Dynamic Performance of Vehicle–Guideway Bridge Systems for Low–Medium-Speed Maglev Trains Under Earthquakes

This paper developed a numerical model for predicting the seismic responses of vehicle–guideway bridge systems for low–medium-speed (LMS) maglev trains. Each vehicle was characterized as a multi-rigid-body with 50 degree of freedoms (DOFs), and the guideway bridge was modeled by the finite element method. The actively controlled electromagnetic forces were considered in simulating the vehicle–guideway interaction relationship. Subsequently, the equations of motion for the vehicle–guideway coupled system under earthquake were, respectively, established in relative and absolute coordinate systems to quantify the effect of structural pseudo-static components, so that the seismic effect can be taken into account. Case study was then conducted to thoroughly discuss the seismic responses of the vehicle–guideway coupled system in both time and frequency domains. Furthermore, parametric study was carried out to determine the effect of key parameters (i.e. vehicle speed, stiffness of guideway) on the system’s responses. The results show that the conventional seismic analysis method relative motion method (RMM) (ignoring the structural pseudo-static component) will considerably underestimate the seismic responses of the coupled system, especially of the vehicle. It is suggested that the formulation be established in the absolute coordinate system (i.e. using direct solution method, DSM) for more actual prediction. The frequency responses indicate that the vibrations of vehicle–guideway coupled system under earthquake relate significantly to the natural frequencies of vehicle and bridge, while the same is not true for the vehicle-induced excitation.

AstroSeis: A 3D Boundary Element Modeling Code for Seismic Wavefields in Irregular Asteroids and Bodies

We developed a 3D elastic boundary element method computer code, called AstroSeis, to model seismic wavefields in a body with an arbitrary shape, such as an asteroid. Besides the AstroSeis can handle arbitrary surface topography, it can deal with a liquid core in an asteroid model. Both the solid and liquid domains are homogenous in our current code. For seismic sources, we can use single forces or moment tensors. The AstroSeis is implemented in the frequency domain, and the frequency-dependent Q can be readily incorporated. The code is in MATLAB (see Data and Resources), and it is straightforward to set up the model to run the code. The frequency-domain calculation is advantageous to study the long-term elastic response of a celestial body due to a cyclic force, such as the tidal force, with no numerical dispersion issue suffered by many other methods requiring volume meshing. Our AstroSeis has been benchmarked with other methods such as normal-mode summation and the direct solution method. This open-source AstroSeis will be a useful tool to study the interior and surface processes of asteroids.

3D Displacement Field of Wenchuan Earthquake Based on Iterative Least Squares for Virtual Observation and GPS/InSAR Observations

The acquisition of a 3D displacement field can help to understand the crustal deformation pattern of seismogenic faults and deepen the understanding of the earthquake nucleation. The data for 3D displacement field extraction are usually from GPS/interferometric synthetic aperture radar (InSAR) observations, and the direct solution method is usually adopted. We proposed an iterative least squares for virtual observation (VOILS) based on the maximum a posteriori estimation criterion of Bayesian theorem to correct the errors caused by the GPS displacement interpolation process. Firstly, in the simulation examples, both uniform and non-uniform sampling schemes for GPS observation were used to extract 3D displacement. On the basis of the experimental results of the reverse fault, the normal fault with a strike-slip component, and the strike-slip fault with a reverse component, we found that the VOILS method is better than the direct solution method in both horizontal and vertical directions. When a uniform sampling scheme was adopted, the percentages of improvement for the reverse fault ranged from 3% to 9% and up to 70%, for the normal fault with a strike-slip component ranging from 4% to 8% and up to 68%, and for the strike-slip fault with a reverse component ranging from 1% to 8% and up to 22%. After this, the VOILS method was applied to extract the 3D displacement field of the 2008 Mw 7.9 Wenchuan earthquake. In the East–West (E) direction, the maximum displacement of the hanging wall was 1.69 m and 2.15 m in the footwall. As for the North–South (N) direction, the maximum displacement of the hanging wall was 0.82 m for the southwestern, 0.95 m for the northeastern, while that of the footwall was 0.77 m. In the vertical (U) direction, the maximum uplift was 1.19 m and 0.95 m for the subsidence, which was significantly different from the direct solution method. Finally, the derived vertical displacements were also compared with the ruptures from field investigations, indicating that the VOILS method can reduce the impact of the interpolated errors on parameter estimations to some extent. The simulation experiments and the case study of the 3D displacement field for the 2008 Wenchuan earthquake suggest that the VOILS method proposed in this study is feasible and effective, and the degree of improvement in the vertical direction is particularly significant.

Rapid Solution of Optimal Control Problems by a Functional Spreadsheet Paradigm: A Practical Method for the Non-Programmer

We devise a practical and systematic spreadsheet solution paradigm for general optimal control problems. The paradigm is based on an adaptation of a partial-parametrization direct solution method which preserves the original mathematical optimization statement, but transforms it into a simplified nonlinear programming problem (NLP) suitable for Excel NLP solver. A rapid solution strategy is implemented by a tiered arrangement of pure elementary calculus functions in conjunction with Excel NLP solver. With the aid of the calculus functions, a cost index and constraints are represented by equivalent formulas that fully encapsulate an underlining parametrized dynamical system. Excel NLP solver is then employed to minimize (or maximize) the cost index formula, by varying decision parameters, subject to the constraints formulas. The paradigm is demonstrated for several fixed and free-time nonlinear optimal control problems involving integral and implicit dynamic constraints with direct comparison to published results obtained by fundamentally different methods. Practically, applying the paradigm involves no more than defining a few formulas using basic Excel spreadsheet skills.

A weighted adjustment of a similarity transformation between two point sets containing errors

For an adjustment of a similarity transformation, it is often appropriate to consider that both the source and the target coordinates of the transformation are affected by errors. For the least squares adjustment of this problem, a direct solution is possible in the cases of specific-weighing schemas of the coordinates. Such a problem is considered in the present contribution and a direct solution is generally derived for the m-dimensional space. The applied weighing schema allows (fully populated) point-wise weight matrices for the source and target coordinates, both weight matrices have to be proportional to each other. Additionally, the solutions of two borderline cases of this weighting schema are derived, which only consider errors in the source or target coordinates. The investigated solution of the rotation matrix of the adjustment is independent of the scaling between the weight matrices of the source and the target coordinates. The mentioned borderline cases, therefore, have the same solution of the rotation matrix. The direct solution method is successfully tested on an example of a 3D similarity transformation using a comparison with an iterative solution based on the Gauß-Helmert model.