A Broadband Impedance Measurement Excitation Signal Design Method Based on Electrochemical Noise Optimization

Abstract

This invention belongs to the field of proton exchange membrane fuel cell condition monitoring and fault diagnosis technology. It discloses a broadband impedance measurement excitation signal design method based on electrochemical noise optimization, comprising: selecting a discrete interval binary sequence (DIBS) as the excitation signal; predicting the power spectrum of the measured battery voltage noise using an AR model; establishing an electrochemical noise equivalent circuit model of the battery based on the battery equivalent circuit model parameters and the AR model; synthesizing the DIBS based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum; and searching for the optimal combination of signal-to-noise ratio and harmonic number based on the synthesized DIBS and combined with the simulation of the battery's electrochemical noise equivalent circuit model to obtain the desired DIBS, which is then used as the impedance measurement excitation signal. This invention can tailor the impedance test excitation signal according to the actual condition of the battery stack, improving measurement accuracy while ensuring measurement speed and reducing interference to the battery system.

Description

Technical Field

[0001] This invention belongs to the field of proton exchange membrane fuel cell condition detection and fault diagnosis technology, and more specifically, relates to a method for designing a broadband impedance measurement excitation signal based on electrochemical noise optimization. Background Technology

[0002] Proton exchange membrane fuel cells (PEMFCs) are a key technology in the new energy industry. They directly convert the chemical energy of hydrogen into electrical energy, offering advantages such as high efficiency, fast response, and low allowable start-up temperature. However, PEMFCs are prone to failures such as membrane dryness, flooding, and oxygen starvation under complex real-world operating conditions, posing a significant challenge to their operational stability and lifespan. Numerous experimental results have demonstrated that electrochemical impedance spectroscopy (EIS) has excellent ability to identify different states of PEMFCs. By applying accurate and efficient EIS extraction techniques, real-time monitoring of the PEMFC's operating status can be achieved.

[0003] Traditional impedance spectrum extraction for PEMFCs often employs sinusoidal wave frequency sweeping, which, while providing relatively accurate results, is extremely time-consuming. In recent years, research on broadband test signals for impedance spectrum extraction has made rapid progress. By designing the amplitude-frequency characteristics of broadband test signals, rich frequency information is integrated into a single signal segment, significantly shortening the impedance spectrum measurement time. Multi-frequency sinusoidal signals, pseudo-random binary sequences, and Discrete Interval Binary Sequences (DIBS) have all been verified as effective broadband test signals. However, as measurement time decreases, the signal-to-noise ratio of the test signal also decreases, resulting in coarser impedance data and lower measurement accuracy for proton exchange membrane fuel cell impedance spectra. Generally, the amplitude of the test signal should not exceed 5% of the steady-state current amplitude of the battery. To combat noise, current technologies often design the test signal amplitude to be at the maximum limit, i.e., 5% of the steady-state current amplitude. While this provides some resistance to noise, a larger test signal amplitude also causes greater disturbance to the battery system. Optimizing the design of a wideband test signal to resist the influence of noise and improve the measurement accuracy of the impedance spectrum of a proton exchange membrane fuel cell while minimizing disturbance to the battery system is a challenge! Summary of the Invention

[0004] To address the aforementioned deficiencies or improvement needs of existing technologies, this invention provides a broadband impedance measurement excitation signal design method based on electrochemical noise optimization. The aim is to design the impedance test excitation signal specifically according to the actual conditions of the proton exchange membrane fuel cell stack, thereby improving measurement accuracy while ensuring the speed of impedance spectrum measurement and reducing interference to the battery system.

[0005] To achieve the above objectives, this invention provides a method for designing wideband impedance measurement excitation signals based on electrochemical noise optimization, comprising:

[0006] Step 1: Under constant current operation conditions of the proton exchange membrane fuel cell, measure the voltage noise of the cell over a period of time to obtain the voltage noise sequence;

[0007] Step 2: Based on the voltage noise sequence, solve for the parameters of the p-order AR model of the battery voltage noise; and use the p-order AR model to estimate the voltage noise power spectrum of the battery.

[0008] Step 3: By connecting a Gaussian noise-driven current source in parallel in the R-CPE loop of the ideal equivalent circuit model of the proton exchange membrane fuel cell and a colored noise-driven voltage source in series in the main circuit, the electrochemical noise equivalent circuit model of the proton exchange membrane fuel cell is obtained; wherein, the voltage of the colored noise-driven voltage source is determined based on the p-order AR model parameters.

[0009] Step 4: Based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, fit the amplitude of the discrete interval binary sequence DIBS at the desired harmonic frequency to obtain the fitted DIBS.

[0010] Step 5: Input the fitted DIBS into the electrochemical noise equivalent circuit model, simulate the electrochemical impedance spectrum, calculate the deviation E between the electrochemical impedance spectrum and the ideal electrochemical impedance spectrum calculated based on the ideal equivalent circuit model, and optimize and update the current harmonic number and signal-to-noise ratio by minimizing the deviation E and the fitted DIBS amplitude.

[0011] Step 6: Based on the optimized and updated harmonic number and signal-to-noise ratio, jump to step 4 for the next iteration until the preset iteration termination condition is reached, to obtain the desired harmonic number N0 and signal-to-noise ratio, and thus obtain the desired DIBS; use the desired DIBS as the excitation signal for the broadband impedance measurement.

[0012] Further, in step 4, based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, the amplitude of the discrete interval binary sequence DIBS at the desired harmonic frequency is fitted to obtain the fitted DIBS, specifically including:

[0013] S41. Calculate the frequency domain representation of a multi-frequency sinusoidal signal: Among them, A k and θ k Let be the expected amplitude and phase of the multi-frequency sinusoidal signal at the k-th desired harmonic frequency, respectively. r k Let P be the signal-to-noise ratio at the current k-th desired harmonic frequency. k Z is the amplitude of the estimated voltage noise power spectrum at the k-th desired harmonic frequency. ideal (0) is the intersection value of the ideal electrochemical impedance spectrum with the real axis at low frequency; the desired harmonic frequency is determined by the preset test frequency range and the current harmonic number;

[0014] S42, the frequency domain expression S k Performing an inverse Fourier transform yields the time-domain signal: s k =ifft(S k ), and thus obtain the time-domain signal d of DIBS. k =sgn(s k ); where sgn(·) is the sign function, if s k =0, then d k =a, a~U{-1,1}, a~U{-1,1} means that a follows a discrete uniform distribution on the set {-1,1};

[0015] S43, regarding the time-domain signal d k Perform a Fourier transform to obtain the frequency domain signal of DIBS: D k =fft(d k ); and calculate the frequency domain signal D. k phase φ k ;

[0016] S44. Calculate the reciprocal of energy utilization rate, P = Σ|D k | / Σ|D sk |;wherein, D sk This represents the actual amplitude of DIBS at the k-th desired harmonic frequency.

[0017] S45. Calculate the sum of squares of the expected amplitude: den=Σ|A k | 2 , and the sum of the dot products of the expected amplitude and the actual amplitude, num = Σ|A k |·|D sk |, thus obtaining the scaling factor qp_x = num / den; construct the objective function C = P + ε, where ε = Σ[(A k ·qp_x-D sk ) / D sk ] 2If the objective function value in the current iteration is less than the objective function value in the previous iteration, then the time-domain signal d of DIBS... k No change, otherwise update d k =1 / qp_x; Jump to step S43 for the next iteration;

[0018] S46, when abs(θ) k -φ k When the value is less than a preset threshold, or when the preset number of iterations is reached, the iteration ends, and the fitted DIBS time-domain signal d is output. k ; where abs(·) represents the absolute value operation.

[0019] Furthermore, the formula for calculating the desired harmonic frequency is as follows:

[0020]

[0021] Among them, f k Let f be the k-th desired harmonic frequency, k∈{1,2,…,N*}, N* be the current harmonic number; t be the duration of DIBS; min For the minimum test frequency, f max This represents the maximum test frequency; [·] indicates the rounding function; [·] down This represents the floor function.

[0022] Further, in step 2, based on the voltage noise sequence, the p-order AR model parameters of the battery voltage noise are solved, including:

[0023] Using the voltage noise sequence and the order p of the AR model as input, the Burg algorithm is used to solve for the parameters of the p-order AR model;

[0024] The goodness of fit and complexity of the p-order AR model obtained by using the Akaike Information Content Criterion (AIC) are evaluated. The smallest model order that minimizes the AIC evaluation index or makes the AIC evaluation index tend to be stable is selected as the optimal order of the AR model, and the parameters of the p-order AR model of battery voltage noise are obtained.

[0025] Furthermore, the AIC evaluation index is calculated as follows:

[0026] AIC(p)=N EN ln(σ 2 )+2p

[0027] Where, N EN σ is the length of the voltage noise sequence; 2 Let V be the variance of the prediction error of the p-order AR model for battery voltage noise.

[0028] Furthermore, in step 3, the voltage U of the colored noise driven voltage source N (n) is;

[0029]

[0030] Among them, a i Let w(·) be the i-th parameter of the AR model; w(·) is a parameter that follows a mean of 0 and a variance of σ. 2 Gaussian white noise, σ 2 Let n be the variance of the prediction error of the p-th order AR model; n∈{1,2,…,N} EN}, N EN The length of the voltage noise sequence is given.

[0031] Furthermore, in step 5, the deviation E is calculated as follows:

[0032]

[0033] Where F is the impedance test frequency set; Z fit (ω) represents the impedance value of the simulated electrochemical impedance spectrum at a test angular frequency of ω; Z ideal (ω) represents the theoretical impedance value of the ideal electrochemical impedance spectrum at a test angular frequency of ω; Z ideal (0) is the intersection value of the ideal electrochemical impedance spectrum with the real axis at low frequency.

[0034] Furthermore, a competitive particle swarm optimization algorithm is used to optimize and update the current harmonic number and signal-to-noise ratio. The objective function Obj is:

[0035]

[0036] Where Amp(N0,r) represents the fitted DIBS amplitude when the expected harmonic number of DIBS is N0 and the signal-to-noise ratio is r; α is the penalty term.

[0037] The present invention also provides a method for real-time detection of the operating status of a proton exchange membrane fuel cell, comprising:

[0038] The impedance spectrum of a proton exchange membrane fuel cell is calculated based on a broadband impedance measurement excitation signal; wherein the broadband impedance measurement excitation signal is generated using any of the broadband impedance measurement excitation signal design methods described above.

[0039] The operating status of the proton exchange membrane fuel cell is monitored in real time based on the impedance spectrum.

[0040] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the program, when executed by a processor, implements the wideband impedance measurement excitation signal design method as described above, or implements the real-time detection method for the operating status of a proton exchange membrane fuel cell as described above.

[0041] In summary, the above-described technical solutions conceived in this invention can achieve the following beneficial effects:

[0042] (1) Based on the actual conditions of the proton exchange membrane fuel cell stack, this invention specifically designs the impedance test excitation signal to improve measurement accuracy and reduce interference to the battery system while ensuring measurement speed. Specifically, the broadband impedance measurement excitation signal design method based on electrochemical noise optimization of this invention establishes an equivalent circuit model of PEMFC electrochemical noise based on the measured voltage noise of the PEMFC stack. Based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, the desired amplitude-frequency characteristics of the DIBS excitation signal (the amplitude of DIBS at the desired harmonic frequency) are fitted. By optimizing the harmonic number and signal-to-noise ratio of DIBS through simulation, the interference of battery voltage noise can be suppressed to the greatest extent while minimizing the impact on the battery system. Compared with directly designing the amplitude of the test signal to the maximum, the DIBS test signal obtained by the electrochemical noise optimization method of this invention has a lower amplitude, less disturbance to the battery system, and takes into account the influence of PEMFC electrochemical noise. When applied to impedance spectroscopy measurement, the measurement accuracy is high; the obtained DIBS test signal is a broadband impedance measurement excitation signal, ensuring rapid impedance spectrum measurement.

[0043] (2) Preferably, when synthesizing DIBS, the reciprocal of the energy utilization rate P is calculated. Based on the calculated reciprocal of the energy utilization rate P, the least squares method is used to fit the expected amplitude-frequency characteristics of DIBS. While suppressing the interference of battery voltage noise to the greatest extent, the energy utilization rate of DIBS can be optimized, and its energy can be concentrated more at the test frequency point, effectively suppressing its harmonic distortion.

[0044] (3) Furthermore, considering that an AR model with too low an order may lead to inaccurate power spectrum estimation and omission of important spectral information, while an AR model with too high an order may introduce false spectral peaks, resulting in distorted power spectrum estimation and increased computational complexity, this invention uses AIC to evaluate the merits of p-order AR models and selects the optimal p-order AR model to improve the accuracy of test signal design and reduce computational complexity. Attached Figure Description

[0045] Figure 1 This is a schematic diagram of a broadband impedance measurement excitation signal design method based on electrochemical noise optimization provided in an embodiment of the present invention;

[0046] Figure 2 This is a flowchart of the DIBS design method based on electrochemical noise optimization in an embodiment of the present invention;

[0047] Figure 3 This is the electrochemical noise of the PEMFC measured in this embodiment of the invention when it is running at a constant current of 10A.

[0048] Figure 4 This is a graph showing the variation of the AIC evaluation index of the AR model with the model order in an embodiment of the present invention;

[0049] Figure 5 This is the voltage noise power spectrum estimated by the 128th order AR model in this embodiment of the invention;

[0050] Figure 6 This is a diagram of the second-order R-CPE electrochemical noise equivalent circuit model of PEMFC in an embodiment of the present invention;

[0051] Figure 7 The DIBS time-domain waveform and its amplitude-frequency characteristic diagram are shown in the embodiment of the present invention, with a test frequency range of 0.5 to 1000 Hz, a harmonic number of 15, and a signal-to-noise ratio of 30.

[0052] Figure 8 The CSO optimization curves for the desired harmonic number and signal-to-noise ratio of DIBS in this embodiment of the invention are shown.

[0053] Figure 9 The following is a diagram showing the DIBS time-domain waveform and its amplitude-frequency response for a test frequency range of 0.5–1000 Hz, a harmonic number of 28, and a signal-to-noise ratio of 13 in this embodiment of the invention.

[0054] Figure 10 The simulated current excitation and voltage response diagrams are obtained under the DIBS design parameters based on the embodiments of the present invention.

[0055] Figure 11 The impedance spectrum is obtained by simulation under the DIBS design parameters based on the embodiments of the present invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0057] Example 1

[0058] like Figures 1-2As shown in the figure, this invention provides a method for designing a wideband impedance measurement excitation signal based on electrochemical noise optimization. Studies have shown that DIBS has the highest signal-to-noise ratio for the same maximum time-domain amplitude. Therefore, a discrete-interval binary sequence is selected as the wideband impedance measurement excitation signal. The design steps are as follows:

[0059] Step 1: Under the condition of maintaining a constant current operation of the proton exchange membrane fuel cell, the voltage noise of the cell is measured over a period of time to obtain the voltage noise sequence. In this embodiment of the invention, the test object is the EOS1000 fuel cell of Shanghai Panye Hydrogen Energy Technology Co., Ltd. Figure 3 This is the voltage noise measured for the fuel cell under a constant current operating condition of 10A.

[0060] Step 2: Establish a p-order AR model for battery voltage noise, i.e., an autoregressive (AR) model. Based on the voltage noise sequence, solve for the optimal p-order AR model parameters and obtain the variance σ of the AR model's prediction error for battery voltage noise. 2 Using this p-order AR model, estimate the voltage noise power spectrum of the battery;

[0061] Step 3: Based on the equivalent circuit model parameters of the proton exchange membrane fuel cell, establish the electrochemical noise equivalent circuit model of the proton exchange membrane fuel cell. This electrochemical noise equivalent circuit model is obtained by connecting a Gaussian noise-driven current source in parallel in the R-CPE loop of the ideal equivalent circuit model of the proton exchange membrane fuel cell and a colored noise-driven voltage source in series in the main circuit. The R-CPE loop is a parallel loop composed of resistive elements and constant-phase elements. The Gaussian noise-driven current source can be equivalent to the fluctuations in the R-CPE element parameters that follow a Gaussian distribution. The voltage of the colored noise-driven voltage source is determined based on the p-order AR model parameters.

[0062] Step 4: Based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, fit the amplitude of DIBS at the desired harmonic frequency to obtain the current DIBS; wherein, the initial signal-to-noise ratio and initial harmonic number of DIBS are determined empirically.

[0063] Step 5: Input the current DIBS into the electrochemical noise equivalent circuit model of the proton exchange membrane fuel cell, simulate the current electrochemical impedance spectrum, calculate the deviation E between the electrochemical impedance spectrum and the ideal electrochemical impedance spectrum calculated based on the ideal equivalent circuit model, and optimize and update the current harmonic number and signal-to-noise ratio with minimizing the deviation E and the amplitude of the current DIBS as the optimization objective.

[0064] Step 6: Based on the optimized and updated harmonic number and signal-to-noise ratio, jump to step 4 for the next iteration until the preset iteration termination condition is reached, and obtain the desired harmonic number N0 and signal-to-noise ratio SNR to generate the desired DIBS; use the generated desired DIBS as the excitation signal for broadband impedance measurement.

[0065] Preferably, in step 2, the Burg algorithm is used to solve for the parameters of the p-order AR model and the corresponding prediction error variance σ. 2 The goodness of fit and complexity of the obtained p-order AR model were evaluated using the Akaike Information Criterion (AIC). The smallest model order that minimizes the AIC evaluation index AIC(p) or makes the AIC evaluation index tend to be stable was selected as the optimal order of the AR model, thus obtaining the optimal p-order AR model.

[0066] In this embodiment of the invention, the Burg algorithm is used to solve for the parameters of the p-order AR model and the corresponding prediction error variance σ. 2 The pseudocode for the corresponding algorithm implementation is shown below:

[0067]

[0068] In the above algorithm, This represents the prediction error of the preceding term for the k-th value in the original sequence when the model order is i. This represents the prediction error of the subsequent term of the k-th value in the voltage noise sequence x(n) when the model order is i.

[0069] In practical applications, an AR model with too low an order may lead to inaccurate power spectrum estimation and omission of important spectral information; an AR model with too high an order may introduce spurious spectral peaks, resulting in distorted power spectrum estimation and increasing computational complexity. Therefore, it is necessary to evaluate the obtained AR model. In this embodiment of the invention, AIC is used to evaluate the performance of a p-order AR model. The AIC(p) is calculated as follows:

[0070] AIC(p)=N EN ln(σ 2 )+2p

[0071] Where, N EN Let x(n) be the length of the voltage noise sequence, n∈{1,2,…,N} EN}; p is the order of the AR model; σ 2 This represents the variance of the prediction error of the AR model for battery voltage noise.

[0072] The method of estimating the voltage noise power spectrum of a voltage noise sequence using a p-order AR model is an existing technique.

[0073] In this embodiment of the invention, the model parameters of AR models of orders 1 to 256 are obtained sequentially, and the Akaike information content of each AR model is calculated according to the above formula, resulting in the following... Figure 4 The curve shown. By viewing... Figure 4 The curve data shown indicates that the Akaike information content tends to stabilize after the 128th order. Furthermore, considering that data processing in this invention is performed by a PC with powerful computing capabilities, a 128th order AR model was chosen to estimate the voltage noise power spectrum. The noise power spectrum estimated by the 128th order AR model is shown below. Figure 5 As shown.

[0074] Preferably, in step 3, the ideal equivalent circuit model of the proton exchange membrane fuel cell is a second-order R-CPE (R-Constant Phase Element) circuit model. Therefore, the established electrochemical noise equivalent circuit model of the proton exchange membrane fuel cell is obtained by connecting a Gaussian noise-driven current source in parallel in the R-CPE loop of the ideal equivalent circuit model and a colored noise-driven voltage source in series in the main circuit. The output of the colored noise-driven voltage source is predicted by the established AR model.

[0075] In this embodiment of the invention, a second-order R-CPE electrochemical noise equivalent circuit model for a fuel cell was established, such as... Figure 6 As shown. Figure 6 In the diagram, E0 represents the open-circuit voltage of the fuel cell, and R... ohm For the resistance loss model of fuel cells, R ct_c -CPE1 circuit is the activation loss model for fuel cells, R mt -CPE2 circuit is the mass transfer loss model for fuel cells. U N (t) is a voltage source driven by colored noise, and its value is determined by the established 128th-order AR model according to the following formula:

[0076]

[0077] Among them, a i Here are the coefficients of the AR model; w(·) represents the coefficients of the model with a mean of 0 and a variance of σ. 2 (i.e., the aforementioned prediction error variance σ) 2 =ρ p Gaussian white noise.

[0078] In this embodiment of the invention, the R-CPE circuit model of the proton exchange membrane fuel cell refers to a parallel circuit composed of a resistive element and a constant-phase element, wherein the impedance Z of the constant-phase element is... CPE Determine by the following formula:

[0079]

[0080] Where Y is a characteristic parameter of the CPE; ω is the angular frequency of the input current signal of the proton exchange membrane fuel cell; and γ is the exponential parameter of the CPE, with a value between -1 and 1.

[0081] The electrochemical noise equivalent circuit model of the proton exchange membrane fuel cell is obtained by connecting a Gaussian noise-driven current source in parallel in the R-CPE loop of the ideal equivalent circuit model and a colored noise-driven voltage source in series in the main circuit. The Gaussian noise-driven current source can be considered equivalent to random fluctuations in the component parameters of the loop. Therefore, in this model, a random resistance value is connected in series in the resistor bypass, and a random CPE parameter is connected in parallel in the CPE bypass, making the R-CPE loop impedance calculation formula become:

[0082]

[0083] Among them, R-CPE circuit refers to R ct_c -CPE1 circuit and R mt -CPE2 loop; In this embodiment of the invention, δ follows a Gaussian distribution with a mean of 0 and a variance of 0.01; R q Let q be the resistance components of q R-CPE circuits, q∈{1,2}, where q=1 represents R ct_c -CPE1 circuit, q=2 represents R mt -CPE2 loop, γ q Y represents the exponential parameter of the q-th CPE. q Let q be the characteristic parameter of the q-th CPE; j is the imaginary unit.

[0084] Preferably, in step 4, based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, the amplitude of the broadband impedance measurement excitation signal at the desired harmonic frequency is fitted to obtain the current broadband impedance measurement excitation signal, including:

[0085] The VDB (Van Den Bos) algorithm is used to calculate the reciprocal P of the current energy utilization rate; specifically, it includes:

[0086] S41. Calculate the frequency domain representation of a multi-frequency sinusoidal signal: Among them, A k For a multi-frequency sinusoidal signal at the k-th desired harmonic frequency f k The expected amplitude at that point is determined by the current signal-to-noise ratio and the estimated voltage noise power spectrum. r k Let P be the signal-to-noise ratio at the current k-th desired harmonic frequency. k Z represents the amplitude of the battery electrochemical noise at the k-th desired harmonic frequency in the frequency domain, i.e., the amplitude of the estimated voltage noise power spectrum at the k-th desired harmonic frequency. ideal(0) represents the intersection of the theoretical impedance spectrum of the ideal equivalent circuit model with the real axis at low frequencies, i.e. Figure 6 medium resistance R ohm R ct_c R mt The sum of the resistance values. θ k The phase of the multi-frequency sinusoidal signal at the k-th desired harmonic frequency. The desired harmonic frequency is determined by a preset test frequency range and the current harmonic number. DIBS is obtained by zero-crossing detection of the multi-frequency sinusoidal signal.

[0087] S42, Frequency Domain Expression S k Performing an inverse Fourier transform yields the time-domain signal: s k =ifft(S k ), and thus obtain the time-domain signal d of DIBS. k =sgn(s k ); sgn(·) is the sign function, if s k =0, then d k =a, a~U{-1,1}, a~U{-1,1} means that a follows a discrete uniform distribution on the set {-1,1}, that is, the probability of a taking ±1 is 0.5.

[0088] S43, Regarding the time-domain signal d k Perform a Fourier transform to obtain the frequency domain signal of DIBS: D k =fft(d k ). Calculate the frequency domain signal D k phase φ k ;

[0089] S44. Calculate the reciprocal of energy utilization rate, P = Σ|D k | / Σ|D sk |;wherein, D sk This represents the actual amplitude of DIBS at the k-th desired harmonic frequency.

[0090] Based on the reciprocal P of the currently calculated energy utilization rate, the least squares method is used to fit the amplitude of DIBS at the desired harmonic frequency to obtain the current broadband impedance measurement excitation signal, specifically including:

[0091] S45. Calculate the sum of squares of the expected amplitude of a multi-frequency sinusoidal signal: den=Σ|A k | 2 And calculate the sum of the dot products of the expected amplitude of the multi-frequency sinusoidal signal and the actual amplitude of DIBS, num = Σ|A k |·|D sk |, obtain the scaling factor qp_x = num / den; calculate the sum of squares of the relative errors ε = Σ[(A k·qp_x-D sk ) / D sk ] 2 Thus, the objective function C = P + ε is constructed; if the objective function in the current iteration is less than the objective function value in the previous iteration, then the time-domain signal d of DIBS... k No change, otherwise d k =1 / qp_x; Jump to step S43 for the next iteration.

[0092] S46, when abs(θ) k -φ k When the value is less than a preset threshold, or when the preset maximum number of iterations is reached, the iteration ends, and the current DIBS time-domain signal d is output. k .

[0093] In this embodiment of the invention, the pseudocode for the VDB algorithm using the least squares method to fit the desired amplitude-frequency response is shown below:

[0094]

[0095]

[0096] In this embodiment of the invention, the desired harmonic frequency is determined according to a logarithmic distribution within a preset test frequency range, and the calculation formula is as follows:

[0097]

[0098] Among them, f k Let f be the k-th desired harmonic frequency, k∈{1,2,…,N*}; t is the duration of DIBS; min Minimum test frequency; f max The maximum test frequency; N* is the current harmonic number; [·] represents the rounding function; [·] down This represents the floor function.

[0099] In this embodiment of the invention, the initial signal-to-noise ratio and harmonic number are determined empirically, and the desired harmonic frequency is determined according to a logarithmic distribution within the test frequency range. The initial DIBS is synthesized using the VDB algorithm with least squares fitting of the desired amplitude-frequency characteristics. First, the test frequency range is determined to be 0.5–1000 Hz, the harmonic number is 15, and the signal-to-noise ratio is 30. After dividing the test frequency range into equal intervals of 0.125 Hz, the desired frequency is determined according to the above formula. Finally, the initial DIBS and its amplitude-frequency characteristics are generated, as shown below. Figure 7 As shown. In other embodiments, other fitting methods may be selected to fit the amplitude of DIBS at the desired harmonic frequency.

[0100] Figure 7In the diagram, the blue dashed lines represent the actual amplitude-frequency distribution of the DIBS, while the red dashed lines represent the desired amplitude-frequency distribution. The quality of the current DIBS is measured using the root mean square error W of the desired amplitude-frequency characteristics as defined by the following formula and the aforementioned energy utilization rate. It is found that the generated DIBS has an error of 4.3% in its amplitude-frequency distribution relative to the desired distribution, and an energy utilization rate of 22.13%. Furthermore, dividing the frequency components into equidistant 0.125Hz intervals allows for a signal period of 8 seconds, facilitating the determination of the DIBS excitation duration.

[0101]

[0102] Among them, D k A represents the actual amplitude of DIBS at the desired frequency. k This represents the expected amplitude.

[0103] Preferably, in step 5, the deviation E is calculated as follows:

[0104]

[0105] Where F is the impedance test frequency set, which is the set of N* harmonic frequencies determined by a logarithmic distribution within a preset test frequency range; Z fit (ω) represents the impedance value of the current electrochemical impedance spectrum obtained from simulation at a test signal angular frequency of ω; Z ideal (ω) represents the theoretical impedance value of the ideal electrochemical impedance spectrum calculated based on the ideal equivalent circuit model at a test signal angular frequency of ω.

[0106] Preferably, minimizing the deviation E and the amplitude of the current broadband impedance measurement excitation signal are the optimization objectives. The Competitive Swarm Optimizer (CSO) algorithm is used to optimize and update the current harmonic number and signal-to-noise ratio. The objective function Obj optimized using the CSO algorithm is:

[0107]

[0108] Where Amp(N0,r) represents the amplitude of DIBS synthesized by the VDB algorithm when the expected harmonic number of DIBS is N0 and the signal-to-noise ratio is r; α is a penalty term, which is set to 50 here.

[0109] In this embodiment of the invention, the CSO algorithm adopts a neighborhood competition mechanism, and the inertia factor adopts a linear decreasing strategy. The specific parameters are shown in Table 1:

[0110] Table 1 CSO Algorithm Parameter Table

[0111]

[0112] In Table 1, the variables refer to the two-dimensional row vector composed of signal-to-noise ratio and harmonics.

[0113] In this embodiment of the invention, for each particle parameter in the iteration process, five simulations are performed to obtain the average value in order to reduce randomness.

[0114] The simulation object is Figure 6 The second-order R-CPE electrochemical noise ECM shown assumes that a 10A constant current load is connected to both ends of the circuit. The simulation process is equivalent to superimposing the DIBS signal onto the constant current load, calculating the voltage response across the ECM, and then determining the impedance.

[0115] The impedance Z at the test point test The value can be obtained by taking the quotient of the ECM voltage response U and the excitation signal I using the Fourier transform, and then selecting the value at the desired frequency component. The calculation formula is as follows:

[0116]

[0117] Among them, FU(ω k Let ω be the k-th desired harmonic angular frequency of the ECM voltage response U in the frequency domain. k Fourier transform at ω; FI(ω) k Let ω be the k-th desired harmonic angular frequency of the excitation signal I in the frequency domain. k The Fourier transform at the k-th desired harmonic frequency f, which is the multi-frequency sinusoidal signal mentioned above. k Expected amplitude A at point k .

[0118] In this embodiment of the invention, the selected circuit parameters are shown in Table 2:

[0119] Table 2 ECM Parameter List

[0120]

[0121] After each update of the harmonic number or signal-to-noise ratio, a new DIBS is synthesized using the VDB algorithm with least squares fitting of the desired amplitude-frequency response. Based on the CSO results, the signal-to-noise ratio and harmonic number are determined, and the final DIBS is generated.

[0122] Figure 8 The results of CSO are displayed. It can be seen that after approximately 30 iterations, the expected harmonic number of DIBS converges to between 25 and 30, and the signal-to-noise ratio converges to between 10 and 15. Therefore, the final generated DIBS harmonic number can be determined to be 28, and the signal-to-noise ratio to be 13. The final DIBS time-domain waveform and amplitude-frequency distribution are shown below. Figure 9 As shown.

[0123] Simulation was performed using the DIBS generated with the above design parameters, and the results were as follows: Figure 10 The voltage response and current excitation waveforms are shown. When injecting the DIBS excitation signal, it is necessary to ensure that the system is in a steady state. Therefore, the total simulation time is set to 9s, and a DIBS excitation signal lasting one cycle is injected from 0.5 to 8.5s.

[0124] After the simulation, the excitation and response signals were captured in the interval from 0.5 to 8.5 s, and the impedance Z at the test points was calculated as described above. test The impedance spectrum was calculated using the formula, and the results are as follows: Figure 11 The green scatter plots are shown in the image. Least-squares fitting is performed on the scatter plots to obtain the component parameters of the second-order R-CPE circuit model. The fitted impedance spectrum is then plotted as shown below. Figure 11 As shown by the solid red line. Figure 11 In the diagram, the blue dashed line represents the impedance spectrum of the standard model. Following the fitting error calculation method for the deviation E, its value is approximately 2.34%, a relatively small error. According to relevant literature, the most common water flooding and membrane dryness faults in PEMFCs will affect the low-frequency resistance, i.e., the Z-axis defined by the deviation E. ideal (0) increases by at least 20%, so the error is acceptable.

[0125] As a preferred option, in step 6, the desired broadband impedance measurement excitation signal obtained by modeling based on the measured voltage noise data and impedance data can be modulated using various methods such as self-made circuits, electronic loads, and function generators. It has high versatility and flexibility, and high engineering application value.

[0126] This invention can be applied to the field of fuel cell condition monitoring and fault diagnosis. By optimizing the amplitude-frequency distribution of the DIBS, a highly accurate impedance spectrum can be obtained while minimizing the signal amplitude, which can then be used for subsequent fault diagnosis. Embodiments of this invention are illustrated below. Figure 1 After designing the DIBS parameters as shown in the process diagram, good results were achieved in the test, verifying the effectiveness of the present invention.

[0127] Example 2

[0128] This invention provides a method for real-time detection of the operating status of a proton exchange membrane fuel cell, comprising:

[0129] The impedance spectrum of the proton exchange membrane fuel cell was calculated using the desired broadband impedance measurement excitation signal generated by the broadband impedance measurement excitation signal design method based on electrochemical noise optimization in Example 1.

[0130] Based on this impedance spectrum, the operating status of the proton exchange membrane fuel cell can be monitored in real time.

[0131] Example 3

[0132] This invention provides a computer-readable storage medium storing a computer program thereon, which, when executed by a processor, implements the steps of the method in embodiment 1 or 2 above.

[0133] Specifically, the memory may include high-speed random access memory, as well as non-volatile memory, such as hard disks, RAM, plug-in hard disks, smart media cards (SMC), secure digital cards (SD), flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0134] The relevant technical solutions are the same as above, and will not be repeated here.

[0135] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing a broadband impedance measurement excitation signal based on electrochemical noise optimization, characterized in that, include: Step 1: Under constant current operation conditions of the proton exchange membrane fuel cell, measure the voltage noise of the cell over a period of time to obtain the voltage noise sequence; Step 2: Based on the voltage noise sequence, solve for the battery voltage noise. p AR model parameters; and using the above p The voltage noise power spectrum of the battery is estimated using an AR model. Step 3: By connecting a Gaussian noise-driven current source in parallel in the R-CPE loop of the ideal equivalent circuit model of the proton exchange membrane fuel cell and a colored noise-driven voltage source in series in the main circuit, the electrochemical noise equivalent circuit model of the proton exchange membrane fuel cell is obtained; wherein, the voltage of the colored noise-driven voltage source is based on the... p Determine the parameters of the AR model; Step 4: Based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, fit the amplitude of the discrete interval binary sequence DIBS at the desired harmonic frequency to obtain the fitted DIBS. Step 5: Input the fitted DIBS into the electrochemical noise equivalent circuit model to simulate the electrochemical impedance spectrum, and calculate the deviation between the electrochemical impedance spectrum and the ideal electrochemical impedance spectrum calculated based on the ideal equivalent circuit model. E To minimize the deviation E The fitted DIBS amplitude is used as the optimization target to optimize and update the current harmonic number and signal-to-noise ratio; Step 6: Based on the optimized and updated harmonic number and signal-to-noise ratio, proceed to Step 4 for the next iteration until the preset iteration termination condition is met, and the desired harmonic number is obtained. N 0 and signal-to-noise ratio, thereby obtaining the desired DIBS; the desired DIBS is used as the excitation signal for the broadband impedance measurement; In step 3, the voltage of the colored noise driven voltage source for; in, a i For the AR model i Order parameter; w (∙) represents a sequence with a mean of 0 and a variance of . σ 2 Gaussian white noise, σ 2 for p The variance of the prediction error of the AR model; n ∈{1,2,…, }, The length of the voltage noise sequence is given.

2. The broadband impedance measurement excitation signal design method according to claim 1, characterized in that, In step 4, based on the current harmonic number, signal-to-noise ratio, and estimated voltage noise power spectrum, the amplitude of the discrete interval binary sequence DIBS at the desired harmonic frequency is fitted to obtain the fitted DIBS, specifically including: S41. Calculate the frequency domain representation of a multi-frequency sinusoidal signal: ;in, and These are the multi-frequency sinusoidal signals at the 1st... k The desired amplitude and phase at each desired harmonic frequency , In the current number k Signal-to-noise ratio at the desired harmonic frequency To estimate the voltage noise power spectrum in the first... k The amplitude at the desired harmonic frequency The value is the intersection point of the ideal electrochemical impedance spectrum with the real axis at low frequencies; the desired harmonic frequency is determined by the preset test frequency range and the current harmonic number. S42, Expressing the frequency domain Performing the inverse Fourier transform yields the time-domain signal: Thus, the time-domain signal of DIBS is obtained. ;in, If it is a sign function, then ,but , express It follows a discrete uniform distribution on the set {-1, 1}; S43, regarding the time-domain signal Perform a Fourier transform to obtain the frequency domain signal of DIBS: And calculate the frequency domain signal. phase ; S44. Calculate the reciprocal of energy efficiency. ;in, D sk For DIBS in the k The actual amplitude at the desired harmonic frequency; S45. Calculate the sum of squares of the expected amplitude. and the sum of the dot product of the expected amplitude and the actual amplitude To obtain the scaling factor Construct the objective function ,in, If the objective function value in the current iteration is less than the objective function value in the previous iteration, then the time-domain signal of DIBS... No change, otherwise update Proceed to step S43 for the next iteration. S46, when The iteration ends when the value is less than a preset threshold or when the preset number of iterations is reached, and the fitted DIBS time-domain signal is output. ;in, This indicates the absolute value operation.

3. The broadband impedance measurement excitation signal design method according to claim 2, characterized in that, The formula for calculating the desired harmonic frequency is as follows: in, f k For the first k One desired harmonic frequency, k ∈{1,2,…, N* }, N* This represents the current harmonic number; t For the duration of DIBS; f min Minimum test frequency, f max This represents the maximum test frequency; [·] indicates the rounding function; [·] down This represents the floor function.

4. The broadband impedance measurement excitation signal design method according to claim 1, characterized in that, In step 2, the battery voltage noise is solved based on the voltage noise sequence. p The parameters of the AR model include: Based on the voltage noise sequence and the order of the AR model p Using Burg's algorithm as input, the solution is obtained. p Parameters of the AR model; The results obtained using the Akaike Information Content Criterion (AIC) were evaluated. p The goodness of fit and complexity of the AR model were considered. The minimum model order that minimizes the AIC evaluation index or makes the AIC evaluation index tend to stabilize was selected as the optimal order of the AR model. The battery voltage noise was then obtained. p AR model parameters.

5. The broadband impedance measurement excitation signal design method according to claim 4, characterized in that, The AIC evaluation index is calculated as follows: in, The length of the voltage noise sequence; For the p The variance of the prediction error of the AR model for battery voltage noise.

6. The broadband impedance measurement excitation signal design method according to any one of claims 1-5, characterized in that, In step 5, the deviation E The calculation method is as follows: in, F This is a set of frequencies for impedance testing. Z fit ( ω The simulated electrochemical impedance spectroscopy at a test angular frequency of is ω The impedance value at that time; Z ideal ( ω The ideal electrochemical impedance spectrum at the test angular frequency is... ω The theoretical impedance value at that time; The value is the intersection point of the ideal electrochemical impedance spectrum with the real axis at low frequencies.

7. The broadband impedance measurement excitation signal design method according to claim 6, characterized in that, A competitive particle swarm optimization algorithm is used to optimize and update the current harmonic number and signal-to-noise ratio, and to optimize the objective function. Obj for: in, Amp ( N 0, r This indicates that when the desired harmonic number of DIBS is... N 0, signal-to-noise ratio is r The DIBS amplitude fitted over time; This is a penalty item.

8. A method for real-time detection of the operating status of a proton exchange membrane fuel cell, characterized in that, include: The impedance spectrum of a proton exchange membrane fuel cell is calculated based on a broadband impedance measurement excitation signal; wherein the broadband impedance measurement excitation signal is generated using the broadband impedance measurement excitation signal design method described in any one of claims 1-7. The operating status of the proton exchange membrane fuel cell is monitored in real time based on the impedance spectrum.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the wideband impedance measurement excitation signal design method as described in any one of claims 1-7, or the real-time detection method for the operating status of a proton exchange membrane fuel cell as described in claim 8.

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