Algorithmic Differentiation of the MWGS-Based Arrays for Computing the Information Matrix Sensitivity Equations within the Problem of Parameter Identification

The paper considers the problem of algorithmic differentiation of information matrix difference equations for calculating the information matrix derivatives in the information Kalman filter. The equations are presented in the form of a matrix MWGS (modified weighted Gram–Schmidt) transformation. The solution is based on the usage of special methods for the algorithmic differentiation of matrix MWGS transformation of two types: forward (MWGS-LD) and backward (MWGS-UD). The main result of the work is a new MWGS-based array algorithm for computing the information matrix sensitivity equations. The algorithm is robust to machine round-off errors due to the application of the MWGS orthogonalization procedure at each step. The obtained results are applied to solve the problem of parameter identification for state-space models of discrete-time linear stochastic systems. Numerical experiments confirm the efficiency of the proposed solution.

Recursive Newton-Euler Dynamics and Sensitivity Analysis for Robot Manipulator With Revolute Joints

In this study, recursive Newton-Euler sensitivity equations are derived for robot manipulator motion planning problems. The dynamics and sensitivity equations depend on the 3 × 3 rotation matrices based on the moving coordinates. Compared to recursive Lagrangian formulation, which depends on 4 × 4 Denavit-Hartenberg (DH) transformation matrices, the moving coordinate formulation increases computational efficiency significantly as the number of matrix multiplications required for each optimization iteration is greatly reduced. A two-link manipulator time-optimal trajectory planning problem is solved using the proposed recursive Newton-Euler dynamics formulation. Only revolute joint is considered in the formulation. The predicted joint torque and trajectory are verified with the data in the literature. In addition, the optimal joint forces are retrieved from the optimization using recursive Newton-Euler dynamics.

Probing for stomach using the Focused Impedance Method (FIM)

For probing deep organs of the body using electrical impedance, the conventional method is to use Electrical Impedance Tomography (EIT). However, this would be a sophisticated machine and will be very expensive when a full 3D EIT is developed in the future. Furthermore, for most low income countries such expensive devices may not deliver the benefits to a large number of people. Therefore, this paper suggests the use of simpler techniques like Tetrapolar Impedance Measurement (TPIM) or Focused Impedance Method (FIM) in probing deeper organs. Following a method suggested earlier by one of the authors, this paper studies the possibility of using TPIM and FIM for the stomach. Using a simplified model of the human trunk with an embedded stomach, a finite element simulation package, COMSOL, was used to obtain transfer impedance values and percentage contribution of the stomach region in the total impedance. For this work, judicious placement of electrodes through qualitative visualizations based on point sensitivity equations and equipotential concepts were made, which showed that reasonable contribution of the stomach region is possible through the use of TPIM and FIM. The contributions were a little over 20% which is of similar order of the cross-sectional area percentage of the stomach with respect to that of the trunk. For the case where the conductivity of the stomach region was assumed about 4 times higher, the contributions increased to about 38%. Through further studies this proposed methods may contribute greatly in the study of deeper organs of the body.

On the Optimal Design of Doppler Scatterometers

Pencil-beam Doppler scatterometers are a promising remote sensing tool for measuring ocean vector winds and currents from space. While several point designs exist in the literature, these designs have been constrained by the hardware they inherited, and the design is sub-optimal. Here, guidelines to optimize the design of these instruments starting from the basic sensitivity equations are presented. Unlike conventional scatterometers or pencil-beam imagers, appropriate sampling of the Doppler spectrum and optimizing the radial velocity error lead naturally to a design that incorporates a pulse-to-pulse separation and pulse length that vary with scan angle. Including this variation can improve radial velocity performance significantly and the optimal selection of system timing and bandwidth is derived. Following this, optimization of the performance based on frequency, incidence angle, antenna length, and spatial sampling strategy are considered. It is shown that antenna length influences the performance most strongly, while the errors depend only on the square root of the transmit power. Finally, a set of example designs and associated performance are presented.

On the Optimal Design of Doppler Scatterometers

Pencil-beam Doppler scatterometers are a promising remote sensing tool for measuring ocean vector winds and currents from space. While several point designs exist in the literature, these designs have been constrained by the hardware they inherited, and the design is sub-optimal. Here, I present guidelines to optimize the design of these instruments starting from the basic sensitivity equations. Unlike conventional scatterometers or pencil-beam imagers, appropriate sampling of the Doppler spectrum and optimizing the radial velocity error lead naturally to a design that incorporates a pulse-to-pulse separation and pulse length that vary with scan angle. Including this variation can improve radial velocity performance significantly and the optimal selection of system timing and bandwidth is derived. Following this, optimization of the performance based on frequency, incidence angle, antenna length, and spatial sampling strategy are considered. It is shown that antenna length influences the performance most strongly, while the errors depend only on the square root of the transmit transmit power. Finally, a set of example designs and associated performance are presented.

Passive Regulation of Thermally Induced Axial Force and Displacement in Microbridge Structures

The analytical model of a mechanism for regulating the thermally induced axial force and displacement in a fixed–fixed microbeam is presented in this article. The mechanism which consists of a set of parallel chevron beams replaces one of the fixed ends of the microbeam. The thermomechanical behavior of the system is modeled using Castigliano’s theorem. The effective coefficient of thermal expansion is used in the analytical model. The analytical model takes into account both the axial and bending deformations of the chevron beams. The model provides a closed-form equation to determine the thermally induced axial force and displacement in the microbeam. In addition, the model is used to derive the equations for the sensitivities of the microbeam’s axial force and displacement to the variations of the design parameters involved. Moreover, the model produces the stiffness of the chevron beams. The effect of the stiffness of the chevron beams on the dynamic behavior of the microbeam is discussed. The analytical model is verified by finite element modeling using a commercially available software package. Using the analytical model, two special cases are highlighted: a system with thermally insensitive axial force and a system with thermally insensitive axial displacement. The main application of the model presented in this article is in the design of sensors and resonators that require robustness against changes of temperature in the environment. The analytical model and the sensitivity equations can be easily integrated into optimization algorithms.