Frequency Response Analysis Research Articles

Efficient Structural Dynamic Analysis Using Condensed Finite Element Matrices and Its Application to a Stiffened Plate

In this study, we propose effective formulations for modal, frequency response, and transient analyses using condensed matrices of the finite element (FE) model. Employing the iterated improved reduced system (IIRS) method, a transformation matrix is defined that condenses the stiffness and inertial effects of nodes to be neglected into nodes of interest. Using this, the condensed mass and stiffness matrices are derived. With these two condensed matrices, a condensed damping matrix is derived using the Rayleigh damping. By considering the condensed matrices in the original structural dynamic formulation based on the global FE matrices, the condensed structural dynamic formulation is derived, and the approximated solutions are calculated from this condensed formulation. To verify the performance of the proposed formulation, we perform a structural dynamic analysis on a stiffened plate, and by comparison with the solutions calculated from the global FE matrices, the proposed formulations have been found to provide highly accurate solutions with an excellent computational efficiency.

Resolving vibro‐acoustics in poroelastic media via a multiscale virtual element method

AbstractWe introduce a novel heterogeneous multi‐scale method for the frequency response analysis of waves propagating in porous domains with a complex micro‐structure. In this, the domain is decomposed onto polygonal coarse elements each clustering its local micro‐structure. The micro‐structure is resolved using the virtual element method hence providing ample flexibility into capturing fine scale heterogeneities of arbitrary polygonal shapes. The upscaling is performed through a set of numerically evaluated multi‐scale basis functions. Rather than evaluating the basis for a broad band set of frequencies, a reduced order modeling approach is opted for. In this, the basis is evaluated for a select subset of frequencies, that is used as a basis for the evaluation of the remaining set through a proper orthogonal decomposition procedure. The solution of the coupled governing equations is then performed at the coarse‐scale at a reduced computational cost. The performance of the method in terms of accuracy and computational efficiency is evaluated through a set of numerical examples for poro‐elastic materials with heterogeneities of various shapes.

Improvement in Inter-Turn Faults Detection in Poles of Synchronous Machines by FRA Grounding Connection

Inter-turn faults are among the most common failures in electrical machines. While Frequency Response Analysis, (FRA) has been extensively used for power transformers diagnosis for the last 40 years. In this conventional, accurate and non-destructive technique for power transformer diagnosis, it is a usual practice to connect the chassis of the FRA test device to the transformer housing, normally grounded. The same practice has been applied for pole diagnosis, although no procedure has yet been established as standard since pole diagnosis using FRA is still an experimental technique. Nevertheless, this paper shows a different approach to diagnose inter-turns faults in poles by isolating the FRA chassis from the iron core. In this way, the capacity to ground has less influence, increasing FRA test sensitivity for inter-turn fault diagnosis. The method has been verified by experimental results in several spare poles belonging to 106 MVA and 40 MVA synchronous hydro-generators and also by two simulation models with both types of connections, grounded and FRA-isolated, achieving positive results.

Data-driven fractional order phase-lead and proportional–integral feedback control strategy with application to a reluctance-actuated compliant micropositioning system

This paper aims to overcome complex dynamic problems such as low damping resonant frequency, resonant point drift, and uncertainty of dynamic model of the large stroke micropositioning stage, based on Maxwell reluctance actuator. A composite control method of data-driven fractional phase-lead proportional-integral feedback controller with series hysteresis compensator is proposed. Firstly, the working principle of the Maxwell reluctance actuator is briefly explained, a large stroke flexure micropositioning system is built, and its motor constant and stiffness characteristics are experimentally measured. Secondly, aiming at the rapid phase drop caused by low damping resonance, a data-driven fractional order phase-lead and proportional-integral feedback controller is designed, and the parameters of the fractional order feedback controller are experimentally adjusted based on the iterative feedback tuning algorithm. And the intrinsic hysteresis nonlinearity of the reluctance actuator is firstly compensated by a Prandtl–Ishlinskii model hysteresis compensator which is always placed in the feedback loop of the control system. Then, the proposed controller is compared with other controllers. The experimental results show that this method has a significant suppression effect on high-frequency noise, and the tracking error is significantly reduced, which proves the effectiveness of this stage and control method. • Based on the Maxwell reluctance actuator, a large stroke flexure micropositioning system is built. • A fractional order phase-lead proportional integral controller is proposed, and the integer order approximation of the controller is completed by using oustaloup approximation method • The data-driven method of iterative feedback tuning is used to obtain the parameters of the fractional order controller. • Through the analysis and comparison of linearity, sensitivity function and open-loop frequency response, the advantages of the proposed controller are fully proved.

Synchronous Salient Poles Fault Localization by SFRA and Fault Diagram Method

Sweep Frequency Response Analysis (SFRA) is an extended and non-invasive technique used for transformer condition assessment. In the last years, its proven sensitivity and ease of testing have generated interest for rotating machine applications. Since SFRA measurements are curves plotted on Bode diagrams, the failures can be detected by comparison between a reference curve (performed at healthy conditions), and a curve obtained after an incident. However, the interpretation of results is a hard task because the usual way of interpreting the results still being by visual inspection, then, extensive knowledge and appropriate experience are required. To solve it, in previous publications, the authors developed a method called “Fault Diagram” to analyze SFRA results based on fitting the measurement with an equivalent three-variable circuit. This paper presents several improvements in the method based on changing the equivalent circuit, the optimization algorithm and the frequency range analyzed. Furthermore, the paper provides experimental results of the method's application in a 40 MVA synchronous machine pole. SFRA results presentation into a 3D plot provide information about the fault type (ground or inter-turn fault), location, number of faulty turns and fault resistance with more defined tendencies than in previous research.

Sensitivity analysis of nonlinear frequency response of defected structures

The computation of the steady-stateresponse of large finite element discretized systems subject to periodic excitations is unfeasible because of excessive run time and memory requirements. One could in principle resort to reduced order models stemming from the high fidelity counterparts, which typically require a solution time orders of magnitude smaller. However, when many simulations are required, as in the case of parametric studies, the overall effort could be still significant and the analysis process could be severely hindered. In this work, we propose a sensitivity approach to assess the influence of model parameters on the nonlinear dynamic response. As opposed to the costly evaluation of reduced order solutions over a range of excitation frequencies and model parameters, the sensitivities of a nominal response allow one to approximate the dynamic response by a simple evaluation of an expansion in the directions spanning the parameter space. Special care must be taken on the closure equation that needs to be appended to the system of equations stemming from the harmonic balance method. We discuss the limitations of the current constant frequency approach and propose an improvement. We demonstrate the merits of the proposed approach on a micro-electro-mechanical system affected by parameterized manufacturing defects. Leveraging from a previous contribution, the nonlinear response and the sensitivities are obtained from a reduced order model which is analytical in the defect parameters. Our procedure is able to deliver accurate probability density functions of quantities of interest (e.g. nonlinear resonance peaks, triple solution bandwidth, etc) against statistical distributions of manufacturing defects at negligible computational cost.

Design and Robust Performance Analysis of Low-Order Approximation of Fractional PID Controller Based on an IABC Algorithm for an Automatic Voltage Regulator System

In this paper, a low-order approximation (LOA) of fractional order PID (FOPID) for an automatic voltage regulator (AVR) based on the modified artificial bee colony (ABC) is proposed. The improved artificial bee colony (IABC) high-order approximation (HOA)-based fractional order PID (IABC/HOA-FOPID) controller, which is distinguished by a significant order approximation and by an integer order transfer function, requires the use of a large number of parameters. To improve the AVR system’s performance in terms of transient and frequency response analysis, the memory capacity of the IABC/HOA-FOPID controller was lowered so that it could fit better in the corrective loop. The new robust controller is named the improved artificial bee colony (IABC) low-order approximation (LOA)-based fractional order PID (IABC/LOA-FOPID). The performance of the proposed IABC/LOA-FOPID controller was compared not only to the original ABC algorithm-tuned PID controller, but also to other controllers tuned by state-of-the-art meta-heuristic algorithms such as the improved whale optimization algorithm (IWOA), particle swarm optimization (PSO), cuckoo search (CS), many optimizing liaisons (MOL), genetic algorithm (GA), local unimodal sampling (LUS), and the tree seed algorithm (TSA). Step response, root locus, frequency response, robustness test, and disturbance rejection abilities are all compared. The simulation results and comparisons with the proposed IABC/LOA-FOPID controller and other existing controllers clearly show that the proposed IABC/LOA-FOPID controller outperforms the optimal PID controllers found by other algorithms in all the aforementioned performance tests.

Diagnosing Disk-Space Variation in Distribution Power Transformer Windings Using Group Method of Data Handling Artificial Neural Networks

Monitoring centers in the smart grid exchange the collected data by sensors and smart meters to monitor the current conditions and performance of electric power components. Distribution Power Transformers (DPTs) have a key role in maintaining the integrity of power flow in the smart grid. Online monitoring of DPTs to detect possible faults can potentially increase the reliability of modern power systems. Mechanical defects of DPTs are the major issues in their proper operation that must be detected in their early stage of occurrence. One of the most effective solutions for diagnosing mechanical defects in DPTs is Frequency Response Analysis (FRA). In this study, an appropriate condition monitoring scheme for DPTs is developed to identify even minor winding defects. Disk-Space Variation (DSV), a common DPT windings fault, is applied to the 20 kV-winding of a 1.6 MVA DPT in various locations and with different severity. Their corresponding frequency responses are then computed, and all four components of the frequency responses, i.e., amplitude, argument, and real and imaginary parts, are evaluated. Different data-driven-based indices are implemented to extract appropriate feature vectors in the preprocessing stage. Group Method of Data Handling (GMDH) Artificial Neural Networks is proposed to assist monitoring centers in interpreting FRA signatures and identifying DPT defects at primary stages. GMDH has a data-dependent structure, which gives high flexibility to modeling nonlinear characteristics of FRA test results with different data sizes. It is demonstrated that the proposed approach is capable of accurately determining the fault location and fault severity. The proposed Artificial Intelligence (AI)-based approach is used to extract essential features from frequency response traces in order to detect the position and degree of Disk-Space Variation (DSV) in the DPT windings. The experimental results verify the effectiveness of the proposed methods in determining the severity and location of DSV defects.

Experimental and numerical vibration analysis of surface mechanical attrition treatment

The surface mechanical attrition treatment creates a nanocrystal layer with improved mechanical properties without changing the surface chemistry. Vibration produces residual stresses in a layer close to the surface by successive impacts on the material surface. Vibration treatments represent a “green” alternative to surface treatments without the use of chemicals and high temperatures. Depending on the operating frequency and amplitude of a particular vibration platform, the most decisive parameter to be controlled for the efficiency of the application is the velocity. Vibration platforms in the SMAT process are ultrasonic and mechanically based platforms. This work presents a vibration platform where velocity is below 1 m/s, which is the lowest operating speed defined in the SMAT process. This work includes both analytical and numerical solutions to the natural frequency values of the vibrating table. The operating conditions were determined by finding the natural frequency values. The amplitude, velocity, and acceleration relations of the vibrating table that will occur during the process were found using the frequency response analysis method. ANSYS and MATLAB were used for numerical and analytical solutions, respectively. Numerical and analytical results were in agreement with the experimental modal analysis.

Non-intrusive frequency response analysis of nonlinear systems with interval uncertainty: A comparative study

This paper investigates the non-intrusive frequency response function (FRF) computation of nonlinear vibration systems subject to interval uncertainty. The arc-length ratio (ALR) method is generalized into non-probabilistic nonlinear problems and the interpolation technique is introduced to adapt the ALR for classic predictor-corrector algorithms. The ALR method is comparatively studied with the polar angle interpolation (PAI), which is another state-of-the-art technique for uncertainty propagation in nonlinear FRFs. Applications of the two techniques to two nonlinear systems, i.e., a dual-rotor with rotor/stator contact and a two degrees-of-freedom system with cubic nonlinearity, are presented. The in-depth case studies reveal the essence of the two methods and their strengths and limitations. It is found that the ALR is a powerful tool for various problems while the PAI may fail in nonlinear systems whose FRFs have extreme curvatures or complex shape structures. However, the PAI can transform the uncertain FRF bands into a traditional frequency sense. As the uncertainty propagation methods constructed in the present study are non-intrusive, they can be conveniently generalized into other nonlinear problems. Thus, the findings and conclusions in this study will guide future research on the dynamic responses of general nonlinear mechanical systems.

Multi-Point Interaction of Partially Conductive Cracks with Sweep Frequency Eddy Currents in Electromagnetic Non-Destructive Evaluation

An investigation of real corrosion cracks that can be partially conductive in electromagnetic non-destructive evaluation using sweep-frequency eddy-current frequency-response analysis is carried out in this study. A new approach incorporating innovative solutions is proposed. The goal was to increase the probability of detection of real corrosion cracks in contrast to the conventional sweep-frequency method that is based on single-point signal detection. The proposed procedure was tested on real material specimens where differential responses were gained from real corrosion cracks. Seven austenitic steel plate specimens having corrosion cracks were inspected. Eddy-current responses due to the material cracks were sensed, while a multi-point approach was used for this purpose. The presented unique results clearly showed that the detection ability of a fixed probe driven with sweep-frequency excitation signal could be increased when the multi-point detection is used, and the gained signals are further mathematically processed.

Forced Frequency Response Analysis of a Gudgeon Pin

In this study, forced frequency response analysis was applied on the gudgeon pin. Ansys Mechanical 19.2 program was used to analyze the vibration on the gudgeon pin. Once completed in the finite element analysis, a note from the modal results, the model's natural frequencies range from 38721 to 79346 Hertz for the first 12 modes. According to the modal analysis results, the gudgeon pin will not be subjected to resonance during working. Therefore, a frequency scan including modal analysis is required to detect resonant frequencies that may coincide with the natural frequencies of the first 12 modes obtained in modal analysis. Consequently, harmonic analysis has been solved using the mode superposition method with 50 intervals with 1000 Hz steps in the range of 30000-80000 Hz. To dampen the resonant frequencies, harmonic analyzes were repeated using six different constant damping ratios, and the results were compared.

Forced Periodic Operation of Methanol Synthesis in an Isothermal Gradientless Reactor

AbstractMethanol synthesis from synthesis gas with heterogeneous Cu/ZnO/Al2O3 catalysts in an isothermal gradientless reactor is described. In a theoretical study, the potential of forced periodic operation (FPO) for improving reactor performance in terms of methanol production rate and methanol yield is explored. The approach is based on a detailed kinetic model and combines nonlinear frequency response (NFR) analysis with rigorous numerical multi‐objective optimization. Optimal steady‐state operation is compared with optimal forced periodic operation for a given benchmark problem with and without inert nitrogen in the feed. Further, the significant influence of the saturation capacity of the solid phase on the dynamic behavior in response to step changes and periodic input modulations is studied.

WITHDRAWN: Design of a probe-type acoustic tweezer by acoustic-streaming field optimization

• The evaluation criteria of acoustic-streaming field optimization are proposed. • The optimized capture condition is concluded by finite element analysis. • Ultrasonic vibration device for optimized capture vibration parameter is designed. • The probe-type acoustic tweezer can capture, translate and release objects. This paper presents a novel design process of a probe-type acoustic tweezer for micro/nano manipulation. The qualitative evaluation criteria of manipulation-oriented acoustic-streaming field are proposed, and the optimized capture condition is concluded by finite element optimization accordingly for the first time. The scheme of ultrasonic vibration device for optimized capture condition is proposed, which is composed of two parallel-connected sandwich piezoelectric transducers. Initial structural parameters of the vibration device are determined by an analytical model based on the electromechanical equivalent theory, and it is further optimized using finite element method. Dynamic performances of the vibration device are then analyzed through modal analysis and frequency response analysis. A prototyped vibration device is fabricated and experimental investigations are conducted to further test its characteristics. The results show that the device can vibrate with the optimized capture condition. The experimental setup of the probe-type acoustic tweezer system is established, and it is proven that it can successfully capture, translate and release nanowires. Graphical Abstract. .

Diagnosis of Power Transformer Winding Deformation Based on Centroid Analysis of 3D Frequency Response Curve

Background: As the frequency of transformer winding faults becomes higher and higher, the frequency response analysis used to detect the winding status has attracted more and more attention. At present, there is still a lack of reliable and intelligent technologies for detecting the state of transformer windings in this field. Methods: In this paper, a transformer winding deformation diagnosis method based on centroid analysis of 3D frequency response curve is proposed. A 3D coordinate system is established with frequency, amplitude, and phase as the x, y, and z, respectively. The proposed method calculates the centroid of each 3D frequency response curve through an algorithm, and establishes a 3D coordinate system with the centroid of the normal winding 3D frequency response curve as the origin. The deviation distance and deviation angle between the centroid of mass of the 3D frequency response curve of the faulty winding in different frequency bands and the centroid of the 3D frequency response curve of the normal winding and the correlation coefficient of the traditional Frequency Response Analysis (FRA) curve. are calculated. The deviation distance and angle of the centroid and the correlation coefficient of the calculated frequency band are input as features into the Support Vector Machine (SVM) for intelligent diagnosis to achieve fault classification and optimizing its parameters with three optimization algorithms respectively. Results: The fault classification is realized by analyzing the distribution intervals of the centroids of the 3D frequency response curves of the three simulated faults. The accuracy of fault diagnosis using the 3D frequency response curve feature is significantly higher than the accuracy when using the traditional FRA curve feature and it proves the effectiveness of the proposed method. Conclusion: The proposed model can effectively identify different fault types and the diagnostic rate of the fault type is 100%.

A proper generalized decomposition-based harmonic balance method with arc-length continuation for nonlinear frequency response analysis

The objective of this study is to incorporate the proper generalized decomposition (PGD) into the harmonic balance method (HBM) for an efficient numerical continuation of nonlinear frequency response. PGD utilizes the low-dimensional subspaces of the HBM response, approximating the solution as a low-rank separated representation of spatial and harmonic components. The progressive Galerkin approach is employed to formulate subproblems for each component, and the solution is built on the fly without prior assumption or computation of nonlinear response characteristics. During the numerical continuation, the spatial modes obtained at the previous computation are utilized as a reduced basis, and arc-length constraint is applied to follow the proper path of the frequency response curve. Numerical studies demonstrate that the proposed method allows significant computational savings compared to HBM, while accurately reflecting the nonlinear behavior.

Capacitive energy storage from single pore to porous electrode identified by frequency response analysis

Rate capability, peak power, and energy density are of vital importance for the capacitive energy storage (CES) of electrochemical energy devices. The frequency response analysis (FRA) is regarded as an efficient tool in studying the CES. In the present work, a bi-scale impedance transmission line model (TLM) is firstly developed for a single pore to a porous electrode. Not only the TLM of the single pore is re-parameterized but also the particle packing compactness is defined in the bi-scale. Subsequently, the CES properties are identified by FRA, focused on rate capability vs. characteristic frequency, peak power vs. equivalent series resistance, and energy density vs. low frequency limiting capacitance for a single pore to a porous electrode. Based on these relationships, the CES properties are numerically simulated and theoretically predicted for a single pore to a porous electrode in terms of intra-particle pore length, intra-particle pore diameter, inter-particle pore diameter, electrolyte conductivity, interfacial capacitance & exponent factor, electrode thickness, electrode apparent surface area, and particle packing compactness. Finally, the experimental diagnosis of four supercapacitors (SCs) with different electrode thicknesses is conducted for validating the bi-scale TLM and gaining an insight into the CES properties for a porous electrode to a single pore. The calculating results suggest, to some extent, the inter-particle pore plays a more critical role than the intra-particle pore in the CES properties such as the rate capability and the peak power density for a single pore to a porous electrode. Hence, in order to design a better porous electrode, more attention should be given to the inter-particle pore.

Analytical Model for Transverse Vibrations of Spinning Membranes

Spinning membrane structures are of benefit to space applications because they can be deployed without such mass resources as booms. On the other hand, the lack of supporting structures can lead to undesirable deformations that are dominated by a complex partial differential equation. In this paper, an analytical description for transverse vibrations of spinning membranes is presented. It is shown that the eigenfunctions can be written using the Zernike polynomials; in the presented framework, however, a more practical representation that focuses on the physical characteristics of the vibrations is developed. Furthermore, response to external forces, or controls, is formulated by introducing an extended form of an impulse response function (IRF) that includes spatial information in addition to time information. The deformation under arbitrary forces can be calculated through a convolution integral with the extended IRF. Moreover, the Fourier transform of the IRF gives the frequency response function, which can be useful in designing a vibration control system. To verify the validity of the developed model, the analytical solution is compared to the numerical solution in the finite element analysis. Results demonstrate that both solutions agree in the modal analysis, frequency response analysis, and transient response analysis.

Comparison of L-Shaped and U-Shaped Beams in Bidirectional Piezoelectric Vibration Energy Harvesting.

The traditional single degree of freedom linear piezoelectric vibration energy harvester (PVEH), such as the cantilever type, mainly works and resonates in a single direction and at a single frequency. To adapt broadband and bidirectional ambient vibration, this paper designs and compares two PVEHs of L-shaped beam and U-shaped beam through COMSOL simulation and prototype test. FEA modeling is introduced for accurate structure design with modal analysis, voltage frequency response analysis, and proof mass analysis with multiphysics electromechanical coupling simulation. Two PVEH prototypes with different gravity angles and clamping angles are tested at 0.1 g acceleration to find the optimal angle for maximum output power. The best clamping angle of L-PVEH is 135° with RMS power of 0.3 mW at 7.9 Hz, and that of U-PVEH is 45° with RMS power of 0.4 mW at 5.0 Hz. The proposed U-PVEH shows more advantages in low broadband and bidirectional vibration energy harvesting.

Data‐Driven Tuning for Two‐Degree‐of Freedom Control Using Initial Control Signals and Initial Controller Parameters

A new data‐driven approach based on initial controller parameters and initial experimental data was proposed to tune a controller such that the response of the closed‐loop and open‐loop systems are close to the desired control response. This method is called virtual internal model tuning (VIMT). In VIMT, one‐shot closed‐loop output data are required. Practically, there are cases where it is important to focus on the input rather than on the output. This study extends VIMT to the case where only one‐shot input data and initial controller parameters are obtained through closed‐loop experiments. Furthermore, we discuss the advantage of the proposed method compared to the conventional VIMT via frequency response analysis of weight function. In this study, I investigated the control performance of the proposed methods through experimental verification. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC.