Error analysis for the lidar backward inversion algorithm

Here we depart from the inhomogeneous solution of a lidar equation using the backward inversion algorithm that is nowadays generally referred to as the Klett method. In particular, we develop an error sensitivity study that relates errors in the user-input parameters boundary extinction and exponential term in the extinction-to-backscatter relationship to errors in the inverted extinction profile. The validity of the analysis presented is limited only by the validity of application of the inversion algorithm itself, its numerical performance having been tested for optical depths in the 0.01-10 range. Toward this end, we focus on an introductory background about how uncertainties in these two parameters can apply to a family of inverted extinction profiles rather than a single profile and on its range-dependent behavior as a function of the optical thickness of the lidar inversion range. Next, we performed a mathematical study to derive the error span of the inverted extinction profile that is due to uncertainties in the above-mentioned user calibration parameters. This takes the form of upper and lower range-dependent error bounds. Finally, appropriate inversion plots are presented as application examples of this study to a parameterized set of atmospheric scenes inverted from both synthesized elastic-backscatter lidar signals and a live signal.     

Eigensolution using lagrangian interpolation

A computationally efficient and accurate solution technique for large-order eigenvalue problems with small to medium bandwidth is presented. The algorithm—called the Sub-Polynomial Iteration (SPI) method—solves for the eigenvalues and corresponding eigenvectors. directly without any transformation to the standard form. The method is an efficient combination of several separate techniques including Sturm sequence, Lagrangian polynomial interpolation, inverse iteration with shift and Gram-Schmidt orthogonalization. Computer run times for a set of sample solution indicate the efficiency of the SPI method.     

A variable elimination method to improve the parsimony of MLR models using the successive projections algorithm

The successive projections algorithm (SPA) is a variable selection technique designed to minimize collinearity problems in multiple linear regression (MLR). This paper proposes a modification to the basic SPA formulation aimed at further improving the parsimony of the resulting MLR model. For this purpose, an elimination procedure is incorporated to the algorithm in order to remove variables that do not effectively contribute towards the prediction ability of the model as indicated by an F-test. The utility of the proposed modification is illustrated in a simulation study, as well as in two application examples involving the analysis of diesel and corn samples by near-infrared (NIR) spectroscopy. The results demonstrate that the number of variables selected by SPA can be reduced without significantly compromising prediction performance. In addition, SPA is favourably compared with classic Stepwise Regression and full-spectrum PLS. A graphical user interface for SPA is available at www.ele.ita.br/kawakami/spa/.     

Fatigue limit prediction of notched components using short crack growth theory and an asymptotic interpolation method

Mechanical components have stress risers, such as notchs, corners, welding toes and holes. These geometries cause stress concentrations in the component and reduce the fatigue strength and life of the structure. Fatigue crack usually initiates at and propagates from these locations. Traditional fatigue analysis of notched specimens is done using an empirical formula and a fitted fatigue notch factor, which is experimentally expensive and lacks physical meaning. A general methodology for fatigue limit prediction of notched specimens is proposed in this paper. First, an asymptotic interpolation method is proposed to estimate the stress intensity factor (SIF) for cracks at the notch root. Both edge notched and center notched components with finite dimension correction are included into the proposed method. The small crack correction is included in the proposed asymptotic solution using El Haddad’s fictitious crack length. Fatigue limit of the notched specimen is estimated using the proposed stress intensity factor solution when the realistic crack length is approaching zero. A wide range of experimental data are collected and used to validate the proposed methodology. The relationship between the proposed methodology and the traditionally used fatigue notch factor approach is discussed.     

An efficient implementation of reconfigurable interpolation root-raised cosine FIR filter for software-defined radio application

This brief presents an efficient binary common subexpression elimination (BCSE)-based approach for designing reconfigurable interpolation root-raised cosine (RRC) finite-impulse-response (FIR) filter, whose coefficients change during runtime for multistandard wireless communication system called software-defined radio (SDR). Reconfiguration can be done conveniently by storing the coded coefficients in the lookup tables (LUTs), and loading the required coefficient set over the interpolation filter. In the proposed method based on 4-bit BCSE algorithm, first the number of binary common subexpressions (BCSs) formed in the coefficients is reduced. Hence, multiplexers, shifters, and adders in the multiplier structure are reduced, which results in the improvement of operating frequency. The number of addition operations is further reduced using programmable adders and an efficient polyphase interpolation structure is implemented to reduce the hardware cost. The proposed design has 49.5% less area-delay product and 28.6% improved frequency of operation when compared to a 2-bit BCSE-based technique reported earlier when implemented on Xilinx field-programmable gate array (FPGA) device XC2VP4FF672-6. Similarly, the proposed design supports 93.14 MHz operating frequency, which is 59.2% and 74.2% greater when compared to 2-bit BCSE- and 3-bit BCSE-based approach when implemented on XC2V3000FF1152-4. The proposed structure also shows improved performance in terms of speed and area when compared to distributed arithmetic (DA)-based and multiply-accumulate (MAC)-based approaches.     

A successive parameter estimation algorithm for chirplet signal decomposition

In ultrasonic imaging systems, the patterns of detected echoes correspond to the shape, size, and orientation of the reflectors and the physical properties of the propagation path. However, these echoes often are overlapped due to closely spaced reflectors and/or microstructure scattering. The decomposition of these echoes is a major and challenging problem. Therefore, signal modeling and parameter estimation of the nonstationary ultrasonic echoes is critical for image analysis, target detection, and object recognition. In this paper, a successive parameter estimation algorithm based on the chirplet transform is presented. The chirplet transform is used not only as a means for time-frequency representation, but also to estimate the echo parameters, including the amplitude, time-of-arrival, center frequency, bandwidth, phase, and chirp rate. Furthermore, noise performance analysis using the Cramer Rao lower bounds demonstrates that the parameter estimator based on the chirplet transform is a minimum variance and unbiased estimator for signal-to-noise ratio (SNR) as low as 2.5 dB. To demonstrate the superior time-frequency and parameter estimation performance of the chirplet decomposition, ultrasonic flaw echoes embedded in grain scattering, and multiple interfering chirplets emitted by a large, brown bat have been analyzed. It has been shown that the chirplet signal decomposition algorithm performs robustly, yields accurate echo estimation, and results in SNR enhancements. Numerical and analytical results show that the algorithm is efficient and successful in high-fidelity signal representation.     

A Hermite interpolation algorithm for hypersingular boundary integrals

This paper presents a conforming C¹ boundary integral algorithm based on Hermite interpolation. This work is motivated by the requirement that the surface function multiplying a hypersingular kernel be differentiable at the collocation nodes. The unknown surface derivatives utilized by the Hermite approximation are determined, consistent with other boundary values, by writing a tangential hypersingular equation. Hypersingular equations are primarily invoked for solving crack problems, and the focus herein is on developing a suitable approximation for this geometry. Test calculations for the Laplace equation in two dimensions indicate that the algorithm is a promising technique for three-dimensional problems.     

First-order PMD compensation using optical FIR filter

We present a synthesis algorithm to design an optical finite impulse response (FIR) filter for compensating a first-order polarization mode dispersion (PMD) by minimizing the differential group delay (DGD). The desired frequency response was approximated using two widely used methods in designing digital FIR filters: the Fourier series expansion method and the frequency sampling method. A numerical simulation was performed for an eighth-order filter to demonstrate the difference between the two methods. The simulation results produced a sharper cutoff for the Fourier series expansion and higher stopband attenuation for the frequency sampling method. The Fourier series method produced better results in reducing the DGD.     

Performance of Reed?Solomon codes using the Guruswami?Sudan algorithm with improved interpolation efficiency

List decoding is a novel method for decoding Reed-Solomon (RS) codes that generates a list of candidate transmitted messages instead of one unique message as with conventional algebraic decoding, making it possible to correct more errors. The Guruswami-Sudan (GS) algorithm is the most efficient list decoding algorithm for RS codes. Until recently only a few papers in the literature suggested practical methods to implement the key steps (interpolation and factorisation) of the GS algorithm that make the list decoding of RS codes feasible. However, the algorithm's high decoding complexity is unsolved and a novel complexity-reduced modification to improve its efficiency is presented. A detailed explanation of the GS algorithm with the complexity-reduced modification is given with simulation results of RS codes for different list decoding parameters over the AWGN and Rayleigh fading channels. A complexity analysis is presented comparing the GS algorithm with our modified GS algorithm, showing the modification can reduce complexity significantly in low error weight situations. Simulation results using the modified GS algorithm show larger coding gains for RS codes with lower code rates, with more significant gains being achieved over the Rayleigh fading channels.     

A successive sampling control chart using multiple dependent state sampling over two successive occasions

In this paper, successive sampling (SS) mean monitoring control chart is proposed for two successive occasions using multiple dependent state (MDS) sampling and characterized as MDS-SS control chart. The sample size is selected on the basis of SS for the control statistic in two pairs of the control limits. The average run length is evaluated, and the performance of the proposed concept over the existing SS control chart is presented using a real-life example. The SS monitoring chart concept is compiled with MDS, and it becomes more sophisticated in detection of warning signs.     

Stress concentration factor prediction by the multi-dimensional Lagrangian interpolation method

A new approach based on the multi-dimensional Lagrangian interpolation method, which is widely used in the finite element method, is proposed for the prediction of stress concentration factor for tubular joints. When comparing with the parametric regression method, this new method uses the same set of numerical parametric study results as its inputs. The accuracy of the proposed method is validated by applying it to predict the stress concentration factor and hot spot stress of partially overlapped circular hollow section K-joints. Numerical results indicated that the new method is more reliable and accurate than the parametric regression method.     

Low-power differential coefficients-based FIR filters using hardware-optimised multipliers

A minimal-difference differential coefficients method is presented for low power and high-speed realisation of differential-coefficients-based finite impulse response filters. The conventional differential coefficients method (DCM) uses the difference between adjacent coefficients whereas we identify the coefficients that have the least difference between their magnitude values and use these minimal difference values to encode the differential coefficients. Our minimal-difference differential coefficients can be coded using fewer bits, which in turn reduces the number of full additions required for coefficient multiplication. By employing a differential-coefficient partitioning algorithm and a pseudofloating-point representation, we show that the number of full adders and the net memory needed to implement the coefficient multipliers can be significantly reduced. The proposed method is combined with common subexpression elimination for further reduction of complexity. Experimental results show the average reductions of full adder, memory and energy dissipated achieved by our method over the DCM are 40, 35 and 50%, respectively     

Effects of noise on lidar data inversion with the backward algorithm

The lidar data-inversion algorithm widely known as the Klett method (and its more elaborate variants) has long been used to invert elastic-lidar data obtained from atmospheric sounding systems. The Klett backward algorithm has also been shown to be robust in the face of uncertainties concerning the boundary condition. Nevertheless electrical noise at the photoreceiver output unavoidably has an impact on the data-inversion process, and describing in an explicit way how it affects retrieval of the atmospheric optical coefficients can contribute to improvement in inversion quality. We examine formally the way noise disturbs backscatter-coefficient retrievals done with the Klett backward algorithm, derive a mathematical expression for the retrieved backscatter coefficient in the presence of noise affecting the signal, and assess the noise impact and suggest ways to limit it.     

Regression trees approach for flow-time prediction in wafer manufacturing processes using constraint-based genetic algorithm

Understanding the factors associated with the flow-time of wafer production is crucial for workflow design and analysis in wafer fabrication factories. Owing to wafer fabrication complexity, the traditional human approach to assigning the due-date is imprecise and prone to failure, especially when the shop status is dynamically changing. Therefore, assigning a due-date to each customer order becomes a challenge to production planning. The paper proposes a constraint-based genetic algorithm approach to determine the flow-time. The flow-time prediction model was constructed and compared with other approaches. Better computational effectiveness and prediction results from the constraint-based genetic algorithm are demonstrated using experimental data from a wafer-manufacturing factory.     

Three‐dimensional numerical solution for wear prediction using a mortar contact algorithm

A finite element formulation to compute the wear between three‐dimensional flexible bodies that are in contact with each other is presented. The contact pressure and the bodies displacements are calculated using an augmented Lagrangian approach in combination with a mortar method, which defines the contact kinematics. The objective of this study is to characterize the wear rate coefficients for bimetallic pairs and to numerically predict the wear depths in new component designs. The proposed method is first validated with the classical pin‐on‐disc problem. Then, experimental results of wear for the metallic pairs used in internal combustion engine valves and inserts are presented and are taken as a reference solution. An example is provided that shows agreement of the numerical and experimental solution. Finally, the proposed algorithm is used to predict the wear in an application example: the wear in an internal combustion engine valve. Copyright © 2013 John Wiley & Sons, Ltd.     

A backward algorithm for computing optimal controls for single-stage hybrid manufacturing systems

This paper concerns optimal control problems in single-stage manufacturing systems. The control variables comprise parameters of the jobs' processing times, and the cost functional involves measures of both jobs' due dates and products' physical characteristics. The system is configured for processing a finite number of jobs in a given order, and it is modelled as a hybrid dynamical system cast in a deterministic setup. The paper identifies a necessary and sufficient optimality condition having an intuitive geometric appeal, and it develops an efficient, low-complexity algorithm for computing the optimal controls. Numerical experiments testify to the efficacy of the proposed algorithm.     

NURBS curve interpolation algorithm based on tool radius compensation method

This paper focuses on developing an algorithm that can generate toolpaths in NURBS form for smooth, high speed and accurate machining. The initial toolpaths are obtained by tool radius compensation method which is based on the workpiece boundary offsetting. According to different lengths and the continuous short block (CSB) criterion, these offset linear segments can be regarded as CSBs or long straight segments. Junctions are located where the curvature value is greater than the preset curvature threshold value or where it changes abruptly, or at the two end points of any long straight segment. During machining, the NURBS fitting module first looks ahead several CSBs and converts them into parametric curves in real time. During the conversion, continuities of the position, slope or even curvature at the transition of the parametric curves and unfitted line segments can be guaranteed. Then the acceleration/deceleration feedrate-planning scheme is proposed to determine the transition feedrate at the junction between the fitted curves and unfitted long straight segments, and the corner feedrate within the fitted curve. Simulations and experiments show that the proposed algorithm can significantly improve machining accuracy and reduce cutting time to satisfy today’s high-speed and high-accurate machining requirements.     

Complex correction of data acquisition channels using FIR equalizerfilters

The common conviction about FIR (finite impulse response) digital filters is that the number of necessary taps, to reach the same performance as provided by IIR (infinite impulse response) digital filters, is usually too large. Moreover, the standard FIR filter design algorithm (Remez exchange) allows the design of linear-phase filters only. Therefore, IIR filters are often preferred over FIR ones, without any further investigations. This paper presents a case study of complex (amplitude and phase) equalization of the passband of a commercial anti-aliasing filter. The novelty is the usage of an FIR filter for this purpose (or an FIR one, combined with a low-order IIR filter), and a thorough discussion of the special design aspects. It turns out that for the given anti-aliasing filter (a Cauer filter of order 11) an FIR filter of length 60···100 can perform as well as a 26/26 (numerator order/denominator order) IIR one. The properties are even better if a low-order IIR filter is used in combination with an FIR one (orders, e.g., 1/1+40/0). Because of the absence of stability problems and the ease of implementation, the use of FIR filters is suggested