Electrochemical impedance analyzer and method of the same

Abstract

To provide an electrochemical impedance analyzer capable of addressing a case where each circular arc of Nyquist diagram indicated by EIS data of a measured battery may include a plurality of reaction resistance components and highly accurately deriving an equivalent circuit from the EIS data.SOLUTION: An electrochemical impedance analyzer 10 comprises a storage part 14 storing a material property database 14a including material feature quantity data, an acquisition part 12a acquiring EIS data, and an analysis part 12b deriving the equivalent circuit. The analysis part 12b identifies time constant of each of a first reaction resistance component and a plurality of second reaction resistance components by reference to the material property database 14a when one first reaction resistance component composing the equivalent circuit is determined to be composed by parallel connection of the plurality of second reaction resistance components, and derives the equivalent circuit by performing fitting processing using the identified time constant.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to an electrochemical impedance analysis apparatus and method, and in particular to a method for deriving an equivalent circuit model for the impedance of a battery from AC impedance data obtained by measuring a battery (an all-solid-state battery or a solid electrolyte sample) using electrochemical impedance spectroscopy. [Background technology]

[0002] Conventionally, the internal state of a battery has been analyzed nondestructively using spectroscopic data (hereinafter, also referred to as "EIS data") obtained by measurements using electrochemical impedance spectroscopy (EIS; also known as AC impedance method). That is, the impedance indicated by the EIS data (the battery's impedance for each frequency, consisting of a real part and an imaginary part) is replaced with an equivalent circuit model, and each circuit component constituting the equivalent circuit is derived using a complex nonlinear least squares method or the like to minimize the error with the EIS data (this process is called a "fitting process"), and the state of the elementary processes in the battery is determined from the EIS data by attributing them to the elementary processes of each electrochemical reaction inside the battery (see, for example, Patent Document 1).

[0003] The device in Patent Document 1 determines the number of reaction resistance components, which are one of the circuit components included in the equivalent circuit, from the number of arcs included in the Nyquist diagram, and derives an equivalent circuit in which the determined reaction resistance components are connected in series by a fitting process. Here, the reaction resistance component refers to a resistance component due to a charge transfer reaction, and the equivalent circuit is a circuit component (hereinafter also referred to as "R / / CPE") consisting of a parallel connection of a resistance component R and a CPE (Constant Phase Element), which is a capacitance component that takes into account inductive relaxation.

[0004] In this specification, the definitions of terms related to equivalent circuits are as follows: An equivalent circuit is a circuit that models a battery or battery materials, and is generally composed of multiple circuit components connected together. A circuit component is a circuit model that corresponds to an elementary process in a battery, and is composed of one or more circuit elements (resistance component, capacitance component, inductance component, CPE, Warburg, etc.). A circuit element is an element in an equivalent circuit whose characteristics are determined by specific circuit parameters such as resistance values. Furthermore, "deriving an equivalent circuit" means calculating the circuit parameters of each circuit element that constitutes the equivalent circuit through a fitting process. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Laid-Open No. 2013-250223 Summary of the Invention [Problem to be solved by the invention]

[0006] However, the method of deriving an equivalent circuit using the technology of Patent Document 1 may underestimate the number of reaction resistance components in an actual battery. This is because each arc of the Nyquist diagram may contain the impedance of multiple reaction resistance components (i.e., multiple time constant components). In such cases, the technology of Patent Document 1 cannot divide the EIS data to the granularity of the properties of each material that actually constitutes the battery, which makes it difficult to feed back the derived equivalent circuit into the material design work when designing and developing battery materials.

[0007] Therefore, an object of the present disclosure is to provide an electrochemical impedance analyzer and method that can handle cases where multiple reaction resistance components may be contained within each arc of a Nyquist diagram indicated by EIS data of a battery under test, and that can derive an equivalent circuit from EIS data with high accuracy. [Means for solving the problem]

[0008] In order to achieve the above object, an electrochemical impedance analyzer according to one embodiment of the present disclosure is an electrochemical impedance analyzer that derives an equivalent circuit modeling a battery under test from EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy, and includes: a storage unit that stores a material property database composed of material feature amount data that associates at least (1) condition information including the constituent materials of the battery with (2) circuit parameters including a time constant of a reaction resistance component that is one of the circuit components of the equivalent circuit and is a parallel connection element between a resistor and a CPE; and an interpreter that acquires the EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy. and an analysis unit that performs a fitting process to derive an equivalent circuit that fits the acquired EIS data and output information about the derived equivalent circuit, wherein the analysis unit identifies the time constants of each of the first reaction resistance component and the plurality of second reaction resistance components when one first reaction resistance component that constitutes the equivalent circuit is considered to be composed of a parallel connection of a plurality of second reaction resistance components by referring to the material property database, and performs the fitting process using the identified time constants to separate the first reaction resistance component into the plurality of second reaction resistance components and identify the resistance components included in the plurality of second reaction resistance components, thereby deriving the equivalent circuit.

[0009] In order to achieve the above object, an electrochemical impedance analysis method according to one embodiment of the present disclosure is an electrochemical impedance analysis method for deriving an equivalent circuit modeling a battery under test from EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy, the method including: an acquisition step of acquiring EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy; and (2) referring to a material property database constituted by material feature amount data correlating at least (1) condition information including the constituent materials of the battery with circuit parameters including a time constant of a reaction resistance component which is one of the circuit components of the equivalent circuit and is a parallel connection element between the resistance and the CPE, thereby and an analysis step of performing a fitting process to derive an equivalent circuit that fits the EIS data acquired in the acquisition step and output information about the derived equivalent circuit, wherein in the analysis step, the time constants of each of the first reaction resistance component and the plurality of second reaction resistance components, when one first reaction resistance component that constitutes the equivalent circuit is considered to be composed of a parallel connection of a plurality of second reaction resistance components, are identified by referring to the material property database, and the fitting process is performed using the identified time constants to separate the first reaction resistance component into the plurality of second reaction resistance components and identify the resistance components included in the plurality of second reaction resistance components, thereby deriving the equivalent circuit.

[0010] The present disclosure can be realized not only as an electrochemical impedance analysis apparatus and an electrochemical impedance analysis method, but also as a program for causing a computer to execute the steps included in the electrochemical impedance analysis method, or as a computer-readable recording medium such as a DVD on which the program is recorded. [Effects of the Invention]

[0011] The present disclosure provides an electrochemical impedance analyzer and method that can handle cases where multiple reaction resistance components may be contained within each arc of a Nyquist diagram shown by EIS data of a battery under test, and that can derive an equivalent circuit from EIS data with high accuracy. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 1 is a block diagram showing the configuration of an electrochemical impedance analyzer according to an embodiment. [Figure 2] FIG. 2 is a flowchart showing the operation of the electrochemical impedance analyzer according to the embodiment. [Figure 3] FIG. 3 is a diagram showing an example of EIS data acquired in step S10 (preparatory processing) of FIG. [Figure 4] FIG. 4 is a diagram showing an example of an equivalent circuit that is acquired in step S10 (preparatory processing) of FIG. 2 and is to be subjected to fitting processing. [Figure 5] FIG. 5 is a diagram showing an example of the structure of a material property database included in the electrochemical impedance analyzer according to the embodiment. [Figure 6] FIG. 6 is a flowchart showing the detailed procedure of step S11 (searching the material property database) in FIG. [Figure 7] FIG. 7 is a diagram illustrating the process of dividing one reaction resistance component into a plurality of parallel configurations by the analysis unit included in the electrochemical impedance analyzer according to the embodiment. [Figure 8] FIG. 8 is a diagram showing a method for identifying an initial resistance value corresponding to a specified temperature by linear regression using an Arrhenius plot. [Figure 9] FIG. 9 is a flowchart showing the detailed procedure of step S15 (matching check) in FIG. [Figure 10] FIG. 10 is a diagram showing an execution example (circuit parameters) of step S17 (output of analysis results) in FIG. [Figure 11A] FIG. 11A is a diagram showing another example (Nyquist diagram) of an execution example in step S17 (output of analysis results) in FIG. [Figure 11B] FIG. 11B is an enlarged view of the high frequency range of the Nyquist diagram of FIG. 11A. [Figure 12]FIG. 12 is a diagram showing another example (Bode diagram) of an execution example in step S17 (output of analysis results) of FIG. [Figure 13] FIG. 13 is a diagram showing another example (DRT spectrum) of an execution example in step S17 (output of analysis results) in FIG. DETAILED DESCRIPTION OF THE INVENTION

[0013] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the drawings. Note that each embodiment described below represents a specific example of the present disclosure. Numerical values, materials, equivalent circuits, circuit components, circuit elements, connection configurations and circuit parameters of circuit elements, steps, order of steps, etc. shown in the following embodiments are merely examples and are not intended to limit the present disclosure. Furthermore, each drawing is not necessarily an exact illustration. In each drawing, substantially identical configurations are assigned the same reference numerals, and duplicate explanations are omitted or simplified.

[0014] 1 is a block diagram showing the configuration of an electrochemical impedance analyzer 10 according to an embodiment. The electrochemical impedance analyzer 10 is an apparatus that derives an equivalent circuit that models a battery under test, such as a secondary battery, from EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy, and includes an input unit 11, a control unit 12, an output unit 13, and a storage unit 14. Specifically, the electrochemical impedance analyzer 10 can be realized by a computer device that stores and executes a program that implements an electrochemical impedance analysis method.

[0015] The storage unit 14 is a device for storing various data and programs, including a material property database 14a composed of a collection of material feature data, which is a record that associates at least (1) condition information including the constituent materials of the battery with (2) circuit parameters including the time constant of a reaction resistance component, which is one of the circuit components of the equivalent circuit, and is realized, for example, by a hard disk.

[0016] The input unit 11 is an input device that receives instructions from the user of this analysis device and outputs them to the control unit 12, and receives data output from external devices such as measuring instruments and outputs them to the control unit 12, and is realized, for example, by a keyboard, a mouse, a communication interface, etc.

[0017] The output unit 13 is an output device that presents information to a user or outputs information to an external device, and is realized by, for example, a display, a communication interface, or the like.

[0018] The control unit 12 is a control device that includes an acquisition unit 12a that acquires EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy, and an analysis unit 12b that performs a fitting process to derive an equivalent circuit that fits the acquired EIS data and output the derived equivalent circuit to the output unit 13, and is realized, for example, by a program and a processor that executes the program.

[0019] More specifically, the acquisition unit 12a acquires EIS data via the input unit 11 from a frequency response analyzer (not shown), which is a measuring instrument that performs measurements on the battery under test using electrochemical impedance spectroscopy, and acquires EIS data from the memory unit 14 that has already been measured by the frequency response analyzer and stored in the memory unit 14.

[0020] In more detail, in the fitting process, to address the possibility that multiple reaction resistance components may be included within each arc of the Nyquist diagram indicated by the EIS data of the battery under test, the analysis unit 12b identifies the time constants of the first reaction resistance component and the multiple second reaction resistance components when a single first reaction resistance component (combined resistance component) constituting the equivalent circuit is considered to be composed of multiple second reaction resistance components (separated resistance components, including multiple components) connected in parallel, by referring to the material property database 14a. Then, by performing a fitting process using the identified time constants as fixed values, the first reaction resistance component is separated into multiple second reaction resistance components, and the resistance components included in the multiple second reaction resistance components are identified, thereby deriving an equivalent circuit. At this time, the analysis unit 12b identifies the resistance components included in the multiple second reaction resistance components through the fitting process using the relationship that the time constant of the first reaction resistance component is equal to a linear combination of the time constants of the multiple second reaction resistance components weighted by the resistance components of each of the multiple second reaction resistance components. In addition, in the fitting process, the analysis unit 12b may perform the fitting process after fixing the time constants of the first reaction resistance component and the plurality of second reaction resistance components identified by referring to the material property database 14a, or the resistance components included in the plurality of second reaction resistance components calculated using a linear combination, as initial values.

[0021] Next, the operation of the electrochemical impedance analyzer 10 according to the embodiment configured as above will be described. Fig. 2 is a flowchart showing the operation of the electrochemical impedance analyzer 10 according to the embodiment (i.e., the procedure of the electrochemical impedance analysis method).

[0022] First, a preparation process for the fitting process is performed (S10). Specifically, in accordance with instructions from a user, the acquisition unit 12a acquires EIS data to be analyzed, i.e., EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy (acquisition step). For example, the acquisition unit 12a acquires EIS data via the input unit 11 from a frequency response analyzer, which is a measuring instrument that performs electrochemical impedance spectroscopy measurements on the battery under test, or acquires EIS data from the storage unit 14 that has already been measured by the frequency response analyzer and stored in the storage unit 14. At this time, the acquisition unit 12a also acquires measurement information related to the battery under test and its constituent materials, environmental conditions, measurement conditions, etc., by user input via the input unit 11 or from measurement record data already stored in the storage unit 14.

[0023] Furthermore, in this embodiment, as part of the preparatory processing of step S10, the acquisition unit 12a acquires the configuration of the equivalent circuit at the start of the fitting process (i.e., the configuration of the equivalent circuit for which specific circuit parameters have not been determined) in accordance with instructions from the user. In other words, in this embodiment, in addition to automatically generating the equivalent circuit configuration based on the Nyquist diagram and performing the fitting process, the analysis unit 12b determines the configuration of the equivalent circuit by creating and connecting circuit components for each elementary process based on the user's selection of a proposal by the analysis unit 12b using past fitting results with similar material feature data. The analysis unit 12b then performs the fitting process on the determined equivalent circuit configuration while taking into account each constraint. By utilizing past fitting results, the fitting accuracy of the reaction resistance components corresponding to elementary processes within the grains (bulk) and at the grain boundaries of the battery under test, which appear in the high-frequency range of the Nyquist diagram, is improved. This maintains the fitting accuracy of the diffusion resistance components corresponding to elementary processes appearing in the low-frequency range, thereby improving the fitting accuracy across the entire range and speeding up the fitting process.

[0024] Next, the analysis unit 12b searches for material feature quantity data in the material property database 14a that matches the condition information such as the constituent materials of the battery under test, based on the EIS data, measurement information, and equivalent circuit configuration obtained in step S10, thereby specifying the initial values ​​of each circuit parameter for fitting processing, and also specifying the frequency range of each reaction resistance component that constitutes the equivalent circuit (S11).

[0025] Next, the analysis unit 12b specifies a change parameter array such as temperature based on the measurement information obtained in step S10, sets the specified change parameter array as a loop parameter, identifies characteristic change frequency points, which are frequencies at which the behavior of the impedance indicated by the EIS data changes significantly, and divides the frequency range at the characteristic change frequency points (S12). Here, the change parameter array is an array of parameters (for example, parameters of environmental conditions such as temperature, sample conditions, and measurement conditions) that are expected to contribute to the EIS data characteristics when EIS data measurements are repeated.

[0026] Next, the analysis unit 12b performs a fitting process (analysis step S13) for each frequency range divided in step S12 in accordance with the loop parameters set in step S12, thereby calculating the circuit parameters of each circuit component constituting the equivalent circuit (i.e., deriving the equivalent circuit), the number of loops indicated by the loop parameters (S13 to S14). At this time, the analysis unit 12b may perform the fitting process after fixing, as initial values, the time constants of the first reaction resistance component and the plurality of second reaction resistance components identified by referring to the material property database 14a, or the resistance components included in the plurality of second reaction resistance components calculated using a linear combination.

[0027] Next, the analysis unit 12b determines whether the derived equivalent circuit is consistent with the change parameter array identified in step S12 (S15), and if there is no consistency (No in S16), it updates the change parameter array and the frequency range (S16a) and executes the equivalent circuit fitting process under the conditions (S12 to S16).

[0028] As a result, if it is determined that there is consistency (Yes in S16), the analysis unit 12b outputs various information related to the derived equivalent circuit as the analysis result to the output unit 13 (S17), and the process ends.

[0029] Hereinafter, the details of steps S10 (preparation processing), S11 (searching the material property database), S13 (fitting processing), S15 (consistency check), and S17 (output of analysis results) in FIG. 2 will be explained with specific examples.

[0030] [Step S10 (preparation process)] Fig. 3 is a diagram showing an example of EIS data acquired in step S10 (preparatory processing) of Fig. 2. More specifically, Fig. 3(a) is a Nyquist diagram (the horizontal axis is the real part Z' of the impedance Z, and the vertical axis is the imaginary part Z'' of the impedance Z), Fig. 3(b) is an enlarged view of the high frequency range of the Nyquist diagram of Fig. 3(a), and Fig. 3(c) and Fig. 3(d) are Bode plots (the frequency dependence of the absolute value |Z| of the impedance (Fig. 3(c)) and the frequency dependence of the phase theta of the impedance (Fig. 3(d)).

[0031] Fig. 4 is a diagram showing an example of the configuration of an equivalent circuit to be subjected to fitting processing, obtained in step S10 (preparatory processing) of Fig. 2. In this diagram, R1 / / CPE1 is a reaction resistance component corresponding to the elementary process within the grains (bulk) of the battery under test, R2 / / CPE2 is a reaction resistance component corresponding to the elementary process at the grain boundaries of the battery under test, R3 / / CPE3 is a reaction resistance component corresponding to the elementary process at the interface between the positive electrode and electrolyte of the battery under test, (R4+Wo) / / CPE4 is a reaction resistance component and diffusion resistance component corresponding to the elementary process within the positive electrode of the battery under test, R5 / / CPE5 is a reaction resistance component corresponding to the elementary process at the interface between the negative electrode and electrolyte of the battery under test, and CPE is a diffusion resistance component corresponding to the elementary process within the negative electrode of the battery under test.

[0032] Such an example of the equivalent circuit configuration can be determined by the user's selection from the proposals made by the analysis unit 12b, which refers to the material property database 14a, when past fitting results similar to the battery under test in terms of condition information, etc. in the material feature quantity data are registered in the material property database 14a. Details will be described later in "Proposal of the Configuration of an Equivalent Circuit."

[0033] [Step S11 (Search material property database)] (1) Structure of the material property database The material property database 14a searched in step S11 (search material property database) of FIG. 2 is a collection of material feature data, which are records in which, for example, various circuit parameters (including resistance R, time constant tau, and exponent phi) that identify the corresponding reaction resistance component are associated with each combination of battery specification information, material conditions, environmental conditions, and measurement conditions (collectively referred to as condition information), the type of elementary process, EIS data, DRT spectrum, and the like. This information is, for example, information in which condition information, measurement data, and fitting results that were the subject of a fitting process performed in the past are registered. Furthermore, not all items constituting the material feature data are necessarily registered. For example, if a fitting process was performed in the past, many items including the condition information and fitting results at that time may be registered.

[0034] Here, battery specification information refers to data showing the detailed specifications and performance of a battery. Material conditions refer to conditions related to the battery's constituent materials. Environmental conditions refer to conditions related to the battery's operating environment, such as temperature. Measurement conditions refer to conditions related to the battery's state or measurement when EIS data, such as SOC (State of Charge) and cycle count, are obtained. Among the circuit parameters (resistance R, time constant tau, and exponent phi) that specify the reactive resistance component (R / / CPE), resistance R is the resistance value of the resistance component that makes up the reactive resistance component. Here, the time constant tau is the relaxation time (tau = R·T^(1 / phi)). The CPE exponent phi is the exponent phi when the CPE impedance Z is expressed as Z = 1 / [T(j*ω)^phi]. T is the CPE constant (CPE-T), j is an imaginary number, and ω is the angular frequency. The DRT spectrum is two-dimensional data obtained using the Distribution of Relaxation Times method, with the X axis representing relaxation time tau [seconds] (log-based. When expressed in frequency f [Hz], the relationship is f=1 / (2π·tau)), and the Y axis representing relaxation time distribution γ [Ω·seconds], and its area represents the resistance value [Ω]. The DRT method is a technique for obtaining an approximate solution to the integral equation for the relaxation time distribution (Fredholm integral equation of the first kind) derived from the inverse Fourier transform of EIS data, using methods such as Tikhonov regularization.

[0035] FIG. 5 is a diagram showing an example structure (an example of a transaction table) of the material property database 14a included in the electrochemical impedance analyzer 10 according to the embodiment. In FIG. 5, PK indicates a primary key, which corresponds to the "material property ID" column. Furthermore, FK indicates a foreign key, and the columns referencing the IDs of the respective external tables include "battery specification information," "material conditions," "environmental conditions," "measurement conditions," "elementary process information," "data feature information," and "DRT peak." Here, a separately defined DRT peak table includes columns for specifying the DRT spectrum ("DRT-time constant T," "DRT-resistance R," "DRT-Phi"), etc. Furthermore, the data array information for "EIS data (frequency f, impedance real part Z', impedance imaginary part Z'')" and "DRT data (frequency f, relaxation time distribution γ)" is stored as a file, and file path information indicating the storage location of each file is included in the columns of the table.

[0036] (2) Details of search process 6 is a flowchart showing the detailed procedure of step S11 (searching the material property database 14a) in FIG. 2. First, based on the measurement information obtained in step S10, the user or the analysis unit 12b sets condition information such as the battery under test and its constituent materials, environmental conditions, and measurement conditions as search items for searching the material property database 14a (S20), and then executes a search (S21). For example, when determining the initial values ​​of the circuit parameters of R1 / / CPE1, material feature quantity data having the same bulk battery specification information as the battery under test is searched for. Similarly, material feature quantity data matching the corresponding battery specification information is searched for for the reaction resistance components in each of the elementary processes of R2 / / CPE2 to R5 / / CPE5.

[0037] As a result, if material feature quantity data that matches the condition information of the battery under test is found (Yes in S22), the user or the analysis unit 12b specifies the initial values ​​of each circuit parameter of the equivalent circuit for fitting processing based on the found material feature quantity data, and also specifies the frequency range of the reaction resistance component that constitutes the equivalent circuit (S26). For example, if the found material feature quantity data includes circuit parameters that specify the reaction resistance component (resistance R, time constant tau, exponent phi), such circuit parameters are set as initial values, and the frequency range corresponding to the circuit parameters is specified.

[0038] On the other hand, if no material feature data matching the condition information of the battery under test is found (No in S22), the user or the analysis unit 12b classifies the EIS data and searches the material property database 14a for material feature data in which a DRT spectrum having a waveform similarity higher than a predetermined value to the DRT spectrum of the battery under test is registered by attempting a waveform similarity evaluation. As a result, if material feature data having a waveform similarity higher than a predetermined value is found by the waveform similarity evaluation (Yes in S24), the circuit parameters included in the material feature data are specified as initial values ​​for the fitting process (S26).

[0039] If no material feature data matching the condition information of the battery under test is found (No in S22), instead of or in addition to the waveform similarity evaluation described above, the user or the analysis unit 12b may estimate the time constant or resistance value of the reaction resistance component using a material property regression model, which is a machine learning model trained using the material feature data registered in the material property database 14a, and perform the fitting process by using the estimated time constant or resistance value as the initial value of the fitting process or as a constraint condition in the fitting process.

[0040] On the other hand, if no material feature data having a waveform similarity higher than the predetermined value is found (No in S24), the user or the analysis unit 12b converts the EIS data into a DRT spectrum, and identifies the time constant related to the material characteristics in the battery under test by time constant difference analysis using the obtained DRT spectrum, and extracts and generates material feature data (S25).

[0041] Here, the waveform similarity evaluation and material property regression model in step S23, and the DRT analysis and time constant difference analysis in step S25 will be described in detail.

[0042] (3) DRT analysis and time constant difference analysis DRT analysis is a technique that separates reaction resistance components using the relaxation time distribution function (also called "DRT spectrum") using the aforementioned DRT method. In other words, the position of each peak (relaxation time) that appears in the DRT spectrum indicates the time constant of each reaction resistance component that makes up the equivalent circuit. Therefore, DRT analysis can identify the time constant of each reaction resistance component that makes up the equivalent circuit. Note that DRT analysis assumes an equivalent circuit that consists of N RC parallel circuits connected in series.

[0043] Therefore, if it is difficult to analyze all reaction resistance components and attribute them to elementary processes, or if only some components need to be analyzed, the user or the analysis unit 12b can use the time constant difference analysis described below to identify time constants related to the material properties within the battery that are the subject of detailed analysis, and extract and generate material feature quantity data. This enables subdivision into circuit elements within the range related to the desired elementary processes and material properties. Conversely, for components and bands that are not of interest, the analysis method proposed in this document can be carried out without refining the model. About time constant difference analysis: In the time constant difference analysis, the user or the analysis unit 12b performs the process in the following procedure.

[0044] (i) Each EIS data is measured while changing only the conditions of the battery material that contribute to the reaction resistance component (such as electrode density), and the time constant is derived by DRT analysis.

[0045] (ii) When the time constants obtained under each condition in the same frequency range are compared and a change of a certain level or more is observed, it can be said that the reaction resistance component including those time constants has a correlation with the battery material and the specified conditions (i.e., the condition information of the battery under test).

[0046] (iii) For each material condition, record the transition of the time constant obtained in (ii) above when the environmental conditions (temperature, etc.) and measurement conditions (SOC, number of cycles, etc.) are changed.

[0047] (iv) Each material characteristic data (material specifications, attributed elementary processes, condition parameters, resistance component R, time constant tau, exponent phi) including the time constant obtained in (iii) above is registered in the material property database 14a.

[0048] (4) Waveform similarity evaluation The waveform similarity evaluation is a method for searching for material feature data similar to the set condition information from the material property database 14a when material feature data matching the set condition information cannot be found in the material property database 14a. Specifically, there are two types of waveform similarity evaluation: one using an autoencoder and the other using a one-dimensional CNN (convolutional neural network).

[0049] The waveform similarity evaluation using an autoencoder follows the steps below.

[0050] (i) A DRT spectrum in a specified frequency range is generated from EIS data corresponding to the condition information to be searched.

[0051] (ii) An autoencoder model is generated using the generated DRT spectrum as input.

[0052] (iii) Next, material feature quantity data having condition information similar to the condition information used as the search source is extracted by searching the material property database 14a.

[0053] (iv) Based on the extracted material feature data, a DRT spectrum is generated under the same conditions as in step (i) above.

[0054] (v) The DRT spectrum generated in step (iv) above is input to the autoencoder model generated in step (ii) above, and the cosine similarity is calculated using the output value of the autoencoder.

[0055] (vi) Extract the material feature data with the highest cosine similarity.

[0056] Here, an autoencoder is a neural network model that compresses input data into a lower-dimensional representation and then learns to reconstruct the original input data from that compressed representation. The compressed representation serves as an efficient internal representation of the original input data, which can be used to evaluate the similarity of the data. As the autoencoder model learns, it learns important features of the data and can use them to evaluate the similarity of unknown data. In other words, the reconstruction error of the data (the difference between the original data and the reconstructed data) can be used as an indicator of how unusual or similar the data is to the model.

[0057] The other waveform similarity evaluation is a waveform similarity evaluation using a one-dimensional CNN. During inference, features are extracted from the material feature data input to the one-dimensional CNN, and a similarity metric is used to evaluate the waveform similarity, making it possible to search for material feature data that has a high waveform similarity to the material feature data being compared from the material property database 14a.

[0058] (5) Material property regression model When performing equivalent circuit fitting of new EIS data using the material property database 14a, if material feature quantity data that completely matches the specified conditions is not found, a material property regression model is generated, and the analysis unit 12b obtains the fitting initial value of the reaction resistance component that is correlated with the specified material property by inference using the material property regression model.

[0059] For example, when a time constant that matches the specified conditions for each material cannot be directly obtained via the material property database 14a, a material property regression model is generated using material feature data extracted from the material property database 14a, and the analysis unit 12b estimates the desired time constant using the generated material property regression model.

[0060] Specifically, first, in the learning phase, dependent parameters are input into a machine learning model based on a data set for a specified material, and a machine learning model that outputs a resistance value or a time constant value is generated as a material property regression model using supervised machine learning or the like. Then, in the inference phase, the analysis unit 12b uses the generated material property regression model to infer the resistance value or time constant value for the specified material under specified conditions for each elementary process. The obtained values ​​are applied as initial values ​​for the circuit parameters of the equivalent circuit, and are fixed or semi-fixed before performing the fitting process. Note that "fixed" means to exclude the value from the variables in the fitting process. Also, "semi-fixed" means to set the value as "fixed" in the initial fitting process and to use it as a variable in subsequent fitting processes.

[0061] The input parameters are preferably condition data values ​​that depend on the specified output, and multiple data can be specified, such as temperature, SOC, number of cycles, electrode density, and porosity. The output parameters are resistance components and time constants. The type of material property regression model can be changed as appropriate depending on the material properties and the characteristics and conditions of the training data. For example, it may be a machine learning model using a decision tree such as random forest or LightGBM, or a deep learning model using a neural network.

[0062] (6) Proposal of equivalent circuit configuration If the material property database 14a contains past fitting results that have similar battery specification information, material conditions, environmental conditions, and measurement conditions to those of the battery under test, the analysis unit 12b can provide examples of those results and propose equivalent circuit configurations. Specifically, there are two methods: one based on data similarity judgments based on various conditions, and the other based on similarity judgments based on EIS data and DRT spectra.

[0063] - Methods based on data similarity judgment based on various conditions: If there are past fitting results using data that are similar to the battery under test in terms of specifications, material conditions, environmental conditions, and measurement conditions, the analysis unit 12b searches for past fitting results that match these various conditions, and proposes these fitting results and the configuration of the equivalent circuit by presenting them to the output unit 13.

[0064] - Method based on similarity judgment using EIS data and DRT spectra: This method utilizes classification using a two-dimensional CNN for image recognition. Specifically, the analysis unit 12b outputs EIS data within a user-specified frequency range as a Nyquist diagram. In this case, when the X-axis and Y-axis are set to the ranges of minimum and maximum values ​​for each axis, the axis range that maximizes the display range on the output unit 13 is fixed, while the other axis range is set to the same. Furthermore, the data on the other axis is drawn as centered as possible. In this state, a two-dimensional black-and-white image is acquired (i.e., the data points on the Nyquist diagram and the lines connecting them are displayed in white). A CNN is applied to this image, and the CNN is trained to classify and learn each battery type or constituent material type to generate a classification CNN model. Each classification is associated with a typical circuit configuration. The analysis unit 12b uses this classification CNN model to infer unknown EIS data and propose an equivalent circuit configuration. If the classification accuracy is low, the analysis unit 12b may determine that classification is impossible and perform the aforementioned waveform similarity evaluation using the waveforms of the EIS data and DRT spectrum.

[0065] By determining the configuration of the equivalent circuit based on a proposal by the analysis unit 12b based on such past fitting results, it is possible to prevent the equivalent circuit finally derived from differing depending on the person who created the configuration of the equivalent circuit.

[0066] [Step S13 (fitting process)] (1) Fitting processing method In step S13 (fitting process) of FIG. 2 , the analysis unit 12b optimizes each circuit parameter by fitting an equivalent circuit having circuit parameters determined as initial values ​​or determined in the immediately preceding fitting process to the EIS data obtained by measurement. More specifically, the analysis unit 12b performs the fitting process by, for example, performing a nonlinear least-squares optimization calculation. When solving the nonlinear least-squares method, it is preferable to apply an optimization calculation method that is relatively less dependent on the initial values ​​of each circuit parameter of the equivalent circuit and does not result in a fitting error. Examples of such optimization calculation methods include the Random Walk Metropolis-Hastings (RW) method, the Steepest Descent (SD) method, and the Levenberg-Marquardt (LM) method. According to the RW method, specified parameters are fixed (i.e., excluded from variables), and the fitting process is repeated for a number of Monte Carlo trials until the specified fitting error range is reached. The obtained results are used as initial values, and the specified parameters are also used to perform the fitting process for a number of Monte Carlo trials.

[0067] The analysis unit 12b performs a determination process to attribute the R / / CPE element (reaction resistance component) obtained by the fitting process to the elementary process of the battery. In this case, the elementary process attribution determination process is performed based on the agreement between the material feature amount data registered in the material property database 14a, which has been acquired in advance, and the time constant of the reaction resistance component.

[0068] (2) Subdivision of reaction resistance components In the fitting process, the analysis unit 12b can further subdivide the reaction resistance component R / / CPE into multiple reaction resistance components R / / CPE in a series or parallel configuration. At this time, the analysis unit 12b subdivides the obtained reaction resistance component R / / CPE to a granularity that the user determines can express the desired material characteristics. Below, the subdivision methods for the series configuration and the parallel configuration are described.

[0069] Subdivision into series configurations: When further subdividing the reaction resistance component R / / CPE into multiple series configurations, the analysis unit 12b subdivides the reaction resistance component R / / CPE into multiple reaction resistance components R / / CPE with time constants for each peak if the peak in the DRT spectrum can be separated by optimizing the λ value in the DRT analysis (i.e., the constraint condition of Tikhonov regularization).If subdivision is not possible due to insufficient resolution of the measurement frequency, the analysis unit 12b increases the measurement points of the sweep frequency only in the frequency range in question to improve the resolution of the measurement frequency, and applies the DRT method again.

[0070] Subdivision into parallel configurations: The above-mentioned DRT analysis is based on a theorem that assumes a series connection of reaction resistance components, and does not support the case of subdividing multiple reaction resistance components connected in parallel. Furthermore, when multiple reaction resistance components R / / CPE are connected in parallel, it is not possible to separate each reaction resistance component R / / CPE from the combined resistance component.

[0071] However, if the time constant or ionic conductivity of the reaction resistance component corresponding to each material characteristic is known, it is possible to further subdivide the reaction resistance component R / / CPE into multiple parallel configurations by fixing these values ​​and performing fitting processing.

[0072] 7A and 7B are diagrams illustrating the process of subdividing one reaction resistance component R / / CPE into multiple parallel configurations by the analysis unit 12b included in the electrochemical impedance analyzer 10 according to the embodiment. More specifically, Fig. 7A shows the reaction resistance component R3 / / CPE3 element, which is the combined resistance component before separation, Fig. 7B shows the result of subdividing the reaction resistance component R3 / / CPE3 element into parallel configurations of reaction resistance components R3-1 / / CPE3-1 and R3-2 / / CPE3-2, which are the resistance components after separation, and Fig. 7C shows an example of the circuit parameters of the combined resistance component and the results of the subdivision performed by the analysis unit 12b (i.e., each circuit parameter).

[0073] As shown in Figure 7(b), if a reaction resistance component R3-1 / / CPE3-1 consisting of a resistance component R3-1 and a capacitance component C3-1, and a reaction resistance component R3-2 / / CPE3-2 consisting of a resistance component R3-2 and a capacitance component C3-2 are connected in parallel, and the resistance component of this combined resistance is R3-3 and the capacitance component is C3-3, the time constant R3-3·C3-3 of the combined resistance component can be calculated using the following equation.

[0074] R3-3 C3-3 ={(R3-1·R3-2) / (R3-1+R3-2)}·(C3-1+C3-2) ={R3-2 / (R3-1+R3-2)}·R3-1·C3-1 +{R3-1 / (R3-1+R3-2)}·R3-2·C3-2

[0075] From this, the time constant of the combined resistance component (R3-3·C3-3) can be determined from the ratio of each resistance component (R3-1:R3-2), and its value will be a value between the time constants of each reaction resistance component (if R3-1·C3-1<=R3-2·C3-2, then R3-1·C3-1<=R3-3·C3-3<=R3-2·C3-2). Furthermore, if the three time constants (R3-1·C3-1, R3-2·C3-2, R3-3·C3-3), resistance component R3-3, and capacitance component C3-3 are known, then resistance components R1 and R2 can be derived from the above equation by fitting.

[0076] In other words, the analysis unit 12b considers that one first reaction resistance component (composite resistance component) constituting the equivalent circuit is composed of a parallel connection of multiple second reaction resistance components (separated resistance components), and identifies the resistance components contained in the multiple second reaction resistance components using the relationship that the time constant of the first reaction resistance component is equal to a linear combination of the time constants of each of the multiple second reaction resistance components weighted by the resistance components of each of the multiple second reaction resistance components.

[0077] Here, the reaction resistance component R3-1 / / CPE3-1 and the reaction resistance component R3-2 / / CPE3-2 are defined as reaction resistance components due to different material properties in the relevant elementary process, and if the time constants (R3-1·C3-1, R3-2·C3-2) under the specified conditions for each material are known, then by performing a fitting process with these values ​​as initial and fixed values, the resistance components R1 and R2 can be derived, and the combined resistance can be separated into a parallel configuration of multiple reaction resistance components R / / C.

[0078] Note that each capacitance component C above corresponds to the CPE constant (CPE-T value) of each CPE. Furthermore, it is assumed that the Phi value of CPE3-1 (CPE3-1-P) and the Phi value of CPE3-2 (CPE3-2-P) are the same. If these are different, the synthesis formula for the CPE-T value will be different from the above.

[0079] For example, when obtaining the initial value of the reaction resistance component R3 / / CPE3 at the interface between the positive electrode and the electrolyte, if the inside of the positive electrode is composed of a composite material of different materials A and B, the analysis unit 12b, by referring to the material property database 14a, considers that the reaction resistance component R3 / / CPE3 is composed of the following two reaction resistance components connected in parallel as an equivalent circuit, and derives the initial values ​​of the circuit parameters of the reaction resistance component R3 / / CPE3.

[0080] (i) Reaction resistance component R3-1 / / CPE3-1 at the interface under the same conditions for material A only (ii) Reaction resistance component R3-2 / / CPE3-2 at the interface under the same conditions for material B only

[0081] That is, the analysis unit 12b obtains the circuit parameters (i) and (ii) above using a material property regression model based on the time constants of materials A and B registered in the material property database 14a and the fitting process, and calculates the composite impedance from these to derive the circuit parameters of the reaction resistance component R3 / / CPE3 as initial values. As a specific example, if the values ​​shown in Figure 7(c) are calculated as the circuit parameters (i) and (ii) above, the analysis unit 12b can calculate the composite impedance of the parallel connection to derive the circuit parameters of the reaction resistance component R3 / / CPE3 as R3 = 10k, CPE3-T = 1.5m, and CPE3-Phi = 0.8.

[0082] (3) Identification of initial values ​​using changing parameters When the analysis unit 12b determines the initial value of the reaction resistance component R3 / / CPE3, if the desired material feature data is not included in the material property database 14a but material feature data for other change parameters can be extracted, the analysis unit 12b can also identify the initial value from a material property regression model that has learned the relationship between them.

[0083] For example, assume that the temperature of the environmental conditions is from 323.15[K] to 413.15[K] in 10[K] intervals and that material feature quantity data is obtained from the material property database 14a. If the temperature of the battery to be subjected to the fitting process is 423.15[K], each circuit parameter equivalent to 423.15[K] is obtained from the material property regression model that has learned the relationship between temperature and each circuit parameter.

[0084] If the change parameter is temperature and the parameter to be determined is resistance, and the circuit parameters are of the same material, the conductivity at a specified temperature (the white dots in Figure 8) can be determined using linear regression on an Arrhenius plot (X axis: 1000 / absolute temperature [K], Y axis: ln(conductivity)) as shown in Figure 8, and the resistance value can be determined from there by back-calculating the relational expression that derives conductivity from resistance value. Figure 8 is a diagram showing a method for identifying the resistance value corresponding to a specified temperature as an initial value by linear regression using an Arrhenius plot.

[0085] [Step S15 (Consistency check)] Fig. 9 is a flowchart showing the detailed procedure of step S15 (consistency check) in Fig. 2. First, the analysis unit 12b inputs the change parameters such as temperature set in step S12 (setting of loop parameters) in Fig. 2, and generates a verification regression model (hereinafter also referred to as "verification regression model") that outputs the resistance components and time constant arrays of the reaction resistance components that constitute the equivalent circuit derived in step S13 (fitting process) in Fig. 2, in the same manner as the method for creating the material property regression model described above (S30).

[0086] Then, the analysis unit 12b verifies the accuracy of the generated verification regression model (S31). Specifically, the analysis unit 12b determines whether the resistance component and the time constant of the reaction resistance component obtained by inputting the change parameter such as temperature registered in the material property database 14a are values ​​(outliers) that are significantly different from the resistance component and the time constant of the reaction resistance component corresponding to the change parameter such as temperature registered in the material property database 14a, or whether the accuracy of the verification regression model calculated based on the difference therebetween is a value lower than a threshold value (S32).

[0087] As a result, if the resistance component and time constant output by the verification regression model are outliers, or if the accuracy of the verification regression model is lower than the threshold (Yes in S32), the analysis unit 12b determines that there is no consistency (S33), but if neither of these is the case (No in S32), it determines that there is consistency (S34).

[0088] This determines whether the equivalent circuit derived in step S13 (fitting process) in FIG. 2 is consistent with the change parameters such as temperature set in step S12 (setting of loop parameters) in FIG.

[0089] [Step S17 (Output of analysis results)] Fig. 10 is a diagram showing an execution example (circuit parameters) of step S17 (output of analysis results) in Fig. 2. Here, an example of each circuit parameter constituting the equivalent circuit shown in Fig. 4 derived by the analysis unit 12b is shown.

[0090] The analysis unit 12b can output not only the numerical analysis results shown in FIG. 10, but also the analysis results in the form of graphs, and various intermediate data obtained in the course of the fitting process.

[0091] FIG. 11A is a diagram showing another example (Nyquist diagram) of an execution example of step S17 (output of analysis results) in FIG. 2. FIG. 11B is an enlarged view of the high-frequency range of the Nyquist diagram of FIG. 11A. These diagrams show the Nyquist diagram of the equivalent circuit derived by the fitting process (i.e., the overall impedance data; the plot line located in the center of the graph) and the impedance data of each separated reaction resistance component (multiple arc-shaped plot lines located below the graph). Note that, when the output unit 13 is a display, each of these plot lines is drawn on the display in a different color indicated by the legend, but the colors are omitted in FIGS. 11A and 11B.

[0092] 12 is a diagram showing another example (Bode plot) of an execution example of step S17 (output of analysis results) in FIG. 2. Here, the equivalent circuit derived by the fitting process and the Bode plots of each reaction resistance component constituting the equivalent circuit are superimposed. FIG. 12(a) shows the frequency dependence of the absolute value of the impedance, and FIG. 12(b) shows the frequency dependence of the phase of the impedance. In FIG. 12, the corresponding colors shown in FIGS. 11A and 11B are omitted.

[0093] Fig. 13 is a diagram showing another example (DRT spectrum) of an execution example by step S17 (output of analysis results) in Fig. 2. Here, the equivalent circuit derived by the fitting process and the DRT spectrum of each reaction resistance component constituting the equivalent circuit are shown superimposed. Also in Fig. 12, the illustration using the corresponding colors shown in Figs. 11A and 11B is omitted.

[0094] The analysis unit 12b not only outputs the analysis results in the form of numerical values ​​and graphs, but also searches the material property database 14a for material feature data that is closest to the resistance component and time constant of the reaction resistance component specified by the user via the input unit 11 among the EIS data to be analyzed (i.e., the derived equivalent circuit) by the waveform similarity evaluation described above, and outputs the elementary process registered in the obtained material feature data (for example, “positive electrode layer / SE (solid electrolyte) layer-interface resistance component” registered as elementary process ID=1 in FIG. 5) to the output unit 13 as a candidate elementary process for the specified reaction resistance component.

[0095] As described above, the electrochemical impedance analyzer 10 according to this embodiment is an apparatus for deriving an equivalent circuit modeling a battery under test from EIS data obtained by measuring the battery under test by electrochemical impedance spectroscopy, and includes at least: (1) a storage unit 14 for storing a material characteristic database 14a configured with material characteristic amount data that associates condition information including the constituent materials of the battery with circuit parameters including a time constant of a reaction resistance component that is one of the circuit components of the equivalent circuit and is a parallel connection element between the resistor and the CPE; and an acquisition unit 12 for acquiring EIS data obtained by measuring the battery under test by electrochemical impedance spectroscopy. a, and an analysis unit 12b that performs a fitting process to derive an equivalent circuit that fits the acquired EIS data and output information about the derived equivalent circuit, and the analysis unit 12b identifies the time constants of the first reaction resistance component and the multiple second reaction resistance components when one first reaction resistance component that constitutes the equivalent circuit is considered to be composed of multiple second reaction resistance components connected in parallel by referring to the material property database 14a, and performs a fitting process using the identified time constants to separate the first reaction resistance component into multiple second reaction resistance components and identify the resistance components included in the multiple second reaction resistance components, thereby deriving the equivalent circuit.

[0096] As a result, by referring to the material property database 14a, the time constants of the first reaction resistance component and the plurality of second reaction resistance components when the first reaction resistance component is considered to be composed of a parallel connection of a plurality of second reaction resistance components are identified, and the fitting process is performed using the identified time constants. Therefore, unlike the conventional technology, it is possible to deal with cases where a plurality of reaction resistance components may be included within each arc of the Nyquist diagram indicated by the EIS data of the battery under test, and an equivalent circuit can be derived from the EIS data with high accuracy.

[0097] More specifically, the analysis unit 12b identifies the resistance components included in the plurality of second reaction resistance components by using a relationship in which the time constant of the first reaction resistance component is equal to a linear combination of the time constants of each of the plurality of second reaction resistance components weighted by the resistance components of each of the plurality of second reaction resistance components. As a result, by utilizing the relationship of the linear combination, the resistance components of the plurality of second reaction resistance components connected in parallel that constitute the first reaction resistance component can be quantitatively calculated.

[0098] Here, the analysis unit 12b may perform the fitting process after fixing the time constants of the first reaction resistance component and the plurality of second reaction resistance components identified by referring to the material property database 14a, or the resistance components included in the plurality of second reaction resistance components calculated using a linear combination, as initial values. This allows the first reaction resistance component to be separated into a parallel connection of the plurality of second reaction resistance components with high accuracy by the fitting process using appropriate initial values.

[0099] Furthermore, the analysis unit 12b may perform the fitting process by estimating the time constants or resistance values ​​of the first reaction resistance component and the plurality of second reaction resistance components using a material property regression model, which is a machine learning model trained using material feature data registered in the material property database 14a, and using the estimated time constants or resistance values ​​as initial values ​​for the fitting process or as constraint conditions for the fitting process. This enables the fitting process to be performed reliably using appropriate initial values ​​that reflect the characteristics of many material feature data registered in the material property database 14a, even if no material feature data matching the condition information is found, thereby realizing a highly accurate fitting process.

[0100] Furthermore, when the analysis unit 12b cannot search for material feature data using the condition information corresponding to the battery under test in reference to the material property database 14a, it (1) generates a first relaxation time distribution spectrum obtained by an approximate solution to an integral equation of the relaxation time distribution derived from the inverse Fourier transform of the EIS data corresponding to the condition information, (2) searches the material property database 14a for material feature data having conditions similar to those of the condition information, (3) generates a second relaxation time distribution spectrum corresponding to the material feature data obtained by the search from the material property data obtained by the search, and (4) identifies the time constant using the material property data obtained by the search when the waveforms of the first relaxation time distribution spectrum and the second relaxation time distribution spectrum are similar. This allows the material feature data closest to the condition information to be extracted from the material property database 14a, enabling fitting processing using appropriate initial values ​​and achieving high-precision fitting processing.

[0101] Furthermore, if past fitting results corresponding to condition information similar to that of the battery under test are registered in the material property database 14a, the analysis unit 12b searches the past fitting results to propose an equivalent circuit configuration for the impedance of the battery under test. This allows an objective proposal of an equivalent circuit configuration at the start of the fitting process, preventing the final equivalent circuit from differing depending on the person who created the equivalent circuit configuration.

[0102] Furthermore, the material feature quantity data in the material property database 14a includes candidates for elementary processes corresponding to the time constants of the reaction resistance components, and the analysis unit 12b refers to the material property database 14a to extract and present candidates for elementary processes corresponding to the designated reaction resistance components from the first reaction resistance component and the second reaction resistance component identified for the acquired EIS data. This presents candidates for elementary processes occurring in the battery under test, thereby supporting the material design and development of batteries.

[0103] Furthermore, the analysis unit 12b performs a fitting process on multiple EIS data obtained by electrochemical impedance spectroscopy measurements of the same battery under test, where the EIS data are different in at least one of material, environment, and measurement conditions, to derive equivalent circuits corresponding to each of the multiple EIS data, and determines the validity of the fitting process by checking the consistency of the derived equivalent circuits with the multiple EIS data. This ensures high accuracy in the fitting process, as the validity of the derived equivalent circuits is determined.

[0104] The electrochemical impedance analysis method according to the present embodiment is an electrochemical impedance analysis method for deriving an equivalent circuit modeling a battery under test from EIS data obtained by measuring the battery under test by electrochemical impedance spectroscopy, and includes the steps of: acquiring EIS data obtained by measuring the battery under test by electrochemical impedance spectroscopy; and referencing a material characteristic database 14a that includes material feature amount data that associates at least (1) condition information including the constituent materials of the battery with (2) circuit parameters including a time constant of a reaction resistance component that is one of the circuit components of the equivalent circuit and is a parallel connection element between the resistor and the CPE. and an analysis step of performing a fitting process to derive an equivalent circuit that fits the EIS data acquired in the acquisition step and output information about the derived equivalent circuit. In the analysis step, the time constants of the first reaction resistance component and the plurality of second reaction resistance components, when one first reaction resistance component constituting the equivalent circuit is considered to be composed of a plurality of second reaction resistance components connected in parallel, are identified by referring to the material property database 14a, and a fitting process is performed using the identified time constants to separate the first reaction resistance component into a plurality of second reaction resistance components and identify the resistance components included in the plurality of second reaction resistance components, thereby deriving the equivalent circuit. Furthermore, a program according to the present disclosure is a program that causes a computer to execute the steps included in the electrochemical impedance analysis method.

[0105] As a result, by referring to the material property database 14a, the time constants of the first reaction resistance component and the plurality of second reaction resistance components when the first reaction resistance component is considered to be composed of a parallel connection of a plurality of second reaction resistance components are identified, and the fitting process is performed using the identified time constants. Therefore, unlike the conventional technology, it is possible to deal with cases where a plurality of reaction resistance components may be included within each arc of the Nyquist diagram indicated by the EIS data of the battery under test, and an equivalent circuit can be derived from the EIS data with high accuracy.

[0106] While the electrochemical impedance analysis apparatus and method according to the present disclosure have been described above based on the embodiments, the present disclosure is not limited to these embodiments. As long as they do not deviate from the gist of the present disclosure, various modifications conceivable by those skilled in the art to the present embodiments and other forms constructed by combining some of the components of the embodiments are also included within the scope of the present disclosure. [Industrial Applicability]

[0107] The present disclosure can be used as an electrochemical impedance analyzer, and in particular as a highly accurate electrochemical impedance analyzer that can handle cases where multiple reaction resistance components may be contained within each arc of a Nyquist diagram indicated by EIS data of a battery under test. [Explanation of symbols]

[0108] 10. Electrochemical impedance analyzer 11 Input section 12 Control Unit 12a Acquisition part 12b Analysis section 13 Output section 14 Storage section 14a Material Properties Database

Claims

1. An electrochemical impedance analyzer that derives an equivalent circuit that models a battery under test from EIS (Electrochemical Impedance Spectroscopy) data obtained by measuring the battery under test using electrochemical impedance spectroscopy, a storage unit that stores a material property database that is configured by material feature quantity data that associates at least (1) condition information including the constituent materials of the battery with (2) circuit parameters including a time constant of a reaction resistance component that is one of the circuit components of the equivalent circuit and is a parallel connection element between a resistor and a CPE (Constant Phase Element); an acquisition unit that acquires EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy; an analysis unit that performs a fitting process to derive an equivalent circuit that fits the acquired EIS data and output information about the derived equivalent circuit; the analysis unit specifies time constants of each of the first reaction resistance component and the plurality of second reaction resistance components when one first reaction resistance component constituting the equivalent circuit is considered to be composed of a parallel connection of a plurality of second reaction resistance components by referring to the material property database, and performs the fitting process using the specified time constants to separate the first reaction resistance component into the plurality of second reaction resistance components and specify resistance components included in the plurality of second reaction resistance components, thereby deriving the equivalent circuit; Electrochemical impedance analyzer.

2. the analysis unit identifies resistance components included in the plurality of second reaction resistance components using a relationship in which a time constant of the first reaction resistance component is equal to a linear combination of time constants of the plurality of second reaction resistance components weighted by the resistance components of the plurality of second reaction resistance components.

2. The electrochemical impedance analyzer according to claim 1.

3. the analysis unit performs the fitting process after fixing, as initial values, the time constants of the first reaction resistance component and the plurality of second reaction resistance components specified by referring to the material property database, or the resistance components included in the plurality of second reaction resistance components calculated using the linear combination.

3. The electrochemical impedance analyzer according to claim 2.

4. the analysis unit estimates time constants or resistance values ​​of the first reaction resistance component and the plurality of second reaction resistance components using a material property regression model, which is a machine learning model trained using material feature amount data registered in the material property database, and performs the fitting process by using the estimated time constants or resistance values ​​as initial values ​​of the fitting process or as constraint conditions in the fitting process.

2. The electrochemical impedance analyzer according to claim 1.

5. When the analysis unit cannot search for the material feature quantity data using the condition information corresponding to the battery under test in referring to the material property database, (1) it generates a first relaxation time distribution spectrum obtained by an approximate solution to an integral equation of a relaxation time distribution derived from an inverse Fourier transform of EIS data, corresponding to the condition information; (2) it searches the material property database for material feature quantity data having conditions similar to those of the condition information; (3) it generates a second relaxation time distribution spectrum corresponding to the material feature quantity data obtained by the search, from the material feature quantity data obtained by the search; and (4) it identifies the time constant using the material feature quantity data obtained by the search, when the waveform of the first relaxation time distribution spectrum and the waveform of the second relaxation time distribution spectrum are similar.

2. The electrochemical impedance analyzer according to claim 1.

6. When past fitting results corresponding to condition information similar to the condition information of the battery under test are registered in the material property database, the analysis unit searches the past fitting results to propose a configuration of an equivalent circuit for the impedance of the battery under test.

2. The electrochemical impedance analyzer according to claim 1.

7. the material feature quantity data in the material property database includes candidates for elementary processes corresponding to the time constants of the reaction resistance components; The analysis unit extracts and presents candidates for elementary processes corresponding to designated reaction resistance components from the first reaction resistance component and the second reaction resistance component identified for the acquired EIS data by referring to the material property database.

2. The electrochemical impedance analyzer according to claim 1.

8. The analysis unit performs the fitting process on a plurality of EIS data obtained by electrochemical impedance spectroscopy measurements on the same battery under test, where the EIS data are different in at least one of material, environment, and measurement conditions, to derive equivalent circuits corresponding to the plurality of EIS data, and determines the validity of the fitting process by confirming the consistency of the derived equivalent circuits with the plurality of EIS data.

2. The electrochemical impedance analyzer according to claim 1.

9. An electrochemical impedance analysis method for deriving an equivalent circuit modeling a battery under test from EIS (Electrochemical Impedance Spectroscopy) data obtained by measuring the battery under test by electrochemical impedance spectroscopy, comprising: an acquisition step of acquiring EIS data obtained by measuring the battery under test using electrochemical impedance spectroscopy; and an analysis step of performing a fitting process to derive an equivalent circuit that fits the EIS data acquired in the acquisition step by referring to a material property database that is configured by material feature amount data that associates at least (1) condition information including the constituent materials of the battery with (2) circuit parameters including a time constant of a reaction resistance component that is one of the circuit components of the equivalent circuit and is a parallel connection element between a resistance and a CPE (Constant Phase Element), and outputting information related to the derived equivalent circuit. In the analysis step, when one first reaction resistance component constituting the equivalent circuit is considered to be composed of a plurality of second reaction resistance components connected in parallel, the time constants of the first reaction resistance component and the plurality of second reaction resistance components are identified by referring to the material property database, and the fitting process is performed using the identified time constants to separate the first reaction resistance component into the plurality of second reaction resistance components, and resistance components included in the plurality of second reaction resistance components are identified, thereby deriving the equivalent circuit. Electrochemical impedance analysis method.

10. A program that causes a computer to execute the steps included in the electrochemical impedance analysis method according to claim 9.

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