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## Abstract

The mixture effect of the long-term variations is a main challenge in single channel singular spectrum analysis (SSA) for the reconstruction of the annual signal from GRACE data. In this paper, a nonlinear long-term variations deduction method is used to improve the accuracy of annual signal reconstructed from GRACE data using SSA. Our method can identify and eliminate the nonlinear long-term variations of the equivalent water height time series recovered from GRACE. Therefore the mixture effect of the long-term variations can be avoided in the annual modes of SSA. For the global terrestrial water recovered from GRACE, the peak to peak value of the annual signal is between 1.4 cm and 126.9 cm, with an average of 11.7 cm. After the long-term and the annual term have been deducted, the standard deviation of residual time series is between 0.9 cm and 9.9 cm, with an average of 2.1 cm. Compared with the traditional least squares fitting method, our method can reflect the dynamic change of the annual signal in global terrestrial water, more accurately with an uncertainty of between 0.3 cm and 2.9 cm.

## Abstract

NASA’s new Earth-Observing satellite namely ICESat-2 estimates the elevation of ice sheets, glaciers, sea ice, land surface, and canopy with the help of photon counting ATLAS sensor on-board. Higher-level data products like ATL08 uses an iterative filtering approach of the signal photons for capturing canopy height and terrain height. This article provides results from the evaluation of best-fit elevation on land from ICESat-2 ATL08 data product with DGPS surveyed points. 40 points were surveyed for elevation in the arid region with different topographies of varied surface cover. Mean bias error computed from the best-fit elevation from ICESat-2 ATL08 data product and corresponding DGPS surveyed points is near close to zero for the segments created from strong beams. The conformity between these two sets of elevation values is better than 12 cm (RMSE) if we use the segments from strong beam for the topographic variations ranging from flat to almost flat type.

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## Abstract

This paper proposes precise point positioning (PPP) methods that offer an accuracy of a few decimetres (dm) with triple frequency GNSS data. Firstly, an enhanced triple frequency linear combination is presented for rapid fixing of the extra wide-lane (EWL) and wide-lane (WL) ambiguities for GPS, Beidou-2 and Galileo. This has improved performance compared to the Melbourne-Wübbena (MW) linear combination, and has 6.7 % lower measurement noise for the GPS L1/L2 signals, 12.7 % for L1/L5 and 0.7 % for L2/L5. Analysis with tested data showed a 5–6 % reduction in time required to fix the $N21$ and $N51$ ambiguities.

Once the EWL/WL ambiguities are fixed with the proposed linear combinations, three methods are presented that aim to provide positioning accuracy of a few dm. In the first approach, the three EWL/WL ambiguities in their respective phase equations are used to derive a low-noise ionosphere-free (IF) linear combination. The second method uses a low noise IF combination with two carrier-phase EWL/WL equations and a single pseudorange measurement. The third method uses a low noise IF combination with a single carrier phase EWL equation and two pseudorange measurements. These proposed methods can provide dm level positioning accuracy if carrier phase measurements with mm precision is tracked by the receiver. When comparing these combinations with a combination proposed in [], it is found that superior performance is achieved with the third method when carrier phase noise is >5–6 mm for GPS and Beidou-2 and >2–3 mm for Galileo. This model only requires the EWL ambiguity to be fixed which typically takes just one epoch of data. Thus, the user achieves instant decimetre level PPP accuracy.

## Abstract

Bridges are critical to economic and social development of a country. In order to ensure the safe operation of bridges, it is of great significance to accurately predict displacement of monitoring points from bridge Structural Health System (SHM). In the paper, a CEEMDAN-KELM model is proposed to improve the accuracy of displacement prediction of bridge. Firstly, the original displacement monitoring time series of bridge is accurately and effectively decomposed into multiple components called intrinsic mode functions (IMFs) and one residual component using a method named complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN). Then, these components are forecasted by establishing appropriate kernel extreme learning machine (KELM) prediction models, respectively. At last, the prediction results of all components including residual component are summed as the final prediction results. A case study using global navigation satellite system (GNSS) monitoring data is used to illustrate the feasibility and validity of the proposed model. Practical results show that prediction accuracy using CEEMDAN-KELM model is superior to BP neural network model, EMD-ELM model and EMD-KELM model in terms of the same monitoring data.

## Abstract

The International GNSS Service (IGS) provides high-accuracy clock products for both GNSS satellites and stations. On board of each GNSS satellite are located 3–4 atomic oscillators. In the case of CORS oscillators, the majority of them are equipped with internal oscillators and a part uses external, high-rate clocks. In the IGS network there are four types of external oscillators: quartz, rubidium, caesium and H-maser. These CORS are often reference stations for precise GNSS measurements or for time transfer. In this paper the author provides analyses of the internal and external stability of the reference stations oscillators via the usage of Allan variations. The results show a strong advantage of the external clocks over internal ones by about five orders of magnitude.

## Abstract

The key concept of the virtual reference station (VRS) network-based technique is to use the observables of multiple reference stations to generate the network corrections in the form of a virtual reference station at a nearby user’s location. Regarding the expected positioning accuracy, the novice GNSS data processing strategies have been adopted in the server-side functional model for mitigating distance-dependent errors including atmospheric effects and orbital uncertainty in order to generate high-quality virtual reference stations. In addition, the realistic stochastic model also plays an important role to take account of the unmodelled error in the rover-side processing. The results of our previous study revealed that the minimum norm quadratic unbiased estimation (MINQUE) stochastic model procedure can improve baseline component accuracy and integer ambiguity reliability, however, it requires adequate epoch length in a solution to calculate the elements of the variance-covariance matrix. As a result, it may not be suitable for urban environment where the satellite signal interruptions take place frequently, therefore, the ambiguity resolution needs to be resolved within the limited epochs. In order to address this limitation, this study proposed the stochastic model based on using the residual interpolation uncertainty (RIU) as the weighting schemes. This indicator reflects the quality of network corrections for any satellite pair at a specific rover position and can be calculated on the epoch-by-epoch basis. The comparison results with the standard stochastic model indicated that the RIU-weight model produced slightly better positioning accuracy but increased significant level of the ambiguity resolution successful rate.

## Abstract

There is extremely strict precision requirement for the lateral breakthrough error of long immersed tunnel in the offshore island and tunnel project, but the point location layout range of the outer plane control network is limited in the artificial island, and the space inside the tunnel is long and narrow, which is not conducive to high-precision through-measurement control. In order to further reduce the influence of the error of the plane control network on the lateral breakthrough error of the immersed tunnel, a mathematical model of the influence of the lateral breakthrough error caused by the orientation direction of the outer control point and the position of the breakthrough point has been established through the theoretical analysis in this study, and the favorable orientation directions and the favorable penetration point are analyzed. It is suggested through simulation analysis that the direction that is as consistent with that from the entrance (outlet) point to the penetration point as possible is as the advantageous orientation, which could minimize the lateral penetration error and ensure high-precision rendezvous and docking of the immersed tunnel. This study is instructive for similar engineering practices.

## Abstract

Today, short- and long-term structural health monitoring (SHM) of bridge infrastructures and their safe, reliable and cost-effective maintenance has received considerable attention. From a surveying or civil engineer’s point of view, vibration-based SHM can be conducted by inspecting the changes in the global dynamic behaviour of a structure, such as natural frequencies (i. e. eigenfrequencies), mode shapes (i. e. eigenforms) and modal damping, which are known as modal parameters. This research work aims to propose a robust and automatic vibration analysis procedure that is so-called robust time domain modal parameter identification (RT-MPI) technique. It is novel in the sense of automatic and reliable identification of initial eigenfrequencies even closely spaced ones as well as robustly and accurately estimating the modal parameters of a bridge structure using low numbers of cost-effective micro-electro-mechanical systems (MEMS) accelerometers. To estimate amplitude, frequency, phase shift and damping ratio coefficients, an observation model consisting of: (1) a damped harmonic oscillation model, (2) an autoregressive model of coloured measurement noise and (3) a stochastic model in the form of the heavy-tailed family of scaled t-distributions is employed and jointly adjusted by means of a generalised expectation maximisation algorithm. Multiple MEMS as part of a geo-sensor network were mounted at different positions of a bridge structure which is precalculated by means of a finite element model (FEM) analysis. At the end, the estimated eigenfrequencies and eigenforms are compared and validated by the estimated parameters obtained from acceleration measurements of high-end accelerometers of type PCB ICP quartz, velocity measurements from a geophone and the FEM analysis. Additionally, the estimated eigenfrequencies and modal damping are compared with a well-known covariance driven stochastic subspace identification approach, which reveals the superiority of our proposed approach. We performed an experiment in two case studies with simulated data and real applications of a footbridge structure and a synthetic bridge. The results show that MEMS accelerometers are suitable for detecting all occurring eigenfrequencies depending on a sampling frequency specified. Moreover, the vibration analysis procedure demonstrates that amplitudes can be estimated in submillimetre range accuracy, frequencies with an accuracy better than 0.1 Hz and damping ratio coefficients with an accuracy better than 0.1 and 0.2 % for modal and system damping, respectively.