuits. For each comparison between the two EIS spectra, the absolute differences between corresponding data points. If more than 80% of these differences fell below a 3% threshold, the corresponding EIS spectra was removed. This filtering approach aimed to achieve a more diverse dataset for training.

[0057] Example 4:

[0058] ML Model Training:

[0059] To identify the most suitable approach for analysing the pre-processed EIS data, three machine learning models were used for the experimentation:

[0060] 1. Decision Tree

[0061] 2. CatBoost

[0062] 3. LightGBM

[0063] All three belong to the gradient boosting family, a powerful technique known for constructing robust models by sequentially adding decision trees on the errors of previous ones. This iterative approach allows the model to learn increasingly complex relationships within the data.

[0064] The choice of these specific algorithms was based on their strengths in handling different aspects of the data analysis task. Decision Trees offer the advantage of interpretability, allowing for a clear understanding of the decision-making process behind the model's predictions. CatBoost and LightGBM, on the other hand, excel at handling categorical features and efficiently tackling large datasets, making them well- suited for the potential complexities of EIS data.

[0065] The present invention employs a grid search approach to optimize the hyperparameters for each model, ensuring they were fine-tuned for the specific characteristics of our EIS data. Following hyperparameter optimization, each model was trained on the pre-processed dataset, and their performance was evaluated using standard metrics like accuracy.

[0066] Example 5:

[0067] Experimental Data Pre-processing and Division

[0068] A visual representation of the raw dataset for all the circuits is shown in figure 3 and the visualization for the normalised dataset shown in figure 4. The application of ‘ StandardScaler’ during data pre-processing resulted in a normalized EIS dataset with a mean of zero and a standard deviation of one for all features. This normalization addressed potential biases introduced by features with significantly different scales. For instance, the features in figure 3 C-F are extremely identical. A close observation of the normalised datasets for the same in figure 4- C-F, reveals clear shift in the data distribution towards the standard normal form after applying StandardScaler. The standardization improved the performance of the chosen machine learning model by ensuring all features contributed equally during the training process.

[0069] Example 6:

[0070] Selection of ML algorithm:

[0071] The evaluation process aimed to identify the most suitable machine learning model / process for classifying simulated EIS data from various electrochemical circuits. Three prominent algorithms were explored: CatBoost, LightGBM, and decision trees and the models were evaluated using standard performance metric of accuracy.

[0072] The training and testing efficiency of these models is presented in figure 5. The training accuracy of Decision Tree was highest (1), but the testing accuracy dropped to 0.697. This drop was highest when compared to other models where the drop was lesser. This is due to overfitting in the training process of the Decision Tree. The difference between the training and testing accuracy for Decision Tree was maximum as shown in figure 6 and 7.

[0073] CatBoost had the least difference in the training and testing accuracy, and in the later sections it had the best testing accuracy, hence, CatBoost consistently achieved the highest performance across all evaluation metrics. This suggests that CatBoost effectively learned the underlying relationships within the simulated EIS data, leading to more accurate circuit classifications.

[0074] It is understood that several potential factors contribute to CatBoost' s superior performance (which employs claimed method of the present invention) because of the following features: a) It utilizes symmetric trees during the boosting process, potentially leading to more efficient training compared to the asymmetric trees employed by LightGBM and decision trees. b) Secondly, CatBoost' s ordered boosting approach mitigates potential overfitting issues commonly observed in traditional boosting algorithms. c) Finally, CatBoost excels at handling categorical features, which might be present within the simulated EIS data depending on the specific ECMs being modelled. These combined strengths likely allowed CatBoost to capture more robust and generalizable patterns within the data, ultimately leading to more accurate circuit classifications. While decision trees offer the advantage of interpretability, their performance often falls short compared to more advanced boosting techniques like CatBoost and LightGBM. LightGBM, on the other hand, can be highly competitive in terms of raw performance. However, in this specific case, CatBoost's potential advantages in efficiency, overfitting mitigation, and potentially better suitability for the characteristics of the simulated EIS data appeared to make it the optimal choice for this research. All the three models tested in this study are compared with few other models present in the literature as shown in Table 4-1. The prediction efficiency of these models is slightly less than the reported model, but the dataset for the reported models encompasses maximum upto 5 circuits, whereas, we have trained the model for 7 circuits. Also, the datasets used in this study is quite broad and encompasses EIS spectra of several applications whereas the reported models were confined to a particular application.

[0075] Example 7:

[0076] Effect of dataset on model accuracy

[0077] The effect of change in datasets on the models training and testing accuracy is shown in figure 6.

[0078] On comparing the efficiency of case 1, which is the base case, with case 2, the accuracy of all the models increased, while the accuracy of all the models decreased in case 3. The highest accuracy obtained was 77.55%, given by the CatBoost Model in Case 2.

[0079] In Case 2, the accuracy increases compared to the base case. As the range has been narrowed down (starting from a higher minimum in both R1 and R2). This might have led to the exclusion of less relevant features or data points, resulting in a better model fit and generalization. The narrowed ranges result in a more focused dataset or parameter set that better captures the underlying patterns or relationships the model is trying to learn.

[0080] In Case 3, the accuracy decreases. The expansion of the range in both R1 and R2 (starting from a lower minimum) could have included more features or data points that are not as predictive or are noisy, thus reducing the model's performance.

[0081] As can be seen in figure 6, Catboost had the minimum effect on accuracy due to change in dataset, hence CatBoost is a better choice. 8:

[0082] Effect of data filtering on model accuracy

[0083] The rationale behind this filtering approach lies in the concept of model generalizability. By removing highly similar datasets, we aimed to prevent the model from overfitting to specific data patterns and instead encourage it to learn broader relationships within the EIS data. This was performed as mentioned description above mentioned. Post data filtration, there was a minor decrease -2-3% in the dataset of circuit 1,3,4 and 5. However, no datapoints were eliminated from the circuit 2,6 and 7 as tabulated in Table 4-2. The comparison between the testing accuracy of each model before and after data Alteration is shown in figure 7. As can be seen in figure 7, there is a substantial increase in accuracy by 10.24% (from a previously obtained highest accuracy of 75.71% to 85.95% highest accuracy now, both in the case of CatBoost).

[0084] The performance of CatBoost was also evaluated using a confusion matrix as shown in figure 8. The model achieved an overall accuracy of 85.93%. The models accuracy was heavily affected in the case of circuit 3, 5 and 6 with an accuracy of 47.9%, 50.02% and 62.37% respectively. There is a significant false positive and negatives between circuit 3 and circuit 5. Also there is significant false negative for circuit 6 with circuit 1 (-38%). These findings will guide further model refinement to improve classification accuracy.

Claims

We Claim:

1. A machine learning method for classifying simulated Electrochemical Impedance Spectroscopy (EIS) data from various electrochemical circuits comprising steps of: a) Generating a customised EIS dataset for each circuit by mathematical equation / s for equivalent impedance for each circuit wherein the values for each component of the circuit are varied to generate 10000 combination for each circuit; b) Normalising the dataset for each circuit individually to eliminate the potential biases introduced by features with varying scales; c) Filtering the data based on absolute difference by comparing the datasets of different circuits; and for each comparison between the two EIS spectra, the absolute differences between corresponding data points was determined; wherein if more than 80% of these differences fell below a 3% threshold, the corresponding EIS spectra was removed to achieve a more diverse dataset for training.

2. The method as claimed in claim 1, wherein for each combination of the component values, impedance of the circuit across a frequency range spanning over a wide range of ImHz to 1 MHz.

3. The method as claimed in claim 1, wherein during the data normalization process, each feature is transformed within the EIS dataset to have a mean of zero and a standard deviation of one, to ensure all features contribute equally during the machine learning model training process.

4. The method as claimed in claim 1, comprises the step of: a) optimizing the hyperparameters for each model, ensuring they are finetuned for the specific characteristics of the EIS data;b) Following hyperparameter optimization, each model was trained on the pre-processed dataset, and their performance was evaluated using standard metrics like accuracy.

5. The method as claimed in claim 1, comprises the further steps of: a) feeding an input data by the user to a program which processes the data and filters non-physical and causal data sets; b) the data is then fed to the first set of ML model which predicts the circuit type; which is further confirmed by the user about the circuit type; c) Thereafter, the input data and user approved circuit type is fed to the second model which predicts the values of each circuit element for the provided data set.

6. A system for classifying simulated Electrochemical Impedance Spectroscopy (EIS) data from various electrochemical circuits comprises a processor to perform the steps of: a) Generating a customised EIS dataset for each circuit by mathematical equation / s for equivalent impedance for each circuit wherein the values for each component of the circuit are varied to generate 10000 combination for each circuit; b) Normalising the dataset for each circuit individually to eliminate the potential biases introduced by features with varying scales; c) Filtering the data based on absolute difference by comparing the datasets of different circuits; and for each comparison between the two EIS spectra, the absolute differences between corresponding data points was determined; wherein if more than 80% of these differences fell below a 3% threshold, the corresponding EIS spectra was removed to achieve a more diverse dataset for training.

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