The growing demand for sustainable energy solutions highlights the need to extend the use of lithium-ion batteries (LIBs) in first-life applications (e.g., electric vehicles) or repurpose them for second-life uses like energy storage. However, most existing research primarily focuses on first-life applications, with limited attention to the unique challenges of second-life batteries, where accurate estimation of the State of Health (SOH) at low levels (<80%) becomes increasingly difficult due to nonlinear degradation mechanisms. This study addresses this gap by introducing a machine learning approach leveraging Nonlinear Frequency Response Analysis (NFRA) data for SOH estimation in second-life applications down to 60%. NFRA outperformed traditional Electrochemical Impedance Spectroscopy (EIS), achieving >98% prediction accuracy for second-life batteries, even when trained on first-life data alone, and >96.7% using published datasets. NFRA captures nonlinear responses, such as energy losses linked to Li+ transport and solid-electrolyte interface dynamics, which EIS fails to detect. Two predictive models, Long Short-Term Memory (LSTM) networks and Nonlinear Autoregressive with External Input (NARX), were tested, with LSTM reducing root mean square error (RMSE) by up to 30% compared to NARX. NFRA consistently reduced RMSE by over 39% relative to EIS in second-life phases. These findings establish NFRA as a reliable tool for enhancing SOH predictions, enabling safer, more efficient battery repurposing and extended lifetimes. • Combines NFRA with LSTM and NARX to estimate battery SOH • NFRA detects nonlinear effects (e.g., Li + transport, SEI dynamics) missed by EIS. • LSTM significantly lowers RMSE compared to NARX. • Uses first-life data to predict second-life performance

Frequency response analysis (FRA) is recognized as an effective method in power transformer winding fault diagnosis. However, the traditional numerical index methods focus on the overall features of FRA curves, making it difficult to capture subtle deformations in transformer windings. Similarly, existing digital image processing methods rely on a single feature or a simple feature combination without adaptive fusion. These methods ignore differences in the data distributions of features, leading to feature mismatch, the loss of sensitive fault information, and lower diagnostic accuracy. To solve this problem, a novel adaptive multiple-image-feature fusion method for transformer winding fault diagnosis is proposed. First, a multi-dimensional feature space combining image pixel matrix similarity, morphological features, and image texture features is built to decode the difference in fault of FRA images. Second, the multiple kernel learning (MKL) framework is used to dynamically adjust the fusion weights of different kernels to make features compatible and remove redundant information. Finally, comparative and ablation experiments show that the proposed method outperforms the traditional methods in identifying different types and levels of faults. The method achieves over 99% accuracy in fault type identification across SVM, KNN, and RF classifiers. For radial deformation (RD) severity prediction, the accuracy of the proposed model is 93.37% with SVM and 94.85% with KNN, outperforming the full-feature concatenation method. These results confirm the method’s robustness and diagnostic precision.

Harvesting energy from ambient sound offers a sustainable power solution for distributed sensors and intelligent devices, yet the inherently low energy density of acoustic waves severely limits conversion efficiency. Overcoming this bottleneck requires confining sound with minimal radiation leakage to maximize electromechanical coupling. Here, we introduce a topology-optimized waveguide-resonator structure that exploits bound states in the continuum (BICs) to achieve high-quality acoustic resonance for efficient energy harvesting. The optimized geometry enforces symmetry-protected confinement, resulting in strong pressure localization and amplification at target frequencies while mitigating dissipative loss. Numerical eigenmode and frequency-response analyses demonstrate ultra-narrowband high-Q resonances with dramatically enhanced energy concentration within the optimized cavity-cluster. Experimental validation confirms that the proposed BIC-enabled harvester delivers a substantial increase in output voltage and power density. This work establishes BIC physics as a new paradigm for compact acoustic energy harvesters and offers a generalized design strategy for next-generation self-powered systems requiring high performance at low-frequency excitation.

Abstract This study investigates vibration suppression in quasi-zero stiffness isolators (QZSIs), which, despite their superior low-frequency isolation capability, are highly sensitive to nonlinear effects and prone to resonance amplification and chaotic oscillations that can severely degrade system performance. To address this critical limitation, a nonlinear derivative feedback (NDF) controller is proposed as a cost-effective and robust solution to enhance stability and suppress undesired vibrations. Approximate analytical solutions (AS) are derived using the multiple timescales method (MTSM) and validated against numerical solutions (NS) obtained with the fourth-order Runge–Kutta (RK-4) method. By eliminating secular terms, resonance conditions and stability regions are identified via frequency and resonance response analyses, supported by the Routh–Hurwitz stability criterion. The nonlinear dynamic behavior of the controlled system is further examined using bifurcation diagrams, Lyapunov exponent spectra (LES), Poincaré maps (PMs), and phase portraits to reveal transitions between periodic, quasi-periodic, and chaotic motions. Compared with other control strategies, the proposed NDF controller achieves superior vibration suppression efficiency of up to 99.511% while maintaining a lower implementation cost. The results confirm that NDF control significantly improves the dynamic response, stability, and chaos mitigation of QZSIs, thereby enhancing their reliability in practical applications such as aerospace, infrastructure, healthcare devices, and renewable energy systems. The novelty of this work lies in providing a comprehensive analytical and nonlinear dynamic assessment of NDF-controlled QZSIs offering new insights into resonance suppression and the long-term stability of highly sensitive isolation systems.

Accurately extracting deviation features in frequency response curves, which reflect winding deformation states, and selecting appropriate machine learning algorithms are critical for achieving a precise quantitative diagnosis of winding deformation based on frequency response analysis (FRA). To address the existing challenges in transformer winding fault diagnosis, including the absence of a systematic feature evaluation framework for frequency response data and the limited recognition accuracy of machine learning models, a novel hybrid feature selection and diagnostic framework was developed. First, a high-dimensional feature pool comprising 25 numerical indices was extracted from experimental FRA curves. To eliminate feature redundancy and arbitrary selection, a hybrid mechanism integrating maximum-relevance, minimum-redundancy (mRMR) with random forest (RF) was developed to dynamically construct task-specific optimal feature subsets. Furthermore, an inverse-distance-weighted K-nearest neighbors (IKNN) model was introduced to enhance diagnostic sensitivity by accounting for feature-space distance variations. Experimental results obtained from a laboratory winding model demonstrate that the proposed mRMR-RF-IKNN model significantly outperforms traditional and optimized benchmarks across multiple macro-evaluation metrics. This study provides a systematic, intelligent screening mechanism that ensures high-precision identification of both the types and severity of faults in power transformers.

Modal analysis is a technique used to identify the dynamic properties of structures, such as natural frequencies, vibration modes and damping. This analysis is essential to predict structural behavior under different excitation conditions and to ensure the integrity and safety of projects. Among the instruments that perform modal tests, the impact hammer is generally used, however the commercial models available on the market are expensive, which makes them difficult for educational institutions with limited budget to access. Thus, this work developed an impact hammer designed to measure the excitation impact force in small to medium-sized structures which will also perform modal analysis. The objective was to create an economically viable and more accessible alternative when compared to the equipment available on the market. Furthermore, the project serves as a didactic kit, facilitating the teaching and understanding of the principles related to structural vibration. In order to perform the appropriate measurements, the hammer has a load cell, seismic mass and analog electronics, this allows the measurement of impact forces and perform the frequency response analysis of a body. Additionally, this instrument was developed through machining, which allowed the creation of an internal cavity to house the components. The handle was produced using stainless stell, designed to internally incorporate the electronic circuits for the system to operate. Calibration was performed using Bump Test and based on Newton's Second Law, using the previously determined seismic mass and the acceleration of gravity as a reference. To this end, a device was built that standardizes the acceleration applied to the system, allowing repetitions and controlled impacts. Moreover, in each test, the electrical voltage generated by the compression of the piezoelectric cell was analyzed. The final validation of the system was an experiment in which a clamped steel bar was subjected to impact excitation. The results achieved were satisfactory when compared with the theoretical model of the bar and with data obtained from a commercial instrument, ensuring accuracy with an error of 5%.

Frequency response analysis plays an important role in many applications, allowing for the assessment of a system's vibration response level when subjected to operational loading. This assessment enables the approval or proposal of improvements in the design project, or corrections of systematic failures related to structural performance or damping treatment. In large-scale industrial manufacturing processes, the integration of numerical simulations with experimental validations is widely used, demonstrating efficiency in cost reduction, and minimizing development and reprocessing time. However, oversimplification in constitutive models or uncertainties regarding material properties, constraints, or loading types can lead to divergences between simulated predictions and measured responses, representing a bottleneck in the new product development process. Therefore, the appropriate characterization of each material and component of the system is essential for correctly calibrating the mathematical model used in assessing the frequency response, to ensure accurate predictions of the system's behavior. In the present work, an actual case of a pipeline system composed of a vulcanized rubber hose is studied to enhance the prediction accuracy of the system's response. For modeling the coupled mechanical system, the finite element method is used, utilizing the commercial simulation tool ABAQUS to determine the frequency response function of the transmissibility. This involves applying an excitation force at one end of the pipeline system and measuring the response at the other end. The vulcanized rubber hose is modeled to exhibit viscoelastic behavior. For this purpose, a dynamic mechanical analysis is carried out to obtain the storage modulus and loss factor, both as functions of frequency. Subsequently, a fractional derivative constitutive model for the rubber hose is identified. This numerical model is subjected to validation and calibration through several experimental tests. It is expected that the results will not only ensure accurate predictions for the response of this specific pipeline system but also enable the development of an efficient methodology, which can be systematically applied in processes that involve developing new components and systems of higher complexity.

This article presents two diagnostic techniques for assessing the mechanical and electrical condition of oil-immersed power transformers: sweep frequency response analysis (SFRA) and dissolved gas analysis (DGA). The SFRA method detects potential mechanical faults in transformer windings by applying the correlation coefficient (Rxy). For a 63 MVA, 115/23/11 kV transformer, experimental results show that the winding is considered normal when RLF ≥ 2.0, RMF ≥ 1.0, and RHF ≥ 0.6, whereas RLF &lt; 0.6 indicates severe deformation. In contrast, the DGA method identifies internal faults such as partial discharge, low-energy and high-energy discharges, and thermal faults by analyzing gas concentrations in the insulating oil. For a 20 MVA, 110/22 kV transformer, measured gas concentrations (µl/l, ppm) include H₂ (0.00), CH₄ (40.43), C₂H₆ (18.24), C₂H₄ (20.92), C₂H₂ (0.00), CO₂ (8932.66), and CO (2131.18), corresponding to a “thermal fault below 300°C.” Both diagnostic methods are integrated into user-friendly MATLAB-based tools to support testing centers in Vietnam. The combination of SFRA and DGA enhances diagnostic accuracy, enables timely maintenance decisions, and contributes to improving the reliability of power supply systems.

Isolation tables used in semiconductor factories are generally classified as non-structural elements. However, isolation tables installed for vibration control are integrated with fabrication facility (FAB) structures and can change the natural frequency of the overall system. In this study, a basic FAB lattice structure and a combined model with isolation tables were modeled using ANSYS Workbench. Modal and frequency response analyses showed that the natural frequency of the basic FAB structure (15.644 Hz) changed to 12.75 Hz ~ 19.75 Hz depending on the isolation tables and type of foundation. These results indicate that isolation tables can contribute to the structural behavior of FAB structures and should be considered in the design of vibration-sensitive semiconductor factories.

ABSTRACT The harmonic current and vibration of a converter transformer are effective pieces of information for detecting mechanical faults in the winding. In this paper, the ratio of vibration acceleration to the current squared is defined as the vibration frequency response function (VFRF) of the winding, and then, a novel online vibration frequency response analysis (VFRA) method is constructed. A harmonic load platform is built to simulate the real operating environment of the converter transformer, and it is verified by experimental methods that online VFRA is a simpler and more convenient method for winding mechanical condition detection than offline VFRA. The effects of different factors such as current magnitude and harmonic content on the online VFRA are investigated, and the converter transformer winding mechanical condition is detected by combining the VFRF trace with two numerical indices of Lin's concordance coefficient (LCC) and improved comparative standard deviation (CSD). Laboratory experiments demonstrate that online VFRA has high stability and can effectively diagnose winding looseness faults of different degrees. In contrast to the traditional frequency response analysis (FRA) and short‐circuit impedance (SCI) methods, online VFRA has higher sensitivity and detection capability, and is a better method for online monitoring of the winding mechanical condition.

Electromagnetic and structural dynamic coupling in a two-degree-of-freedom system

Purpose Accurate interpretation of frequency response analysis (FRA) data is crucial for power transformer windings. To address this challenge, this study suggests a new auto-synthesis method to derivate a high-frequency Equivalent Ladder Network Circuit Model (ELNCM) aimed at investigating and interpreting the transformer winding (TRW) characteristics. Design/methodology/approach The precise ELNCM is attained using the transfer function (TF) extracted from the measured FRA data. From where, five winding parameters are recited, mainly, the total ground capacitance Cgeff, the equivalent inductance Leq and capacitance Ceq, the voltage distribution factor α and series capacitance Cs. After that, the precise self and mutual inductances (Ls,Mij) of the proposed ELNCM identification are carried out using artificial intelligence (AI). As the self and mutual inductances cannot be measured directly, this paper presents an AI approach, namely, Logistic Chaotic Archimedes Optimization Algorithm (LCAOA) for improved precision. Findings The physical parameters (Leq,Ceq,Cgeff,α, Cs ) are directly extracted from the FRA data, which is very useful in practical studies. Through the obtained results, actual identification is ensured by faithfully seeing the FRA curves created from TF-AI-ELNCM. Originality/value Going further, unlike previous studies, the proposed method eliminates the need for geometrical data and not necessitate any specific arrangement on the transformer winding. The methodology presented offers substantial practical benefits for transformer winding diagnosis, it eliminates the need for lookup tables or specific configuration models.

This study proposes a vibration reduction design method for electron beam imaging systems based on virtual material modeling. Equivalent anisotropic material properties were introduced to represent complex internal structural layouts. Frequency response analysis was performed over a bandwidth of 0–500 Hz, with excitation forces derived from operational disturbances. Simulation results show that the first resonant peak amplitude was reduced by 46.8%, and the overall vibration energy decreased by 34.1% compared with conventional homogeneous material designs. The approach enables efficient vibration control during early-stage design without increasing structural mass.

To investigate how the relaxation rates (R1, R2) and asymmetry indices (AI), derived from phase-cycled balanced steady-state free precession (pc-bSSFP) data, depend on the orientation of white matter (WM) fiber tracts at different field strengths. Phase-cycled bSSFP data acquired at 3 and 9.4T in the healthy human brain were processed using motion-insensitive rapid configuration relaxometry (MIRACLE) and a frequency response analysis to derive R1, R2, and AI values, respectively. Fractional anisotropy (FA) and fiber-to-field angle (θ) were estimated based on 3T diffusion tensor imaging. The orientation dependence of R1, R2, and AI in WM was characterized using literature model fits as well as Monte Carlo random walk simulations to explore the influence of field strength and susceptibility effects. R2 and AI exhibited a pronounced orientation dependence while the influence of anisotropy on R1 was weaker, but noticeable. The observed anisotropy increased systematically from 3 to 9.4T. Literature models assuming either a susceptibility or a generalized magic angle effect described the R2 and AI anisotropy to a high degree (R2 ≥ 0.99). The calculated partial contributions of susceptibility to R2 anisotropy increased from 24.0%-39.0% at 3T to 77.0%-87.1% at 9.4T. The Monte Carlo simulations were able to reproduce the characteristics of R2 anisotropy, but not its strength. Microstructure-driven relaxation anisotropy considerably affects pc-bSSFP relaxometry, in particular R2. The findings indicate that R2 anisotropy is driven by susceptibility at ultra-high fields whereas additional mechanisms likely contribute at lower field strengths.

A clear understanding of how visual information affects postural sway is crucial for assessing normal balance control and developing diagnostic and rehabilitation methods for balance disorders. However, a quantitative model of sway responses to visual perturbations with improved accuracy is still needed. We used virtual reality to apply rotational visual perturbations (0.04-1 Hz, 2.5°-15°) to 14 healthy adults. Participants were splinted at the knee and hip to ensure the ankle strategy was used. Postural responses, including body angles and ankle torques, were recorded. Initial analysis demonstrated that right-eye dominant subjects showed more coherent body sway responses, possibly related to the higher magnitude of the optical flow in the right half-plane of the visual field. Detailed analysis was therefore focused on eight subjects with large, coherent responses. A detrending method was applied to angles and torques based on the inverse Fourier transform to remove frequencies below the smallest stimuli frequency. Our methodology yielded a model with improved accuracy between the visual input and body angle output, that is, coherence values close to 1. Frequency response analysis revealed a low-pass gain characteristic and a linear phase decrease showing a consistent delay in the system across all amplitudes. A parametric model fitted to the frequency response yielded a delayed, second-order, low-pass transfer function. The transfer function gain decreased with increasing stimulus amplitude, demonstrating a nonlinear response reflecting reduced responsiveness to larger visual amplitudes. In conclusion, this paper provides an experimental and analytical framework to accurately quantify the nonlinear dynamics of postural responses to visual stimuli.NEW & NOTEWORTHY This paper introduces a framework to quantify nonlinear postural responses to visual stimuli. Leg splints constrained movement to enforce ankle strategy. Right-eye dominant subjects showed more coherent responses, possibly related to stronger optical flow in the right half of the visual field. To address nonstationarities, we applied inverse Fourier-based detrending, improving model accuracy. Our methodology achieved a novel nonlinear, delayed, second-order low-pass model with high accuracy, distinguishing it from existing models in the literature.

Transformers are essential power transformation equipment in power systems. Winding deformation is one of the main forms of transformer winding faults, which may cause performance degradation or even overall damage to the equipment. As the commonly used methods for diagnosing winding deformation, frequency response analysis (FRA) has problems such as the reliance on expert experience, insufficient universality for windings of different voltage levels and connection methods, etc. If the equivalent network parameters of the windings are identified based on the frequency response curve, the universality and effectiveness can be fundamentally guaranteed. This paper presents a comprehensive review and classification of domestic and international methods for parameter identification of transformer winding equivalent network based on FRA. It elaborates on the principles of parameter identification, as well as the correlation mechanism between frequency response curves and the equivalent network model of transformer windings. In addition, an evaluation is conducted on the principles, strengths, and key challenges of different algorithmic of parameter identification. Drawing upon existing research cases, practical recommendations are provided for the application of different algorithms. Finally, the challenges currently facing research in transformer winding parameter identification are analyzed, and potential future development trends are discussed.

The dramatic growth in the emerging optical applications, including Lidar, short-range optical communication, and optical integrated sensing and communication (ISAC) calls for high-bandwidth transimpedance amplifiers (TIA) with low noise and low power in advanced CMOS technology nodes. To address the issues of existing TIA design, including the conventional RGC structure and the dual-feedback regulated cascode (RGC) TIA, design with complex feedback paths, i.e., limited bandwidth, extra noise, and high power consumption for enough bandwidth, this paper presents a novel TIA with the following key contributions. A novel RGC structure with cascode-feedback is proposed to increase feedback gain, thereby extending bandwidth and reducing noise. Design strategy of the proposed RGC TIA in a low-power advanced CMOS process is carried out to exploit weak inversion operation to achieve better power efficiency. Frequency response and noise analysis are also conducted to achieve target bandwidth and noise performance. The proposed TIA is designed and simulated in 40 nm CMOS with a target PD capacitance of 0.15 pF, achieving a −3 dB bandwidth of 9.2 GHz and a transimpedance gain of 71 dBΩ. The average input-referred noise current spectral density is 18.3 pA/. Operating at 1.2 V, the core circuits consume only 6.6 mW, excluding the output buffer. Compared with prior RGC TIA designs, the proposed TIA achieves a 7.4×~243× enhancement in figure of merit.

Frequency Response Analysis (FRA) is a well-established technique for the condition monitoring of power transformers. The use of FRA for rotating electrical machines is nowadays a prominent research area. In previous works, the use of FRA for synchronous machine field winding diagnostics has been studied, but some key factors remain uncertain in this application. The moisture content is one of the uncertainty factors that could be envisaged as potentially influential. Therefore, the influence of moisture content on the FRA response of poles of synchronous machines is addressed in this paper. For this purpose, numerous experimental tests have been carried out on an extracted pole of a 40-MVA hydro-generator, with different moisture contents, considering healthy state, ground faults, and interturn faults. The main contribution of this work is to prove that, in contrast to what occurs in ordinary insulation testing, the moisture content does not have a significant influence on the FRA response of the pole, discarding this method for moisture diagnostics. However, this fact makes FRA very interesting for in-situ inspection, as it is independent of the moisture content. This way, it is not required to dry the machine before testing.

ABSTRACT With the increasing trend in the electrification of transportation and renewable energy sources, the reliability of rotating electric machines is becoming crucial, and this has driven active research on identifying new test methods. There has been an increasing interest in evaluating the effectiveness of frequency response analysis for testing rotating machines as it has been proven to be a convenient, noninvasive and versatile test. Active research on evaluating the feasibility of applying frequency response analysis for maintenance testing and quality assurance of rotating machines and components has been performed over the last 7–8 years. The purpose of this article is to provide a summary and critical analysis of the latest research published on the application of frequency response analysis (FRA) to rotating electric machines. The challenges and recommendations for future work are given based on a critical evaluation of the literature to support research and development efforts towards industrial needs.

ABSTRACT This article proposes an innovative analytical method that estimates winding inductances directly from measurable frequency response analysis (FRA) data. The method constructs a polynomial function based on the inverse‐square sum of short‐circuit natural frequencies and equivalent inductance, incorporating a coupling factor that captures the extent of mutual interaction between discs. Unlike earlier numerical and optimisation‐based methods that typically involve a large number of inductance parameters, the proposed approach yields a physically meaningful real positive solution for the coupling factor. The approach offers a practical analytical solution for indirectly measuring the self‐ and mutual inductances of uniform windings, involving the measurement of relevant winding parameters—such as equivalent inductance, short‐circuit natural frequencies and series and shunt capacitances—using frequency response impedance data. The method then estimates self‐ and mutual inductances for uniform windings by solving a generalised polynomial developed for an N ‐section model, enabling the derivation of all windings' inductances. Experimental validation on isolated transformer windings demonstrated strong agreement between measured and estimated FRA curves, with root mean square error (RMSE) values below . These results confirm that the method offers a practical, traceable and accurate measurement‐based solution for inductance estimation, with potential applications in transformer condition assessment and fault diagnosis.