First-order Shape Research Articles

A new computational method for predicting the thermal bow of a rotor

In a heavy-duty gas turbine, when hot rotor is left cooled in standstill condition, thermal bow occurs due to natural convection, which may result in high vibrations in a subsequent restart. Usually, a turning gear is immediately started after shutdown of gas turbine to slowly roll and uniformly cool the rotor in order to prevent thermal bow, which is called turning gear operation. The minimum turning time and the acceptable temperature of wheel space are two important indexes of turning gear operation, and their determination highly depends on accurate prediction of thermal bow. This paper proposes an analytical method to predict the thermal bow behavior of rotors with complex structures and investigates the effect of turning time on thermal bow. First, the general form of analytical solution of rotor thermal bow is derived and validated through both finite element analysis and experiments. Then the analytical solution is applied in a heavy-duty gas turbine to predict the most severe thermal bow behavior of the rotor with no turning gear in operation before standstill. Finally, the effect of turning time on thermal bow is investigated, and the indexes to achieve acceptable thermal bow are discussed. Results show that the shape of thermal bow of the gas turbine rotor is close to the first-order mode shape; the peak of the most severe thermal bow reaches 0.7 mm after 3.8 h of cooling and the decrease of thermal bow is much slower than the increase. Besides, the maximum thermal bow of the rotor due to insufficient turning gear operation presents an exponential decay with turning time and lies in linear relationship with the temperature of the same location. These two relationships help determine the minimum turning time and acceptable temperature of wheel space to attain an acceptable bow and thus have practical significance to develop and optimize turning gear operations.

Shape optimization approach to defect-shape identification with convective boundary condition via partial boundary measurement

We aim to identify the geometry (i.e., the shape and location) of a cavity inside an object through the concept of thermal imaging. More precisely, we present an identification procedure to determine the geometric shape of a cavity with convective boundary condition in a heat-conducting medium using the measured temperature on a part of the surface of the object. The inverse problem of identifying the cavity is resolved by shape optimization techniques, specifically by minimizing a least-squares type cost functional over a set of admissible geometries. The computation of the first-order shape derivative or shape gradient of the cost is carried out through minimax formulation, which is then justified by the Correa–Seeger theorem coupled with function space parametrization technique. We further characterize its boundary integral form using some identities from tangential calculus. Then, we utilize the computed expression for the shape gradient to implement an effective boundary variation algorithm for the numerical resolution of the shape optimization problem. To avoid boundary oscillations or irregular shapes in our approximations, we execute the gradient-based scheme using the $$H^1$$ gradient method with perimeter regularization. Also, we propose a novel application of the said method in computing the mean curvature of the free boundary appearing in the shape gradient of the cost functional. We illustrate the feasibility of the proposed method by testing the numerical scheme to several cavity identification problems. Additionally, we also give some numerical examples for the case of corrosion detection since its inverse problem interpreted in the framework of electrostatic imaging is closely related to the focused problem.

High‐linearity SAR‐VCO MASH ΔΣ ADC with second‐order noise shaping

A novel 0-2 Multi-Stage Noise Shaping (MASH) analogue-to-digital converter (ADC) is proposed. The first stage is implemented using a 4-bit SAR ADC. The second stage uses a voltage controlled oscillator (VCO)-based quantiser (VCOQ). Unlike earlier VCOQs which provide first-order noise shaping, the VCOQ proposed in this Letter achieves second-order noise filtering. To implement this noise shaping, the quantisation noise of the VCOQ is extracted as a pulse-width-modulated signal, and it is fed back to the VCO input using a charge pump circuit. In the proposed scheme, the input signal to the VCO is small. Therefore, the linearity requirement of this block is relaxed. Also, any error related to the charge pump circuitry will be first-order shaped at the output. Simulation results confirm the second-order noise shaping of the output of the ADC, and an excellent (14-bit signal-to-noise and distortion ratio) performance with the over-sampling ratio of 16.

VCO‐based ADC with a simplified DAC for non‐linearity correction

The performance of open-loop ADCs implemented with VCOs is limited by VCO non-linearity and first-order noise shaping. The resolution limitation imposed by first-order noise shaping can be compensated by a ring oscillator VCO with many output phases. Linearity can also be improved by using a feedback loop around the VCO closed with a DAC. However, a long ring oscillator may require a DAC with a prohibitive number of bits if feedback is used to compensate distortion. This Letter proposes an ADC architecture based on the Leslie-Singh Sigma-Delta () modulator that allows to implement a distortion correction loop around a VCO with a simplified DAC of few levels, yet keeping a large number of output quantisation levels to maintain resolution. The Letter discusses the system-level architecture and shows an implementation circuit example to verify the effective correction of distortion.

A 250-MHz Pipelined ADC-Based <inline-formula> <tex-math notation="LaTeX">$f_{S}/4$ </tex-math> </inline-formula> Noise-Shaping Bandpass ADC

A new $f_{S}/4$ bandpass $\Delta \Sigma$ -analog-to-digital converter (ADC) architecture is realized by feeding back the delayed quantization noise inherently produced by a pipelined ADC. Designed in a 55-nm global foundry (GF) LP-CMOS process, the prototype ADC sampling at 250 MHz achieves an Signal-to-Noise+Distortion Ratio of 72, 75.8, 80.1, and 85.3 dB in a 15.64-, 7.82-, 3.91-, and 1.953-MHz band, respectively, around a center frequency of 62.5 MHz with only first-order noise shaping, while consuming 103 mW of power, and achieving a maximum figure-of-merit of 158 dB.

High-efficiency and high-accuracy digital speckle correlation for full-field image deformation measurement

Many works around the digital speckle correlation (DSC) are to improve the computational efficiency and measurement accuracy in recent years. This work aims to improve the efficiency and accuracy of DSC for both single-point and full-field points used in mechanical properties test of materials. For this purpose, first, a subpixel initial guess for the inverse compositional Gauss–Newton algorithm (IC-GN) with the first-order shape function is introduced for single-point image registration. Then, with the aid of strategy of subset image edge extend interpolation (SIEEI), the efficiency and accuracy of full-field displacement and deformation measurement are improved simultaneously. The SIEEI is employed to reduce mean squared difference errors caused by traditional bicubic interpolation algorithm. Comparative studies between the traditional IC-GN algorithm and the proposed algorithms are presented using simulated speckle images and CCD images. The proposed method achieves more executive efficiency and more accuracy for single-point and full-field points image registration. The computational efficiency of the proposed algorithms increases 7.5% for full-field registration using CCD images. The mean of squared difference errors of the SIEEI method is less than the traditional bicubic interpolation algorithm. The presented approach shows great potentials for challenging application, such as mechanical properties test of materials.

Slope failure and mass transport processes along the Queen Charlotte Fault, southeastern Alaska

Abstract The Queen Charlotte Fault defines the Pacific–North America transform plate boundary in western Canada and southeastern Alaska for c. 900 km. The entire length of the fault is submerged along a continental margin dominated by Quaternary glacial processes, yet the geomorphology along the margin has never been systematically examined due to the absence of high-resolution seafloor mapping data. Hence the geological processes that influence the distribution, character and timing of mass transport events and their associated hazards remain poorly understood. Here we develop a classification of the first-order shape of the continental shelf, slope and rise to examine potential relationships between form and process dominance. We found that the margin can be split into six geomorphic groups that vary smoothly from north to south between two basic end-members. The northernmost group (west of Chichagof Island, Alaska) is characterized by concave-upwards slope profiles, gentle slope gradients (<6°) and relatively low along-strike variance, all features characteristic of sediment-dominated siliciclastic margins. Dendritic submarine canyon/channel networks and retrogressive failure complexes along relatively gentle slope gradients are observed throughout the region, suggesting that high rates of Quaternary sediment delivery and accumulation played a fundamental part in mass transport processes. Individual failures range in area from 0.02 to 70 km 2 and display scarp heights between 10 and 250 m. Transpression along the Queen Charlotte Fault increases southwards and the slope physiography is thus progressively more influenced by regional-scale tectonic deformation. The southernmost group (west of Haida Gwaii, British Columbia) defines the tectonically dominated end-member: the continental slope is characterized by steep gradients (>20°) along the flanks of broad, margin-parallel ridges and valleys. Mass transport features in the tectonically dominated areas are mostly observed along steep escarpments and the larger slides (up to 10 km 2 ) appear to be failures of consolidated material along the flanks of tectonic features. Overall, these observations highlight the role of first-order margin physiography on the distribution and type of submarine landslides expected to occur in particular morphological settings. The sediment-dominated end-member allows for the accumulation of under-consolidated Quaternary sediments and shows larger, more frequent slides; the rugged physiography of the tectonically dominated end-member leads to sediment bypass and the collapse of uplifted tectonic features. The maximum and average dimensions of slides are an order of magnitude smaller than those of slides observed along other (passive) glaciated margins. We propose that the general patterns observed in slide distribution are caused by the interplay between tectonic activity (long- and short-term) and sediment delivery. The recurrence (<100 years) of M > 7 earthquakes along the Queen Charlotte Fault may generate small, but frequent, failures of under-consolidated Quaternary sediments within the sediment-dominated regions. By contrast, the tectonically dominated regions are characterized by the bypass of Quaternary sediments to the continental rise and the less frequent collapse of steep, uplifted and consolidated sediments.

Shape Aware Quadratures

With Shape Aware Quadratures (SAQ), for a given set of quadrature nodes, order, and domain of integration, the quadrature weights are obtained by solving a system of suitable moment fitting equations in least square sense. The moments in the moment equations are approximated over a simplified domain (Ω0) that is a reasonable approximation of the original domain (Ω) that are then corrected for the deviation of the shape of Ω0 from Ω via shape correction factors. This idea was already successfully utilized in the Adaptively Weighted Numerical Integration (AW) method [1–3], where moments were computed over simplified but homeomorphic domain and then corrected using first-order shape sensitivity, allowing efficient and accurate integration of integrable functions over arbitrary domains.With SAQ, more general shape correction factors can be derived based on a variety of sensitivity analysis techniques such as shape sensitivity (SSA) and topological sensitivity (TSA). Using the right kind/order of shape correction factors for moment approximation enables the resulting quadrature (from the moment fitting equations) to efficiently adapt to the shape of the original domain even in the presence of thousands of small features. We derive shape correction factors based on SSA and TSA of moment integrals. We also demonstrate the efficacy of SAQ in integrating bivariate/trivariate polynomials over several 2D/3D domains in the presence of small features.

A Highly Digital Second-Order Oversampling TDC

A second-order, single loop ΔΣ time-to-digital converter (TDC) is presented in this letter. The proposed TDC uses two differential current-controlled oscillators as phase domain integrators. The proposed architecture does not require excess loop delay compensation or nonlinearity calibration. Digital differentiation using XOR implements an intrinsic first-order high-pass shaping of static element mismatch in the current steering digital-to-analog converter. A prototype TDC in 65-nm CMOS process has linearity of 8.1 bits, integrated noise of 3.8 ps and energy efficiency of 0.45 pJ/code over a bandwidth of 2.5 MHz.

Radiomic Biomarkers to Refine Risk Models for Distant Metastasis in HPV-related Oropharyngeal Carcinoma

Distant metastasis (DM) is the main cause of death for patients with human papillomavirus (HPV)-related oropharyngeal cancers (OPCs); yet, there are few reliable predictors of DM in this disease. The role of quantitative imaging (ie, radiomic) analysis was examined to determine whether there are primary tumor features discernible on imaging studies that are associated with a higher risk of DM developing. Radiation therapy planning computed tomography scans were retrieved for all nonmetastatic p16-positive OPC patients treated with radiation therapy or chemoradiation therapy at a single institution between 2005 and 2010. Radiomic biomarkers were derived from each gross tumor volume. The biomarkers included 4 representative radiomic features from tumor first-order statistics, shape, texture, and wavelet groups, as well as a combined 4-feature signature. Univariable Cox proportional hazards models for DM risk were identified. The discriminative performance of prognostic univariable and multivariable models was compared using the concordance index (C-index). Subgroup analyses were performed. There were 300 HPV-related OPC patients who were eligible for the analysis. A total of 36 DM events occurred within a median follow-up period of 5years. On univariable analysis, top results included the 4 representative radiomic features (C-index, 0.670-0.686; P<.001), the radiomic signature (C-index, 0.670; P<.001), tumor stage (C-index, 0.633; P<.001), tumor diameter (C-index, 0.653; P<.001), and tumor volume (C-index, 0.674; P<.001), which demonstrated moderate discrimination of DM risk. Combined clinical-radiomic models yielded significantly improved performance (C-index, 0.701-0.714; P<.05). In subgroup analyses, the radiomic biomarkers consistently stratified patients for DM risk, particularly for those cohorts with greater risks (C-index, 0.663-0.796), such as patients with stage III disease. Radiomic biomarkers appear to classify DM risk for patients with nonmetastatic HPV-related OPC. Radiomic biomarkers could be used either alone or with other clinical characteristics in the assignment of DM risk in future HPV-related OPC clinical trials.

A Pulse Frequency Modulation Interpretation of VCOs Enabling VCO-ADC Architectures With Extended Noise Shaping

In this paper, we propose to study voltage controlled oscillators (VCOs) based on the equivalence with pulse frequency modulators (PFMs). This approach is applied to the analysis of VCO-based analog-to-digital converters (VCO-ADCs) and deviates significantly from the conventional interpretation, where VCO-ADCs have been described as the first-order $\Delta \Sigma $ modulators. A first advantage of our approach is that it unveils systematic error components not described by the equivalence with a conventional $\Delta \Sigma $ modulator. A second advantage is that, by a proper selection of the pulses generated by the PFM, we can theoretically construct an open loop VCO-ADC with an arbitrary noise shaping order. Unfortunately, with the exception of the first-order noise shaping case, the required pulse waveforms cannot easily be implemented on the circuit level. However, we describe circuit techniques to achieve a good approximation of the required pulse waveforms, which can easily be implemented by practical circuits. Finally, our approach enables a straightforward description of multistage $\Delta \Sigma $ modulator architectures, which is an alternative and practically feasible way to realize a VCO-ADC with extended noise shaping.

Quantifying the Impact of Random Surface Perturbations on Reflective Gratings

We present a novel deterministic method capable of calculating statistical moments of transverse electric polarized fields scattered by perfect electric conductor gratings with small surface random perturbations. Based on a first-order shape Taylor expansion, the resulting electric field integral equations are solved via the method of moments with constant hierarchical basis or Haar wavelets. This allows for a sparse tensor approximation, significantly reducing the number of required unknowns and yielding a higher rate of convergence than a dense approximation. Moreover, the proposed approach converges faster than Monte Carlo simulations with significantly less computational effort. Validation of the proposed approach is performed for several cases, and realistic simulations applied to the calculation and prediction of grating efficiency reveal the applicability of the method.

Investigations of self-excited vibration in splitter plate with a cavity in the supersonic mixing layer

The combustion efficiency strongly depends on the mixing process of fuel–air for a combined cycle engine. For an efficient mixing process, self-excited vibration of splitter plate is more practical than that of forced vibration. We have carried out a comprehensive numerical and experimental study of self-excited vibration. Finite element method (FEM) is applied to analyze the natural modal of vibration. Large eddy simulations (LES) are employed for the mechanistic study of self-excited vibration and their influence factors are evaluated from the experimental studies. Displacements are accurately measured by a non-intrusive laser vibrometer. It is found that the first-order vibration shape is quasi-two-dimensional and responsible for improved mixing. We found that self-excited vibration of the splitter plate is motivated by a cavity due to the acoustic self-oscillation. Moreover, self-excited vibration depends on the gap distance between fixed rod and splitter plate, static pressure difference between upper and lower nozzle outlet, length to depth ratio (K) and aft wall angle (θ). At zero gap distance, the frequency is up to 2.5 times higher than that of 3 mm gap distance. So, reduction in gap distance can efficiently increase the frequency of self-excited vibration, which is an encouraging point for the future study.

Maximizing the first eigenfrequency of structures subjected to uniform boundary erosion through the level set method

Erosion of structure may result in non-trivial loss of performance. For instance, erosion may make structure members break apart and results in localized vibration eigenmodes, which will make the first eigenfrequency of eroded structure become smaller. To obtain a robust design whose first eigenfrequency is not disproportionately affected by boundary erosion, we first examine a generic deterministic structural optimization problem defined in the level-set framework. Relying on the analysis of the first-order shape derivative and the optimality conditions, several important conclusions are obtained. Then, the optimization problem of maximizing the first eigenfrequency of structures subjected to uniform erosion is introduced. In each iteration of optimization, erosion is intentionally created, and a mode recognition technique is employed to identify the actual first eigenfrequency, i.e., not belonging to localized eigenmodes. The boundary of the un-eroded structure is optimized to improve the performance of the eroded structure. The shape derivative defined on the boundary of the eroded structure is mapped to the boundary of the un-eroded one by resorting to velocity extension of the level set method.

Computer-Aided Grading of Gliomas Combining Automatic Segmentation and Radiomics

Gliomas are the most common primary brain tumors, and the objective grading is of great importance for treatment. This paper presents an automatic computer-aided diagnosis of gliomas that combines automatic segmentation and radiomics, which can improve the diagnostic ability. The MRI data containing 220 high-grade gliomas and 54 low-grade gliomas are used to evaluate our system. A multiscale 3D convolutional neural network is trained to segment whole tumor regions. A wide range of radiomic features including first-order features, shape features, and texture features is extracted. By using support vector machines with recursive feature elimination for feature selection, a CAD system that has an extreme gradient boosting classifier with a 5-fold cross-validation is constructed for the grading of gliomas. Our CAD system is highly effective for the grading of gliomas with an accuracy of 91.27%, a weighted macroprecision of 91.27%, a weighted macrorecall of 91.27%, and a weighted macro-F1 score of 90.64%. This demonstrates that the proposed CAD system can assist radiologists for high accurate grading of gliomas and has the potential for clinical applications.

An Energy-Efficient Hybrid SAR-VCO $\Delta \Sigma $ Capacitance-to-Digital Converter in 40-nm CMOS

This paper presents a highly digital, 0-1 MASH capacitance-to-digital converter (CDC). The CDC works by sampling a reference voltage on the sensing capacitor and then quantizing the charge stored in it by a 9-bit successive approximation register analog-to-digital converter. The residue is fed to a ring voltage-controlled oscillator (VCO) $\Delta \Sigma $ and quantized in time domain. The outputs from the two stages are combined to produce a quantized output with the first-order noise shaping. The proposed two-stage architecture reduces the impact of the VCO’s nonlinearity. A digital calibration technique is used to track the VCO’s gain across process, voltage, and temperature. The absence of any operational amplifier and low oversampling ratio for the VCO results in high energy efficiency. A prototype CDC in a 40-nm CMOS process achieves a 64.2-dB SNR while operating from a 1-V supply and using a sampling frequency of 3 MHz. The prototype achieves a CDC figure of merit of 55 fJ/conversion-step.

A Low-Power Wide Dynamic-Range Current Readout Circuit for Ion-Sensitive FET Sensors.

This paper presents an amplifier-less and digital-intensive current-to-digital converter for ion-sensitive FET sensors. Capacitance on the input node is utilized as a residue accumulator, and a clocked comparator is followed for quantization. Without any continuous-time feedback circuit, the converter performs a first-order noise shaping of the quantization error. In order to minimize static power consumption, the proposed circuit employs a single-ended current-steering digital-to-analog converter which flows only the same current as the input. By adopting a switching noise averaging algorithm, our dynamic element matching not only mitigates mismatch of current sources in the current-steering DAC, but also makes the effect of dynamic switching noise become an input-independent constant. The implemented circuit in 0.35 μm CMOS converts the current input with a range of 2.8 μ A to 15 b digital output in about 4 ms, showing a DNL of +0.24/-0.25 LSB and an INL of + 1.98/-1.98 LSB while consuming 16.8 μW.

Wide‐band high‐accuracy ΔΣ ADC using segmented DAC with DWA and mismatch shaping

A discrete-time ΔΣ analogue-to-digital converter utilising a multi-bit successive approximation register quantiser and a segmented digital-to-analogue converter (DAC) is proposed. By adding the delayed DAC output to the modulator input and removing it at the modulator output in the digital domain, the mismatch error is filtered. Thus, a first-order DAC mismatch error shaping is realised. This improves the DAC linearity without introducing an extra delay in the feedback path. Segmenting the DAC and processing the least significant bit and most significant bit segments separately, the dynamic range remains unaffected.

A 2.2-ps Two-Dimensional Gated-Vernier Time-to-Digital Converter With Digital Calibration

This brief presents a two-dimensional (2-D) Vernier time-to-digital converter (TDC) which uses two 3-stage gated ring oscillators (GROs) in the $X/Y$ Vernier branches. The already small Vernier quantization noise (∼10.6 ps) is improved by the first-order noise shaping of the GRO. Moreover, since all the delay differences between the $X$ and $Y$ phases can be used (rather than only the diagonal line of the one-dimensional architecture), the intrinsic large latency time of the Vernier architecture is dramatically reduced. The TDC is implemented in a 65-nm CMOS process and consumes 2.3 mA from 1.0 V. The measured total noise integrated over a bandwidth of 1.25 MHz yields an equivalent TDC resolution of 2.2 ps, whereas the average latency time (within 2 ns) is less than 1/6 of that in a standard Vernier TDC.

Theoretical estimation of systematic errors in local deformation measurements using digital image correlation

The measurement accuracy using the digital image correlation (DIC) method in local deformations such as the Portevin–Le Chatelier bands, the deformations near the gap, and the crack tips has raised a major concern. The measured displacement and strain results are heavily affected by the calculation parameters (such as the subset size, the grid step, and the strain window size) due to under-matched shape functions (for displacement measurement) and surface fitting functions (for strain calculation). To evaluate the systematic errors in local deformations, theoretical estimations and approximations of displacement and strain systematic errors have been deduced when the first-order shape functions and quadric surface fitting functions are employed. The following results come out: (1) the approximate displacement systematic errors are proportional to the second-order displacement gradients and the ratio is only determined by the subset size; (2) the approximate strain systematic errors are functions of the third-order displacement gradients and the coefficients are dependent on the subset size, the grid step and the strain window size. Simulated experiments have been carried out to verify the reliability. Besides, a convenient way by comparing displacement results measured by the DIC method with different subset sizes is proposed to approximately evaluate the displacement systematic errors.