Mean Phase Difference Research Articles

The MLDAR Model: Machine Learning-Based Denoising of Structural Response Signals Generated by Ambient Vibration

Engineers have consistently prioritized the maintenance of structural serviceability and safety. Recent strides in design codes, computational tools, and Structural Health Monitoring (SHM) have sought to address these concerns. On the other hand, the burgeoning application of machine learning (ML) techniques across diverse domains has been noteworthy. This research proposes the combination of ML techniques with SHM to bridge the gap between high-cost and affordable measurement devices. A significant challenge associated with low-cost instruments lies in the heightened noise introduced into recorded data, particularly obscuring structural responses in ambient vibration (AV) measurements. Consequently, the obscured signal within the noise poses challenges for engineers in identifying the eigenfrequencies of structures. This article concentrates on eliminating additive noise, particularly electronic noise stemming from sensor circuitry and components, in AV measurements. The proposed MLDAR (Machine Learning-based Denoising of Ambient Response) model employs a neural network architecture, featuring a denoising autoencoder with convolutional and upsampling layers. The MLDAR model undergoes training using AV response signals from various Single-Degree-of-Freedom (SDOF) oscillators. These SDOFs span the 1–10 Hz frequency band, encompassing low, medium, and high eigenfrequencies, with their accuracy forming an integral part of the model’s evaluation. The results are promising, as AV measurements in an image format after being submitted to the trained model become free of additive noise. This with the aid of upscaling enables the possibility of deriving target eigenfrequencies without altering or deforming of them. Comparisons in various terms, both qualitative and quantitative, such as the mean magnitude-squared coherence, mean phase difference, and Signal-to-Noise Ratio (SNR), showed great performance.

Predicting the data structure prior to extreme events from passive observables using echo state network

Extreme events are defined as events that largely deviate from the nominal state of the system as observed in a time series. Due to the rarity and uncertainty of their occurrence, predicting extreme events has been challenging. In real life, some variables (passive variables) often encode significant information about the occurrence of extreme events manifested in another variable (active variable). For example, observables such as temperature, pressure, etc., act as passive variables in case of extreme precipitation events. These passive variables do not show any large excursion from the nominal condition yet carry the fingerprint of the extreme events. In this study, we propose a reservoir computation-based framework that can predict the preceding structure or pattern in the time evolution of the active variable that leads to an extreme event using information from the passive variable. An appropriate threshold height of events is a prerequisite for detecting extreme events and improving the skill of their prediction. We demonstrate that the magnitude of extreme events and the appearance of a coherent pattern before the arrival of the extreme event in a time series affect the prediction skill. Quantitatively, we confirm this using a metric describing the mean phase difference between the input time signals, which decreases when the magnitude of the extreme event is relatively higher, thereby increasing the predictability skill.

Thermo-capillarity in microfluidic binary systems via phase modulated sinusoidal thermal stimuli

In this article, we have explored the theoretical aspects of thermo-capillarity driven hydrodynamics at the interface of an immiscible binary-fluid system within a microfluidic domain. The top and bottom walls of the microfluidic confinement are exposed to sinusoidal thermal stimuli with different mean values, wave numbers, and phase differences. We explore the influence of different governing parameters on the thermal and hydrodynamic transport due to interfacial thermo-capillarity and within the constituent fluids. To this end, we deduce the full solutions for the temperature field, hydrodynamics, and the interfacial deformation characteristics in an analytical framework, by appealing to the assumption of the creeping flow (vanishingly small Reynolds, Marangoni, and Capillary number regime) and nearly un-deformed interface. Complicated spatial distribution of the isotherms is generated across the fluids, leading to spatially varying thermal gradients across and along the interface. This leads to periodic circulation of the fluids within the microchannel due to the sinusoidal thermal stimulus. It is observed that the interfacial flow strength depends on the relative film thickness and the thermal conductivities of the two fluids. Vortex enveloping phenomenon is observed for lower values of film thickness ratio when the thermal conductivity of the lower fluid is higher relative to the upper fluid. The findings may hold significance for the design and development of thermal stimulus-controlled spatial mixing and solute transport mechanisms in reactive micro- and nano-fluidic devices.

Time-specific associations of wearable sensor-based cardiovascular and behavioral readouts with disease phenotypes in the outpatient setting of the Chronic Renal Insufficiency Cohort.

Patients with chronic kidney disease are at risk of developing cardiovascular disease. To facilitate out-of-clinic evaluation, we piloted wearable device-based analysis of heart rate variability and behavioral readouts in patients with chronic kidney disease from the Chronic Renal Insufficiency Cohort and controls (n = 49). Time-specific partitioning of heart rate variability readouts confirm higher parasympathetic nervous activity during the night (mean RR at night 14.4 ± 1.9 ms vs. 12.8 ± 2.1 ms during active hours; n = 47, analysis of variance (ANOVA) q = 0.001). The α2 long-term fluctuations in the detrended fluctuation analysis, a parameter predictive of cardiovascular mortality, significantly differentiated between diabetic and nondiabetic patients (prominent at night with 0.58 ± 0.2 vs. 0.45 ± 0.12, respectively, adj. p = 0.004). Both diabetic and nondiabetic chronic kidney disease patients showed loss of rhythmic organization compared to controls, with diabetic chronic kidney disease patients exhibiting deconsolidation of peak phases between their activity and standard deviation of interbeat intervals rhythms (mean phase difference chronic kidney disease 8.3 h, chronic kidney disease/type 2 diabetes mellitus 4 h, controls 6.8 h). This work provides a roadmap toward deriving actionable clinical insights from the data collected by wearable devices outside of highly controlled clinical environments.

Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section

Abstract A theoretical investigation is carried out to analyze the oscillatory flow of second-grade fluid under the periodic pressure gradient in a long tube of isosceles right triangular cross section in the present study. The analytical expressions for the velocity profile and phase difference are obtained. The numerical solutions are calculated by using the finite difference method with Crank–Nicolson (C–N) scheme. In comparison with the Newtonian fluid (λ = 0), the effects of retardation time, Deborah number and Womersley number on the velocity profile and phase difference are discussed numerically and graphically. For smaller Womersley number, the behavior of second-grade fluid is dominated by viscosity. For larger Womersley number α = 20, the flow becomes more difficult to be generated under periodic pressure gradient with increasing retardation time. Furthermore, the analytical expressions of the mean velocity amplitude and phase difference are given explicitly for discussing.

Absolutely Consistent Fiber-Optic Phase Synchronization Based On Fixed-Phase-Reference Optical Active Compensation

An absolutely consistent fiber-optic phase synchronization scheme based on fixed-phase-reference optical active compensation is proposed. By measuring the time interval of time pulse and the phase difference of frequency signal, and then using the optical delay line to compensate the phase change in real time according to a fixed phase reference, the phase period ambiguity and the phase-lock control initial randomness are eliminated, realizing a stable and repeatable fixed phase difference between different sites. Then the phase synchronization performances of stability and absolute consistence have been demonstrated through experiments in different scenarios. The phase difference fluctuation within 10000 s is only ±0.0006 rad, showing an ultra-high stability. Under the total of 5 different operations, including the signal source restart, system restart, adding 20 m additional fiber, adding 1 km additional fiber, and adding 2 km additional fiber, the maximum inconsistency of the mean phase difference is about 1% of one full cycle. The proposed and verified absolutely consistent phase synchronization method can well maintain the coherence in transferring frequency signal, having important application prospects in radar network and other time-frequency-phase synchronization-based coherent detection.

ALIXE: a phase-combination tool for fragment-based molecular replacement.

Fragment-based molecular replacement exploits the use of very accurate yet incomplete search models. In the case of the ARCIMBOLDO programs, consistent phase sets produced from the placement and refinement of fragments with Phaser can be combined in order to increase their signal before proceeding to the step of density modification and autotracing with SHELXE. The program ALIXE compares multiple phase sets, evaluating mean phase differences to determine their common origin, and subsequently produces sets of combined phases that group consistent solutions. In this work, its use on different scenarios of very partial molecular-replacement solutions and its performance after the development of a much-optimized set of algorithms are described. The program is available both standalone and integrated within the ARCIMBOLDO programs. ALIXE has been analysed to identify its rate-limiting steps while exploring the best parameterization to improve its performance and make this software efficient enough to work on modest hardware. The algorithm has been parallelized and redesigned to meet the typical landscape of solutions. Analysis of pairwise correlation between the phase sets has also been explored to test whether this would provide additional insight. ALIXE can be used to exhaustively analyse all partial solutions produced or to complement those already selected for expansion, and also to reduce the number of redundant solutions, which is particularly relevant to the case of coiled coils, or to combine partial solutions from different programs. In each case parallelization and optimization to provide speedup makes its use amenable to typical hardware found in crystallography. ARCIMBOLDO_BORGES and ARCIMBOLDO_SHREDDER now call on ALIXE by default.

Inter-channel phase differences during sleep spindles are altered in Veterans with PTSD

Sleep disturbances are common complaints in patients with post-traumatic stress disorder (PTSD). To date, however, objective markers of PTSD during sleep remain elusive. Sleep spindles are distinctive bursts of brain oscillatory activity during non-rapid eye movement (NREM) sleep and have been implicated in sleep protection and sleep-dependent memory processes. In healthy sleep, spindles observed in electroencephalogram (EEG) data are highly synchronized across different regions of the scalp. Here, we aimed to investigate whether the spatiotemporal synchronization patterns between EEG channels during sleep spindles, as quantified by the phase-locking value (PLV) and the mean phase difference (MPD), are altered in PTSD. Using high-density (64-channel) EEG data recorded from 78 combat-exposed Veteran men (31 with PTSD and 47 without PTSD) during two consecutive nights of sleep, we examined group differences in the PLV and MPD for slow (10–13 Hz) and fast (13–16 Hz) spindles separately. To evaluate the reproducibility of our findings, we set apart the first 47 consecutive participants (18 with PTSD) for the initial discovery and reserved the remaining 31 participants (13 with PTSD) for replication analysis. In the discovery analysis, compared to the non-PTSD group, the PTSD group showed smaller MPDs during slow spindles between the frontal and centro-parietal channel pairs on both nights. We obtained reproducible results in the replication analysis in terms of statistical significance and effect size. The PLVs during slow or fast spindles did not significantly differ between groups. The reduced inter-channel phase difference during slow spindles in PTSD may reflect pathological changes in the underlying thalamocortical circuits. This novel finding, if independently validated, may prove useful in developing sleep-focused PTSD diagnostics and interventions.

Effect of Impairment-Oriented and Function-Oriented Exercises on Mouth Function in Subjects with Systemic Sclerosis

Purpose: The aim of this study was to develop an exercise protocol to improve maximal mouth opening (MMO), tongue protrusion (Tprot), tongue strength (Tstren), and lip strength (Lstren), and to assess its effects on subjects with scleroderma. Methods: We performed four replicated single-system studies in a consecutive sample of subjects with scleroderma. An instrumented assessment measured MMO, Tprot, Tstren, and Lstren. Each day, subjects were assessed and performed orofacial exercises conducted by speech therapists. Treatments were first aimed at improving mouth physical characteristics by impairment-oriented exercises and then to improve skills with function-oriented exercises. Results: The mean phase differences between assessment and treatment phases across subjects were from 0.88 to 9.56 mm in MMO, from 2.03 to 12.3 mm in Tprot, from –0.12 to 5.35 N in Tstren, and from –0.84 to 5.19 N in Lstren. After treatment, 3 subjects crossed the 5th percentile discriminating normal from abnormal performances for both Tstren and Tprot, while this occurred in 2 subjects for MMO and Lstren. Conclusions: The results of this study suggest that rehabilitation appears to be useful in reducing tongue and lip impairments and in improving oral functions in subjects with scleroderma.

Common-Mode Noise Suppression Technique in Interferometric Fiber-Optic Sensors

Efficient suppression of common-mode noises (CMNs) is significant for the performance of interferometric fiber-optic sensor system. To suppress CMNs, a reference interferometer is normally required as noise canceller. In this paper, we firstly report a detailed correlation analysis between the outputs of the sensing and reference interferometers. By using a band-limited noise decomposing method, we show that the correlation coefficient of the two interferometer outputs is a strong function over their mean phase difference, which appears as the limiting factor of the CMN suppression effect. Based on the analysis, we propose a novel CMN suppression technique by locking the mean phase value of the sensing interferometer using a reference interferometer with a 3 × 2 coupler. Experimental results show that our technique can increase the correlation coefficient between the outputs of sensing and reference interferometers by 6% (to 0.93) and reduce its standard deviation by $\sim$ 70% compared to traditional method. The CMNs suppression factor is measured as $-$ 8.49 dB in the frequency range from 300 Hz to 1 kHz, comparing to $\sim -$ 6 dB achieved by traditional method of simple subtraction. Our results set a new benchmark on the noise level of interferometric fiber-optic sensors.

Compromised Dynamic Cerebral Autoregulation in Patients With Depression.

Background: Patients with depression tend to have various comorbid neurological symptoms, but the mechanisms remain unclear. The purpose of this study was to analyze the characteristics of dynamic cerebral autoregulation in depressed patients. Methods: Patients (aged ≥ 18 years) who were diagnosed with depression [17-item Hamilton Depression Rating Scale (HAMD) > 17] or suspected of depression (HAMD > 7) were enrolled in this study. Medically healthy volunteers were recruited as controls. The subjects also received the 7-item HAMD. We simultaneously recorded noninvasive continuous arterial blood pressure and bilateral middle cerebral artery blood flow velocity from each subject. Cerebral autoregulation was assessed by analyzing the phase difference using transfer function analysis. Results: This study enrolled 54 patients with suspected depression, 45 patients with depression, and 48 healthy volunteers. The mean phase difference values were significantly lower in the patients with depression (F = 9.071, P < 0.001). In the multiple regression analysis, depression was negatively correlated with the phase difference values. Conclusions: Dynamic cerebral autoregulation was compromised in patients with depression and negatively correlated with the depression score. Improving dynamic cerebral autoregulation may be a potential therapeutic method for treating the neurological symptoms of depression.

Extrapolating baseline trend in single-case data: Problems and tentative solutions.

Single-case data often contain trends. Accordingly, to account for baseline trend, several data-analytical techniques extrapolate it into the subsequent intervention phase. Such extrapolation led to forecasts that were smaller than the minimal possible value in 40% of the studies published in 2015 that we reviewed. To avoid impossible predicted values, we propose extrapolating a damping trend, when necessary. Furthermore, we propose a criterion for determining whether extrapolation is warranted and, if so, how far out it is justified to extrapolate a baseline trend. This criterion is based on the baseline phase length and the goodness of fit of the trend line to the data. These proposals were implemented in a modified version of an analytical technique called Mean phase difference. We used both real and generated data to illustrate how unjustified extrapolations may lead to inappropriate quantifications of effect, whereas our proposals help avoid these issues. The new techniques are implemented in a user-friendly website via the Shiny application, offering both graphical and numerical information. Finally, we point to an alternative not requiring either trend line fitting or extrapolation.

What works for which riders, and to what extent? Evaluating the effectiveness of a New Zealand therapeutic riding intervention using a single-case experimental design

Therapeutic horse riding (THR) is a complex intervention using horses and horse-related activities to positively influence health in people who experience disability. It is difficult to meaningfully evaluate the effectiveness of complex rehabilitation interventions with parallel randomised controlled trial methods when used in isolation. Reducing intervention complexities to simple variables for the purposes of minimising bias can enhance claims regarding causal associations between variables, but can result in difficulties translating the findings from these studies to ‘real world’ clinical practice where complexity is a certainty. This study aimed to evaluate the effectiveness of a therapeutic horse riding (THR) intervention using a single-case experimental design (SCED). A randomised, multiple-baseline SCED replicated across 12 participants, was used to quantitatively evaluate in which riders, and to what extent, changes in balance, functional performance, social responsiveness, quality of life and participation outcomes occurred as a result of the 20-week THR intervention. Analysis of data included analysis of individual participant responses (i.e., visual analysis, descriptive nonparametric approaches, analyses considering baseline stability evaluated with Mean Phase Difference and Slope and Level Change procedures) and between participant responses (i.e., Modified Brinley plots, estimation of effect sizes). An inconsistent intervention response to THR was seen across participants in the SCED. Participation outcomes measured using the Canadian Occupation Performance Measure (COPM) demonstrated the most consistent positive between-phase difference (performance score ES = 1.23; satisfaction score ES = 1.11). However, when taking baseline data stability into account these improvements only reached clinical significance for two of the participants. Being involved in THR may improve participation outcomes for some children who live with the experience of disability. SCED's provide a rigorous but clinically meaningful way to evaluate the effectiveness of complex rehabilitation interventions in real world.

FEASIBILITY OF DETERMINING DYNAMIC RENAL AUTOREGULATION IN HUMANS USING COMBINED INTRARENAL PRESSURE AND FLOW MEASUREMENTS

Objective: Renal autoregulation is important for maintenance of renal perfusion, glomerular filtration and may be of prognostic value in hypertensive-induced kidney damage. In animal models, transfer function analysis of spontaneous blood pressure fluctuations has been used to assess the (patho)physiology of renal autoregulation. Our aim was to determine the feasibility of measuring renal autoregulation in humans using combined intrarenal pressure and flow measurements. Design and method: We performed intrarenal pressure and flow velocity measurements in clinically stable patients with an indication for renal or coronary angiography, aged 18–75 and with eGFR > 45 ml/min/1.73m2. Measurements were conducted at baseline and under hyperaemia following intrarenal injection of dopamine 30 μgram/kg. Transfer function analysis was performed on the beat-to-beat pressure and flow data. Autoregulation was assessed by the time difference between the peaks in the pressure and flow signal, and was quantified as the average phase difference over the manually selected coherent peak around the sympathetic frequency (period 6 to 14 seconds).Results: We included 21 patients, of which assessment of autoregulation was successful in 11 patients. In the remaining group it was not possible to find a coherent signal, mostly due to lack of blood pressure variations in the sympathetic frequency domain. During baseline, the mean phase difference was 32 degrees (range 11 to 45 degrees), where flow leads pressure. Under hyperaemia, in 7 patients the phase difference could be determined, which showed a reduction to a phase difference of 10 degrees (range −12 to19 degrees, p = 0.003 compared to baseline). An example of the spectrum before and after infusion of dopamine is shown in Figure A. The individual phase differences at baseline and under hyperaemia are shown in Figure B. Conclusions: Measurement of renal autoregulation in humans is feasible provided that patients have sufficient spontaneous blood pressure variations. The disappearance of renal autoregulatory responses during dopamine infusion may provide useful information regarding the degree of induced hyperaemia.

The Clinical Trials Mosaic: Toward a Range of Clinical Trials Designs to Optimize Evidence-Based Treatment.

ObjectiveDichotomizing clinical trials designs into nomothetic (e.g., randomized clinical trials or RCTs) versus idiographic (e.g., N-of-1 or case studies) precludes use of an array of hybrid designs and potential research questions between these extremes. This paper describes unique clinical evidence that can be garnered using idiographic clinical trials (ICTs) to complement RCT data. Proposed and illustrated herein is that innovative combinations of design features from RCTs and ICTs could provide clinicians with far more comprehensive information for testing treatments, conducting pragmatic trials, and making evidence-based clinical decisionsMethodMixed model trajectory analysis and unified structural equations modeling were coupled with multiple baseline designs in (a) a true N-of-1 pilot study to improve severe autism-related communication deficits and (b) a small sample preliminary study of two complimentary interventions to relieve wheelchair discomfort.ResultsEvidence supported certain mechanisms of treatment outcomes and ruled out others. Effect sizes included mean phase differences (i.e., effectiveness), trajectory slopes, and differences in path coefficients between study phases.ConclusionsICTs can be analyzed with equivalent rigor as, and generate effect sizes comparable to, RCTs for the purpose of developing hybrid designs to augment RCTs for pilot testing innovative treatment, efficacy research on rare diseases or other small populations, quantifying within-person processes, and conducting clinical trials in many situations when RCTs are not feasible.

Sleep-Dependent Oscillatory Synchronization: A Role in Fear Memory Consolidation.

Sleep plays an important role in memory consolidation through the facilitation of neuronal plasticity; however, how sleep accomplishes this remains to be completely understood. It has previously been demonstrated that neural oscillations are an intrinsic mechanism by which the brain precisely controls neural ensembles. Inter-regional synchronization of these oscillations is also known to facilitate long-range communication and long-term potentiation (LTP). In the present study, we investigated how the characteristic rhythms found in local field potentials (LFPs) during non-REM and REM sleep play a role in emotional memory consolidation. Chronically implanted bipolar electrodes in the lateral amygdala (LA), dorsal and ventral hippocampus (DH, VH), and the infra-limbic (IL), and pre-limbic (PL) prefrontal cortex were used to record LFPs across sleep-wake activity following each day of a Pavlovian cued fear conditioning paradigm. This resulted in three principle findings: (1) theta rhythms during REM sleep are highly synchronized between regions; (2) the extent of inter-regional synchronization during REM and non-REM sleep is altered by FC and EX; (3) the mean phase difference of synchronization between the LA and VH during REM sleep predicts changes in freezing after cued fear extinction. These results both oppose a currently proposed model of sleep-dependent memory consolidation and provide a novel finding which suggests that the role of REM sleep theta rhythms in memory consolidation may rely more on the relative phase-shift between neural oscillations, rather than the extent of phase synchronization.

多軸一定応力振幅下の高サイクル疲労寿命予測

Multiaxial high cycle fatigue life prediction under constant stress amplitude is proposed. This new criterion, which extends the proposed fatigue limit criterion by the authors in the previous papers, uses the unified equivalent shear stress amplitude. The material properties for the proposed criterion are the axial fatigue limit and the true fracture strength. The multiaxial high cycle fatigue tests for life prediction accuracy verification was carried out with S45C and SCM440. The fatigue tests were conducted under combined axial and torsion stresses with mean stress and phase difference. The criterion error is better than that of the Susmel criterion. The proposed criterion predicted the experimental fatigue life to be within a factor of 3.

Markerless four-dimensional-cone beam computed tomography projection-phase sorting using prior knowledge and patient motion modeling: A feasibility study

During cancer radiotherapy treatment, on-board four-dimensional-cone beam computed tomography (4D-CBCT) provides important patient 4D volumetric information for tumor target verification. Reconstruction of 4D-CBCT images requires sorting of acquired projections into different respiratory phases. Traditional phase sorting methods are either based on external surrogates, which might miscorrelate with internal structures; or on 2D internal structures, which require specific organ presence or slow gantry rotations. The aim of this study is to investigate the feasibility of a 3D motion modeling-based method for markerless 4D-CBCT projection-phase sorting. Patient 4D-CT images acquired during simulation are used as prior images. Principal component analysis (PCA) is used to extract three major respiratory deformation patterns. On-board patient image volume is considered as a deformation of the prior CT at the end-expiration phase. Coefficients of the principal deformation patterns are solved for each on-board projection by matching it with the digitally reconstructed radiograph (DRR) of the deformed prior CT. The primary PCA coefficients are used for the projection-phase sorting. PCA coefficients solved in nine digital phantoms (XCATs) showed the same pattern as the breathing motions in both the anteroposterior and superoinferior directions. The mean phase sorting differences were below 2% and percentages of phase difference < 10% were 100% for all the nine XCAT phantoms. Five lung cancer patient results showed mean phase difference ranging from 1.62% to 2.23%. The percentage of projections within 10% phase difference ranged from 98.4% to 100% and those within 5% phase difference ranged from 88.9% to 99.8%. The study demonstrated the feasibility of using PCA coefficients for 4D-CBCT projection-phase sorting. High sorting accuracy in both digital phantoms and patient cases was achieved. This method provides an accurate and robust tool for automatic 4D-CBCT projection sorting using 3D motion modeling without the need of external surrogate or internal markers.

Efficient Common-Mode Noise Suppression for Fiber-Optic Interferometric Sensor Using Heterodyne Demodulation

Common-mode noises (CMNs) are frequently encountered in all types of fiber sensor systems. Through involving a reference interferometer, here we report the application of a differential delay heterodyne scheme to suppress CMNs in fiber-optic interferometric sensor systems. The contributions of CMNs are shared by both sensing and reference interferometers and are further suppressed by heterodyne demodulation. For the first time, we develop the full theoretical model describing this method, and experimental results are also presented to confirm the theory. Theoretical analysis shows that the CMN suppression effect (SE, defined as the ratio of the noise floor of the sensing interferometer after and before suppression) is sensitive to several key parameters, including the mean phase difference, the ratio of the visibility, and ac amplitude between the two interferometers. Experimental results show that the proposed method can suppress CMNs by ~24 dB within the frequency range of 20 Hz to 1 kHz. The measured CMN SE agrees well with the theory. The CMN suppression method and the theory reported here can also be extended to other interferometric systems.

Annual variation detected by GPS, GRACE and loading models

Most GPS coordinate time series, surface displacements derived from the Gravity Recovery and Climate Experiment (GRACE), and loading models display significant annual signals at many regions. This paper compares the annual signals of the GPS position time series from the Crustal Dynamics Data Information System (CDDIS), estimates of loading from GRACE monthly gravity field models calculated by three processing centers (Center of Spatial Research, CSR; Jet Propulsion Laboratory, JPL; GeoForschungsZentrum, GFZ) and three geophysical fluids models (National Center for Environmental Prediction, NCEP; Estimating the Circulation and Climate of the Ocean, ECCO; Global Land Data Assimilation System, GLDAS) for 270 globally distributed stations for the period 2003-2011. The results show that annual variations derived from the level-2 products from the three GRACE product centers are very similar. The absolute difference in annual amplitude between any two centers is never larger than 1.25 mm in the vertical and 0.11 mm in horizontal displacement. The mean phase differences of the GRACE results are less than ten days for all three components. When we correct the GPS vertical coordinate time series using the GRACE annual amplitudes using the products from three GRACE analysis centers, we find that we are able to reduce the GPS annual signal in the vertical at about 80% stations and the average reduction is about 47%. In the north and the east, the annual amplitude is reduced on 77% and 72% of the stations with the average reduction 32% and 33%. We also compare the annual surface displacement signal derived from two environmental models; the two models use the same atmospheric and non-tidal ocean loading and differ only in the continental water storage model that we use, either NCEP or GLDAS. We find that the model containing the GLDAS continental water storage is able to better reduce the annual signal in the GPS coordinate time series.