Convex Research Articles

Trajectory control strategy for multi-tool synchronous electrochemical machining of blisk channels

The blisk is a core component of an aero-engine, and electrochemical machining (ECM) is the primary method for its manufacture. Among several ECM methods for blisks, multi-tool synchronous machining is the most efficient and advantageous for machining channels. The allowance distribution of the blank after blisk channel machining directly influences the blade profile accuracy. This paper proposes a trajectory control strategy to homogenize the allowance distribution of the blisk channel in multi-tool ECM. The strategy includes the design of the three-dimensional space motion of the tool and blisk, as well as the regulated feed speed. The structural characteristics of the blisk channel and the principle of ECM allow for designing and optimizing the multi-dimensional trajectory. The electric field simulations elucidate the influence law of the three-axis feed speed on the side gap. An algorithm is adopted to iteratively optimize the speeds for different positions to realize multi-dimensional motion control and allowance homogenization. The proposed trajectory control strategy is applied to ECM experiments for the blisk channel. Compared with the constant feed speed mode, the regulated speed strategy reduces the maximum allowance difference between the convex (CV) profiles by 36.18% and that between the concave (CC) profiles by 37.73%. Subsequently, the one-time ECM of eight blisk channels was successfully realized. The average time for a single channel was 12.5 min, significantly improving the machining efficiency. In conclusion, the proposed method is effective and can be extended for synchronously machining various blisk types with twisted channels.

Bone density in postmenopausal women with scoliosis is associated with markers of degenerative joint disease.

Bone mineral density (BMD) measured with dual x-ray absorptiometry (DXA) is the clinical standard for the diagnosis of osteoporosis and prediction of bone fracture risk. In the aging skeleton, osteoporosis is often concomitantly present with degenerative joint disease (DJD). In this study, we evaluated tissue-level changes in the differentially loaded concave (CC) and convex (CV) sides of the lumbar spine in a sample of postmenopausal women with scoliosis. We used a cumulative degeneration score to assess osteophyte formation, the severity of sclerotic morphology, and marrow changes as markers of DJD in the lumbar spine and examined the correlation between markers of DJD and BMD. More severe osteophyte growth and sclerosis were present on the CC side of the spine. The degenerative score (DS) was higher on the CC side of the lumbar spine compared with the CV side. While CC BMD was positively correlated with CC DS and marrow, CV DS was not correlated with CV BMD. Marrow changes were correlated with DS on the CC lumbar spine. These results highlight the importance of mechanoadaptive as well as broader inflammatory processes in the manifestation of degenerative changes and local mineral deposition at the lumbar spine. DXA-based BMD measurement of osteoporosis need to be contextualized within the biomechanical and degenerative conditions of a joint rather than using a strict threshold cutoff.

Effect of slope curvature and gradient on soil properties affecting erodibility of coastal plain sands in Akwa Ibom State, Nigeria

A study was conducted to assess the effect of slope curvature and gradient on soil properties affecting erodibility of coastal plain sands in Akwa Ibom State. Twelve locations comprising six each of concave (CC) and convex (CV) slopes, and three slope gradients, namely, gentle (GS), moderate (MS) and steep slopes (SS) in CC and CV were identified for the study. Bulk and core soil samples were collected from the top 30 cm soil depth at three slope positions of slope curvature and gradient categories for physical and chemical characterization, and derivation of microaggregate stability indices and erodibility factor, K. Results showed that coarse sand (CS), fine sand (FS), bulk density (Bd), total porosity (TP) and saturated hydraulic conductivity (Ksat) were significantly (p ≤ 0.05) higher on CC than CV, and among the slope gradients, GS > MS > SS. The interaction of slope curvature and gradients was significantly higher on CC than CV. A similar pattern of differences was also observed inorganic matter (SOM), calcium (Ca), magnesium (Mg), and other exchangeable cations, but the effect of slope curvature and gradients interaction was not significant. The microaggregate stability indices, water dispersible clay (WDC), water dispersible silt (WDS), dispersion ratio (DR), clay dispersion ratio (CDR), modified clay ratio (MCR), clay flocculation index (CFI), aggregated silt + clay (ASC) and aggregated clay (AC) were significantly higher on CV than CC, and differences among slope gradients and interaction of slope curvature and gradients were not significant. The erodibility factor, K, was significantly higher on CV than CC, while the slope gradients were similar in their effects on K. Linear regression analysis showed that K-factor was highly significantly related to CS, FS, Si, Cl, Bd, TP and Ksat, as well as WDC, WDS, CDR, DR, CR, MCR, CFI, ASC and AC. However, CS, Si, Ksat, Cl, ASC and WDS which explained > 40% of the variability in Kfactor could be relied upon as indices of soil erodibility in the coastal plain sands in Akwa Ibom State.

Existence of solutions and solving method of lexicographic problem of convex optimization with the linear criteria functions

Among vector problems, the lexicographic ones constitute a broad significant class of problems of optimization. Lexicographic ordering is applied to establish rules of subordination and priority. Hence, a lot of problems including the ones of complex system optimization, of stochastic programming under a risk, of the dynamic character, etc. may be presented in the form of lexicographic problems of optimization. We have revealed the conditions of existence of solutions of multicriteria of lexicographic optimization problems with an unbounded set of feasible solutions on the basis of applying the properties of a recession cone of a con vex feasible set, the cone which puts it in order lexicographically with respect to optimization criteria. The obtained conditions may be successfully used while developing algorithms for finding the optimal solutions of the mentioned problems of lexicographic optimization. A method of finding the optimal solutions of convex lexico graphic problems with the linear functions of criteria is built and grounded on the basis of ideas of the method of linearization and the Kelley cutting plane method.

A hybrid algorithm of orthogonal perturbation method and convex optimization for beamforming of sparse antenna array

ABSTRACT In order to realize the beamforming and suppress the side lobe of the sparse antenna array, a hybrid sparse antenna array optimization algorithm based on orthogonal perturbation method (OPM) and convex (CVX) optimization is proposed. The algorithm aims at the expected beam response of main lobe and the suppression of peak side lobe level (PSLL). The OPM is used to optimize the array layout, and it can improve the time performance of pattern synthesis with its deterministic numerical characteristic. Because it is a local optimization algorithm, its optimal effect depends on the initial array layout and element excitation coefficient. Therefore, considering that the local optimal solution of the CVX algorithm is the global optimal solution, the CVX algorithm is used to obtain the optimal element excitation coefficient to achieve the expected beam response of the main lobe. The simulation results show that the hybrid algorithm can achieve a good trade-off between the optimization time, beam response, and the suppression of the PSLL.

Research on Side Lobe Suppression of Time-Modulated Sparse Linear Array Based on Particle Swarm Optimization

An efficient pattern synthesis approach is proposed for the synthesis of a time-modulated sparse linear array (TMSLA) in this paper. Due to the introduction of time modulation, the low/ultralow side lobe level can be obtained with a low amplitude dynamic range ratio. Besides, it helps reduce the difficulty of antenna feeding system effectively. Based on particle swarm optimization (PSO) and convex (CVX) optimization, this paper proposes a hybrid optimization method to suppress the grating lobes of the sparse arrays, peak side lobe level (PSLL), and peak sideband level (PSBL). Firstly, the paper utilizes the CVX optimization as a local optimization algorithm to optimize the elements’ switch-on duration time, which reduces the side lobe of the array. Secondly, with the PSBL as the objective function, the paper adopts the PSO as a global optimization algorithm to optimize the elements’ positions and switch-on time instant, which helps reduce the loss of sideband power caused by time modulation. With respect to the time modulation model, variable aperture sizes (VAS) and more flexible pulse-shifting (PS) schemes are used in this paper. Owing to the introduction of time modulation and CVX optimization, the proposed method is much more feasible and efficient than conventional approaches. Furthermore, it has better array pattern synthesis performance. Numerical examples of the TMSLA and comparisons with the reference are presented to demonstrate the effectiveness of the proposed method.

The texture, structure and nutrient availability of artificial soil on cut slopes restored with OSSS – Influence of restoration time

Outside soil spray seeding (OSSS) is widely used to restore cut slopes in southwest of China, and artificial soil is often sprayed onto cut slopes to establish a soil layer for revegetation. The stability of artificial soil layer and its supply of water and nutrients for plants is crucial for successful restoration. To evaluate the long-term effectiveness of OSSS, the texture, structure and nutrient availability of artificial soil were studied, various soil samples were obtained from three cut slopes with different restoration time (restored with OSSS in 1996, 2003 and 2007 respectively) and one natural developed slope (NS). The properties measured including soil particle size distribution (PSD), texture, fractal dimension of PSD (Dm), the bias (CS) and peak convex (CE) coefficients of aggregate size distribution, structure failure rate, bulk density, moisture, pH, soil organic carbon (SOC), calcium carbonate content, Available nitrogen (NA), Available phosphorus (PA), and Available potassium (KA). The results showed that different restoration time resulted in significant differences in soil PSD, Dm, CS, CE, structure failure rate, bulk density, moisture, pH, NA, and KA. And these properties improved with increasing restoration age. However, there is still a huge disparity in soil texture, structure, and the availability of nutrients and moisture between the cut slopes and NS over a restoration period of up to 17 years, and this is caused by the little fine particles and the lack of slow release fertilizers and organic fertilizers in the artificial soil, resulting in poorer soil structure stability, retention and availability of moisture and nutrients on the cut slopes. Overall, the OSSS technique shows a long-term effectiveness in southwest of China, but there is still room for improvement.

The influence of the emergence profile on the amount of undetected cement excess after delivery of cement-retained implant reconstructions.

To test whether or not one of two emergence profile designs (concave or convex) is superior to the other in terms of remaining cement following cementation of reconstructions on individualized abutments and careful cement removal. A central incisor with a single implant-supported reconstruction was selected as a model. Six types of abutments (n=10) with two different emergence profile designs (concave (CC) and convex (CV)) and three crown-abutment margin depths (epimucosal, 1.5mm submucosal, 3mm submucosal) were fabricated through a CAD/CAM procedure. Lithium disilicate reinforced ceramic crowns were cemented with chemically polymerized resin cement. A blinded investigator attempted to remove all cement excess. Thereafter, the entire reconstruction was unscrewed and analyzed for the overall amount and the depth of cement excess. Kruskal-Wallis and Mann-Whitney tests were used to investigate differences between groups. When more than two groups were compared between each other, a Bonferroni correction of the P value was performed. Concave abutments presented significantly more cement remnants than CV abutments when the entire abutment area of the epimucosal margin groups was evaluated (CC0mm: mean 2.31mm2 (SD 0.99) vs. CV0mm: mean 1.57mm2 (SD 0.55); P=0.043). A statistically significant increase in remnants was detected when the crown-abutment margin was located more submucosally for every abutment studied (0mm vs. 1.5mm: P<0.000, 0mm vs 3mm: P<0.000, 1.5mm vs. 3mm: P<0.000). The buccal quadrant demonstrated the least, whereas the oral and interdental quadrants showed the greatest amount of cement excess. Concave emergence profile abutments and deep crown-abutment margin positions increased the risk of cement excess. Oral and interdental areas are more prone to cement remnants than other surface areas.

Time-space analysis, synthesis, and room response modeling of virtual-reality sound fields using microphone and loudspeaker arrays

This paper proposes a unified framework to analyze and synthesize spatial sound fields. In the analysis phase, an unbaffled 24-element circular microphone array (CMA) is utilized to “encode” the sound field based on plane-wave decomposition, whereas in the synthesis phase, a 32-element rectangular loudspeaker array is employed to “decode” the above-encoded sound field based on pressure matching. Plane-wave decomposition can be implemented in two ways. First, a two-stage algorithm uses the minimum variance distortionless response (MVDR) beamformer to estimate the directions of significant plane-wave components. Next, the amplitude coefficients of plane waves are calculated using the Tikhonov regularization (TIKR) algorithm. Alternatively, a one-stage algorithm that treats the sound field as a great number of plane-wave components uniformly distributed at all angles can be used. In this case, either TIKR or convex (CVX) optimization can be utilized to solve the underdetermined problem for a minimum-norm solution or a minimum-cardinality solution. The same technique is also useful in establishing the response model for a reverberation room with all direct sounds and reflections coded into plane-wave components. In the synthesis phase, pressure matching is achieved by the inverse of the preceding room response model for rendering loudspeakers in the reproduction room.

The physico-chemical properties and structural characteristics of artificial soil for cut slope restoration in Southwestern China.

Cut slopes are frequently generated by construction work in hilly areas, and artificial soil is often sprayed onto them to promote ecological rehabilitation. The artificial soil properties are very important for effective management of the slopes. This paper uses fractal and moment methods to characterize soil particle size distribution (PSD) and aggregates composition. The fractal dimension (D) showed linear relationships between clay, silt, and sand contents, with coefficients of determination from 0.843 to 0.875, suggesting that using of D to evaluate the PSD of artificial soils is reasonable. The bias (CS) and peak convex (CE) coefficients showed significant correlations with structure failure rate, moisture content, and total porosity, which validated the moment method to quantitatively describe soil structure. Railway slope (RS) soil has lower organic carbon and soil moisture, and higher pH than natural slope soil. Overall, RS exhibited poor soil structure and physicochemical properties, increasing the risk of soil erosion. Hence, more effective management measures should be adopted to promote the restoration of cut slopes.

Acoustic Source Localization and Deconvolution-Based Separation

This paper examines two fundamental issues in sound field analysis: acoustic sources localization and separation. Algorithms are developed to locate and separate acoustic signals on the basis of plane-wave decomposition. In the localization stage, directions of plane waves are determined using either minimum variance distortionless response (MVDR) method or multiple signal classification (MUSIC) method. For broadband scenarios, coherent and incoherent techniques are utilized in the localization procedure. In the separation stage, two approaches with overdetermined and underdetermined settings can be employed. In the overdetermined approach, Tikhonov regularization (TIKR) is utilized to recover the source signals. In the underdetermined approach, the steering matrix is augmented by including the directions that have been determined in the localization stage. Hence, the separation problem is formulated into a compressive sensing (CS) problem which can be effectively solved by using convex (CVX) optimization. Simulation and experiments are conducted for a 24-element circular array. Objective tests using perceptual evaluation of speech quality (PESQ) tests and subjective listening tests demonstrate that the proposed methods yield speech signals with well separated and improved quality, as compared to the mixed signals.

Deconvolution-based acoustic source localization and separation algorithms

In this paper, localization and separation of acoustic sources are examined. Depending on the number of sources in relation to the array channels, the problem is investigated in terms of underdetermined and overdetermined configurations. In the underdetermined configuration, virtual monopole sources are assumed in uniformly spaced angles. The problem is then formulated into compressive sampling (CS) problem which can be solved by using the linearly constrained -norm convex (CVX) optimization. The solution yields the directions of real sources and the source signal spectrum, which enables localization and reconstruction of sources at one shot. In the underdetermined configuration, source localization and signal separation is carried out in two steps. First, the directions of arrival (DOA) are estimated with Minimum Variance Distortionless Response (MVDR) or Multiple Signal Classification (MUSIC). Next, Tikhonov regularization (TIKR) is utilized to recover the source spectrum. In the localization problem for both configurations, Neyman-Pearson detector is employed to determine thresholds for source detection. Numerical and experimental results show that the proposed methods produce improved speech quality in terms of mean opinion score (MOS) in perceptual evaluation of speech quality (PESQ) test.

Convex expansion of condenser plates

In this paper we introduce an ew notion of the con vex expansion (convex hull) of condenser plates invariant with respect to M ¨ obius transformations of the space. If one plate is the point at infinity, then the convex expansion of another bounded plate coincides with its usual convex hull. The convex expansion of plates does not decrease the condenser capacity. The main theorem shows that in the case of a flat condenser with connected plates it cannot increase more than threefold. In particular, if the monitoring of the hidden deformation of a condenser with flat plates (with the constancy of its M ¨ obius invariant hull) shows the decrease of its capacity more than twice, then this indicates to the violation of the connectivity, i.e., the destruction of the plate. This result is applicable to nondestructive testing.

Phase statistics approach to human ventricular fibrillation

Ventricular fibrillation (VF) is known to be the most dangerous cardiac arrhythmia, frequently leading to sudden cardiac death (SCD). During VF, cardiac output drops to nil and, unless the fibrillation is promptly halted, death usually ensues within minutes. While delivering life saving electrical shocks is a method of preventing SCD, it has been recognized that some, though not many, VF episodes are self-terminating, and understanding the mechanism of spontaneous defibrillation might provide newer therapeutic options for treatment of this otherwise fatal arrhythmia. Using the phase statistics approach, recently developed to study financial and physiological time series, here, we reveal the timing characteristics of transient features of ventricular tachyarrhythmia (mostly VF) electrocardiogram (ECG) and find that there are three distinct types of probability density function (PDF) of phase distributions: uniform (UF), concave (CC), and convex (CV). Our data show that VF patients with UF or CC types of PDF have approximately the same probability of survival and nonsurvival, while VF patients with CV type PDF have zero probability of survival, implying that their VF episodes are never self-terminating. Our results suggest that detailed phase statistics of human ECG data may be a key to understanding the mechanism of spontaneous defibrillation of fatal VF.

Waveform vector analysis of orthogonal electrocardiograms: Quantification and data reduction

Quantification of vectorcardiogram (VCG) analysis by waveform vector analysis (WVA) provides a more stable data base for computer analysis of P, ST and T vectors than does polar-cardiography. Furthermore, compared with data bases composed of Cartesian or polar coordinates of ‘instantaneous’ vectors, it reduces the data and also reduces noise by smoothing. This method is applicable to electrocardiogram (ECG) analysis also. Modified Chebyshev polynomials up to the quaternary term are used as waveform functions for signal representation of scalar ECG, and corresponding waveform coefficients quantify the mean value, gradient, degree of concavity or convexity, biphasic or sigmoid shape, and triphasic or quarternary features. Applied to a vector function of time, the waveform coefficients comprise components of the five vectors—mean (MV), gradient (GV), convex (CV), sigmoid (SV), and quaternary vectors (QV). A waveform power index is derived to express the contribution of each component to overall variation. P, ST, and T vectors of 1,984 rest and exercise VCG of 992 male subjects were analyzed. Representation of the vector function was considered adequate when the approximation error was <25 μV (root mean square; RMS) for each scalar component. In 95% of the records, two waveform vectors adequately reproduced the ST vectors, four were needed for P vectors, and five for T vectors.

Utility Analysis and Repetitive Gambling

Friedman and Savage have provided us with a hypothesis with which to explain widely observed reactions of individuals to risk taking and risk avoiding opportunities^1) Their hypothesis consists of a particular configuration for the utility of income function ; a utility of income function which begins with a convex segment [diminishing marginal utility of income], then has a concave segment and terminates with a convex segment. It is the concave segment that explains why an individual will engage in a risk taking situation [gamble] even when it is unfair ? when the expected payoff is less than the wager. The con vex segments rationalize the risk avoiding behavior exemplified by an individual purchasing insurance even though the premium payments reduce income by more than the expected loss from assuming the risk. This paper uses the hypo thesis of a concave utility function to analyse the extensively observed pheno menon of repetitive gambling behavior.

A Perimetric Correlation

THE PEARSON product-moment correlation co efficient has been the most commonly used index of linear association between two variables, and it has served as the basic model for t?any forms of uni variate and multivariate statistics. Several compu tational schemes and approaches have been devel oped for arriving at, or approximating, the product moment correlation, such as those by Hs? [3], Jen kins [ 4], and Leigh-Dugmore [ 5]. Even in this age of computers, these methods have proved valuable for didactic purposes as well as easy, rapid checks on more extensive calculations. The purpose of the present paper is to present an areal approach to the correlation problem, show its relationship to the usual product-moment correlation, and to indicate some of its advantages and disadvantages and pos sible extensions. The principle of the perimetric correlation was shown graphically by Anderson [ l]. Basically, it involves the definition of a polygon (preferably con vex) about the perimeter of the points in the bivari ate distribution, the computation of the area of the polygon from the coordinates, X?, Y?, of its ver texes, and the use of this area as a ratio, with suit able constants, to the rectangular joint-range area of the two variables. The area, Ap,of such a poly gon with k vertexes numbered sequentially in order of occurrence along the perimeter, such as in the scattergram in Figure 1, is computed as the abso lute (positive) value of