Direct Linear Method Research Articles

A Practical Distributed Finite-Time Control Scheme for Power System Transient Stability

Power system transient stability control is gaining huge attention in present time. Inspired by the consistency theory of multi-agent system, a distributed finite-time frequency control framework is presented to improve the frequency dynamic of the transient process by adjusting the steam valving. The stability of the proposed distributed frequency control scheme is ensured by including the Lyapunov-based constraints. The communication delay is fully considered in the deigned distributed frequency control framework which has no limitations on communication delay by fully utilizing the local information. Meanwhile, the proposed cyber-physical topology divides the power system into several clusters according to the physical coupling between generators. The designed distributed control scheme based on the proposed cyber-physical topology owns the capability to defend denial-of-service (DoS) attacks which may influence the performance of distributed control scheme, which is also presented in theoretical proof. The designed voltage control based on the direct feedback linearization method can be applied to coordinate all existing frequency controls, in the premise of the system stability. The performance of the proposed control scheme is evaluated under the cases of different communication delays and DoS attacks through the simulation on New England 39-bus system.

A closed-form single-pose calibration method for the camera–projector system

To improve the calibration efficiency of the structured light stereo vision system, a closed-form single-pose calibration method is proposed. Previous works calibrate the structured light stereo vision system via the planar-based method since the world coordinates of the projected pixels are easy to find. But the disadvantage of these methods is that multiple poses are required, so that the mechanical movement is necessary in these calibration methods. In this paper, the inherent geometry between the spheres and their image is exploited deeply. Thus, a sphere-based calibration method is proposed. The proposed method first calibrates the camera from the image of the absolute conic through an improved algorithm. Then, the three-dimensional coordinates of the projected pixels are found via the inherent geometrical relation. Next, the projector is calibrated using the direct linear method. Finally, the distortion of the projector is found through the nonlinear optimization method with an improved updating direction. Experiments demonstrate that not only the calibration efficiency is improved, but also the calibration accuracy is improved.

A moment estimation–based method for the path planning of manipulators with kinematic system reliability constraints

Since the path planning plays a significant role in the manipulator’s control, the system reliability evaluation and optimization for path planning are studied with consideration of the joint clearance. A simple moment estimation–based method is proposed; a linear performance function is first established using the extreme value distribution theory. Based on the maximum entropy principle, the first four moments of variables are utilized to derive a best-fit probability density function to feature the characteristics of the system distribution rather than an empirical assumption of the normality. To meet the system reliability criterion constraints, a sensitivity analysis is conducted using the direct linearization method. With modification in the tolerance of sensitive parameters, the reliability can be improved efficiently. Traditional methods, such as the first-order second moment method, the first-order reliability method, and Monte Carlo simulation, are popular in this research field and therefore they are applied as benchmark methods for comprehensive comparisons in the accuracy and efficiency. A typical serial manipulator is applied as an example to validate the feasibility of our proposed method.

An Objective Criterion for Selection of the Best Option in Hansen’s Method for Paleostress Estimation from Homogeneous Fault-Slip Data

Hansen’s direct linear inversion method is a rapid and robust technique for paleostress estimation from fault-slip observations. The method uses six- and nine-dimensional spaces and requires a user judgement of the best solution from four possible options, i.e., the tensors 6D, 6Df, 9D and 9Df. We propose an objective criterion for selection of the best solution. Using each of the four possible options, as the reduced stress tensor, 6D, 6Df, 9D and 9Df, the criterion computes the slip vector on each fault plane in a given population of homogeneous fault-slip data. The option that gives minimum average angle between the computed slip vectors and the true or observed slip vectors on the corresponding fault planes is the best solution. The criterion is successfully tested on 236 synthetic and 5 natural examples representing a variety of stress states in different tectonic settings. One example of the natural fault-slip observations contains a vorticity component, whereas all other test examples are devoid of vorticity. In the triaxial stress states, two correct solutions are obtained, one of which is either 6D or 6Df, and the other is 9D or 9Df. In the stress states that are characterized by axial compression or axial extension, the correct solution is either 6D or 6Df and the use of nine-dimensional space fails to invert the observations. In the natural example that contains a vorticity component, only 9D gave the correct result.

Transient temperature effects on biofilters in recirculating systems ammonia removal rates

Acclimation of biological filters and ammonia oxidation at transient temperature regimes was the focus of the research. A batch system of automated temperature controlled tanks was used to determine effects of temperature on biofilter response to total ammonia nitrogen utilization. Each tank contained internal biofilters loaded with synthetic chemical feedstock. The biofilters were exposed to temperature regimes of 13 °C, 20 °C and 30 °C steady state temperatures in the first experiment, and cyclical (diurnal) temperatures of 20 ± 3 °C and 30 ± 3 °C in the second experiment. A direct linear regression line method was used, with tau (τ) value from the slope of the linear regression line used to determine the biofilter substrate utilization response to varying temperature regimes.Biofilter response was determined as the capability to utilize total ammonia nitrogen (TAN) by ammonia oxidizing bacteria (AOB). Tau (τ) values for ammonia oxidation were 40.73 day−1, 58.81 day−1 and 159.70 day−1 at 13 °C, 20 °C and 30 °C respectively. Total ammonia nitrogen substrate utilization rates as indicated in a decay plot differed significantly (P < 0.05) between temperature regimes 20 and 30 °C. However substrate utilization between 13 and 20 °C were not different (P > 0.05). Ammonia oxidation tau values were 118.20 day−1 and 223.50 day−1 at (20 ± 3 °C) and (30 ± 3 °C) diurnal temperatures respectively. These were significantly different (P < 0.05). The data in this study can be applied to future seeded or acclimating biofilters operating within these temperature ranges.

Total Chemical Synthesis of SUMO and SUMO-Based Probes for Profiling the Activity of SUMO-Specific Proteases.

SUMO is a post‐translational modifier critical for cell cycle progression and genome stability that plays a role in tumorigenesis, thus rendering SUMO‐specific enzymes potential pharmacological targets. However, the systematic generation of tools for the activity profiling of SUMO‐specific enzymes has proven challenging. We developed a diversifiable synthetic platform for SUMO‐based probes by using a direct linear synthesis method, which permits N‐ and C‐terminal labelling to incorporate dyes and reactive warheads, respectively. In this manner, activity‐based probes (ABPs) for SUMO‐1, SUMO‐2, and SUMO‐3‐specific proteases were generated and validated in cells using gel‐based assays and confocal microscopy. We further expanded our toolbox with the synthesis of a K11‐linked diSUMO‐2 probe to study the proteolytic cleavage of SUMO chains. Together, these ABPs demonstrate the versatility and specificity of our synthetic SUMO platform for in vitro and in vivo characterization of the SUMO protease family.

Experimental verification on wrinkling behavior given by wrinkling analysis using the tension field theory

This study investigates the physical meaning of membrane surface features given by a wrinkling analysis based on tension field theory and wrinkle strain, which releases the compressive stress in membranes in tension field theory. A rectangular membrane was subjected to shear loading, and the wrinkle geometry and strain field were measured by photogrammetry using a direct linear transformation method. The experimental model was then subjected to a wrinkling analysis based on tension field theory, and the calculated wrinkled membrane behavior was quantitatively compared to the measured results. The analyzed membrane surface features approximately represented the neutral curved surface bisecting the actual wrinkle geometry (the difference was approximately 10% of the maximum wrinkle amplitude), even when the membrane surface feature was not initially flat. The wrinkle strain, defining an in-plane shrinkage strain that releases compressive stress on the membrane in tension field theory, agreed with the experimentally observed in-plane shrinkage strain regardless of the formation process of the wrinkles. The relation between the in-plane shrinkage strain and ratio of the wrinkle amplitude to the half-wavelength of the wrinkles was then derived from inextensional theory. This relation appropriately described the relation measured in the experiment, confirming that inextensional theory describes the wrinkle formation. The results of this study will assist the evaluation of the simulation results using tension field theory for the development of future lightweight, membrane-based space structures such as sunshields and solar sails.

Tolerance analysis of mechanical assemblies based on the product of exponentials formula

Many existing tolerancing models deal with the tolerance analysis of mechanical assemblies using linear stack-up function, which will cause truncation errors for nonlinear assembly problem. This article proposes a new method for describing the variation propagation based on the product of exponentials formula. Both the length deviations and the angle deviations are uniformly represented by twist coordinates. Accordingly, the nonlinear stack-up functions relating the assembly functional requirements to the manufacturing variations can be derived, and no truncation errors generated. A three-dimensional assembly case is studied exploiting the proposed method and the direct linearization method, respectively. It appears that the product of exponentials formula can bring consistent tolerance analysis results with the exact geometric solutions, whereas there are some small errors in the analysis results of direct linearization method. The precision of tolerance estimation via the product of exponentials formula is improved by 0.52% at the most compared with that by the direct linearization method. Due to the elimination of local datum reference frames, the product of exponentials formula can also lead to a more concise description of tolerance accumulation than the direct linearization method.

Water Sensation During Passive Propulsion for Expert and Nonexpert Swimmers.

This study determined whether expert swimmers, compared with nonexperts, have superior movement perception and physical sensations of propulsion in water. Expert (national level competitors, n = 10) and nonexpert (able to swim 50 m in > 3 styles, n = 10) swimmers estimated distance traveled in water with their eyes closed. Both groups indicated their subjective physical sensations in the water. For each of two trials, two-dimensional coordinates were obtained from video recordings using the two-dimensional direct linear transformation method for calculating changes in speed. The mean absolute error of the difference between the actual and estimated distance traveled in the water was significantly lower for expert swimmers (0.90 ± 0.71 meters) compared with nonexpert swimmers (3.85 ± 0.84 m). Expert swimmers described the sensation of propulsion in water in cutaneous terms as the "sense of flow" and sensation of "skin resistance." Therefore, expert swimmers appear to have a superior sense of distance during their movement in the water compared with that of nonexpert swimmers. In addition, expert swimmers may have a better perception of movement in water. We propose that expert swimmers integrate sensations and proprioceptive senses, enabling them to better perceive and estimate distance moved through water.

Direct Linear System Identification Method for Multistory Three-dimensional Building Structure with General Eccentricity

A method of physical-parameter system identification is proposed here for three-dimensional (3D) building structures with in-plane rigid floors in which the stiffness and damping coefficients of each structural frame in the 3D building structure are identified from the measured floor horizontal accelerations. A batch processing least-squares estimation method for many discrete time-domain measured data is proposed for the direct identification of the stiffness and damping coefficients of each structural frame. While previous researches on the system identification of 3D building structures are limited to a class of structures with regular eccentricity, the present paper removes this limitation. Advantageous features of the proposed identification method are that it is unnecessary to specify the stiffness eccentricities (location of center of stiffness) before identification and the identification of all stiffness and damping parameters can be performed simultaneously. The reliability and accuracy of the proposed method are demonstrated by numerical simulations.

Method of the direct linearization of mixed nonlinearities

This paper describes the method of the direct linearization of mixed nonlinear forces, which is used to analyze nonlinear oscillatory systems. This method has been compared with other methods in order to demonstrate their resemblance in terms of the practical results. In contrast to well-known methods of nonlinear system analysis, direct linearization methods allow computational cost (time and effort) to be reduced by several orders, which considerably increases their effectiveness.

Application of the median method to estimate the kinetic constants of the substrate uncompetitive inhibition equation

In 1974, Eisenthal and Cornish-Bowden published the direct linear plot method, which used the median to estimate the Vmax and Km from a set of initial rates as a function of substrate concentrations. The robustness of this non-parametric method was clearly demonstrated by comparing it with the least-squares method. The authors commented that the method cannot readily be generalized to equations of more than two parameters. Unfortunately, this comment has been misread by other authors. Comments such as “this method cannot be extended directly to equations with more than two parameters” were found in some publications. In addition, recently, the most drastic comment was published: “this method cannot be applied for the analysis of substrate inhibition.” Given all of these presumptions, we have been motivated to publish a demonstration of the contrary: the median method can be applied to more than two-parameter equations, using as an example, the substrate uncompetitive inhibition equation. A computer algorithm was written to evaluate the effect of simulated experimental error of the initial rates on the estimation of Vmax, Km and KS. The error was assigned to different points of the experimental design. Four different KS/Km ratios were analyzed with the values 10, 100, 1000 and 10,000. The results indicated that the least-squares method was slightly better than the median method in terms of accuracy and variance. However, the presence of outliers affected the estimation of kinetic constants using the least-squares method more severely than the median method. The estimation of KS using the median method to estimate 1/KS was much better than the direct estimation of KS, causing a negative effect of non-linearity of KS in the kinetic equation. Considering that the median method is free from the assumptions of the least-squares method and the arbitrary assumptions implicit in the linearization methods to estimate the kinetic constants Vmax, Km and KS from the substrate uncompetitive inhibition equation, the median method is highly superior to all published methods, including the non-linear regression by least squares. We concluded that the median method can be applied to the substrate uncompetitive inhibition equation and other equations with more than two parameters. In addition, as we can project, the median method is the most reliable and robust method for the estimation of kinetic parameters from enzyme kinetic models.

ハンマー投における高重量ハンマーを使用したトレーニングが投てき距離および技術に及ぼす影響の検討

The purpose of this study was to investigate the cumulative effect of training with the heavier hammer (8.0 kg). Sixteen male hammer throwers were divided into a TR group (n=8) and a CT group (n=8). The TR group trained with the heavier hammer (8.0 kg) for 4 weeks. In order to investigate the effect of the training, tests were conducted before and after training. Utilizing 3 high-speed video cameras (300 fps), the 3-dimensional coordinates of the hammer head and 25 landmarks on the body were obtained by the direct linear transformation method. The results showed that in the TR group, the throwing record was increased and the release velocity increased due to an increase of velocity increment during the turn. The maximum centrifugal force was increased in the all double support phase after training in the TR group. With regard to the lower limb joint angles, bending motion of the hip and the knee joint was emphasized after training in the TR group. These results suggest that throwing with the heavier hammer is an effective training method for improving the throwing distance, and for throwing action against the increased load during the turn phase.

Experimental study on relaxation time in direction changing movement

Controlled experiments were conducted to clarify the movement characteristics of pedestrians in direction changing processes. We track pedestrians’ trajectories and map them into real space coordinates by the direct linear transformation method. In the acceleration process, the relaxation time and free moving speed in our experiments respectively equal 0.659 s and 1.540 m/s, which are consistent with those for Chinese participants in other experiments. Meanwhile, the values of relaxation time in the direction changing process are calculated by a derived equation from the concept of the social force model. It is observed that the relaxation time is not an invariable parameter, and tends to increase with an increase in the angular difference. Furthermore, results show that pedestrians are insensitive to a tiny angular difference between instantaneous velocity and desired velocity. These experimental results presented in this work can be applied in model development and validation.

Static output feedback stabilization for fractional-order systems in T-S fuzzy models

This paper investigates the stabilization problem of fractional-order Takagi-Sugeno (T-S) fuzzy systems via static output feedback control. It provides a direct linear matrix inequality method for the control design, which overcomes the drawback of two-step design approaches and avoids requiring special structures in design matrices. The present method serves as an important alternative for both fractional-order and integer-order systems, and illustrative examples show the merits of the delivered results.

Near-Infrared Camera Calibration for Optical Surgical Navigation

Near-infrared optical tracking devices, which are important components of surgical navigation systems, need to be calibrated for effective tracking. The calibration results has a direct influence on the tracking accuracy of an entire system. Therefore, the study of calibration techniques is of theoretical significance and practical value. In the present work, a systematic calibration method based on movable plates is established, which analyzes existing calibration theories and implements methods using calibration reference objects. First, the distortion model of near-infrared cameras (NICs) is analyzed in the implementation of this method. Second, the calibration images from different positions and orientations are used to establish the required linear equations. The initial values of the NIC parameters are calculated with the direct linear transformation method. Finally, the accurate internal and external parameters of the NICs are obtained by conducting nonlinear optimization. Analysis results show that the relative errors of the left and right NICs in the tracking system are 0.244 and 0.282 % for the focal lengths and 0.735 and 1.111 % for the principal points, respectively. The image residuals of the left and right image sets are both less than 0.01 pixel. The standard error of the calibration result is lower than 1, and the measurement error of the tracking system is less than 0.3 mm. The experimental data show that the proposed method of calibrating NICs is effective and can generate favorable calibration results.

Direct and Optimal Linear Active Methods for Stabilization of LC Input Filters and DC/DC Converters Under Voltage Mode Control

The switching mode power electronic converter with feedback loop control functions as a constant power load (CPL). CPLs have negative input impedance which may cause system instability. Both passive and active stabilization methods can solve this problem. However, active stabilization methods are more power efficient. Several active stabilization methods have been proposed for DC/AC inverter based CPLs. However, active stabilization methods for DC/DC converter based CPLs under voltage mode control have received little attention. In this paper, two linear active methods, the direct method and the optimal method, for the DC/DC buck converter under voltage mode control are proposed. In these two methods, feedforward loops are designed to modify the input impedance of the DC/DC converter to stabilize the system. Comparing with the direct method, the optimal method can achieve a shorter settling time and has smaller undesirable damped oscillation on the output voltage. Experimental results are reported to verify the effectiveness of these two methods.

On Filon methods for a class of Volterra integral equations with highly oscillatory Bessel kernels

This paper focuses on the convergence of a class of collocation methods for Volterra integral equations of the second kind with highly oscillatory Bessel functions. Compared to existing theoretical results, sharper frequency-related convergence rates of these methods are established by exploring the asymptotic expansions of solutions and solving error equations. Theoretical results in this paper show the direct Filon method and continuous linear collocation method share the same convergence rate. Both of them admit a better convergence rate compared to the piecewise constant collocation method in solving Volterra integral equations with highly oscillatory Bessel kernels. These results are verified by numerical experiments.

Application of composite small calibration objects in traffic accident scene photogrammetry.

In order to address the difficulty of arranging large calibration objects and the low measurement accuracy of small calibration objects in traffic accident scene photogrammetry, a photogrammetric method based on a composite of small calibration objects is proposed. Several small calibration objects are placed around the traffic accident scene, and the coordinate system of the composite calibration object is given based on one of them. By maintaining the relative position and coplanar relationship of the small calibration objects, the local coordinate system of each small calibration object is transformed into the coordinate system of the composite calibration object. The two-dimensional direct linear transformation method is improved based on minimizing the reprojection error of the calibration points of all objects. A rectified image is obtained using the nonlinear optimization method. The increased accuracy of traffic accident scene photogrammetry using a composite small calibration object is demonstrated through the analysis of field experiments and case studies.

Error Reduction in Spatial Robots Based on the Statistical Uncertainty Analysis

ABSTRACT Kinematic accuracy of the robot end-effector is decreased by many uncertainties. In order to design and manufacture robots with high accuracy, it is essential to know the effects of these uncertainties on the motion of robots. Uncertainty analysis is a useful method which can estimate deviations from desired path in robots caused by uncertainties. This paper presents an applied formulation based on Direct Linearization Method (DLM), for 3D statistical uncertainty analysis of open- loop mechanisms and robots. The maximum normal and parallel components of the position error on the end-effector path are introduced. In this paper, uncertainty effects of both linear and angular variations in performance of spatial open-loop mechanisms and robots are considered. Based on the relations for the percent contributions of manufacturing variables, for the position error reduction, the tolerances that have the most significant effects on the commutated uncertainty zone of the end-effector position can be modified. The proposed method is illustrated using a spatial manipulator with three-revolute joints and verified with a Monte Carlo simulation method. Finally, normal and parallel distances to end-effector path are determined as error bands for all over range of motion. The results of applying this method demonstrate that estimating the position error in mechanisms and robots can be done efficiently and precisely.