Linear Frequency Domain Analysis Research Articles

High-Performance Attitude Control Design of Supersonic Tailless Aircraft: A Cascaded Disturbance Rejection Approach

This paper focuses on the triaxial augmentation ability of the active disturbance rejection control (ADRC) technique on the tailless layout with a fully moving wing tip to achieve high control performance for the supersonic tailless aircraft. Firstly, the stability characteristics and controllability of the flying wing layout are analyzed to determine the coupling characteristics of this kind of aircraft. Secondly, an attitude controller is designed based on ADRC theory, and the linear ADRC frequency domain analysis method is introduced to analyze the influence of the bandwidth of linear extended stator on the control system. In addition, the tuning process of the attitude control law is given. Carrier dropping simulations of flight missions under nominal condition, model parameter perturbation, and wind disturbance are conducted. The results show that the designed controller can achieve full-speed domain triaxial augmentation of supersonic flying wing. This work has the potential to significantly boost the engineering acceptability and robustness of supersonic aircraft control design in real-world scenarios. The presented cascaded ADRC approach can significantly improve the performance and robustness of supersonic vehicles.

Wind induced dynamic response and fatigue assessment – Nonlinear time domain versus linear stochastic analysis

By performing the nonlinear dynamic analysis and calculating the wind induced fatigue damage, this paper compares the fatigue calculation results with that obtained from a linear stochastic dynamic analysis in frequency domain. It is noticed that, since linear frequency domain analysis often involves a linearization of relevant non-linear load effects, associated with non-linear drag, coherence of wind loading in space, large deformation and local plasticity development, into the linear solution of dynamic equilibrium equations, and also because the power spectrum of critical stress (quasi-static and dynamic) due to wind loading may not be narrow-banded, initiated by the influence of the background components of incident turbulence, across wind-induced vibrations, wind directional effects and structural damping and so on, the inappropriate use of the linear spectral method developed for Gaussian processes can mis-predict the dynamic response, leading to a significant bias in the fatigue damage assessment. It is found that the disadvantages of the linear method aforementioned have to be compromised by additional assumption of uncertainties implemented in calculating dynamic response, often resulting in an over-conservative evaluation in fatigue damage estimation. The wind induced fatigue calculation procedure using non-linear dynamic analysis can be widely adopted for various types of structures, which can significantly reduce the uncertainties without compromising the safety requirement.

Thermoacoustics and combustion instability analysis for multi-burner combustors

This paper presents a low-order thermoacoustic model for multi-burner combustors and proposes a control theoretic approach to linear combustion instability analysis in frequency domain, taking acoustic and flame interaction effects among burners into account under a non-zero mean flow condition. Our thermoacoustic model can deal with can-annular and annular combustors in a unified way and is given as a multi-input multi-output transfer function matrix from heat fluctuation input vector to velocity fluctuation output vector. We also propose a flame transfer function matrix description where off-diagonal components describe the effects of a local acoustic field of one burner location on the flame response at another burner location. The discrete rotational symmetry of burner arrangement in a combustor makes it possible to diagonalize both the aforementioned thermoacoustic and flame transfer function matrices analytically from a spatial discrete-time Fourier transformation. The decoupled thermoacoustic transfer function matrix provides a characterization of acoustic resonances, particularly the longitudinal-azimuthal coupled modes unique to multi-burner combustors. In addition, from the Bloch wave interpretation, we find general patterns in the mode shape of a multi-burner combustor and its relations to the mode shape of a single-burner combustor. Furthermore, from a diagonalized closed loop transfer function matrix, a simple combustion instability condition for a multi-burner combustor is developed. This stability condition shows how a single-burner combustor and a multi-burner combustor are different quantitatively, when it comes to combustion instability. Numerical examples are presented to validate our thermoacoustic model against three-dimensional FEM results, and to illustrate our developments and findings.

Rear-Steering Based Decentralized Control of Four-Wheel Steering Vehicle

In order to improve the lateral and directional performance of vehicles, this paper proposes a novel rear-steering based decentralized control (RDC) algorithm for four-wheel-steering (4WS) vehicles. Based on a linearized single-track vehicle model, a prototype of the RDC algorithm for linear conditions is derived. Linear analysis in frequency domain shows that the RDC can significantly reduce the magnitude and increase the phase lag of sideslip response as well as enlarge the bandwidth of yaw response in a broad frequency range. Through the incorporation of a novel sliding mode controller, the RDC algorithm is further extended for nonlinear applications. Analysis based on nonlinear model shows that, the RDC can guarantee the performance of the closed-loop (CL) system in the presence of uncertainties in system parameters and state feedback values. Moreover, the RDC is robust to arbitrary lateral disturbances and can guarantee that the vehicle converges to reference yaw rate and zero sideslip. Simulation results show that the RDC can effectively improve the lateral and directional performance of the vehicle in comparison with previous control methods. Excellent robustness to external disturbance and road friction variation is reported as well.

Influences of earthquake input models on nonlinear seismic performances of minaret-foundation-soil interaction systems

Minarets, which are tall and slender structures, are important elements of mosques. Seismic performances of minarets can be strongly affected by the nonlinear dynamic soil-structure interaction and earthquake input mechanism models. The present paper investigates the influences of different earthquake input mechanism models on the nonlinear seismic performances of tall and slender minarets considering nonlinearity of both soil and structure behaviors. Three different minaret types constructed with concrete, masonry brick and stone materials are selected for the applications. Direct soil-structure interaction (SSI) approach is taken into account in the 3D finite element models of the minaret-foundation-soil interaction systems. Tie contact between the soil and foundation interfaces and infinite elements on the far sides of the soil domain are utilized in the 3D models. Nonlinear behaviors of masonry and concrete units, and homogenous soil domain are modeled using Concrete Damage Plasticity (CDP) and Mohr-Coulomb failure criteria. The standard rigid-base free, massless-foundation free, massed-foundation free and massed-foundation deconvolved earthquake input models are considered in the nonlinear seismic analyses. Three different earthquake records are selected for the nonlinear analyses and they are matched to the target response spectrum with return period of 475 years. The deconvolved ground motions at the rigid half-space bedrock are calculated from the matched records using the equivalent linear frequency domain analyses. Frequency and mode shapes, displacements, drift ratios, tensile strain and stress propagation patterns and damage ratios of brick, stone and concrete minaret models subjected to combined horizontal and vertical ground motions are determined for four earthquake input mechanism models and compared with each other.

Abstract P399: The Relationship Between Heart Rate Variability and Common Carotid Artery Intima-media Thickness. The ELSA-Brasil

Background: Both conditions as a more width common carotid artery intima-media thickness (cIMT), and a low heart rate variability (HRV) have been associated with cardiovascular health-adverse outcomes. Although previous studies have somehow explored the relationship between these markers, they have not credited the influences exerted by factors such as aging, demographics, and lifestyle variables. Aim: to investigate whether cardio autonomic alterations are accompanied or not by subclinical atherosclerosis, in apparently healthy men and women aged 35 to 74 years-old examined at the baseline of the Brazilian Longitudinal Study of Adult Health (ELSA-Brasil). Methods: The Heart Rate Variability was evaluated on 5-min segments of beat-to-beat heart rate recordings using linear time and frequency domain analyses. The c-IMT images were performed using a Toshiba (Aplio XG™) with a 7.5 MHz linear transducer. The c-IMT was measured in the outer wall during three cardiac cycles. The images were analyzed with specific software (MIA™, Coralville, IA). For this study, c-IMT was defined as the average between the mean left and mean right c-IMT values, and it was analyzed as a continuous and categorized variable (P<75 or P >= 75). Multiple linear models using continuous variables and multivariate logistic regression with categorized cIMT and HRV quartiles were performed. Results: Out of 7,201 participants eligible for analyses, 1,685 (23.4%) presented cIM >= 75th percentile. We found significantly reduced HRV variables in subjects with cIMT>=P75 in comparison to those with cIMT<P75: standard deviation of NN interval (SDNN) 33.0 ms vs. 37.0ms( P< 0.001); root of the mean of the sum of the squares of differences between adjacent NN intervals (RMSSD) 22.0 ms vs. 26.0ms (P< 0.001); Low-Frequency 191.0ms 2 vs. 260.0ms 2 ( P< 0.001); High-Frequency 164.0 ms 2 vs. 238.5ms 2 ( P< 0.001). In a crude analysis, an increased Odds Ratio (OR)and 95% Confidence Intervals for cIMT >=P75 was verified within the lowest two quartiles of Low-Frequency:1st quartile, OR = 1.75 (95%CI: 1.39 to 2.19); 2nd quartile, OR= 1.53 (1.25 to 1.87).The same was observed for High-Frequency:1st quartile, OR = 1.94 (1.38 to 2.73); 2nd quartile, OR= 1.60 (1.20 to 2.15). However, those associations did not remain after adjustments for anthropometric and clinical variables for Low-Frequency (1st quartile, OR= 1.08 (0.83 to 1.40); 2nd quartile, OR= 1.22 (0.97 to1.55), and for High Frequency, 1st quartile, OR= 1.16 (0.77 to 1.73); 2nd quartile, OR= 1.17 (0.83 to 1.64). Conclusions: Subjects with cIMT greater or equal to 75th percentile presented lower HRV values. However, no independent relationships were detected between cIMT and HRV after multivariate adjustment, suggesting that they may assess different and complementary domains and provide relevant, useful, and non-redundant information of cardiovascular risk.

Relationship between heart rate variability and carotid intima-media thickness in the Brazilian Longitudinal Study of Adult Health - ELSA-Brasil.

Both increased carotid intima-media thickness (cIMT) and low heart rate variability (HRV) have been associated with cardiovascular mortality and morbidity. Thus, the aim of this study was to investigate whether cardio autonomic alterations are accompanied or not by subclinical atherosclerosis in participants of the Brazilian Longitudinal Study of Adult Health (ELSA-Brasil). cIMT measures and 5-min HRV analyses were performed in apparently healthy adults. Heart rate variability was evaluated by linear time and frequency domain analyses. cIMT was defined as the average between the mean left and mean right cIMT values and was analysed as continuous and categorized variables (P≥75 or P<75). Multiple linear models using continuous variables and multivariate logistic regression with categorized cIMT and HRV quartiles were performed. Out of 7256 participants eligible for analyses, 23·4% presented cIMT≥75th percentile. Heart rate variability variables were reduced in cIMT≥P75 in comparison with cIMT<P75: SDNN 33·0 versus 37·0ms, P<0·001; RMSSD 22·0 versus 26·0ms, P<0·001; LF 191·0 versus 260·0ms2 , P<0·001; HF 164·0 versus 238·5ms2 , P<0·001. In crude analysis, an increased odds ratio for cIMT≥P75 was verified within the lowest two quartiles of LF and HF, but significances did not remain after adjustments for anthropometric and clinical variables. Considering the entire sample, subjects with cIMT≥P75 presented lower HRV values, but no independent relationships were detected between cIMT and HRV after multivariate adjustment.

Abstract P357: Subclinical Hypothyroidism Alters Autonomous Nervous System. The Brazilian Longitudinal Study of Adult Health (ELSA-Brasil)

Introduction: Lifetime stressful conditions have been related to a higher risk of coronary heart diseases events. One recognized way is related to the disbalance of a parasympathetic and sympathetic system that can be mediated by several humoral factors, including thyroid hormones. Although the role of thyroid hormones on cardiovascular system regulation on the autonomous nervous system was very well-defined decades ago for normal conditions and there is scarce information concern to the association between subclinical thyroid disorders and the autonomous nervous system. Hypothesis: Subclinical thyroid dysfunctions are associated with autonomic disturbances assessed by the heart rate variability evaluated by linear and nonlinear variables following postural changes. Methods: At baseline of the ELSA-Brasil study (15105 adults aged 35-74 years old), we evaluated the heart variability rate at the supine position for everyone, and sampled 855 participants to repeat a standing measure of the heart rate variability. Subclinical hypothyroidism was defined as thyroid-stimulating hormone &gt;4 IU/ml for people with normal free-thyroxine levels. The cardiac autonomic nervous function was evaluated by linear time and frequency domain analyses (standard deviation of consecutive RRi - SDNN; root mean square of successive differences between adjacent regular R-R intervals - RMSSD; low frequency - LF; high frequency - HF; LF/HF ratio) as well as by nonlinear symbolic dynamics (patterns with no variation - “0V”; patterns with one variation - “1V”; patterns with two variations - 2V). Results: After exclusions, 666 (93.8%) euthyroid and 44 (6.2%) participants with subclinical hypothyroidism were eligible for analyses. At the baseline, supine rest measurement, the “0V” symbolic pattern, which reflects sympathetic modulation, was higher (31.8 vs. 24.2; P= .01) and “2V”, representing parasympathetic activity, was lower than in the euthyroid group (18.0 vs. 25.3; P= .02). Comparing the variation between positions, the “0V” pattern showed a lower delta in subclinical hypothyroidism than in euthyroid subjects (6.8 vs. 14.2%; P= .04). Additionally, it is suggested that a symbolic analysis of heart rate dynamics is an alternative and, possibly, a more sensitive method for cardiac autonomic assessment following standing position in this population. Conclusion: Subclinical hypothyroidism presented lower sympathetic and parasympathetic tonus at rest and a blunted sympathetic response to active postural change, marked by reduced variation in the “0V” of symbolic analysis.

Finite water depth effects on the performance of a wave farm

The present paper focuses on the numerical investigation and the assessment of finite water depth effects on the performance (hydrodynamic behavior and energy absorption) of a wave farm. The farm consists of nine, free floating, mutually interacting, heaving Wave Energy Converters (WECs), arranged in a 3 × 3 rectilinear grid. The WECs' Power Taking Off (PTO) mechanism, actuated from their heave motion, is modelled as a linear damping system. Linear frequency domain analysis is implemented under the action of head regular and irregular waves, while three different installation depths are examined. For defining the PTO's damping coefficient, the water depth effect on the heave radiation damping coefficient is considered. Moreover, in the case of irregular waves, an incident wave spectrum with finite depth spectral formulation (TMA spectrum) is deployed for taking into account limited water depth conditions. Constructive and destructive interactions among the WECs in terms of power absorption are appropriately quantified, and the water depth effects on the existence and the extent of these interactions are assessed. The results of the present study illustrate that water depth effects are pronounced in the case of irregular waves, where the water depth's decrease leads to a significant decrease in the WECs' response and the farm's absorbed power, especially for the smallest examined installation depth. However, the comparison of absorbed power losses with power resource losses demonstrates that although the farm's installation at smaller water depth results in significant power resource losses, the farm's capture efficiency is not so intensively reduced.

Recovery of heart rate variability after treadmill exercise analyzed by lagged Poincaré plot and spectral characteristics.

The aim of this study was to analyze the recovery of heart rate variability (HRV) after treadmill exercise and to investigate the autonomic nervous system response after exercise. Frequency domain indices, i.e., LF(ms2), HF(ms2), LF(n.u.), HF(n.u.) and LF/HF, and lagged Poincaré plot width (SD1 m ) and length (SD2 m ) were introduced for comparison between the baseline period (Pre-E) before treadmill running and two periods after treadmill running (Post-E1 and Post-E2). The correlations between lagged Poincaré plot indices and frequency domain indices were applied to reveal the long-range correlation between linear and nonlinear indices during the recovery of HRV. The results suggested entirely attenuated autonomic nervous activity to the heart following the treadmill exercise. After the treadmill running, the sympathetic nerves achieved dominance and the parasympathetic activity was suppressed, which lasted for more than 4min. The correlation coefficients between lagged Poincaré plot indices and spectral power indices could separate not only Pre-E and two sessions after the treadmill running, but also the two sessions in recovery periods, i.e., Post-E1 and Post-E2. Lagged Poincaré plot as an innovative nonlinear method showed a better performance over linear frequency domain analysis and conventional nonlinear Poincaré plot.

Power performance and dynamic response of the WLC wave energy converter based on hydroelastic analysis

In the present paper, a novel Wave Energy Converter (WEC) named hereafter as Water Level Carpet (WLC) is introduced. Its dynamic response and performance are evaluated based on hydroelastic analysis and are presented for both regular and irregular waves. WLC consists of four floating modules inter-connected flexibly in two directions with hinges and Power Take-Off (PTO) mechanisms with known damping characteristics. The dynamic response (e.g. axial load at hinges, motions) and the estimation of the produced power of the WLC are evaluated through linear hydroelastic analysis in frequency domain with the use of a radiation/diffraction 3D hydroelastic model considering the effect of both the flexibility of the WLC as well as the damping forces associated with the energy extraction by the PTO mechanisms. The results that are obtained demonstrate the relationship between the produced power and the dynamic response of the WLC as well as the relationship between the damping coefficients of the PTO with the axial loads of WLC’s hinges. The produced power of WLC obtains its maximum value for wave frequencies close to the resonance of the generalized degrees of freedom irrespectively of the direction that the waves have. Moreover, the results that are obtained emphasize the importance of the hydroelastic analysis for the assessment of the performance of this type of WEC.

Rotor-state feedback control design to improve helicopter turbulence alleviation in hover

A helicopter flight control system with rotor-state feedback to improve turbulence alleviation in hover is presented. First, a flight dynamic model coupled with turbulence model is developed and validated. Then, an integrated control strategy with a rotor-state feedback control law is proposed based on the baseline control system. The feedback gains of body and rotor states are designed in synergy to improve turbulence alleviation in the interested frequency range of handling qualities. Subsequently, the effects of the rotor-state feedback gains on both the stability of rotor dynamics and helicopter turbulence alleviation are analyzed in detail. Finally, the effectiveness of the integrated control system is evaluated with linear analysis in frequency domain and nonlinear simulation in time domain. The results indicate that with the rotor-state feedback control law integrated into the control system, the helicopter turbulence alleviation in the interested frequency range is improved with less degradation in helicopter stability margins, and the roll and pitch rate responses of helicopter to turbulence, measured with Root-Mean-Square (RMS) values, are reduced by more than 50% and 35% respectively.

Development of a nearshore oscillating surge wave energy converter with variable geometry

This paper presents an analysis of a novel wave energy converter concept that combines an oscillating surge wave energy converter (OSWEC) with control surfaces. The control surfaces allow for a variable device geometry that enables the hydrodynamic properties to be adapted with respect to structural loading, absorption range and power-take-off capability. The device geometry is adjusted on a sea state-to-sea state time scale and combined with wave-to-wave manipulation of the power take-off (PTO) to provide greater control over the capture efficiency, capacity factor, and design loads. This work begins with a sensitivity study of the hydrodynamic coefficients with respect to device width, support structure thickness, and geometry. A linear frequency domain analysis is used to evaluate device performance in terms of absorbed power, foundation loads, and PTO torque. Previous OSWEC studies included nonlinear hydrodynamics, in response a nonlinear model that includes a quadratic viscous damping torque that was linearized via the Lorentz linearization. Inclusion of the quadratic viscous torque led to construction of an optimization problem that incorporated motion and PTO constraints. Results from this study found that, when transitioning from moderate-to-large sea states the novel OSWEC was capable of reducing structural loads while providing a near constant power output.

Time Domain Analysis on Deck Wetness of a Caisson Wet-towed in Irregular Waves

A numerical analysis on deck wetness is carried out for a large caisson directly wet-towed by tugs in irregular waves. A constant panel method is used for linear analysis in frequency domain and a statistical post-processing for the deck wetness is presented. Hydrodynamic coefficients obtained from the frequency domain computation are imported for time domain analysis which enables complete modeling for towing equipment, environment, etc. Both frequency and time domain computations over two sea states are performed and comparison is made. In the time domain analysis, towing systems of various arrangements of tugs are investigated from short-term prediction for the largest deck wetness and the number of occurrences of deck wetness.

PRESENTING A NEW METHOD FOR IDENTIFYING FAULT LOCATION IN MICROGRIDS, USING HARMONIC IMPEDANCE

Microgrid presents an efficient and novel solution for integrating many new energy generating resources with traditional distribution networks. Having an appropriate protective scheme is a fundamental challenge in achieving microgrid plans. It is proven that traditional protective plans are not efficient for protecting microgrid, since the network is dynamic and the level of fault current changes continually. Accordingly, this paper presents a novel method to detect fault in microgrids. Presented plan of this paper is based on calculating harmonic impedance. Harmonic impedance can be calculated using linear analysis in frequency domain. Generally, in this plan, communicative equipment is applied to monitor the network, and a Supervisory Remote Control Unit is used for calculations and commanding. Using this controller, the proposed method would be able to use online calculation for fault detection and unlike studies which use offline data, the proposed method is not limited to a special structure. Using the proposed method, different type of faults, especially high impedance faults, are detectable and locatable. Consequently, the presented method provides many features for protective system such as selectivity and also ability to detect symmetrical, asymmetrical, and high impedance faults. In addition, fault detecting is independent from microgrid control system and hence reliability and flexibility of protection and control system increased. The presented method is applied to IEEE 14 buses test network. The obtained results are reported and discussed.

Time and frequency domain analyses of the Hualien Large-Scale Seismic Test

In the nuclear industry, the equivalent-linear frequency domain analysis method has been the de facto standard procedure primarily due to the method's computational efficiency. This study explores the feasibility of applying the nonlinear time domain analysis method for the soil–structure-interaction analysis of nuclear power facilities. As a first step, the equivalency of the time and frequency domain analysis methods is verified through a site response analysis of one-dimensional soil, a dynamic impedance analysis of soil–foundation system, and a seismic response analysis of the entire soil–structure system. For the verifications, an idealized elastic soil–structure system is used to minimize variables in the comparison of the two methods. Then, the verified analysis methods are used to develop time and frequency domain models of Hualien Large-Scale Seismic Test. The predicted structural responses are compared against field measurements. The models are also analyzed with an amplified ground motion to evaluate discrepancies of the time and frequency domain analysis methods when the soil–structure system behaves beyond the elastic range. The analysis results show that the equivalent-linear frequency domain analysis method amplifies certain frequency bands and tends to result in higher structural acceleration than the nonlinear time domain analysis method. A comparison with field measurements shows that the nonlinear time domain analysis method better captures the frequency distribution of recorded structural responses than the frequency domain analysis method. However, the time domain analysis method requires significantly larger modeling efforts and computing time than the equivalent linear frequency domain analysis method.

Power Production of the Novel WLC Wave Energy Converter in Deep and Intermediate Water Depths

In the present paper contour plots of the power production of the Wave Energy Converter named as Water Level Carpet (WLC) are presented for deep and intermediate water depths. WLC consists of four rectangular shaped floating modules connected flexibly in two directions by connectors and by Power Take-Off (PTO) mechanisms with known damping characteristics. Initially, patents dealing with Wave Energy Converters and more specifically with oscillating bodies are presented. Afterwards, the estimation of the power production of the WLC is assessed through spectral analysis along with linear hydroelastic analysis in frequency domain. Shoaling phenomena are included in the spectral analysis. The hydroelastic analysis is performed in frequency domain with a radiation/diffraction 3D hydroelastic model considering both the effect of the flexibility of the WLC as well as the damping forces associated with the energy extraction by the PTO mechanism. The power production of WLC obtains large meaningful values for wave frequencies close to the resonance of the generalized degrees of freedom. The WLC introduced in the present paper can be considered as a promising WEC for further future development that can be used efficiently in both deep and intermediate water depths. Keywords: Water Level Carpet (WLC), wave energy converters, power production, hydroelasticity, shoaling effects.

随机信号通过线性系统的教学研讨

随机信号通过线性系统是随机信号分析教学中的重要内容。由于随机信号通过线性系统涉及到线性系统理论以及信号的时频域分析理论，从而导致学生对该部分内容较难以理解和掌握。本文首先介绍线性时不变系统和窄带系统，然后分别从时域和频域对经过线性系统的信号进行分析，并分析了白噪声经过线性系统，最后通过设计实例和实验让学生们对该部分的内容加以应用。文章对于随机信号通过线性系统的教学有一定的指导作用，并且有助于学生更好地理解和工程应用。 Random signal by the linear system is an important content in the teaching of random signal analysis. Random signal by the linear system involves linear system theory and time frequency domain analysis theory of signal, which lead students to understand and grasp the contents of this part uneasily. In this paper, the linear time invariant system and the narrow band system are introduced firstly, and then the signal of the linear system is analyzed respectively from the time domain and the frequency domain. The white noise is also analyzed by linear system. Finally, designing examples and experiments make students know how to use the content of this part. This article has some guidance to the teaching of random signal by the linear system and can help students to better understand and apply.

Numerical Simulation of Multiple Floating Structures With Nonlinear Constraints

Abstract A versatile and efficient numerical analysis is developed to compute the responses of a moored floating system composed of multiple floating structures. Structures such as tankers, semisubmersibles, FPSOs, SPARs, TLPs, and SPMs connected by mooring lines, connectors or fenders may be analyzed individually or collectively including multiple interaction. The analysis is carried out in the time domain assuming rigid body motion for the structures, and the solution is generated by a forward integration scheme. The analysis includes the nonlinearities in the excitation, damping, and restoring terms encountered in a typical mooring system configuration. It also allows for instabilities in the tower oscillation as well as slack mooring lines. Certain simplifications in the analysis have been made, which are discussed. The exciting forces in the analysis are wind, current, and waves (including a steady and an oscillating drift force), which are not necessarily collinear. The waves can be single frequency or composed of multiple frequency components. For regular waves either linear, stretched linear or fifth order theory may be used. The irregular wave may be included as a given spectral model (e.g., PM or JONSWAP). The vessels are free to respond to the exciting forces in six degrees of freedom—surge, sway, heave, roll, pitch, and yaw. The tower, when present, is free to respond in two degrees of freedom—oscillation and precession. The loads in the mooring lines are determined from prescribed tension-strain tables for the lines. Rigid mooring arms can be analyzed by allowing for compression in the load-strain table. Fenders may be input similarly through load compression tables. In order to establish the stability and accuracy of the solution, comparison of the results with linearized frequency domain analysis was made. The analysis is verified by several different model test results for different structure configurations in regular and random seas. Some of the interesting aspects of nonlinear system are shown with a few examples.

A simple method for incorporating transformer phase-shifts in a sparsity-oriented single-phase harmonic penetration algorithm

Abstract Transformer phase-shifts can play an important role in the study of harmonic penetration within a power system. The incorporation of these quantities in the conventional Linear Frequency Domain Analysis (LFDA) technique, which is widely used for large-scale power systems harmonic analysis, leads to the problem of unnecessary additional computation time and memory requirements. The problem is sought to be due to the asymmetry in the system admittance matrix when the transformer phase-shifts are included in the algorithm. A new method is described that solves the problem by retaining the system admittance matrix symmetrical throughout the computation process, thus enabling the use of efficient symmetrical sparsity techniques for solving the system unknowns. The validity of the method is substantiated by comparing our results with the results of conventional LFDA technique for a small 4-bus system and the IEEE 40-bus industrial system. The study of the results also demonstrates the importance of transformer phase-shifts in determining the correct harmonic distortion level in a system with multiple harmonic sources.