Battery State Of Health Research Articles

A Predictive Approach for Lithium-Ion Battery SOH using LSTM Neural Networks Enhanced by Health Matrix Optimization

The State of Health (SOH) is a critical performance metric that characterizes the condition of lithium-ion batteries, directly influencing their lifespan and operational efficiency. In order to enhance the accuracy of SOH predictions for batteries and reduce operational risks, a novel approach has been introduced. This method, based on Health Matrix Optimization for Long Short Term Memory (LSTM) neural networks, aims to optimize the prediction process. Initially, the Spearman correlation coefficient method is employed to analyze the correlation of battery state data. Through the use of a heatmap, data points with strong correlations to SOH are identified, leading to the creation of a health feature matrix. This matrix is then utilized to fine-tune the hyperparameters of the LSTM neural network, resulting in refined approximations. Subsequently, by employing this optimized LSTM neural network, accurate predictions of the SOH for lithium-ion batteries are made. The results demonstrate a notable improvement in prediction accuracy by 35.71% and a significant increase in prediction speed by 35.5% when compared to traditional methods. This innovative approach proves to be effective in enhancing battery performance and longevity.

An efficient state-of-health estimation method for lithium-ion batteries based on feature-importance ranking strategy and hybrid kernel extreme learning machine algorithm

The safe and reliable operation of battery systems depends critically on accurately and dependably estimating the state of health (SOH) of lithium-ion batteries (LIBs). However, accurate prediction of SOH still needs improvement due to the complex battery aging mechanism. This paper introduces a hybrid kernel extremum learning machine (HKELM) for estimating battery SOH. To improve estimation accuracy, we enhance the standard dung beetle optimization algorithm (DBO) with a new initialized population, adaptive weights method, and improved population diversification. We then use the enhanced IDBO algorithm to optimize the parameters of HKELM. This study examines two distinct anode types of LIBs from NASA and Oxford datasets. Fifty significant features are extracted from charging voltage, current, temperature, and incremental capacity (IC) curves. The importance indices of these features are then computed using statistical analyses, including Pearson's correlation coefficient and Spearman's rank correlation coefficient, followed by optimal ranking. The optimal number of final features is determined by comparing various combinations of high-level features, thus reducing model complexity and improving estimation accuracy. This paper proposes the IDBO-HKELM algorithm for SOH estimation. Compared to other methods, the algorithm shows superior estimation performance and anti-interference capability. Both B0007 and Cell8 estimate SOH with MAE < 0.15, RMSE <0.2, and R2 > 99.9 %. Experimental results demonstrate the robustness of the proposed method, achieving accurate and noise-immune SOH estimation.

Evaluation of Advances in Battery Health Prediction for Electric Vehicles from Traditional Linear Filters to Latest Machine Learning Approaches

In recent years, there has been growing interest in Li-ion battery State-of-Health (SOH) estimation due to its critical role in ensuring the safe and reliable operation of Electric Vehicles (EVs). Effective energy management and accurate SOH prediction are essential for the reliability and sustainability of EVs. This paper presents an in-depth review of SOH estimation techniques, starting with an overview of seminal methods that lay the theoretical groundwork for battery modeling and SOH prediction. The review then evaluates recent advancements in Machine Learning (ML) and Artificial Intelligence (AI) techniques, emphasizing their contributions to improving SOH estimation. Through a rigorous screening process, the paper systematically assesses the evolution of these advanced methods, addressing specific research questions to evaluate their effectiveness and practical implications. Key findings highlight the potential of hybrid models that integrate Equivalent Circuit Models (ECMs) with Deep Learning approaches, offering enhanced accuracy and real-time performance. Additionally, the paper discusses limitations of current methods, such as challenges in translating laboratory-based models to real-world conditions and the computational complexity of some prospective methods. In conclusion, this paper identifies promising future research directions aimed at optimizing hybrid models and overcoming existing constraints to advance SOH estimation and battery management in Electric Vehicles.

Battery health state prediction based on lightweight neural networks: A review

Battery health state prediction based on lightweight neural networks: A review

Joint estimation of SOH and RUL for lithium batteries based on variable frequency and model integration

The safe and stable operation of lithium-ion batteries in electric vehicles is crucial. Aiming at the problems of a large workload of online estimation and prediction and inability to weigh the whole life cycle of the battery in the joint estimation of SOH (State of Health) and RUL (Remaining Useful Life) for traditional lithium-ion batteries, this paper proposes an optimization scheme for the joint analysis of SOH-RUL. First, the article extracts suitable health features. It utilizes an integrated Extreme Learning Machine (ELM) to estimate the SOH of the battery and inputs the estimates into a Regression Vector Machine (RVM) model for RUL prediction. To better cope with the phenomenon of "sudden capacity change" in batteries, this paper divides the entire life cycle into the early and late stages. A lower estimation frequency and model integration are employed in the early stage.In contrast, the estimation frequency and model integration are increased later to balance speed and safety in total life cycle estimation. Finally, validation was performed on the NASA and CALCE datasets, comparing the effect of constant estimated frequency and model integration with that of varying estimated frequency and model integration at different aging stages. The RMSE of SOH estimation error for both datasets is within 2% during the early and late stages, and the SOH estimation error for the entire lifecycle is within 2%. The absolute RUL prediction error for the NASA dataset is below five times; for the CALCE dataset, it is below 20 times in most cases.

Combining Multi-Indirect Features Extraction and Optimized GPR Algorithm for Online State of Health Estimation of Lithium-ion Batteries

Abstract With the wide application of lithium batteries (LIBs) in electrified transportation and smart grids, especially in the pure electric vehicle industry, the accurate health maintenance monitor of LIBs has emerged as critical for safe battery operation. Although many data-driven methods with state of health (SOH) estimation for LIBs have been proposed, the problems of industrial generation and computational cost still need to be improved further. In contrast, this paper carried out a low-complexity SOH estimation method for LIBs. Specifically, the seven health indicators are extracted firstly to characterize battery health status from voltage, current, temperature and other data that can be obtained online. Then, the optimized gaussian process regression (GPR) algorithm is proposed with proper computational cost. Ultimately, combining a multi-indirect features extraction and optimized GPR algorithm, the online SOH estimation for LIBs was established and verified with NASA experiment data. The experimental results show that the maximum Mean Absolute Percentage Error (MAPE) of SOH estimation from the proposed method is 1.4496 and the minimum MAPE only reaches 0.5635. More importantly, the optimized GPR for SOH estimation can achieve a maximum 65.37% improvement under multiple evaluation criteria compared to traditional GPR. The method proposed in this paper is helpful for realizing on-line SOH estimation in battery management systems.

State-of-health estimation of lithium-ion batteries using multiple correlation analysis-based feature screening and optimizing echo state networks with the weighted mean of vectors

Lithium-ion batteries (LIBs) are widely employed in electric vehicles (EVs) and energy storage systems owing to their high energy density, low self-discharge rate, and superior longevity. As a vital evaluation index for the degradation state of LIBs, the state of health (SOH) must be accurately estimated. This study adopts an electrochemical impedance spectroscopy (EIS)-based equivalent circuit model (ECM) to estimate battery SOH. The internal dynamic electrical behaviors of LIBs are decoupled by the distribution of relaxation times (DRT) method, whereby the critical degradation features are extracted from the DRT curves and the fitted ECM parameters. Subsequently, referring to the ensemble learning approach (ELA), the multiple correlation analysis (MCA) is utilized to identify the most pertinent degradation features. The battery data are subjected to a comprehensive analysis with five types of correlations to ascertain the optimal number and combination of health indicators (HIs). Furthermore, the weighted mean of vectors (INFO) algorithm is employed to optimize the hyperparameters in the echo state network (ESN) model for SOH estimation. The echo state networks model optimized with the weighted mean of vectors algorithm (INFO-ESN) is verified with eight types of LIBs under different operating conditions. Experimental results of the proposed method manifest that the root mean square error (RMSE) and mean absolute error (MAE) of the battery SOH range from 0.32 % to 1.06 %, thereby verifying the accuracy and robustness of the proposed method.

A Method for Estimating the SOH of Lithium-Ion Batteries Based on Graph Perceptual Neural Network

The accurate estimation of battery state of health (SOH) is critical for ensuring the safety and reliability of devices. Considering the variation in health degradation across different types of lithium-ion battery materials, this paper proposes an SOH estimation method based on a graph perceptual neural network, designed to adapt to multiple battery materials. This method adapts to various battery materials by extracting crucial features from current, voltage, voltage–capacity, and temperature data, and it constructs a graph structure to encapsulate these features. This approach effectively captures the complex interactions and dependencies among different battery types. The novel technique of randomly removing features addresses feature redundancy. Initially, a mutual information graph structure is defined to illustrate the interdependencies among battery features. Moreover, a graph perceptual self-attention mechanism is implemented, integrating the adjacency matrix and edge features into the self-attention calculations. This enhancement aids the model’s understanding of battery behaviors, thereby improving the transparency and interpretability of predictions. The experimental results demonstrate that this method outperforms traditional models in both accuracy and generalizability across various battery types, particularly those with significant chemical and degradation discrepancies. The model achieves a minimum mean absolute error of 0.357, a root mean square error of 0.560, and a maximum error of 0.941.

Data-driven energy utilization for plug-in hybrid electric bus with driving patten application and battery health considerations

The efficient utilization of energy is a crucial consideration for plug-in hybrid electric buses (PHEB). However, achieving the optimal energy management strategy (EMS) for PHEB necessitates the harmonious optimization of both driving conditions and battery status. Consequently, an innovative EMS that integrates the data-driven prediction of the driving cycles and battery health status. Explicitly, the bi-directional long short-term memory algorithm is employed to reconstruct and train the health status data of power batteries, enabling the accurate estimation of their State of Health (SOH) values. Moreover, a database of historical driving behavior is meticulously collected through a real-world PHEB platform, and the driving cycles for a certain while are predicted with the clustering algorithm. Then, this invaluable information on the battery status and driving cycles is seamlessly introduced into an adaptive-network-based fuzzy inference system (ANFIS) to regulate of the energy conversion factor in the following equivalent consumption minimization strategy (ECMS). Besides, the offline global optimization of equivalent fuel consumption with the Pontryagin's minimum principle (PMP) is preliminarily conducted to generate the pre-established energy conversion factors, facilitating convenient access to the engine and motor's reasonable power distribution range. Finally, simulations and experiments have validated the effectiveness of the proposed EMS, demonstrating a 23.57 % reduction in battery SOC depletion and a 10.53 % decrease in fuel consumption compared to traditional ECMS methods. More importantly, the proposed method has been validated for its executability in embedded devices through real-world bench experiments. This research holds significant reference value for energy utilization and practical implementation in the PHEB, thereby contributing to the advancement of knowledge in this field.

Exploiting the Electrochemical Impedance Spectroscopy Frequency Profiles for State-of-Health Predication of Lithium-Ion Battery

Battery Management Systems (BMS) are essential for optimizing battery performance and extending lifespan through continuous monitoring and decision-making via control sensors. The State of Health (SOH) is one of the BMS metrics that provides valuable information on battery health and degradation. However, one of the main challenges in the BMS domain development is finding accurate and effective algorithms for battery SOH prediction, especially for electric vehicles and grid-connected energy storage systems. This study introduces a new SOH prediction method using wavelet-convolutional neural regression networks (CNRN) algorithms. The methodology involves extracting detailed frequency profiles from Electrochemical Impedance Spectroscopy (EIS) data, which are processed through wavelet transformation to capture both time and frequency domain features. These transformed profiles are then input into the CNRN model for SOH prediction. The results demonstrate improved SOH prediction accuracy with EIS frequency profiles, evidenced by a reduction in root mean square error (RMSE) compared to the standard EIS profile. This improvement is due to the fact that the wavelet-CNRN algorithm efficiently captures both the time and frequency features of the battery impedance. Moreover, the performance of the proposed algorithm demonstrated robustness in early end-of-life (EOL) prediction, thereby enhancing the reliability and safety of BMS functions.

Energy storage battery state of health estimation based on singular value decomposition for noise reduction and improved LSTM neural network

Accurate estimation of the State of Health (SOH) of batteries is important for intelligent battery management in energy storage systems. To solve the problems of poor quality of data features as well as the difficulty of model parameter adjustment, this study proposes a method for estimating the SOH of lithium batteries based on denoising battery health features and an improved Long Short-Term Memory (LSTM) neural network. First, in this study, three health features related to SOH decrease were selected from the battery charge/discharge data, and the singular value decomposition technique was applied to the noise reduction of the features to improve their correlation with the SOH. Then, the whale optimization algorithm is improved using cubic chaotic mapping to enhance its global optimization-seeking capability. Then, the Improved Whale Optimization Algorithm (IWOA) is used to optimize the model parameters of LSTM, and the IWOA-LSTM model is applied to the battery SOH estimation. Finally, the model proposed in this research is validated against the Center for Advanced Life Cycle Engineering (CALCE) battery dataset. The experimental results show that the prediction error of battery SOH by the method proposed in this study is less than 0.96%, and the prediction error is reduced by 49.42% compared to its baseline model. The method presented in the article achieves accurate estimation of the SOH, providing a reference for practical engineering applications.

A Review on Lithium-Ion Battery Modeling from Mechanism-Based and Data-Driven Perspectives

As the low-carbon economy continues to advance, New Energy Vehicles (NEVs) have risen to prominence in the automotive industry. The design and utilization of lithium-ion batteries (LIBs), which are core component of NEVs, are directly related to the safety and range performance of electric vehicles. The requirements for a refined design of lithium-ion battery electrode structures and the intelligent adjustment of charging modes have attracted extensive research from both academia and industry. LIB models can be divided into mechanism-based models and data-driven models; however, the distinctions and connections between these two kinds of models have not been systematically reviewed as yet. Therefore, this work provides an overview and perspectives on LIB modeling from both mechanism-based and data-driven perspectives. Meanwhile, the potential fusion modeling frameworks including mechanism information and a data-driven method are also summarized. An introduction to LIB modeling technologies is presented, along with the current challenges and opportunities. From the mechanism-based perspective of LIB structure design, we further explore how electrode morphology and aging-related side reactions impact battery performance. Furthermore, within the realm of battery operation, the utilization of data-driven models that leverage machine learning techniques to estimate battery health status is investigated. The bottlenecks for the design, state estimation, and operational optimization of LIBs and potential prospects for mechanism-data hybrid modeling are highlighted at the end. This work is expected to assist researchers and engineers in uncovering the potential value of mechanism information and operation data, thereby facilitating the intelligent transformation of the lithium-ion battery industry towards energy conservation and efficiency enhancement.

Research on monitoring and energy management systems for energy storage stations on the power generation side

Abstract Addressing the challenges of limited operational efficiency, inadequate battery safety, inflexible system scalability, inadequate AGC/AVC functionality, and low levels of intelligent operation and maintenance encountered by energy storage power stations integrated with new energy generation sources, this article delves into the pivotal role of these power stations on the generation side. It meticulously examines the network architecture, functional framework, and pivotal technologies underpinning the system. Furthermore, the article proposes a comprehensive monitoring and energy management system tailored specifically for energy storage on the generation side. The system uses micro-service architecture and container technology to realize the processing and storage of massive data. Through complete isolation of the information network and control network and millisecond communication with GOOSE, the charging and discharging response speed of the energy storage station is greatly improved. The power allocation algorithm based on device status recognition completes the system’s high-precision power control of PCS, and this system uses big data analysis and data mining technology to conduct a comprehensive statistical analysis of battery health status, power station operation efficiency, and equipment operation status and energy consumption. The design of the system has favorable technical and application guidance for the subsequent energy management design and engineering application of the energy storage power station.

SOH early prediction of lithium-ion batteries based on voltage interval selection and features fusion

- Accurate state of health (SOH) of batteries is a crucial prerequisite for ensuring the safety and stable operation of electric vehicles. However, existing conventional prediction methods do not consider the influence of early-stage capacity variations on full-cycle SOH with extensive test data. This paper develops a SOH early prediction method of lithium-ion batteries based on voltage interval selection and features fusion. To identify the battery SOH curves with high similarity under identical charge-discharge conditions, a double correlation based early-stage SOH similarity analysis method is presented. To minimize the amount of voltage training data collected during feature extraction, a voltage interval selection method considering sampling time and features correlation is introduced. Meanwhile, a feature fusion method combining entropy weight and correlation factor is used to reduce the impact of redundant health feature information. To address the problems of low accuracy and computational inefficiency using the least squares support vector machine (LSSVM) model, a grey wolf optimizer-LSSVM-adaptive boosting model is developed for battery SOH prediction. The experimental results show that the coefficients of determination remain above 0.98, indicating high SOH prediction accuracy using the developed method. Compared to other methods, the mean absolute errors based on the developed method are maintained below 1.5 %.

State of Health Prediction in Electric Vehicle Batteries Using a Deep Learning Model

Accurately estimating the state of health (SOH) of lithium-ion batteries plays a significant role in the safe operation of electric vehicles. Deep learning (DL)-based approaches for estimating state of health (SOH) have consistently been the focus of study in recent years. In the current era of electric mobility, the utilization of lithium-ion batteries (LIBs) has evolved into a necessity for energy storage. Ensuring the safe operation of EVs requires a precise assessment of the state-of-health (SOH) of LIBs. To estimate battery SOH accurately, this paper employs a deep learning (DL) algorithm to enhance the estimation accuracy of SOH to obtain accurate SOH measurements. This research introduces the Diffusion Convolutional Recurrent Neural Network (DCRNN) with a Support Vector Machine-Recursive Feature Elimination (SVM-RFE) algorithm (DCRNN + SVM-RFE) for enhancing classification and feature selection performance. The data gathered from the dataset were pre-processed using the min–max normalization method. The Center for Advanced Life Cycle Engineering (CALCE) dataset from the University of Maryland was employed to train and evaluate the model. The SVM-RFE algorithm was used for feature selection of pre-processed data. DCRNN algorithm was used for the classification process to enhance prediction precision. The DCRNN + SVM-RFE model’s performance was calculated using Mean Absolute Percentage Error (MAPE), Mean Squared Error (MAE), Mean Squared Error (MSE), and Root MSE (RMSE) metric values. The proposed model generates accurate results for SOH prediction; all RMSEs are within 0.02%, MAEs are within 0.015%, MSEs were within 0.032%, and MAPEs are within 0.41%. The mean values of RMSE, MSE, MAE, and MAPE were 0.014, 0.026, 0.011, and 0.32, respectively. Experiments confirmed that the DCRNN + SVM-RFE model has the highest accuracy among those that predict SOH.

State of Health Estimations for Lithium-Ion Batteries Based on MSCNN

Lithium-ion batteries, essential components in new energy vehicles and energy storage stations, play a crucial role in health-status investigation and ensuring safe operation. To address challenges such as limited estimation accuracy and a weak generalization ability in conventional battery state of health (SOH) estimation methods, this study presents an integrated approach for SOH estimation that incorporates multiple health indicators and utilizes the multi-scale convolutional neural network (MSCNN) model. Initially, the aging characteristics of the battery are comprehensively analyzed, and then the health indicators are extracted from the charging data, including the temperature, time, current, voltage, etc., and the statistical transformation is performed. Subsequently, Pearson’s method is employed to analyze the correlation between these health indicators and identify those with strong correlations. A regression-prediction model based on the MSCNN model is then developed for estimating battery SOH. Finally, validation using a publicly available lithium-ion battery dataset demonstrates that, under similar operating conditions, the mean absolute error (MAE) for SOH estimation is less than 0.67%, the mean absolute percentage error (MAPE) is less than 0.37%, and the root mean square error (RMSE) is less than 0.74%. The MSCNN has good generalization for datasets with different working conditions.

Edge–cloud collaborative estimation lithium-ion battery SOH based on MEWOA-VMD and Transformer

The State of Health (SOH) of lithium-ion batteries significantly impacts the performance, safety, and reliability of the battery, making it a crucial component of the battery management system. Addressing the issues of inadequate accuracy and lack of robustness in current SOH estimation methods, this study introduces a novel methodology for estimating SOH in lithium-ion batteries. It leverages the multi-population evolution whale optimization algorithm optimized variational mode decomposition (MEWOA-VMD) in conjunction with Transformer architecture. This framework enhances the efficiency and accuracy of SOH estimation by leveraging the computational capabilities of edge devices for real-time data processing, as well as the robust data processing power and model training advantages offered by cloud computing. Specifically, MEWOA is utilized to optimize VMD parameters, enabling MEWOA-VMD to fully decompose the capacity signal of lithium-ion batteries. This results in a component showing a global attenuation trend and a set of fluctuating components that represent capacity regeneration, thereby minimizing the impact of capacity regeneration on SOH estimation. Subsequently, all components are collectively input into the Transformer, marking the first application of this method for input. To enhance convergence speed and training efficiency, the layer normalization (LN) layer within the neural network architecture is proactively advanced. Finally, various artificial neural networks are compared and validated on three publicly available datasets. Furthermore, Gaussian noise is introduced into the original data to validate robustness. To confirm the practical applicability of the proposed method, real-world vehicle data is used for SOH estimation. The results indicate that the proposed method achieves a maximum MSE of no more than 0.009% across three publicly available datasets, showcasing improved accuracy and stability in SOH estimation. The practical applicability is further validated using real-world vehicle data, proving the proposed method’s potential for application in edge cloud-based battery management systems.

A novel lithium-ion battery state-of-health estimation method for fast-charging scenarios based on an improved multi-feature extraction and bagging temporal attention network

Accurately estimating the state of health (SOH) of fast-charging lithium-ion batteries is crucial for safely and reliably operating battery systems. However, handling data scarcity and rapid charging scenarios under diverse operational conditions is challenging. In this paper, a novel approach for estimating the SOH of lithium-ion batteries (LIBs) is introduced based on an improved multisegment feature extraction and bagging temporal attention network. First, four health features, including the time differences observed at equal voltages, the cumulative integral of voltage changes, the total circuit charge variation and the levels of slope peaks, are identified. Second, a residual bidirectional long short-term memory (Bi-LSTM) attention mechanism is designed to focus on the temporal dimension of battery data by incorporating a multilayered complex neural network design comprising convolutional layers, pooling layers, Bi-LSTM layers and fully connected layers. This design effectively captures the features and relationships contained in battery data. The predictions derived from randomly initialized parameters and multiple submodels are stacked to improve the generalizability of the model. Finally, comprehensive evaluations are conducted through comparative experiments, ablation studies and noise experiments, with six evaluation metrics considered across three datasets. The MAE, RMSE, MAEP and MAXE of the proposed model reach 0.366, 0.605, 0.519 and 1.56, respectively. The results indicate that the proposed method enhances the robustness, resilience and generalizability of the estimates produced under different conditions and noise scenarios.

A label-free battery state of health estimation method based on adversarial multi-domain adaptation network and relaxation voltage

The state of health (SOH) estimation of lithium-ion batteries is crucial for the operational reliability and safety of electric vehicles. However, traditional data-driven methods face problems of label shortage and domain discrepancy caused by diverse battery types and operating conditions. This paper proposes a label-free SOH estimation method based on adversarial multi-domain adaptation technique and relaxation voltage (RV). Firstly, the raw RV and integral voltage are proposed to construct the two-dimensional input sequence to ensure high adaptability across various target domains. Secondly, a two-dimensional convolutional neural network integrated with fully connected layers is developed to establish the feature extractor and SOH estimator, which paves the way for effective knowledge transfer. Furthermore, an adversarial multi-domain adaptation method with a domain discriminator is developed to optimize the extraction of domain-invariant features and enable accurate SOH estimation without SOH labels. Datasets of 50 batteries with different temperatures and materials are used for the validation. The proposed method shows outstanding performance, achieving the average RMSE and MAE of 0.0274 and 0.0240 across various working temperatures, and 0.0177 and 0.0148 across different battery types. It suggests that the proposed method can achieve robust adaptive battery SOH estimation across multiple target domains without using SOH labels.

State of health estimation for lithium-ion batteries based on multi-scale frequency feature and time domain feature fusion method

Abstract Accurately estimating the state of health (SOH) of lithium-ion batteries is important for improving battery safety performance. The single time-domain feature extraction is hard to efficiently extract discriminative features from strongly nonlinear coupled data, leading to difficulties in accurately estimating the battery SOH. To this end, this paper proposes a multi-scale frequency domain feature and time domain feature fusion method for SOH estimation of lithium-ion batteries based on the Transformer model. Firstly, the voltage, current, temperature and time information of the battery are extracted as time domain features; secondly, the battery signal is processed by a multi-scale filter bank based on Mel-frequency cepstral coefficients (MFCC) to obtain the multi-scale frequency domain features; then, a parallel focusing network (PFN) is designed to fuse the time domain features with the frequency domain features, which yields low-coupling complementary discriminative features; finally, constructing the SOH estimation mechanism based on the Transformer deep network model. The algorithm is validated by NASA and Oxford datasets, the mean's absolute error (MAE) and root mean square error (RMSE) are as low as 0.06% and 0.23%, respectively.