Data-driven diagnosis of high temperature PEM fuel cells based on the electrochemical impedance spectroscopy: Robustness improvement and evaluation

Utilizing machine learning techniques for data-driven diagnosis of high temperature PEM fuel cells is beneficial and meaningful to the system durability. Nevertheless, ensuring the robustness of diagnosis remains a critical and challenging task in real application. To enhance the robustness of diagnosis and achieve a more thorough evaluation of diagnostic performance, a robust diagnostic procedure based on electrochemical impedance spectroscopy (EIS) and a new method for evaluation of the diagnosis robustness was proposed and investigated in this work. To improve the diagnosis robustness: (1) the degradation mechanism of different faults in the high temperature PEM fuel cell was first analyzed via the distribution of relaxation time of EIS to determine the equivalent circuit model (ECM) with better interpretability, simplicity and accuracy;(2) the feature extraction was implemented on the identified parameters of the ECM and extra attention was paid to distinguishing between the long-term normal degradation and other faults;(3) a Siamese Network was adopted to get features with higher robustness in a new embedding. The diagnosis was conducted using 6 classic classification algorithms—support vector machine (SVM), K-nearest neighbor (KNN), logistic regression (LR), decision tree (DT), random forest (RF), and Naive Bayes employing a dataset comprising a total of 1935 collected EIS. To evaluate the robustness of trained models: (1) different levels of errors were added to the features for performance evaluation;(2) a robustness coefficient (Roubust_C) was defined for a quantified and explicit evaluation of the diagnosis robustness. The diagnostic models employing the proposed feature extraction method can not only achieve the higher performance of around 100% but also higher robustness for diagnosis models. Despite the initial performance being similar, the KNN demonstrated a superior robustness after feature selection and re-embedding by triplet-loss method, which suggests the necessity of robustness evaluation for the machine learning models and the effectiveness of the defined robustness coefficient. This work hopes to give new insights to the robust diagnosis of high temperature PEM fuel cells and more comprehensive performance evaluation of the data-driven method for diagnostic application.

Semi-supervised estimation of capacity degradation for lithium ion batteries with electrochemical impedance spectroscopy

Machine learning-based methods have emerged as a promising solution to accurate battery capacity estimation for battery management systems.However,they are generally developed in a supervised manner which requires a considerable number of input features and corresponding capacities,leading to prohibitive costs and efforts for data collection.In response to this issue,this study proposes a convolutional neural network(CNN)based method to perform end-to-end capacity estimation by taking only raw impedance spectra as input.More importantly,an input reconstruction module is devised to effectively exploit impedance spectra without corresponding capacities in the training process,thereby significantly alleviating the cost of collecting training data.Two large battery degradation datasets encompassing over 4700 impedance spectra are developed to validate the proposed method.The results show that accurate capacity estimation can be achieved when substantial training samples with measured capacities are given.However,the estimation performance of supervised machine learning algorithms sharply deteriorates when fewer samples with measured capacities are available.In this case,the proposed method outperforms supervised benchmarks and can reduce the root mean square error by up to 50.66%.A further validation under different current rates and states of charge confirms the effectiveness of the proposed method.Our method provides a flexible approach to take advantage of unlabelled samples for developing data-driven models and is promising to be generalised to other battery management tasks.

Solid-state impedance spectroscopy studies of dielectric properties and relaxation processes in Na_(2)O–V_(2)O_(5)–Nb_(2)O_(5)–P_(2)O_(5) glass

Solid-state impedance spectroscopy(SS-IS)was used to investigate the influence of structural modifications resulting from the addition of Nb2O5 on the dielectric properties and relaxation processes in the quaternary mixed glass former(MGF)system 35Na_(2)O–10V_(2)O_(5)–(55-x)P_(2)O_(5)–xNb_(2)O_(5)(x=0–40,mol%).The dielectric parameters,including the dielectric strength and dielectric loss,are determined from the frequency and temperature-dependent complex permittivity data,revealing a significant dependence on the Nb2O5 content.The transition from a predominantly phosphate glass network(x<10,region I)to a mixed niobate–phosphate glass net-work(10≤x≤20,region II)leads to an increase in the dielectric parameters,which correlates with the observed trend in the direct-cur-rent(DC)conductivity.In the predominantly niobate network(x≥25,region III),the highly polarizable nature of Nb5+ions leads to a fur-ther increase in the dielectric permittivity and dielectric strength.This is particularly evident in Nb-40 glass-ceramic,which contains Na_(13)Nb_(35)O_(94) crystalline phase with a tungsten bronze structure and exhibits the highest dielectric permittivity of 61.81 and the lowest loss factor of 0.032 at 303 K and 10 kHz.The relaxation studies,analyzed through modulus formalism and complex impedance data,show that DC conductivity and relaxation processes are governed by the same mechanism,attributed to ionic conductivity.In contrast to glasses with a single peak in frequency dependence of imaginary part of electrical modulus,M″(ω),Nb-40 glass-ceramic exhibits two distinct contributions with similar relaxation times.The high-frequency peak indicates bulk ionic conductivity,while the additional low-fre-quency peak is associated with the grain boundary effect,confirmed by the electrical equivalent circuit(EEC)modelling.The scaling characteristics of permittivity and conductivity spectra,along with the electrical modulus,validate time-temperature superposition and demonstrate a strong correlation with composition and modification of the glass structure upon Nb_(2)O_(5) incorporation.

Analysis of electrochemical impedance and XRD spectroscopy for complex self-assembled film on silver

Self-assembled monolayers （SAMs） of （3-mercaptopropy） trimethoxysilane （3-MtrF） chemisorbed on silver surfaces were chemically ＂modified by 1-octadecanethiol to form self-assembled mixed-monolayers （SAMM） and the co-polymer of N-vinylcarbazole and methyl methacrylate ester （to form complex selfassembled film （CSAF））. The oxidation resistance of these barriers on silver surfaces and some influential factors concerned processes were analyzed by electrochemical impedance spectroscopy （EIS） in a 10% NaOH aqueous solution at oxidation potential. X-ray diffraction （XRD） spectroscopy shows that the oxidation occurring on the silver surface may be restrained effectively due to the coating barrier, and CSAF（Ⅱ） is the best one. Studies also reveal that oxide processes of bare silver and a series of modified silver electrodes in a 10% NaOH aqueous solution are of more than two relaxation time constants.

Study of Cobalt Electrodeposition onto Stainless Steel Using Electrochemical Impedance Spectroscopy （IES）

This paper describes the study of cobalt growth mechanism obtained by electrodeposition method with variation of pH solution. The electrochemical impedance spectroscopy （EIS） and scanning electronic microscopy （SEM） results were possible conclude that the cobalt electrodeposited at pH = 5.40 presented approximately an area three times larger than the cobalt electrodeposited at pH = 2.70. In addition, the cobalt electrodeposited at pH = 2.70 had a value of charge transfer resistance equal to 151.6 f2＂cm2 and the cobalt electrodeposited at pH = 5.40 this value corresponds to 67.4 f2＇cm. This occurs because the increased in micro-porosity increase the diffusion of electrolyte on cobalt electrodeposits easily the corrosion process.

Constituent phases of the passive film formed on 2205 stainless steel by dynamic electrochemical impedance spectroscopy

The passive film formed on 2205 duplex stainless steel（DSS） in 0.5 M NaHCO3＋0.5 M NaCl aqueous solution was characterized by electrochemical measurements,including potentiodynamic anodic polarization and dynamic electrochemical impedance spectroscopy（DEIS）.The results demonstrate that there is a great difference between the passive film evolutions of ferrite and austenite.The impedance values of ferrite are higher than those of austenite.The impedance peaks of ferritic and austenitic phases correspond to the potential of 0.15 and 0.25 V in the low potential range and correspond to 0.8 and 0.75 V in the high potential range.The evolutions of the capacitance of both phases are reverse compared to the evolutions of impedance.The thickness variations obtained from capacitance agree well with those of impedance analysis.The results can be used to explain why pitting corrosion occurs more easily in austenite phase than in ferrite phase.

Fast Evaluation of Degradation Degree of Organic Coatings by Analyzing Electrochemical Impedance Spectroscopy Data

The degradation coefficient is proposed to evaluate the degradation degree of organic coatings by directly anaIyzing the Bode plots of the electrochemical impedance spectroscopy （EIS） data. This paper investigated the degradation of phenolic epoxy coating/tinplate system by EIS and the degradation coefficient value, which correlates well with the results of breakpoint frequency and variation of phase angle at 10 Hz. Furthermore, the degradation process was confirmed by scanning electron microscope （SEM） and scanning probe microscopy （SPM）. It is concluded that degradation coefficient can be used for the fast evaluation of degradation degree of organic coatings in practical appli- cations.

Electrochemical impedance spectroscopy study on the corrosion of the weld zone of 3Cr steel welded joints in CO_2 environments

The welded joints of 3Cr pipeline steel were fabricated with commercial welding wire using the gas tungsten arc welding （GTAW） technique. Potentiodynamic polarization curves, linear polarization resistance （LPR）, electrochemical impedance spectroscopy （EIS）, scan- ning electron microscopy （SEM）, and energy-dispersive spectrometry （EDS） were used to investigate the corrosion resistance and the growth of a corrosion film on the weld zone （WZ）. The changes in electrochemical characteristics of the film were obtained through fitting of the EIS data. The results showed that the average corrosion rate of the WZ in CO2 environments first increased, then fluctuated, and finally de- creased gradually. The formation of the film on the WZ was divided into three stages： dynamic adsorption, incomplete-coverage layer forma- tion, and integral layer formation.

Study on pitting process of 316L stainless steel by means of staircase potential electrochemical impedance spectroscopy

Pitting corrosion of 316L stainless steel in NaCl solution was investigated by means of staircase potential electrochemical impedance spectroscopy（SPEIS）.The investigation focused on the transition of stainless steel from the passive state to pitting corrosion.Based on the evolution of electrical parameters of the equivalent electrical circuit,it is suggested that the most probable mechanism of pit creation is the film breaking model.The result demonstrates that staircase potential electrochemical impedance spectroscopy is an effective method for the investigation of pitting corrosion.

ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY STUDY OF CORROSION INHIBITION OF MODIFIED LIGNOSULPHONATE FOR CARBON STEEL

The corrosion inhibition for carbon steel in circulating cooling water by modified lignosulphonate has been investigated using electrochemical impedance spectroscopy technique. Results show that the inhibition efficiency of modified lignosulphonate GCL2 is a great improvement on that of lignosulphonate. The maximum inhibition efficiency of GCL2 reaches 99.21% at the concentration of 400mg·L^-1 at 303K. The corrosion inhibition of GCL2 is attributed to forming adsorption film on the metal surface for the electrochemical impedance spectroscopy in GCL2 solution shows more than one time-constant.Moreover,results also indicate that it is more efficient in stirring solution than in still solution for GCL2 because the constant of adsorption in stirring solution is much larger than that in still solution. The adsorption of inhibitor GCL2 follows Langmuir＇s adsorption isotherm.

Localized Electrochemical Impedance Spectroscopy Study on the Corrosion Behavior of Fe-Cr Alloy in the Solution with Cl^- and SO_4^(2-)

The corrosion behaviors of Fe-Cr alloy under three different pH values solutions with C1- and SO42- were investigated by localized electrochemical impedance spectroscopy （LEIS） measurements and the corrosion products were analyzed by laser Raman spectrometry. The results show that the high corrosion resistance of Fe-Cr Alloy is attributed to a passive film which is formed more easily when the alloy contains a large quantity of Cr element. However, its corrosion resistance varies in the solutions with different pH values, especially in the initial corrosion. The average impedance values in neutral and alkaline solution are much higher than that in acidic solution because the passive film is more likely to dissolve in the acidic condition. Moreover, the destructive effect of C1- and SO42 ions on the passive film is also demonstrated in corrosion process through the change of the impedance value with the steeping time.

Interpretation of electrochemical impedance spectroscopy(EIS) circuit model for soils

Based on three different kinds of conductive paths in microstructure of soil and theory of electrochemical impedance spectroscopy(EIS), an integrated equivalent circuit model and impedance formula for soils were proposed, which contain 6 meaningful resistance and reactance parameters. Considering the conductive properties of soils and dispersion effects, mathematical equations for impedance under various circuit models were deduced and studied. The mathematical expression presents two semicircles for theoretical EIS Nyquist spectrum, in which the center of one semicircle is degraded to simply the equivalent model. Based on the measured parameters of EIS Nyquist spectrum, meaningful soil parameters can easily be determined. Additionally, EIS was used to investigate the soil properties with different water contents along with the mathematical relationships and mechanism between the physical parameters and water content. Magnitude of the impedance decreases with the increase of testing frequency and water content for Bode graphs. The proposed model would help us to better understand the soil microstructure and properties and offer more reasonable explanations for EIS spectra.

Prediction of fuel cell performance degradation using a combined approach of machine learning and impedance spectroscopy

Accurate prediction of performance degradation in complex systems such as solid oxide fuel cells is crucial for expediting technological advancements.However,significant challenges still persist due to limited comprehension of degradation mechanisms and difficulties in acquiring in-situ features.In this study,we propose an effective approach that integrates long short-term memory(LSTM) neural network and dynamic electrochemical impedance spectroscopy(DEIS).This integrated approach enables precise prediction of future evolutions in both current-voltage and EIS features using historical testing data,without prior knowledge of degradation mechanisms.For short-term predictions spanning hundreds of hours,our approach achieves a prediction accuracy exceeding 0.99,showcasing promising prospects for diagnostic applications.Additionally,for long-term predictions spanning thousands of hours,we quantitatively determine the significance of each degradation mechanism,which is crucial for enhancing cell durability.Moreover,our proposed approach demonstrates satisfactory predictive ability in both time and frequency domains,offering the potential to reduce EIS testing time by more than half.

Effect of sulphate-reducing bacteria on the electrochemical impedance spectroscopy characteristics of 1Cr18Ni9Ti

The electrochemical characteristics of 1Cr18Ni9Ti in sulphate-reducing bacteria （SRB） solutions and the biofilm of SRB on the surface of the 1Cr18Ni9Ti electrode were studied by electrochemical, microbiological, and surface analysis methods. Electrochemical impedance spectroscopy （EIS） of 1Cr18Ni9Ti was measured in the solutions with and without SRB at the culture time of 2, 4, 8 d, respectively. The measurement used two test methods, the nonimmersion electrode method and the immersion electrode method. It was found that the polarization resistance （Rp） of 1Cr18Ni9Ti in the solutions without SRB is the greatest for each test method. When using the nonimmersion electrode method, Rp shifts negatively at first and then positively, and the time constant is only one. Although using the immersion electrode method, the Rp shifts positively at first and then negatively, and the time constant also changes when the biofilm forms. The biofilm observed through SEM is with pores. It was demonstrated that SRB has accelerated corrosion action on 1Cr18Ni9Ti. The protection effect of the biofilm on the electrode depends on the compact degree of the film.

Model reduction of fractional impedance spectra for time–frequency analysis of batteries, fuel cells, and supercapacitors

Joint time–frequency analysis is an emerging method for interpreting the underlying physics in fuel cells,batteries,and supercapacitors.To increase the reliability of time–frequency analysis,a theoretical correlation between frequency-domain stationary analysis and time-domain transient analysis is urgently required.The present work formularizes a thorough model reduction of fractional impedance spectra for electrochemical energy devices involving not only the model reduction from fractional-order models to integer-order models and from high-to low-order RC circuits but also insight into the evolution of the characteristic time constants during the whole reduction process.The following work has been carried out:(i)the model-reduction theory is addressed for typical Warburg elements and RC circuits based on the continued fraction expansion theory and the response error minimization technique,respectively;(ii)the order effect on the model reduction of typical Warburg elements is quantitatively evaluated by time–frequency analysis;(iii)the results of time–frequency analysis are confirmed to be useful to determine the reduction order in terms of the kinetic information needed to be captured;and(iv)the results of time–frequency analysis are validated for the model reduction of fractional impedance spectra for lithium-ion batteries,supercapacitors,and solid oxide fuel cells.In turn,the numerical validation has demonstrated the powerful function of the joint time–frequency analysis.The thorough model reduction of fractional impedance spectra addressed in the present work not only clarifies the relationship between time-domain transient analysis and frequency-domain stationary analysis but also enhances the reliability of the joint time–frequency analysis for electrochemical energy devices.

Early Debonding Detection of Rebar-Concrete Interface due to External Loading Utilizing AC Impedance Spectroscopy

A novel method for detecting early damage at the steel-concrete interface due to external loading based on AC impedance spectroscopy technology was proposed.Firstly,alkali pretreatment was introduced to ensure the accuracy and repeatability of the AC impedance test.Secondly,the AC impedance spectroscopy between the steel bar and concrete surface of different bonding positions was tested,and then the physical quantities reflecting the bonding damage condition were obtained by equivalent circuit fitting.Theoretical debonding position calculation and AC conductive structure analysis indicate that the change of interface resistance and interface capacitance can seize the development of bonding damage during the loading process.As the interface damage develops,obvious changes in interface resistance and interface capacitance are observed,and they cannot be recovered after unloading.

Understanding Lithium-ion Transport in Sulfolane- and Tetraglyme-Based Electrolytes Using Very Low-Frequency Impedance Spectroscopy

With the increasing interest in highly concentrated electrolyte systems,correct determination of the cation transference number is important.Pulsed-field gradient NMR technique,which measures self-diffusion coefficients,is often applied on liquid electrolytes because of the wide accessibility and simple sample preparation.However,since the assumptions of this technique,that is,complete salt dissociation,all ions participating in motion,and all of them moving independently,no longer hold true in concentrated solutions,the transference numbers,thus obtained are often over-estimated.In the present work,impedance spectroscopy at a frequency range of 1 MHz to 0.1 mHz was used to examine the concentration effect on lithium-ion transference number under anion-blocking conditions T abc Liþfor two electrolytes:lithium bis(fluorosulfonyl)imide(LiFSI)in sulfolane(SL)and lithium bis(trifluorosulfonyl)imide(LiTFSI)in tetraglyme(G4).The T abc Liþof the former was almost an order of magnitude higher than that of the latter.It also appeared to increase with increasing concentration while the latter followed an opposite trend.The faster Li^(+)transport in the SL system is attributed to the formation of a liquid structure consisting of extended chains/bridges of SL molecules and the anions,which facilitate a cation-hopping/ligand-exchanged-typed diffusion mechanism by partially decoupling the cations from the anions and solvent molecules.The G4 system,in contrast,is dominated by the formation of long-lived,stable[Li(G4)]+solvation cages that results in a sluggish Li+transport.The difference between the two transport mechanisms is discussed via comparison of the bulk ionic conductivity,viscosity,ion self-diffusion coefficients,and the Onsager transport coefficients.

Impedance spectroscopy for quantum dot light-emitting diodes

Impedance spectroscopy has been increasingly employed in quantum dot light-emitting diodes(QLEDs)to investigate the charge dynamics and device physics.In this review,we introduce the mathematical basics of impedance spectroscopy that applied to QLEDs.In particular,we focus on the Nyquist plot,Mott-Schottky analysis,capacitance-frequency and capacitance-voltage characteristics,and the d C/d V measurement of the QLEDs.These impedance measurements can provide critical information on electrical parameters such as equivalent circuit models,characteristic time constants,charge injection and recombination points,and trap distribution of the QLEDs.However,this paper will also discuss the disadvantages and limitations of these measurements.Fundamentally,this review provides a deeper understanding of the device physics of QLEDs through the application of impedance spectroscopy,offering valuable insights into the analysis of performance loss and degradation mechanisms of QLEDs.

ELECTROCHEMICAL IMPEDANCE SPECTROSCOPY DURING CORROSION PROCESS OF 8090 Al-Li ALLOY IN EXCO SOLUTION

The corrosion behavior and electrochemical impedance spectroscopy (EIS) features of 8090 Al-Li alloys in EXCO solution were investigated, and the EIS was simulated using an equivalent circuit. At the beginning of immersion in EXCO solution, the EIS is comprised by a depressed capacitive arc at high-mediate frequency and an inductive arc at low frequency, and the inductive component decreases and disappears with im- mersion time. Once exfoliation or severe pitting corrosion is produced, two capacitive arcs appear in the EIS. These two capacitive arcs are originated from the two parts of the corroded alloy surface, the original flat alloy surface and the new inter-face exposed to the aggressive EXCO solution due to the exfoliation or pitting corrosion. Some corrosion development features of 8090 Al-Li alloys in EXCO solution can be obtained through simulated EIS information.

Exfoliation corrosion susceptibility of 8090 Al-Li alloy examined by electrochemical impedance spectroscopy

The exfoliation corrosion susceptibility and electrochemical impedance spectrosc opy(EIS) of rolled and peak-aged 8090 Al-Li alloys in EXCO solution were studi ed,and the EIS after exfoliation was simulated. Once exfoliation occurs,two ca pacitive arcs appear in the EIS at high-mediate frequency and mediate-low freq uency respectively. The exfoliation-attacked alloy surface consists of two part s,an original flat alloy surface and a new inter-face exposed to EXCO solution due to the exfoliation. The capacitance corresponding to the new exfoliation in ter-face increases approximately linearly with time at early exfoliation stage,due to the enlargement of the new inter-face. Then it maintains stable,due to the corrosion product covering on the new inter-face. The exfoliation suscepti bility can be judged through the average slope of the capacitance vs time curve of the early exfoliation stage. This average slope of the rolled 8090 alloy is m uch higher than that of the peak-aged 8090 alloy,accordingly the rolled 8090 a lloy is more susceptible to exfoliation than the peak-aged 8090 alloy.