Multidimensional Motion Research Articles

Pricing Multidimensional American Options

A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. A free-boundary value approach is adopted and the value function is obtained via fundamental solution methods. There are many applications for the valuation of perpetual options of American style, which are of interest for finance and managerial decisions.

A novel method for measuring radial and axial errors in a cylindrical coordinate system using a combined double ball bar

Multiaxis machine tools are widely used in manufacturing. The measurement of motion error is important to improve the machining accuracy of machine tools. A double ball bar (DBB), as a high-precision single-dimensional position reading device, is widely used to measure the motion error of the circular path of machine tools. However, the motion errors contain the cylindrical radial and axial errors with respect to the circular path plane. Therefore, the measurement results of the DBB are incomplete because they do not contain axial errors. To measure the motion error of the circular path accurately, completely and concisely, a novel measurement method based on the combined DBB (C-DBB) is proposed in this paper, which can directly measure the radius and axial motion error of the circular path in one measurement. First, the measuring principle of the C-DBB method is introduced, and the measurement model of the radius and axial motion error of the circular path is established. Then, a measuring device using the C-DBB method was designed based on the lever principle, and the error parameters of the designed device were analyzed. According to the error analysis results, the measurement results of the C-DBB method were compensated and corrected. Finally, the C-DBB method is used to measure the circular path on the vertical CNC milling machine, and the results are compared with the measurement results using the DBB method. It is shown that the proposed C-DBB method can obtain high-precision multidimensional motion error in a single measurement, and the designed measuring device based on the C-DBB method has high repeatability and good circular path measuring ability. The proposed method provides an effective method for machine tool multidimensional motion error measurement and compensation.

Collapse failure analysis and fragility analysis of a transmission tower-line system subjected to the multidimensional ground motion of different input directions

Transmission lines, which are important for maintaining economic and social operations, are vulnerable to collapse damage due to the effect of multidimensional ground motion. In this paper, a three-dimensional finite element model of a transmission tower-line system is established. Twenty ground motion records were selected from the international ground motion database. The acceleration time history is orthogonally decomposed to obtain the acceleration time history along the X direction and Y direction of the model in different input directions. Based on the incremental dynamic analysis method, the influence of different ground motion input directions regarding the collapse failure of transmission tower-line systems is studied. Taking the section draft ratio of the tangent tower as the criterion, the influence of the seismic input direction on the collapse of the peak ground acceleration (PGA) and vulnerable area of the tangent tower is analyzed. The influence of the input direction on the collapse fragility of transmission tower-line systems under different conditions is investigated based on the fragility analysis method, and the collapse margin ratio is used to evaluate the seismic capacity of transmission tower-line systems. A comparison of the results indicates that the input direction of the ground motion has a great influence on the collapse of the PGA, and the difference in the various directions is up to 0.34 g. Additionally, the change in the input direction makes it possible for collapse to occur between the fourth and fifth sections. Last, the results also indicate that the input direction of the ground motion has a great disturbance on the collapse fragility of transmission tower-line systems. The influence of the input direction of ground motion should be considered under the condition of rare ground motion (0.32–0.46 g) and extremely rare ground motion (0.54–0.64 g) in the design of the structure. The direction along and vertical to the tower-line is not the worst input direction of the transmission tower-line system. Considering only the seismic input of these two directions will cause a significant overestimation of the seismic capacities of transmission tower-line systems.

Deep Learning Algorithm based Wearable Device for Basketball Stance Recognition in Basketball

With the continuous improvement of technology, modern sports training is gradually developing towards precision and efficiency, which requires more accurate identification of athletes' sports stances. The study first establishes a classification structure of basketball stance, then designs a hardware module to collect different stance data by using inertial sensors, thus extracting multidimensional motion stance features. Then the traditional convolutional neural network (CNN) is improved by principal component analysis (PCA) to form the PCA+CNN algorithm. Finally, the algorithm is simulated and tested. The outcomes demonstrated that the average discrimination error rate of the improved PCA+CNN algorithm in the Human 3.6M dataset was 3.15%, which was a low error rate. In recognition of basketball sports pose, the wearable based on the improved algorithm had the highest accuracy of 99.4% and took the quietest time of 18s, which was better than the other three methods. It demonstrated that the method had high discrimination precision and recognition efficiency, which could provide a reliable technical means to improve the science of basketball sports training plan and training effect.

Star formation in IC1396: Kinematics and subcluster structure revealed by Gaia

Aims. We investigate the star formation history of the IC1396 region by studying its kinematics and completing the population census. Methods. We used multiwavelength data, combining optical spectroscopy to identify and classify new members and near-infrared photometry to trace shocks, jets, and outflows as well as the interactions between the cluster members and the cloud. We also used Gaia EDR3 data to identify new potential members in the multidimensional proper motion and parallax space. Results. The revised Gaia EDR3 distance is 925±73 pc, slightly closer than previously obtained with DR2. The Gaia data reveal four distinct subclusters in the region. These subclusters are consistent in distance but display differences in proper motion. This result, with their age differences, hints toward a complex and varied star formation history. The Gaia data also unveil intermediate-mass objects that tend to evade spectroscopic and disk surveys. Our analysis has allowed us to identify 334 new members. We estimate an average age of ∼4 Myr, confirming previous age estimates. With the new members added to our study, we estimate a disk fraction of 28%, lower than previous values, due to our method detecting mainly new, diskless, intermediate-mass stars. We find age differences between the subclusters, which offers evidence of a complex star formation history with different episodes of star formation.

An Improved Innovation Robust Outliers Detection Method for Airborne Array Position and Orientation Measurement System

The airborne array position and orientation measurement system (array POS) is a key device for high-resolution multi-dimensional real-time imaging motion compensation of military reconnaissance mapping. Abnormal values will appear in array POS inertial devices and measurement data in an environment of strong interference, which often leads to a decrease or even divergence in the combination accuracy. The existing detection methods based on innovation characteristics are only sensitive to measurement outliers, which are the abnormal data caused by the strong interference environment. In this paper, an improved innovation robust outliers detection method is proposed, which is valid for both measurement outliers and inertial device outliers. First, the improved outliers detection method based on the innovation of array POS is described. The gain matrix is adaptively adjusted by using the statistical characteristics of innovation. At the same time, the information distribution coefficient is adaptively adjusted by using the filtering performance of the sub filter, which realizes the detection and correction of measurement outliers. Then, the outlier detection method of inertial devices based on extrapolation prediction is added. The predicted value of the inertial device is extrapolated by the fourth-order difference method, and the outliers are recognized and eliminated by the adaptive threshold, which contributes to improving the robustness and accuracy of array POS. STD is selected in this paper to statistic the accuracy of array POS. Compared with the traditional federated Kalman filtering (KFK) methods, the accuracies of position, speed, heading angle and horizontal attitude angle of the left node and right node are all improved when there are outliers in the measurement data. Compared with the fault-tolerant federated combination method based on innovation characteristics, the accuracies of position, speed, heading angle and horizontal attitude angle of the left node and right node are all improved when there are abnormal values in the inertial device data.

Optimal convergence rate of modified Milstein scheme for SDEs with rough fractional diffusions

We develop a new framework for error analysis on stochastic numerical schemes, with the rough path theory and stochastic backward error analysis. Based on our approach, we prove that the almost sure convergence rate of the modified Milstein scheme for stochastic differential equations driven by multiplicative multidimensional fractional Brownian motion with Hurst parameter H∈(14,12) is (2H−12)− for sufficiently smooth coefficients, which is optimal in the sense that it is consistent with the best probable convergence rate of implementable approximations of the Lévy area of fractional Brownian motion. Our result gives a positive answer to the conjecture proposed in [12] for the case H∈(13,12), and reveals for the first time that numerical schemes constructed by a second-order Taylor expansion converge for the case H∈(14,13].

A novel motion planning algorithm for a three DoF foldable parallel compensation platform based on prediction and B-spline

Foldable parallel mechanisms are suitable to compensate for the motion of vessels due to their compact structure, multidimensional motion, and large carrying capacity. However, the vessel sways violently under harsh sea conditions, challenging the rational utilization of the mechanism workspace. This work proposes a novel motion planning algorithm based on motion prediction and the B-spline for a three-degrees-of-freedom foldable parallel compensation platform. First, for harsh sea conditions, the motion law of a guardian vessel is studied, and the encoder-decoder model is used to predict the roll, pitch, and heave motions of the vessel. Second, we propose a multidimensional motion compensation strategy under the limits of the mechanism dimensions. Then, a backward kinematics model is developed. Its workspace under the structural and actuator limitations is proposed. Finally, based on the theory of the nonuniform rational B-spline curve and target motion prediction, a dynamic motion planning algorithm is proposed, and experiments are conducted. The motion planning algorithm can provide smooth motion commands under the mechanism workspace, velocity, acceleration constraints. It can be realized using asynchronous calculation, which meets real-time motion control requirements.

The Design of Cone and Pendulum Scanning Mode Using Dual-Camera with Multi-Dimensional Motion Imaging Micro-Nanosatellite

This paper focuses on the design of a new optical cone and pendulum scanning imaging mode for micro-nanosatellites. This kind of satellite uses a high-resolution camera with a small imaging plane to achieve high-resolution and ultra-wide coverage imaging through the three-dimensional motion of the camera’s wobble, satellite spin, and satellite orbital motion. First, this paper designs a single-camera constant speed OCPSI (optical cone and pendulum scanning imaging) mode. On the premise of ensuring coverage, the motion parameters and imaging parameters are derived. Then, in order to improve the performance and imaging quality of the system, a dual-camera variable speed OCPSI mode is designed. In this method, in order to reduce the overlap ratio, the camera is oscillated at a variable speed. Turn on the cameras in turn at the same time to minimize the overlap. This paper details these working modes. The simulation experiment is carried out using the satellite orbit of 500 km, the focal length of 360 mm, the pixel size of 2.5 μm, the resolution of [5120 × 5120], the number of imaging frames in the pendulum scanning hoop of 10, and the initial camera inclination angle of 30°. The single-camera constant speed OCPSI mode has an effective swath of 1060 km at a ground sampling distance of 5.3 m. The dual-camera variable speed OCPSI mode has an effective width of 966 km under the same conditions. Finally, the ground experiment prototype of OCPSI imaging theory is designed. We choose a camera with a pixel size of 3.45 μm, a resolution of [1440 × 1080], and a focal length of 25 mm. The ground experiment was carried out at the initial camera inclination angle of 10°, the number of imaging frames in the pendulum scanning hoop of 3, and the orbit height of 11 m. The experimental result is that the effective width of OCPSI imaging mode reaches 10.8 m. Compared with the traditional push-broom mode using the same camera, the effective width of 1.64 m is increased by seven times, and the effective width of 3.83 m is increased by three times compared to the traditional whisk-broom imaging mode. This study innovatively integrates three-dimensional motion imaging into aerospace remote sensing and provides a reference for the research on the realization of high-resolution and ultra-wide coverage of micro-nano remote sensing satellites.

Deep and Convolutional Neural Networks for identifying vertically-propagating incoming seismic wave motion into a heterogeneous, damped soil column

Identification of the incoming seismic wave motion at a geotechnical site plays an integral role in the seismic analysis and design of the critical components of the civil infrastructure. Current practice relies on using one-dimensional models for the soil medium at the site, and a process called deconvolution, which identifies seismic input due to measurements made at the ground surface. Using multi-dimensional models for the underlying soil medium becomes important when a site exhibits considerable heterogeneity or change in topography. These situations necessitate using a gradient-based optimization method for inverting the multi-dimensional incoming seismic-wave motion. However, such methods are computationally expensive and time consuming.We explore the effectiveness and robustness of a data-informed framework for the inverse-source problem, due to its potential in reducing the computational cost, compared to a gradient-based approach. We design deep and convolutional neural network architectures to predict the incoming wave motion based on measurements made at the ground surface. We demonstrate their effectiveness and robustness on blind test examples, where measured data are contaminated with noise, and when the incident signals in the training data set may or may not resemble a realistic seismic signal. Lastly, the presented artificial neural networks are shown to be effective in predicting incoming wave motion when the subsurface material properties lack accuracy, or are uncertain, which is likely the case in realistic situations. While only one-dimensional problems are considered here, generalization of our data-informed approach to handle multi-dimensional problems appears to be straightforward. Overall, our data-informed approach seems to be robust, fast, and promising for identifying the incoming seismic wave motion.

Representation for action recognition with motion vector termed as: SDQIO

The active human action motion characteristics from moving areas within a particular spectrum are conveyed by the information extraction domain of video data. Meanwhile, most of the video data frequencies are encoded with silent information that has significant redundancy, resulting in low processing efficiency in conventional video models that accept raw frames as input. Human action recognition remains challenging for the computer vision domain in videos. To address this issue, this study introduces SDQIO, a novel video content extractor that focuses on obtaining multiscale and multidimensional motion information for fast action detection. The ultimate goal of our SDQIO is to develop an effective action recognition module (SDQIO) by identifying five distinct types of action capture operators and extensively assessing their effects on movement prediction over short and long periods. Our SDQIO uses a multi-differentiation modeling approach to gather motion-type information over the whole clip. Extensive experiments revealed that our technique outperforms all other action recognition algorithms by a significant margin on standard action datasets, attaining state-of-the-art and equivalent outcomes.

A slope deformation measurement method based on laser datum and complex target motion model

Highway slope stability analysis and monitoring is of great significance to ensure the safety of highway infrastructure. Based on the consideration of complex target motion model, a high-precision laser datum highway slope multi-dimensional deformation measurement method is proposed in this paper, which overcomes the problem of low measurement accuracy in traditional methods, and realizes high-precision real-time monitoring of highway slope stability. Firstly, the measurement principle and deformation data solution method combining the laser benchmark and the intelligent photoelectric imaging target are given. Then, considering the multi-dimensional complex motion of the photoelectric imaging target, a solution model of the multi-dimensional motion parameters of the measuring point considering the multi-dimensional complex motion vector of the target is deduced. Then, the inclination sensor is used as the measurement method of the multi-dimensional inclination of the target, combined with the high-precision processing algorithm of target spot center based on image processing, the high-precision measurement of multi-dimensional deformation of target plane is realized; Finally, the prototype of the measurement system is built and compared in the laboratory, and the actual highway slope is measured and verified in the outfield. The experimental results show that the measurement error considering the complex target movement is less than 0.25 mm, which is greatly improved compared with the traditional method, and meets the needs of high-precision slope relative deformation measurement.

Basketball Motion Posture Recognition Based on Recurrent Deep Learning Model

In order to improve the training effect of athletes and effectively identify the movement posture of basketball players, we propose a basketball motion posture recognition method based on recurrent deep learning. A one-dimensional convolution layer is added to the neural network structure of the deep recurrent Q network (DRQN) to extract the athlete pose feature data before the long short-term memory (LSTM) layer. The acceleration and angular velocity data of athletes are collected by inertial sensors, and the multi-dimensional motion posture features are extracted from the time domain and frequency domain, respectively, and the posture recognition of basketball is realized by DRQN. Finally, the new reinforcement learning algorithm is trained and tested in a time-series-related environment. The experimental results show that the method can effectively recognize the basketball motion posture, and the average accuracy of posture recognition reaches 99.3%.

Stochastic modeling of spreading and dissipation in mixed-chaotic systems that are driven quasistatically.

We analyze energy spreading for a system that features mixed chaotic phase space, whose control parameters (or slow degrees of freedom) vary quasistatically. For demonstration purpose we consider the restricted three-body problem, where the distance between the two central stars is modulated due to their Kepler motion. If the system featured hard chaos, one would expect diffusive spreading with coefficient that can be estimated using linear-response (Kubo) theory. But for mixed phase space the chaotic sea is multilayered. Consequently, it becomes a challenge to find a robust procedure that translates the sticky dynamics into a stochastic model. We propose a Poincaré-sequencing method that reduces the multidimensional motion into a one-dimensional random walk in impact space. We test the implied relation between stickiness and the rate of spreading.

Multidimensional Self-Propelled Motion Based on Nonlinear Science

Self-propelled objects, which exhibit characteristic features of motion, are proposed based on nonlinear science. At first, a self-propelled object with length like undulatory swimming is designed, i.e., the phase of oscillation at several points on the object is propagated in the opposite direction of motion. Second, the vertical oscillation of a camphor disk is created at an amphiphilic molecular layer developed on water. The proposed systems suggest that nonlinearity can enhance the autonomy of self-propelled objects as multidimensional motion.

Design and characteristic analysis of multi-degree-of-freedom ultrasonic motor based on spherical stator.

The multidimensional motion ultrasonic motor with a single spherical stator is studied in this paper. It has the characteristics of miniaturization and can be used in precision motion applications. By bonding six identical pieces of piezoelectric ceramic onto the stator and applying the voltage signal of high frequency, the deformation of the inverse piezoelectric effect is used to excite the stator yaw vibration mode. The orthogonal superposition of the modes of the spherical stator on the driving foot produces elliptical trajectory around X, Y, and Z directions by different excitation methods. According to the yaw vibration mode of the spherical stator, 12 driving feet are designed to drive the rotation of the spherical rotor. The structure and mechanical characteristics of the motor are simulated by using simulation software, and the transient response of the stator driving foot was obtained, which proved its feasibility. Finally, the output performance of the motor in actual operation is given through experiments, which provides a new reference scheme in the field of precise multi-degree-of-freedom motion. At a voltage of 100V and a frequency of 26.7kHz, the prototype has a no-load speed of 73, 70, and 114 rpm around X, Y, and Z axes, respectively.

Effects of Self-Lubricant Coating and Motion on Reduction of Friction and Wear of Mild Steel and Data Analysis from Machine Learning Approach.

The applications of coated mild steels are gaining significant attention in versatile industrial areas because of their better mechanical properties, anticorrosive behavior, and reproducibility. The life period of this steel reduces significantly under relative motion in the presence of friction, which is associated with the loss of billion-dollar every year in industry. Productivity is hampered, and economic growth is declined. Several pieces of research have been conducted throughout the industries to seeking the processes of frictional reduction. This study is attributed to the tribological behavior of electroplated mild steel under various operating parameters. The efficiency of commercial lubricant and self-lubrication characteristics of coated layer plays a significant role in the reduction of friction. The reciprocating and simultaneous motion in relation to pin as well as disc are considered during experimentation. The lubricating effects in conjunction with motions are responsible for compensating the friction and wear at the desired level. During frictional tests, the sliding velocity and loads are changed differently. The changes in roughness after frictional tests are observed. The coated and rubbing surfaces are characterized using SEM (Scanning Electron Microscopy) analysis. The coating characteristics are analyzed by EDS (Energy Disperse Spectroscopy), FTIR (Fourier-transform Infrared Spectroscopy), and XRD (X-ray diffraction analysis) methods. The lubrication, reciprocating motion, and low velocity result in low friction and wear. The larger the imposed loads, the smaller the frictional force, and the larger the wear rate. The machine learning (ML) concept is incorporated in this study to identify the patterns of datasets spontaneously and generate a prediction model for forecasting the data, which are out of the experimental range. It can be desired that the outcomes of this research will contribute to the improvement in versatile engineering fields, such as automotive, robotics, and complex motion-based mechanisms where multidimensional motion cannot be ignored.

Hurst exponent estimation of fractional surfaces for mammogram images analysis

The work presents a methodology to precise simulation and parameter estimation of multidimensional fractional Brownian motion (fBm). The simulation approach uses circulant embedding algorithm and solution of Poisson equation, while generalizing it to multiple dimensions. For estimation, a method using Wishart distribution and maximum likelihood is presented and verified on simulated data. Unlike approximate methods for generating multidimensional fBm and its Hurst exponent estimation, this approach shows unbiased results for all processes with short memory and majority of cases with long memory. The methodology is applied to mammography screening images to find significant differences between benign and cancerous breast lumps.

A Motion Capturing and Energy Harvesting Hybridized Lower-Limb System for Rehabilitation and Sports Applications.

Lower‐limb motion monitoring is highly desired in various application scenarios ranging from rehabilitation to sports training. However, there still lacks a cost‐effective, energy‐saving, and computational complexity‐reducing solution for this specific demand. Here, a motion capturing and energy harvesting hybridized lower‐limb (MC‐EH‐HL) system with 3D printing is demonstrated. It enables low‐frequency biomechanical energy harvesting with a sliding block‐rail piezoelectric generator (S‐PEG) and lower‐limb motion sensing with a ratchet‐based triboelectric nanogenerator (R‐TENG). A unique S‐PEG is proposed with particularly designed mechanical structures to convert lower‐limb 3D motion into 1D linear sliding on the rail. On the one hand, high output power is achieved with the S‐PEG working at a very low frequency, which realizes self‐sustainable systems for wireless sensing under the Internet of Things framework. On the other hand, the R‐TENG gives rise to digitalized triboelectric output, matching the rotation angles to the pulse numbers. Additional physical parameters can be estimated to enrich the sensory dimension. Accordingly, demonstrative rehabilitation, human‐machine interfacing in virtual reality, and sports monitoring are presented. This developed hybridized system exhibits an economic and energy‐efficient solution to support the need for lower‐limb motion tracking in various scenarios, paving the way for self‐sustainable multidimensional motion tracking systems in near future.

Optimal portfolio execution with a Markov chain approximation approach

AbstractWe study the problem of executing a large multi-asset portfolio in a short time period where the objective is to find an optimal trading strategy that minimizes both the trading cost and the trading risk measured by quadratic variation. We contribute to the existing literature by considering a multi-dimensional geometric Brownian motion model for asset prices and proposing an efficient Markov chain approximation (MCA) approach to obtain the optimal trading trajectory. The MCA approach allows us not only to numerically compute the optimal strategy but also to theoretically analyse the influence of factors such as price impact, risk aversion and initial asset price on the optimal strategy, providing both quantitative and qualitative guidance on the trading behaviour. Numerical results verify the theoretical conclusions in the paper. They further illustrate the effects of cross impact and correlations on the optimal execution strategy in a multi-asset liquidation problem.