Lifetime Extension Approach Based on Levenberg-Marquardt Neural Network and Power Routing of DC-DC Converters

Depósito de investigación de la Universidad de Sevilla https://idus.us.es/ This is an Accepted Manuscript of an article published IEEE Transactions on Industrial Electronics available at: 10.1109/TIE.2023.3325548 “© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other Works” IEEE TRANSACTIONS ON POWER ELECTRONICS 1 Lifetime Extension Approach Based on Levenberg-Marquardt Neural Network and Power Routing of DC-DC Converters Jiusi Zhang, Student Member, IEEE, Jilun Tian, Student Member, IEEE, Abraham Marquez Alcaide, Member, IEEE, Jose Ignaclo Leon, Fellow, IEEE, Sergio Vazquez, Senior Member, IEEE, Leopoldo Garc´ ıa Franquelo, Life Fellow, IEEE, Hao Luo, Senior Member, IEEE, Shen Yin, Fellow, IEEE Abstract—The power conversion system based on the modular connection has widespread applications in various power electronic systems. To accurately estimate the state of health without recognizing the systematic mathematical model and to extend the lifetime, this paper proposes a lifetime extension approach based on the Levenberg-Marquardt back propagation neural network (LM-BPNN) and power routing of interleaved DC-DC boost conversion systems. The LM-BPNN model is constructed based on the voltage, current, and temperature data generated by the system. On the basis of the trained LM-BPNN, the realtime cumulated damage estimation of each power cell in the conversion system can be accomplished. Applying the power routing concept, the DC-DC boost conversion system allocates different power to the cells according to the cumulated damage of each cell, thereby delaying the failure of cells with higher cumulated damage. Numerical simulation results show that the proposed lifetime extension approach can extend the overall system lifetime. Furthermore, an experimental setup of the interleaved DC-DC boost conversion is constructed to verify the proposed approach, which is of great significance for predictive maintenance in the industrial system. Index Terms—Interleaved DC-DC conversion system, Levenberg-Marquardt back propagation neural network, Power routing, Lifetime, Extension I. INTRODUCTION The modern power systems have become more and more complex with large-scale structures, so that the intelligent grids have gained more and more attention [1]–[5]. In the intelligent grid technology, new power converter topologies, advanced power device technologies, and control and modulation methods have become current research hotspots [6]–[8]. Due to these advances, the power converters can meet the demand for electric energy, which ensures the normal operation of the power grid [9]–[12]. This work was supported by the National Natural Science Foundation of China under Grant 62073104. Jiusi Zhang, Jilun Tian, and Hao Luo are with the Department of Control Science and Engineering, Harbin Institute of Technology, Harbin 150001, China (e-mail: hit [email protected]; [email protected]; [email protected]). Abraham Marquez Alcaide, Jose Ignaclo Leon, Sergio Vazquez, and Leopoldo Garc´ ıa Franquelo are with the Department of Electronic Engineering, School of Engineers, University of Seville, Seville, Spain (e-mail: [email protected]; [email protected]; ser[email protected]; [email protected]). Shen Yin is with the Department of Mechanical and Industrial Engineering, Faculty of Engineering, Norwegian University of Science and Technology, 7034, Trondheim, Norway (e-mail: [email protected]). To face these requirements, using modular converters is an attractive solution. The power conversion system based on modular connection refers to connecting several power converters in series or parallel. The nominal power is usually equally shared among the different power cells [13], [14]. The power conversion systems based on the modular connection are widely used in various power electronic equipment ranging from low power to high power [15], [16]. As a typical power conversion system based on modular connection, the parallel DC-DC conversion system keeps the losses below acceptable levels by sharing the current among the power cells during the operation. As an example of parallel-connected DC-DC converters, Fig. 1 represents the electrical schematic of Vensys 60/1200 commercial wind power generation system [17]. Each stage of the system adopts a parallel modular connection mode. The DC rectified voltage is generated according to the diode rectifier bridge, and is boosted by an interleaved boost DC-DC conversion system. Finally, the voltage is connected to the main grid through two parallel-connected two-level voltage source inverters. Output Filter Diode Rectifier WRSG PMSG (LV) Gearbox 3-Cell Boost converter 2 x 2-Level-VSI Fig. 1. The electrical schematic of Vensys 60/1200 commercial wind power generation system During the operation of a power electronic system, power devices are influenced by the factors such as high thermal stress, power loss, and ambient temperature. Therefore, it is required an accurate estimation of the state of health (SOH) of the power electronic systems in real-time. This SOH estimation will help the system manufacturer improve the reliability, and the fault-tolerant capability [18]–[20]. In work presented in [21], it is verified that the failure of power devices is mainly related to thermal stress caused by solder joint fatigue. Furthermore, repeated thermal cycles will cause irregular expansion and contraction of power device materials, thereby causing failure. The reference [22] proposed adaptive joint extended Kalman filter (AJEKF) and adaptive dual Kalman This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 2 filter (ADKF) approaches to predict the remaining useful lifetime (RUL) of the interleaved DC-DC boost conversion system used in electric vehicles. In recent years, the application of artificial intelligence to achieve reliability analysis of power electronics has attracted more and more attention. Zhao et al. processed an in-depth overview of the design, control, and maintenance of power electronics with the aid of artificial intelligence approaches [23]. Considering the nonlinear electronics thermal characteristics of power devices, Chiozzi et al. proposed a neural network (NN)-based modeling approach for power devices, which is helpful to reproduce circuit conditions [24]. Facing the uncertainty of life estimation, Eleffendi et al. proposed an online approach based on the Kalman filter and recursive least squares to monitor key semiconductor parameters, to achieve predictive maintenance [25]. In the conventional interleaved boost DC-DC conversion system, each converter cell manages the same power by applying an equalized current sharing control strategy. In this way, assuming ideal conditions, the power loss, thermo-mechanical fatigue, and cumulative aging of each power cell are the same. However, in practical operation, the relevant parameters of different devices, such as on-resistance, state voltage drop, and the thermal expansion coefficients of the material are diverse. Furthermore, replacing damaged modular units after failure also inevitably leads to aging mismatches among the power modules, which can be shown in Fig. 2. Therefore, designing an effective strategy to alleviate the aging mismatch problem in a modular system has become a significant research problem in the field of power electronics technology [17]. In [17], the aging process of the interleaved boost DC-DC conversion system is studied, and a method that can easily manage the power distribution of system cells is proposed. On the other hand, considering the failure mechanism of sensitive cells in the system, in [26], an approach is proposed to delay the occurrence of system failure, thereby increasing the system lifetime. Module 1 Module 2 Module 3 Module 1 Module 2 Module 3 Module 1 Module 2 Module 3 Module 1 Module 4 Module 3 Time Healthy Modules Equalized degrading Sudden Failure Module Replacement Fig. 2. Degrading evolution in a modular DC-DC conversion system considering replacements and failures In any case, the topic of the lifetime extension for the power electronic systems needs further research based on the following: •Application of data-based approaches for the problem of alleviating aging degree mismatch in the modular power conversion system. •Limitation of the conventional model-based approaches to estimate the SOH of the system without recognizing the accurate mathematical model. To face these difficulties, this paper proposes a novel lifetime extension approach for interleaved DC-DC boost conversion systems based on Levenberg-Marquardt back propagation neural network (LM-BPNN) and power routing strategy. The main contributions of this paper can be summarized as follows: •Without prior knowledge and a mathematical model, a data-based health state estimation approach is proposed to overcome the shortcomings of model-based approaches, which can effectively estimate the SOH in real-time. •Considering the proposed SOH estimation, a power routing strategy is applied to allocate different power to each power cell in the system with the aid of the data-based cumulated damage estimation approach. In this sense, the power distribution can be optimized, and the problem of aging mismatch is alleviated. •Numerical simulation results show that the proposed lifetime extension approach can extend the overall system lifetime. Furthermore, an experimental setup of the interleaved DC-DC boost conversion is constructed to verify the proposed approach. This paper is organized as follows: Section II states the research problem. Section III illustrates the lifetime extension approach based on the LM-BPNN and power routing strategy. Section IV uses a numerical simulation to verify the proposed approach. Section V constructs an experimental setup of the interleaved DC-DC boost conversion to verify the proposed lifetime extension approach. Finally, section VI presents some conclusions of the work. II. PROBLEM STATEMENT This paper aims to estimate the SOH of an interleaved DCDC boost conversion system with the aid of a data-based approach. Furthermore, the problem of mismatched aging in the system is alleviated, and the overall system lifetime can be extended. To facilitate discussion, the complete Vensys 60/1200 system shown in Fig. 1 can be simplified into the form of an interleaved DC-DC boost conversion system, as shown in Fig. 3. The diode rectifier bridge and the active front-end are assumed to be equivalent to the voltage sources Vdand Vo, respectively. The SOH estimation approach proposed in this paper is based on the historical data generated by the system during the operational process. It is supposed that the data in the i-th working cycle can be expressed as x(i) = x(i,1), x(i,2), ..., x(i,p), where pis the number of sensors. Correspondingly, the true value of the systematic SOH under the current cycle is y(i). The original dataset can be reconstructed by combining x(i)and y(i), which is expressed as D={(x(i), y(i))|i= 1,2, ..., m}, where mis the total number of samples. On this basis, the SOH estimation approach proposed in this paper takes the historical data (training data) as the input of the data-based learning algorithm model. The best mapping function Φ : x(i)→y(i)is learned by training the model. Furthermore, based on the trained algorithm model This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 3 DC DC 2-L VSI C C Diode Rectifier V d V o L Sn I n vn Fig. 3. Simplified structure of Vensys 60/1200 system and online working data, the real-time SOH estimation can be achieved. Correspondingly, root mean square error (RMSE) and mean absolute error (MAE) are considered as indicators to evaluate the SOH estimation performance [27], [28]. The RMSE is defined as: RMSE =v u u t 1 n n X i=1 (SOHei −SOHti)2,(1) where nis the number of samples in the testing sets, i is the index of the samples, SOHei and SOHti are SOH estimated value and SOH ground truth of the i-th testing sample, respectively. Furthermore, MAE is shown as follows: MAE =1 n n X i=1 |SOHei −SOHti|.(2) Eqs. (1)-(2) measure the difference between the SOH ground truth and the estimated value. The smaller the value, the better the SOH estimation performance of the algorithm model. It should be noted that this paper implements the health management of the power cells according to the SOH of each power cell in the DC-DC boost conversion system. Specifically, in order to evaluate the health status of the system, the cumulated damage of each cell is calculated as the SOH by rainflow counting method according to the amplitude temperature 4Tand the average thermal cycle temperature Tj,m, which is widely adopted in power conversion systems [26]. The principle of the rainflow counting method is shown in Fig. 4, which can isolate the task profile of the temperature derivative change. The temperature transition from hot to cold is reflected. In addition, the temperature difference between the two operational points is calculated. On this basis, the number of thermal cycles to failure Nfcan be acquired by the rainflow counting algorithm [26], as follows: Nf=α(4T)(−β)e Ea kB(Tj,m + 273◦C),(3) where α,βare device dependent parameters, respectively. Eais the excitation energy of the device material, and kB is Boltzmann constant. On this basis, the cumulated damage Time TjTj Thermal Cycle Fig. 4. An example of the rainflow algorithm Dcan be defined according to the Miner fatigue cumulative principle: D=X i Ni Nfi ,(4) where Niis the number of thermal cycles, and Nfiis the maximum number of thermal cycles that the device can withstand. Through Eqs. (3)-(4), the cumulated damage D is dependent on a history of the information, the junction temperature, and temperature changes, from the initial working point. Although the rainflow counting method can consider historical information, as shown in Eqs. (3)-(4), it should be noted that only temperature information is considered. On the other hand, when using the machine learning algorithm, the mapping relationship between current, voltage, temperature, and cumulated damage at the current moment is constructed. Due to the more comprehensive feature information, the mapping relationship between input and cumulated damage can be constructed even without historical temperature information. In this sense, we attempt to adopt a neural networkbased approach to construct the mapping relationship between current, voltage, temperature, and cumulated damage at the current moment in this paper. From a theoretical point of view, when the cumulated damage Dbecomes 1, it means that, on average, the power device will fail. But Drepresents a cumulated probabilistic measure of the failure. Depending on the application and how critical it is, the acceptable cumulated damage is different. For instance, in regular applications, the maximum value in the failure probability is 20%. As for aeronautical applications this threshold is set from 0.1% to 1%. This paper sets the maximum value of the cumulated damage to 20%. When the cumulative damage reaches 20%, the power cell should be replaced. III. LIFETIME EXTENSION APPROACH The lifetime extension approach for interleaved DC-DC conversion systems proposed in this paper is mainly composed of an LM-BPNN algorithm and a power routing strategy. The research flow of the approach is shown in Fig. 5. The LMBPNN algorithm includes two parts: offline training and online estimation. For the offline training part, the feature variables, This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 4 Interleaved DC-DC boost converter system Offline Systematic Data Feature Extraction Train LM-BPNN Algorithm Model SOH Input Online Systematic Data Feature Extraction Trained LMBPNN Algorithm Model Power Routing Strategy Offline Training Online Estimation Relationship Transformation LM-BPNN Life Extension Fig. 5. Research flow such as current, voltage, and temperature data generated by the DC-DC conversion system during the operation are extracted as the input of the LM-BPNN, and the cumulated damage at the corresponding time is the label. Afterward, the LM-BPNN is used to establish the mapping relationship between feature variables and cumulated damage. Regarding the power routing strategy, this part consists of a power routing control loop and a power module control loop. The power routing control loop takes the cumulated damage from the LM-BPNN as the input, and outputs the power sharing factor of each power cell in the DC-DC conversion system. The power module control loop is essentially an internal closed-loop control to track the desired per-cell power. According to the power sharing factor, the duty cycle of each DC-DC power cell is changed to fulfill the required power distribution, leading to achieving an equalization of the cumulated damage of all the power cells. A. Levenberg-Marquardt back propagation neural network (LM-BPNN) BPNN has a strong self-adaptive learning ability, which completes the mapping from input to output by automatically learning the implicit relationship in the data [29], [30]. The gradient descent algorithm is generally used to update the weight parameters in the conventional BPNN [31]. The mean square error is used as the loss function to train the BPNN: F(θ) = 1 2m m X i=1 (fθ(xi)−yi)2,(5) where mis the number of samples in the training set, xi and yiare the input vector and the label of the i-th sample, respectively. fθ(xi)is the estimated value of the network in the i-th sample, and θis the composition of the weight and the bias vector: θ=      w11 w12 · · · w1nb1 w21 w22 · · · w2nb2 . . .. . ..... . .. . . wn1wn2· · · wnn bn      ,(6) where nis the dimension. However, the traditional gradient descent algorithm has disadvantages, such as low training efficiency and worse convergence. For this reason, this paper introduces the LM algorithm to optimize the BPNN. The LM algorithm combines the advantages of the gradient descent and the Gauss-Newton algorithm. In detail, the LM algorithm can maintain the rapid convergence of gradient descent algorithm, while having the optimal characteristics of the Gauss-Newton algorithm [32]. The training process of the BPNN can essentially be regarded as the solution to the minimum value of F(θ)for the nonlinear least squares problem, as follows: min θ∈RnF(θ) = 1 2(r(θ))Tr(θ) = 1 2 m X i=1 [ri(θ)]2(m≥n), (7) where r(θ)is residual function of θ, which can be specifically shown as: r(θ)=[r1(θ), r2(θ), ..., rm(θ)]T.(8) It is assumed that Ja(θ)is the Jacobian matrix of r(θ), shown as follows: Ja(θ)=[∇r1(θ),∇r2(θ), ..., ∇rm(θ)]T =      ∂r1 ∂θ1 ∂r1 ∂θ2· · · ∂r1 ∂θn ∂r2 ∂θ1 ∂r2 ∂θ2· · · ∂r2 ∂θn . . .. . ..... . . ∂rm ∂θ1 ∂rm ∂θ2· · · ∂rm ∂θn      .(9) The gradient g(θ)of F(θ)can be expressed as: g(θ) = m X i=1 ri(θ)∇ri(θ) = (Ja(θ))Tr(θ).(10) It should be noted that the LM algorithm is improved on the basis of the Gauss-Newton method, which changes the step size in the iteration. For the k-th iteration, the gradient can be described by: 4k=−h(Ja(θk))TJa(θk) + ukIi−1 (Ja(θk))Tr(θk),(11) where ukis the penalty factor, and Iis the unit matrix. When the value of ukis large, the LM algorithm is equivalent to the gradient descent algorithm, because the elements on the main diagonal occupy a dominant position. On the other hand, when This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 5 the value of ukis small, the LM algorithm is equivalent to the Gauss-Newton method. The details about LM-BPNN can be referred to [32]. In general, larger ukis used in the initial stage of the training process to accelerate the convergence of the network. In the later stage of the training process, smaller ukis used to avoid the oscillations generated by the gradient descent algorithm, so that the network can be converted to the global optimal solution as much as possible. In this sense, the cumulated damage can be accurately estimated. B. Power routing strategy The power routing strategy structure of the interleaved DCDC boost conversion system is shown in Fig. 6 [17]. The essence of the power routing strategy is to allocate different power to corresponding power cells by adjusting the transient current through the inductor according to the actual situation of the cumulated damage. PIPI vn V0 Vd* Vd 1 Pn * SoHAging Balancing +- vn * In * kn P* kn In +- Vd * Vd -.#1// dn Dn Fig. 6. The power routing strategy structure The power routing strategy of the interleaved DC-DC power system consists of a power routing control loop and an internal power module control loop. 1) Power routing control loop: The cumulated damage obtained in the LM-BPNN is taken as the input in the power routing control loop. The output is the power sharing factor of each cell in the DC-DC conversion through specific distribution rules that will be introduced later. In this paper, the cumulated damage of each power cell is used as the SOH to measure its health status. The damage of the power device is closely related to its temperature and the suffered cycles thermal amplitudes. In this sense, the greater power managed by a power cell will increase its temperature, leading to accelerating the aging of the corresponding power devices. Therefore, to balance the aging of all power devices as much as possible, the purpose of the power routing control loop is to allocate lower power to cells with higher cumulated damage, and to allocate higher power to cells with lower cumulated damage. The parameter kiin Fig. 6 is the power sharing factor of the i-th power cell, which determines the actual power to be managed by each cell. To ensure the normal operation of the system, it is worth noting that whatever the power distribution inside the system is, the sum of the power sharing factors of all cells should be equal to 1, which can be expressed as: q X i=1 ki= 1,(12) where qis the number of cells in the system. Considering a conventional operation of an interleaved DC-DC boost system, the power sharing factors of all the power cells are equal: k1=k2=... =ki=... =kq=1 q.(13) To allocate different power to each cell, it is assumed that the cumulated damage of the i-th cell is Di. The value of the i-th cell power sharing factor kican be expressed as: ki= q P j=1 Dγ j−Dγ i (q−1) q P j=1 Dγ j ,(14) where γis an exponential term, which aims to increase the difference between the cumulated damage of different cells to speed up the power equalization by making more robust the power routing method. In particular, when the damage of all cells is the same, Eq. (14) achieves to the equalized operation described in Eq. (13), leading to the conventional interleaved operation of the power system. 2) Internal power module control loop: The power module control loop is essentially a closed-loop control with a power tracking objective, as shown in Fig. 6. According to the power sharing factors calculated by the power routing control method, the duty cycle of each cell is determined to complete the objective of power distribution. The control scheme presented in [17], is widely used in the interleaved parallel power modules. For the i-th power cell, the closedloop control determines the power P∗ ito be managed by i-th power cell by using the power sharing factor, and divides it by the input voltage Vdto obtain the reference current I∗ ithat has to flow through the inductor. Afterward, the reference inductor voltage v∗ ican be determined through an internal control loop implemented with another PI controller. Finally, by means of normalization, the duty cycle dito generate the gate driving pulse (Si) of each module is obtained by applying a simple PWM method. IV. NUMERICAL SIMULATION ANALYSIS A. Systematic introduction To test the proposed lifetime extension approach, this paper uses a two-cell interleaved DC-DC boost conversion system for numerical simulation analysis. The structure diagram of the system is shown in Fig 3. The power device used in the conversion system is the IRFP4227 Mosfet. Moreover, the relevant parameters of the system are summarized in Table I. Both DC-DC power cells are connected to an input power source and an output capacitor. All the experiments are performed at an ambient temperature equal to 40°C. Based on the parameter configuration listed in Table I, the power curve of the DC-DC boost conversion system ranges from 0 to 3kW, whose value is accompanied by a certain random disturbance. The specific 20 minutes power profile is shown in Fig. 7. It should be noted that the power profile represented in Fig. 7 is repeated to form complete days. On the basis of the parameter configuration and operating power This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 6 TABLE I PARAMETERS IN THE DC-DC BOOST CONVERTER SYSTEM Parameter Value Number of cells 2 Input voltage (V) 50 Output voltage (V) 140 Switching frequency (kHz) 5 Boost inductance (mH) 3 Ambient temperature (°C) 40 described above, the cumulated damage of each power cell in the DC-DC boost conversion system is obtained by the rainflow counting method [33]. Fig. 7. Power profile applied to the complete DC-DC power system B. Cumulated damage estimation based on LM-BPNN In the interleaved DC-DC boost conversion system, the whole simulation time of an operational process is set to one year. For each simulation cycle, namely, each day, feature variables, such as the current, voltage, and temperature of the power device are extracted as the input of the LM-BPNN model. Correspondingly, the output of the LM-BPNN is the cumulated damage at the end of the day. It should be noted that the cumulated damage is calculated according to the rainflow counting method in Eqs. (3)-(4) for each day, which is used as the label of the training data. To simulate various unbalanced initial aging scenarios, the initial damages are randomly assigned to the two cells in the DC-DC boost conversion system. The data from multiple operational conditions can be obtained to verify the effectiveness of the LM-BPNN estimation algorithm proposed in this paper. The ratio of training data to test data is set to 5:1 in this paper. In detail, the data of 30 operational processes are used as training data, and the data of 6 operational processes are used as testing data to verify the estimation performance. To prevent overfitting in the training process, this paper adopts the 10-fold cross-validation method to adjust parameters, such as the network learning rate and the number of network neurons, to acquire a great cumulative damage estimation performance. The details of the 10-fold cross-validation are shown in Fig. 8. In detail, the training dataset is divided into ten parts, each part of which is used as test data for verification in turn, and nine of them are used as training data for model training. The average of the ten experiments measures the final indicator. Test Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train Train Train Train Test Train Train Train Train Train Train Train ... Train Train Train Train Train Train Train Train Train Test Result 1 Result 2 Result 3 ... Result 10 Iteration 1 Iteration 2 Iteration 3 Iteration 10 Fig. 8. 10-fold cross-validation To better demonstrate the influence of features on the cumulated damage, this work uses four features, namely, the current and temperature of two cells of the interleaved DCDC boost conversion system in an operational process (see an example to visualize the features in Fig. 9a). Furthermore, the corresponding cumulated damage is shown in Fig. 9b. It can be seen from Fig. 9 that there is a correlation between the current, temperature features of the two cells and the cumulated damage, which also provides the feasibility of constructing the mapping relationship between the characteristics and the cumulated damage in this work. Fig. 9. The visualization of features and cumulated damage Considering that the amount of data collected in the parallel DC-DC boost conversion system is small, the number of layers of the network is set to two. On this basis, a grid search is performed in a two-layer network to determine the number of neurons in each layer, so that a better cumulated damage estimation performance can be obtained. In detail, the possible values of the number of neurons in the two-layer network are set to 16, 32, and 64. Table II lists the results of the RMSE and MAE of the two power cells of the DC-DC boost conversion system under multiple network configurations using 10-fold cross-validation. When the number of neurons in the twolayer network is 16 and 32, respectively, LM-BPNN has better estimation performance. The hyperparameter configuration of LM-BPNN is summarized in Table III. To better demonstrate the estimation performance of the proposed approach on the testing dataset, the error distribution of the two power cells of the DC-DC boost conversion system in the testing data under multiple network configurations is represented, which is shown in Fig. 10. It can be seen from Fig. 10 that the error of the two power cells is mainly distributed on both sides of zero, which is concentrated in the order of magnitude of 10−5. It can also confirm that the proposed approach has a great cumulative damage estimation performance. This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 7 TABLE II THE ESTIMATION RESULTS OF THE TWO POWER CELLS USING 10-FOLD CROSS-VALIDATION Configuration Parameter Cell1Cell2 RMSE MAE RMSE MAE 1 (16,16) 9.293 ×10−58.856 ×10−51.789 ×10−41.334 ×10−4 2 (16,32) 2.782 ×10−52.220 ×10−54.006 ×10−52.138 ×10−5 3 (16,64) 1.258 ×10−49.372 ×10−51.386 ×10−48.562 ×10−5 4 (32,16) 4.983 ×10−54.596 ×10−58.359 ×10−56.968 ×10−5 5 (32,32) 1.454 ×10−41.128 ×10−42.364 ×10−41.512 ×10−4 6 (32,64) 3.589 ×10−33.141 ×10−46.798 ×10−34.485 ×10−4 7 (64,16) 7.025 ×10−46.858 ×10−41.783 ×10−31.052 ×10−3 8 (64,32) 1.751 ×10−38.992 ×10−41.963 ×10−31.616 ×10−3 9 (64,64) 6.896 ×10−36.334 ×10−45.038 ×10−33.856 ×10−3 TABLE III HYPERPARAMETER CONFIGURATION Hyperparameter Value Number of layers 2 Number of neurons (16,32) Learning rate 0.001 Epoch 1000 Activation function tanh To demonstrate the cumulated damage estimation performance of the proposed LM-BPNN, this paper represents the cumulated damage estimation results of the LM-BPNN in the six operational processes of the testing data, shown in Fig. 11. It should be noted that the training data and testing data in the paper are performed under the power routing strategy, and the power profile applied to the system is consistent with Fig. 6. It can be seen that the estimated cumulated damage curve coincides nicely with the actual cumulative damage curve, which represents that the estimation performance of LMBPNN is excellent. Table IV lists the results of the RMSE and MAE of the testing data in the cumulated damage estimation of these six operational processes. TABLE IV THE ESTIMATION RESULTS OF CUMULATED DAMAGE Operational Cell Initial RMSE MAE number Damage 1Cell10.105 3.348 ×10−62.386 ×10−6 Cell20.052 1.835 ×10−54.301 ×10−6 2Cell10.124 8.350 ×10−66.081 ×10−6 Cell20.032 2.908 ×10−51.162 ×10−5 3Cell10.153 1.239 ×10−41.004 ×10−4 Cell20.063 1.205 ×10−48.024 ×10−5 4Cell10.083 8.920 ×10−68.335 ×10−6 Cell20.032 1.237 ×10−58.924 ×10−6 5Cell10.073 5.011 ×10−63.929 ×10−6 Cell20.022 9.320 ×10−65.025 ×10−6 6Cell10.108 1.744 ×10−51.200 ×10−5 Cell20.010 5.075 ×10−51.819 ×10−5 To demonstrate the superiority of the approach proposed in this paper, the Cell2of the first operational process, whose initial damage is 0.052, is used as an example to compare the estimation performance of LM-BPNN and other data-based estimation approaches, such as ridge regression (Ridge), support vector regression (SVR), ElasticNet regression (ElasticNet), Lasso regression (Lasso), AdaBoost regression (AdaBoost), Fig. 10. The error distribution of the two power cells k-Nearest Neighbor (KNN), partial least squares regression (PLS), and long-short term memory network (LSTM). Fig. 12 represents the estimation results of various methods on the testing data. From Fig. 12, it can be seen that the estimated cumulated damage of the proposed LM-BPNN is the closest to the ground truth. Correspondingly, the evaluation indicators are shown in Table V. It can be seen from Fig. 12 and Table V that the LM-BPNN proposed in this paper has the best estimated performance on cumulated damage compared with other data-based estimation approaches. Although the uncertainty for unit heterogeneity may cause slight errors between the estimated damage and the ground truth, it is acceptable from the results. The reason is that the state of health can be reflected through the feature variables of each power cell. Therefore, the machine learning algorithm is considered to construct a mapping relationship between current, voltage, temperature and cumulated damage, which can acquire excellent estimation performance. C. Simulation results of power routing strategy To represent the lifetime extension performance of the power routing strategy on the interleaved DC-DC boost conversion system, this paper shows the cumulated damage before and after the introduction of the power routing strategy. Specifically, for the first operation in the testing data, the initial damages of the two power cells in the system are set to 0.105 and 0.052, respectively. It should be noted that the maximum power sharing factor is set to 0.8, so that an excessive power mismatch among the cells is avoided. The cumulated damage value, cumulated damage difference, and power sharing factor of the two cells are plotted in Fig. 13. According to the power routing strategy, since the initial damages of the two cells in the interleaved DC-DC boost conversion system are different, the two cells will have different power sharing factors to manage different power in each cell. It can be seen from Fig. 13 that the cumulated damage difference between the two cells in the system is continuously reduced by applying the power routing strategy. The damage growth of cells with higher cumulated damage will be significantly slower than the cells with lower cumulated damage to delay the failure of cells with higher cumulated damage and to extend the overall system lifetime. The numerical simulation result represents that the lifetime of the system without the power routing strategy and under the power routing strategy is 2771 days and 3005 days, respectively, from which the effectiveness of the proposed lifetime extension approach can be verified. This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information. IEEE TRANSACTIONS ON POWER ELECTRONICS 8 0 100 200 300 Time (days) (a) Operation 1 0.04 0.06 0.08 0.1 0.12 Cumulated Damage Ground Truth Estimated Damage of Cell1 Estimated Damage of Cell2 0 100 200 300 Time (days) (b) Operation 2 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Cumulated Damage Ground Truth Estimated Damage of Cell1 Estimated Damage of Cell2 0 100 200 300 Time (days) (c) Operation 3 0.05 0.1 0.15 Cumulated Damage Ground Truth Estimated Damage of Cell1 Estimated Damage of Cell2 0 100 200 300 Time (days) (d) Operation 4 0.04 0.06 0.08 0.1 Cumulated Damage Ground Truth Estimated Damage of Cell1 Estimated Damage of Cell2 0 100 200 300 Time (days) (e) Operation 5 0.02 0.04 0.06 0.08 Cumulated Damage 0 100 200 300 Time (days) (f) Operation 6 0 0.05 0.1 Cumulated Damage 50 52 54 56 58 60 0.034 0.036 0.038 0.04 90 92 94 96 98 100 0.07308 0.0731 0.07312 0.07314 0.07316 Fig. 11. The estimation results of LM-BPNN in the six operational processes of the testing data TABLE V THE COMPARISON OF THE CUMULATED DAMAGE ESTIMATION RESULTS USING DIFFERENT APPROACHES Approach Ridge SVR ElasticNet Lasso AdaBoost KNN PLS LSTM LM-BPNN RMSE 4.433 ×10−32.373 ×10−22.186 ×10−21.793 ×10−27.448 ×10−35.606 ×10−33.527 ×10−33.222 ×10−31.835 ×10−5 MAE 3.824 ×10−32.192 ×10−21.985 ×10−21.641 ×10−26.646 ×10−34.552 ×10−32.793 ×10−32.580 ×10−34.301 ×10−6 0 50 100 150 200 250 300 350 Time (days) 0.05 0.06 0.07 0.08 0.09 0.1 Cumulated Damage KNN LSTM PLS AdaBoost LM-BPNN Ground Truth 310 320 330 340 0.105 0.1055 0.106 0.1065 Fig. 12. The estimation results of the cumulated damage using different databased approaches It is worth mentioning that the principle of neural network training is consistent when faced with a DC-DC conversion system that contains more cells. The feature variables, such as the current, voltage, and temperature of each cell are extracted as the input of the LM-BPNN model, so that the cumulated damage estimation can be achieved. In this sense, the life extension approach proposed in this paper has great scalability. The reason is that the principle is consistent. V. EXPERIMENTAL SETUP To verify the lifetime extension approach, an experimental setup of the interleaved DC-DC boost conversion is constructed, shown in Fig. 14. For each boost module, the power device is a 200V MOSFET IRFP4227PbF from Infineon Technologies. Furthermore, these two DC-DC converters are connected to input power. The output is a parallel circuit of a resistor and a capacitor. The interleaved DC-DC boost conversion system is controlled by DS1004 from the DSpace solution. The interleaved modulation, data acquisition, and control scheme are implemented in the DSpace platform. In detail, the parameters in the DC-DC boost conversion system are summarized in Table VI. In addition, the temperature of the power module is measured by a data logging interface of the thermocouple, shown in Fig. 15. TABLE VI PARAMETERS IN THE DC-DC BOOST CONVERTER SYSTEM Parameter Value Number of cells 2 Input voltage (V) 50 Output voltage (V) 140 Switching frequency (kHz) 4 Boost inductance (mH) 3 Output capacitor (mF) 5.6 Load resistor (Ω) 44 Ambient temperature (°C) 25 In the offline training preparation stage of the experiment, the two converter cells just shipped in the DC-DC boost converter system are arranged in a symmetrical manner. Under this This article has been accepted for publication in IEEE Transactions on Power Electronics. This is the author's version which has not been fully edited and content may change prior to final publication. Citation information: DOI 10.1109/TPEL.2023.3275791 © 2023 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See https://www.ieee.org/publications/rights/index.html for more information.